# Nominal-wage contracts and real activity: evidence from the German economy.

I. Introduction

The research on microfoundations of the Phillips Curve over the last two decades has produced two alternative new-classical explanations of the short-run output-inflation trade-off: the nominal-wage contracting variety explanation of Fischer [4] and Gray [7], and the equilibrium explanation of Lucas [11].(1) Both explanations are similar in their prediction that real activity responds to aggregate demand disturbances through price surprises that they generate. They are very different, however, in mechanisms that generate such response.

The contracting theory emphasizes the existence of long-term contractual arrangements that, in their simplest form, fix wage schedules in nominal terms for a predetermined period (the life of the contract) and leave the level of employment at the discretion of the firm. In this framework, a positive aggregate demand shock that occurs after the contract negotiation date will cause an increase in the general price level, a decrease in the real wage, and an increase in employment and output.

By contrast, the equilibrium theory makes imperfect information central to the non-neutrality of nominal disturbances. According to this theory, agents lack full current information about aggregate variables and thus cannot dichotomize unanticipated price movements into their relative and absolute components. In this framework, unanticipated changes in aggregate demand lead to positive movements in output and employment because their price level effects are confused with relative price movements.(2) Differences between the contracting and equilibrium explanations of the response of real activity to aggregate demand shocks provide empirically testable hypotheses. Gray, Kandil, and Spencer [8] test for the proposition that, while both theories predict a positive output response to aggregate demand shocks, the size of the response is larger in the contracting model than in the equilibrium alternative. Their results, based on U.S. industry data, overwhelmingly support this prediction.(3) David Card [1I investigates the response of employment to real wage changes induced by aggregate price surprises. His results, using data on individual contracts in the unionized sector of Canadian manufacturing, support the prediction of the simple contracting model: employment responds negatively to real wage changes induced by aggregate price surprises.

This paper provides additional support for the role of nonminal-wage contracts by investigating another distinctive prediction of this theory. This prediction is in regard to the effect of multi-step-ahead aggregate demand shocks on aggregate real activity. More specifically, if contracts are multi-period and synchronized, the cyclical pattern of real activity in the contracting model will depend on multi-step-ahead aggregate demand disturbances. By contrast, the equilibrium model acknowledges a role for only one-step-ahead disturbances.

Overlapping contracts, a major characteristic of contracts in the U.S. labor market, tend to disguise the distinctive time series behavior of aggregate real activity implied by the simplest synchronized contracting model. Adjustment costs further reduce the feasibility of distinguishing empirically between the two models by driving the cyclical as well as the secular components of real activity away from the predictions of the simplest synchronized contracting model.

This study minimizes the difficulties posed by overlapping contracts by employing data on aggregate real activity pertaining to an economy in which contracts are essentially synchronized. Evidence suggests that the German economy meets this requirement. Most annual wage contracts in this economy are negotiated at the end of the first quarter and the beginning of the second quarter of each year and cover the subsequent four quarters.(4) Thus the validity of the contracting model can be tested by investigating the effect of two-to-four step ahead aggregate demand disturbances on aggregate real activity.

The empirical results suggest that multi-step-ahead aggregate demand disturbances had positive and statistically significant effects on three measures of real activity in the West German economy - real GNP, industrial production, and industrial employment - over the 1965.I-86.IV sample period.(5) Thus, nominal-wage contracts might play an important role in determining aggregate real activity. The remainder of the paper is organized as foflows: section II highlights the theoretical implications of the contracting and equilibrium models and formulates their distinguishing implications, section III explains the empirical methodology, and section IV reports the empirical results. A summary of major findings and the conclusions of the study then follow.

II. Model

The simple equilibrium and contracting models discussed above suggest aggregate supply functions of the following general form:

[y.sub.t] = [y.sup.*.sub.t] + [beta]p[S.sub.t] + [e.sub.t] (1) where [y.sub.t] represents the level of real activity at time t, [y.sup.*.sub.t] is the error made in forecasting the price level, and [e.sub.t] is a zero mean disturbance term. The specification of p[S.sub.t] differs in the two models. The equilibrium model assumes a one-period lag in the availability of information. Thus, in the absence of adjustment costs, price prediction errors of only one period ahead are relevant. That is,

p[S.sub.t] = [p.sub.t] - [E.sub.t-1 p.sub.t] (2) where [p.sub.t] denotes the logarithm of the general price level at time t and [E.sub.t]-1[p.sub.t] the expectation of [p.sub.t] conditioned on information available at time t - 1.

The specification of p[S.sub.t] in the contracting model, however, is more complicated, since it depends on such features of the economy as the synchronized versus staggered nature of contracts and their duration. In the case of Germany, annual wage contracts are essentially synchronized and expire at the end of the first quarter. Thus I designate the second quarter of each year as the first period, the third quarter as the second period, the fourth quarter as the third period, and finally, the first quarter of the following year as the fourth period of the contract. This implies that output in the second quarter will depend on one-step-ahead price surprises, output in the third quarter on two-step-ahead price surprises, . . . , and output in the first quarter of the following year on four-step-ahead price surprises. That is,

[y.sup.i.sub.t] = [y.sup.*.sub.t] = [beta][[p.sub.t] - [E.sub.t-i p.sub.t]] + [e.sub.t], i = 1,...,4. (3)

where [y.sup.i.sub.t] is output i th period of the contract, and [E.sub.t-i p.subt] is the expectation of [p.sub.t] conditioned on information available at the time of the contract negotiation date (t - i).

A simple framework to empirically distinguish between the two models is to decompose the multi-step-ahead price surprises into the one-step-ahead component, which is common to both equilibrium and contracting models, and the more-than-one-step-ahead component, which is distinctive to the contracting model as:

p[S.sub.t] = [[p.sub.t] - [E.sub.t-1 p.sub.t]] + [[E.sub.t-1 p.sub.t] - [E.sub.t-1 p.sub.t]], i =

1,...,4, (4) where the second term on the right-hand-side captures the forecast errors attributed to contract periods other than the first period.

Substituting equation (4) into equation (3) and generalizing the model by allowing different coefficients on the two price surprise terms yields,

[y.sub.i.sub.t] = [y.sup.*.sub.t] + [beta.sub.1][[p.sub.t] - [E.sub.t-1 p.sub.t]] +

[beta.sub.2][[E.sub.t-1 p.sub.t] - [E.sub.t-i p.sub.t]] + [e.sub.t]. (5)

The hypotheses to be tested involve the price surprise coefficients, [beta]1 and, [beta]2, which appear in equation (5). The contracting model predicts strictly positive values of the two parameters. In contrast, the equilibrium model predicts a non-negative value for [beta]1 and a zero value for [beta]2.

III. Empirical Methodology

Empirical estimation of the aggregate supply equation (5) requires proxies for one-to-four step-ahead price forecasts and the natural rate component of real activity. The construction of the proxies is explained next.

Price Prediction Errors

The proxies for one-to-four step-ahead price forecasts are based on estimates of four forecasting equations describing the processes generating the price level in each period of the contract. The information set in each forecasting equation includes a constant and four lags of the general price level (p) and the measure of real activity (y).(6) However, the lag length in each forecasting equation is adjusted to correspond to the number of periods elapsed since the contract negotiation date. For example, the one-step-ahead price forecasting equation includes the first-to-fourth lags of p and y, while the two-step-ahead price forecasting equation includes the second-to-fifth lags of p and y, and so on. The predicted values generated by these four regressions constitute the proxies for one-to-four step-ahead price forecasts. Next, the multi-step-ahead price forecasts series, [E.sub.t-i p.sub.t] (i = 1,...,4) is constructed by introducing four dummy variables, D l-D4, representing the first to fourth periods of the contracts. D1 takes a value of one if real activity occurs in the first period of contracts and zero otherwise. Similarly, D2 - D4 are constructed for the second to fourth periods of the contracts. Finally, [E.sub.t-i p.sub.t] is obtained as,

[E.sub.t-1 p.sub.t] = D1 [multiplied by] [E.sub.t-1 p.sub.t] + D2 [multiplied] [E.sub.t-2 p.sub.t]

+ D3 [multiplied] [E.sub.t-3 p.sub.t] + D4 [multiplied by] [E.sub.t-4 p.sub.t]. (6)

The proxies for one-step-ahead, [E.sub.t-1 p.sub.t], and multi-step-ahead, [E.sub.t-i p.sub.t], forecasts are substituted into the aggregate supply equation (5).

The Natural Rate

To take into account the natural rate component of real activity I apply the empirical methodology of Nelson and Plosser [13] by testing the time series properties of the measures of real activity.(7) Applications of this test to the three quarterly measures of real activity fail to reject the null hypothesis of difference stationary process.(8) This requires estimating the aggregate supply equation in a first-differenced form as,

[Dy.sub.t] = [alpha] + [beta.sub.1] D[[p.sub.t] - [E.sub.t-1 p.sub.t]] + [beta.sub.2] D[[E.sub.t-i

p.sub.t]] + [lambda][Dy.sub.t-1] + [v.sub.t], (7) where D is the first-difference operator, and the lagged dependent variable captures the effect of significant adjustment costs.

IV. Estimation and Results

The aggregate supply equation (7) and the four price forecasting equations are estimated jointly, subject to the restriction imposed by the identity (6), using a nonlinear three-stage least squares procedure.(9) To account for the possibility of any serial correlation in the residuals of the aggregate supply equation, [v.sub.t], a fourth-order autoregressive process is also introduced.

Table I contains the results of estimating the aggregate supply equation using three measures of real activity: real GNP (RGNP), index of industrial production (IIP), and industrial employment (EMP). At least four interesting results emerge from the table. First, multi-step-ahead price surprises do have an important effect on real activity, consistent with the prediction of the simple contracting theory. The coefficient of this variable, [beta.sub.2,] is positive and statistically significant at the 5 percent critical level in employment and industrial output equations, and at the 10 percent level in the real GNP equation. Second, one-step-ahead price surprises do not have a substantial impact on real activity. While [beta.sub.1] estimates have the correct positive signs, they are statistically insignificant in two of the three equations. Third, the estimates of [beta.sub.2] coefficient are substantially larger than those of [beta.sub.1]. Thus aggregate demand shocks that occur in the later periods of contracts are substantially more important in explaining movements in real activity. Finally, the results imply that the effects of nominal wage rigidities in Germany may persist up to four quarters, i.e., over the full contract period.

An Alternative Specification of the Model

A potential source of bias in the empirical estimation of equation (7) is the omission of the effect of supply-side disturbances on real activity. This omission is potentially troublesome since it can cause a negative bias in the estimates of the price surprise coefficients [8; 9]. Thus the lack of significance on estimates of the coefficient of one-step-ahead price surprises might be caused by this omission.

A solution to this problem is to replace the price surprises with proxies for aggregate demand shocks.(10) One such proxy is nominal GNP. Thus, I re-estimate equation (7) with nominal GNP

surprises along with four forecasting equations for one-to-four step ahead nominal GNP forecasts. The forecasts are based on an information set that includes four lags of the log of nominal GNP and a measure of real activity.(11)

Table II reports the results. Estimates of [beta.sub.2] are now significant in all three specifications at the 5 percent critical level. However, the estimates of [beta.sub.1] are still insignificant in two of the three cases. Thus the results of Table II are broadly consistent with the findings in Table I on the role of multi-step-ahead price surprises in determining real activity.

[TABULAR DATA OMITTED]

V. Concluding Remarks

This paper tests for an important and distinguishing prediction of the synchronized multi-period nominal-wage contracting model. This prediction reflects the role of multi-step-ahead aggregate-demand disturbances in determining aggregate real activity. The empirical results, using quarterly data on the German economy from 1965.1 to 1986. IV, are broadly consistent with this prediction. More specifically, multi-step-ahead aggregate-demand disturbances have positive and significant impacts on measures of aggregate output and employment. Furthermore, the results indicate that the effect of nominal wage rigidities in Germany may persist up to four quarters, i.e., over the full contract period. Thus, multi-period nominal-wage contracts may provide a channel through which nominal demand shocks affect real activity.

References

[1.] Card, David, "Unexpected Inflation, Real Wages, and Employment Determination in Union Contracts." American Economic Review, September 1990, 669-88. [2.] Cullingford, E. C. M. Trade Unions in West Germany. London: Wilton House Publications, 1976. [3.] Dickey, David A. and Wayne A. Fuler, "Distribution of Estimators for Autoregressive Time Series with Unit Root." American Statistical Association Journal, June 1979, 427-31. [4.] Fischer, Stanley, "Long-term Contracts, Rational Expectations, and the Optimal Money Supply Rule." Journal of Political Economy, February 1977, 163-90. [5.] Fuller, Wayne A. Introduction to Statistical Time Series. New York: John Wiley and Son, 1976. [6.] OECD Economic Surveys: Germany. Part: OECD, 1991/1992. [7.] Gray, Jo Anna, "On Indexation and Contract Length." Journal of Political Economy, February 1978, 1-18. [8.] _____, Magda Kandil and David E. Spencer, "Does Contractual Wage Rigidity Play a Role In Determining Real Activity?" Southern Economic Journal, April 1992, 1042-57. [9.] ----- and David E. Spencer, " Price Prediction Errors and Real Activity: A Reassessment." Economic Inquiry, October 1990, 658-81. [10.] Kandil, Magda, "Variations in the Response of Real Output to Aggregate Demand Shocks: a Cross-Industry Analysis." Review of Economics and Statistics, April 1991, 480-88. [11.] Lucas, Robert E., Jr., "Some International Evidence on Output-Inflation Trade-Offs." American Economic Review, June 1973, 326-34. [12.] Mohammadi, Hassan and Michael A. Nelson, "Monetary Innovations, Capital Taxation, and Real Wage Movements: Some New Evidence." Southern Economic Journal, April 1993, 629-40. [13.] Nelson, Charles R. and Charles I. Plosser. "Trends and Random Walks in Macroeconomic Time Series." Journal of Monetary Economics, September 1982, 139-62. [14.] Pagan, A., "Econometric Issues in the Analysis of Regressions with Generated Regressors." International Economic Review, February 1984, 221-47. [15.] -----, "Two-Stage and Related Estimators and Their Applications." Review of Economic Studies 53 1986, 517-38. [16.] Sargent, Thomas J. and Neil Wallace, "Rational Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule." Journal of Political Economy, April 1975, 241-54.

(1.) These models are neo-classical in the sense that they satisfy the natural rate hypothesis and use rational expectations. (2.) As is well known, the policy implications of equilibrium and contracting models are also vastly different. Contracting models support active monetary policy, provided that the monetary authority can react at intervals shorter than those at which contracts are negotiated. By contrast, equilibrium models are subject to the policy iffelevance proposition of Sargent and Wallace [16], given that private agents have the same information set as the monetary authority. (3.) This test is, however, based on the implicit assumption that the behavior of real activity in the non-contract sector of the economy is best represented by the equilibrium model. Furthermore, the test does not resolve the observational equivalence problem that exists between the two classes of models in a framework diat nests the implications of the two theories. (4.) For example, measured by the number of workers covered by collective bargaining, in 1992, 44.2% of annual wage contracts expired on March 31, 10.3% in April 30, and 7.7% in May and June. These contracts covered major industries such as metals, energy, printing, construction, retail trade, textiles, clothing, and chemicals. Thus, niore than 62% of new wage contracts became effective during the second quarter of the year. This constitutes more than 40% of total employment in Germany in the same year. A similar pattern is observed for odier years. Thus it is reasonable to assume the second quarter of each year as the beginning of a four-quarter contract. Additional infonnation on the nature of collective bargaining in Germany is found in [6, 65-9] and a historical perspective on trade unionism in Germany is found in [2]. I am indebted to Mr. Heinz Mattiesen, Labor Counselor at the Embassy of the Federal Republic of Germany, for providing the data on contract expiration dates. (5.) The data were compiled from several issues of the International Financial Statistics, International Monetary Fund. (6.) Several other macro variables were also considered as possible candidates for inclusion in the information set. They included the real price of energy, the government surplus, the call rate, and the M1 money stock. However, tests of Granger causality did not support any significant predictive power for any of these variables. (7.) Traditionally, the natural rate component is assumed to follow a trend stationary (TS) process and is modeled as a deterministic trend. The alternative difference stationary (DS) process proposed by Nelson and Plosser [13] is based on the statistical consideration that variations in the natural rate can be relatively large. In such cases, the TS specification can lead to an overestimation of both persistence and magnitude of business cycles. Thus appropriate specification of the natural rate requires tests of the stochastic properties of the real activity measures under consideration. Nelson and Plosser's test is an augmented version of the Dickey-Fuller [3; 5] test, which contains both TS and DS hypotheses as subsets. (8.) For all three measures of real activity, the null hypothesis of a difference stationary process could not be rejected against the trend stationary alternative. The t-statistics are well below the 5 percent critical value of -3.45 reported in Fuller [5]. The results are available upon request. (9.) An alternative approach is a two-step procedure. In the first step, the four price equations are estimated. The fitted values from these equations constitute the proxies for the one-to-four step-ahead price forecasts. Substituting the price forecasts into identity (6) will provide the proxy for the multi-step-ahead price forecasts. The second step entails substituting the one-step and multi-step price-forecasts into the aggregate supply equation (7) and applying ordinary least squares. However, as Pagan [14; 15] shows, the use of two-step procedure requires an adjustment in the covariance matrix of the second-step estimators. Application of nonlinear three-stage least squares avoids the use of first-step regression proxies by estimating the four price forecasting equations jointly with the aggregate supply equation and the identity (6). This procedure allows for cross-equation restrictions, takes into account the endogeneity of the price level, and provides asymptotically efficient estimates. The endogeneity of the price level is taken into account using instrumental variables. The instrument list includes seven lags of a real activity measure, nominal GNP, the call rate, and real oil prices, as well as cuffent and seven lags of M1, government surplus, and the Mark/Dollar exchange rate. Applications of this procedure are also found in Gray, Kandil, and Spencer [8], Gray and Spencer [9], Kandil [10], and Mohammadi and Nelson [12]. (10.) An alternative solution is to introduce proxies for anticipated and unanticipated supply shocks directly to the model. This requires estimating a more complicated model, which includes four additional forecasting equations for the supply shocks. (11.) The potential endogeneity of nominal GNP is also taken into account by using instrumental variables. The list of instruments is identical to that used for the price level.

The research on microfoundations of the Phillips Curve over the last two decades has produced two alternative new-classical explanations of the short-run output-inflation trade-off: the nominal-wage contracting variety explanation of Fischer [4] and Gray [7], and the equilibrium explanation of Lucas [11].(1) Both explanations are similar in their prediction that real activity responds to aggregate demand disturbances through price surprises that they generate. They are very different, however, in mechanisms that generate such response.

The contracting theory emphasizes the existence of long-term contractual arrangements that, in their simplest form, fix wage schedules in nominal terms for a predetermined period (the life of the contract) and leave the level of employment at the discretion of the firm. In this framework, a positive aggregate demand shock that occurs after the contract negotiation date will cause an increase in the general price level, a decrease in the real wage, and an increase in employment and output.

By contrast, the equilibrium theory makes imperfect information central to the non-neutrality of nominal disturbances. According to this theory, agents lack full current information about aggregate variables and thus cannot dichotomize unanticipated price movements into their relative and absolute components. In this framework, unanticipated changes in aggregate demand lead to positive movements in output and employment because their price level effects are confused with relative price movements.(2) Differences between the contracting and equilibrium explanations of the response of real activity to aggregate demand shocks provide empirically testable hypotheses. Gray, Kandil, and Spencer [8] test for the proposition that, while both theories predict a positive output response to aggregate demand shocks, the size of the response is larger in the contracting model than in the equilibrium alternative. Their results, based on U.S. industry data, overwhelmingly support this prediction.(3) David Card [1I investigates the response of employment to real wage changes induced by aggregate price surprises. His results, using data on individual contracts in the unionized sector of Canadian manufacturing, support the prediction of the simple contracting model: employment responds negatively to real wage changes induced by aggregate price surprises.

This paper provides additional support for the role of nonminal-wage contracts by investigating another distinctive prediction of this theory. This prediction is in regard to the effect of multi-step-ahead aggregate demand shocks on aggregate real activity. More specifically, if contracts are multi-period and synchronized, the cyclical pattern of real activity in the contracting model will depend on multi-step-ahead aggregate demand disturbances. By contrast, the equilibrium model acknowledges a role for only one-step-ahead disturbances.

Overlapping contracts, a major characteristic of contracts in the U.S. labor market, tend to disguise the distinctive time series behavior of aggregate real activity implied by the simplest synchronized contracting model. Adjustment costs further reduce the feasibility of distinguishing empirically between the two models by driving the cyclical as well as the secular components of real activity away from the predictions of the simplest synchronized contracting model.

This study minimizes the difficulties posed by overlapping contracts by employing data on aggregate real activity pertaining to an economy in which contracts are essentially synchronized. Evidence suggests that the German economy meets this requirement. Most annual wage contracts in this economy are negotiated at the end of the first quarter and the beginning of the second quarter of each year and cover the subsequent four quarters.(4) Thus the validity of the contracting model can be tested by investigating the effect of two-to-four step ahead aggregate demand disturbances on aggregate real activity.

The empirical results suggest that multi-step-ahead aggregate demand disturbances had positive and statistically significant effects on three measures of real activity in the West German economy - real GNP, industrial production, and industrial employment - over the 1965.I-86.IV sample period.(5) Thus, nominal-wage contracts might play an important role in determining aggregate real activity. The remainder of the paper is organized as foflows: section II highlights the theoretical implications of the contracting and equilibrium models and formulates their distinguishing implications, section III explains the empirical methodology, and section IV reports the empirical results. A summary of major findings and the conclusions of the study then follow.

II. Model

The simple equilibrium and contracting models discussed above suggest aggregate supply functions of the following general form:

[y.sub.t] = [y.sup.*.sub.t] + [beta]p[S.sub.t] + [e.sub.t] (1) where [y.sub.t] represents the level of real activity at time t, [y.sup.*.sub.t] is the error made in forecasting the price level, and [e.sub.t] is a zero mean disturbance term. The specification of p[S.sub.t] differs in the two models. The equilibrium model assumes a one-period lag in the availability of information. Thus, in the absence of adjustment costs, price prediction errors of only one period ahead are relevant. That is,

p[S.sub.t] = [p.sub.t] - [E.sub.t-1 p.sub.t] (2) where [p.sub.t] denotes the logarithm of the general price level at time t and [E.sub.t]-1[p.sub.t] the expectation of [p.sub.t] conditioned on information available at time t - 1.

The specification of p[S.sub.t] in the contracting model, however, is more complicated, since it depends on such features of the economy as the synchronized versus staggered nature of contracts and their duration. In the case of Germany, annual wage contracts are essentially synchronized and expire at the end of the first quarter. Thus I designate the second quarter of each year as the first period, the third quarter as the second period, the fourth quarter as the third period, and finally, the first quarter of the following year as the fourth period of the contract. This implies that output in the second quarter will depend on one-step-ahead price surprises, output in the third quarter on two-step-ahead price surprises, . . . , and output in the first quarter of the following year on four-step-ahead price surprises. That is,

[y.sup.i.sub.t] = [y.sup.*.sub.t] = [beta][[p.sub.t] - [E.sub.t-i p.sub.t]] + [e.sub.t], i = 1,...,4. (3)

where [y.sup.i.sub.t] is output i th period of the contract, and [E.sub.t-i p.subt] is the expectation of [p.sub.t] conditioned on information available at the time of the contract negotiation date (t - i).

A simple framework to empirically distinguish between the two models is to decompose the multi-step-ahead price surprises into the one-step-ahead component, which is common to both equilibrium and contracting models, and the more-than-one-step-ahead component, which is distinctive to the contracting model as:

p[S.sub.t] = [[p.sub.t] - [E.sub.t-1 p.sub.t]] + [[E.sub.t-1 p.sub.t] - [E.sub.t-1 p.sub.t]], i =

1,...,4, (4) where the second term on the right-hand-side captures the forecast errors attributed to contract periods other than the first period.

Substituting equation (4) into equation (3) and generalizing the model by allowing different coefficients on the two price surprise terms yields,

[y.sub.i.sub.t] = [y.sup.*.sub.t] + [beta.sub.1][[p.sub.t] - [E.sub.t-1 p.sub.t]] +

[beta.sub.2][[E.sub.t-1 p.sub.t] - [E.sub.t-i p.sub.t]] + [e.sub.t]. (5)

The hypotheses to be tested involve the price surprise coefficients, [beta]1 and, [beta]2, which appear in equation (5). The contracting model predicts strictly positive values of the two parameters. In contrast, the equilibrium model predicts a non-negative value for [beta]1 and a zero value for [beta]2.

III. Empirical Methodology

Empirical estimation of the aggregate supply equation (5) requires proxies for one-to-four step-ahead price forecasts and the natural rate component of real activity. The construction of the proxies is explained next.

Price Prediction Errors

The proxies for one-to-four step-ahead price forecasts are based on estimates of four forecasting equations describing the processes generating the price level in each period of the contract. The information set in each forecasting equation includes a constant and four lags of the general price level (p) and the measure of real activity (y).(6) However, the lag length in each forecasting equation is adjusted to correspond to the number of periods elapsed since the contract negotiation date. For example, the one-step-ahead price forecasting equation includes the first-to-fourth lags of p and y, while the two-step-ahead price forecasting equation includes the second-to-fifth lags of p and y, and so on. The predicted values generated by these four regressions constitute the proxies for one-to-four step-ahead price forecasts. Next, the multi-step-ahead price forecasts series, [E.sub.t-i p.sub.t] (i = 1,...,4) is constructed by introducing four dummy variables, D l-D4, representing the first to fourth periods of the contracts. D1 takes a value of one if real activity occurs in the first period of contracts and zero otherwise. Similarly, D2 - D4 are constructed for the second to fourth periods of the contracts. Finally, [E.sub.t-i p.sub.t] is obtained as,

[E.sub.t-1 p.sub.t] = D1 [multiplied by] [E.sub.t-1 p.sub.t] + D2 [multiplied] [E.sub.t-2 p.sub.t]

+ D3 [multiplied] [E.sub.t-3 p.sub.t] + D4 [multiplied by] [E.sub.t-4 p.sub.t]. (6)

The proxies for one-step-ahead, [E.sub.t-1 p.sub.t], and multi-step-ahead, [E.sub.t-i p.sub.t], forecasts are substituted into the aggregate supply equation (5).

The Natural Rate

To take into account the natural rate component of real activity I apply the empirical methodology of Nelson and Plosser [13] by testing the time series properties of the measures of real activity.(7) Applications of this test to the three quarterly measures of real activity fail to reject the null hypothesis of difference stationary process.(8) This requires estimating the aggregate supply equation in a first-differenced form as,

[Dy.sub.t] = [alpha] + [beta.sub.1] D[[p.sub.t] - [E.sub.t-1 p.sub.t]] + [beta.sub.2] D[[E.sub.t-i

p.sub.t]] + [lambda][Dy.sub.t-1] + [v.sub.t], (7) where D is the first-difference operator, and the lagged dependent variable captures the effect of significant adjustment costs.

IV. Estimation and Results

The aggregate supply equation (7) and the four price forecasting equations are estimated jointly, subject to the restriction imposed by the identity (6), using a nonlinear three-stage least squares procedure.(9) To account for the possibility of any serial correlation in the residuals of the aggregate supply equation, [v.sub.t], a fourth-order autoregressive process is also introduced.

Table I contains the results of estimating the aggregate supply equation using three measures of real activity: real GNP (RGNP), index of industrial production (IIP), and industrial employment (EMP). At least four interesting results emerge from the table. First, multi-step-ahead price surprises do have an important effect on real activity, consistent with the prediction of the simple contracting theory. The coefficient of this variable, [beta.sub.2,] is positive and statistically significant at the 5 percent critical level in employment and industrial output equations, and at the 10 percent level in the real GNP equation. Second, one-step-ahead price surprises do not have a substantial impact on real activity. While [beta.sub.1] estimates have the correct positive signs, they are statistically insignificant in two of the three equations. Third, the estimates of [beta.sub.2] coefficient are substantially larger than those of [beta.sub.1]. Thus aggregate demand shocks that occur in the later periods of contracts are substantially more important in explaining movements in real activity. Finally, the results imply that the effects of nominal wage rigidities in Germany may persist up to four quarters, i.e., over the full contract period.

An Alternative Specification of the Model

A potential source of bias in the empirical estimation of equation (7) is the omission of the effect of supply-side disturbances on real activity. This omission is potentially troublesome since it can cause a negative bias in the estimates of the price surprise coefficients [8; 9]. Thus the lack of significance on estimates of the coefficient of one-step-ahead price surprises might be caused by this omission.

A solution to this problem is to replace the price surprises with proxies for aggregate demand shocks.(10) One such proxy is nominal GNP. Thus, I re-estimate equation (7) with nominal GNP

surprises along with four forecasting equations for one-to-four step ahead nominal GNP forecasts. The forecasts are based on an information set that includes four lags of the log of nominal GNP and a measure of real activity.(11)

Table II reports the results. Estimates of [beta.sub.2] are now significant in all three specifications at the 5 percent critical level. However, the estimates of [beta.sub.1] are still insignificant in two of the three cases. Thus the results of Table II are broadly consistent with the findings in Table I on the role of multi-step-ahead price surprises in determining real activity.

[TABULAR DATA OMITTED]

V. Concluding Remarks

This paper tests for an important and distinguishing prediction of the synchronized multi-period nominal-wage contracting model. This prediction reflects the role of multi-step-ahead aggregate-demand disturbances in determining aggregate real activity. The empirical results, using quarterly data on the German economy from 1965.1 to 1986. IV, are broadly consistent with this prediction. More specifically, multi-step-ahead aggregate-demand disturbances have positive and significant impacts on measures of aggregate output and employment. Furthermore, the results indicate that the effect of nominal wage rigidities in Germany may persist up to four quarters, i.e., over the full contract period. Thus, multi-period nominal-wage contracts may provide a channel through which nominal demand shocks affect real activity.

References

[1.] Card, David, "Unexpected Inflation, Real Wages, and Employment Determination in Union Contracts." American Economic Review, September 1990, 669-88. [2.] Cullingford, E. C. M. Trade Unions in West Germany. London: Wilton House Publications, 1976. [3.] Dickey, David A. and Wayne A. Fuler, "Distribution of Estimators for Autoregressive Time Series with Unit Root." American Statistical Association Journal, June 1979, 427-31. [4.] Fischer, Stanley, "Long-term Contracts, Rational Expectations, and the Optimal Money Supply Rule." Journal of Political Economy, February 1977, 163-90. [5.] Fuller, Wayne A. Introduction to Statistical Time Series. New York: John Wiley and Son, 1976. [6.] OECD Economic Surveys: Germany. Part: OECD, 1991/1992. [7.] Gray, Jo Anna, "On Indexation and Contract Length." Journal of Political Economy, February 1978, 1-18. [8.] _____, Magda Kandil and David E. Spencer, "Does Contractual Wage Rigidity Play a Role In Determining Real Activity?" Southern Economic Journal, April 1992, 1042-57. [9.] ----- and David E. Spencer, " Price Prediction Errors and Real Activity: A Reassessment." Economic Inquiry, October 1990, 658-81. [10.] Kandil, Magda, "Variations in the Response of Real Output to Aggregate Demand Shocks: a Cross-Industry Analysis." Review of Economics and Statistics, April 1991, 480-88. [11.] Lucas, Robert E., Jr., "Some International Evidence on Output-Inflation Trade-Offs." American Economic Review, June 1973, 326-34. [12.] Mohammadi, Hassan and Michael A. Nelson, "Monetary Innovations, Capital Taxation, and Real Wage Movements: Some New Evidence." Southern Economic Journal, April 1993, 629-40. [13.] Nelson, Charles R. and Charles I. Plosser. "Trends and Random Walks in Macroeconomic Time Series." Journal of Monetary Economics, September 1982, 139-62. [14.] Pagan, A., "Econometric Issues in the Analysis of Regressions with Generated Regressors." International Economic Review, February 1984, 221-47. [15.] -----, "Two-Stage and Related Estimators and Their Applications." Review of Economic Studies 53 1986, 517-38. [16.] Sargent, Thomas J. and Neil Wallace, "Rational Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule." Journal of Political Economy, April 1975, 241-54.

(1.) These models are neo-classical in the sense that they satisfy the natural rate hypothesis and use rational expectations. (2.) As is well known, the policy implications of equilibrium and contracting models are also vastly different. Contracting models support active monetary policy, provided that the monetary authority can react at intervals shorter than those at which contracts are negotiated. By contrast, equilibrium models are subject to the policy iffelevance proposition of Sargent and Wallace [16], given that private agents have the same information set as the monetary authority. (3.) This test is, however, based on the implicit assumption that the behavior of real activity in the non-contract sector of the economy is best represented by the equilibrium model. Furthermore, the test does not resolve the observational equivalence problem that exists between the two classes of models in a framework diat nests the implications of the two theories. (4.) For example, measured by the number of workers covered by collective bargaining, in 1992, 44.2% of annual wage contracts expired on March 31, 10.3% in April 30, and 7.7% in May and June. These contracts covered major industries such as metals, energy, printing, construction, retail trade, textiles, clothing, and chemicals. Thus, niore than 62% of new wage contracts became effective during the second quarter of the year. This constitutes more than 40% of total employment in Germany in the same year. A similar pattern is observed for odier years. Thus it is reasonable to assume the second quarter of each year as the beginning of a four-quarter contract. Additional infonnation on the nature of collective bargaining in Germany is found in [6, 65-9] and a historical perspective on trade unionism in Germany is found in [2]. I am indebted to Mr. Heinz Mattiesen, Labor Counselor at the Embassy of the Federal Republic of Germany, for providing the data on contract expiration dates. (5.) The data were compiled from several issues of the International Financial Statistics, International Monetary Fund. (6.) Several other macro variables were also considered as possible candidates for inclusion in the information set. They included the real price of energy, the government surplus, the call rate, and the M1 money stock. However, tests of Granger causality did not support any significant predictive power for any of these variables. (7.) Traditionally, the natural rate component is assumed to follow a trend stationary (TS) process and is modeled as a deterministic trend. The alternative difference stationary (DS) process proposed by Nelson and Plosser [13] is based on the statistical consideration that variations in the natural rate can be relatively large. In such cases, the TS specification can lead to an overestimation of both persistence and magnitude of business cycles. Thus appropriate specification of the natural rate requires tests of the stochastic properties of the real activity measures under consideration. Nelson and Plosser's test is an augmented version of the Dickey-Fuller [3; 5] test, which contains both TS and DS hypotheses as subsets. (8.) For all three measures of real activity, the null hypothesis of a difference stationary process could not be rejected against the trend stationary alternative. The t-statistics are well below the 5 percent critical value of -3.45 reported in Fuller [5]. The results are available upon request. (9.) An alternative approach is a two-step procedure. In the first step, the four price equations are estimated. The fitted values from these equations constitute the proxies for the one-to-four step-ahead price forecasts. Substituting the price forecasts into identity (6) will provide the proxy for the multi-step-ahead price forecasts. The second step entails substituting the one-step and multi-step price-forecasts into the aggregate supply equation (7) and applying ordinary least squares. However, as Pagan [14; 15] shows, the use of two-step procedure requires an adjustment in the covariance matrix of the second-step estimators. Application of nonlinear three-stage least squares avoids the use of first-step regression proxies by estimating the four price forecasting equations jointly with the aggregate supply equation and the identity (6). This procedure allows for cross-equation restrictions, takes into account the endogeneity of the price level, and provides asymptotically efficient estimates. The endogeneity of the price level is taken into account using instrumental variables. The instrument list includes seven lags of a real activity measure, nominal GNP, the call rate, and real oil prices, as well as cuffent and seven lags of M1, government surplus, and the Mark/Dollar exchange rate. Applications of this procedure are also found in Gray, Kandil, and Spencer [8], Gray and Spencer [9], Kandil [10], and Mohammadi and Nelson [12]. (10.) An alternative solution is to introduce proxies for anticipated and unanticipated supply shocks directly to the model. This requires estimating a more complicated model, which includes four additional forecasting equations for the supply shocks. (11.) The potential endogeneity of nominal GNP is also taken into account by using instrumental variables. The list of instruments is identical to that used for the price level.

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Author: | Mohammadi, Hassan |
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Publication: | Southern Economic Journal |

Date: | Jul 1, 1993 |

Words: | 3402 |

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