The Dynamic Behavior of Wages and Prices: Cointegration Tests within a Large Macroeconomic System.

• Author: Schmidt, Martin B.

Martin B. Schmidt [*]

The dynamic relationship between wages and prices has long held a central place within the economic literature. Most macroeconomic models make assumptions as to the causal relationship between the two variables. Unfortunately, empirical investigations have produced widely divergent results. In particular, the present paper examines the results of time-series studies and argues that the lack of a consensus is due to improperly specified models. Once the wage-price relationship is embedded within a multiple vector system, identification of a wage-price cointegrating relationship is significantly improved. In addition, the increased efficiency yields evidence in favor of the dual feedback between wages and prices.

1. Introduction

   A belief in a systematic and stable relationship between wage and price behavior underlies much of standard macroeconomic theory. While most models share this belief, they differ dramatically when it comes to their presumed direction of causal influence. For example, the original Phillips curve relationship hypothesized that price inflation imparts pressure on wages. Such an assumption is indicative of prices having a unidirectional impact on the wage process. In contrast, the notion that prices are set at a given percentage markup over wage costs is popular within post-Keynesian economic thought. Interestingly, such models maintain that the wage process performs an independent causal role in the inflationary process. Furthermore, the expectations-augmented Phillips curve combines these theories and would, therefore, predict joint causality between price inflation and wage inflation. Finally, in order to complete the possibilities, many monetarist models fail to recognize any systematic relationship, let alo ne any causal relationship, between the two economic variables.

   Given the importance of the relationship in determining the relative merit of these opposing theories, it is not surprising that a large empirical literature exists investigating the causal responses of prices and wages. In an early study, Barth and Bennett (1975) combined consumer prices, hourly wages of production workers, and a monetary variable into a three-variable system. By examining the significance of future lags (either 4 or 8) of each variable, they determined that consumer prices were significant in explaining hourly wages, indicating that consumer prices caused hourly wages. In contrast, future hourly wages were insignificant in explaining the current behavior of consumer prices and therefore wages did not cause prices. Also, in order to highlight the importance of money in the process, money was found to cause movements in prices.

   Ashenfelter and Card (1982) reported markedly different results. They modified the Barth and Bennett study to include the unemployment rate and a nominal interest rate while dropping the money variable. Using a four-variable vector autoregressive (VAR) system (with a lag of 4), the results from Granger-type equations provided strong evidence of wages Granger-causing prices. However, there was only weak support for prices Granger-causing wages. In addition, the influence of unemployment on prices and wages was rejected. Interest rates, however, did play a strong role in the behavior of prices although not for wages.

   Shannon and Wallace (1986) adjusted these early studies on two levels. First, they chose unit labor costs to control for wage increases associated with productivity gains, which would not be expected to be inflationary. The second was to include a measure of output into the VAR model. Once income and money were added to the VAR equations containing the GNP deflator and unit labor costs, the results fall in line with Ashenfelter and Card, as Granger causality was estimated only from wages to prices.

   Overall, these early studies indicated that the relationship between wages and prices was sensitive to the choice of additional right-hand-side variables. In addition, they provided at least marginal support for the importance of income, money, and nominal interest rate variables in altering the estimation of the wage-price relationship. However, the time-series behavior of most of these series, wages and prices included, is generally believed to be nonstationary, and therefore much of the variability in the results may have had to do with the "spurious" nature of regressing nonstationary series on each other.

   An intuitive solution to control for the "spurious" effect would be to difference the nonstationary series until each series becomes stationary. Since the estimation would then involve stationary variables, the unreliability and inefficiency of the estimation would clearly be removed. However, as Hendry (1986) and Granger (1988) argue, differencing economic time-series data removes all the information about the long-run relationships. In the case where variables are cointegrated, important information would be lost. In addition, Hakkio and Rush (1989) show that taking first differences of cointegrated variables in order to obtain a stationary series may result in an omitted variable bias.

   Rather than omit what may be relevant information, the focus has moved toward analyzing the cointegrating relationship between the GNP deflator and unit labor costs. [1] However, the question of Granger causality is more complicated when variables are cointegrated. A rejection of Granger causality requires not only that the lagged variables be insignificant but also that the speed of adjustment coefficient be zero. Vector error-correction equations (VEC) modify the VAR structure to incorporate the speed of adjustment variable(s). [2]

   Two recent studies have incorporated both cointegration and VEC estimation. Both Mehra (1991) and Darrat (1994) reexamine the relationship between price and wage inertia accounting for the nonstationary behavior of the data. Surprisingly, the two obtain contradictory results. Using unit labor costs, the GNP deflator and an output-gap variable, Mehra offers augmented Dickey-Fuller (ADF) test results that indicate that both unit labor cost and the GNP deflator have two unit roots, that is, I(2), while the output-gap variable has one, that is, I(1). Consistent with the ADF results, cointegration to I(0) is then found between the differences of prices and the difference of unit labor costs but not between their levels. Also, the inclusion of the speed of adjustment parameters within the VEC yields support for Granger causality from prices to wages. However, the results fail to generalize as wages were not found to Granger-cause prices.

   Following Lutkepohl (1982), Darrat argues that Mehra's Granger-causality tests are subject to an "omission-of-variables" bias. In addition, since cointegration and VEC models are closely related to Granger causality, these also may suffer from the same bias. Darrat suggests that the wage-price relationship would be more accurately estimated within a general inflation equation. Specifically, Darrat follows much of the earlier literature by including a money variable and an interest rate variable in addition to introducing a measure of exchange rates into the wage-price vector. Once these omitted variables are included, Darrat is unable to find a cointegrating relationship between either the levels or the differences of unit labor cost and the GNP deflator. The results support Gordon's (1988) view that prices and wages have little to offer one another and that wages "live a life of their own.

   The present paper is equally concerned with the possible biases introduced when estimating improperly specified cointegrating vectors. Recent theoretical work by Phillips (1991) and Johansen (1992) demonstrates that the omission of relevant variables in an analysis of cointegration may produce biased and inefficient estimates of the number of both cointegrating relationships and cointegrating coefficients. Given the fact that most, if not all, economic variables and/ or relationships are not determined in isolation, estimating these in a single equation format may subject the results to the concerns raised by Johansen and Phillips. Recent studies by King et al. (1991), Cutler et al. (1997), and Cutler, Davies, and Schmidt (1997) have found empirical support for the efficiency gains associated with embedding a single macroeconomic equation within the framework of a larger macroeconomic system.

   Therefore, unlike Darrat, who introduces additional variables into the wage-price vector itself, the present paper opts to embed the wage-price vector within a larger set of macroeconomic relations. Such an approach allows the vector to be estimated within a set of simple, stable, and theoretically consistent relationships. The system of equations incorporates many of the additional right-hand variables suggested in the previous studies but introduces them in a more systematic way. Therefore, the approach may be viewed as less arbitrary than what would be necessitated by the constant inclusion and exclusion of right-hand-side variables whose theoretical importance may be argued and whose impact may vary over time.

   The macroeconomic system used here, with its multiple vectors, follows King et al. (1991), Cutler et al. (1997), and Cutler, Davies, and Schmidt (1997). King et al. examine the behavior of six macroeconomic variables (real income, consumption, investment, real money balances, the nominal interest rate, and the inflation rate). From these, they are able to estimate investment, money, and consumption functions. Cutler et al. modify the King et al. system of variables to include imports and are able to derive the additional import function. Cutler, Davies, and Schmidt incorporate nominal Ml and the GNP deflator and find stronger evidence of an Ml demand relationship than much of the previous literature. For the present purpose, unit labor costs are added to the King et al. model. Therefore, the wage-price...