Wage growth and the inflationary process: a reexamination.

Darrat, Ali F.

I. Introduction

The nature of the relationship between wage growth and inflation has long been the subject of on-going debate. The expectations-augmented Phillips-curve theory contends that the two variables are mutually causal. However, the original wage-type Phillips-curve model argues it is inflation that causes wage growth rather than vice versa. The price-markup scheme holds an opposite view and asserts that wage growth plays an independent causal role in the inflationary process. Of course, other theories (e.g., the monetarist) deny the presence of any reliable linkage between wages and prices.

Researchers have also expended enormous effort attempting to investigate empirically the relationship between wage growth and inflation, but with mixed results. For example, Mehra [24] and Ashenfelter and Card [1] report results suggesting a bidirectional causality; Barth and Bennett [2] and Stein [37; 38] find causality running from prices to wages without feedback; while Shannon and Wallace [34] and Hill and Robinson [19] report results showing causality only in the reverse direction, from wages to prices. Still, Gordon [11], Bazdarich [4], Batten [3], and Mehra [27] find no causal linkage between the two variables. Clearly, such remarkably mixed evidence is unfortunate in light of the profound implications that the precise wage/price relationship may have for economic and public policy.

A more recent and quite interesting study is that of Mehra [28]. Mehra employed the technique of cointegration and error-correction modelling on U.S. quarterly data for the period 1959:1-1989:3. He concluded that inflation and wage growth are cointegrated, implying that their long-run movements are correlated as the expectations-augmented Phillips-curve theory predicts. However, contrary to this theory, and in accordance with the original wage-type Phillips-curve view, Mehra argued that the inflation-wage growth long-run correlation is primarily the outcome of the former causing the latter.

Mehra's model encompasses three basic variables; namely, prices (p), productivity-adjusted wages (w), and an output-gap proxy (g).(1) He tested each of the three variables (in logs) for the presence of unit roots, finding evidence of two unit roots in p and w, but a single unit root in g. Mehra then examined cointegration of the two variables having two unit roots (p, w). His results suggest that first-differences (but not levels) of prices and wages are cointegrated. Following Granger [14; 15], this finding if valid implies an error-correction model for inflation and wage growth and the presence of a Granger-causation between the two variables, at least in one direction. As mentioned, Mehra's results suggest that Granger-causality exists, but only from inflation to wage growth.

While interesting, Mehra's cointegration inferences may suffer from a serious omission-of-variable problem potentially biasing his results. Granger [15] has shown that cointegration and Granger-causality are closely related concepts. As such, cointegration tests may also be sensitive to the omission-of-variables phenomenon discussed by Lutkepohl [22] for Granger-causality tests. It is well-known that causality (and, by extension, also cointegration) inferences in a trivariate inflation model are not necessarily robust to inclusion of other relevant macroeconomic variables that could influence inflation. Interestingly, cointegration results recently reported by Miller [29] indicate that omission of important variables from a basic model did significantly distort his cointegration findings.

Literature on inflation provides a logical extension to Mehra's model. In particular, three additional variables appear potentially important for the inflationary process: namely, money supply, foreign exchange rate, and interest rates. The quantity theory of money places substantial weight on monetary changes in determining growth in aggregate demand and thus inflation. Empirical support of this monetarist view of inflation is overwhelming, as exemplified in the work of Fama [8], Dwyer and Hafer [5], and Hallman, Porter and Small [17]. In fact, in other studies, Mehra [25; 26; 27] also reports results indicating the significant role of money growth in the U.S. inflationary process.

A theoretical basis for linking inflation to exchange rates can be found in the theory of purchasing power parity [9; 12; 30]. Several empirical studies have uncovered significant relationships between movements in the dollar's exchange rate and U.S. price behavior, especially since the advent of the floating exchange rates in 1973. Examples include Sachs [31], Solomon [36], Whitt, Koch and Rosenweig [41], and Himarios [20]. Finally, for models of nominal income and its components (e.g., prices), Sims [35] strongly recommends the inclusion of interest rates. Several empirical studies have confirmed Sims's contention, including Fackler [7], Litterman and Weiss [21], and Stock and Watson [39]. Furthermore, Mehra [27] also finds evidence of the importance of interest rates (and money growth) in determining U.S. inflation.

The preceding discussion suggests the appropriateness of testing a general inflation model that encompasses the possible roles of money supply, foreign exchange rates and interest rates along with the two factors examined by Mehra [28]; namely wages and the output gap.(2)

The main purpose of this paper therefore is to reexamine Mehra's conclusions regarding the wage-price causal linkage in the context of a broader model. The empirical results from cointegration tests and the implied error-correction representation significantly alter Mehra's results and indicate their fragility to the omission of important variables. The following section discusses the results from unit-roots and cointegration tests. Next, findings for Granger-causality are analyzed. Concluding remarks are offered in the final section.

II. Test Results for Unit Roots and Cointegration

Following Mehra, I employ the augmented Dickey-Fuller (ADF) test to examine unit roots in each of the six variables. These are again the price level (p), productivity-adjusted wages (w), an output-gap (g), money stock (m), foreign exchange rates (e), and interest rates (r). As in Mehra, p is measured by the log of the fixed-weight GNP deflator, w is the log of the index of unit labor cost of the nonfarm business sector, and g is the log of real GNP over potential real output. The money variable (m) is the log of M1(3) and the foreign exchange rate (e) is the log of the exchange rate between the Japanese yen and the U.S. dollar. Hafer [16] finds evidence favoring the use of a bilateral exchange rate over the more common trade-weighted exchange rates in studying the exchange rate/inflation linkage. Given the fact that Japan is the largest trading partner with the U.S., I use the yen/dollar exchange rate. Indeed, in their September 1985 exchange-rate conference, the Group of Five (G-5) countries increasingly focused on the value of the yen relative to the dollar as a key indicator of the dollar's behavior in foreign markets [32].(4) Finally, the interest rate (r) variable is the log of the three-month Treasury Bill rate.(5) To use comparable data, all series come (as in Mehra's) from the Citibank data bank, except for data on potential real output which is similarly compiled from the Board of Governors of the Federal Reserve System. Like Mehra, my estimation period starts in 1959:1 but it extends to 1991:4. Terminating the sample period at 1989:3 used by Mehra produced similar results. Following Mehra, supply stock variables (relative prices of energy, food and imports) were included in the testing equations when they proved significant. Also included were dummy variables representing the periods during and immediately after Nixon's wage and price controls. For ease of comparison, I employ similar notations to those of Mehra's.

Table I reports the results from applying the ADF test on the six variables in levels and first differences. The results from the [[Phi].sub.3] statistics suggest the presence of two unit roots in four of the variables considered; namely, prices (p), wages (w), money stock (m), and exchange rates (e). The remaining two variables, output-gap (g) and interest rates (r), appear to exhibit a single unit root. None of the t-statistics for the time trend proves significant. These results seem robust to Schwert's [33] argument that the above unit root tests may be biased if the time series are generated by moving as well as autoregressive elements. Following Mehra, the results were checked for this difficulty by using longer lags than those suggested by the FPE criterion, and repeating the unit root tests. The results provided similar inferences.

The second step is to use the Engle and Granger [6] procedure to test for cointegration among the four variables having two unit roots. Table II displays the results of testing for cointegration between the four variables expressed in levels and first-differences. Unlike Mehra's, these results suggest that residuals from the regressions of wages in both the levels and first-differences have unit roots. On the other hand, residuals from the remaining three regressions (of p, m, and e) have unit roots only in the levels, but not in first-differences. These findings indicate that while the levels of prices, money stock and exchange rates are not cointegrated, the growth rates of TABULAR DATA OMITTED these variables are cointegrated. Hence, long-run movements in the growth rates of prices, money stock, and exchange rates are correlated.

In sum, the above results suggest that, contrary to Mehra, growth in wages is not cointegrated with growth in prices and thus their long-run movements appear uncorrelated. As discussed earlier, Mehra's finding appears to be the result of omitting some relevant variables (particularly money stock and exchange rates) from his cointegrating regressions.(6)

III. Test Results for Granger-Causality

The above unit-root and cointegration test results suggest that prices, money stock, and exchange rates have an error-correction representation of the form:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

TABULAR DATA OMITTED

[Mathematical Expression Omitted]

where the [Epsilon]'s are the disturbance terms, and the error-correction terms z's are the residuals obtained from the cointegrating regressions in first-differences reported in Table II. That is:

[z.sub.1] = [Delta][p.sub.t] - a - [b.sub.1][Delta][w.sub.t] - [b.sub.2][Delta][m.sub.t] - [b.sub.3][Delta][e.sub.t] - [b.sub.4][g.sub.t] - [b.sub.5][r.sub.t]

[z.sub.2] = [Delta][m.sub.t] - [[Phi].sub.0] - [[Phi].sub.1][Delta][p.sub.t] - [[Phi].sub.2][Delta][w.sub.t] - [[Phi].sub.3][Delta][e.sub.t] - [[Phi].sub.4][g.sub.t] - [[Phi].sub.5][r.sub.t]

[z.sub.3] = [Delta][e.sub.t] - [[Lambda].sub.0] - [[Lambda].sub.1][Delta][p.sub.t] - [[Lambda].sub.2][Delta][w.sub.t] - [[Lambda].sub.3][Delta][m.sub.t] - [[Lambda].sub.4][g.sub.t] - [[Lambda].sub.5][r.sub.t].

Since [Delta]p, [Delta]m, and [Delta]e appear to be cointegrated, there must be Granger-causality between them in at least one direction [15]. The null hypothesis that money stock does not Granger-cause prices, for example, is rejected not only if the [[Lambda].sub.2]'s in (1) are jointly significant, but also if [h.sub.1] is significant. Therefore, this error-correction representation of Granger-causality allows for the finding that money stock Granger-causes prices, even when the group coefficients on the money stock variable in the inflation equation are jointly insignificant, provided the error-correction coefficient ([h.sub.1]) is significant. Conversely, money is said to Granger-cause prices even if the error-correction coefficient is insignificant, provided that lags on the money stock are jointly significant.

Before discussing the empirical results from the EC model, a number of issues seem important. First, when conducting the unit-root and the cointegration tests, Mehra used the Akaike FPE procedure to determine the appropriate lag structure on all variables. However, when estimating his error-correction model, Mehra abandoned the FPE criterion without any explanation and employed instead "some arbitrarily selected lag lengths." For consistency, nonetheless, results from applying the same FPE procedure should also be reported. Therefore, unlike Mehra, I also report results from the error-correction model on the basis of the FPE criterion in addition to reporting results using similar lag specifications that were arbitrarily selected by Mehra. To check on the robustness of the results, I also used Hendry's general-to-specific approach to determine the lag profile for the EC model [10].

Second, there is the possibility that a structural shift may have occurred around the fourth quarter of 1979 corresponding to the change in the Federal Reserve operating strategy. This was apparently the reason that Mehra reported results for the sub-period terminated in 1979:4. However, this shift does not appear significant, judged by the similarity of Mehra's results for the full and sub-period samples. Yet, rather than ignoring altogether the structural instability issue when estimating the EC model,(7) I used the Chow test to check instability of each estimated equation, using 1979:4 as the breaking date. Only the money growth equation appears generally unstable across lag specifications. I used the Gujarati dummy-variable approach and isolated significant intercept- and slope-dummy variables that remain in the final equations.(8) Third, I tested all regressions in Table III for significant autocorrelations using the Breusch-Godfrey test and found none. Moreover, Ramsey's RESET test could not reject the hypothesis of no specification errors.

TABULAR DATA OMITTED

Finally, the method of estimating the EC equations requires some discussion. Apparently, Mehra used ordinary least-squares to estimate his wage and price regressions. Yet, more efficient estimates are possible using methods like the Zellner Seemingly-Unrelated Regressions (SUR) procedure, provided the errors across equations exhibit significant correlation. This is the case in the implied EC model, particularly for the money and exchange rate equations whose errors are highly significant at better than the one-percent level (correlation coefficient = 0.26, t = 3.06). Therefore, results for the three-equation EC model reported in Table III come from the Zellner SUR technique for each triad of equations.(9)

These results indicate that the error-correction coefficients in the price regressions across alternative lag specifications are generally not statistically significant. Also interesting is the finding that lags on the wage variable in the price regressions [Mathematical Expression Omitted] are statistically insignificant. Together with an insignificant error-correction coefficient, these results imply that wages do not Granger-cause prices. Such evidence further corroborates the earlier finding that long-run movements in wages and prices are not correlated. The price regressions in Table III also show that the remaining variables (money stock, exchange rates, output-gap, and to a lesser extent also interest rates) generally Granger-cause prices across the alternative specifications (see the values of [Mathematical Expression Omitted], [Mathematical Expression Omitted], [Mathematical Expression Omitted], and [Mathematical Expression Omitted]). The overall statistical significance of these variables in the error-correction model may serve as additional evidence for the potential bias in Mehra's trivariate price equations.

Table III further suggests that the error-correction coefficients in the money and exchange rate regressions are statistically significant across alternative specifications. This finding implies the presence of Granger-causality from all right-hand-side variables included in these regressions to the money and exchange rate variables. Note that the exchange-rate variable in the money equation and the money variable in the exchange-rate equation consistently appear with significant lagged coefficients. Combined with a significant error-correction coefficient in the respective regressions, it can be argued that a strong bidirectional Granger-causality exists between money stock and exchange rates. Although the other four variables also Granger-cause money and exchange rates (prices, wages, output-gap, and interest rates), it appears that their Granger-causality effect is transmitted primarily through the error-correction term in the respective regressions.

IV. Conclusion

This paper reexamines the issue of causality between wages and prices using unit-root and co-integration tests and their implied error-correction representation. Unlike Mehra's [28] recent trivariate model (wages, prices, and output-gap), I expand the model to include other theoretically relevant determinants of the inflationary process; namely, money supply, exchange and interest rates. It is well-known that omitting relevant variables can bias inferences from Granger-causality tests. The results reported in this paper demonstrate that cointegration inferences too, as reported in Mehra, are subject to similar omission-of-variable biases.

The most striking finding in this paper is that, contrary to Mehra's conclusion, wages and prices are not cointegrated and thus do not exhibit a reliable long-run relationship.(10) This finding is consistent, at least in spirit, with Gordon's [13] regression results and offers a new piece of evidence supporting Gordon's view that wages and prices are irrelevant to each other, and that they "live a life of their own".(11) The life of prices, it should be noted, seems correlated over the long-run with the behavior of money supply and exchange rates (rather than with wages). The results further show that Granger-causality underlying the movements in prices, money stock, and exchange rates is not one-sided, but rather mutual and complex. Therefore, a fruitful inquiry into the behavior of prices should be performed within a simultaneous-equation framework that emphasizes the joint determination of prices, money supply, and exchange rates.

1. In addition, some of Mehra's regressions included price-control dummies and supply-shock (relative-price) variables for food, energy, and imports.

2. A theoretical derivation of a similar general model of inflation can be found in Haslag and Ozment [18] and Stockton and Struckmeyer [40]. These researchers report further empirical evidence showing the superiority of such general inflation models to alternative views that ignore one or more possible determinants underlying the inflationary process.

3. Use of M2 or the monetary base instead of M1 did not alter the main conclusions of the paper. Results using these alternative monetary aggregates are available upon request.

4. The increased share and importance of Japan in U.S. international trade is also evident in the recent heated discussion in government and popular media circles regarding the huge trade deficit between the two countries. Note also that the need to employ a comparable sample period to that of Mehra's precluded the use of trade-weighted exchange rates whose series does not date back to 1959.

5. Alternative measures, like the 4-6 month commercial paper rate, yielded similar results.

6. Interestingly, my finding of no reliable relationship between inflation and wage growth is consistent with the Granger-noncausality evidence between the two variables reported by Mehra [27]. Instead of the wage growth, Mehra concluded that the output gap, money growth and interest rates are the three main causal variables underlying the U.S. inflation.

7. Lutkepohl [23] demonstrates that structural stability is required to produce reliable inferences from Granger-causality tests.

8. The significant dummy variables in the FPE and general-to-specific selected money equations are the intercept-dummy and the slope-dummy for the first lag of interest rates. For other money equations, the significant dummy variables are the first and third lags of interest rates in the four common-lag model; and the first lag of interest rates along with the first and fourth lags of the output gap. None of the dummy variables is significant in the eight common-lag model.

9. Following Mehra, the price-control dummies and the supply-stock variables for food, energy, and imports were included in each equation (using alternative lags) only when they prove statistically significant.

10. It should be noted that available cointegration tests are all designed to searching for long-run linear relationships among macroeconomic variables. Thus, the evidence reported above does not necessarily preclude the possibility that wages and prices may still exhibit, in some unknown fashion, a non-linear long-run relationship.

11. Earlier, Gordon arrived at essentially the same verdict. He states, "the wage-push hypothesis appears to be alive and well as an explanation of wage rate, but not as a theory of inflation" [11, 433].

References

1. Ashenfelter, Orley and David Card, "Time Series Representation of Economic Variables and Alternative Models of the Labor Market." Review of Economic Studies, 1982, 761-81.

2. Barth, James R. and James T. Bennett, "Cost-Push Versus Demand-Pull Inflation: Some Empirical Evidence." Journal of Money, Credit and Banking, August 1975, 391-97.

3. Batten, Dallas S., "Inflation: The Cost-Push Myth." Federal Reserve Bank of St. Louis, Review, June/July 1981, 20-26.

4. Bazdarich, Michael T., "Inflation and Monetary Accommodation in the Pacific Basin." Federal Reserve Bank of San Francisco, Economic Review, Summer 1978, 23-36.

5. Dwyer, Gerald P. and R. W. Hafer, "Is Money Irrelevant?" Federal Reserve Bank of St. Louis, Review, May/June 1988, 3-17.

6. Engle, Robert F. and Clive W. J. Granger, "Cointegration and Error-Correction: Representation, Estimation, and Testing." Econometrica, March 1987, 251-76.

7. Fackler, James S., "An Empirical Analysis of the Markets for Goods, Money and Credit." Journal of Money, Credit and Banking, February 1985, 28-42.

8. Fama, Eugene F., "Inflation, Output, and Money." Journal of Business, April 1982, 201-31.

9. Frenkel, Jacob A., "Purchasing Power Parity: Doctrin Perspective and Evidence for the 1920s." Journal of International Economics, May 1978, 169-91.

10. Gilbert, C. L., "Professor Hendry's Econometric Methodology." Oxford Bulletin of Economics and Statistics, August 1986, 282-303.

11. Gordon, Robert T., "World Inflation and Monetary Accommodation in Eight Countries" Brookings Papers on Economic Activity, 1977, 409-468.

12. -----. "Inflation, Flexible Exchange Rates, and the Natural Rate of Unemployment," in Workers, Jobs, and Inflation, edited by Martin N. Baily. Washington, D.C.: The Brookings Institution, 1982.

13. -----. "The Role of Wages in the lnflationary Process." American Economic Review, May 1988, (Papers and Proceedings), 276-83.

14. Granger, Clive W. J., "Developments in the Study of Cointegrated Economic Variables." Oxford Bulletin of Economics and Statistics, August 1986, 213-28.

15. -----. "Some Recent Developments in the Concept of Causality." Journal of Econometrics, September/October 1988, 199-211.

16. Hafer, R. W., "Does Dollar Depreciation Cause Inflation?" Federal Reserve Bank of St. Louis, Review, July/August 1989, 16-28.

17. Hallman, Jeffrey J., Richard D. Porter and David H. Small, "M2 Per Unit of Potential GNP as an Anchor for the Price Level." American Economic Review, September 1991, 841-58.

18. Haslaq, Joseph H. and D'Ann M. Ozment, "Money Growth, Supply Shocks, and Inflation." Federal Reserve Bank of Dallas, Economic Review, May 1991, 1-17.

19. Hill, John K. and Kenneth J. Robinson, "Money, Wages, and Factor Scarcity as Predictors of Inflation." Federal Reserve Bank of Dallas, Economic Review, May 1989, 21-29.

20. Himarios, Daniel, "The Impact of the Exchange Rate on U.S. Inflation and GNP Growth: Comment." Southern Economic Journal, April 1989, 1044-51.

21. Littermon, Robert B. and Lawrence Weiss, "Money, Real Interest Rates and Output: A Re-interpretation of Postwar U.S. Data." Econometrica, January 1985, 128-56.

22. Lutkepohl, Helmut, "Non-Causality Due to Omitted Variables." Journal of Econometrics, August 1982, 367-78.

23. -----. "The Stability Assumption in Tests of Causality Between Money and Income," in Econometrics of Structural Change: Studies in Empirical Economics, edited by Walter Kramer-West Germany: Physica-Verlaq Heidelberg, 1989.

24. Mehra, Yash P., "Money Wages, Prices, and Causality." Journal of Political Economy, December 1977, 1227-44.

25. -----. "The Forecast Performance of Alternative Models of Inflation." Federal Reserve Bank of Richmond, Economic Review, September/October 1988, 10-18.

26. -----. "Cointegration and a Test of the Quarterly Theory of Money." Federal Reserve Bank of Richmond, Working Paper 89-2, April 1989.

27. -----. "Real Output and Unit Labor Costs as Predictors of Inflation." Federal Reserve Bank of Richmond, Economic Review, September/October 1990, 31-39.

28. -----. "Wage Growth and the Inflationary Process: An Empirical Note." American Economic Review, September 1991, 931-37.

29. Miller, Stephen M., "Monetary Dynamics: An Application of Cointegration and Error-Correction Modeling." Journal of Money, Credit and Banking, May 1991, 139-54.

30. Officer, Lawrence H., "The Purchasing-Power Parity Theory of Exchange Rates: A Review Article" International Monetary Fund, Staff Papers, March 1976, 1-60.

31. Sachs, Jeffrey D., "The Dollar and the Policy Mix: 1985." Brookings Papers on Economic Activity, 1985, 117-85.

32. Sakamoto, Tomohiko, "The Japan-US Bilateral Trade." Federal Reserve Bank of San Francisco, Economic Review, Spring 1988, 3-13.

33. Schwert, G. Williams, "Effects of Model Specification on Tests for Unit Roots in Macroeconomic Data." Journal of Monetary Economics, July 1987, 73-103.

34. Shannon, Russell and Myles S. Wallace, "Wage and Inflation: An Investigation into Causality." Journal of Post-Keynesian Economics, Winter 1986, 182-91.

35. Sims, Christopher, "Macroeconomic and Reality." Econometrica, January 1980, 1-48.

36. Solomon, Robert. "Effects of the Strong Dollar," in The U.S. Dollar-Recent Developments. Outlook, and Policy Options. Federal Reserve Bank of Kansas City, 1985, pp. 65-88.

37. Stein, Jerome L., "The Acceleration of Inflation." Journal of Post-Keynesian Economics, Fall 1979, 26-42.

38. -----, "Reply to McKenna and Zannoni." Journal of Post-Keynesian Economics, Spring 1984, 479-80.

39. Stock, James and Mark Watson, "Interpreting the Evidence on Money-Income Causality." Journal of Econometrics, January 1989, 161-82.

40. Stockton, David T. and Charles S. Struckmeyer, "Tests of the Specification and Predictive Accuracy of Non-nested Models of Inflation." Review of Economics and Statistics, May 1989, 275-83.

41. Whitt, Joseph A., Paul D. and J. A. Rosenweig, "The Dollar and Prices: An Empirical Analysis." Federal Reserve Bank of Atlanta, Economic Review, October 1986, 4-18.