Downward Price Inflexibility, Ratchet Effects, and the Inflationary Impact of Import Price Changes: Some Empirical Evidence

Morris Goldstein

doi:10.5089/9781451969450.024.A002

Author:

Mr. Morris Goldstein

Mr. Morris Goldstein https://isni.org/isni/0000000404811396 International Monetary Fund

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Publication Date:: 01 Jan 1977

eISBN:: 9781451969450

Language:: English

Keywords:: SP; earnings; price level; rate of change; model III; model VI; inflation model; Exchange rate adjustments; Inflation; Deflation; Demand elasticity

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This paper examines the effect of import price changes on the domestic rate of inflation for each of five large industrial countries—namely, the United States, the Federal Republic of Germany, Japan, the United Kingdom, and Italy. Its primary purpose is to provide empirical tests of the hypothesis that there is an asymmetry, or ratchet effect, as between the effect of positive versus negative changes in import prices on the rate of change of domestic prices. Since devaluations and revaluations are usually regarded as giving rise, respectively, to positive and negative changes in import prices (as measured in domestic currency), the existence of such a ratchet effect would have obvious implications for the global inflationary impact of exchange rate changes as well.

Abstract

This study differs from earlier ones on this general subject in a number of respects. First and foremost, it not only estimates the effect of changes in import prices on domestic prices for a group of countries but also tests for a possible asymmetry in this relationship.¹ Second, the empirical tests are carried out using a variety of alternative models of inflation in the open economy. This was done primarily to minimize the danger that the test results for the asymmetry hypothesis could be peculiar to only one set of assumptions about the determinants of inflation. As a by-product of this exercise, however, one also obtains some interesting information on the relative performance of the various inflation models themselves.² Third, both aggregated (gross domestic product (GDP) deflator) and disaggregated (price of manufactures) price data are used in the empirical tests to provide at least some minimal degree of protection against aggregation bias in the results. Finally, the various inflation models are estimated (using annual data) for both the periods 1958-73 and 1958-70. This was done so as to yield a general impression of the temporal stability of the estimated parameters, and to determine more particularly whether the period 1971-73—so characterized by a transition of exchange rate regimes and by relatively large import price changes—was exercising an undue influence on the test results.

The plan of the paper is as follows. Section I introduces and discusses the ratchet hypothesis as applied to exchange rate changes (and to import price changes alone). Section II presents the various alternative inflation models that are to be used to test the ratchet hypothesis, and also gives the specific forms of the econometric tests that are to be conducted. Section III presents and discusses the empirical results, and Section IV gives the study’s principal conclusions and policy implications. The Appendix contains data sources and definitions of the variables used in the equations.

I. The Ratchet Hypothesis

Although explanations of inflation that give a prominent role to downward price inflexibility have been a recurrent theme in the inflation literature for many years (e.g., Means (1935) on “administered” inflation and Schultze (1959) on “demand-shift” inflation), it is only recently that downward price rigidities and ratchet effects have been part of the discussion of the (global) inflationary impact of exchange rate changes. In large part, they seem to have been introduced either as an additional (marginal) argument for why flexible exchange rates may have a (global) inflationary bias or,³ in a more specific context, as a structural factor in explaining why or how “floating” could have contributed to the rapid inflation of the past few years.⁴

In its simplest and perhaps most popular form, the asymmetry (or ratchet) hypothesis states that flexible exchange rates have an inflationary bias, both for individual countries and for the world economy, because in a world of downward price inflexibility, devaluations lead to price increases in the devaluing country but produce no (or smaller) offsetting price decreases in the revaluing country. Thus, for example, were country A to devalue its exchange rate by 10 per cent vis-à-vis country B, and then one year later reverse the process by revaluing by 10 per cent—so as to cause no net change in the exchange rate over the whole period—then, so goes the ratchet argument, domestic prices would be higher in both countries and so too would the world price level. This outcome is to be contrasted with that in a world of flexible prices where nominal prices would be expected to rise in the devaluing country and fall in the revaluing one. That is, the asymmetry argument says that downward price rigidities dictate that all, or at least most, price adjustment to an exchange rate change takes place in the devaluing country via price increases.

Quite clearly the crucial element, and indeed the only unconventional one, in the ratchet hypothesis is the proposition that domestic prices either do not fall or fall by less in the revaluing country. As such, it is worth reviewing the various explanations that have been offered for this proposition, even though the main focus of this paper questions whether there is a ratchet effect rather than why there might be one.

One interpretation of the proposition has been put forward by Professors Laffer and Mundell, or at least has been attributed to them by Wanniski (1974).⁵ Their argument begins from the assumption that national economies are now so closely integrated that goods arbitrage will ensure both that the real price of tradable goods (i.e., the price of one good relative to another) is the same in all markets, and that the “law of one price” holds true.⁶ In its aggregate form,⁷ the law of one price states that the domestic price level will equal the foreign (world) price level multiplied by the exchange rate, that is, P_d = P_f.e and thus, Ṗ_d = Ṗ_f + ė. While this relationship ensures that an exchange rate change will not alter the relative prices of foreign and domestic goods,⁸ it does not specify which price level, P_d or P_f, will bear the major part of the adjustment. Here, Laffer and Mundell assert that it will be the price level in the devaluing country that bears the major adjustment role, both because producers in the devaluing country will seek to avoid a fall in the real international purchasing power of their incomes and because the response of prices and money wages to the exchange rate change will be more rapid in that country than in the revaluing one.⁹ In brief, then, the Laffer-Mundell thesis is that domestic prices will not fall (or will fall by only a little) in the revaluing country because export price increases in the devaluing country will lead to little (or no) fall in the revaluing country’s import prices.

While the Laffer-Mundell result is certainly possible, it would seem to be more the special than the usual case. As is well known, the distribution of price changes between the devaluing country and the revaluing country after an exchange rate change will depend on the sizes of demand and supply elasticities and marginal spending propensities for traded (and nontraded) goods in the devaluing country relative to those in the revaluing country (countries).¹⁰ As long as these parameters are roughly similar in the two countries, there is no reason to expect one country to absorb most or all of the price change. Also, considering just the import price change in the revaluing country, one would expect some fall in import prices (in domestic currency) unless the absolute value of the price elasticity of demand for imports was very large relative to the price elasticity of supply for imports ¹¹—a condition that would seem to be at variance with most econometric estimates of these import demand and supply elasticities.¹² Finally, even if one considers the possibility that exporters in the devaluing country have some monopoly power—a rather tenuous assumption for tradable goods—it would not necessarily follow that they would increase their supply prices by the full extent of the devaluation. This is so because the profit-maximizing price for a monopolist can be written (from the marginal revenue-marginal cost equality) as

P = M C {(1 - \frac{1}{E})}^{- 1}

where MC is the marginal cost and E is the price elasticity of demand. This suggests, in turn, that the monopolist will raise his price if either the marginal cost increases or the price elasticity of demand falls.¹³ While one or both of these might change after an exchange rate change, it is not clear why they should change in such a way as to lead to a new price that completely offsets the exchange rate change.

The Laffer-Mundell hypothesis (at least in its strong form) also carries the empirical implication that decline in the domestic currency price of imports should occur infrequently. Pigott, Sweeney, and Willett (1975) have documented, however, that such declines occurred in about 35 per cent of the quarters during the period 1957-74, at least for the United States, the United Kingdom, Canada, Japan, the Federal Republic of Germany, and France, taken together; the corresponding figure for the decline in export prices was 29 per cent, and these qualitative conclusions apply equally well to annual data over a slightly longer period. As regards specific exchange rate changes, one might note (counter to the Laffer-Mundell thesis) that the domestic currency price of imports fell in the year following the revaluations of both 1961 and 1969 in the Federal Republic of Germany. Some empirical evidence on export price behavior after tariff reductions also casts doubt on the complete offsetting hypothesis. For example, Kreinin (1961, p. 317), in a study of price behavior of exporters toward the U.S. market during the 1950s, concluded that: “It appears plausible that close to half of the benefit of tariff concessions granted by the United States accrued to foreign exporters in the form of increased export prices.” Finally, in a recent study of the “pass-through” effect of exchange rate changes for eight major currencies under the Smithsonian agreement of 1971, Kreinin (1977) found that exporters typically offset only about zero to 40 per cent of a devaluation by raising the domestic currency price of exports, thus again rejecting the complete offsetting hypothesis.

A second route to explaining or rationalizing the existence of asymmetrical exchange rate effects is to look at various alternative price stabilization rules for both the devaluing country and the revaluing country. Dornbusch (1975) has recently done just this within the context of a two-country, general equilibrium model where there is one traded and one nontraded good in each country. Dornbusch first reminds us that an exchange rate change can have real effects only if some other nominal variable in the system is fixed. For example, the familiar “elasticity approach” to devaluation—where (i) relative prices (of traded to nontraded goods) rise in the devaluing country and fall in the revaluing one; (ii) the domestic price level increases in the devaluing country and falls abroad; and (iii) prices of traded goods rise less than proportionately to the devaluation and fall less than proportionately abroad—implies that both countries adjust expenditure so as to stabilize the price of nontraded goods. The new “monetary approach” to the balance of, payments, in contrast, assumes that it is the nominal supply of money that is the fixed variable in the system. More to the point at hand, Dornbusch shows that the overall price level can rise in both countries after an exchange rate change if the home (devaluing) country stabilizes the price of traded goods and the foreign (revaluing) country stabilizes the price of nontraded goods.¹⁴ Interestingly enough, if these price stabilization assignments are reversed, then the overall price level falls in both countries.

Dornbusch’s analysis is useful because it shows one way in which prices can rise in the revaluing country without assuming downward price inflexibility. However, to show that this is possible is not to say that it is probable. In fact, if one had to pick (on a priori grounds) which of the alternative price stabilization rules was most likely, the one where both countries seek to stabilize the price of nontraded goods would seem to be a reasonable choice, since these goods are produced and sold (by definition) within the country’s own borders and this, in turn, presumably makes stabilization easier.

A third avenue to the revaluation-can-be-inflationary conclusion is to make certain assumptions about the government’s policy objectives and about its policy reaction to revaluation. A good example of this genre is the recent study by Shields, Tower, and Willett (1977). In that paper, the authors show that under many of the assumptions typically employed to illustrate that devaluation is inflationary (e.g., factor immobility, downward wage and price inflexibility, and the expansion of aggregate demand by monetary authorities in response to increases in unemployment), revaluation can similarly be shown to be inflationary. In particular, Shields and others consider the case of a country that revalues when there is no excess demand in either the export or import-competing sector. In such a case, assuming usual substitution effects in consumption and production, output and employment can be expected to fall in the export and import-competing sectors of the revaluing country. Faced with this situation, the monetary authorities are presumed to increase the money supply and aggregate demand in order to eliminate the prospective increase in unemployment, thereby also promoting inflation. Here, it is not only the (assumed) structural characteristics of the economy that cause revaluation to be inflationary but also the reluctance of the authorities to permit revaluation to induce any increase in unemployment above the government’s target rate.

To some observers, for example, Kenen (1977), the Shields-Sweeney-Willett analysis merely provides one more example of the familiar proposition that the politics of full employment can cause inflation even when all other policies and circumstances would drive prices down. Further, it is inevitable, no matter what one assumes thereafter, that if prices are assumed to be inflexible downward, the end result will be either no change or an increase in prices.¹⁵ This is not to say, however, that the scenario outlined by Shields and others is not accurate as a description of what usually occurs in the real world. In this regard, quite a few prominent economists (e.g., Hicks (1974), Solow (1975)) seem to be convinced that prices now are less flexible downward than they used to be because governments are now less willing (rightly or wrongly) to incur the unemployment costs of aggregate demand-reducing policy—a point that they claim is not lost on workers or producers. On the other hand, the unusually high unemployment rates of 1974 and 1975 in most industrial countries suggest that it is presuming too much to assume that governments will automatically increase aggregate demand in response to every prospective increase in unemployment, be it induced by revaluation or other means.

A fourth and final rationalization for the ratchet hypothesis focuses on a possible asymmetry in the effect of positive versus negative changes in import prices on the change in domestic prices. In brief, the argument here begins from the proposition that there are costs to changing prices in imperfectly competitive markets, and that firms will therefore change their prices only in response to those cost and demand changes that they view as permanent.¹⁶ To obtain the ratchet or asymmetry conclusion, it is then necessary only to assume that negative changes in import prices are viewed as more temporary than are positive changes.

This approach, too, is not without its problems. First of all, the distinction expected in theory is that between permanent and transitory changes, and this distinction need not coincide with that between positive and negative changes. That is, the theory of “normal cost” pricing leads to the conclusion that there will be sticky prices but not that they will (necessarily) be sticky in only one direction.¹⁷ Second, for many large industrial countries, negative changes in import prices (in domestic currency) have occurred too frequently in the postwar period (Pigott and others (1975)) to be regarded as unusual events.¹⁸ For example, whereas negative import price changes occurred in only 4 of the 18 years during the period 1956-73 in the United Kingdom, negative changes occurred ten times for the Federal Republic of Germany during the same period. Third, an asymmetry in pricing behavior as between positive and negative cost changes has the disturbing long-run implication that, ceteris paribus, profit rates would be continually rising over time, since firms would be fully passing forward cost increases but would not be (fully) passing on cost decreases. This difficulty can, be circumvented by interpreting the ratchet argument as denoting an asymmetry in the time response of prices to positive versus negative cost changes. That is, instead of assuming that the elasticity of price with respect to positive cost (or demand) changes is greater than that for negative changes, it would be assumed that the speed of adjustment of the actual to the desired price is faster for positive than for negative import price changes. In this latter case, the long-run (or equilibrium) price elasticity would be independent of the direction of the import price change but the short-run (or impact) elasticity would not. Finally, the basic assumption that producers change prices only in response to those cost or demand changes that they deem as permanent is not yet conclusively established.¹⁹ Many empirical studies of pricing behavior (e.g., Nordhaus and Godley (1972)) support such a hypothesis, but others do not (e.g., Sahling (1974)).

Regardless of which explanation of the ratchet hypothesis conforms most closely to the facts, it is important to try to establish empirically whether such a ratchet effect exists at all. In what follows, an attempt is made to make such an empirical determination, at least with respect to the relationship between import price changes and domestic price changes.

II. Models of Inflation in an Open Economy

In this section, a number of alternative models of inflation in an open economy are introduced and reviewed briefly. The selection of models to be included in the study was guided by the following considerations. First and foremost, since the primary purpose of the study is to test the ratchet hypothesis as it applies to the domestic inflationary impact of import price changes, the selected models should contain import prices as one of the explanatory variables.²⁰ One inflation model that omits import prices has been included but only as a basis for comparison of the set of models containing import prices. Second, it was required that the models have appeared frequently in the published literature and have been previously estimated on aggregate price data for at least one of the five countries in our sample. Thus, no new models of inflation are introduced here. Third, within the preceding constraints, an attempt has been made to select a group of models that embodies a fairly wide set of alternative hypotheses about the determinants of inflation.

On the basis of the foregoing criteria, six inflation models were selected for the empirical analysis, and their specifications are presented. For expositional convenience, the following notation is used throughout the remainder of this section: Pd for the domestic price index (i.e., the GDP deflator), PM for the import price index (measured in domestic currency), W for the index of money wage rates (or average hourly earnings), u for the unemployment rate, QMH for the index of labor productivity (i.e., real output per man-hour), Q for the index of real output, y for an index of the level of excess demand in the product market (e.g., the ratio of actual to potential industrial production), Pd^e for an index of the expected domestic price, and the superscript * for the percentage change in a variable, for example,

\overset{*}{P} d_{t} = \ln P d_{t} - \ln P d_{t - 1} \approx (P d_{t} - P d_{t - 1}) / P d_{t - 1}

Finally, since each of the six models has been discussed in some detail in the literature, only a brief further description of each is provided here.

model i

\begin{matrix} \begin{matrix} \overset{*}{P} d = a_{0} + a_{1} \overset{*}{W} + a_{2} Q \overset{*}{M} H + a_{3} P \overset{*}{M} & (1) \end{matrix} \\ a_{1}, a_{3} > 0; a_{2} < 0 \end{matrix}

Model I, which has been quite popular in empirical work (e.g., Lipsey and Parkin (1970), Ball and Duffy (1972), Goldstein (1974)), expresses the rate of price change as a function of the rate of change of variable costs. While it can be derived in more than one way, one important underlying assumption is that firms set their prices with an aim toward obtaining a constant percentage markup (or profit margin). In many of its empirical applications, the variable QMH (actual labor productivity) has been replaced by trend, or “normal,” labor productivity (i.e., a weighted average of current and past changes in QMH) under the argument that firms will change prices only in response to those cost changes deemed permanent. Regarding its treatment of import prices, Model I implicitly views imports more as a (say, third) factor in the production function than as a finished good that competes with domestically produced finished goods. The usual interpretation (e.g., Lipsey and Parkin (1970)) of the theoretical restrictions on the coefficients in equation (1) is that (i) the coefficient on Q $\overset{*}{M}$ H should be equal to minus the coefficient on $\overset{*}{W}$ (a₂ = – a₁); (ii) the coefficients on $\overset{*}{W}$ and P $\overset{*}{M}$ should be approximately equal to (but larger than) the share of wages and imports in final price; and (iii) the constant term, a₀, should be equal to zero. Finally, as regards estimation of equation (1), there may be a simultaneity problem (at least with aggregate data) between money wage changes and price changes.

model ii

\begin{matrix} \begin{matrix} \overset{*}{P} d = b_{0} + b_{1} \overset{*}{W} + b_{2} Q \overset{*}{M} H + b_{3} P \overset{*}{M} + b_{4} y \\ b_{1}, b_{3}, b_{4} > 0; b_{2} < 0 \end{matrix} & (2) \end{matrix}

Model II, like Model I, is a structural price-change equation where prices are assumed to be set as a markup over actual (or normal) costs. Also, like Model I, it implicitly views import prices as a cost of production. It differs from Model I in one important respect, namely, that the markup factor is posited to be directly related to the level of excess demand in the product market (rather than assumed to be constant). That is, producers are hypothesized to raise prices when product markets are tight and to shade prices when product markets are loose. The list of candidates to proxy the level of excess demand has included the ratio of unfilled orders to shipments, the change in the ratio of inventories to shipments, and various actual-to-trend industrial production measures. This model, or slight variations on it, appears prominently in the studies by Schultze and Tryon (1965), Eckstein and Fromm (1968), and Tobin (1972), among others.

model iii

\begin{matrix} \begin{matrix} \overset{*}{P} d = c_{0} + c_{1} u^{- 1} + c_{2} Q \overset{*}{M} H + c_{3} P \overset{*}{M} \\ c_{1}, c_{3} > 0; c_{2} < 0 \end{matrix} & (3) \end{matrix}

Model III represents a reduced form price-change equation that emanates from combining a structural price-change equation (like equation (1)) with a simple (Phillips-curve type) wage adjustment model. To illustrate its origin, consider the following familiar, two-equation wage-price model:

\begin{matrix} \overset{*}{P d} = d_{0} + d_{1} \overset{*}{W} + d_{2} Q \overset{*}{M} H + d_{3} P \overset{*}{M} & (3 a) \end{matrix}

\begin{matrix} \overset{*}{W} = e_{0} + e_{1} u^{- 1} + e_{2} \overset{*}{P} d & (3 b) \end{matrix}

Equation (3 a) is merely Model I. Equation (3 b) is a form of the Phillips curve where the rate of change in money wages is hypothesized to depend positively on the level of excess demand in the labor market (proxied above by the reciprocal of the unemployment rate) and on the expected rate of inflation (proxied above by the actual rate of inflation).

Solving equations (3 a) and (3 b) for $\overset{*}{P}$ d, one obtains the reduced form price-change equation (3)—that is, Model III. In terms of the structural parameters ²¹

c_{0} = \frac{d_{0} + d_{1} e_{0}}{(1 - d_{1} e_{2})}; c_{1} = \frac{d_{1} e_{1}}{(1 - d_{1} e_{2})}; c_{2} = \frac{d_{2}}{(1 - d_{1} e_{2})}; c_{3} = \frac{d_{3}}{(1 - d_{1} e_{2})}

Since Model III deals explicitly with the endogeneity of $\overset{*}{W}$ (and its simultaneous relationship with $\overset{*}{P}$ d), it captures the induced, later-round, wage-price-spiral effects on prices of any disturbance. In particular, observe that the reduced form coefficient on P $\overset{*}{M}$ in Model III is larger by the factor [1/(1−d₁e₂)] than is the structural coefficient on P $\overset{*}{M}$ in Models I and II. Also note that the condition for this model to be stable is that the product of the coefficients on $\overset{*}{W}$ and $\overset{*}{P}$ d be less than unity, that is, that (d₁e₂) < 1.²² Finally, it might be worth pointing out that although the change in labor productivity (Q $\overset{*}{M}$ H) carries a negative sign in equation (3), its sign would be ambiguous if one also entered Q $\overset{*}{M}$ H with a positive sign in the structural wage-change equation (3 b); the implicit argument here (Kuh (1967)) is that in equilibrium (i.e., when there is no excess demand for labor) the time path of money wages will follow the time path of (the value of) labor’s marginal product. Thus, as regards the empirical estimation of Model III, one cannot dismiss a positive coefficient on Q $\overset{*}{M}$ H out of hand.

model iv

\begin{matrix} \begin{matrix} \overset{*}{P} d = f_{0} + f_{1} u^{- 1} + f_{2} \overset{*}{Q} + f_{3} P \overset{*}{M} \\ f_{1}, f_{3} > 0; f_{2} < 0 \end{matrix} & (4) \end{matrix}

Model IV, which (apparently) owes its origin to Kwack (1977), is also, like Model III, a reduced form model that results from combining a variable-cost price equation with a Phillips-type wage equation. It differs from Model III only in that the change in real output $\overset{*}{Q}$ replaces the change in labor productivity (real output per man-hour). Kwack argues that $\overset{*}{Q}$ should carry a negative coefficient for two reasons: (i) with employment fixed, an increase in real output will reduce unit costs; and (ii) with the flow of new orders (demand) fixed, an increase in real output will reduce the level of excess demand. Some readers will also be aware that Model IV can rather easily be transformed into an equation of the form

\begin{matrix} \begin{matrix} \overset{*}{P} d & = g_{0} + g_{1} u^{- 1} + g_{2} Δ u^{- 1} + g_{3} P \overset{*}{M} \\ g_{1} {, g}_{2}, g_{3} > 0 \end{matrix} & (4 a) \end{matrix}

by invoking the familiar statistical relationship (widely known as Okun’s Law) between the change in the unemployment rate and the change in real output (relative to its trend rate)

\begin{matrix} Δ u^{- 1} = j_{1} (\overset{*}{Q} / \bar{Q}) & (4 b) \end{matrix}

Thus, inflation models of the form represented by equation (4 a)—for example, Spitäller (1971)—are really quite close relatives of Model IV, and these models should produce empirical results similar to Model IV as long as equation (4 b) fits the data reasonably well.

model v

\begin{matrix} \begin{matrix} \overset{*}{P} d & = k_{0} + k_{1} u^{- 1} + k_{2} \overset{*}{Q} + k_{3} P \overset{*}{M} + k_{4} {\overset{*}{P} d}_{- 1} \\ k_{1}, k_{3}, k_{4} > 0; k_{2} < 0 \end{matrix} & (5) \end{matrix}

Model V, which also appears in Kwack’s (1975) work, is the result of combining inflation Model IV with a partial-adjustment mechanism that specifies how actual prices adjust to equilibrium (or desired) prices. Equation (5) emanates from the following two equations:

\begin{matrix} \begin{matrix} \overset{*}{P} d_{t}^{e} \end{matrix} = m_{0} + m_{1} u^{- 1} + m_{2} \overset{*}{Q} + m_{3} P \overset{*}{M} & (5 a) \end{matrix}

\begin{matrix} \begin{matrix} \overset{*}{P} d_{t} \end{matrix} - \begin{matrix} \overset{*}{P} d_{t - 1} \end{matrix} = θ (\overset{*}{P} d_{t}^{e} - \begin{matrix} \overset{*}{P} d_{t - 1} \end{matrix}); 0 \leq θ \leq 1 & (5 b) \end{matrix}

Equation (5 b) is simply Model IV interpreted as the equilibrium rate of price change. Equation (5 b) is the partial-adjustment mechanism that relates the change in the actual inflation rate (as between periods t and t− 1) to the difference between the equilibrium inflation rate in period t and the actual inflation rate in period t− 1; θ is the coefficient of adjustment. The implicit notion behind this model is that there are “costs” (both pecuniary and nonpecuniary) associated with the adjustment of actual prices to equilibrium prices, and that these costs constrain instantaneous adjustment. The partial-adjustment mechanism also introduces a distributed lag structure with geometrically declining weights (i.e., a Koyck lag) into the price-change equation.²³

Substituting equation (5 a) into (5 b) and solving for $\overset{*}{P}$ d_t, one obtains equation (5), that is, Model V. Relating equation (5) to the underlying parameters in equations (5 a) and (5 b), it can easily be shown that

\begin{matrix} k_{0} = θ m_{0} > 0; k_{1} = θ m_{1} > 0; k_{2} = θ m_{2} > 0; \\ k_{3} = θ m_{3} > 0; and k_{4} = (1 - θ) > 0 \end{matrix}

model vi

\begin{matrix} \begin{matrix} \overset{*}{P} d & = n_{1} y_{- 1} + n_{2} y_{- 2} + n_{3} \overset{*}{P} d_{- 1} \\ n_{1}, n_{3} > 0; n_{2} < 0 \end{matrix} & (6) \end{matrix}

Model VI, which is attributable to Cross and Laidler (1976), is one of a whole class of models that view the inflation rate as being determined by the level of excess demand (for goods and services) and by the expected rate of inflation.²⁴ The particular specification of equation (6) emerges from the following two equations:

\begin{matrix} \begin{matrix} \overset{*}{P} d \end{matrix} = r_{1} y_{- 1} + \begin{matrix} \overset{*}{P} {d^{e}}_{- 1} \end{matrix} & (6 a) \end{matrix}

\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \overset{*}{P} d^{e} \end{matrix} = \begin{matrix} \overset{*}{P} {d^{e}}_{- 1} + λ (\overset{*}{P} d - \overset{*}{P} {d^{e}}_{- 1}) \end{matrix} \end{matrix} & 0 \leq λ \leq 1 \end{matrix} & (6 b) \end{matrix}

where $\overset{*}{P}$ d^e is this time the expected rate of inflation.²⁵ Equation (6 a) says that the inflation rate will be a positive function of the level of excess demand and the expected rate of (domestic) inflation, both lagged one period (year). Equation (6 b) is the familiar adaptive expectations hypothesis, whereby the current inflation forecast is equal to the past period’s forecast plus some fraction (A) of the past period’s forecast error.²⁶ By substituting equation (6 b) into (6 a) and solving for $\overset{*}{P}$ d, one obtains equation (6) where

n₁ = r₂; n₂ = −(1 − λ)r₁; and n₃ = 1

Model VI is meant to be exhaustive in its treatment of the determinants of inflation. Any factor that is expected will affect $\overset{*}{P}$ d via the expected rate of inflation ( $\overset{*}{P}$ d^e), and any factor that is unexpected will make its influence felt via its effect on excess demand. In particular, it is assumed that an increase in the inflation rate in the rest of the world will affect $\overset{*}{P}$ d via its effect on the domestic rate of monetary expansion and, hence, on the domestic level of excess demand (y). Thus, in contrast to the preceding models, Model VI does not contain import prices (P $\overset{*}{M}$ ) as a separate explanatory variable.²⁷ Put into other words, Model VI assumes that the proximate determinants of inflation are exclusively domestic. As regards the theoretical restrictions on the coefficients, Model VI requires that (i) the coefficient on the lagged inflation rate should not be significantly different from unity, and (ii) the coefficient on y_t-2 should be negative and smaller in absolute value than that on y_t-1, which, in turn, should be positive.

the asymmetry test

As stated earlier, it is the intention of this study to test whether there is an asymmetry as between the effects of positive versus negative changes in import prices on the change in domestic prices. To conduct such a test, the following procedure was adopted. For each country in the sample, the data series on import price changes (P $\overset{*}{M}$ ) was examined and those observations representing negative changes in import prices were identified. A new dummy variable, P $\overset{*}{M}$ ·N, was then created, where N takes the value of one when the import price change is negative and the value zero when the import price change is positive. The dummy variable for negative import price changes (P $\overset{*}{M}$ ·N) and the variable for all import price changes—positive or negative—(P $\overset{*}{M}$ ) were then entered as separate regressors in each inflation model. If negative changes in import prices have a different proportionate effect on domestic price changes than do positive changes, then the estimated coefficient on P $\overset{*}{M}$ ·N in the estimated regression equation should be negative and significantly different from zero. To illustrate, the asymmetry test as applied to Model I would take the following form:

\begin{matrix} \begin{matrix} \overset{*}{P} d = a_{0} + a_{1} \overset{*}{W} + a_{2} Q \overset{*}{M} H + a_{3} P \overset{*}{M} + a_{4} P \overset{*}{M} \cdot N \\ a_{1}, a_{3} > 0; a_{2} < 0; a_{4} \leq 0 \end{matrix} & (7) \end{matrix}

An asymmetry in the effect of P $\overset{*}{M}$ on $\overset{*}{P}$ d is then indicated if a₄ is significantly different from zero.

There are several points to note about this test. First, the econometric procedure described is formally equivalent to dividing the import price-change variable into positive and negative changes, entering the positive and negative changes as separate regressors into the price-change equation, and then testing for the equality of the coefficients on the positive and negative import price-change variables. Both tests produce exactly the same results. The only advantage of the test used here is that it requires performing a t-test on only one coefficient (namely, a₄) rather than on the difference between two coefficients.

Second, the size of the coefficient on P $\overset{*}{M}$ ·N permits one to identify weak, strong, and extreme versions of the asymmetry hypothesis. To be specific, since the effect of a negative change in import prices on domestic prices is given by (a₃+a₄) while that of a positive change is given by a₃, one can establish the following implications: ²⁸ (i) if |a₃| > |a₄|, domestic prices will fall after a fall in import prices, but the proportionate effect of negative import price changes will be smaller than that for positive changes (i.e., weak asymmetry hypothesis); (ii) if |a₄| = |a₃| domestic prices will, ceteris paribus, remain constant after a negative import price change (i.e., strong asymmetry hypothesis); and (iii) if |a₄| > |a₃|, domestic prices will rise after a fall in import prices, although as long as |a₄| < 2 · |a₃|, the domestic price rise will be smaller than that which would take place after a positive change in import prices of the same size (i.e., the extreme asymmetry hypothesis).

Third, in those cases where there is more than one P $\overset{*}{M}$ variable in the equation (say, ${P \overset{*}{M}}_{t} and {P \overset{*}{M}}_{t - 1}$ ), and especially when the two import price variables are quite collinear, it is preferable to test for an asymmetry by performing an F-test on the set of slope dummy variables rather than by performing a t-test on ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ separately. That is, suppose the equation takes the following form:

\begin{matrix} \begin{matrix} \overset{*}{P} d_{t} & = a_{0} + a_{1} {\overset{*}{W}}_{t} + a_{2} Q \overset{*}{M} H_{t} + a_{3} P {\overset{*}{M}}_{t} + a_{4} P \overset{*}{M} N_{t} + a_{5} P {\overset{*}{M}}_{t - 1} + a_{4} P \overset{*}{M} N_{t - 1} \\ \begin{matrix} \begin{matrix} a_{1}, a_{3}, a_{5} > 0; \end{matrix} & a_{2}, a_{4}, a_{6} < 0 \end{matrix} \end{matrix} & (8) \end{matrix}

In this case, one can test the joint influence of ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ on $\overset{*}{P}$ d_t by estimating equation (8) with and without the slope dummies and by then testing for a significant improvement in the explanatory power as indicated by the usual F-statistic (Kmenta (1971), p. 370). This F-test will be a weaker test for asymmetry than requiring that a₄ and a₆ each be significantly different from zero.²⁹ In fact, if either a₄ or a₆ is significantly different from zero (as indicated by their estimated t-values), then the joint influence of ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ will also be judged significantly different (via the F-test). On the other hand, it is quite possible for neither ${P \overset{*}{M} N}_{t} nor {P \overset{*}{M} N}_{t - 1}$ to have a significant t-value but for their joint influence to still be judged significant. Since one is presumably interested in the total impact of negative import price changes on $\overset{*}{P}$ d, the usual F-test has a definite appeal.

Fourth and finally, to interpret the above-described asymmetry test as reflecting solely the different impact of positive and negative changes in import prices, it is necessary to assume both that large changes in import prices do not have a different proportionate impact on domestic prices than do small changes, and that a given change in import prices will have the same effect on domestic prices, regardless of whether the import price change reflects an exchange rate change or a change in supplier export prices. To the extent that either of these assumptions is not accurate, some unknown bias will be introduced into the reported asymmetry results.

the data and choice of variables

As a final preliminary to reporting the empirical results, it is necessary to make a few remarks about the data and variables that appear in the empirical work. As mentioned at the beginning, five countries are included in the empirical analysis—the United States, the Federal Republic of Germany, Japan, the United Kingdom, and Italy. The primary criteria used to select the countries were (i) that a data base exist for that country that was both broad enough to cover all the variables appearing in Models I-VI and generally consistent with the data available for other countries, and (ii) that the country exhibited at least two (annual) declines in the domestic currency price of imports during the period 1958-73. A listing of the dates and sizes of these import price declines for each of the five countries is given in Table 1. In brief, the figures there show that import prices (in local currency) fell in 4 of the 16 years for the United States and the United Kingdom, in 5 years for Italy, in 9 years for Japan, and in 10 years for the Federal Republic of Germany.

Table 1.

Five Large Industrial Countries: Instances of Negative Import Price Changes, 1958-73¹

(In percent)

^¹PM is the annual percentage change in the unit value index for total imports (expressed in domestic currency).

Table 1.

Five Large Industrial Countries: Instances of Negative Import Price Changes, 1958-73¹

(In percent)

United States	$P \overset{*}{M^{1}}$	Fed. Rep. of Germany $P \overset{*}{M^{1}}$		Japan	$P \overset{*}{M^{1}}$	United Kingdom $P \overset{*}{M^{1}}$		Italy	$P \overset{*}{M^{1}}$
1958	−5.09	1958	−9.62	1958	−20.10	1958	−7.45	1958	−12.81
1959	−1.75	1959	−2.94	1959	−1.14	1959	−1.02	1959	− 7.24
				1960	− 1.58			1960	− 1.31
1961	−1.40	1961	−3.37	1961	− 0.21	1961	−1.94	1961	− 2.34
1962	−2.39	1962	−2.38	1962	− 3.14	1962	−1.05	1962	− 0.45
		1963	−0.80
		1967	−1.17	1967	− 0.52
		1968	−2.98	1968	− 0.73
				1969	− 0.32
		1970	−1.98
		1971	−1.01
		1972	−2.56	1972	− 7.76

^¹PM is the annual percentage change in the unit value index for total imports (expressed in domestic currency).

Table 1.

Five Large Industrial Countries: Instances of Negative Import Price Changes, 1958-73¹

(In percent)

United States	$P \overset{*}{M^{1}}$	Fed. Rep. of Germany $P \overset{*}{M^{1}}$		Japan	$P \overset{*}{M^{1}}$	United Kingdom $P \overset{*}{M^{1}}$		Italy	$P \overset{*}{M^{1}}$
1958	−5.09	1958	−9.62	1958	−20.10	1958	−7.45	1958	−12.81
1959	−1.75	1959	−2.94	1959	−1.14	1959	−1.02	1959	− 7.24
				1960	− 1.58			1960	− 1.31
1961	−1.40	1961	−3.37	1961	− 0.21	1961	−1.94	1961	− 2.34
1962	−2.39	1962	−2.38	1962	− 3.14	1962	−1.05	1962	− 0.45
		1963	−0.80
		1967	−1.17	1967	− 0.52
		1968	−2.98	1968	− 0.73
				1969	− 0.32
		1970	−1.98
		1971	−1.01
		1972	−2.56	1972	− 7.76

^¹PM is the annual percentage change in the unit value index for total imports (expressed in domestic currency).

The empirical tests in Section III are all conducted on annual data. The use of annual data, of course, carries both advantages and disadvantages. On the one hand, annual data, and the limited degrees of freedom that go with them, limit one to considering models with only a small number of explanatory variables. Also, it can reduce the precision (say, vis-à-vis quarterly data) with which one can hope to estimate the timing (i.e., the lags) of the relationships involved. On the other hand, for the specific purposes of this study, annual data had at least four things to recommend them. First, since the asymmetry test used here (equation (7)) requires two import price variables (P $\overset{*}{M}$ and P $\overset{*}{M}$ ·N) for each lagged or unlagged value of P $\overset{*}{M}$ that is included in the regression, the use of annual data both considerably reduces the number of parameters that have to be estimated and facilitates interpretation of the asymmetry results. Second, since annual changes in import prices are likely to be regarded as more permanent than quarterly changes, the use of annual data reduces the problem of disentangling positive/ negative asymmetries from transitory/permanent ones. Third, since quarterly data on import prices were available for all five countries, it was possible to use the quarterly data to test for lags of P $\overset{*}{M}$ on $\overset{*}{P}$ d that were less than one year apart. That is, by converting the quarterly data to a four-quarter rate of change basis, it was possible to relate $\overset{*}{P}$ d_t to import price changes lagged one or two quarters ( $P {\overset{*}{M}}_{t - 1 / 4} and P {\overset{*}{M}}_{t - 1 / 2}$ ) as well as to unlagged import prices or to import prices lagged one year. Finally, by pooling the data across countries (i.e., by creating a cross section of time series), it is possible to reduce the problem of few observations.

Turning to the choice of variables used in estimating Models I-VI, several comments are in order. For the aggregate results (which form the bulk of the analysis), two alternative dependent variables were used—the percentage change in the GDP deflator, and the percentage change in the consumer price index. Because the results were quite similar (especially regarding the asymmetry tests), only the GDP deflator equations are reported in the text. Where the change in money wages was called for as an explanatory variable, the measure used was the percentage change in compensation per man-hour in manufacturing as constructed by the U.S. Bureau of Labor Statistics (1975). These wage data from the Bureau of Labor Statistics (BLS), while not covering the whole economy, have the offsetting dual advantage of providing both a comprehensive (inclusive of overtime, fringe benefits) measure of labor cost and one that is relatively consistent across countries. For similar reasons, the labor productivity variable used was based on BLS data on real output per man-hour in manufacturing. Here, however, following earlier studies (Eckstein and Fromm (1968), Ball and Duffy (1972), Nordhaus and Godley (1972)), a measure of “normal,” or trend, productivity was used rather than actual productivity. More specifically, the measure employed (ln QMH^N) was a weighted three-year moving average of actual labor productivity with weights equal to 0.5 for year t and 0.25 each for years t− 1 and t−2. This weighting pattern was imposed (rather than estimated) to conserve on degrees of freedom; it is, however, broadly consistent with earlier empirical price-change studies. The unemployment rate used was the reciprocal of the unemployment rate for the whole economy (u^-1). Again, to facilitate intercountry comparisons, the unemployment rates were converted to U.S. definitions as indicated in the BLS Handbook (1975). The proxy used for the level of excess demand was the logarithm of the ratio of actual industrial production to “potential” industrial production, as constructed by Ripley (1976), where potential industrial production is generated by calculating geometric ten-year centered moving averages of actual industrial production. The measure of import prices employed was the percentage change in the unit value index for total imports (expressed in domestic currency). A more precise description of the variables and data sources is given in the Appendix.

To guard against the danger that the test results would be very sensitive to the choice of variables just outlined, some attempt was made to “spot-check” the empirical results by re-estimating some of the models with alternative variables. Thus, for example, some equations were estimated substituting (i) average hourly earnings in the whole economy for compensation per man-hour in manufacturing; (ii) actual productivity for normal productivity; (iii) actual (or normal) unit labor cost for the separate wage and productivity variables; (iv) the unemployment rate for its reciprocal. In brief, these experiments suggested that the qualitative nature of the asymmetry results was not very sensitive to these modifications.

III. Empirical Results

This section presents the results of estimating Models I-VI, with special attention directed toward the results of the asymmetry tests for import price changes. The results for aggregate price changes (i.e., percentage changes in the GDP deflator) during the period 1958-73 are considered first, followed in turn by the aggregate price change results for the period 1958-70 and by the (1958-73) results for disaggregated price changes (i.e., percentage changes in the GDP deflator for manufacturing). Unless otherwise indicated, all the equations are estimated by ordinary least squares. In each of the tables presented, the numbers in parentheses below the estimated coefficients are t-values, ${\bar{R}}^{2}$ is the coefficient of determination (adjusted for degrees of freedom), SEE is the standard error of the estimate (also adjusted for degrees of freedom), and D-W is the Durbin-Watson statistic.

aggregate price changes, 1958–73

Because the main concern in this paper is with the asymmetry test results and because the number of inflation models tested is large, it should suffice to briefly summarize the estimation results when the effect of positive and negative import price changes was constrained to be equal, that is, when equations (1)-(6) were estimated without the asymmetry variables (P $\overset{*}{M}$ N).³⁰

In the estimates for Model I, all the explanatory variables carried the expected signs and most were statistically significant at the 5 per cent confidence level. The estimated coefficients on import price changes were statistically significant at (or near) the 5 per cent level in all countries except the Federal Republic of Germany;³¹ and the sizes of the estimated coefficients on P $\overset{*}{M}$ were reasonably similar to other existing estimates of the effect of $\overset{*}{P}$ M on $\overset{*}{P}$ d for these countries.³² The fits for equation (1) were quite respectable (with ${\bar{R}}^{2}$ s ranging from 0.77 for Japan to 0.91 for the United States); in fact, as is shown later, they compared quite favorably with the fits of the competing inflation models considered here. There was, however, also one disturbing feature about the estimates of Model I, namely, that the theoretical constraints on the coefficients of equation (1) were not satisfied; that is, the coefficient on $\overset{*}{W}$ was rarely (the U.K. case is the exception) equal in absolute value to the coefficient on Q $\overset{*}{M}$ H^N, and the coefficients on $\overset{*}{W}$ and P $\overset{*}{M}$ often departed rather substantially from the shares of wages and imports in the final price (in GDP).

Model II, which treats the markup over actual (or normal) costs as a positive function of the level of excess demand, yielded results very similar to those for Model I. The most significant finding here was that the excess demand variable (ln y) was not statistically significant in any of the five country equations, and in fact carried the wrong sign in three cases. Thus, there was no evidence from these equations that excess demand affects price changes independently of its influence on factor costs.

Model III, which represents the reduced form of Model I, yielded reasonably good results for the United States, the Federal Republic of Germany, and Italy but less satisfactory results for Japan and the United Kingdom. Also, the fits of these reduced form equations were uniformly poorer than those for the structural price-change equations. The proxy for excess demand in the labor market (u or ln y) carried the correct sign and was statistically significant in three (the United States, the Federal Republic of Germany, and Italy) of the five cases. Import price changes were again significant in all the equations except

for the Federal Republic of Germany. As expected (in subsection on Model III), the coefficients on P $\overset{*}{M}$ were larger in Model III than for Models I and II, where the wage-price-spiral effects of import price changes were not taken into account. In fact, a comparison of the estimated coefficients on P $\overset{*}{M}$ as between Models I and III suggested that the long-run effect of P $\overset{*}{M}$ on $\overset{*}{P d}$ (when $\overset{*}{W}$ is endogenous) was 1.7 times larger than the short-run effect for the United States, 1.6 times larger for Japan, 1.6 times larger for the United Kingdom, and 3.8 times larger for Italy.

The estimates for Model IV, which differs from Model III only in that $\overset{*}{Q}$ replaces Q $\overset{*}{M}$ H, were very similar to those for Model III, although the explanatory power of Model IV was slightly lower than that for Model III. Model V, which incorporates the partial-adjustment mechanism, yielded excellent results for the United States, reasonably good results for the Federal Republic of Germany and the United Kingdom, and rather mediocre to poor results for Italy and Japan. Also, the import price-change variables were significant and correctly signed in all five cases. The lagged dependent variable was statistically significant in the equations for the United States, the Federal Republic of Germany, and the United Kingdom. Recall from Section II that the estimated coefficent on $\overset{*}{P}$ d_-1 provides an estimate of (one minus) the speed of adjustment of the actual to the desired rate of price change. As such, the estimates of Model V suggested relatively rapid adjustment for Italy and Japan, relatively slow adjustment for the Federal Republic of Germany and the United Kingdom, and an intermediate speed of adjustment for the United States.

Model VI, which is the Cross-Laidler excess demand cum expectations model, yielded quite good results for all countries except Japan (where the results could be categorized only as nonsense).³³ While the explanatory power of this model is lower than that of the models described previously,³⁴ the coefficient estimates are quite consistent with the model’s theoretical constraints and predictions. In particular, the coefficient on the lagged inflation term did not differ significantly from unity for four of the five countries—implying the absence of a long-run trade-off between excess demand and the rate of inflation, and the coefficient on the twice-lagged excess demand variable is negative and smaller in absolute value than that on the once-lagged excess demand variable (which is itself positive). On the minus side, the two excess demand variables were significant only for the United States and the Federal Republic of Germany (although the estimates for the United Kingdom are close to being statistically significant).

A quick overview of the relative explanatory power of the six models can be obtained from Table 2, in which an ordinal ranking of the models is presented for each of the five countries. The rankings were made on the basis of the standard error of estimate (SEE) of each model,³⁵ since, as mentioned earlier, the SEE (as opposed to the ${\bar{R}}^{2}$ ) is not affected if the model is estimated without a constant (as was true here with Model VI).

Table 2.

Five Large Industrial Countries: Ordinal Ranking of Models on Basis of Goodness of Fit (SEE) Using Annual Data 1958-73

Table 2.

Five Large Industrial Countries: Ordinal Ranking of Models on Basis of Goodness of Fit (SEE) Using Annual Data 1958-73

Model	United States	Fed. Rep. of Germany	Japan	United Kingdom	Italy	Average Ranking Across All Countries
1	2	2	2	2	1	2nd	(1.8)
2	3	1	1	1	2	1st	(1.6)
3	6	4	4	5	3	4th	(4.4)
4	4	6	3	6	4	5th	(4.6)
5	1	3	5	3	5	3rd	(3.4)
6	5	5	6	4	6	6th	(5.2)

Table 2.

Five Large Industrial Countries: Ordinal Ranking of Models on Basis of Goodness of Fit (SEE) Using Annual Data 1958-73

Model	United States	Fed. Rep. of Germany	Japan	United Kingdom	Italy	Average Ranking Across All Countries
1	2	2	2	2	1	2nd	(1.8)
2	3	1	1	1	2	1st	(1.6)
3	6	4	4	5	3	4th	(4.4)
4	4	6	3	6	4	5th	(4.6)
5	1	3	5	3	5	3rd	(3.4)
6	5	5	6	4	6	6th	(5.2)

In brief, the rankings in Table 2 indicate that, on average, the two models with the highest explanatory power were the structural inflation models, that is, Models II and I. These were followed in explanatory power by their reduced forms, that is, by Models V, III, and IV, in which the change in money wages was replaced by its exogenous determinants, principally the unemployment rate or the ratio of actual to normal industrial production. Of the three similar reduced form models (i.e., Models III, IV, and V), the one that incorporated time lags via the partial-adjustment mechanism (Model V) seemed to perform best (particularly for the United States). Model VI (the Cross-Laidler model) generally produced appreciably larger SEEs than the other models, although it did produce estimates that were consistent with its underlying theoretical constraints. As a final note on these rankings, the comparative advantage of Models II and I often fell considerably (if it did not disappear altogether) when these two models were estimated by two-stage least squares, that is, when $\overset{*}{W}$ was replaced by its estimated value.³⁶

asymmetry results, 1958-73

The results of testing for an asymmetry in the effect of positive versus negative changes in import prices on the change in the GDP deflator are presented (country by country) in Tables 3-7. Recall from Section II that when there is only one set of import price change variables in the equation (i.e., ${P \overset{*}{M}}_{t} and {P \overset{*}{M}}_{t - 1}$ ), then an asymmetry of the postulated type will be indicated when the coefficient on the slope dummy variable P $\overset{*}{M}$ N is negative and significantly different from zero as indicated by a conventional t-test on that coefficient.³⁷ When there are two sets of import price change variables in the equation (i.e., P $\overset{*}{M}$ _t, P $\overset{*}{M}$ N_t and P $\overset{*}{M}$ _t-1, P $\overset{*}{M}$ N_t-1), a better test of the asymmetry hypothesis can be conducted by performing an F-test on the two slope dummy variables taken together, that is, by testing whether the joint influence of ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ significantly improves the explanatory power of the equation;³⁸ this latter test is particularly appropriate when the import price variables are highly collinear.

Looking first at the results for the United States in Table 3, one finds a pattern of mixed support for the asymmetry hypothesis, with evidence of an asymmetry indicated in Models III, IV, V, but not in Models I and II. Also, even where the dummy variable on import price changes is insignificant, it almost always carries the expected negative sign. Further, and somewhat surprisingly, in those cases where an asymmetry is indicated, the sizes of the estimated coefficient(s) on P $\overset{*}{M}$ N suggest that, ceteris paribus, negative import price changes lead to positive changes in domestic prices.

Table 3.

United States: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

√ = presence of an asymmetry

Table 3.

United States: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} & Δ \ln P d \end{matrix} & = \underset{(0.42)}{0.004} + \underset{(4.56)}{0.651} Δ \ln W_{t} - \underset{(2.36)}{0.343} Δ \ln Q M H_{t}^{N} + \underset{(1.77)}{0.110} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.16)}{0.021} Δ \ln P M N_{t} + \underset{(1.09)}{0.113} Δ \ln P M_{t - 1} - \underset{(0.25)}{0.046} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.888 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0053 \end{matrix} & D - W = 2.07 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} & Δ \ln P d = \end{matrix} & \underset{}{- \underset{(1.46)}{0.47}} + \underset{(4.49)}{0.629} Δ \ln W_{t} - \underset{(0.26)}{0.063} Δ \ln Q M H_{t}^{N} + \underset{(2.81)}{0.142} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.08)}{0.157} Δ \ln P M N_{t} + \underset{(1.48)}{0.096} \ln y_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.895 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0051 \end{matrix} & D - W = 2.26 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \sqrt III \end{matrix} & Δ \ln P d \end{matrix} & = \underset{(0.14)}{0.002} + \underset{(2.24)}{0.141} u_{t}^{- 1} - \underset{(2.38)}{0.482} Δ \ln Q M H_{t}^{N} + \underset{(2.60)}{0.210} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.80)}{0.180} Δ \ln P M N_{t} + \underset{(1.81)}{0.290} Δ \ln P M_{t - 1} - \underset{(1.24)}{0.362} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.762 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0077 \end{matrix} & D - W = 1.07 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \sqrt IV \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(1.79)}{0.020} + \underset{(5.18)}{0.234} u_{t}^{- 1} - \underset{(4.03)}{0.337} Δ \ln Q_{t} + \underset{(2.33)}{0.136} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.07)}{0.178} Δ \ln P M N_{t} + \underset{(3.08)}{0.381} Δ \ln P M_{t - 1} - \underset{(2.65)}{0.619} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.862 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0059 \end{matrix} & D - W = 1.63 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \sqrt V \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(3.28)}{0.017} + \underset{(7.13)}{0.149} u_{t}^{- 1} - \underset{(3.00)}{0.135} Δ \ln Q_{t} + \underset{(7.84)}{0.177} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.19)}{0.186} Δ \ln P M N_{t} + \underset{(7.71)}{0.540} Δ \ln P d_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.963 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0030 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

√ = presence of an asymmetry

Table 3.

United States: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} & Δ \ln P d \end{matrix} & = \underset{(0.42)}{0.004} + \underset{(4.56)}{0.651} Δ \ln W_{t} - \underset{(2.36)}{0.343} Δ \ln Q M H_{t}^{N} + \underset{(1.77)}{0.110} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.16)}{0.021} Δ \ln P M N_{t} + \underset{(1.09)}{0.113} Δ \ln P M_{t - 1} - \underset{(0.25)}{0.046} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.888 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0053 \end{matrix} & D - W = 2.07 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} & Δ \ln P d = \end{matrix} & \underset{}{- \underset{(1.46)}{0.47}} + \underset{(4.49)}{0.629} Δ \ln W_{t} - \underset{(0.26)}{0.063} Δ \ln Q M H_{t}^{N} + \underset{(2.81)}{0.142} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.08)}{0.157} Δ \ln P M N_{t} + \underset{(1.48)}{0.096} \ln y_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.895 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0051 \end{matrix} & D - W = 2.26 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \sqrt III \end{matrix} & Δ \ln P d \end{matrix} & = \underset{(0.14)}{0.002} + \underset{(2.24)}{0.141} u_{t}^{- 1} - \underset{(2.38)}{0.482} Δ \ln Q M H_{t}^{N} + \underset{(2.60)}{0.210} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.80)}{0.180} Δ \ln P M N_{t} + \underset{(1.81)}{0.290} Δ \ln P M_{t - 1} - \underset{(1.24)}{0.362} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.762 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0077 \end{matrix} & D - W = 1.07 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \sqrt IV \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(1.79)}{0.020} + \underset{(5.18)}{0.234} u_{t}^{- 1} - \underset{(4.03)}{0.337} Δ \ln Q_{t} + \underset{(2.33)}{0.136} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.07)}{0.178} Δ \ln P M N_{t} + \underset{(3.08)}{0.381} Δ \ln P M_{t - 1} - \underset{(2.65)}{0.619} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.862 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0059 \end{matrix} & D - W = 1.63 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \sqrt V \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(3.28)}{0.017} + \underset{(7.13)}{0.149} u_{t}^{- 1} - \underset{(3.00)}{0.135} Δ \ln Q_{t} + \underset{(7.84)}{0.177} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.19)}{0.186} Δ \ln P M N_{t} + \underset{(7.71)}{0.540} Δ \ln P d_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.963 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0030 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

√ = presence of an asymmetry

The results for the Federal Republic of Germany, given in Table 4, are much less supportive of the asymmetry argument. In only one of the six models tested—namely, Model III—is the slope dummy variable on import prices close to being significant, although it does carry the expected negative sign in all cases. On the other hand, not too much should be made of the asymmetry results for that country because, as mentioned previously, the import price-change variable itself was rarely significant.

Table 4.

Federal Republic of Germany: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Table 4.

Federal Republic of Germany: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} & Δ \ln P d = \end{matrix} & \underset{(3.25)}{0.065} + \underset{(5.63)}{0.459} Δ \ln W_{t} - \underset{(4.51)}{1.20} Δ \ln Q M H_{t}^{N} + \underset{(0.87)}{0.185} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.51)}{0.141} Δ \ln P M N_{t - 1 / 4} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.864 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0073 \end{matrix} & D - W = 1.94 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(1.22)}{0.46} + \underset{(2.63)}{0.325} Δ \ln W_{t} - \underset{(4.86)}{1.37} Δ \ln Q M H_{t}^{N} + \underset{(1.33)}{0.286} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.06)}{0.307} Δ \ln P M N_{t - 1 / 4} + \underset{}{\underset{(1.40)}{0.119} \ln y_{t}} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.875 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0070 \end{matrix} & D - W = 2.13 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(3.91)}{1.21} + \underset{(4.38)}{0.293} \ln y_{t} - \underset{(6.36)}{1.81} Δ \ln Q M H_{t}^{N} + \underset{(2.24)}{0.536} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.11)}{0.667} Δ \ln P M N_{t - 1 / 4} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.808 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0087 \end{matrix} & D - W = 1.93 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} IV \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(5.50)}{2.70} + \underset{(5.13)}{0.600} \ln y_{t} - \underset{(3.95)}{0.732} Δ \ln Q_{t} + \underset{(0.71)}{0.148} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.81)}{0.240} Δ \ln P M N_{t - 1 / 4} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.621 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0122 \end{matrix} & D - W = 0.81 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} V \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(3.32)}{1.47} + \underset{(3.24)}{0.320} \ln y_{t} + \underset{(0.33)}{0.072} Δ \ln Q_{t} + \underset{(0.71)}{0.428} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.79)}{0.231} Δ \ln P M N_{t - 1 / 4} \end{matrix} + \underset{(4.29)}{0.772} Δ \ln P d_{t - 1} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.847 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0078 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

Table 4.

Federal Republic of Germany: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} & Δ \ln P d = \end{matrix} & \underset{(3.25)}{0.065} + \underset{(5.63)}{0.459} Δ \ln W_{t} - \underset{(4.51)}{1.20} Δ \ln Q M H_{t}^{N} + \underset{(0.87)}{0.185} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.51)}{0.141} Δ \ln P M N_{t - 1 / 4} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.864 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0073 \end{matrix} & D - W = 1.94 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(1.22)}{0.46} + \underset{(2.63)}{0.325} Δ \ln W_{t} - \underset{(4.86)}{1.37} Δ \ln Q M H_{t}^{N} + \underset{(1.33)}{0.286} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.06)}{0.307} Δ \ln P M N_{t - 1 / 4} + \underset{}{\underset{(1.40)}{0.119} \ln y_{t}} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.875 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0070 \end{matrix} & D - W = 2.13 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(3.91)}{1.21} + \underset{(4.38)}{0.293} \ln y_{t} - \underset{(6.36)}{1.81} Δ \ln Q M H_{t}^{N} + \underset{(2.24)}{0.536} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.11)}{0.667} Δ \ln P M N_{t - 1 / 4} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.808 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0087 \end{matrix} & D - W = 1.93 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} IV \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(5.50)}{2.70} + \underset{(5.13)}{0.600} \ln y_{t} - \underset{(3.95)}{0.732} Δ \ln Q_{t} + \underset{(0.71)}{0.148} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.81)}{0.240} Δ \ln P M N_{t - 1 / 4} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.621 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0122 \end{matrix} & D - W = 0.81 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} V \end{matrix} & Δ \ln P d = \end{matrix} & - \underset{(3.32)}{1.47} + \underset{(3.24)}{0.320} \ln y_{t} + \underset{(0.33)}{0.072} Δ \ln Q_{t} + \underset{(0.71)}{0.428} Δ \ln P M_{t - 1 / 4} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.79)}{0.231} Δ \ln P M N_{t - 1 / 4} \end{matrix} + \underset{(4.29)}{0.772} Δ \ln P d_{t - 1} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.847 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0078 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

The asymmetry results for Japan, as shown in Table 5, point rather strongly to the presence of a significant asymmetry for import price changes. Also, the Japanese results consistently favor the weak form of the asymmetry hypothesis. That is, they imply that negative import price changes will lead to negative changes in domestic prices but that this elasticity with respect to negative changes will be smaller than that for positive changes.

Table 5.

Japan: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

√ = presence of an asymmetry

Table 5.

Japan: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(0.56)}{0.009} + \underset{(1.28)}{0.203} \ln W_{t} + \underset{(0.40)}{0.084} Δ \ln Q M H_{t}^{N} + \underset{(3.06)}{0.437} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.91)}{0.333} Δ \ln P M N_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.814 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0116 \end{matrix} & D - W = 1.28 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & \underset{(0.39)}{0.172} + \underset{(1.27)}{0.212} \ln W + \underset{(0.53)}{0.143} Δ \ln Q M H_{t}^{N} - \underset{(0.37)}{0.037} \ln y_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(2.89)}{0.432} Δ \ln P M_{t} - \underset{(1.85)}{0.338} Δ \ln P M N_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.798 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0121 \end{matrix} & D - W = 1.27 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \sqrt III & Δ \ln P d = \end{matrix} & - \underset{(0.98)}{0.024} - \underset{(0.46)}{0.014} u_{t}^{- 1} + \underset{(1.77)}{0.292} Δ \ln Q M H_{t}^{N} + \underset{(5.47)}{0.577} Δ \ln {P M}_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(3.12)}{0.464} Δ \ln P {M N}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.791 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0123 \end{matrix} & D - W = 1.34 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \sqrt IV & Δ \ln P d = \end{matrix} & - \underset{(0.62)}{0.23} + \underset{(0.70)}{0.058} \ln y_{t} + \underset{(0.48)}{0.068} Δ \ln Q_{t} + \underset{(5.09)}{0.593} Δ \ln {P M}_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.67)}{0.415} Δ \ln P {M N}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = - 0.762 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0131 \end{matrix} & D - W = 1.44 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \sqrt V & Δ \ln P d = \end{matrix} & - \underset{(0.33)}{0.14} + \underset{(0.40)}{0.036} \ln y_{t} + \underset{(0.63)}{0.096} Δ \ln Q + \underset{(4.91)}{0.587} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.44)}{0.395} Δ \ln P M N_{t - 1} + \underset{(0.67)}{0.141} Δ \ln P d_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.749 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0135 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

√ = presence of an asymmetry

Table 5.

Japan: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(0.56)}{0.009} + \underset{(1.28)}{0.203} \ln W_{t} + \underset{(0.40)}{0.084} Δ \ln Q M H_{t}^{N} + \underset{(3.06)}{0.437} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(1.91)}{0.333} Δ \ln P M N_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.814 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0116 \end{matrix} & D - W = 1.28 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & \underset{(0.39)}{0.172} + \underset{(1.27)}{0.212} \ln W + \underset{(0.53)}{0.143} Δ \ln Q M H_{t}^{N} - \underset{(0.37)}{0.037} \ln y_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(2.89)}{0.432} Δ \ln P M_{t} - \underset{(1.85)}{0.338} Δ \ln P M N_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.798 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0121 \end{matrix} & D - W = 1.27 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \sqrt III & Δ \ln P d = \end{matrix} & - \underset{(0.98)}{0.024} - \underset{(0.46)}{0.014} u_{t}^{- 1} + \underset{(1.77)}{0.292} Δ \ln Q M H_{t}^{N} + \underset{(5.47)}{0.577} Δ \ln {P M}_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(3.12)}{0.464} Δ \ln P {M N}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.791 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0123 \end{matrix} & D - W = 1.34 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \sqrt IV & Δ \ln P d = \end{matrix} & - \underset{(0.62)}{0.23} + \underset{(0.70)}{0.058} \ln y_{t} + \underset{(0.48)}{0.068} Δ \ln Q_{t} + \underset{(5.09)}{0.593} Δ \ln {P M}_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.67)}{0.415} Δ \ln P {M N}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = - 0.762 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0131 \end{matrix} & D - W = 1.44 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \sqrt V & Δ \ln P d = \end{matrix} & - \underset{(0.33)}{0.14} + \underset{(0.40)}{0.036} \ln y_{t} + \underset{(0.63)}{0.096} Δ \ln Q + \underset{(4.91)}{0.587} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(2.44)}{0.395} Δ \ln P M N_{t - 1} + \underset{(0.67)}{0.141} Δ \ln P d_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.749 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0135 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

√ = presence of an asymmetry

The results for the United Kingdom stand in sharp contrast to those for Japan and the United States—and to a lesser extent, also differ from those for the Federal Republic of Germany. In particular, as Table 6 shows, the slope dummy variable on import price changes is never significant, and in most cases, it in fact carries a positive sign. This latter result would imply that negative changes in import prices lead to a larger positive change in domestic prices than do positive import price changes of the same size, although the results are never statistically significant.

Table 6.

United Kingdom: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Table 6.

United Kingdom: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(1.34)}{0.030} + \underset{(3.38)}{0.424} Δ \ln W_{t} - \underset{(1.42)}{0.582} Δ \ln Q M H_{t}^{N} + \underset{(1.24)}{0.082} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.37)}{0.076} Δ \ln P M N_{t} + \underset{(1.22)}{0.135} Δ \ln P M_{t - 1} + \underset{(0.20)}{0.047} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.780 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0110 \end{matrix} & D - W = 1.93 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & \underset{(0.64)}{0.41} + \underset{(3.17)}{0.413} Δ \ln W_{t} - \underset{(1.43)}{0.604} Δ \ln Q M H_{t}^{N} + \underset{(1.32)}{0.092} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.77)}{0.469} Δ \ln P M N_{t} + \underset{(1.04)}{0.120} Δ \ln P M_{t - 1} - \underset{(0.11)}{0.028} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.766 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0113 \end{matrix} & D - W = 2.16 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} III & Δ \ln P d = \end{matrix} & \underset{(3.78)}{0.092} - \underset{(0.53)}{0.036} u_{t}^{- 1} - \underset{(1.66)}{1.07} Δ \ln Q M H_{t}^{N} + \underset{(1.65)}{0.172} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.66)}{0.199} Δ \ln P M N_{t} + \underset{(1.08)}{0.184} Δ \ln P M_{t - 1} + \underset{(0.91)}{0.309} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.515 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0163 \end{matrix} & D - W = 1.77 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} IV & Δ \ln P d = \end{matrix} & \underset{(3.31)}{0.077} - \underset{(1.05)}{0.068} u_{t}^{- 1} - \underset{(1.22)}{0.482} Δ \ln Q_{t} + \underset{(1.24)}{0.123} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.05)}{0.014} Δ \ln P M N_{t} + \underset{(0.78)}{0.143} Δ \ln P M_{t - 1} + \underset{(0.73)}{0.263} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.455 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0172 \end{matrix} & D - W = 1.42 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} V & Δ \ln P d = \end{matrix} & \underset{(0.08)}{0.002} + \underset{(0.58)}{0.036} u_{t}^{- 1} - \underset{(0.54)}{0.123} Δ \ln Q_{t} + \underset{(1.21)}{0.158} Δ \ln P M_{t - 1} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.922)}{0.2239} Δ \ln P M N_{t - 1} + \underset{(3.13)}{0.800} Δ \ln P d_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.706 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0127 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

Table 6.

United Kingdom: Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(1.34)}{0.030} + \underset{(3.38)}{0.424} Δ \ln W_{t} - \underset{(1.42)}{0.582} Δ \ln Q M H_{t}^{N} + \underset{(1.24)}{0.082} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.37)}{0.076} Δ \ln P M N_{t} + \underset{(1.22)}{0.135} Δ \ln P M_{t - 1} + \underset{(0.20)}{0.047} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.780 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0110 \end{matrix} & D - W = 1.93 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & \underset{(0.64)}{0.41} + \underset{(3.17)}{0.413} Δ \ln W_{t} - \underset{(1.43)}{0.604} Δ \ln Q M H_{t}^{N} + \underset{(1.32)}{0.092} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.77)}{0.469} Δ \ln P M N_{t} + \underset{(1.04)}{0.120} Δ \ln P M_{t - 1} - \underset{(0.11)}{0.028} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.766 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0113 \end{matrix} & D - W = 2.16 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} III & Δ \ln P d = \end{matrix} & \underset{(3.78)}{0.092} - \underset{(0.53)}{0.036} u_{t}^{- 1} - \underset{(1.66)}{1.07} Δ \ln Q M H_{t}^{N} + \underset{(1.65)}{0.172} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.66)}{0.199} Δ \ln P M N_{t} + \underset{(1.08)}{0.184} Δ \ln P M_{t - 1} + \underset{(0.91)}{0.309} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.515 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0163 \end{matrix} & D - W = 1.77 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} IV & Δ \ln P d = \end{matrix} & \underset{(3.31)}{0.077} - \underset{(1.05)}{0.068} u_{t}^{- 1} - \underset{(1.22)}{0.482} Δ \ln Q_{t} + \underset{(1.24)}{0.123} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} - \underset{(0.05)}{0.014} Δ \ln P M N_{t} + \underset{(0.78)}{0.143} Δ \ln P M_{t - 1} + \underset{(0.73)}{0.263} Δ \ln P M N_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.455 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0172 \end{matrix} & D - W = 1.42 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} V & Δ \ln P d = \end{matrix} & \underset{(0.08)}{0.002} + \underset{(0.58)}{0.036} u_{t}^{- 1} - \underset{(0.54)}{0.123} Δ \ln Q_{t} + \underset{(1.21)}{0.158} Δ \ln P M_{t - 1} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.922)}{0.2239} Δ \ln P M N_{t - 1} + \underset{(3.13)}{0.800} Δ \ln P d_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.706 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0127 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

Finally, Table 7 provides the asymmetry results for Italy. Like the U. S. results, the Italian results show a mixed pattern with significant asymmetries appearing in more than half of the models (namely, in Models III, IV, and V). The sign on P $\overset{*}{M}$ N is always negative. Also, like the U. S. results, the sizes of the coefficients on the P $\overset{*}{M}$ N variables suggest the strong form of the asymmetry hypothesis, that is, that negative import price changes will lead to an increase in domestic prices; at the same time, however, the extent of the asymmetry seems to decline over time, as evidenced by the fact that the coefficient on P $\overset{*}{M}$ N_t-1 is typically considerably smaller than that on P $\overset{*}{M}$ N_t; thus, in the Italian case, the asymmetry may be more in the timing response to positive versus negative changes than in the long-run effect.

Table 7.

Italy: Asymmetry Tests Using Annual Data, 1958–73

(dependent variable = percentage change in gdp deflator)

√ = presence of an asymmetry

Table 7.

Italy: Asymmetry Tests Using Annual Data, 1958–73

(dependent variable = percentage change in gdp deflator)

Model Number
$\begin{matrix} I Δ \ln P d = & \underset{(0.66)}{0.006} + \underset{(6.19)}{0.388} Δ \ln W_{t} - \underset{(0.68)}{0.069} Δ \ln Q M H_{t}^{N} + \underset{(1.71)}{0.096} Δ \ln P M_{t} \\ - \underset{(0.08)}{0.008} Δ \ln P M N_{t} \\ \begin{matrix} {\begin{matrix} \begin{matrix} \bar{R} \end{matrix} \end{matrix}}^{2} = 0.874 & \begin{matrix} \begin{matrix} \bar{S E E} = 0.0102 \end{matrix} & D - W = 1.30 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & \underset{(1.28)}{0.53} + \underset{(4.23)}{0.326} Δ \ln W_{t} - \underset{(1.14)}{0.123} Δ \ln Q M H_{t}^{N} + \underset{(1.29)}{0.117} \ln y_{t - 2} \\ + \underset{(2.18)}{0.151} Δ \ln P M_{t} - \underset{(0.62)}{0.064} Δ \ln P M N_{t} \\ \begin{matrix} {\begin{matrix} \begin{matrix} \bar{R} \end{matrix} \end{matrix}}^{2} = 0.881 & \begin{matrix} \begin{matrix} \bar{S E E} = 0.0099 \end{matrix} & D - W = 1.18 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \sqrt III & Δ \ln P d = - \underset{(2.93)}{0.081} + \underset{(4.74)}{0.421} u_{t}^{- 1} - \underset{(0.06)}{0.008} Δ \ln Q M H_{t}^{N} + \underset{(5.72)}{0.298} Δ \ln P M_{t} \\ - \underset{(3.72)}{5.48} Δ \ln P M N_{t} + \underset{(2.00)}{0.300} Δ \ln P M_{t - 1} - \underset{(1.08)}{0.232} Δ \ln P M N_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.840 \end{matrix} & \begin{matrix} \bar{S E E} = 0.0115 & D - W = 2.56 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \sqrt IV & Δ \ln P d = - \underset{(2.28)}{0.076} + \underset{(4.56)}{0.415} u_{t}^{- 1} - \underset{(0.27)}{0.064} Δ \ln Q_{t} + \underset{(5.81)}{0.296} Δ \ln P M_{t} \\ - \underset{(3.80)}{5.49} Δ \ln P M N_{t} + \underset{(1.41)}{0.264} Δ \ln P M_{t - 1} - \underset{(0.78)}{0.191} Δ \ln P M N_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.841 \end{matrix} & \begin{matrix} \bar{S E E} = 0.0114 & D - W = 2.57 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \sqrt V & Δ \ln P d = & \underset{(1.80)}{0.053} + \underset{(3.76)}{0.386} u_{t}^{- 1} - \underset{(1.12)}{0.315} Δ \ln Q_{t} + \underset{(4.68)}{0.296} Δ \ln P M_{t} \\ - \underset{(3.04)}{0.522} Δ \ln P M N_{t} + \underset{(0.06)}{0.015} Δ \ln P d_{t - 1} \\ \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.798 & \bar{S E E} = 0.0129 \end{matrix} \end{matrix}$

√ = presence of an asymmetry

Table 7.

Italy: Asymmetry Tests Using Annual Data, 1958–73

(dependent variable = percentage change in gdp deflator)

Model Number
$\begin{matrix} I Δ \ln P d = & \underset{(0.66)}{0.006} + \underset{(6.19)}{0.388} Δ \ln W_{t} - \underset{(0.68)}{0.069} Δ \ln Q M H_{t}^{N} + \underset{(1.71)}{0.096} Δ \ln P M_{t} \\ - \underset{(0.08)}{0.008} Δ \ln P M N_{t} \\ \begin{matrix} {\begin{matrix} \begin{matrix} \bar{R} \end{matrix} \end{matrix}}^{2} = 0.874 & \begin{matrix} \begin{matrix} \bar{S E E} = 0.0102 \end{matrix} & D - W = 1.30 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & \underset{(1.28)}{0.53} + \underset{(4.23)}{0.326} Δ \ln W_{t} - \underset{(1.14)}{0.123} Δ \ln Q M H_{t}^{N} + \underset{(1.29)}{0.117} \ln y_{t - 2} \\ + \underset{(2.18)}{0.151} Δ \ln P M_{t} - \underset{(0.62)}{0.064} Δ \ln P M N_{t} \\ \begin{matrix} {\begin{matrix} \begin{matrix} \bar{R} \end{matrix} \end{matrix}}^{2} = 0.881 & \begin{matrix} \begin{matrix} \bar{S E E} = 0.0099 \end{matrix} & D - W = 1.18 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \sqrt III & Δ \ln P d = - \underset{(2.93)}{0.081} + \underset{(4.74)}{0.421} u_{t}^{- 1} - \underset{(0.06)}{0.008} Δ \ln Q M H_{t}^{N} + \underset{(5.72)}{0.298} Δ \ln P M_{t} \\ - \underset{(3.72)}{5.48} Δ \ln P M N_{t} + \underset{(2.00)}{0.300} Δ \ln P M_{t - 1} - \underset{(1.08)}{0.232} Δ \ln P M N_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.840 \end{matrix} & \begin{matrix} \bar{S E E} = 0.0115 & D - W = 2.56 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \sqrt IV & Δ \ln P d = - \underset{(2.28)}{0.076} + \underset{(4.56)}{0.415} u_{t}^{- 1} - \underset{(0.27)}{0.064} Δ \ln Q_{t} + \underset{(5.81)}{0.296} Δ \ln P M_{t} \\ - \underset{(3.80)}{5.49} Δ \ln P M N_{t} + \underset{(1.41)}{0.264} Δ \ln P M_{t - 1} - \underset{(0.78)}{0.191} Δ \ln P M N_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.841 \end{matrix} & \begin{matrix} \bar{S E E} = 0.0114 & D - W = 2.57 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \sqrt V & Δ \ln P d = & \underset{(1.80)}{0.053} + \underset{(3.76)}{0.386} u_{t}^{- 1} - \underset{(1.12)}{0.315} Δ \ln Q_{t} + \underset{(4.68)}{0.296} Δ \ln P M_{t} \\ - \underset{(3.04)}{0.522} Δ \ln P M N_{t} + \underset{(0.06)}{0.015} Δ \ln P d_{t - 1} \\ \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.798 & \bar{S E E} = 0.0129 \end{matrix} \end{matrix}$

√ = presence of an asymmetry

In view of both the limited number of observations and the mixed results on the asymmetry test obtained from the individual country regressions, it seemed worthwhile to conduct the test also on the pooled data for all five countries. The results of that exercise are portrayed in Table 8, in which one can find estimates of Models I, II, III, IV, and V, both including and excluding the slope dummy variables on P $\overset{*}{M}$ . Each of the pooled regressions was also estimated with and without shift (intercept) dummy variables for the different countries, that is, the slope coefficients were restricted to be equal across countries but the intercept of the regression was not.³⁹ These country shift dummies (DUK, DG, DJ, and DI) appear in Table 8 only for those equations in which they significantly improved the explanatory power of the model.

Table 8.

Five Large Industrial Countries: Pooled Results of Asymmetry Tests Using Annual Data, 1958–73

(Dependent variable = percentage change in GDP deflator)

Table 8.

Five Large Industrial Countries: Pooled Results of Asymmetry Tests Using Annual Data, 1958–73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} I & Δ \ln P d = & \underset{(3.72)}{0.011} + \underset{(13.16)}{0.445} Δ \ln W_{t} - \underset{(3.96)}{0.218} Δ \ln Q M H_{t}^{N} + \underset{(5.28)}{0.108} Δ \ln P M_{t} \\ + \underset{(1.87)}{0.052} Δ \ln P M_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.807 \end{matrix} & \bar{S E E} = 0.0105 \end{matrix} \end{matrix}$
$\begin{matrix} I & Δ \ln P d = & \underset{(3.25)}{0.011} + \underset{(12.91)}{0.447} Δ \ln W_{t} - \underset{(3.89)}{0.221} Δ \ln Q M H_{t}^{N} + \underset{(3.43)}{0.100} Δ \ln P M_{t} \\ + \underset{(0.40)}{0.022} Δ \ln P M N_{t} + \underset{(1.11)}{0.065} Δ \ln P M_{t - 1} - \underset{(0.23)}{0.018} Δ \ln P M N_{t - 1} \\ \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.802 & \bar{S E E} = 0.0106 \end{matrix} \end{matrix}$
$\begin{matrix} II & Δ \ln P d = & \underset{(0.45)}{0.068} + \underset{(12.83)}{0.442} Δ \ln W_{t} - \underset{(3.97)}{0.223} Δ \ln Q M H_{t}^{N} + \underset{(0.52)}{0.017} Δ \ln y_{t} \\ + \underset{(5.03)}{0.106} Δ \ln P M_{t} + \underset{(1.89)}{0.053} Δ \ln P M_{t - 1} \\ \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.805 & \bar{S E E} = 0.0105 \end{matrix} \end{matrix}$
$\begin{matrix} II & Δ \ln P d = & - \underset{(0.47)}{0.081} + \underset{(12.42)}{0.443} Δ \ln W_{t} - \underset{(3.90)}{0.224} Δ \ln Q M H_{t}^{N} + \underset{(0.54)}{0.020} \ln y_{t} \\ + \underset{(3.41)}{0.010} Δ \ln P M_{t} + \underset{(0.26)}{0.015} Δ \ln P M N_{t} + \underset{(1.22)}{0.076} Δ \ln P M_{t - 1} \\ - \underset{(0.39)}{0.034} Δ \ln P M N_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.800 \end{matrix} & \bar{S E E} = 0.0106 \end{matrix} \end{matrix}$
$\begin{matrix} III & Δ \ln P d = & - \underset{(2.06)}{0.51} + \underset{(2.17)}{0.118} \ln y_{t} - \underset{(1.71)}{0.243} Δ \ln Q M H_{t}^{N} + \underset{(6.28)}{0.245} Δ \ln P M_{t} \\ + \underset{(2.19)}{0.101} Δ \ln P M_{t - 1} + \underset{(2.50)}{0.015} D U K + \underset{(3.40)}{0.026} D G + \underset{(3.87)}{0.042} D J \\ + \underset{(3.48)}{0.025} D I \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.474 \end{matrix} & \bar{S E E} = 0.0173 \end{matrix} \end{matrix}$
$\begin{matrix} III & Δ \ln P d = & - \underset{(2.05)}{0.56} + \underset{(2.15)}{0.129} \ln y_{t} - \underset{(1.52)}{0.231} Δ \ln Q M H_{t}^{N} + \underset{(5.19)}{0.246} Δ \ln P M_{t} \\ - \underset{(0.15)}{0.015} Δ \ln P M N_{t} + \underset{(1.33)}{0.137} Δ \ln P M_{t - 1} - \underset{(0.40)}{0.057} Δ \ln P M N_{t - 1} \\ + \underset{(2.43)}{0.015} D U K + \underset{(3.23)}{0.025} D G + \underset{(3.50)}{0.041} D J + \underset{(3.24)}{0.024} D I \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.460 \end{matrix} & \bar{S E E} = 0.0174 \end{matrix} \end{matrix}$
$\begin{matrix} IV & Δ \ln P d = & - \underset{(3.03)}{0.79} + \underset{(3.14)}{0.179} \ln y_{t} - \underset{(3.14)}{0.330} Δ \ln Q_{t} + \underset{(6.56)}{0.216} Δ \ln P M_{t} \\ + \underset{(1.78)}{0.080} Δ \ln P M_{t - 1} + \underset{(1.84)}{0.011} D U K + \underset{(3.29)}{0.020} D G + \underset{(5.42)}{0.045} D J \\ + \underset{(3.59)}{0.021} D I \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.519 \end{matrix} & \bar{S E E} = 0.0165 \end{matrix} \end{matrix}$
$\begin{matrix} IV & Δ \ln P d = & - \underset{(3.12)}{0.90} + \underset{(3.22)}{0.203} \ln y_{t} - \underset{(3.15)}{0.334} Δ \ln Q_{t} + \underset{(5.42)}{0.238} Δ \ln P M_{t} \\ - \underset{(0.87)}{0.077} Δ \ln P M N_{t} + \underset{(1.05)}{0.104} Δ \ln P M_{t - 1} - \underset{(0.36)}{0.048} Δ \ln P M N_{t - 1} \\ + \underset{(1.76)}{0.011} D U K + \underset{(3.21)}{0.020} D G + \underset{(5.26)}{0.044} D J + \underset{(3.43)}{0.021} D I \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.512 \end{matrix} & \bar{S E E} = 0.0167 \end{matrix} \end{matrix}$
$\begin{matrix} V & Δ \ln P d = & - \underset{(3.39)}{0.79} + \underset{(3.43)}{0.176} \ln y_{t} - \underset{(1.87)}{0.188} Δ \ln Q_{t} + \underset{(5.24)}{0.167} Δ \ln P M_{t} \\ + \underset{(4.60)}{0.462} Δ \ln P d_{t - 1} + \underset{(1.05)}{0.006} D U K + \underset{(1.92)}{0.011} D G + \underset{(2.98)}{0.025} D J \\ + \underset{(2.24)}{0.013} D I \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.613 \end{matrix} & \bar{S E E} = 0.0148 \end{matrix} \end{matrix}$
$\begin{matrix} V & Δ \ln P d = & - \underset{(3.45)}{0.85} + \underset{(3.50)}{0.189} \ln y_{t} - \underset{(1.91)}{0.193} Δ \ln Q_{t} + \underset{(4.58)}{0.186} Δ \ln P M_{t} \\ - \underset{(0.76)}{0.060} Δ \ln P M N_{t} + \underset{(4.44)}{0.452} Δ \ln P d_{t - 1} + \underset{(1.03)}{0.006} D U K \\ + \underset{(1.91)}{0.011} D G + \underset{(2.97)}{0.025} D J + \underset{(2.19)}{0.012} D I \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.611 \end{matrix} & \bar{S E E} = 0.0148 \end{matrix} \end{matrix}$

Table 8.

Five Large Industrial Countries: Pooled Results of Asymmetry Tests Using Annual Data, 1958–73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} I & Δ \ln P d = & \underset{(3.72)}{0.011} + \underset{(13.16)}{0.445} Δ \ln W_{t} - \underset{(3.96)}{0.218} Δ \ln Q M H_{t}^{N} + \underset{(5.28)}{0.108} Δ \ln P M_{t} \\ + \underset{(1.87)}{0.052} Δ \ln P M_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.807 \end{matrix} & \bar{S E E} = 0.0105 \end{matrix} \end{matrix}$
$\begin{matrix} I & Δ \ln P d = & \underset{(3.25)}{0.011} + \underset{(12.91)}{0.447} Δ \ln W_{t} - \underset{(3.89)}{0.221} Δ \ln Q M H_{t}^{N} + \underset{(3.43)}{0.100} Δ \ln P M_{t} \\ + \underset{(0.40)}{0.022} Δ \ln P M N_{t} + \underset{(1.11)}{0.065} Δ \ln P M_{t - 1} - \underset{(0.23)}{0.018} Δ \ln P M N_{t - 1} \\ \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.802 & \bar{S E E} = 0.0106 \end{matrix} \end{matrix}$
$\begin{matrix} II & Δ \ln P d = & \underset{(0.45)}{0.068} + \underset{(12.83)}{0.442} Δ \ln W_{t} - \underset{(3.97)}{0.223} Δ \ln Q M H_{t}^{N} + \underset{(0.52)}{0.017} Δ \ln y_{t} \\ + \underset{(5.03)}{0.106} Δ \ln P M_{t} + \underset{(1.89)}{0.053} Δ \ln P M_{t - 1} \\ \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.805 & \bar{S E E} = 0.0105 \end{matrix} \end{matrix}$
$\begin{matrix} II & Δ \ln P d = & - \underset{(0.47)}{0.081} + \underset{(12.42)}{0.443} Δ \ln W_{t} - \underset{(3.90)}{0.224} Δ \ln Q M H_{t}^{N} + \underset{(0.54)}{0.020} \ln y_{t} \\ + \underset{(3.41)}{0.010} Δ \ln P M_{t} + \underset{(0.26)}{0.015} Δ \ln P M N_{t} + \underset{(1.22)}{0.076} Δ \ln P M_{t - 1} \\ - \underset{(0.39)}{0.034} Δ \ln P M N_{t - 1} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.800 \end{matrix} & \bar{S E E} = 0.0106 \end{matrix} \end{matrix}$
$\begin{matrix} III & Δ \ln P d = & - \underset{(2.06)}{0.51} + \underset{(2.17)}{0.118} \ln y_{t} - \underset{(1.71)}{0.243} Δ \ln Q M H_{t}^{N} + \underset{(6.28)}{0.245} Δ \ln P M_{t} \\ + \underset{(2.19)}{0.101} Δ \ln P M_{t - 1} + \underset{(2.50)}{0.015} D U K + \underset{(3.40)}{0.026} D G + \underset{(3.87)}{0.042} D J \\ + \underset{(3.48)}{0.025} D I \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.474 \end{matrix} & \bar{S E E} = 0.0173 \end{matrix} \end{matrix}$
$\begin{matrix} III & Δ \ln P d = & - \underset{(2.05)}{0.56} + \underset{(2.15)}{0.129} \ln y_{t} - \underset{(1.52)}{0.231} Δ \ln Q M H_{t}^{N} + \underset{(5.19)}{0.246} Δ \ln P M_{t} \\ - \underset{(0.15)}{0.015} Δ \ln P M N_{t} + \underset{(1.33)}{0.137} Δ \ln P M_{t - 1} - \underset{(0.40)}{0.057} Δ \ln P M N_{t - 1} \\ + \underset{(2.43)}{0.015} D U K + \underset{(3.23)}{0.025} D G + \underset{(3.50)}{0.041} D J + \underset{(3.24)}{0.024} D I \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.460 \end{matrix} & \bar{S E E} = 0.0174 \end{matrix} \end{matrix}$
$\begin{matrix} IV & Δ \ln P d = & - \underset{(3.03)}{0.79} + \underset{(3.14)}{0.179} \ln y_{t} - \underset{(3.14)}{0.330} Δ \ln Q_{t} + \underset{(6.56)}{0.216} Δ \ln P M_{t} \\ + \underset{(1.78)}{0.080} Δ \ln P M_{t - 1} + \underset{(1.84)}{0.011} D U K + \underset{(3.29)}{0.020} D G + \underset{(5.42)}{0.045} D J \\ + \underset{(3.59)}{0.021} D I \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.519 \end{matrix} & \bar{S E E} = 0.0165 \end{matrix} \end{matrix}$
$\begin{matrix} IV & Δ \ln P d = & - \underset{(3.12)}{0.90} + \underset{(3.22)}{0.203} \ln y_{t} - \underset{(3.15)}{0.334} Δ \ln Q_{t} + \underset{(5.42)}{0.238} Δ \ln P M_{t} \\ - \underset{(0.87)}{0.077} Δ \ln P M N_{t} + \underset{(1.05)}{0.104} Δ \ln P M_{t - 1} - \underset{(0.36)}{0.048} Δ \ln P M N_{t - 1} \\ + \underset{(1.76)}{0.011} D U K + \underset{(3.21)}{0.020} D G + \underset{(5.26)}{0.044} D J + \underset{(3.43)}{0.021} D I \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.512 \end{matrix} & \bar{S E E} = 0.0167 \end{matrix} \end{matrix}$
$\begin{matrix} V & Δ \ln P d = & - \underset{(3.39)}{0.79} + \underset{(3.43)}{0.176} \ln y_{t} - \underset{(1.87)}{0.188} Δ \ln Q_{t} + \underset{(5.24)}{0.167} Δ \ln P M_{t} \\ + \underset{(4.60)}{0.462} Δ \ln P d_{t - 1} + \underset{(1.05)}{0.006} D U K + \underset{(1.92)}{0.011} D G + \underset{(2.98)}{0.025} D J \\ + \underset{(2.24)}{0.013} D I \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.613 \end{matrix} & \bar{S E E} = 0.0148 \end{matrix} \end{matrix}$
$\begin{matrix} V & Δ \ln P d = & - \underset{(3.45)}{0.85} + \underset{(3.50)}{0.189} \ln y_{t} - \underset{(1.91)}{0.193} Δ \ln Q_{t} + \underset{(4.58)}{0.186} Δ \ln P M_{t} \\ - \underset{(0.76)}{0.060} Δ \ln P M N_{t} + \underset{(4.44)}{0.452} Δ \ln P d_{t - 1} + \underset{(1.03)}{0.006} D U K \\ + \underset{(1.91)}{0.011} D G + \underset{(2.97)}{0.025} D J + \underset{(2.19)}{0.012} D I \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.611 \end{matrix} & \bar{S E E} = 0.0148 \end{matrix} \end{matrix}$

The pooled results in Table 8 provide no support for the asymmetry hypothesis. Although the asymmetry variables ( ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ ) usually carry the expected negative sign (Models I and II being the exceptions), these variables are nowhere significantly different from zero and, in fact, the adjusted R² is always lower in the equation with the slope dummies than in the corresponding equation without them. Thus, the experience of our five sample countries taken as a whole for the period 1958-73 does not suggest the presence of an asymmetry in the effect of import price changes on domestic price changes.

aggregate price changes, 1958-70

Because empirical relationships in the general area of wage/price determination have often proved to be quite unstable over time, it is worth investigating whether the empirical results for the period 1958-73 apply to other time periods as well. Given the limited number of observations available with annual data and given that the period 1971-73 was a turbulent transition period as regards the exchange rate regime, it seemed reasonable to regard the (fixed exchange rate) period 1958-70 as an attractive supplementary estimation period. As such, the asymmetry tests were redone for the period 1958-70 on both the pooled data (for all five countries) and the individual country data.⁴⁰

The pooled results appear in Table 9. The most salient finding is that (as in the pooled results for the period 1958-73) there is no evidence of an asymmetry in the effect of import price changes on domestic prices. More specifically, in none of the five models tested is either of the slope dummy variables on import price changes significantly different from zero; nor is the adjusted R² in the equations with the slope dummies ( ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ ) ever higher than that in the equations where positive and negative import price changes are constrained to have the same effect on domestic prices. Thus, for the five industrial countries taken as a whole, there is no more support for the asymmetry hypothesis in the period 1958-70 than there was in the results for the period 1958-73.

Table 9.

Five Large Industrial Countries: Pooled Results of Asymmetry Tests Using Annual Data, 1958-70

(Dependent variable = percentage change in GDP deflator)

Table 9.

Five Large Industrial Countries: Pooled Results of Asymmetry Tests Using Annual Data, 1958-70

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(4.22)}{0.012} + \underset{(11.16)}{0.407} Δ \ln W_{t} - \underset{(3.46)}{0.183} Δ \ln Q M H_{t}^{N} + \underset{(4.43)}{0.120} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(3.13)}{0.087} Δ \ln P M_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.773 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0091 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(3.30)}{0.011} + \underset{(10.97)}{0.410} Δ \ln W_{t} - \underset{(3.29)}{0.182} Δ \ln Q M H_{t}^{N} + \underset{(1.63)}{0.108} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.25)}{0.022} Δ \ln P {M N}_{t} + \underset{(1.70)}{0.121} Δ \ln P M_{t - 1} - \underset{(0.51)}{0.045} Δ \ln P {M N}_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.766 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0093 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & - \underset{(0.42)}{0.66} + \underset{(10.14)}{0.402} Δ \ln W_{t} - \underset{(3.46)}{0.185} Δ \ln Q M H_{t}^{N} + \underset{(0.50)}{0.017} \ln y_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(3.92)}{0.115} Δ \ln P M_{t} + \underset{(3.09)}{0.086} Δ \ln P M_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.770 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0092 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & - \underset{(0.54)}{0.090} + \underset{(9.80)}{0.400} Δ \ln W_{t} - \underset{(3.26)}{0.182} Δ \ln Q M H_{t}^{N} + \underset{(0.60)}{0.022} \ln y_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(1.63)}{0.108} Δ \ln P M_{t} + \underset{(0.15)}{0.013} Δ \ln P {M N}_{t} + \underset{(1.77)}{0.129} Δ \ln P M_{t - 1} \end{matrix} \\ - \underset{(0.64)}{0.058} Δ \ln P {M N}_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.763 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0093 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} III & Δ ln P d = \end{matrix} & - \underset{(3.13)}{0.72} + \underset{(3.23)}{0.163} Δ ln y_{t} - \underset{(1.56)}{0.199} Δ ln Q M H_{t}^{N} + \underset{(3.68)}{0.194} Δ ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(2.72)}{0.117} Δ ln P M_{t - 1} + \underset{(2.06)}{0.012} D U K + \underset{(2.49)}{0.018} D G + \underset{(3.26)}{0.033} D J \end{matrix} \\ + \underset{(2.92)}{0.020} D I \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.452 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0142 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} III & Δ \ln P d = \end{matrix} & - \underset{(3.04)}{0.74} + \underset{(3.16)}{0.166} \ln y_{t} - \underset{(1.35)}{0.188} Δ \ln Q M H_{t}^{N} + \underset{(2.00)}{0.206} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.13)}{0.018} Δ \ln P {M N}_{t} + \underset{(1.20)}{0.138} Δ \ln P M_{t - 1} - \underset{(0.21)}{0.031} Δ \ln P {M N}_{t - 1} \end{matrix} \\ + \underset{(1.94)}{0.011} D U K + \underset{(2.34)}{0.017} D G + \underset{(2.95)}{0.033} D J + \underset{(2.73)}{0.019} D I \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.432 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0144 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} IV & Δ \ln P d = \end{matrix} & \underset{(4.17)}{- 1.03} + \underset{(4.27)}{0.231} \ln y_{t} - \underset{(3.11)}{0.292} Δ \ln Q_{t} + \underset{(3.12)}{0.142} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(2.20)}{0.092} Δ \ln P M_{t - 1} + \underset{(1.47)}{0.007} D U K + \underset{(2.51)}{0.014} D G + \underset{(4.84)}{0.037 D J} \\ + \underset{(3.12)}{0.017} D I \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.512 \end{matrix} & \bar{S E E} = 0.0134 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} IV & Δ \ln P d = \end{matrix} & \underset{(4.06)}{- 1.04} + \underset{(4.17)}{0.233} \ln y_{t} - \underset{(2.96)}{0.288} Δ \ln Q_{t} + \underset{(1.68)}{0.165} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.26)}{0.033} Δ \ln P {M N}_{t} + \underset{(0.84)}{0.092} Δ \ln P M_{t - 1} - \underset{(0.04)}{0.004} Δ \ln {P M N}_{t - 1} \\ + \underset{(1.42)}{0.008} D U K + \underset{(2.47)}{0.014} D G + \underset{(4.63)}{0.037} D J + \underset{(3.03)}{0.017} D I \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.495 \end{matrix} & \bar{S E E} = 0.0136 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} V & Δ \ln P d = \end{matrix} & \underset{(4.03)}{- 0.97} + \underset{(4.09)}{0.217} \ln y_{t} - \underset{(2.14)}{0.212} Δ \ln Q_{t} + \underset{(2.93)}{0.130} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(1.18)}{0.052} Δ \ln P M_{t - 1} + \underset{(2.12)}{0.268} Δ \ln P d_{t - 1} + \underset{(1.15)}{0.006} D U K \\ + \underset{(1.91)}{0.011} D G + \underset{(2.99)}{0.027} D J + \underset{(2.19)}{0.013} D I \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.541 \end{matrix} & \bar{S E E} = 0.0130 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} V & Δ \ln P d = \end{matrix} & - \underset{(4.20)}{1.02} + \underset{(4.26)}{0.226} \ln y_{t} - \underset{(2.15)}{0.215} Δ \ln Q_{t} + \underset{(2.77)}{0.323} Δ \ln P d_{t - 1} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(1.73)}{0.162} Δ \ln P M_{t} - \underset{(0.45)}{0.055} Δ \ln P {M N}_{t} + \underset{(1.04)}{0.005} D U K \end{matrix} \\ + \underset{(1.74)}{0.010} D G + \underset{(2.80)}{0.025} D J + \underset{(1.97)}{0.011} D I \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.531 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0131 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

Table 9.

Five Large Industrial Countries: Pooled Results of Asymmetry Tests Using Annual Data, 1958-70

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(4.22)}{0.012} + \underset{(11.16)}{0.407} Δ \ln W_{t} - \underset{(3.46)}{0.183} Δ \ln Q M H_{t}^{N} + \underset{(4.43)}{0.120} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(3.13)}{0.087} Δ \ln P M_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.773 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0091 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} I & Δ \ln P d = \end{matrix} & \underset{(3.30)}{0.011} + \underset{(10.97)}{0.410} Δ \ln W_{t} - \underset{(3.29)}{0.182} Δ \ln Q M H_{t}^{N} + \underset{(1.63)}{0.108} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(0.25)}{0.022} Δ \ln P {M N}_{t} + \underset{(1.70)}{0.121} Δ \ln P M_{t - 1} - \underset{(0.51)}{0.045} Δ \ln P {M N}_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.766 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0093 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & - \underset{(0.42)}{0.66} + \underset{(10.14)}{0.402} Δ \ln W_{t} - \underset{(3.46)}{0.185} Δ \ln Q M H_{t}^{N} + \underset{(0.50)}{0.017} \ln y_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} + \underset{(3.92)}{0.115} Δ \ln P M_{t} + \underset{(3.09)}{0.086} Δ \ln P M_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.770 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0092 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} II & Δ \ln P d = \end{matrix} & - \underset{(0.54)}{0.090} + \underset{(9.80)}{0.400} Δ \ln W_{t} - \underset{(3.26)}{0.182} Δ \ln Q M H_{t}^{N} + \underset{(0.60)}{0.022} \ln y_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(1.63)}{0.108} Δ \ln P M_{t} + \underset{(0.15)}{0.013} Δ \ln P {M N}_{t} + \underset{(1.77)}{0.129} Δ \ln P M_{t - 1} \end{matrix} \\ - \underset{(0.64)}{0.058} Δ \ln P {M N}_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.763 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0093 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} III & Δ ln P d = \end{matrix} & - \underset{(3.13)}{0.72} + \underset{(3.23)}{0.163} Δ ln y_{t} - \underset{(1.56)}{0.199} Δ ln Q M H_{t}^{N} + \underset{(3.68)}{0.194} Δ ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(2.72)}{0.117} Δ ln P M_{t - 1} + \underset{(2.06)}{0.012} D U K + \underset{(2.49)}{0.018} D G + \underset{(3.26)}{0.033} D J \end{matrix} \\ + \underset{(2.92)}{0.020} D I \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.452 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0142 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} III & Δ \ln P d = \end{matrix} & - \underset{(3.04)}{0.74} + \underset{(3.16)}{0.166} \ln y_{t} - \underset{(1.35)}{0.188} Δ \ln Q M H_{t}^{N} + \underset{(2.00)}{0.206} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.13)}{0.018} Δ \ln P {M N}_{t} + \underset{(1.20)}{0.138} Δ \ln P M_{t - 1} - \underset{(0.21)}{0.031} Δ \ln P {M N}_{t - 1} \end{matrix} \\ + \underset{(1.94)}{0.011} D U K + \underset{(2.34)}{0.017} D G + \underset{(2.95)}{0.033} D J + \underset{(2.73)}{0.019} D I \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.432 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0144 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} IV & Δ \ln P d = \end{matrix} & \underset{(4.17)}{- 1.03} + \underset{(4.27)}{0.231} \ln y_{t} - \underset{(3.11)}{0.292} Δ \ln Q_{t} + \underset{(3.12)}{0.142} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(2.20)}{0.092} Δ \ln P M_{t - 1} + \underset{(1.47)}{0.007} D U K + \underset{(2.51)}{0.014} D G + \underset{(4.84)}{0.037 D J} \\ + \underset{(3.12)}{0.017} D I \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.512 \end{matrix} & \bar{S E E} = 0.0134 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} IV & Δ \ln P d = \end{matrix} & \underset{(4.06)}{- 1.04} + \underset{(4.17)}{0.233} \ln y_{t} - \underset{(2.96)}{0.288} Δ \ln Q_{t} + \underset{(1.68)}{0.165} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.26)}{0.033} Δ \ln P {M N}_{t} + \underset{(0.84)}{0.092} Δ \ln P M_{t - 1} - \underset{(0.04)}{0.004} Δ \ln {P M N}_{t - 1} \\ + \underset{(1.42)}{0.008} D U K + \underset{(2.47)}{0.014} D G + \underset{(4.63)}{0.037} D J + \underset{(3.03)}{0.017} D I \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.495 \end{matrix} & \bar{S E E} = 0.0136 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} V & Δ \ln P d = \end{matrix} & \underset{(4.03)}{- 0.97} + \underset{(4.09)}{0.217} \ln y_{t} - \underset{(2.14)}{0.212} Δ \ln Q_{t} + \underset{(2.93)}{0.130} Δ \ln P M_{t} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(1.18)}{0.052} Δ \ln P M_{t - 1} + \underset{(2.12)}{0.268} Δ \ln P d_{t - 1} + \underset{(1.15)}{0.006} D U K \\ + \underset{(1.91)}{0.011} D G + \underset{(2.99)}{0.027} D J + \underset{(2.19)}{0.013} D I \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\begin{matrix} \bar{R} \end{matrix}}^{2} = 0.541 \end{matrix} & \bar{S E E} = 0.0130 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} V & Δ \ln P d = \end{matrix} & - \underset{(4.20)}{1.02} + \underset{(4.26)}{0.226} \ln y_{t} - \underset{(2.15)}{0.215} Δ \ln Q_{t} + \underset{(2.77)}{0.323} Δ \ln P d_{t - 1} \\ \begin{matrix} \begin{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} + \underset{(1.73)}{0.162} Δ \ln P M_{t} - \underset{(0.45)}{0.055} Δ \ln P {M N}_{t} + \underset{(1.04)}{0.005} D U K \end{matrix} \\ + \underset{(1.74)}{0.010} D G + \underset{(2.80)}{0.025} D J + \underset{(1.97)}{0.011} D I \end{matrix} \\ \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.531 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0131 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$

Table 9 also contains a number of other results that are worth mentioning, if only briefly. First, there is no clear indication that the effect of import prices on domestic prices was different during the two periods; for example, Models I, II, and V display somewhat larger coefficients on $\overset{*}{P} M_{t} plus \overset{*}{P} M_{t - 1}$ for the period 1958-70 than for the period 1958-73, but Models III and IV give the opposite result (Table 8). Second, there is some evidence from the estimates of Model V that the influence of past domestic price changes on the current rate of inflation was lower in the period 1958-70 than in the period 1958-73. Estimates of the Cross-Laidler model (Model VI) on the pooled-data set (not reported in Tables 8 and 9) yield the same general conclusion. Third, the structural price-change equations that include the change in money wages as an explanatory variable—that is, Models I and II—again seem to have substantially higher explanatory power than the reduced form models that endogenize money wages (Models III-V).

The asymmetry results for individual countries for the period 1958-70 can be summarized as follows. The U. S. results for that period were similar to those for the period 1958-73. Again, the asymmetry variables almost always carried the expected negative sign, and these variables were significantly different from zero at the 5 per cent confidence level in two of the five models tested—namely, Models III and IV. Also, the sizes of the estimated coefficients on ${P \overset{*}{M} N}_{t} and {P \overset{*}{M} N}_{t - 1}$ where significant, again indicated support for the strong form of the asymmetry hypothesis.

The asymmetry results for the Federal Republic of Germany and the United Kingdom were also quite similar to the asymmetry results for the period 1958-73. That is, the equations for those two countries consistently found no evidence of an asymmetry. The results for Italy for 1958-70 provided less support for the asymmetry hypothesis than did the results for 1958-73—with only one model (Model III) indicating a significant asymmetry coefficient for the earlier period. A sharper contrast with the results for 1958-73 occurred for Japan, where the results for 1958-70 find no evidence of the asymmetries associated with import prices that were so pervasive in the equations for 1958-73 (Table 5). This suggests in turn that the import price changes during the period 1971-73 were exercising perhaps undue influence on the earlier asymmetry results for Japan. At the same time, however, it is not obvious (in the absence of additional testing) just what this influence was. While import price changes were larger during the period 1971-73 than for the period 1958-70, this was true of both positive and negative import prices; in fact, the positive (Japanese) import price changes of 1971 and 1973 were larger relative to the average positive import price change of the period 1958-70 than was the large negative import price change of 1972 relative to the negative changes of the period 1958-70. Thus, on the surface, it would not appear as if the asymmetry results for Japan for 1958-73 would be attributable to large/small differences in the size of import price changes. Clearly, further work on the Japanese equations would be desirable.

disaggregated price changes for manufactures, 1958-73

In the equations reported thus far, the rate of change of domestic prices has been related, inter alia, to the rate of change of import prices where both the domestic and import price indices covered a wide variety of goods and where different categories of imports had presumably different degrees of substitutability with domestic goods. This situation can be contrasted with much of the theoretical literature on the effect of import prices on domestic prices where it is common to assume that imported and domestic (tradable) goods are close substitutes. In such a case, one is led to the conclusion that the sole determinant of the domestic price of good i will be the import price of good i, and, further, that the coefficient on the import price variable will be unity.⁴¹

In an effort to determine whether the asymmetry results reported earlier would be significantly affected if a somewhat more homogeneous group of goods was considered, the asymmetry tests were redone using data on manufactures. Quite obviously, manufactures is still much too aggregate and broad a category of goods to discover whether asymmetries do or do not exist among close substitutes. Yet it does eliminate most nontradable goods from the estimation, and it has the practical advantage of yielding fairly consistent data on most of the necessary variables for the sample of countries considered here.

Originally, the equations were run using both the wholesale price index for manufactures and the GDP deflator for manufacturing as alternative dependent variables. The estimates using wholesale prices were, however (with the exception of the United States), simply not credible, and so only the results for the GDP deflator for manufacturing are reported here. The import price index used in these equations was the unit value index for manufactures. The other variables (e.g., $\overset{*}{W}$ and y) are the same as those used in the aggregate equations, since, as previously mentioned, those variables already referred to manufacturing.

The results of the asymmetry tests for a pooled sample of four countries (the United States, the Federal Republic of Germany, Japan, and the United Kingdom) are presented in Table 10. Italy had to be excluded from the group because of lack of data for import prices of manufactures.⁴² Also, for reasons of fatigue, the tests were done using four rather than five inflation models.

Table 10.

Four Large Industrial Countries: ¹ Pooled Disaggregated Results of Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

^¹The excluded country is Italy.

^²Modification of Model V that uses $Δ \ln Q M H_{t}^{N}$ rather than Δln Q_t.

Table 10.

Four Large Industrial Countries: ¹ Pooled Disaggregated Results of Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \underset{(0.23)}{0.001} + \underset{(7.89)}{0.625} Δ \ln W_{t} - \underset{(5.24)}{0.582} Δ \ln Q M H_{t}^{N} + \underset{(1.09)}{0.045} Δ \ln P {Mm}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.493 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0188 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.28)}{0.002} + \underset{(7.79)}{0.616} Δ \ln W_{t} - \underset{(5.00)}{0.560} Δ \ln Q M H_{t}^{N} \end{matrix} \\ + \underset{(1.67)}{0.102} Δ \ln P M m_{t} - \underset{(1.26)}{0.141} Δ \ln P M N m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.498 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0187 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.84)}{0.27} + \underset{(7.41)}{0.607} Δ \ln W_{t} - \underset{(5.30)}{0.596} Δ \ln Q M H_{t}^{N} + \underset{(0.85)}{0.059} \ln y_{t} \end{matrix} \\ + \underset{(0.83)}{0.036} Δ \ln P M m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.491 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0189 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(1.29)}{0.42} + \underset{(7.13)}{0.585} Δ \ln W_{t} - \underset{(5.14)}{0.575} Δ \ln Q M H_{t}^{N} + \underset{(1.28)}{0.092} \ln y_{t} \end{matrix} \\ + \underset{(1.72)}{0.104} Δ \ln P M m_{t} - \underset{(1.59)}{0.185} Δ \ln P M N m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.504 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0186 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.65)}{1.12} + \underset{(2.68)}{0.248} \ln y_{t} - \underset{(1.93)}{0.397} Δ \ln Q M H_{t}^{N} + \underset{(1.80)}{0.117} Δ \ln P M m_{t} \end{matrix} \\ + \underset{(2.17)}{0.019} D U K + \underset{(2.39)}{0.025} D G + \underset{(2.48)}{0.037} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.138 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0246 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.35)}{1.03} + \underset{(2.39)}{0.230} \ln y_{t} - \underset{(1.88)}{0.388} Δ \ln Q M H_{t}^{N} + \underset{(0.43)}{0.048} Δ \ln P M m_{t} \end{matrix} \\ + \underset{(0.76)}{0.135} Δ \ln P M N m_{t} + \underset{(2.22)}{0.091} D U K + \underset{(2.35)}{0.025} D G + \underset{(2.54)}{0.039} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.125 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0248 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} V^{2} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.53)}{1.09} + \underset{(2.57)}{0.242} \ln y_{t} - \underset{(1.95)}{0.449} Δ \ln Q M H_{t}^{N} + \underset{(0.87)}{0.138} Δ \ln P d m_{t - 1} \end{matrix} \\ + \underset{(1.46)}{0.106} Δ \ln P M m_{t} + \underset{(1.87)}{0.017} D U K + \underset{(2.19)}{0.025} D G + \underset{(2.33)}{0.040} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.110 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0250 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} V^{2} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.69)}{1.16} + \underset{(2.71)}{0.257} \ln y_{t} - \underset{(1.33)}{0.330} Δ \ln Q M H_{t}^{N} + \underset{(0.75)}{0.119} Δ \ln P d m_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} + \underset{(1.91)}{0.166} Δ \ln P M m_{t} - \underset{(1.25)}{0.214} Δ \ln P M N m_{t} + \underset{(1.81)}{0.017} D U K \end{matrix} \\ + \underset{(1.85)}{0.022} D G + \underset{(1.59)}{0.030} D J \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.119 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0249 \end{matrix} \end{matrix} \end{matrix}$

^¹The excluded country is Italy.

^²Modification of Model V that uses $Δ \ln Q M H_{t}^{N}$ rather than Δln Q_t.

Table 10.

Four Large Industrial Countries: ¹ Pooled Disaggregated Results of Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \underset{(0.23)}{0.001} + \underset{(7.89)}{0.625} Δ \ln W_{t} - \underset{(5.24)}{0.582} Δ \ln Q M H_{t}^{N} + \underset{(1.09)}{0.045} Δ \ln P {Mm}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.493 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0188 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.28)}{0.002} + \underset{(7.79)}{0.616} Δ \ln W_{t} - \underset{(5.00)}{0.560} Δ \ln Q M H_{t}^{N} \end{matrix} \\ + \underset{(1.67)}{0.102} Δ \ln P M m_{t} - \underset{(1.26)}{0.141} Δ \ln P M N m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.498 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0187 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.84)}{0.27} + \underset{(7.41)}{0.607} Δ \ln W_{t} - \underset{(5.30)}{0.596} Δ \ln Q M H_{t}^{N} + \underset{(0.85)}{0.059} \ln y_{t} \end{matrix} \\ + \underset{(0.83)}{0.036} Δ \ln P M m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.491 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0189 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(1.29)}{0.42} + \underset{(7.13)}{0.585} Δ \ln W_{t} - \underset{(5.14)}{0.575} Δ \ln Q M H_{t}^{N} + \underset{(1.28)}{0.092} \ln y_{t} \end{matrix} \\ + \underset{(1.72)}{0.104} Δ \ln P M m_{t} - \underset{(1.59)}{0.185} Δ \ln P M N m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.504 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0186 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.65)}{1.12} + \underset{(2.68)}{0.248} \ln y_{t} - \underset{(1.93)}{0.397} Δ \ln Q M H_{t}^{N} + \underset{(1.80)}{0.117} Δ \ln P M m_{t} \end{matrix} \\ + \underset{(2.17)}{0.019} D U K + \underset{(2.39)}{0.025} D G + \underset{(2.48)}{0.037} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.138 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0246 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.35)}{1.03} + \underset{(2.39)}{0.230} \ln y_{t} - \underset{(1.88)}{0.388} Δ \ln Q M H_{t}^{N} + \underset{(0.43)}{0.048} Δ \ln P M m_{t} \end{matrix} \\ + \underset{(0.76)}{0.135} Δ \ln P M N m_{t} + \underset{(2.22)}{0.091} D U K + \underset{(2.35)}{0.025} D G + \underset{(2.54)}{0.039} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.125 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0248 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} V^{2} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.53)}{1.09} + \underset{(2.57)}{0.242} \ln y_{t} - \underset{(1.95)}{0.449} Δ \ln Q M H_{t}^{N} + \underset{(0.87)}{0.138} Δ \ln P d m_{t - 1} \end{matrix} \\ + \underset{(1.46)}{0.106} Δ \ln P M m_{t} + \underset{(1.87)}{0.017} D U K + \underset{(2.19)}{0.025} D G + \underset{(2.33)}{0.040} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.110 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0250 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} V^{2} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.69)}{1.16} + \underset{(2.71)}{0.257} \ln y_{t} - \underset{(1.33)}{0.330} Δ \ln Q M H_{t}^{N} + \underset{(0.75)}{0.119} Δ \ln P d m_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} + \underset{(1.91)}{0.166} Δ \ln P M m_{t} - \underset{(1.25)}{0.214} Δ \ln P M N m_{t} + \underset{(1.81)}{0.017} D U K \end{matrix} \\ + \underset{(1.85)}{0.022} D G + \underset{(1.59)}{0.030} D J \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.119 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0249 \end{matrix} \end{matrix} \end{matrix}$

^¹The excluded country is Italy.

^²Modification of Model V that uses $Δ \ln Q M H_{t}^{N}$ rather than Δln Q_t.

The most important feature of the pooled asymmetry results for manufactures is that the asymmetry variables, while usually negative, are nowhere significantly different from zero at the 5 per cent level, thus once again suggesting that asymmetries are not important for this group of countries viewed together. This result should, however, be treated rather cautiously, because most of the models in Table 10 also indicate an insignificant effect of import prices, be they positive or negative, on domestic prices. This latter finding is rather surprising for, on a priori grounds, one might expect the coefficients on P $\overset{*}{M}$ in these equations to be larger than those in the aggregate equations because the goods in the manufacturing equations are presumably closer substitutes. On the other hand, the insignificance of P $\overset{*}{M}$ could merely reflect substantial collinearity between P $\overset{*}{M}$ and other right-hand variables, particularly wage changes. One other feature of Table 10 worth noting is that Models I and II continue to show substantially higher explanatory power than do the other models.

As regards the asymmetry results for manufactures in individual countries, there was, in brief, no evidence of an asymmetrical effect for P $\overset{*}{M}$ in any country except the United States, and even there the asymmetries were confined to just two models (Models III and IV). Thus, in sum, the disaggregated results suggest that any asymmetries in the effect of import prices on domestic prices are the exception rather than the rule.

IV. Conclusions

The primary purpose of this paper was to provide various empirical tests of the proposition that negative changes in import prices have a different proportionate effect on domestic prices than do positive changes in import prices. The results of these tests can best be summarized as follows.

(1) When the five sample countries (the United States, the Federal Republic of Germany, Japan, the United Kingdom, and Italy) are viewed as a whole via the mechanism of pooled regression equations, there is no evidence of an asymmetry in the effect of import price changes on domestic price changes. This result holds for aggregate price changes (i.e., changes in the overall GDP deflator) during both the period 1958-73 and the shorter period 1958-70 of fixed exchange rates. Further, the same result emerges using more disaggregated price data for manufactures.

(2) The asymmetry results for individual countries are more varied, and it is here that the asymmetry, or ratchet, hypothesis obtains some, albeit limited, support. More specifically, in the aggregate price-change equations, there is some evidence of an asymmetry in the effect of P $\overset{*}{M}$ on $\overset{*}{P}$ d for the United States, Italy, and Japan. For the United States and Italy, a significant asymmetry effect appears in about half of the models tested for the period 1958-73, and in less than half of the models for the period 1958-70. For Japan, a significant asymmetry can be identified consistently in the results for 1958-73, but this must be considered tentative because the results for 1958-70 yield the opposite conclusion. The results for the Federal Republic of Germany and the United Kingdom consistently fail to uncover any asymmetry in the effect of P $\overset{*}{M}$ on $\overset{*}{P}$ d. Finally, in the equations for manufactures, evidence of an asymmetry appears in some models for the United States but not for the Federal Republic of Germany, the United Kingdom, or Japan.

(3) In those cases where asymmetries were evident, the results for the United States and Italy pointed to the strong form of the asymmetry hypothesis, that is, that a negative change in import prices would, ceteris paribus, either leave domestic prices unaffected or actually lead to an increase in domestic prices. In contrast, the asymmetry results for Japan pointed to the more moderate version, that a negative import price change would lead to a fall in domestic prices, although the elasticity would be smaller than that for a positive change. Since the moderate version of the asymmetry hypothesis seems more reasonable in a priori terms than the strong form, the results for the United States and Italy may be concealing some misspecification in the time response of $\overset{*}{P}$ d to positive versus negative changes in import prices.

(4) In those cases where an asymmetry does appear, it most usually appears in the reduced form models (Models III, IV, and V) rather than in the two structural inflation models (Models I and II) where the change in money wages is included as an exogenous determinant of $\overset{*}{P}$ d. Since the estimated coefficient on P $\overset{*}{M}$ in the reduced form models reflects not only the short-run impact of P $\overset{*}{M}$ on $\overset{*}{P}$ d but also the induced, later-round, wage-price-spiral effects of any change in $\overset{*}{P}$ d, there is the suggestion that the asymmetry may actually be occurring in the wage-price pass-through process. That is, the asymmetries in the long-run effect of P $\overset{*}{M}$ on $\overset{*}{P}$ d may fall more in the wage response to price changes and in the price response to wage changes than in the short-run, first round effect of P $\overset{*}{M}$ on $\overset{*}{P}$ d This observation, however, rests more on calculated suspicion than on direct evidence.

All in all, the empirical tests reported in this paper are not supportive of the hypothesis that negative changes in import prices have a significantly different proportionate effect on domestic prices than do positive changes. As such, there would seem to be “virtuous” as well as “vicious” circles in the relationship between import price changes and domestic price changes. At the same time, there is enough mixed evidence from the tests reported here, principally for the United States, Italy, and Japan, to warrant being wary of generalizing this conclusion either across countries or over different time periods. With larger samples, better data on import prices, and perhaps (using) alternative lag distributions for positive versus negative import price changes, it should be possible to progressively whittle down the margin of uncertainty surrounding the practical significance of the ratchet hypothesis.

APPENDIX: Data Definitions and Sources

Domestic prices (Pd): Pd is an index (1970 = 100) of the gross domestic product (GDP) deflator (at market prices). The data are taken from the Organization for Economic Cooperation and Development (OECD), National Accounts of OECD Countries (various issues) and Main Economic Indicators (various issues).

Import prices (PM): PM is the unit value index (1970 = 100) for total imports as measured in domestic currency. The data (both annual and quarterly) are taken from the International Monetary Fund, International Financial Statistics (various issues).

Unemployment rate (u): u is the total unemployment rate, that is, the number of unemployed as a percentage of the civilian labor force. The unemployment rate data for the Federal Republic of Germany, Italy, Japan, and the United Kingdom are adjusted so as to be consistent with the definition and measurement of the U.S. unemployment rate. These adjusted unemployment rates are taken from U.S. Department of Labor, Handbook of Labor Statistics, 1974 (Table 164). In cases where only the unadjusted unemployment rate was available for a single year, the adjusted rate was estimated using the time series relationship between the adjusted and unadjusted rates.

Wages (W): W is an index (1970 = 100) of average hourly compensation of all employees in manufacturing. Average hourly compensation includes not only wages and salaries but also such additional labor costs as contributions of employers to social security and private welfare plans. This wage series was selected because it was judged to be relatively consistent across countries. The data were obtained from U. S. Department of Labor, Handbook of Labor Statistics, 1974 (Table 165) and from unpublished tables kindly provided by the U. S. Bureau of Labor Statistics.

Output per man-hour (QMH): QMH is an index of real output per man-hour for all employees in manufacturing. Its coverage, and the data sources for it, are identical to that for average hourly compensation. Where normal output per man-hour (QMH^N) was used, it was constructed as a three-year weighted moving average of actual output per man-hour with weights equal to 0.5 for year t and 0.25 each for years t− 1 and t−2.

Excess demand (y): y is the ratio of actual industrial production to potential industrial production. Potential industrial production for the period 1957-70 was generated by calculating a geometric, ten-year centered moving average of actual industrial production. For the period 1971-75, estimates of potential industrial production were based on an exponential trend fitted for the period 1965-75. The data for both actual and potential industrial production are described and presented (in graphical form) in Ripley (1976).

Real output (Q): Q is a volume index (1970 = 100) of GDP. The data are taken from the OECD, National Accounts of OECD Countries (various issues) and Main Economic Indicators (various issues).

Domestic price of manufactures (Pdm): Pdm is an index (1970 = 100) of the GDP deflator originating in manufacturing. In brief, the deflator is obtained by dividing the GDP (manufacturing) data in current prices by that in constant prices. The data were obtained from the OECD, National Accounts of OECD Countries, 1961-72 (country table No. 3, Gross domestic product by kind of economic activity), and from unpublished data furnished by the U. S. Bureau of Labor Statistics.

Import prices for manufactures (PMm): PMm is the unit value index (1970 = 100) for manufactured imports (Standard International Trade Classification (SITC) groups 5-8), as measured in domestic currency. The data were taken from national sources.

BIBLIOGRAPHY

Artus, Jacques R., “The Behavior of Export Prices for Manufactures,” Staff Papers, Vol. 21 (November 1974), pp. 583-604.
- Search Google Scholar
- Export Citation
Ball, R. J., T. Burns, and J. S. E. Laury, “The Role of Exchange Rate Changes in Balance of Payments Adjustment: The United Kingdom Case,” Economic Journal, Vol. 87 (March 1977), pp. 1–29.
- Search Google Scholar
- Export Citation
Ball, R. J., and Martyn Duffy, “Price Formation in European Countries,” in The Econometrics of Price Determination, ed. by Otto Eckstein (Washington, 1972), pp. 347–68.
- Search Google Scholar
- Export Citation
Bordo, M., and E. Choudry, “The Behavior of Traded and Nontraded Goods: The Canadian Case, 1962-74,” paper presented at the annual meeting of the Southern Economic Association (October 1976).
- Search Google Scholar
- Export Citation
Branson, William H., “The Trade Effects of the 1971 Currency Realignments,” Brookings Papers on Economic Activity: 1 (1972), pp. 15–69.
- Search Google Scholar
- Export Citation
Cagan, Phillip D., The Hydra-Headed Monster: The Problem of Inflation in the United States, American Enterprise Institute for Public Policy Research (Washington, 1974).
- Search Google Scholar
- Export Citation
Cheng, Hang-Sheng, and Nicholas P. Sargen, “Central-Bank Policy Towards Inflation,” Business Review, Federal Reserve Bank of San Francisco (Spring 1975), pp. 31–40.
- Search Google Scholar
- Export Citation
Crockett, Andrew D., and Morris Goldstein, “Inflation Under Fixed and Flexible Exchange Rates,” Staff Papers, Vol. 23 (November 1976), pp. 509–44.
- Search Google Scholar
- Export Citation
Cross, Rodney, and David Laidler, “Inflation, Excess Demand and Expectations in Fixed Exchange Rate Open Economies: Some Preliminary Empirical Results,” in Inflation in the World Economy, ed. by Michael Parkin and George Zis (Manchester University Press, 1976), pp. 221–55.
- Search Google Scholar
- Export Citation
Dornbusch, Rudiger, “Alternative Price Stabilization Rules and the Effects of Exchange Rate Changes,” Manchester School of Economic and Social Studies, Vol. 43 (September 1975), pp. 275–92.
- Search Google Scholar
- Export Citation
Dornbusch, Rudiger, and Paul Krugman, “Flexible Exchange Rates in the Short Run,” Brookings Papers on Economic Activity: 3 (1976), pp. 537–84.
- Search Google Scholar
- Export Citation
Eckstein, Otto, and Gary Fromm, “The Price Equation,” American Economic Review, Vol. 58 (December 1968), pp. 1159–83.
- Search Google Scholar
- Export Citation
Genberg, Hans, “The Concept and Measurement of the World Price Level and Rate of Inflation,” Journal of Monetary Economics, Vol. 3 (April 1977), pp. 231–52.
- Search Google Scholar
- Export Citation
Goldstein, Morris, “The Effect of Exchange Rate Changes on Wages and Prices in the United Kingdom: An Empirical Study,” Staff Papers, Vol. 21 (November 1974), pp. 694–739.
- Search Google Scholar
- Export Citation
Goldstein, Morris, and Mohsin S. Kahn(1976 a), “Large Versus Small Price Changes and the Demand for Imports,” Staff Papers, Vol. 23 (March 1976), pp. 200–25.
- Search Google Scholar
- Export Citation
Goldstein, Morris, and Mohsin S. Kahn (1976 b), “The Supply and Demand for Exports: A Simultaneous Approach” (unpublished, International Monetary Fund, March 23, 1976). (It is scheduled for publication in the Review of Economics and Statistics.)
- Search Google Scholar
- Export Citation
Hicks, John R., The Crisis in Keynesian Economics (Oxford, 1974).
- Search Google Scholar
- Export Citation
Isard, Peter (1977 a), “The Price Effects of Exchange-Rate Changes,” in The Effects of Exchange Rate Adjustments: The Proceedings of a Conference Sponsored by OASIA Research, Department of the Treasury (hereinafter referred to as The Effects of Exchange Rate Adjustments), ed. by Peter B. Clark, Dennis E. Logue, and Richard James Sweeney (Washington, 1977), pp. 369–86.
- Search Google Scholar
- Export Citation
Isard, Peter (1977 b), “How Far Can We Push the ‘Law of One Price’?” (This paper is scheduled for publication in the American Economic Review.)
- Search Google Scholar
- Export Citation
Jonson, P. D, “Money and Economic Activity in the Open Economy: the United Kingdom, 1880-1970,” Journal of Political Economy, Vol. 84 (October 1976), pp. 979–1012.
- Search Google Scholar
- Export Citation
Kenen, Peter B., “The Inflationary Impact of Exchange Rate Changes: A Comment,” in The Effects of Exchange Rate Adjustments (Washington, 1977), pp. 69–78.
- Search Google Scholar
- Export Citation
Kmenta, Jan, Elements of Econometrics (New York, 1971).
- Search Google Scholar
- Export Citation
Kravis, Irving B., and Robert E. Lipsey, “Export Prices and the Transmission of Inflation,” American Economic Review, Papers and Proceedings of the Eighty-ninth Annual Meeting of the American Economic Association, Vol. 67 (February 1977), pp. 155–63.
- Search Google Scholar
- Export Citation
Kreinin, Mordechai E., “Effects of Tariff Changes on the Prices and Volume of Imports,” American Economic Review, Vol. 51 (June 1961), pp. 310–24.
- Search Google Scholar
- Export Citation
Kreinin, Mordechai E., “The Effect of Exchange Rate Changes on the Prices and Volume of Foreign Trade,” Staff Papers, Vol. 24 (July 1977), pp. 297–329.
- Search Google Scholar
- Export Citation
Kuh, Edwin, “A Productivity Theory of Wage Levels—An Alternative to the Phillips Curve,” Review of Economic Studies, Vol. 34 (October 1967), pp. 333–60.
- Search Google Scholar
- Export Citation
Kwack, Sung Y., “Price Linkage in an Interdependent World Economy: Price Responses to Exchange Rate and Activity Changes,” Board of Governors of the Federal Reserve System, International Finance Discussion Paper No. 56 (mimeographed, January 3, 1975).
- Search Google Scholar
- Export Citation
Kwack, Sung Y., “The Effect of Foreign Inflation on Domestic Prices and the Relative Price Advantage of Exchange-Rate Changes,” in The Effects of Exchange Rate Adjustments (Washington, 1977), pp. 387–98.
- Search Google Scholar
- Export Citation
Laffer, Arthur B., “The Phenomenon of Worldwide Inflation: A Study in International Market Integration,” in The Phenomenon of Worldwide Inflation, ed. by David I. Meiselman and Arthur B. Laffer, American Enterprise Institute for Public Policy Research (Washington, 1975), pp. 27–52.
- Search Google Scholar
- Export Citation
Laidler, David, “Inflation—Alternative Explanations and Policies: Tests on Data Drawn from Six Countries,” in Institutions, Policies and Economic Performance, ed. by Karl Brunner and Allan H. Meltzer, Carnegie-Rochester Conference Series on Public Policy, A Supplementary Series to the Journal of Monetary Economics, Vol. 4 (Amsterdam, 1976), pp. 251–306.
- Search Google Scholar
- Export Citation
Lipsey, Richard G., and J. M. Parkin, “Incomes Policy: A Re-Appraisal,” Economica, New Series, Vol. 37 (May 1970), pp. 115–38.
- Search Google Scholar
- Export Citation
Magee, Stephen P., “Prices, Incomes, and Foreign Trade,” in International Trade and Finance: Frontiers for Research, ed. by Peter B. Kenen (Cambridge University Press, 1975), pp. 175–252.
- Search Google Scholar
- Export Citation
Means, Gardiner C., Industrial Prices and Their Relative Inflexibility (U. S. Senate, 74th Congress, 1st Session, Washington, January 17, 1935).
- Search Google Scholar
- Export Citation
Mundell, Robert A., “The ‘New Inflation’ and Flexible Exchange Rates,” in The New Inflation and Monetary Policy: Proceedings of a Conference Organised by the Banca Commerciale Italiana and the Department of Economics of Università Bocconi in Milan, 1974, ed. by Mario Monti (London, 1976), pp. 142–59.
- Search Google Scholar
- Export Citation
Nordhaus, William D., “Recent Developments in Price Dynamics,” in The Econometrics of Price Determination, ed. by Otto Eckstein (Washington, 1972), pp. 16–49.
- Search Google Scholar
- Export Citation
Nordhaus, William D., and Wynne Godley, “Pricing in the Trade Cycle,” Economic Journal, Vol. 82 (September 1972), pp. 853–82.
- Search Google Scholar
- Export Citation
Nordhaus, William D., and John Shoven, “Inflation 1973: The Year of Infamy,” Challenge, Vol. 17 (May/June 1974), pp. 14–22.
- Search Google Scholar
- Export Citation
Okun, Arthur M., “Inflation: Its Mechanics and Welfare Costs,” Brookings Papers on Economic Activity: 2 (1975), pp. 351–401.
- Search Google Scholar
- Export Citation
Pigott, Charles, Richard J. Sweeney, and Thomas D. Willett, “Some Aspects of the Behavior and Effects of Flexible Exchange Rates,” paper presented at the Conference on Monetary Theory and Policy (Konstanz, June 1975).
- Search Google Scholar
- Export Citation
Ripley, Duncan, “Cyclical Fluctuations in Industrial Countries, 1952-74” (unpublished, International Monetary Fund, January 13, 1976).
- Search Google Scholar
- Export Citation
Sahling, L., “Price Behavior in U. S. Manufacturing: An Economic Analysis,” Federal Reserve Bank of New York (unpublished working paper, May 1974).
- Search Google Scholar
- Export Citation
Schultze, Charles L., Recent Inflation in the United States, Study Paper No. 1 (materials prepared for the Joint Economic Committee in connection with the study of employment, growth, and price levels, 86th Congress, 1st Session, Washington, September 1959).
- Search Google Scholar
- Export Citation
Schultze, Charles L., and Joseph L. Tryon, “Prices and Wages,” in The Brookings Quarterly Econometric Model of the United States, ed. by James S. Duesenberry and others (Chicago, 1965), pp. 281–333.
- Search Google Scholar
- Export Citation
Shields, Roger, Edward Tower, and Thomas D. Willett, “Revaluation Can Be Inflationary: An Analysis of the Inflationary Impact of Demand Shifts in a Simple Policy Dilemma Model,” Annex to R. James Sweeney and Thomas D. Willett, “The Inflationary Impact of Exchange Rate Changes,” in The Effects of Exchange Rate Adjustments (Washington, 1977), pp. 62–69.
- Search Google Scholar
- Export Citation
Sims, Christopher A., “Money, Income, and Causality,” American Economic Review, Vol. 62 (September 1972), pp. 540–52.
- Search Google Scholar
- Export Citation
Solow, Robert M., “The Intelligent Citizen’s Guide to Inflation,” Public Interest, No. 38 (Winter 1975), pp. 30–66.
- Search Google Scholar
- Export Citation
Spitäller, Erich, “Prices and Unemployment in Selected Industrial Countries,” Staff Papers, Vol. 18 (November 1971), pp. 528–69.
- Search Google Scholar
- Export Citation
Stern, Robert M., Jonathan Francis, and Bruce Schumacker, Price Elasticities in International Trade: An Annotated Bibliography, Trade Policy Research Centre (London, 1976).
- Search Google Scholar
- Export Citation
Swoboda, Alexander K., “Monetary Approaches to Worldwide Inflation,” in Worldwide Inflation: Theory and Recent Experience, ed. by Lawrence B. Krause and Walter S. Salant, The Brookings Institution (Washington, 1977), pp. 9–51.
- Search Google Scholar
- Export Citation
Tobin, James, “The ‘Wage-Price Mechanism’ Overview of the Conference,” in The Econometrics of Price Determination, ed. by Otto Eckstein (Washington, 1972), pp. 5–15.
- Search Google Scholar
- Export Citation
U. S. Department of Labor, Handbook of Labor Statistics, 1974, Bureau of Labor Statistics (Washington, 1975).
- Search Google Scholar
- Export Citation
Wanniski, Jude, “The Case for Fixed Exchange Rates,” The Wall Street Journal (June 14, 1974).
- Search Google Scholar
- Export Citation
Wanniski, Jude, “The Mundell-Laffer Hypothesis: A New View of the World Economy,” Public Interest, No. 39 (Spring 1975), pp. 31–52.
- Search Google Scholar
- Export Citation
Whitman, Marina v.N., “Global Monetarism and the Monetary Approach to the Balance of Payments,” Brookings Papers on Economic Activity: 3 (1975), pp. 491–555.
- Search Google Scholar
- Export Citation
Witteveen, H. Johannes, “Inflation and the International Monetary System,” American Economic Review, Papers and Proceedings of the Eighty-seventh Annual Meeting of the American Economic Association, Vol. 65 (May 1975), pp. 108–14.
- Search Google Scholar
- Export Citation

Mr. Goldstein, Assistant Chief of the Special Studies Division of the Research Department, is a graduate of Rutgers University and of New York University. He was formerly a Research Fellow in Economics at the Brookings Institution.

In addition to colleagues in the Fund, the author would like to thank Fred-Olav Sorensen for very helpful discussion of the issues raised in this paper.

Previous empirical studies by Spitäller (1971), Ball and Duffy (1972), Cheng and Sargen (1975), Cross and Laidler (1976), Dornbusch and Krugman (1976), and Kwack (1977) have looked at the relationship between import and domestic price changes (on a multicountry basis) but not at the problem of asymmetry.

Cross and Laidler (1976) have argued that such a comparison of alternative inflation models is necessary if one is to get a thorough test of any one model.

See, for example, Wanniski (1974) and Crockett and Goldstein (1976).

See, for example, Witteveen (1975).

While the writings of Laffer and Mundell repeatedly stress the global advantages of fixed exchange rates and the inability of exchange rate changes to permanently alter relative prices, their published papers (to my knowledge) contain almost no reference to a “ratchet,” or asymmetry, effect. An exception is the brief (and rather oblique) recent reference to such an asymmetry in Mundell (1976). However, since Wanniski’s interpretation of their views has generated considerable attention and since neither Laffer nor Mundell has (again to my knowledge) challenged Wanniski’s exposition, the preceding commentary is based on Wanniski’s preceding two articles (1974; 1975).

The law of one price merely asserts that the same good cannot sell at a different price (expressed in a common currency) in two countries as long as the two countries trade with each other.

For recent empirical evidence on the law of one price, much of which tends to be damaging to the hypothesis even at fairly fine levels of disaggregation, see Laffer (1975), Bordo and Choudry (1976), Genberg (1977), Isard (1977 a), and Kravis and Lipsey (1977). The conditions necessary for the law of one price to be satisfied, or, to say much the same thing, for inflation rates in different countries to converge under fixed exchange rates, are spelled out in Swoboda (1977).

There is, of course, considerable controversy in the literature over whether in fact exchange rate changes do lead to a (long-run) change in relative prices, or rather whether they will have only a temporary effect on the balance of payments via their effects on the domestic price level (and, in turn, on the demand for money). For some empirical evidence on this issue, see Artus (1974), Goldstein (1974), Jonson (1976), Ball and others (1977), Isard (1977 a), and Kwack (1977).

See Wanniski (1975, p. 36) and Mundell (1976, pp. 156-57).

For an exact expression for the country distribution of price changes (at least in a simple model with two countries and one traded and one nontraded good in each country) see Dornbusch (1975), pp. 281-82.

The elasticity of import prices (in domestic currency) with respect to an exchange rate change, call it K, can be expressed as

K = {(1 - \frac{d m}{s m})}^{- 1}

where dm is the own price elasticity of demand for imports, and sm is the own price elasticity of supply for imports. K must lie between zero and unity because, by definition, 0 ≥ dm > − ∞ and 0 ≤ sm ≤ ∞. Clearly, if sm is very large relative to |dm|, K will approach one, whereas K will approach zero in the opposite case. See Branson (1972).

Empirical estimates of demand and supply elasticities for exports and imports can be found in Stern and others (1976) and in Goldstein and Khan (1976 a and b).

This same argument is applied by Cagan (1974) in discussing the hypothesis that concentrated industries and related monopoly pricing behavior can cause inflation.

The overall price level rises in the home (devaluing) country because the price of traded goods rises, while the price of nontraded goods remains constant. In the foreign country, the overall price rise reflects a constant price for traded goods and an increased price for nontraded goods. The reduction in expenditure in the home country acts to stabilize its price of nontraded goods, while the increase in expenditure in the foreign country acts to clear the world market for traded goods (and hence stabilizes its price). See Dornbusch (1975), pp. 287-89.

Shields and others are, of course, well aware of this. Their main point is rather to show that the set of assumptions typically employed to show that devaluation is inflationary will also yield the same result for revaluation.

See, for example, Eckstein and Fromm (1968), Nordhaus (1972), and Okun (1975). The reasons given in the literature for this “sticky” price behavior range from the direct costs of changing prices (e.g., printing costs to inform buyers of new prices), to uncertainty about the firm’s demand curve, to the firm’s desire to provide stable prices to its customers as a “service” (presumably in exchange for a larger market share or a higher average price), to the availability of other adjustment mechanisms (e.g., inventories, order backlogs, output changes), to the firm’s attention toward maximizing long-run rather than short-run profits, etc.

Cagan (1974), for example, has shown how time lags in the adjustment of prices to cost and demand changes can give the impression of downward price inflexibility when, in reality, the stickiness of prices over time has increased in both directions, although not necessarily by the same amount.

Of course, all that would be required for a “weak” version of the asymmetry hypothesis is that negative import price changes be considered more temporary than positive ones; and the postwar evidence does indicate that negative import changes have occurred less frequently than positive ones.

Nordhaus (1972), for example, has shown that normal cost pricing will be a good rule of thumb (i.e., will produce a profit-maximizing result) only under pure competition, when in fact it has been attributed exclusively to concentrated industry behavior.

It should be understood that no claim is being made in this paper that import price changes (be they positive or negative) cause domestic price changes. In fact, there is a good case for viewing both variables as being determined simultaneously by the same fundamental forces in the economy. For example, an increase in the growth rate of a country’s money supply can be expected to lead, ceteris paribus, both to an increase in domestic prices and to a depreciation of the exchange rate (and hence to an increase in import prices). Further, given the limited number of observations, it is doubtful that much would be gained by undertaking formal tests of causality (like those suggested, for example, in Sims (1972)). (The author is indebted to Steve Kohlhagen for some useful discussion of this issue.)

Since the money wage-change equation (3 b) is over-identified, it will not be possible to recapture the structural parameters by estimating the reduced form price equation (3 a) alone.

In terms of the structural equations (3 a) and (3 b), one can also show (Ball and others (1977)) that the conditions necessary to obtain the long-run result that $\overset{*}{P}$ d= $\overset{*}{P}$ M (as in the law of one price) are (i) e₂=1; (ii) d₁=0, d₁=d₂=(1−d₃); and (iii) e₁=0 or u^-1=(e₀ − Q $\overset{*}{M}$ H)/e₁.

One of the difficulties with the Koyck (geometric) lag is that it imposes the same distributed lag pattern on all the explanatory variables, and this may, in many cases, be an inappropriate assumption.

It is not entirely clear whether Model VI should be viewed as a structural or a reduced form price-change equation. Cross and Laidler (1976, p. 222) claim that this model “… is best interpreted as a quasi-reduced form of a more complex structure of wage-price interaction whose precise form is left unspecified.”

Following Cross and Laidler (1976), both equation (6) and equation (6 a) have been specified without a constant term.

As is well known, one problem with the adaptive expectations mechanism is that it will lead to an estimating equation in which the error term is correlated with the lagged dependent variable, thus yielding inconsistent estimators under ordinary least squares; see Kmenta (1971), pp. 474-86.

In an earlier draft of this paper, a second Cross-Laidler (1976) model was included where the expected inflation rate was a weighted average of the expected domestic inflation rate and the expected world inflation rate, thus reintroducing import price changes as a separate explanatory variable. In view of both the poor empirical performance of that model and the number of models already included, it was excluded here. It may well be, however, that the model’s poor performance was due in part to the substitution of import prices for world prices; on this point, see Laidler (1976).

In identifying the weak, strong, and extreme versions of the asymmetry argument, it is assumed throughout that a₃ > 0, and a₄ < 0. If a₄ > 0, it would imply that a negative import price change would lead to a larger positive change in domestic prices than would a positive import price change of the same size.

The F-test will also be a weaker test than requiring the sum of the asymmetry variables to be significantly different from zero, that is, than requiring that (a₄ + a₆) be significantly different from zero using a t-test. In other words, if one finds a significant asymmetry using the t-test on (a₄ + a₆), one will also find a significant asymmetry using the F-test; the converse, however, need not be true. In this sense, by using the F-test, we are making it easier to reject the null hypothesis that there is no asymmetry. In practice, however, the empirical results in Section III are such that the conclusions on the presence of asymmetries are not seriously affected by using an F-test rather than a t-test for those cases where more than one asymmetry variable appears in the equation.

The complete set of the actual estimated regression equations are available from the author upon application to Mr. Goldstein, International Monetary Fund, Washington, D.C. 20431 U.S.A.

Dornbusch and Krugman (1976) also found that the Federal Republic of Germany was the only country in their sample in which import price changes had no significant effect on domestic price changes.

See, for example, Ball and Duffy (1972), Nordhaus and Shoven (1974), Cheng and Sargen (1975), Dornbusch and Krugman (1976), Jonson (1976), and Kwack (1977).

Model VI did somewhat better (although still very poorly) when Δln CPI was used as the dependent variable. Even so, the estimates for Japan were still very different from those of Cross and Laidler (who also used the CPI). This suggests that the Japanese results may be very sensitive to the choice of the excess demand variables.

Since Model VI was estimated without a constant, one cannot compare the R² with those models that contain a constant (because the R² is no longer bounded zero-one in the no-constant case). The SEE is, however, not affected by this modification and thus can serve as a useful yardstick for goodness-of-fit comparisons.

The standard error of estimate, call it θ_u, is defined as

θ_{u} = \sqrt{\frac{Σ (y - \hat{y})}{N}}

where y is the actual value of the dependent variable, ŷ its estimated value, and N is the number of observations. While θ_u will vary with the units in which the dependent variable is measured, this is not a problem here because all the models use the same $\overset{*}{P}$ d (at least for a given country).

For example, when Model I was estimated by two-stage least squares (TSLS), the ${\bar{R}}^{2}$ fell from 0.908 to 0.755 for the United States, and from 0.817 to 0.664 for the United Kingdom. On the other hand, the ${\bar{R}}^{2}$ for the Federal Republic of Germany was not affected by the TSLS estimation. No such comparison was conducted for either Japan or Italy.

For ten degrees of freedom, the critical t-value for rejection of the null hypothesis is about 2.2 (for a two-tailed test).

See Kmenta (1971, p. 370) for the exact form of the F-test applicable to testing whether subsets of coefficients are significantly different from zero.

Of course, one could also permit the intercept to vary over time as well as to allow some slope coefficients to vary both across countries and over time. Another option would be to use a generalized least-squares estimator to correct for any heteroscedasticity and/or autocorrelation. Neither of these options was tested here.

For reasons of space, the individual country results are not reproduced here. They are, however, available from Mr. Goldstein upon request. (See footnote 30.)

See Isard (1977 a).

More specifically, the import price index for Italian manufactures was available only beginning in 1962.

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IMF Staff papers: Volume 24 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1977: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451969450

ISSN:: 1020-7635

Pages:: 272

DOI:: https://doi.org/10.5089/9781451969450.024

Keywords
I. The Ratchet Hypothesis
II. Models of Inflation in an Open Economy
III. Empirical Results
IV. Conclusions
- APPENDIX: Data Definitions and Sources
BIBLIOGRAPHY

Table 10.

Four Large Industrial Countries: ¹ Pooled Disaggregated Results of Asymmetry Tests Using Annual Data, 1958-73

(Dependent variable = percentage change in GDP deflator)

Model Number
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \underset{(0.23)}{0.001} + \underset{(7.89)}{0.625} Δ \ln W_{t} - \underset{(5.24)}{0.582} Δ \ln Q M H_{t}^{N} + \underset{(1.09)}{0.045} Δ \ln P {Mm}_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.493 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0188 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} I \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.28)}{0.002} + \underset{(7.79)}{0.616} Δ \ln W_{t} - \underset{(5.00)}{0.560} Δ \ln Q M H_{t}^{N} \end{matrix} \\ + \underset{(1.67)}{0.102} Δ \ln P M m_{t} - \underset{(1.26)}{0.141} Δ \ln P M N m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.498 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0187 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(0.84)}{0.27} + \underset{(7.41)}{0.607} Δ \ln W_{t} - \underset{(5.30)}{0.596} Δ \ln Q M H_{t}^{N} + \underset{(0.85)}{0.059} \ln y_{t} \end{matrix} \\ + \underset{(0.83)}{0.036} Δ \ln P M m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.491 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0189 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} II \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(1.29)}{0.42} + \underset{(7.13)}{0.585} Δ \ln W_{t} - \underset{(5.14)}{0.575} Δ \ln Q M H_{t}^{N} + \underset{(1.28)}{0.092} \ln y_{t} \end{matrix} \\ + \underset{(1.72)}{0.104} Δ \ln P M m_{t} - \underset{(1.59)}{0.185} Δ \ln P M N m_{t} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.504 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0186 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.65)}{1.12} + \underset{(2.68)}{0.248} \ln y_{t} - \underset{(1.93)}{0.397} Δ \ln Q M H_{t}^{N} + \underset{(1.80)}{0.117} Δ \ln P M m_{t} \end{matrix} \\ + \underset{(2.17)}{0.019} D U K + \underset{(2.39)}{0.025} D G + \underset{(2.48)}{0.037} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.138 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0246 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} III \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.35)}{1.03} + \underset{(2.39)}{0.230} \ln y_{t} - \underset{(1.88)}{0.388} Δ \ln Q M H_{t}^{N} + \underset{(0.43)}{0.048} Δ \ln P M m_{t} \end{matrix} \\ + \underset{(0.76)}{0.135} Δ \ln P M N m_{t} + \underset{(2.22)}{0.091} D U K + \underset{(2.35)}{0.025} D G + \underset{(2.54)}{0.039} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.125 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0248 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} V^{2} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.53)}{1.09} + \underset{(2.57)}{0.242} \ln y_{t} - \underset{(1.95)}{0.449} Δ \ln Q M H_{t}^{N} + \underset{(0.87)}{0.138} Δ \ln P d m_{t - 1} \end{matrix} \\ + \underset{(1.46)}{0.106} Δ \ln P M m_{t} + \underset{(1.87)}{0.017} D U K + \underset{(2.19)}{0.025} D G + \underset{(2.33)}{0.040} D J \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.110 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0250 \end{matrix} \end{matrix} \end{matrix}$
$\begin{matrix} \begin{matrix} \begin{matrix} \begin{matrix} V^{2} \end{matrix} & \begin{matrix} \begin{matrix} Δ \ln P d m = \end{matrix} \end{matrix} \end{matrix} & \begin{matrix} \begin{matrix} \begin{matrix} - \underset{(2.69)}{1.16} + \underset{(2.71)}{0.257} \ln y_{t} - \underset{(1.33)}{0.330} Δ \ln Q M H_{t}^{N} + \underset{(0.75)}{0.119} Δ \ln P d m_{t - 1} \end{matrix} \\ \begin{matrix} \begin{matrix} + \underset{(1.91)}{0.166} Δ \ln P M m_{t} - \underset{(1.25)}{0.214} Δ \ln P M N m_{t} + \underset{(1.81)}{0.017} D U K \end{matrix} \\ + \underset{(1.85)}{0.022} D G + \underset{(1.59)}{0.030} D J \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} {\bar{R}}^{2} = 0.119 \end{matrix} & \bar{\begin{matrix} S E E \end{matrix}} \end{matrix} = 0.0249 \end{matrix} \end{matrix} \end{matrix}$

^¹The excluded country is Italy.

^²Modification of Model V that uses $Δ \ln Q M H_{t}^{N}$ rather than Δln Q_t.

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Abstract

I. The Ratchet Hypothesis

II. Models of Inflation in an Open Economy

model i

model ii

model iii

model iv

model v

model vi

the asymmetry test

the data and choice of variables

III. Empirical Results

aggregate price changes, 1958–73

asymmetry results, 1958-73

aggregate price changes, 1958-70

disaggregated price changes for manufactures, 1958-73

IV. Conclusions

APPENDIX: Data Definitions and Sources

BIBLIOGRAPHY

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