PRICE BLOCK

The experiences of stagflation during the late 1960s and the 1970s have led to a major change in the commonly accepted views on price and wage dynamics. The notion behind the original Phillips curve—that wage rates respond only to excess demand conditions in the labor market—has been replaced by the view, expressed by the expectational Phillips curve, that wage rates are influenced as much, if not more, by inflationary expectations as by actual excess demand conditions. There are two separate arguments behind the new view. The first focuses on the crucial role played by expectations. It concludes that, if inflation is expected to persist, wage rates may continue to increase for some time, even when no excess demand is present. The theoretical justification for this argument can be found in the existence of long-term contractual wage arrangements that oblige market participants to look ahead. If the level of the wage rate, or, more likely, its rate of change, is going to be fixed for a substantial period of time, the arrangement has to take into account not only existing excess demand conditions but also the expected overall rate of inflation during the whole contract period. Long-term contracts, by themselves, only delay the effect of an unexpected change in excess demand conditions on the average money wage rate. The second argument goes further by focusing on the weakness of the response of the money wage rate to excess demand conditions even at the time when new labor contracts are negotiated. The argument is supported by the observation that employees and employers tend to view their relationships in a long-run context that extends far beyond the duration of a particular labor contract. As Hall ((1980), p. 82) has noted, “wages are insensitive to current economic conditions because they are effectively installment payments on the employer’s obligation to transfer a certain amount of wealth to the worker over the duration of the employment arrangement.”

The expectational Phillips curve is now widely accepted as a theory of wage dynamics, and, when combined with some type of cost-plus pricing model, with or without contractual price arrangements in the goods markets, it is also accepted as a theory of price dynamics. The problem is that its policy implications depend upon the assumption made with respect to the formation of price expectations. Practically all econometric models assume that private market participants are exclusively backward-looking and form their price expectations on the basis of the past behavior of the actual price series themselves. Thus, the expectation term in the Phillips curve equation can be replaced by a distributed lag function of past inflation rates. By repeated substitution, the current inflation rate can be expressed, as in the original Phillips curve equation, as a function of an excess demand variable only, although in this case all the lagged values of this variable enter the equation.² From a policy standpoint, the implication of this specification is that inflation can be eliminated only by being “squeezed out” through a period of excess supply. This specification will also, in general, lead to the conclusion that the adjustment period will be long and painful for two reasons. First, the coefficient on the excess supply term tends to be small. Second, inflation rate series tend to be rather erratic, so that inflationary expectations are usually found to adjust slowly to current inflationary developments.³

The rational expectations approach that is used to derive the price block of the model presented in Table 1 starts from the more plausible assumption that private market participants are forward-looking, so that they form their price expectations on the basis of what they expect to be the major factors influencing inflation in the future. If the amount of money is acknowledged as the major determinant of the overall price level in the long run,⁴ then private market participants can be assumed to set long-term contractual rates of change of wages, and by implication the rates of change of prices, on the basis of their expectations about long-run money growth. These expectations will reflect the monetary policy stance of the authorities as it is perceived by private market participants. By changing their policy stance in a convincing manner, the monetary authorities can reduce inflation without having to rely on any excess supply effect. The reduction in inflation will not be immediate because of existing contractual wage arrangements, but the speed of adjustment will be related only to the length of the contract period.

A major difficulty with empirical implementation of a rational expectations approach is that, in the present context, it requires the derivation of a reliable proxy variable for money growth expectations. The general procedure for deriving this proxy is to assume that the monetary authorities are following a specific policy reaction function that becomes known to private market participants from their observation of past events and that is then used by these participants to predict what the monetary authorities are going to do. To the extent that the authorities are found to react to current developments with a lag, it may be possible to form a prediction on the basis of actually known factors. In most cases, however, some factors may enter in the policy reaction function with a short lag, or no lag at all, so that the prediction of money growth may also require forecasting a number of factors known to affect the money supply process.

The policy reaction function used in the present study assumes that the average rate of growth of money over any period of a year and a half is related to the observed rates of change of money in previous quarters, the GNP gap lagged by one quarter, a variable that expresses the policy stance of the monetary authorities during the year and a half considered, and the amount of foreign exchange market intervention during that same period. (See equation (1′) in footnote 2 of Table 1.) The year-and-a-half period is the result of a simplifying assumption. To avoid the complexity of an n-period analysis, the model assumes that, whatever the duration of the contractual wage arrangements, they are based on the anticipated rate of growth of money for the next year and a half. The choice of the period length is arbitrary,⁵ but it was felt that a short period of a few months would not be very relevant for most labor contracts, while anticipations for a period of several years would probably be too diffused to be relevant.

As is done in similar empirical studies, lagged money growth rates are included in equation (1′) because they may contain information on the normal behavior of the authorities that cannot be readily derived from the way they react to values assumed by specific target variables. The lagged output gap is included to isolate the cyclical response of the authorities. The other two variables included in the equation are elements that are concurrent with the money growth being explained. The dummy variable represents the discretionary component of the policy stance.⁶ If the rate of growth of money on the left-hand side of the equation covers a period that includes the beginning of the implementation of a major stabilization program, then its value may deviate substantially from the value that the first two explanatory variables would normally imply. To take this into account, the dummy variable z₁ is given a value that increases from zero to one in proportion to the number of quarters covered by the left-hand-side variable that are affected by the policy shift. If the left-hand-side variable covers a period that immediately follows a policy change, only one or two of the lagged money growth rates included as explanatory variables will be affected by the policy change, so that the historical series cannot be considered to reflect adequately the information available to private market participants. To offset this fact, the value of z₁ is allowed to decay gradually from one to zero in eight quarters.⁷ The complete series for z₁ is given in Appendix II. Finally, the last variable identifies the “unwanted” monetary effects of foreign exchange interventions.⁸

At any point in time, private market participants can look back and estimate the coefficients of the policy reaction function (1′) from past data. To predict money growth, however, it is not enough for them to have an estimate of these coefficients. They must also forecast the discretionary component of the policy stance, as well as the amount of foreign exchange market intervention. In the present model, it is assumed that private market participants do not anticipate discretionary policy changes but that their long-run expectations are revised once a policy change is announced. The change in their expectations depends on the coefficient of the variable z₁, the magnitude of which depends on the effectiveness of past policy changes.

Thus, in equation (1) of Table 1, which is used to predict money growth, the variable z₁ enters, but in a modified form denoted by z₂. The variable z₂ takes the value zero up to the period when the policy change is announced; then, like z₁, it takes a value of one when the policy change is announced, after which z₂ decays gradually. The complete series for z₂ is also given in Appendix II. Finally, equation (1) also assumes that private market participants do not anticipate money growth owing to foreign exchange market interventions so that, prior to interventions, the variable ṙ is expected to be nil. This latter assumption seems reasonable, given that periods of speculation during the fixed-rate regime and interventions during the floating-rate period have been erratic and not easily foreseeable several quarters ahead.

The foregoing specification of long-term money growth expectations abstracts from many factors. It nevertheless represents a substantial improvement over previous empirical studies, most of which do not allow either for the effect of policy surprises on money growth expectations or for developments that can be viewed as having affected money growth ex post but that ex ante were impossible to anticipate.⁹ The two innovations used in the present study—namely, the taking into account of discretionary changes in the policy stance of the monetary authorities and the consideration of unanticipated money growth owing to foreign exchange market intervention—permit a better differentiation of anticipated from unanticipated money. They also make it easier to identify the effects of sudden changes in expectations resulting from discretionary policy changes.

Long-run inflationary expectations in terms of the deflator of domestic demand are defined in equation (2) of Table 1 on the basis of expected money growth, adjusted for growth in potential output and long-run changes in velocity. One-quarter-ahead inflationary expectations in terms of the GDP deflator and the domestic demand deflator are viewed as being formed on the basis of recent inflationary developments.¹⁰ (See equations (3) and (4) of Table 1.) The assumption is that the inflation rate for the next quarter can be more reliably forecast from the observation of recent historical price developments than from the use of any behavioral model linking prices to monetary, fiscal, or other such causal factors. The reasons for this assumption include the difficulty in identifying precisely the timing of monetary and fiscal effects on inflation. Thus, the present model combines the traditional approach, in which expectations are determined by historical developments, with the new rational expectations approach that makes allowance for current events and changes in policies. The former approach is considered more appropriate for the short run, while the latter is considered more appropriate for the long run.

Equation (5) of Table 1 determines the domestic rate of inflation in terms of the GDP deflator by using an expectational Phillips curve where the distributed-lag parameters for the inflationary expectations and the excess demand terms depend on how frequently contractual wage arrangements are being reviewed. The domestic demand deflator is defined in equation (6) of Table 1 as a weighted average of the GDP deflator and the deflator of imports.

OUTPUT BLOCK

The view of price dynamics advanced in the present model has direct implications for output determination. Here again, the important distinction is between anticipated and unanticipated money. To the extent that the current money growth was anticipated at the time existing contracts were entered into, it can be considered to be reflected by prevailing prices, so that it has no impact on output. Unanticipated money, however, is not reflected by existing prices and gives rise to an incipient excess supply of, or demand for, money that may lead to a temporary variation in output. As shown in the rational expectations literature, it is only unexpected monetary shocks that lead to output variations. In contrast to most of this literature, however, unexpected shocks are not viewed as “random disturbances” that could not be anticipated one period (quarter) ahead. Rather, unexpected shocks are viewed as resulting from monetary policy changes that could not be anticipated several quarters ahead when existing contracts were agreed upon. The conceptual difference is important, since the latter view implies that a change in the monetary policy stance of the authorities may lead to a money growth that must be considered as unanticipated and, therefore, may be a source of variation in output for a sustained period of time, rather than for only one quarter.¹¹

Unanticipated money is viewed as affecting output through variations in the expected long-term real interest rate. Equation (7) of Table 1 explains the nominal long-term interest rate by reference to the real money stock, real income, the inflation rate expected over the long run, and the difference between short-run and long-run expected inflation rates. Equation (7) represents an inverted demand-for-money equation, with the normal hypotheses that a higher real money stock leads, in itself, to a lower nominal interest rate, while the sign of the coefficient of the expected long-run inflation terms is indeterminate.¹² The last term represents an expected liquidity squeeze or glut effect. Its coefficient is expected to be positive. When a monetary stabilization program leads to a sudden downward shift in the long-run expected rate of growth of money, the slow speed of price adjustment in the labor and goods markets will normally lead private market participants to expect that prices are going to keep rising in the short term at a rate that is not consistent from a long-run standpoint with the new money growth rate. The excess of the short-run over the long-run expected inflation rate will indicate how severe the liquidity squeeze is likely to become in forthcoming quarters as a result of the change in monetary policy. If this variable is large, private market participants can then be assumed to bid up the interest rate in anticipation of the forthcoming squeeze.

Equation (8) relates output to potential output, the long-term real interest rate, and the impulse coming from real government expenditures and foreign trade. Substantial lagged effects of real interest rate variations on output should be expected, because it may take time for the initial shock to spread through the whole economy. Planning costs for capital projects, in particular, will lead to a delay in the peak response of investment to shocks. Government expenditures and the ratio of exports to imports, all in real terms, are introduced in equation (8) in the form of deviations from past tendencies, so that any temporary acceleration in the growth of these variables initially has a positive impulse effect on the growth of output, followed by a negative impulse effect of equal magnitude that brings output back to its initial growth path. Here again, the impulses may lead to persistent output effects because of slow diffusion. In the long run, however, the present specification implies that the level of output in relation to the level of potential output is influenced only by the real interest rate.¹³

EXCHANGE RATE BLOCK

The exchange rate specification followed by the present model is similar to the one developed in Artus (1976). It is based on a version of the asset-market theory of exchange rate determination that emphasizes the role of financial markets in the short-run determination of exchange rates. At any point in time, the supplies of short-term securities denominated in the various currencies and the short-term interest rates are assumed to be predetermined. The exchange rate is the variable that adjusts, so that the relative yields of the securities denominated in domestic and foreign currencies reach a point at which all existing securities are willingly held. This approach leads to the conclusion that short-run changes in exchange rates are related to expected inflation rate differentials, changes in uncovered short-term interest rate differentials, the relative current balance positions of the various countries, and the changes in those relative positions.¹⁴ A more technical discussion of the approach and the derivation of the exchange rate equation is presented in Appendix I.¹⁵

The exchange rate of the deutsche mark has been floating against a number of major currencies since February 1973, but it has remained pegged against other currencies. Thus, it was not possible to explain the average value of the deutsche mark against all foreign currencies. The problem was solved by specifying an equation for the major floating rate, the deutsche mark/U. S. dollar rate. In this equation, equation (11) of Table 1, the foreign rate of inflation and the foreign rate of interest are measured by the corresponding U. S. variables. The relative strength of the U. S. and German current account balances also enters as an important variable. For the sake of convenience, the current account variables are expressed as ratios of exports of goods and services over imports of goods and services in logarithmic form. All variables in equation (11) are in quarterly average form, except for the current account balance data that refer to flows over quarterly periods.

The specification of short-run exchange rate dynamics followed here clearly allows for substantial “overshooting.” For example, a monetary stabilization policy that leads initially to an increase in the short-run interest rate differential but does not immediately affect the expected short-term inflation rate differential may cause a sharp increase in the real exchange rate for a number of periods. This is particularly true if the coefficient α₂₅ in equation (11) is much larger than one, as the theoretical arguments presented in Appendix I would lead one to expect.

The short-term interest rate variable for the Federal Republic of Germany is determined by equation (12) of Table 1, which is similar to the equation for the long-term interest rate. The current account variable is determined in equations (13) and (14) of Table 1 by reference to activity levels and relative international prices.

REGRESSION RESULTS

The regression results are presented in Table 2. Looking first at the price block, the money growth equation shown in the table is the one based on the full sample period, which extends from the first quarter of 1955 to the fourth quarter of 1979. Both the discretionary monetary policy variable z₁ and the foreign exchange market intervention variable ṙ are found to play a crucial role in the money growth process. This result is important because, as explained previously, discretionary monetary policy changes and foreign exchange market intervention cannot easily be anticipated. Thus, it is possible to make a relatively clear-cut distinction between unanticipated money growth and money growth that had been anticipated through observations of past periods. The results from money growth equations for other periods were fairly similar, and are not indicated here to save space. In the definition of the long-run price expectations variable (equation (2)), the long-run rate of change of the velocity of base money is taken to be zero through 1975 and minus one quarter of 1 percentage point per quarter from 1976 onward.¹⁹ Those are estimates obtained by comparing the long-run changes in GDP and in the stock of base money. As to the results for the equations used to derive short-run price expectations, they show that if expectations are based on the history of the variables concerned, they must be fairly slow to adjust to new developments.

Table 2.

Empirical Results¹

¹The period covered by the left-hand-side variables extends from the third quarter of 1964 to the fourth quarter of 1979, except for equations (1′), (3′), (4′), (7), (11), and (12). As explained in the text, the parameters of equations (1′), (3′), and (4′) are estimated for each period t on the basis of observations for the period extending from the first quarter of 1955 to t. To save space, the results are presented here only for the regression equations covering the period extending from the first quarter of 1955 to the fourth quarter of 1979. The parameters of equations (7), (11), and (12) are estimates from observations on the flexible exchange rate period extending from the fourth quarter of 1973 to the fourth quarter of 1979.

Standard errors of the estimated values of the parameters are shown in parentheses below the coefficients. SEE denotes standard error of the estimate. D-W denotes Durbin-Watson statistic. Columns may not add to totals shown because of rounding.

²−0.05 from 1976 onward.

³Almon constraint: polynomial of degree 3, without zero-constraint.

⁴Almon constraint: polynomial of degree 3, zero-constraint at the end.

⁵Almon constraint: polynomial of degree 3, zero-constraints at the beginning and end.

Table 2.

Empirical Results¹

Price block
	$\begin{array}{cc}\mathrm{\sum }_{j=1}^{j=6}{\dot{m}}_j/6=\mathrm{\sum }_j{\alpha }_{1,j}{\dot{m}}_{-j}-\underset{\mathrm{(0.0158)}}{0.0352}{\left(y-\overline{y}\right)}_{-1}-\underset{\mathrm{(0.0012)}}{0.0096}{z}_1+\underset{\mathrm{(0.0159)}}{0.1215}\mathrm{\sum }_{j=0}^{j=5}{\dot{r}}_j& \left(1^{\prime }\right)\end{array}$
α1.1 = 0.081			α1.5 = 0.151
α1.2 = 0.183			α1.6 = 0.149
α1.3 = 0.127			α1.7 = 0.105
α1.4 = 0.115			α1.8 = 0.034
				${\overline{R}}^2=0.965$
			Total = 0.945 (0.035)	SEE = 0.0044
			Mean lag = 2.999 (0.751)	D-W = 0.462
	${\dot{m}}^{\mathit{el}}=\mathrm{\sum }_j{\alpha }_{1,j}{\dot{m}}_{-j}-0.0352{\left(y-\overline{y}\right)}_{-1}-0.0051z_2\left(1\right)$
	${\dot{p}}^{\mathit{el}}={0.00}^{2/}+{\dot{m}}^{\mathit{el}}-\dot{\overline{y}}\left(2\right)$
	$\dot{p}=\mathrm{\sum }_j{\alpha }_{6,j}{\dot{p}}_{-j}\left(3^{\prime }\right)$
α6.1 = 0.171			α6.4 = 0.358
α6.2 = 0.103			α6.5 = 0.184
α6.3 = 0.269			α6.6 = -0.105
				α6.7 = -0.022
				${\overline{R}}^2=0.406$
			Total = 0.958 (0.106)	SEE = 0.0069
			Mean lag = 1.873 (0.724)	D-W = 1.995
	$\begin{array}{cc}{\dot{p}}^{\mathit{es}}=\mathrm{\sum }_j{\alpha }_{6,j}{\dot{p}}_{-j+1}& \left(3\right)\end{array}$
	$\begin{array}{cc}{\dot{p}}_d=\mathrm{\sum }_j{\alpha }_{7,j}{\dot{p}}_{d,-j}& \left(4^{\prime }\right)\end{array}$
α7.1 = 0.289			α7.4 = 0.274
α7.2 = 0.110			α7.5 = 0.113
α7.3 = 0.111			α7.6 = -0.028
			α7.7 = 0.070
				${\overline{R}}^2=0.330$
			Total = 0.940 (0.100)	SEE = 0.0071
			Mean lag = 2.006 (0.632)	D-W = 1.983
	${\dot{p}}_d^{\mathit{es}}=\mathrm{\sum }_j{\alpha }_{6,j}{\dot{p}}_{d,-j+1}\left(4\right)$
	${\dot{p}}_d=\underset{\left(0.0030\right)}{0.0044}+\mathrm{\sum }_j{\alpha }_{9,j}{\dot{p}}_{-j}^{\mathit{el}}+\mathrm{\sum }_j{\alpha }_{10,j}{(y-\overline{y})}_{-j}+\underset{\left(0.0022\right)}{0.0090}{d}_1+\underset{\left(0.0020\right)}{0.0029}{d}_2\left(5\right)$
α9.0 = 0.233			α10.0 = 0.0494
α9.1 = 0.08			α10.1 = 0.056
α9.2 = 0.12			α10.2 = 0.051
α9.3 = 0.24			α10.3 = 0.039
α9.4 = 0.33			α10.4 = 0.024
α9.5 = 0.29			α10.5 = 0.010
				${\overline{R}}^2=0.501$
Total = 1.285 (0.134)			Total = 0.232 (0.060)	SEE = 0.0053
Mean lag = 2.948 (1.099)			Mean lag = 1.857 (0.673)	D-W = 1.973
	$\dot{p}=0.726{\dot{p}}_d+0.274\left({\dot{p}}_m-\dot{e}\right)\left(6\right)$
Output block
	$i^e=-\underset{\left(0.0903\right)}{0.0803}-\underset{\left(0.0332\right)}{0.0279}(m-p)+\underset{\left(0.0267\right)}{0.0449}y+\underset{\left(0.154\right)}{0.218}{\dot{p}}^{\mathit{et}}-\underset{\left(0.00033\right)}{0.00026}t+\underset{\left(0.162\right)}{0.376}({\dot{p}}^{\mathit{es}}-{\dot{p}}^{\mathit{el}})\left(7\right)$
$\begin{array}{ccc}{\overline{R}}^2=0.873& \mathit{SEE}=0.0014& D-W=0.893\end{array}$
	$y=\overline{y}-\underset{\left(0.0219\right)}{0.0030}+\mathrm{\sum }_j{\alpha }_{19,j}{\left(i^l-{\dot{p}}^{\mathit{el}}\right)}_{-j}+\mathrm{\sum }_j{\alpha }_{20,j}{\left(0.41\overline{g}+0.59\overline{x}\right)}_{-j}+\mathrm{\sum }_j{\beta }_{1,j}\left(0.0090d_1+0.0029d_2\right)\left(8\right)$
α19.0 = -0.1575			β1.0 = 0.0954	α18.0 = 0.284
α19.1 = -0.242			β1.1 = 0.332	α18.1 = 0.068
α19.2 = -0.533			β1.2 = 0.503
α19.3 = -0.727			β1.3 = 0.619	Total = 0.352 (0.060)
α19.4 = -0.837			β1.4 = 0.684	Mean lag = 0.193 (0.051)
α19.5 = -0.875			β1.5 = 0.705
α19.6 = -0.854			β1.6 = 0.690
α19.7 = -0.785			β1.7 = 0.644
α19.8 = -0.681			β1.8 = 0.575
α19.9 = -0.554			β1.9 = 0.489
α19.10 = -0.417			β1.10 = 0.393
α19.11 = -0.281			β1.11 = 0.294
α19.12 = -0.159			β1.12 = 0.199
α19.13 = -0.063			β1.13 = 0.113
α19.14 = -0.006			β1.14 = 0.045
				$\begin{array}{ccc}{\overline{R}}^2=0.873& \mathit{SEE}=0.0014& D-W=0.910\end{array}$
				SEE = 0.0083
Total = -6.858 (2.200)			Total = 6.382 (1.680)	D-W = 1.935
$\tilde{g}=g-(\mathrm{\sum }_{j=1}^{j=12}{0.9}^j{g}_{-j}/\mathrm{\sum }_{j=1}^{j=12}{0.9}^j)\left(9\right)$
$\tilde{x}=x-(\mathrm{\sum }_{j=1}^{j=12}{0.9}^j{x}_{-j}/\mathrm{\sum }_{j=1}^{j=12}{0.9}^j)\left(10\right)$
Exchange rate block
$\dot{e}=-\left({\dot{p}}_d^{\mathit{es}}-{\dot{p}}_{\mathit{d}\mathit{.}\mathit{U.S.}}^{\mathit{es}}\right)-\underset{\left(0.0135\right)}{0.0239}+\underset{\left(1.314\right)}{4.319}\left(\mathrm{\Delta }{i}^s-\mathrm{\Delta }{i}_{\mathit{U.S.}}^s\right)+\underset{\left(0.055\right)}{0.143}\left(\left(b-b_{\mathit{U.S.}}\right)+{\left(b-b_{\mathit{U.S.}}\right)}_{-1}\right)/2-\underset{\left(0.0104\right)}{0.0365}/2+\underset{\left(0.136\right)}{0.020}\mathrm{\Delta }\left(\left(b-b_{\mathit{U.S.}}\right)+{\left(b-b_{\mathit{U.S.}}\right)}_{-1}\right)d_3\left(11\right)$
$\begin{array}{ccc}{\overline{R}}^2=0.600& \mathit{SEE}=0.0263& D-W=1.796\end{array}$
$i^s=-\underset{\left(0.1782\right)}{0.6739}-\underset{\left(0.0590\right)}{0.0052}\left(m-p\right)+\underset{\left(0.0393\right)}{0.1471}y+\underset{\left(0.238\right)}{0.251}{\dot{p}}^{\mathit{es}}-\underset{\left(0.00066\right)}{0.00101}t+\underset{\left(0.247\right)}{0.481}\left({\dot{p}}^{\mathit{es}}-{\dot{p}}^{\mathit{el}}\right)\left(12\right)$
$\begin{array}{ccc}{\overline{R}}^2=0.906& \mathit{SEE}=0.0021& D-W=1.417\end{array}$
$x=\underset{\left(0.1122\right)}{0.5782}-\underset{\left(0.354\right)}{1.602}\left(y-\overline{y}\right)+\underset{\left(0.216\right)}{1.101}\left(y^{*}-{\overline{y}}^{*}\right)-\mathrm{\sum }_j{\alpha }_{37,j}{\left(p_d-p_d^{*}+e\right)}_{-j}+\underset{\left(0.0112\right)}{0.0569}{d}_4\left(13\right)$
α37.0 = -0.2373			α37.9 = -0.063
α37.1 = -0.146			α37.10 = -0.081
α37.2 = -0.082			α37.11 = -0.094
α37.3 = -0.040			α37.12 = -0.099
α37.4 = -0.016			α37.13 = -0.092
α37.5 = -0.008			α37.14 = -0.069
α37.6 = -0.012			α37.15 = -0.028
α37.7 = -0.025			α37.16 = -0.035
α37.8 = -0.043			${\overline{R}}^2=0.587$
			Total = -1.099 (0.282)	SEE = 0.0370
			Mean lag = 6.127 (2.490)	D-W = 1.490
	$b=x+p_d-p_m+e\left(14\right)$

¹The period covered by the left-hand-side variables extends from the third quarter of 1964 to the fourth quarter of 1979, except for equations (1′), (3′), (4′), (7), (11), and (12). As explained in the text, the parameters of equations (1′), (3′), and (4′) are estimated for each period t on the basis of observations for the period extending from the first quarter of 1955 to t. To save space, the results are presented here only for the regression equations covering the period extending from the first quarter of 1955 to the fourth quarter of 1979. The parameters of equations (7), (11), and (12) are estimates from observations on the flexible exchange rate period extending from the fourth quarter of 1973 to the fourth quarter of 1979.

Standard errors of the estimated values of the parameters are shown in parentheses below the coefficients. SEE denotes standard error of the estimate. D-W denotes Durbin-Watson statistic. Columns may not add to totals shown because of rounding.

²−0.05 from 1976 onward.

³Almon constraint: polynomial of degree 3, without zero-constraint.

⁴Almon constraint: polynomial of degree 3, zero-constraint at the end.

⁵Almon constraint: polynomial of degree 3, zero-constraints at the beginning and end.

View Table

Table 2.

Empirical Results¹

Price block
	$\begin{array}{cc}\mathrm{\sum }_{j=1}^{j=6}{\dot{m}}_j/6=\mathrm{\sum }_j{\alpha }_{1,j}{\dot{m}}_{-j}-\underset{\mathrm{(0.0158)}}{0.0352}{\left(y-\overline{y}\right)}_{-1}-\underset{\mathrm{(0.0012)}}{0.0096}{z}_1+\underset{\mathrm{(0.0159)}}{0.1215}\mathrm{\sum }_{j=0}^{j=5}{\dot{r}}_j& \left(1^{\prime }\right)\end{array}$
α1.1 = 0.081			α1.5 = 0.151
α1.2 = 0.183			α1.6 = 0.149
α1.3 = 0.127			α1.7 = 0.105
α1.4 = 0.115			α1.8 = 0.034
				${\overline{R}}^2=0.965$
			Total = 0.945 (0.035)	SEE = 0.0044
			Mean lag = 2.999 (0.751)	D-W = 0.462
	${\dot{m}}^{\mathit{el}}=\mathrm{\sum }_j{\alpha }_{1,j}{\dot{m}}_{-j}-0.0352{\left(y-\overline{y}\right)}_{-1}-0.0051z_2\left(1\right)$
	${\dot{p}}^{\mathit{el}}={0.00}^{2/}+{\dot{m}}^{\mathit{el}}-\dot{\overline{y}}\left(2\right)$
	$\dot{p}=\mathrm{\sum }_j{\alpha }_{6,j}{\dot{p}}_{-j}\left(3^{\prime }\right)$
α6.1 = 0.171			α6.4 = 0.358
α6.2 = 0.103			α6.5 = 0.184
α6.3 = 0.269			α6.6 = -0.105
				α6.7 = -0.022
				${\overline{R}}^2=0.406$
			Total = 0.958 (0.106)	SEE = 0.0069
			Mean lag = 1.873 (0.724)	D-W = 1.995
	$\begin{array}{cc}{\dot{p}}^{\mathit{es}}=\mathrm{\sum }_j{\alpha }_{6,j}{\dot{p}}_{-j+1}& \left(3\right)\end{array}$
	$\begin{array}{cc}{\dot{p}}_d=\mathrm{\sum }_j{\alpha }_{7,j}{\dot{p}}_{d,-j}& \left(4^{\prime }\right)\end{array}$
α7.1 = 0.289			α7.4 = 0.274
α7.2 = 0.110			α7.5 = 0.113
α7.3 = 0.111			α7.6 = -0.028
			α7.7 = 0.070
				${\overline{R}}^2=0.330$
			Total = 0.940 (0.100)	SEE = 0.0071
			Mean lag = 2.006 (0.632)	D-W = 1.983
	${\dot{p}}_d^{\mathit{es}}=\mathrm{\sum }_j{\alpha }_{6,j}{\dot{p}}_{d,-j+1}\left(4\right)$
	${\dot{p}}_d=\underset{\left(0.0030\right)}{0.0044}+\mathrm{\sum }_j{\alpha }_{9,j}{\dot{p}}_{-j}^{\mathit{el}}+\mathrm{\sum }_j{\alpha }_{10,j}{(y-\overline{y})}_{-j}+\underset{\left(0.0022\right)}{0.0090}{d}_1+\underset{\left(0.0020\right)}{0.0029}{d}_2\left(5\right)$
α9.0 = 0.233			α10.0 = 0.0494
α9.1 = 0.08			α10.1 = 0.056
α9.2 = 0.12			α10.2 = 0.051
α9.3 = 0.24			α10.3 = 0.039
α9.4 = 0.33			α10.4 = 0.024
α9.5 = 0.29			α10.5 = 0.010
				${\overline{R}}^2=0.501$
Total = 1.285 (0.134)			Total = 0.232 (0.060)	SEE = 0.0053
Mean lag = 2.948 (1.099)			Mean lag = 1.857 (0.673)	D-W = 1.973
	$\dot{p}=0.726{\dot{p}}_d+0.274\left({\dot{p}}_m-\dot{e}\right)\left(6\right)$
Output block
	$i^e=-\underset{\left(0.0903\right)}{0.0803}-\underset{\left(0.0332\right)}{0.0279}(m-p)+\underset{\left(0.0267\right)}{0.0449}y+\underset{\left(0.154\right)}{0.218}{\dot{p}}^{\mathit{et}}-\underset{\left(0.00033\right)}{0.00026}t+\underset{\left(0.162\right)}{0.376}({\dot{p}}^{\mathit{es}}-{\dot{p}}^{\mathit{el}})\left(7\right)$
$\begin{array}{ccc}{\overline{R}}^2=0.873& \mathit{SEE}=0.0014& D-W=0.893\end{array}$
	$y=\overline{y}-\underset{\left(0.0219\right)}{0.0030}+\mathrm{\sum }_j{\alpha }_{19,j}{\left(i^l-{\dot{p}}^{\mathit{el}}\right)}_{-j}+\mathrm{\sum }_j{\alpha }_{20,j}{\left(0.41\overline{g}+0.59\overline{x}\right)}_{-j}+\mathrm{\sum }_j{\beta }_{1,j}\left(0.0090d_1+0.0029d_2\right)\left(8\right)$
α19.0 = -0.1575			β1.0 = 0.0954	α18.0 = 0.284
α19.1 = -0.242			β1.1 = 0.332	α18.1 = 0.068
α19.2 = -0.533			β1.2 = 0.503
α19.3 = -0.727			β1.3 = 0.619	Total = 0.352 (0.060)
α19.4 = -0.837			β1.4 = 0.684	Mean lag = 0.193 (0.051)
α19.5 = -0.875			β1.5 = 0.705
α19.6 = -0.854			β1.6 = 0.690
α19.7 = -0.785			β1.7 = 0.644
α19.8 = -0.681			β1.8 = 0.575
α19.9 = -0.554			β1.9 = 0.489
α19.10 = -0.417			β1.10 = 0.393
α19.11 = -0.281			β1.11 = 0.294
α19.12 = -0.159			β1.12 = 0.199
α19.13 = -0.063			β1.13 = 0.113
α19.14 = -0.006			β1.14 = 0.045
				$\begin{array}{ccc}{\overline{R}}^2=0.873& \mathit{SEE}=0.0014& D-W=0.910\end{array}$
				SEE = 0.0083
Total = -6.858 (2.200)			Total = 6.382 (1.680)	D-W = 1.935
$\tilde{g}=g-(\mathrm{\sum }_{j=1}^{j=12}{0.9}^j{g}_{-j}/\mathrm{\sum }_{j=1}^{j=12}{0.9}^j)\left(9\right)$
$\tilde{x}=x-(\mathrm{\sum }_{j=1}^{j=12}{0.9}^j{x}_{-j}/\mathrm{\sum }_{j=1}^{j=12}{0.9}^j)\left(10\right)$
Exchange rate block
$\dot{e}=-\left({\dot{p}}_d^{\mathit{es}}-{\dot{p}}_{\mathit{d}\mathit{.}\mathit{U.S.}}^{\mathit{es}}\right)-\underset{\left(0.0135\right)}{0.0239}+\underset{\left(1.314\right)}{4.319}\left(\mathrm{\Delta }{i}^s-\mathrm{\Delta }{i}_{\mathit{U.S.}}^s\right)+\underset{\left(0.055\right)}{0.143}\left(\left(b-b_{\mathit{U.S.}}\right)+{\left(b-b_{\mathit{U.S.}}\right)}_{-1}\right)/2-\underset{\left(0.0104\right)}{0.0365}/2+\underset{\left(0.136\right)}{0.020}\mathrm{\Delta }\left(\left(b-b_{\mathit{U.S.}}\right)+{\left(b-b_{\mathit{U.S.}}\right)}_{-1}\right)d_3\left(11\right)$
$\begin{array}{ccc}{\overline{R}}^2=0.600& \mathit{SEE}=0.0263& D-W=1.796\end{array}$
$i^s=-\underset{\left(0.1782\right)}{0.6739}-\underset{\left(0.0590\right)}{0.0052}\left(m-p\right)+\underset{\left(0.0393\right)}{0.1471}y+\underset{\left(0.238\right)}{0.251}{\dot{p}}^{\mathit{es}}-\underset{\left(0.00066\right)}{0.00101}t+\underset{\left(0.247\right)}{0.481}\left({\dot{p}}^{\mathit{es}}-{\dot{p}}^{\mathit{el}}\right)\left(12\right)$
$\begin{array}{ccc}{\overline{R}}^2=0.906& \mathit{SEE}=0.0021& D-W=1.417\end{array}$
$x=\underset{\left(0.1122\right)}{0.5782}-\underset{\left(0.354\right)}{1.602}\left(y-\overline{y}\right)+\underset{\left(0.216\right)}{1.101}\left(y^{*}-{\overline{y}}^{*}\right)-\mathrm{\sum }_j{\alpha }_{37,j}{\left(p_d-p_d^{*}+e\right)}_{-j}+\underset{\left(0.0112\right)}{0.0569}{d}_4\left(13\right)$
α37.0 = -0.2373			α37.9 = -0.063
α37.1 = -0.146			α37.10 = -0.081
α37.2 = -0.082			α37.11 = -0.094
α37.3 = -0.040			α37.12 = -0.099
α37.4 = -0.016			α37.13 = -0.092
α37.5 = -0.008			α37.14 = -0.069
α37.6 = -0.012			α37.15 = -0.028
α37.7 = -0.025			α37.16 = -0.035
α37.8 = -0.043			${\overline{R}}^2=0.587$
			Total = -1.099 (0.282)	SEE = 0.0370
			Mean lag = 6.127 (2.490)	D-W = 1.490
	$b=x+p_d-p_m+e\left(14\right)$

¹The period covered by the left-hand-side variables extends from the third quarter of 1964 to the fourth quarter of 1979, except for equations (1′), (3′), (4′), (7), (11), and (12). As explained in the text, the parameters of equations (1′), (3′), and (4′) are estimated for each period t on the basis of observations for the period extending from the first quarter of 1955 to t. To save space, the results are presented here only for the regression equations covering the period extending from the first quarter of 1955 to the fourth quarter of 1979. The parameters of equations (7), (11), and (12) are estimates from observations on the flexible exchange rate period extending from the fourth quarter of 1973 to the fourth quarter of 1979.

Standard errors of the estimated values of the parameters are shown in parentheses below the coefficients. SEE denotes standard error of the estimate. D-W denotes Durbin-Watson statistic. Columns may not add to totals shown because of rounding.

²−0.05 from 1976 onward.

³Almon constraint: polynomial of degree 3, without zero-constraint.

⁴Almon constraint: polynomial of degree 3, zero-constraint at the end.

⁵Almon constraint: polynomial of degree 3, zero-constraints at the beginning and end.