The Effect of Exchange Rate Changes on Wages and Prices in the United Kingdom: An Empirical Study

One of the key factors that determine the effect of a discrete change in the exchange rate of a country on its trade balance is the effect on that country’s costs and prices. The larger the rise in money costs, domestic prices, and export prices (in domestic currency) that is induced by a devaluation, the smaller will be the competitive price advantage achieved by the country from devaluation—and hence, ceteris paribus, the smaller will be the improvement in the trade balance.

Abstract

One of the key factors that determine the effect of a discrete change in the exchange rate of a country on its trade balance is the effect on that country’s costs and prices. The larger the rise in money costs, domestic prices, and export prices (in domestic currency) that is induced by a devaluation, the smaller will be the competitive price advantage achieved by the country from devaluation—and hence, ceteris paribus, the smaller will be the improvement in the trade balance.

One of the key factors that determine the effect of a discrete change in the exchange rate of a country on its trade balance is the effect on that country’s costs and prices. The larger the rise in money costs, domestic prices, and export prices (in domestic currency) that is induced by a devaluation, the smaller will be the competitive price advantage achieved by the country from devaluation—and hence, ceteris paribus, the smaller will be the improvement in the trade balance.

This paper provides an empirical analysis of the probable effect of exchange rate changes on aggregate wage and price behavior in the United Kingdom. A simple and widely used two-equation model of wage and price behavior in the United Kingdom is employed in the study. One disadvantage of this model, however, is its partial equilibrium nature, which limits the analysis to providing information on only a few of the important effects of an exchange rate change. Specifically, the model is used to estimate only three effects of an exchange rate change: (1) the effect of a change in import prices on domestic prices (retail prices), (2) the effect of this initial change in retail prices on wage rates, and (3) the effect of this change in money wage rates on retail prices and any subsequent round effects on wage rates and retail prices. In other words, the analysis ignores or considers as exogenous these other effects of an exchange rate change: (1) the effect of an exchange rate change on import prices,1 (2) the effect of changes in import prices and domestic prices on the initiating country’s export prices,2 and (3) the effect of exchange-rate-induced changes in wages and prices on the supply and demand for factors of production, for commodities, and for money.3

The paper has four sections. In Section I, the basic model is introduced and briefly discussed, and the relevant parameters for assessing the impact of exchange rate changes on wages and prices are identified. In Section II, the price equation of the model is estimated (separately at first) to obtain information on the effect of changes in import prices on retail prices. Tests are also conducted to determine whether the devaluation of sterling in 1967 was followed by any change in the relationship between changes in import prices and retail prices. In Section III, the aggregate wage and price equations are estimated for the 1954—71 period (and for certain subperiods) in order to identify the effect of retail price changes on wage rate changes and the effect of wage rate changes on retail price changes. Tests are also conducted to determine whether the devaluation of sterling in 1967 was followed by any significant change in wage or price behavior. The main conclusions of the study are presented at the ends of Sections II and III and in Section IV.

I. A Simple Wage-Price Model

The basic two-equation, wage and price model that has been used in most empirical studies of wage and price behavior in the United Kingdom can be written as: 4

W*t=α0+α1Uti+α2P*ti;α1<0,α2>0(1)
P*t=β0+β1W*ti+β2Q*ti+β3PM*ti;β2<0,β1,β3>0(2)

Where W is an index of money wage rates, P is an index of retail prices, U is the unemployment rate, Q is an index of labor productivity (real output per employee), PM is an index of import prices (in sterling), the superscript asterisk is the proportionate change in a variable from its value four quarters before (for example, P*t=PtPt4Pt4) and the subscript i denotes the appropriate length of the lag (not necessarily the same for all variables).

The wage equation (1) is quickly recognized as one form of the well-known Phillips curve. It incorporates, inter alia, the twin hypotheses that the change in wages is a function of the excess demand for labor and that there exists a stable linear or nonlinear relationship between the excess demand for labor and the unemployment rate. The change in prices (P*) enters the wage equation as an independent influence on W* as a proxy for expected price changes (Pe*t),that is,P*tPe*t.5 The coefficient on P*t, α2, may lie anywhere between zero and unity, depending on the degree of money illusion exhibited by wage earners, the degree of competition in the labor market, the balance of power as between labor and management in wage negotiations, and the magnitude of adjustment costs associated with reopening wage negotiations.

The price equation (2) reflects the hypothesis that firms set their prices with an aim toward obtaining a constant percentage markup or profit margin (call it B). Its derivation is presented in Lipsey and Parkin (1970), and it is repeated here briefly because it will aid in the discussion below. Begin with the identity that the market value of final output (P) is equal to the value of measured costs, plus the value of unmeasured costs, plus residual profits (all expressed as amounts per unit of output):

PWL+PMT+CD+Π(3)

where P, W, and PM are defined as before and where L = the quantity of labor used per unit of output, T = the quantity of imports per unit of output, C = the price per unit of other inputs (called unmeasured inputs and representing materials and capital costs), D = the quantity of unmeasured inputs per unit of output, and Π = profits per unit of output. Now make the following three assumptions: (1) T is constant, (2) unmeasured costs (CD) are a constant function (F) of measured costs (WL + PMT), and (3) firms aim for a constant percentage markup (B) and hence aim for Π = BP. After substituting these three assumptions in the price equation (3), differentiating with respect to time, and performing a few transformations (including replacing L*withQ*), the following ex ante price equation is obtained:

P*={(1+F)(1B)WLP}W*+{(1+F)(1B)PMTP}PM*(4){(1+F)(1B)WLP}Q*

It can be seen by inspection that the price equation (2) is simply a convenient estimating form for equation (4). Also note that equation (4) suggests that there should be three theoretical restrictions on the coefficients in equation (2): (1) the coefficient on Q* should be equal to minus the coefficient on W*;(2) the coefficients on W*andPM* should be equal to the share of wages and imports in the final price, respectively, times the factor (1+F)(1B); and (3) the constant term in equation (2) should be equal to zero.

Since the above wage-price model is well known and has been discussed at length in the literature, it should suffice to mention only a few of its characteristics that apply to the subsequent analysis. First, the presence of P* in the wage equation and W* in the price equation implies that the relationship between W* andP* runs in both directions. This two-way relationship, in turn, has two other implications: (1) any exogenous change in U,Q*, andPM* will initiate a wage-price spiral; however, the wage-price spiral will not be explosive so long as the product of the coefficient on P* in equation (1) and that on W* in equation (2) is less than one, that is, so long as (α2β1) < 1; (2) unless P*orW* is lagged in the model (so that the model becomes recursive rather than simultaneous), ordinary least-squares estimation of equations (1) and (2) will produce biased and inconsistent estimators; however, most previous estimates of the model for small samples have indicated that the ordinary least-squares and two-stage least-squares estimates are quite similar, suggesting that the bias may not be large.6

Second, the model implies that there is a long-run (permanent) tradeoff between the rate of price inflation and the unemployment rate so long as the product of the coefficients on P*andW* is less than one (α2β1) < 1. This can be clearly seen by solving equations (1) and (2) for the reduced form trade-off between P* and U: 7

P*=β0+β1α0+β1α1U+β2Q*+β3PM*(1α2β1)(5)

If α2β1 = 1, then the coefficient on the unemployment rate is infinite and there is no trade-off between P* and U. Also note that the “expectations” view of the Phillips curve, held by Friedman (1968) and Phelps (1968), can be represented in the model by the two conditions P*t=Pe*t (actual price changes equal expected price changes) and α2 = 1 (the wage response to expected price changes is one). If these two conditions are satisfied, then there is a relationship between changes in real wages and the unemployment rate but not between changes in money wages and the unemployment rate. Equivalently, there is no permanent trade-off between W* and U; rather the long-run Phillips curve is a vertical line passing through the natural unemployment rate. Finally, observe that the behavioral assumptions underlying the price equation (2) do not permit the level of excess demand to influence price changes directly. Rather, excess demand affects price changes only through its influence on wage changes, and further it is excess demand in the labor market, not in the product market, that affects P*, that is, the model assumes that the labor market is in disequilibrium but that the product market is not.

the effect of an exchange rate change on wages and prices

With these considerations in mind, it can now be rather easily demonstrated how an exchange rate change will affect domestic prices in this model. First, consider the relationship between the exchange rate change and the change in import prices in the domestic currency (sterling). It can be shown (see Branson, 1972, and Kwack, 1973) that U. K. import prices in sterling will increase by 1 per cent for a 1 per cent U. K. devaluation if no other countries alter their exchange rates, if exporters to the United Kingdom do not alter their dollar supply prices, and if either the own-price elasticity of demand for U. K. imports is zero or the own-price elasticity of supply for U. K. imports is infinite. In practice, however, none of these four conditions is likely to be satisfied, and therefore, following Kwack (1973), it is more appropriate to express the relationship between the import price change and the exchange rate change as

PM*=K(R*+PF*)(6)
PM*R*=K(7)

where R* is the proportionate change in the U. K. exchange rate (expressed as units of sterling per U. S. dollar), PF* is the proportionate change in the dollar supply price of exporters to the United Kingdom, and K is a constant lying between zero and unity.8 As stated previously, it is not our intention in this paper to estimate K, but for expositional purposes, assume that K = 0.8 for the United Kingdom.9

Now consider the relationship between the change in import prices and the change in domestic prices. Here it is useful to distinguish between the short run and the long run. In the short run when wages may be regarded as exogenous, the change in retail prices due to the change in import prices will be

P*PM*=β3(8)

where β3 is the coefficient on PM* from the structural price equation (2). In the long run, however, the change in retail prices given by equation (8) will induce some change in money wages (as wage earners attempt to protect or increase their real incomes), and these wage changes will, in turn, lead to further changes in retail prices and money wages. The final change in retail prices due to the import price change will then be given by

P*PM*=β3(1α2β1)(9)

where α2 and β1 are the coefficients on prices and wages, respectively, from equations (1) and (2).10 equation (9) says that the effect of an import price change on domestic prices depends positively on three parameters: the short-run effect of a change in import prices on the change in domestic prices (β3), the effect of a change in domestic prices on the change in money wage rates (α2), and the effect of a change in money wage rates on the change in domestic prices (β1).11 A comparison of equations (8) and (9) also reveals that the long-run effect of a change in import prices on the change in retail prices will be greater than the short-run effect by the factor 1/(1 – α2β1). If, for example, α2 and β1 each equal 0.5, then the long-run effect will be 1.33 times greater than the short-run effect.

To determine the effect of an exchange rate change on domestic prices, it is merely necessary to substitute equations (7) and (9) in the following equation (10):

P*R*=P*PM*.PM*R*=β3(1α2β1).K(10)

If, for example, K = 0.8, β3 = 0.2, and α1=β2 = 0.5, then a 10 per cent sterling devaluation will lead, in the long run, to an increase in U. K. retail prices of approximately 2 per cent.

Similarly, one can use the model to calculate how much of the competitive price advantage originally achieved by a devaluation will remain after the induced wage and price effects have run their course. More specifically, ignore export prices for expositional convenience, and let the ratio of import prices to domestic prices (PM/P) be a rough index of competitive price advantage. The proportion of the initial price advantage achieved by devaluation that remains after domestic price adjustments to the devaluation have been completed can then be expressed as

PM*R*P*R*PM*R*=K[1(β31α2β1)]K=[1(β31α2β1)](11)

If the devaluation has no effect on domestic prices (P*R*=0), then equation (11) equals one—that is, all of the competitive price advantage originally obtained by the devaluation is retained. On the other hand, if the induced domestic price effects are substantial, say because the economy is very open (β3 is large) or because wage-price interactions are very strong (α2β1 is large), then P*R*PM*R* and equation (11) will equal zero—that is, none of the competitive price advantage will be retained.12 As an example, if it is once again assumed that β3= 0.2 and α2 = β1 = 0.5, then approximately 73 per cent of the original competitive price advantage achieved by devaluation will be retained.

It should also be mentioned that the model can be used to determine the effect of an exchange rate change on the real wage (W/P). As is well known, one of the traditional arguments made for devaluation is that devaluation is a viable method of reducing the real wage in countries where money wages are inflexible downward. The argument, however, rests on the empirical assumption that the money wage response to domestic price changes is less than one (α2 < 1). To see this, first solve equations (1) and (2) for the reduced form equation for W*:

W*=α0+α2β0+α1U+α2β2Q*+α2β3PM*(1α2β1)(12)

The long-run effect of a change in import prices on the change in money wages is then

W*PM*=α2β3(1α2β1)(13)

Similarly, using equation (7), the effect of an exchange rate change on W* is

W*R*=W*PM*.PM*R*=α2β3(1α2β1).K(14)

For the effect of the exchange rate change on the change in real wages, subtract equation (10) from equation (14) to obtain

W*R*=P*R*=α2β3K(1α2β1)β3K(1α2β1)=Kβ3(1α2β1)(α21)(15)

equation (15) implies that a devaluation will reduce the real wage, (W*R*P*R*)<0, so long as the money wage response to retail price changes is less than one (so long as α2 < 1). If, for example,β3 = 0.2, K = 0.8, and α2 =β1 = 0.5, then a 10 per cent devaluation will reduce the real wage by about 1 per cent.13

There remains one other important factor to consider in assessing the effect of an exchange rate change on wage and price behavior. Implicit in all the preceding analysis—and indeed implicit in all previous empirical studies on the effect of exchange rate changes on domestic price behavior (see Cooper, 1968; Kwack, 1973; and Artis, 1971)—is the assumption that the exchange rate change does not affect any of the coefficients (including the constant terms) in the structural wage and price equations (1) and (2). In other words, it is assumed that, given the values of the exogenous variables in equations (1) and (2), wage and price behavior after an exchange rate change will not be different from that during other periods. While there are no compelling theoretical arguments for rejecting this assumption, there are several intuitive arguments for subjecting it to empirical tests. If, for example, devaluations under a fixed exchange rate regime are regarded by the public as unusually inflationary events, and if producers and wage earners respond to devaluation by increasing the size of their price responses to cost changes to avoid any fall in their real incomes, then the coefficients β3, α2, and β1 will be larger after devaluation than they are during other periods. In Sections II and III of this paper, several empirical tests are carried out to determine whether U.K. wage and price behavior after the 1967 devaluation of sterling was different from that otherwise expected. It should be realized, however, that this devaluation is far from ideal for testing the effect of devaluation on wage-price behavior because it was followed by a host of other policy measures (including incomes policy and indirect taxes) that might also have altered wage- price behavior;14 therefore, any observed change in wage-price behavior after the devaluation is difficult to assign to any one policy action. A good test of the hypothesis that wage and price behavior after an exchange rate change differs from behavior in other periods probably requires an analysis of many exchange rate changes so that any consistent departures from normal wage-price behavior can be identified.15

Before proceeding to the empirical analysis, a few notational and data definitions are necessary. The data used in Sections II and III are quarterly observations for the period 1954:1 to 1971:IV (first quarter of 1954 to fourth quarter of 1971).

All variables expressed as proportionate changes (denoted by superscript asterisk) are defined as overlapping four-quarter changes—for example, P*t=(PtPt4)/Pt4orPM*t3=(PMt3PMt7)/PMt7. All data series are seasonally unadjusted; however, as one would expect with the four-quarter formulation, in none of the equations reported below were seasonal dummy variables significant, nor did they alter the coefficients of other variables when they were included in the equations. Some limited experimentation was carried out to find the most appropriate lags for the explanatory variables in the two equations. Dummy variables for periods of incomes policy were often included in the wage and price equations in cases where they improved the fit of the equations.16 The dating of these shift dummies (DIC1–DIC6) is taken from Smith (1968) and the Economist (1972) and is as follows: D1C1 = 1956:1—1956:IV, DIC2 = 1961:III–1962:II, DIC3 = 1962:III–1964:III, DICA = 1965:I–1966:II, DIC5 = 1966:III–1967:II, and DIC6 = 1967:III–1969:IV. A single dummy variable for all periods of incomes policy was also tried in the equations, but it was always inferior to the separate dummies.

A detailed description of all variables and corresponding data sources is presented in the Appendix; in addition, more will be said about the choice of variables in the wage equation in Section III. All equations were estimated by ordinary least-squares, unless otherwise indicated. The numbers in parentheses below the estimated coefficients are t values. The summary statistics for the regression equations are defined as follows: R¯2 is the coefficient of determination (corrected for degrees of freedom); SEE is the standard error of estimate of the regression equation (also corrected for degrees of freedom); and D-W is the Durbin- Watson statistic.

II. The Relationship Between Import Prices and Retail Prices

As demonstrated in Section I, one of the crucial parameters for determining the effect of an exchange rate change on the change in domestic prices is the short-run effect of the import price change on the change in domestic (retail) prices. There are essentially two alternative methods of estimating the short-run effect of a change in import prices on the change in retail prices: the input-output method and the regression method. In the former method, one multiplies the import price change by an estimate of the direct and indirect import content of consumption (or final expenditure) in some recent year to obtain the estimated change in the domestic price index.17 In the regression method, one estimates a domestic price change equation, say similar to equation (2) in which import prices is one of the explanatory variables, and then uses the estimated coefficient on PM* to estimate the effect on domestic prices.

Both approaches have advantages and disadvantages. There are at least three disadvantages of the input-output approach: (1) it does not give any information on the time lag with which import price changes affect domestic prices, (2) it does not permit one to test for any nonlinearities in the P*PM* relationship, and (3) so long as firms use a mark-up pricing rule, the change in domestic prices will be different from that indicated by the import content of consumption or expenditure, as is shown in the coefficient on PM* in equation (4). On the other hand, the regression approach may give a misleading estimate of the effect of PM* onP* when the price change equation is not correctly specified or when the estimated equation suffers from other statistical problems (simultaneous-equations bias, multicollinearity, and so on). In addition, imported finished goods are likely to be counted in both the domestic price index (the retail price index), and the import price index, thereby producing some spurious correlation between P*andPM*; 18 for the United Kingdom, however, this is a relatively minor problem because the direct import content of consumption expenditure is less than 10 per cent (see Barker, 1968). Since both the lag between import price changes and domestic price changes and any nonlinearities in this relationship are of some interest, the regression approach seemed preferable for the purposes of this study.

the lag between import price changes and retail price changes

Before discussing the size of the effect of a change in import prices on the change in retail prices, it is first necessary to determine the time lag between the import price change and the retail price change. To obtain some information on the lag between PM*andP*, the price equation (2) was estimated by ordinary least-squares for the 1954:I–1971: IV period using various alternative lags for PM* Discrete lags on PM* of zero to four quarters were tried as well as a few distributed lags using current and lagged values of PM*.19 It was discovered that a discrete lag of three quarters on PM* gave the best result, both in terms of the fit of the equation and the significance of the import price variable. Burrows and Hitiris (1972) also found that a three-quarter lag on PM* provided the best results in their price equation for the United Kingdom, whereas Smith (1968) and Lipsey and Parkin (1970) used a one-quarter lag on PM*. However, the sample periods used in these studies were different from the period used in the present study. The estimated price equation with the three-quarter lag on PM* is given below as equation (16). Also, for comparative purposes, the price equation with a distributed lag on PM* is presented directly below it (equation 17).

Pt*=1.22(3.92)+0.563(11.67)Wt*0.152(4.13)Qt*+0.13(4.57)PM*t3(16)R2¯=0.78SEE=1.04DW=0.91Period=1954:I-1971:IV
Pt*=1.25(3.73)+0.557(10.59)Wt*0.156(3.63)Qt*+0.066(0.70)PM*t1(17)0.067(0.70)PM*t2+0.15(2.54)PM*t3R2¯=0.77SEE=1.06DW=0.91Period=1954:I-1971:IV

The price equation will be discussed in some detail in Section III. For the time being, note that, aside from a poor Durbin-Watson statistic, price equation (16) is reasonably satisfactory with all coefficients well-determined and with the expected signs.

The three-quarter lag on PM* suggested by equation (16) represents the average time lag for the whole 1954–71 period. One way in which a devaluation might alter the P*PM* relationship in such a manner as to increase inflationary pressures in the economy would be for it to reduce the lag with which PM* affects P*—that is, it could increase the pass- through speed of import costs.20 To obtain some evidence on this type of effect, the regression period was split into two parts (1954:I–1967:11 and 1967:III–1971:IV) which correspond to the periods before and after the November 1967 devaluation of sterling. The price equation was then re-estimated for each of the two subperiods, and various alternative lags were again tried for PM*. The equations revealed that a three-quarter lag on PM* performed best for the 1954–67 period but that a two-quarter lag on PM* was superior for the 1967–71 period. While the superiority of the two-quarter lag over the three-quarter lag for PM* in the latter period is not dramatic (see equations (18) and (19) below), and while the shortening of the lag cannot confidently be linked with the 1967 devaluation as opposed to the whole 1967–71 period, the results are at least not inconsistent with the hypothesis that the 1967 devaluation may have increased the speed with which import price changes were passed forward into retail price changes.21

Pt*=0.274(0.299)+0.653(8.78)Wt*0.146(1.31)Qt*+0.20(3.54)PM*t2(18)R2¯=0.82SEE=1.01DW=0.70Period=1967:III-1971:IV
Pt*=0.423(0.38)+0.658(8.33)Wt*0.004(0.032)Qt*+0.21(3.13)PM*t3(19)R2¯=0.80SEE=1.07DW=0.97Period=1967:III-1971:IV

the P*PM* relationship in the 1954–71 period and after the 1967 devaluation

Given a proper specification of the lag between P*andPM*, the size of the short-run effect of a change in import prices on the change in retail prices will be given by the estimated coefficient on PM* in the price equation. Reference to equation (16) suggests that, ceteris paribus, a change in import prices by 1 per cent will be associated with a change in retail prices by about 0.13 per cent. This estimate of 13 per cent is quite close to estimates of the average import content of consumption for the United Kingdom and is also similar to previous (regression) estimates of the effect of PM* onP*.22 More specifically, estimates by Barker and Lecomber (1970) suggest that the average import content of consumption in the United Kingdom during the 1954–71 period was approximately 17 per cent (0.17).23 Invoking the t distribution, it is clear that the point estimate of 0.13 in equation (16) is not significantly different from 0.17 at the 5 per cent level of confidence.24 Using price equations quite similar to equation (16) on quarterly data, Burrows and Hitiris (1972) also found a coefficient of 0.13 on PM*, whereas both Smith (1968) and Lipsey and Parkin (1970) obtained a coefficient of about 0.09 on PM* (using a one-quarter lag on PM*).25

The estimated coefficient of 0.13 on PM*t3 in equation (16) represents the short-run effect of a change in import prices on the change in retail prices during the entire 1954–71 period. It could well be that the slope of the P*PM* relationship was different for various subperiods during that period. Of particular interest for this study are any shifts in the slope of this relationship in the subperiod following the 1967 devaluation, because such shifts could possibly be the result of changes in pricing behavior induced by the devaluation. To obtain some information on this question, a series of empirical tests was conducted.

In the first test, the emphasis was on the four-year period following the 1967 devaluation. More specifically, the price equation was estimated for the period 1954–71 with the addition of a slope dummy variable on import price changes (D6771. PM*t3). The dummy D6771 takes the value of one for the period 1967:III–1971:IV and the value of zero elsewhere. If the slope of the P*PM* relationship increased in the period 1967–71, owing to the 1967 devaluation or to other factors, then the estimated coefficient on D6771. PM*t3 should be positive and significantly different from zero. The estimated price equation is presented below, where DIC1–DIC6 are shift dummy variables for periods of incomes policy.26

Pt*=0.55(10.68)+0.623(13.84)W*t0.126(3.60)Q*t+0.103(3.26)PM*t3(20)+0.073(1.35)D6771.PM*t30.96(1.91)DICI+2.08(4.31)DIC20.09(0.25)DIC3+1.25(3.12)DIC4+0.075(1.49)DIC5+0.067(0.179)DIC6R2¯=0.85SEE=0.87DW=1.37Period=1954:I-1971:IV

An examination of the estimated coefficient on D6771. PM*t3 in equation (20) reveals that it is positive but not significantly different from zero at the 5 per cent level of confidence. Thus, the null hypothesis that there was no upward shift in the effect of PM* onP* during the 1967–71 period cannot be rejected.

Two further tests for shifts in this relationship placed emphasis on a shorter subperiod immediately following the 1967 devaluation. In the first such test, the price equation was estimated for the period 1954–71 with a slope dummy (DEVPM*t3) on import price changes again included in the equation. In this case, however, DEV takes the value of one for the four quarters 1968:IV–1969:III and the value of zero elsewhere. The period 1968:IV–1969:III is the one-year period after the devaluation of November 1967, after accounting for the three-quarter lag on import price changes. There is no real evidence that all effects of the devaluation on the P*PM* relationship would occur during this period, but it seems reasonable to assume that much of the effect would surface within a period of one year. The estimated equation was

Pt*=0.46(1.38)+0.651(14.13)W*t0.126(3.64)Q*t+0.10(3.34)PM*t3(21)+0.08(1.40)DEV.PM*t31.09(2.23)DICI+2.07(4.30)DIC20.10(0.31)DIC3+1.21(3.06)DIC4+0.72(1.49)DIC5+0.02(0.04)DIC6R2¯=0.85SEE=0.87DW=1.37Period=1954:I-1971:IV

The coefficient on DEV. PM*t3 in equation (21) is positive, but it is not significantly different from zero at the 5 per cent level of confidence.

The hypothesis that the slope of the P*PM* relationship remained unchanged immediately following the devaluation therefore cannot be rejected.

In the third and final test, the slope dummy on import prices (DEV. PM*t3) was again included in the price equation, but this time a slope dummy for wage changes (DV. W*t) was also included in the equation. DV takes the value of one for the four quarters following the 1967 devaluation (1968:I—1968:IV) and the value of zero elsewhere. If the slope of the P*W* relationship increased significantly during this period, then the estimated coefficient on DVW*t should be positive and significantly different from zero. The estimated price equation was

Pt*=0.52(1.51)+0.644(13.75)W*t0.08(0.77)DV.W*t0.130(3.71)Q*t(22)+0.11(3.39)PM*t30.09(1.51)DEV.PMt3+1.11(2.26)DIC1+2.05(4.20)DIC2+0.11(0.33)DIC3+1.19(2.99)DIC4+0.70(1.41)DIC5+0.21(0.43)DIC6R2¯=0.85SEE=0.87DW=1.37Period=1954:I-1971:IV

In equation (22), the coefficient on the slope dummy for wage changes is positive but quite insignificant, suggesting no upward shift in the slope of the P*W* relationship in the year after the 1967 devaluation.27 The coefficient on the slope dummy for import prices is again positive, slightly higher than in equation (21), but still not significantly different from zero at the 5 per cent level of confidence.

In sum, the results contained in equations (20), (21), and (22) suggest that the slope of the P*PM* relationship was not significantly greater in either the period 1968:IV–1969:III or the period 1967:III–1971:IV than for the period 1954:I–1971:IV as a whole. It should be recognized, however, that the evidence on this question is not overwhelming.

There is also one important caution to keep in mind in interpreting the results of the three tests described above. While equations (20), (21), and (22) can be used to determine whether the slope of the P*PM*relationship increased in the period following the 1967 devaluation, they cannot be used alone to obtain an estimate of the effect of the 1967 devaluation itself on the P*PM* relationship. The main difficulty here is that the postdevaluation period (1967:III–1971:IV) includes a period of incomes policy (namely 1967:III–1969:IV), and there is some limited empirical evidence that the effect of PM* onP* (as well as the effect of W* onP*) is smaller during periods of incomes policy than in periods with no incomes policy.28 The consequence of this coincidence of incomes policy and devaluation is that the estimated coefficient on a slope dummy for import price changes will reflect the net effect of the two policies on the P*PM* relationship (as well as the correlation between the two policies) and not the individual effect of either policy. More specifically, it can be shown that if (1) incomes policy had a negative effect on the P*PM* relationship, (2) the devaluation had a positive effect on the P*PM* relationship, and (3) the incomes policy dummy is positively correlated with the slope dummy on import price changes, then the estimated coefficient on the slope dummy for PM* will understate the “true” effect of the 1967 devaluation on the P*PM* relationship.29 Similarly, if incomes policy and the 1967 devaluation are the only two factors affecting the P*PM* relationship, and if the three assumptions listed above are reasonable, then the estimated coefficient on the slope dummy for PM* will provide an estimate of only the lower bound of the effect of the 1967 devaluation on the P*PM* relationship.30

In order to obtain estimates of the separate effects of the two policies, it would be necessary either to estimate a price equation with two slope dummies on PM* (one for each policy) or to have an extraneous estimate of the effect of the 1967:III–1969:IV incomes policy on the P*PM* relationship. In practice, however, neither of these methods is likely to solve the problem. The first method falters because the slope dummy for the postdevaluation period and the slope dummy for the incomes policy period are so highly correlated that their separate effects cannot be adequately separated.31 Similarly, the second method cannot be used in practice because a reliable extraneous estimate of the effect of the 1967:III–1969:IV incomes policy on the P*PM* relationship is not available. Thus, an estimate of the separate effect of the 1967 devaluation on the P*PM* relationship must seemingly await further study.

the effects of large and small import price changes

When trying to estimate the effect of PM* onP*, it may be important to recognize that the import price changes associated with exchange rate changes are likely to be larger than those that occur during normal periods. This observation, in turn, raises the possibility that the relationship between PM*andP* might be different for large and small changes in import prices—that is, that it may be nonlinear.32

To obtain information on this question, the following test procedure was adopted: (1) the data series on PM*t3 was split into two parts: those observations on PM*t3 that are larger than 5 per cent and all others; and (2) the variable for all import price changes (PM*t3) and the variable for only large import price changes (PM*t3 L) were then entered into the price equation as separate regressors. The cut-off line of 5 per cent for small and large changes is admittedly rather arbitrary, but since most parity changes are likely to be 5 per cent or larger, the dividing line is not unreasonable. If large changes in import prices have a greater proportionate effect on retail price changes than do small changes, then the estimated coefficient on the import price variable representing large changes should be positive and significantly different from zero.33

The estimated equation was

Pt*=0.57(1.63)+0.634(14.03)W*t0.129(3.47)Q*t+0.121(2.05)PM*t3(23)+0.006(0.087)PMt3L1.11(2.20)DIC1+2.05(3.91)DIC20.155(0.454)DIC3+1.16(2.89)DIC4+0.643(1.31)DIC5+0.254(0.693)DIC6R2¯=0.84SEE=0.88DW=1.29Period=1954:I-1971:IV

Examination of the estimated coefficient on PM*t3 L in equation (23) reveals that it is positive but not significantly different from zero. Thus, the evidence suggests that large changes in import prices do not have a greater proportionate effect on retail prices than do small changes.

the effects of positive and negative changes in import prices

Just as large and small changes in import prices could conceivably have different effects on retail prices, so too could positive and negative changes.34 This latter question is of some interest here because devaluations and revaluations naturally lead to opposite changes in import prices. To test for this possibility, a procedure identical to that employed above for large versus small changes in import prices was adopted. The estimated equation is reported below, where PM*t3 P refers to all positive changes in import prices, and PM*t3 is again all import price changes (positive or negative). If positive changes in import prices have a greater effect on retail price changes than do negative changes, the estimated coefficient on PM*t3 P should be positive and significantly different from zero.

Pt*=0.316(0.852)+0.635(14.30)W*t0.129(3.39)Q*t+0.078(1.79)PM*t3(24)+0.100(1.39)PM*t3P0.961(1.91)DIC1+2.25(4.49)DIC20.045(0.129)DIC3+1.31(3.21)DIC4+0.789(1.60)DIC5+0.159(0.452)DIC6R2¯=0.85SEE=0.87DW=1.39Period=1954:I-1971:IV

Examination of the estimated coefficient on PM*t3 P in equation (24) reveals that it is positive, quite large (in fact, larger than the coefficient on all import price changes), but still not significantly different from zero at the 5 per cent level of confidence. Thus, the evidence suggests that positive and negative changes in import prices do not have different effects on retail prices, but the evidence should be considered to be more tentative than conclusive.

conclusions about the P*PM* relationship and the 1967 devaluation

The general findings of this section on the short-run effect of a change in import prices on the change in retail prices can be summarized as follows:

(1) Over the 1954–71 period, a change in import prices by 1 per cent was associated with change in retail prices of about 0.13 per cent.

(2) Over the 1954–71 period, the average lag between a change in import prices and the resultant change in retail prices was about three quarters.

(3) There is some evidence that in the four-year period following the 1967 devaluation the lag between PM*andP* was reduced to two quarters.

(4) The slope of the P*PM* relationship does not appear to have been greater after the 1967 devaluation than for the period 1954–71 as a whole, but the evidence on this question is more tentative than conclusive.

(5) The slope of the relationship between changes in wage rates and the resultant change in retail prices was not higher in the year following the 1967 devaluation than for the period 1954–71 as a whole.

(6) Large changes in import prices do not seem to have a greater proportionate effect on retail prices than small changes.

(7) The effect of positive changes in import prices on retail prices does not seem to be significantly different from the effect of negative changes, although, here too, the evidence is far from conclusive.

III. The Relationship Between Wage Changes and Price Changes

Once an import price change has led to some initial change in retail prices via the P*PM* relationship, it is likely that a series of induced wage and price responses will follow in its wake as wage earners and producers attempt to avoid a fall in their real incomes by passing cost increases forward in higher prices. In fact, as equation (11) in Section I demonstrated, the magnitude of these induced wage and price responses will in large part determine how much of the initial competitive price advantage achieved by devaluation will be retained in the period following the devaluation. In this section, the two-equation wage-price model is estimated to obtain information on the effect of retail price changes on money wage changes and on the effect of money wage changes on retail price changes—that is, to obtain estimates of α2 and β1. In addition, several tests are carried out to determine whether wage behavior in the period after the 1967 devaluation was different from what might have been expected in the absence of a devaluation.

Before turning to the empirical results, a few explanatory remarks are in order about the variables appearing in the wage equation. First, recall that the dependent variable in the wage equation is defined as an overlapping four-quarter change: W*t=(WtWt4)/Wt4. This practice of using overlapping four-quarter changes is common to most U.K. wage studies and is based on the twin assumptions that wage adjustments are made once every four quarters and that one fourth of all such adjustments is made each quarter. This procedure is a convenient method for handling the discrete nature of wage adjustments when the fraction of workers receiving wage adjustments in each quarter is unknown. Unfortunately, the four-quarter overlapping technique, while it smooths the wage series, has two serious disadvantages: (1) if the fraction of workers receiving wage adjustments each quarter fluctuates substantially over time, then one of the underlying assumptions of the model is violated and the wage equation may give poor results for at least some time periods; and (2) since the disturbance (error) term in the four-quarter formulation is a moving average of quarterly disturbance terms, the stochastic element will in general be autocorrelated (see Black and Kelejian, 1972). That is, the four-quarter formulation can introduce artificial autocorrelation into the wage equation with the attendant result that the estimated standard errors of the coefficients in the equation will be biased downward.35 With regard to this point, it should be mentioned that most previous wage equations for the United Kingdom have suffered from rather serious autocorrelation, and the wage equations reported in this paper are no exception.36

Second, the wage variable used in this study was the weekly wage rate of all manual workers in all industries and services in the United Kingdom. Weekly wage rates could, in principle, be affected by changes in the number of normal weekly hours worked; however, when the change in normal weekly hours was included as an independent regressor in the wage equation, it was insignificant. In addition, when the change in the average hourly wage rate was used as the dependent variable, the results were very similar. It should also be mentioned that the use of wage rates rather than earnings in the price equation could have some effect on the estimate of the price response to wage changes—that is, on the estimate of the coefficient β1 in equation (2). More specifically, it is widely recognized that wage earnings at places of work (wage rates plus overtime payments for time-rate workers plus productivity payments for payments-by-results workers), rather than centrally negotiated wage rates, are probably the most appropriate labor cost variable for the employer’s price decision. Despite this consideration, this study, as well as most previous U. K. wage-price studies, has used wage rates for two reasons: (1) data on earnings are available only on a semiannual basis while data on wage rates are available quarterly, and (2) it has proved more difficult to specify a reasonable model for earnings changes than for wage changes.37 If earnings (rather than wage rates) were used in the price equation, it is likely that the estimated price response to wage changes would be slightly higher.38

Finally, several proxies for the excess demand for labor were tried (in both linear and nonlinear forms) in the wage equation, including the total unemployment rate for the United Kingdom and the U. K. unemployment rate for wholly unemployed persons. It was found that a five-quarter average of the wholly unemployed rate provided the best results. This variable, denoted as UW5t, is defined as UW5t = (UWt + UWt–1 + UWt–2+ UWt–3 + UWt–4)/5, where UWt is the wholly unemployed rate in period t.39 Note that by specifying the unemployment rate in the above way, both the wage change variable (W*t) and the unemployment rate variable (UW5t) will be centered on the quarter t – 2 and, therefore, UW5t will affect W*t without a lag.

wages, prices, and the misbehaved phillips curve

In order to obtain estimates of the wage response to price changes and of the price response to wage changes, the two-equation wage-price model was estimated for various time periods. Since the results for the 1954–71 period exhibit certain peculiarities which will soon become evident, the results for the 1954:I–1967:II (predevaluation) period are reported first. The ordinary least-squares estimates of the two equations, including incomes policy dummies, were:

Wt*=8.91(7.74)3.14(5.53)UW5t0.16(1.54)P*t+1.99(4.64)DIC1(23)1.16(2.72)DIC2+1.39(3.70)DIC30.28(0.78)DIC41.05(2.74)DIC5R2¯=0.81SEE=0.70DW=1.32Period=1954:I1967:II
Pt*=1.22(2.31)+0.49(4.64)Wt*0.15(4.35)Q*t+1.11(3.83)PM*t30.59(1.04)DIC1(24)+1.92(4.29)DIC20.10(0.33)DIC3+1.23(3.38)DIC4+0.53(1.17)DIC5R2¯=0.77SEE=0.78DW=1.62Period=1954:I1967:II

Inspection of equations (23) and (24) reveals the following points of interest: (1) the explanatory power of the wage and price equations is respectable and the standard errors of estimate are less than 1 percent for both equations (0.70 for W* and 0.78 for P*); (2) all the explanatory variables carry the expected sign and all, except P*t in the wage equation, are significantly different from zero at the 5 per cent level of confidence; (3) the coefficient on P*t in the wage equation is not significantly different from zero at the 5 per cent level of confidence and its value (0.16) implies a high degree of money illusion on the part of wage earners; (4) the product of the coefficients on P*andW* (0.16 X 0.49 = 0.08) is also quite low and implies a small and very damped wage-price response to exchange rate changes or other exogenous disturbances;40 (5) the theoretical constraints on the coefficients in the price equation are not satisfied: the coefficient on W* is three times as large as that on Q* (when they should be of equal absolute value), the coefficients on W*andPM* are less than the shares of wages and imports in final price, and the constant is significantly different from zero; and (6) the incomes policy dummies, where significant, suggest a restraining influence on wages in only two periods (DIC2 and DIC5), a perverse influence on wages in two periods (DIC1 and DIC3), and a perverse influence on prices in two periods (DIC2 and DIC4).

Consider the same two equations estimated (also by ordinary least- squares) for the 1954–71 period.

Wt*=0.04(0.06)+1.31(3.08)UW5t+0.91(11.27)Pt*+2.21(2.90)DIC1(25)2.65(3.84)DIC20.90(1.81)DIC3+1.43(2.42)DIC41.68(2.50)DIC51.38(2.84)DIC6R2¯=0.79SEE=1.26DW=0.97Period=1954:I1971:IV
Pt*=0.56(1.71)+0.63(14.17)W*t+0.13(3.63)Qt*+0.13(4.67)PM*t3(26)1.10(2.22)DIC1+2.07(4.24)DIC20.15(0.45)DIC3+1.16(2.92)DIC4+0.64(1.33)DIC5+0.26(0.76)DIC6R2¯=0.84SEE=0.87DW=1.29Period=1954:I1971:IV

A casual examination of the two price equations (24) and (26) suggests that there have been no fundamental changes in price behavior between the two periods 1954–67 and 1954–71; the coefficient on W*has increased somewhat in equation (26), but the other coefficients are quite similar. This finding was confirmed when equation (26) was re-estimated with the addition of both a shift dummy variable for the 1967:III–1971:IV period and a slope dummy variable (also for the 1967:III–1971:IV period) on each of the explanatory variables.41 That is, none of the dummy variables for the 1967:III–1971: IV period was significantly different from zero at the 5 per cent level of confidence, and the F statistic for the whole set of dummy variables was 1.2, which is below statistical significance at the 5 per cent level of confidence.42

Turning to the wage equation, however, there is a completely different picture. A comparison of wage equations (23) and (25) reveals many substantial changes and vividly illustrates the instability of estimated Phillips-type equations.43 The principal changes in equation (25) vis-à-vis equation (23) are as follows: (1) the explanatory power of the wage equation has deteriorated—note that the SEE of equation (25) is nearly twice as large as that for equation (23)—1.26 versus 0.70; (2) the unemployment rate is quite well-determined in equation (25), but it appears with the wrong (positive) sign, suggesting a positively sloped Phillips curve; 44 (3) the coefficient on P*t in the wage equation, which was 0.16 and insignificant in equation (23), has increased to 0.91 and is now very significant, suggesting almost a complete absence of money illusion; (4) the product of the coefficients on P*andW* (α2 β1) has increased from 0.08 in equations (23) and (24) to 0.57 in equations (25) and (26). Thus, while the wage-price spiral is still stable (non- explosive), the implied wage-price response to exchange rate changes or other exogenous disturbances is now much more substantial; (5) the incomes policy dummies in equation (25) are all significant, except for DIC3, and all but DIC 1 suggest a restraining or anti-inflationary influence on wages. It should also be mentioned that the above conclusions are not altered very much if equations (25) and (26) are estimated by two-stage least-squares instead of ordinary least-squares. The chief changes in the two-stage least-squares estimates are that the coefficient on W* in the price equation rises to 0.73 (versus 0.63 with ordinary least-squares) and that the coefficient on P* in the wage equation falls to 0.68 (versus 0.91 with ordinary least-squares). The product of the coefficients on W* andP* in the two-stage least-squares equations is then 0.73 X 0.68 = 0.50 (versus 0.57 with ordinary least-squares).

The substantial differences in the wage equations between 1954–67 and 1954–71 suggest that a structural shift has taken place during the period from 1967:III to 1971: IV. This suggestion is substantiated when the wage equation is re-estimated for 1954–71 with the addition of a shift dummy (DUM6771) for 1967:III–1971:IV. The estimated equation was

Wt*=4.98(4.96)1.29(2.39)UW5t+0.51(5.65)Pt*+5.98(6.19)DUM6771(27)2.09(3.45)DIC11.76(3.12)DIC2+0.53(1.17)DIC30.74(1.53)DIC41.25(2.31)DIC54.49(7.09)DIC6R2¯=0.87SEE=1.00DW=1.09Period=1954:I1971:IV

An examination of equation (27) reveals that the shift dummy (DUM611X) is highly significant, and its coefficient suggests that annual wage changes over the 1967–71 period were almost six percentage points higher than would otherwise have been expected.45 Also note that when the shift dummy is included in the equation, the unemployment rate regains its expected negative sign, the coefficient on P*t falls to about 0.5, the SEE falls to 1.00, and the coefficients on the incomes policy dummies (especially on DIC6) change quite markedly. Further, observe that using wage equation (27) and price equation (26), the product of the coefficients on W* andP* is 0.63 X 0.51 = 0.32. It should also be mentioned that the wage equation (27) was reestimated with the addition of a slope dummy variable (DUM6771) on both UW5t and P*t to determine whether the slopes of the W*P* andW*UM5t relationships increased in the period 1967:III–1971: IV.46 In brief, the equation revealed that the slope dummy on UW5t was positive and significant, that the slope dummy on P*t was positive but insignificant, and that the shift (intercept) dummy (DUM6771) was negative and insignificant.47 In addition, the explanatory power of the wage equation with the slope dummies on UW5t and P* is higher than that of the wage equation without them (R¯2=0.90 versusR¯2=0.88).48 On the other hand, multicollinearity is a more serious problem in the wage equation with the slope dummies, and this makes the equation less appropriate for obtaining an estimate of the wage response to price changes and for performing tests of other hypotheses where additional variables need to be added to the equation. Thus, equation (27), which excludes the slope dummies, is used in the remainder of this section.

the effects of large and small price and wage changes

Just as large and small import price changes could have different proportionate effects on retail price changes, so too could this large- small distinction be important for estimating both the effect of price changes on wage changes and the effect of wage changes on price changes. In fact, there is some empirical evidence for the United States, supplied by Hamermesh (1970) and Eckstein and Brinner (1972), that the wage response to price changes (cost of living changes) is much greater for large price changes than for small price changes—that is, wage bargains are struck more in real terms when inflation is high than when it is low. No similar evidence is available for the effect of large and small wage changes on price changes. If there is a threshold effect (a nonlinearity) in either the wage response to price changes or in the price response to wage changes, then the previously reported wage and price equations will give a misleading estimate of the induced wage and price response to a devaluation in cases where the devaluation pushes prices and/or wages past the threshold.

In order to test for a differential effect of large and small price changes on W*, the following test procedure was adopted. The price change series (P*t) was first split into two parts—all observations where P*t was greater than 4 per cent, and all observations where P* was less than or equal to 4 per cent. The variable for all changes (P*t) and the variable for large price changes only (P*tL) were then entered into the wage equation as separate regressors. If large changes in prices have a greater proportionate effect on W* than do small changes, then the estimated coefficient on P*tL should be positive and significantly different from zero. The same procedure was used to test for a differential effect of large and small wage changes on P*, but in this case the dividing line between large and small wage changes was 5 per cent. The two estimated equations are reported below, where P*tL refers to large price changes and W*tL refers to large wage changes.

Wt*=4.56(4.14)1.14(2.04)UW5t+0.64(3.93)Pt*0.11(0.96)P*t.L(28)+5.84(5.95)DUM6771+2.15(3.53)DIC11.68(2.91)DIC2+0.37(0.76)DIC30.70(1.44)DIC41.49(2.50)DIC54.43(6.69)DIC6R2¯=0.87SEE=1.00DW=1.12Period=1954:I1971:IV
Pt*=0.63(1.42)+0.61(5.41)W*t+0.02(0.24)Wt.*L0.13(3.60)Q*t(29)+0.12(4.21)PM*131.13(2.20)DIC1+2.08(4.20)DIC20.13(0.35)DIC3+1.18(2.90)DIC4+0.66(1.34)DIC5+0.25(0.70)DIC6R2¯=0.84SEE=0.88DW=1.29Period=1954:I1971:IV

Inspection of equations (28) and (29) reveals that there is no significant difference between the proportionate effect of large and small price changes on W*, and similarly between the effects of large and small wage changes on P*. In both cases, the estimated coefficient on the large wage or price variable is not significantly different from zero at even the 25 per cent level of confidence. The wage equation was also estimated using a large/small dividing line on P* of 3 per cent, but the results were similar to those in equation (28). Thus, the results suggest that the earlier estimates of the wage response to price changes and of the price response to wage changes are not likely to produce misleading estimates of the effect of import price changes on wages and prices because of threshold effects.

wage behavior and expected price changes

Recall that the variable P*t enters the wage equation as a proxy for expected price changes (that is, Pe*t=P*t). It must be recognized, however, that very little is known about how people actually form their price expectations. In view of this gap in knowledge, it seems worthwhile to consider a few alternative hypotheses about price expectations for the wage equation. To illustrate why the formation of price expectations is important for the subject of this paper, consider the following two alternative hypotheses about price expectations: (1) Pe*t=P*t, expected price changes in period t equal actual price changes in period t; and (2) Pe*t=Σi=0nλiP*ti where Σ λi = 1, expected price changes in period t are equal to some weighted average of actual price changes in period t and in earlier periods, where λi is the weight for period ti and where the weights sum to one. Also, assume that wage changes are a function of the unemployment rate and expected price changes, W*t=f(U,Pe*t) and for the moment ignore any feedbacks from W*ttoPe*t. Now suppose that it is desired to determine the effect of an exchange rate change on W*t, given that the exchange rate change leads to some change in prices through the PM*R*andP*PM* relationships. According to the first hypothesis, the exchange rate change will affect W*t only in the current period since Pe*t=P*t According to the second hypothesis, however, the exchange rate change will affect W* in period t and in some future periods since Pe*t depends not only on P*t but also on P*ti—that is, the second hypothesis implies that an exchange rate change will have a distributed lag effect on wages, even ignoring induced wage-price feedbacks. If, for example, the weights in the lag distribution for Pe*t took the form of an inverted V, then one would expect, ceteris paribus, the wage response following a devaluation to rise steadily until a peak response is achieved after x quarters, and thereafter to decline steadily. In such a case, it would also be true that the earlier estimates of the wage response to price changes in this paper would be misleading since only P*t was included in Pe*t.

Since these earlier results have been based on the hypothesis Pe*t=P*t, it is desirable to proceed to some empirical tests of a few alternative expectations hypotheses. Three forms of the hypothesis that expected price changes are a function of past price changes were considered.49

Pe*t=P*t+u(P*tP*t1)(a)
Pe*t=Pe*t1+γ(P*tPe*t1)(b)
Pe*t=Σi=02λiP*t1withΣλi=1(c)

Hypothesis (a) is the extrapolative hypothesis, whereby expected inflation equals the current inflation rate plus a correction factor (w) for the trend in the inflation rate over the past period. If u > 0, the forecaster expects the trend to continue, whereas if u < 0, he expects the past trend to reverse itself. If u = 0, hypothesis (a) reduces to the static expectations hypothesis (Pe*t=P*t). Hypothesis (b) is the adaptive expectations hypothesis, whereby the forecast for the past period is corrected by some fraction γ (0 < γ < 1)of the past forecast period’s error. Hypothesis (c) is a more general expectation scheme, whereby expected inflation (in period t) is equal to some weighted average of actual inflation in period t and in periods t— 1 and t—2, and whereby λi is the weight for period t – i. Substitution of hypotheses (a), (b), and (c) in the wage equation, W*t=α0+α1Ut+α2Pe*t, gives the following three estimating equations for W* (with only observable variables):

Extrapolative price expectations

W*t=α0+α1Ut+α2P*t+α2u(P*tP*t1)(30)

Adaptive price expectations

W*t=α0γ+α1Utα1(1γ)Ut1+α2γP*t+(1γ)W*t1(31)

Distributed lag price expectations

W*t=α0+α1Ut+α2Σi=02P*ti(32)

As Turnovsky (1972) has pointed out, one noteworthy feature of equation (31) is that the estimates of the coefficients on Ut, Ut-1, and W*t1—say b1, b2, and b3—must satisfy the constraint b1 . b3 + b2 = 0, and this constraint can be employed as a test of the adaptive expectations model. This constraint is necessary because an estimating equation identical to equation (31) can be generated by a quite different model based on adjustment costs rather than on expectations.50

Equations (30), (31), and (32) were estimated over the period 1954–71 with and without incomes policy dummies, and with and without the shift dummy (DC/M6771) for the 1967:III–1971:IV period. The equations reported below are the best equations for each hypothesis in terms of R¯2

Wt*=4.99(4.92)1.28(2.36)UW5t+0.51(5.28)Pt*+0.01(0.07)(P*tP*t1)(33)+5.99(6.13)DUM6771+2.10(3.27)DIC11.76(3.09)DIC2+0.54(1.16)DIC30.73(1.46)DIC41.24(2.25)DIC54.49(7.01)DIC6R2¯=0.86SEE=1.01DW=1.09Period=1954:I1971:IV
Wt*=3.68(4.77)2.01(2.13)UW5t+0.68(0.74)UW5t1+0.001(0.012)P*t(34)+0.64(7.35)W*t1+4.79(6.55)DUM6771+0.99(2.09)DIC10.34(0.74)DIC2+0.77(2.27)DIC3+0.04(0.10)DIC40.65(1.53)DIC53.01(5.92)DIC6R2¯=0.93SEE=0.74DW=1.74Period=1954:I1971:IV
Wt*=5.04(4.92)1.29(2.36)UW5t+0.51(3.69)P*t+0.04(0.25)P*t10.07(0.50)P*t2(35)+6.05(6.11)DUM6771+2.15(3.29)DIC11.78(3.08)DIC2+0.56(1.20)DIC30.69(1.36)DIC41.21(2.16)DIC54.51(6.98)DIC6R2¯=0.86SEE=1.01DW=1.10Period=1954:I1971:IV

Inspection of equations (33) and (35) reveals that neither the extrapolative hypothesis nor the distributed lag hypothesis performs very well. In the extrapolative hypothesis, the coefficient on the term representing the trend rate of inflation (P*tP*t1) is insignificantly different from zero, and the other coefficients are practically identical to those in the wage equation (27) where Pe*t was assumed to be equal to P*t. The same conclusion holds for the distributed lag hypothesis represented in equation (35)—the coefficients on P*t1andP*t2 are insignificant, and the other coefficients are practically identical with those in wage equation (27). Turning to the adaptive expectations hypothesis, represented in equation (34), the picture is more mixed. On the plus side, equation (34) has higher explanatory power than any of the other wage equations previously tested, all of the coefficients carry the expected signs, and the estimated adaptive coefficient (γ) is significant and of a size (0.36) consistent with the findings of other researchers (Parkin, 1970, and Ashenfelter and Pencavel, 1974). On the minus side, the coefficient on P*t is very insignificant. Examination of the variance-covariance matrix of equation (34) suggests that there is high collinearity between P*t and the lagged wage variable (W*t1), and this may have contributed to the insignificance of P*t. Since the wage-response to expected price changes is one of the crucial parameters for this study, the insignificance of P*t in equation (34) precludes any reliance on the results of equation (34). In short, it seems reasonable to conclude that none of the above expectations hypotheses is superior to Pe*t=P*t, at least with respect to identifying the wage response to price changes.

wage behavior after the 1967 devaluation

In Section II, several tests were conducted to determine whether there were any significant changes in price behavior in the period following the 1967 devaluation of sterling. It now seems appropriate to conduct a similar series of tests on the wage equation.

One argument sometimes made with respect to devaluations and wage behavior is that the announcement of a devaluation creates such an inflationary psychology in the economy that wage earners will press for and secure wage increases (larger than those that would otherwise be expected) even before the devaluation affects wages through its effect on import and retail prices.51 In order to test for such an “announcement effect” on wages, the wage equation was estimated for the period 1954–71 with a shift dummy included for the one-year period 1968:1—1968:IV following the 1967 devaluation. The estimated equation is given below, where DUM68 is the shift dummy for the announcement effect and DUM6771 is again the shift dummy for the whole 1967:III–1971:IV period.

Wt*=5.19(5.32)1.38(2.65)UW5t+0.49(5.64)P*t+1.45(2.32)DUM68(36)+6.18(6.58)DUM6771+2.08(3.55)DIC11.74(3.17)DIC2+0.58(1.31)DIC30.72(1.54)DIC41.24(2.37)DIC55.16(7.62)DIC6R2¯=0.87SEE=0.96DW=1.16Period=1954:I1971:IV

equation (36) reveals that the announcement dummy (DUM68) is significantly different from zero at the 5 per cent level of confidence, and it carries the expected positive sign.52 More specifically, equation (36) suggests that annual wage changes were 1.4 percentage points higher in the year after the 1967 devaluation than would otherwise have been expected (even after accounting for the upward shift in the wage equation over the 1967–71 period).53 Thus, while the upward shift in the wage equation in 1968 cannot be unambiguously identified with devaluation, the results are not inconsistent with the hypothesis that the devaluation was associated with an inflationary announcement effect on wages.54

A second way in which the 1967 devaluation could have conceivably affected wage behavior would be by changing the wage response to price changes. If, for example, the 1967 devaluation created an inflationary atmosphere under which wage earners became more aware of price changes and reflected this increased awareness by bargaining more than before in real terms, then one would expect, ceteris paribus, the wage response to price changes to have been higher in the year following the devaluation than in other periods. Unfortunately, however, it is very difficult to obtain a reliable estimate of the effect of the 1967 devaluation on the W*P* relationship for at least two reasons. First, the one- year period (1968:I–1968:IV) following the devaluation is also a period of incomes policy, and there is some evidence that the wage response to price changes is lower during periods of incomes policy than during other periods.55 As mentioned previously in Section II, this coincidence of incomes policy and devaluation would cause downward bias in the estimated effect of the devaluation on the W*P* relationship. Second, when a slope dummy (for 1968:I–1968:IV) on price changes was included in the estimating equation, it was discovered that both the sign and significance of the slope dummy were very sensitive to the specification of the wage equation. For example, the slope dummy on P*t appeared with a negative sign when the announcement dummy was included in the equation but appeared with a positive sign when the announcement dummy was excluded from the wage equation. In short, statistical problems were judged to be too pervasive to reach a conclusion about the effect of the devaluation on the slope of the W*P* relationship.

conclusions about the interrelationship between W* ANDP*

The general findings of this section on the interrelationship between wage changes and price changes can be briefly summarized as follows:

  • (1) The product of coefficients on P*andW* in the wage and price equations is always less than one (suggesting a damped wage-price spiral), regardless of the estimation period or estimation method chosen.

  • (2) For the 1954–71 period as a whole, the wage response to price changes was about 0.5, and the price response to wage changes was about 0.6—yielding an estimate of about 0.3 for the quantity (α2β1).

  • (3) Estimates of the wage response to price changes are, however, very unstable, with the estimate for 1954-67 being much smaller than that for 1954–71.

  • (4) For 1954–71, the product of the coefficients on W* andP* obtained from two-stage least-squares estimation is slightly lower than the product obtained from ordinary least-squares estimation.

  • (5) There is evidence of a significant upward shift in the wage equation, but not in the price equation, over the period 1967–71.

  • (6) No empirical support was found for the twin hypotheses that large price changes have a different proportionate effect on wage changes than do small price changes, or that large wage changes have a different proportionate effect on price changes than do small wage changes.

  • (7) The static price expectations hypothesis (Pe*t=P*t) seems to perform as well as or better than the extrapolative, distributed lag, or adaptive expectations hypotheses in the wage equation.

  • (8) There was an upward shift in the wage equation in 1968 that may have reflected an inflationary announcement effect of the 1967 devaluation.

IV. Conclusions of the Study

It has been shown in this paper how a simple, two-equation wage-price model can be used to estimate the effect of an exchange rate change on a country’s wages and domestic prices. More specifically, it has been demonstrated that, under certain assumptions, the effect of an exchange rate change on the change in domestic prices can be calculated from knowledge of four basic parameters: (1) the effect of the exchange rate change on the change in import prices in local currency (K); (2) the short-run effect of the change in import prices on the change in domestic prices (β3); (3) the effect of a change in domestic prices on the change in money wages (α2); and (4) the effect of a change in money wages on the change in domestic prices (β1). In Sections II and III of this paper, estimates of the latter three parameters (β3,α2 and β1) were obtained for the United Kingdom from wage and price equations estimated for the period 1954–71. In brief, the estimates suggested that β3 = 0.13, α2 = 0.51, and β1 =0.63.56 Given these three estimates and given the assumption that K might be approximately equal to 0.8 for a U.K. exchange rate change, one can proceed to calculate the likely effect of a change in the exchange rate on domestic prices, competitive price advantage, and real wages in the United Kingdom.

Suppose the United Kingdom devalues its exchange rate by 10 percent (R* = 0.10), and assume both that other countries do not change their exchange rates and that exporters to the United Kingdom do not change their dollar supply prices. The effect of the 10 per cent devaluation on U.K. retail prices can be obtained from equation (10):

P*R=β3(1α2β1)K(10)
ΔP*=β3KΔR*(1α2β1)=(0.13)(0.8)(0.10)[1(0.51)(0.63)]=0.015(10)

That is, a 10 per cent devaluation will lead to approximately a 1.5 percent increase in U.K. retail prices. In addition, given our estimated lag on PM* of three quarters and given the values of α2 and β1, the implied time lag between the devaluation and the final 1.5 per cent increase in retail prices would be about two years (seven to eight quarters).

An estimate of the proportion of the initial price advantage achieved by devaluation that would remain after domestic price adjustments to the devaluation have been completed can be obtained from equation (11):

PM*R*P*R*PM*R*=[1β3(1α2β1)]=1(0.13)(0.68)=0.81(11)

That is, 81 per cent of the initial competitive price advantage achieved by devaluation will be retained. The 81 per cent figure reflects an increase in import prices of 8 per cent and an increase in retail prices of 1.5 per cent due to the 10 per cent devaluation.

Finally, the effect of the devaluation on real wages is obtained from equation (15):

W*R*P*R*=Kβ31α2β1(α21)(15)
Δ(W*P*)=Kβ3(1α2β1)(α21)ΔR*=0.0075(15)

That is, the 10 per cent devaluation will lead to a decrease in real wages of 0.75 per cent. The 0.75 per cent figure reflects an increase in prices of 1.5 per cent and an increase in money wages of 0.75 per cent.

In interpreting the above results, it should be noted that the values used for β3,α2 and β1 were the estimates for the period 1954–71 as a whole. The estimated wage and price equations of Sections II and III suggest, however, that β3,α2 and β1 were probably higher for 1967–71 than for 1954–71 as a whole.57 In fact, using wage equation (27b) and price equation (26a), one obtains the following values for β3,α2 and β1 for the period 1967–71: β3 = 0.19, α2 = 0.56, and β1 = 0.76.58 Inserting these values into equations (10’), (11), and (15’), again assuming that K = 0.8, yields the following solutions: (1) a 10 per cent devaluation leads to a 2.7 per cent increase in U.K. retail prices (versus 1.5 per cent with old values); (2) 67 per cent of the initial price advantage achieved by devaluation will be retained (versus 81 per cent with the old values);59 and (3) a 10 per cent devaluation will lead to a decrease in real wages of 1.2 per cent (versus a decrease of 0.75 per cent with the old values)—which reflects an increase in prices of 2.7 per cent and an increase in money wages of 1.5 per cent. Thus, the wage-price experience of the period 1967–71 implies a larger domestic price adjustment to exchange rate changes and, hence, a relatively less effective role for devaluation in improving the United Kingdom’s competitive price position.

Finally, this paper has raised the issue of whether wage and price behavior after an exchange rate change is likely to be different from that during other periods. In other words, are the coefficients β3,α2 and β1 (as well as the other coefficients in the wage and price equations) affected by an exchange rate change? On balance, the tests described in Sections II and III of this paper suggest that there were no significant changes in price behavior after the 1967 devaluation but that there were some important changes in wage behavior. Unfortunately, however, it is not possible to relate these changes directly to the devaluation because other factors and policies were operating on wages and prices at the same time.

APPENDIX

Data Definitions and Sources

Wages (W): W is an index of basic weekly wage rates of all manual workers in all industries in services in the United Kingdom. The data from 1953 to 1968 are from Table 13, British Labour Statistics: Historical Abstract 1886–1968 (Her Majesty’s Stationery Office, London, 1971). The data for 1969–71 are from Economic Trends (various issues) and the Monthly Digest of Statistics (various issues). The quarterly figures are averages of monthly data.

Unemployment rate for wholly unemployed persons (UW): UW is the unemployment rate for wholly unemployed persons including those leaving school in the United Kingdom. The data for 1953 to 1968 are from Table 165 in British Labour Statistics, while the data for 1969–71 are from Economic Trends (June 1972) and from the Department of Employment Gazette (various issues). The quarterly figures are averages of monthly data.

Retail prices (P): P is an index of retail prices (all items) for the United Kingdom. The data from 1953 to 1968 are from Tables 91, 95, and 96 in British Labour Statistics, while the data for 1969–71 are from Economic Trends (June 1972). The quarterly figures are averages of monthly data.

Industrial production (IP): IP is the index of industral production (for all index-of-production industries, not just manufacturing) for Great Britain. The data are from the Monthly Digest of Statistics (various issues). The quarterly figures are averages of monthly data.

Employment in index of production industries (EMP): EMP is an index of employees in employment in index of production industries for Great Britain. The data for 1953 to 1968 are from Table 140 in British Labour Statistics, while the data for 1969–71 are from the Department of Employment Gazette (September 1972). The quarterly figures are averages of monthly data.

Output per employee (Q): Q is the variable used in the price equation, and it is defined as IP/EMP.

Import prices (PM): PM is the unit value index of import prices in sterling for the United Kingdom. The data are from the Monthly Digest of Statistics (various issues) and Economic Trends (June 1972). The quarterly figures are averages of monthly data.

All other variables used in the wage and price equations are defined in the text.

REFERENCES

  • Artis, Michael, “Some Aspects of the Present Inflation and the National Institute Model,” in The Current Inflation, ed. by Harry G. Johnson and A. R. Nobay (London, 1971), pp. 337.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ashenfelter, Orley, and John Pencavel, “A Note on Estimating the Determinants of Changes in Wages and Earnings,” Working Paper No. 46, Industrial Relations Section, Princeton University, April 1974.

    • Search Google Scholar
    • Export Citation
  • Ball, R. J., “Inflation and the London Business School Model,” in The Current Inflation, ed. by Harry G. Johnson and A. R. Nobay (London, 1971), pp. 4351.

    • Search Google Scholar
    • Export Citation
  • Barker, Terence S., “Devaluation and the Rise in U.K. Prices,” Bulletin of the Oxford University Institute of Economics and Statistics, Vol. 30 (May 1968), pp. 12941.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Barker, Terence S., and J. R. C. Lecomber, “The Import Content of Final Expenditures for the United Kingdom 1954–1972,” Bulletin of the Oxford University Institute of Economics and Statistics, Vol. 32 (February 1970), pp. 117.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Black, S. W., and H. H. Kelejian, “The Formulation of the Dependent Variable in the Wage Equation,” Review of Economic Studies, Vol. 39 (January 1972), pp. 5559.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Branson, William H., “The Trade Effects of the 1971 Currency Realignments,” Brookings Papers on Economic Activity, No. 1, 1972, pp. 1558.

  • Burrows, Paul, and Theodore Hitiris, “Estimating the Impact of Incomes Policy,” in Incomes Policy and Inflation, ed. by Michael Parkin and Michael T. Sumner (Manchester University Press, 1972), pp. 15162.

    • Search Google Scholar
    • Export Citation
  • Clark, Peter Barton, “The Effects of Recent Exchange Rate Changes on the U.S. Trade Balance” (unpublished, Board of Governors of the Federal Reserve System, 1974).

    • Search Google Scholar
    • Export Citation
  • Cooper, Richard N., “The Balance of Payments,” in Britain’s Economic Prospects, ed. by Richard E. Caves and Associates, The Brookings Institution (Washington, 1968), pp. 14797.

    • Search Google Scholar
    • Export Citation
  • Economist, “Cripp’s Ghost,” Economist, Vol. 245 (October 28-November 3, 1972), p. 78.

  • Eckstein, Otto, and Roger Brinner, “The Inflation Process in the United States” (A study prepared for the use of the Joint Economic Committee, 92nd Cong., 2nd Sess., Washington, 1972).

    • Search Google Scholar
    • Export Citation
  • Friedman, Milton, “The Role of Monetary Policy,” American Economic Review, Vol. 58 (March 1968), pp. 117.

  • Godfrey, Leslie, and Jim Taylor, “Earnings Changes in the United Kingdom 1954-70: Excess Labour Supply, Expected Inflation and Union Influence,” Bulletin of the Oxford University Institute of Economics and Statistics, Vol. 35 (August 1973), pp. 197216.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goldstein, Morris, “The Trade-Off Between Inflation and Unemployment: A Survey of the Econometric Evidence for Selected Countries,” Staff Papers, Vol. 19 (November 1972), pp. 64798.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hamermesh, Daniel S., “Wage Bargains, Threshold Effects, and the Phillips Curve,” Quarterly Journal of Economics, Vol. 84 (August 1970), pp. 50117.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Johnson, Harry G., “The Monetary Approach to Balance of Payments Theory,” in his book, Further Essays in Monetary Economics (Harvard University Press, 1973), pp. 22949.

    • Search Google Scholar
    • Export Citation
  • Hamermesh, Daniel S., and A. R. Nobay, editors, The Current Inflation (London, 1971).

  • Kindleberger, Charles P., International Economics (Homewood, Illinois, 1963).

  • Kwack, Sung Y., “The Effects of Foreign Inflation on Domestic Prices and the Relative Price Advantage of Exchange Rate Changes,” Discussion Paper No. 35, Division of International Finance, Board of Governors of the Federal Reserve System (November 1973).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lipsey, R. G., and J. M. Parkin, “Incomes Policy: A Re-Appraisal,” Economica, Vol. 37 (May 1970), pp. 11538.

  • National Institute of Economic and Social Research, “The Economic Situation: Annual Review,” National Institute Economic Review, No. 47 (February 1969), pp. 384.

    • Search Google Scholar
    • Export Citation
  • Orcutt, Guy H., “Measurement of Price Elasticities in International Trade,” Review of Economics and Statistics, Vol. 32 (May 1950), pp. 11732.

  • Parkin, Michael, “Incomes Policy: Some Further Results on the Determination of the Rate of Change of Money Wages,” Economica, Vol. 37 (November 1970), pp. 386401.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Parkin, Michael, and Michael T. Sumner, Incomes Policy and Inflation (Manchester University Press, 1972).

  • Phelps, Edmund S., “Money-Wage Dynamics and Labor-Market Equilibrium,” Journal of Political Economy, Vol. 76, Pt. 2 (July/August 1968), pp. 678711.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Rowley, J. C. R., and D. A., Wilton, “Quarterly Models of Wage Determination: Some New Efficient Estimates,” American Economic Review, Vol 63 (June 1973), pp. 38089.

    • Search Google Scholar
    • Export Citation
  • Salop, J., “Devaluation, Employment, and the Balance of Trade” (unpublished, Board of Governors of the Federal Reserve System, November 1972).

    • Search Google Scholar
    • Export Citation
  • Schultze, Charles L., “Recent Inflation in the United States,” Study Paper No. 1, in Study of Employment, Growth, and Price Levels (Joint Economic Committee, 86th Cong., 1st Sess., Washington, 1959).

    • Search Google Scholar
    • Export Citation
  • Smith, David C., “Incomes Policy,” in Britain’s Economic Prospects, ed. by Richard E. Caves and Associates, The Brookings Institution (Washington, 1968), pp. 10444.

    • Search Google Scholar
    • Export Citation
  • Solow, Robert M., Price Expectations and the Behavior of the Price Level; lectures given in the University of Manchester (Manchester University Press, 1969).

    • Search Google Scholar
    • Export Citation
  • Turnovsky, Stephen J., “The Expectations Hypothesis and the Aggregate Wage Equation: Some Empirical Evidence for Canada,” Economica, Vol. 39 (February 1972), pp. 117.

    • Crossref
    • Search Google Scholar
    • Export Citation
*

Mr. Goldstein, an economist in 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 his colleagues in the Research Department, the author wishes to express his appreciation to Orley Ashenfelter, George Johnson, Hugh Pitcher, and Robert S. Smith for helpful comments on an earlier draft of this paper. A previous draft of the paper was presented at the winter meetings of the Econometric Society, held in New York, December 1973.

1

For an empirical analysis of the effect of the 1967 devaluation on U.K. import prices, see Barker (1968).

2

See Ball (1971) for an export price equation for the United Kingdom.

3

A theoretical treatment of the effect of exchange rate changes on the supply and demand for factors of production and commodities is presented in Salop (1972). Also see Johnson (1972) for the effect of exchange rate changes on the demand for money.

4

In some wage equations, the change in the proportion of the labor force that is unionized is entered as an additional explanatory variable as a proxy for trade union aggressiveness; see Goldstein (1972) for a review of wage inflation models that use this variable. The unionization rate could not be used in this study because quarterly data on the proportion of the labor force unionized are not available.

5

Unexpected price changes are assumed to affect wage changes through the excess demand for labor (by means of the unemployment rate)—that is, an unexpected price increase lowers the real wage which, in turn, affects both the supply and demand for labor; see Friedman (1968).

6

For a review of this evidence, see Goldstein (1972, pp. 668–73).

7
It should be noted that equation (5) can be rewritten with only U and a constant on the right-hand side as
P*=c+β1α1U(1α2β1)
whereC=(β0+β1α0+β2Q*¯+β3PM*¯(1α2β1))and whereQ*¯and
PM*¯ are the average values of Q* andPM* in the regression. In this way, the trade off between P* and U can be calculated, given the values of the coefficients and the values of PM*¯andQ*¯. Observe also that positive import price changes (PM*) worsen the trade-off between P* and U because β3 > 0, that is, the larger is PM* the larger is P* at any given value of U.
8

Branson (1972, pp. 15–58) has shown that K=(1dmsm)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 ≤ ∞. Note also that equation (6) is written under the assumption that R* and PF* shift the supply curve for U. K. imports by the same degree.

9

In 1967, the United Kingdom devalued the pound sterling by 16.7 per cent in terms of pounds sterling per U. S. dollar (the relevant exchange rate measure for equation (6)) or by 14.3 per cent in terms of U. S. dollars per pound sterling (the more familiar exchange rate measure). If K = 1 and PF* = 0 in equation (6), then the sterling price of imports should have risen by 16.7 per cent. However, over the one-year period 1967:III to 1968:III, PM* rose by about 13 per cent, which (assuming that PF* = 0) suggests a value of 0.78 for K. Recent estimates of K for the United States by Branson (1972) and Clark (1973) also fall in the range of 0.6 and 0.8.

10

Note that equation (9) simply gives the coefficient on PM* from the reduced form price equation (5).

11

It should be clear from the preceding analysis that one can estimate the long-run effect of PM* onP* either by estimating the reduced form price equation (5) or by estimating the structural wage and price equations (1) and (2) and solving for the long-run coefficient on PM* The latter method has been used in this study because it provides estimates of all three relevant parameters (β3, α2, and β1) and because knowledge of each of these parameters is useful in determining the cause of shifts over time in the effect of PM* onP*. It should also be noted that since the wage equation (1) is overidentified it will not be possible to obtain estimates of the structural parameters (β3, α2, and β1) from the estimated coefficient on PM* in the reduced form equation (5) alone.

12

It is also possible that a devaluation could worsen a country’s competitive price advantage (and equation 11 would then be negative). This would occur if (β31α2β1) is greater than one. In practice, however, this is not a likely result for the United Kingdom because the estimates of β3, α2, and β1 made in this study, as well as the estimates made in previous U.K. studies, strongly suggest that (β31α2β1) is substantially less than one.

13

The reduction in the real wage by 1 per cent in the above example reflects an increase in retail prices by 2 per cent and an increase in money wages by 1 per cent.

14

For a list of the policy measures adopted in the year following the 1967 devaluation, see National Institute of Economic and Social Research (1969, p. 5).

15

It should be noted, however, that an analysis of wage and price behavior after the 1949 devaluation of sterling would encounter many of the same problems facing this paper because the 1948:III–1950:III period was also a period of incomes policy. In order to obtain enough observations to test the above hypothesis adequately, it would probably be necessary to study exchange rate changes for many countries.

16

In view of (1) the difficulties associated with obtaining a reliable quarterly index of effective indirect tax rates, and (2) the finding by Lipsey and Parkin (1970) and Solow (1972) that indirect taxes did not have a significant effect on U. K. price changes, indirect taxes were not included in the price change regressions of this study. After this study was virtually completed, however, the author discovered a recent paper by Burrows and Hitiris (1972) that does find a significant effect for indirect tax changes on U. K. retail price changes, at least for the 1955–67 period. Clearly, additional empirical work on the effect of indirect taxes on U.K. prices is called for to determine the appropriate specification of the price equation.

17

For an application of the input-output method to estimating the effect of PM* onP* after the 1967 devaluation, see Barker (1968). In brief, Barker estimated that the 1967 devaluation would lead to a 13.9 per cent increase in sterling import prices and to a 2.8 per cent increase in the price of consumption expenditures.

18

The correlation is spurious only in the statistical sense that part of the dependent variable and part of the PM* variable are identical and this will cause the correlation between P*andPM* to be higher than it would be if the P*andPM* series did not overlap. It does not mean that the direct import content of consumption should be ignored in estimating the effect of PM*onP* when the P* variable includes some finished imported goods.

19

The distributed lags tried for PM* were unrestricted.

20

Whether or not a decrease in the lag between PM*andP* would increase inflationary pressures in the economy depends in large part on the cyclical position of the economy at the time the effect materializes. In addition, in the steady state, the length of the lag is immaterial for P*, as only the size of the coefficient on PM* is of concern.

21

Of course, there could be other factors responsible for the decrease in the lag between PM*andP* in the 1967–71 period. To mention just one possibility, any change in the composition of imports away from raw materials and toward finished goods would decrease the lag between PM*andP* quite apart from any change in pricing behavior.

22

Recall from equation (4) that the coefficient on PM* in the structural price equation should be equal to [(1+F)(1B)]PMTPwherePMTP is the share of imports in final price, F is the ratio of unmeasured costs to measured costs, and B is the mark-up percentage. If both F and B are small, then [(1+F)(1B)]PMTPPMTP.

23

The average import content of consumption expenditure was 19.2 per cent in 1954, and the estimated figure for 1972 is 15.2 per cent (see Barker and Lecomber, 1970, p. 7). The average import content of consumption is used in the above analysis as a proxy for the share of imports in the retail price index because estimates of the latter are, to the author’s knowledge, unavailable.

24

t= 1.40 < t0.05 = 2.000.

25

Smith (1968) also used half-yearly data to estimate some price equations.

In these equations, the coefficient on PM*t1 was about 0.13, which is identical to the coefficient on PM*t3 in equation (16) above.

26

The results without the incomes policy dummies were nearly identical, except that the Durbin-Watson statistic was lower.

27

When the slope dummy on wages was included in the price equation without the slope dummy on import prices present, the coefficient on DV - W*t was positive but quite insignificant.

28

Lipsey and Parkin (1970) estimated separate price equations for periods of incomes policy, periods of no incomes policy, and for the 1948–68 period as a whole. The estimated coefficient on PM* was about 0.07 in the price equation for periods of no incomes policy, 0.001 in the price equation for periods of incomes policy, and 0.08 in the price equation for the whole period. Similarly, the effect of W*onP* was substantially lower in the price equation for periods of incomes policy than in either the price equation for periods of no incomes policy or the price equation for the whole period. It should be noted, however, that Lipsey and Parkin’s empirical results have recently been challenged on many grounds (see the papers in Parkin and Sumner, 1972), so that the effect of incomes policy on the P*PM* relationship should be regarded as essentially an open question.

29
More formally, one can express the bias that results from omitting the effect of incomes policy on the P*PM* relationship from the equation as
E(b^1b2)=b2cDIC6,DEV(a)
where b^1 is the estimated effect of the 1967 devaluation on the P*PM* relationship, b1 is the true effect of the 1967 devaluation on the P*PM* relationship, b2 is the true effect of the 1967:111-1969: IV incomes policy on the P*PM* relationship, and c is the regression coefficient on the devaluation dummy (DEV) when DIC6 is regressed on the devaluation dummy (DEV). Note that if b2 < 0 and 1 > c > 0, then E(b^1b1)<0—that is, the estimated coefficient on the slope dummy for PM* (which is used as a proxy for the effect of the devaluation) will understate the true effect of the 1967 devaluation on the P*PM* relationship.
30

From footnote 29, note that equation (a) implies that b1b^1 when b2 < 0 and 1 > c > 0. That is, the estimated effect of the 1967 devaluation on the P*PM* relationship (b±) will represent a lower bound of “true” effect of the 1967 devaluation when the true effect of incomes policy on the P*PM* relationship is negative and when the correlation between the two policies is positive.

31

Suppose a slope dummy DIC6 PM*t3 is created, where DIC6 equals one for ths 1967:III–1969:IV period and zero elsewhere. Such a dummy variable could be used to test the effect of the 1967: III–1969:IV incomes policy on the slope of the P*PM* relationship. However, a regression of DIC6 PM*t3 on DEV PM*t3—the slope dummy used in equations (21) and (22)—revealed that the R¯2 between the two dummies was > 0.93 and that the coefficient on DEV PM*t3 in the regression was > 0.99. Thus, the two slope dummies for PM* are too collinear to appear in a regression at the same time.

32

A similar point was, of course, made long ago by Orcutt (1950) with respect to the price elasticity of demand (for imports and exports) for large and small price changes. Kindleberger (1963, p. 157) has also argued that the price elasticity of demand is likely to be greater for large than for small price changes because consumers have more inducement to overcome their inertia and the cost of shifting to substitutes. A similar argument for producers, based on the costs of changing prices, can be made for large versus small changes in costs.

33
It should be noted that the test procedure described above is formally equivalent to (1) dividing the import price variable into large and small changes, (2) entering the large and small import price variables as separate regressors into the price equation, and (3) testing for the equality of the estimated coefficients on the large and small import price variables. To see this, consider the following two estimating equations:
P*t=a0+a1X*t+a2PM*tL+a3PM*tS(a)
P*t=c0+c1X*t+c2PM*t+c3PM*tL(b)
where PM*t=PM*tL+PM*tS,S=(1L),S and L are zero-one dummies, and where X*t is an exogenous variable. It can then easily be seen that
P*tPM*tLP*tPM*tS=a2a3=(c2+c3)c2=c3

That is, performing a t test on the coefficient c3 in equation (b) is equivalent to performing a t test on the equality of the coefficients a2 and a3 in equation (a).

34

See Schultze (1959) for a good discussion of assymetries in pricing behavior.

35

See Rowley and Wilton (1973) for an analysis of what happens to the significance of estimated coefficients in quarterly wage equations when an efficient generalized least-squares estimator is employed to remove the autocorrelation in these equations. In brief, Rowley and Wilton find that when the generalized least-squares estimator is employed, the t statistics on the coefficients in the equation are reduced by 50 per cent or more in many cases. The examples used in the Rowley-Wilton study, however, are wage equations for the United States and Canada; no tests are done on U.K. wage equations.

36

In the future, it would probably be useful to re-estimate the wage equations reported in this paper with a generalized least-squares estimator (as outlined by Rowley and Wilton) to see whether the results are significantly affected.

37

See, however, the recent paper by Ashenfelter and Pencavel (1974) for a model of earnings changes in the United Kingdom.

38

Recall from equation (4) that the coefficient on W* in the price equation should be equal to (1+F)(1B)WLP, where WLP is the share of wages in final price, F is the ratio of unmeasured to measured costs, and B is the markup percentage. Since WLP should be higher for earnings than for wage rates (since the former includes overtime payments), the coefficient on W* in the price equation should be higher, ceteris paribus, when earnings are used for W* than when wage rates are used.

39

Lipsey and Parkin (1970) also found that a linear form of the unemployment rate provided the best results.

40

See equations (9) and (10) in Section I.

41
The estimated price equation, with the shift and slope dummy variables (where D2 = 1 for 1967:111-1971:IV and zero elsewhere), was:
Pt*=1.22(2.09)+0.49(4.21)W*t+0.27(1.35)D2Wt*0.15(3.44)Q*t+0.08(0.52)D2Q*t+0.11(3.47)PM*t3(26a)+0.08(1.33)D2PM*t32.60(1.48)D20.59(0.95)DIC1+1.92(3.89)DIC20.10(1.33)DIC3+1.23(3.07)DIC4+0.53(1.06)DIC5+0.80(0.69)DIC6R2¯=0.85SEE=0.86DW=1.38Period = 1954:I1971:IV
42
The calculated F statistic for the whole set of dummy variables (excluding the incomes policy dummies) is obtained by estimating equations (26) and (26a) and then calculating F as
F=[ΔR2][1R22][ΔK][nK2]
where ΔR2 is the change in the R2 (uncorrected for degrees of freedom) between equations (26) and (26a), R22 is the R2 for equation (26a), ΔK is the number of additional variables (vis-à-vis equation (26)) in equation (26a), K2 is the total number of variables in equation (26a), and n is the number of observations. The calculated F statistic of 1.2 suggests that the null hypothesis that the explanatory power of the price equation is not significantly improved by the addition of the set of dummy variables cannot be rejected.
43

As a further example of this instability, compare the coefficients in equations (23) and (25) with those in the following wage equation estimated (also by ordinary least- squares) for the 1950:I–1967:II period.

Wt*=6.20(6.89)1.96(4.06)UW5t+0.50(11.22)P*t3.12(7.04)DIC0+1.68(3.87)DICI(26b)1.88(4.86)DIC2+0.76(2.21)DIC30.89(2.75)DIC41.36(3.51)DIC5R2¯=0.87SEE=0.74DW=1.61Period = 1950:I1967:II

Thus, the estimated wage response to retail price changes fluctuates from 0.16 in equation (23) to 0.91 in equation (25) to 0.5 in equation (26b).

44

Godfrey and Taylor (1973) also found a positive coefficient on the registered unemployment rate in their earnings function for the United Kingdom over the 1955–70 period.

45

A thorough investigation into why the wage equation shifted upward in the period 1967–71 (aside from any effects of the 1967 devaluation) was considered to be beyond the scope of this paper. It might be mentioned, however, that no convincing explanation for this upward shift in the wage equation has yet been found, to judge from the current U.K. wage literature (see the papers in Johnson and Nobay (1971), especially the study by Artis (1971)).*

46
The wage equation with the slope dummies on UW5t and P*t was
Wt*=8.91(5.86)3.14(4.18)UW5t+4.75(2.50)DUM6771.UW5t+0.16(1.16)Pt*(27a)+0.26(1.08)DUM6771.P*t5.19(1.31)DUM6771+1.99(3.51)DIC11.16(2.06)DIC2+1.39(2.80)DIC30.28(0.59)DIC41.05(2.07)DIC53.72(5.77)DIC6R2¯=0.90SEE=0.93DW=1.02Period=1954:I1971:IV
47
When the wage equation was estimated with the slope dummies on UW5t and P*t but without the shift dummy, the estimated equation was
Wt*=8.14(5.76)2.77(3.96)UW5t+2.37(4.24)DUM6771.UW5t+0.22(1.65)Pt*(27b)+0.34(1.39)DUM6771.P*t+2.04(3.60)DIC11.25(2.21)DIC2+1.23(2.54)DIC30.34(0.71)DIC41.07(2.10)DIC54.01(6.54)DIC6R2¯=0.90SEE=0.93DW=1.03Period=1954:I1971:IV
48

The calculated F statistic for the two slope dummies in equation (27a) is 5.9, which is significant at the 1 per cent level. Thus, the null hypothesis that the explanatory power of the wage equation is not significantly improved by addition of the slope dummies on UW5t and Pt is rejected. Strictly speaking, the F test cannot be applied to an equation with a significant autocorrelation, but this problem is ignored here.

49

It might also be the case that expected price changes are a function of past price changes and exchange rate changes—that is, a devaluation might well lead to an increase in people’s price expectations. Unfortunately, a test of this hypothesis really requires direct survey data on price expectations, and such data are generally not available.

50
Following Turnovsky, if one specifies the following equation for desired wage changes
W*^t=b0+b1Ut+b2Ut1+b3P*t,
along with the following adjustment equation
W*tW*t1=λ(W*^tW*t1),(0λ1),
then after eliminating W*^t, one obtains an equation for Wt which is statistically identical to equation (31); however, in this case, the constraint on the coefficients of Ut, Ut–1, and W*t1 need not be satisfied.
51

The author wishes to thank Rudolf Rhomberg for helpful discussion on this point.

52

Once again, it should be kept in mind that the autocorrelation causes the significance of the coefficients to be overstated.

53

The estimated size of this announcement effect should be treated with some caution because the announcement dummy and the last incomes policy dummy (DIC6) are quite collinear.

54

It should also be mentioned that a very similar test was conducted for the price equation but with quite different results. More specifically, when a shift dummy for the 1968:I–1968:IV period was included in the price equation, its coefficient turned out to be small (0.29) and quite insignificant (t = 0.42).

55

Lipsey and Parkin (1970) estimated separate wage equations for periods of incomes policy, periods of no incomes policy, and for the 1948—68 period as a whole. The estimated coefficient on P* in the wage equation was 0.23 for the period of incomes policy, 0.46 for the period of no incomes policy, and 0.48 for the 1948–68 period as a whole.

56

The values for β3 and β1 have been taken from price equation (26). The value for ao was taken from wage equation (27).

57

As previously demonstrated, the fact that the values for β3, α2, and β1 were higher in the 1967–71 period does not necessarily imply that they were significantly different from the values for 1954–71 in a statistical sense.

58

The values for β3, α2, and β1 cited above are obtained by adding the estimated coefficients on the slope dummies for the 1967–71 period to the estimated coefficients on PM*t3, P*t, and W*t.

59

Cooper (1968) has also estimated the effect of a U.K. devaluation on the United Kingdom’s competitive price advantage. In terms of the notation in this paper, Cooper assumes that K = 0.85, (β3 = 0.19, α2 = 0.7 and β1 = 0.7. This implies that about 62 per cent of the initial price advantage achieved by devaluation will be retained (see Cooper, pp. 191–92).

IMF Staff papers: Volume 21 No. 3
Author: International Monetary Fund. Research Dept.