# Inflation: some empirical evidence.

I. Introduction

A great part of the post-Keynesian/monetarist debate arose from disagreement about the causal routes of inflation. In this respect, the question of whether it is possible to implement a test which will distinguish between cost-push and demand-pull inflation has a direct relevance to the selection of policies designed to avoid inflation. The extreme cost-push position advocates that only institutional factors are responsible for causing inflation; therefore, an institutional reform through, for example, prices and incomes polices is called for. Demand-pull adherents propose that long-run solutions to inflation must be based on demand restraint policies. Here, both the monetarist model and the Keynesian inflationary gap model are in agreement. Monetarists, however, claim that "inflation is always and everywhere a monetary phenomenon"(1) and, as such, prefer a regime of monetary control in which the growth rates of money and nominal income are compatible. In other words, monetarists contend that money supply |causes' prices without feedback. By contrast, neo-Keynesians hold that through the inflationary gap, changes in real income (aggregate demand) are expected to cause changes in prices. The endogeneity of income and prices in a simultaneous Keynesian system also implies that income and prices exhibit bidirectional causality.

Conventionally inflation was mainly explained through the wage/price (Phillips curve) approach which has been claimed to explain both demand-pull and cost-push inflation. Samuelson and Solow (1960) argued that if costs and prices are insignificantly sensitive to demand-restraint policies such that unemployment significantly increases, then cost-push inflation is dominant; and likewise the reverse is true for demand-pull inflation. Up to the 1970's markup models dominated inflation theory, but since that time monetarist models have taken over. Gordon (1988) argued that inflation (changes in the GNP deflator) do not statistically explain the behavior of each other; indicating that markup pricing hypothesis is dead. Notwithstanding, one of the by-products of this paper is to signify that such conclusions are probably sensitive to the type of price index used. Furthermore, reduced-form regressions are more indicative of correlation relationships than causal linkages. Of course, a bidirectional causality between wages and prices is supportive of cost-push theory in which case firms are bound to adjust any price expectation by the average costs, indicating that markup pricing may still be alive.

Numerous other studies by, for example, Cushing and McGarvey (1990), Gutherie (1981), Silver and Wallace (1980), and Engle (1978), among others, have examined the causal linkages between the CPI and the producer price index (PPI). Using one-way distributed lags, Gutherie, Silver and Wallace, and Engle found a unidirectional causality going from wholesale prices to consumer prices, a result which is consistent with markup pricing (cost-push) theory. Cushing and McGarvey are supportive of the perfectly flexible price (derived demand) and strong demand elements theory. However, it should be pointed out that using one-way causality testing from producer prices to the CPI to support markup pricing implies a fixed wage rate postulation (as in traditional Keynesian models). Likewise, the perfect (foresight) flexible prices (or the full-employment model) assumes away money illusion such that money wages perfectly adjust with any price changes, indicating a unidirectional causality from prices to money wages. Under imperfect foresight, however, money wages and prices may possess feedback causal links. Moreover, almost all previous studies emphasized mainly the role of money as a measure of aggregate demand, with no reference to the Keynesian aggregate demand (output). On the other hand, studies, such as Leon (1986), which concentrate only on inflation and output growth (without considering the potential effect of money) are probably flawed.

Clearly, the diversity of the results together with the profound importance of the issue of inflation requires further examination.

This paper provides further empirical evidence on wages, income (Keynesian demand), and money (classical demand). Besides being a direct component of costs, the inclusion of wages permits the investigation of their possible spiral influences with prices. To mitigate the inherent simultaneity in the wages and prices process, the contemporaneous lags were dropped such that the regressions were run only on exogenous (predetermined) variables. Note that Granger (1969) recommends dropping the contemporaneous lags for proper causality testing. In addition, adjustment is also made for the possibility of a structural breakdown in the relationship during periods of relatively high inflation (1947-1959 and 1975-1982) and those of relatively low inflation (1960-1974), and the variables are tested for the presence of unit roots. Another point of departure from previous studies in this area is that in this study stationarity tests (to perform Granger and Sims' causality methods) are done using Box-Jenkins' procedure instead of using Sims' filter or simple time trends.

The paper is organized as follows: In section II we described the data and the methodology. In section III we identify and estimate the different series using Box-Jenkins' method to ensure that the series are white-noise. Then we proceed to conduct causality testing using both Sims' and Granger's approaches.(2) Section IV examines the possibility of equilibrium (long-run) relationship between the variables using cointegration tests. In section V we discuss the results of Almon's distributed lags in an attempt to give further insight into the long-run and short-run properties of the cost-push and demand-pull inflations. Section VI concludes the paper.

II. Data and Methodology

The paper envisages the proclaimed monetarist exogeneity of money supply to prices, nominal income, and to real income. The neo-Keynesian inflationary gap theory will be examined by studying the causality linkages of aggregate demand (real income) and prices. The cost-push relationship of wages to prices will also be investigated. Both two-sided distributed-lag (Sims 1972)(3) and one-sided distributed-lag methods (Granger 1969)(4) of causality testing will be employed. Although Sims' approach has been widely used, Granger's method is probably superior. Granger's inclusion of the lagged dependent variable is more likely to purge residual autocorrelation. Furthermore, Granger's method of using only past values of the dependent and independent variables exhausts less degree of freedom; unlike Sims' approach which uses past as well as future values of the independent variable. Using both methods could, therefore, shed some light on the validity (or lack thereof) of previous studies and, moreover, provide some evidence on the robustness of the obtained results (see Feige and Pearce, 1979). In addition, we used Box-Jenkins' procedure to prewhiten each series separately instead of imposing a priori Sims' filter as commonly done in previous work(5). To assume a white-noise series, we selected the ARIMA models (Table I) with insignificant autoregressive and moving-average portions, and with the smallest Box-Pierce Q statistics.

Robust results are also to be maintained through a search for the optimum lag structure of the equations using Theil's minimum residual-variance criterion. In addition, we adopted Berman's (1978) sensitivity tests by selecting forward and backward lengthening procedures and then testing for a candidate lag by "straddling" with other shorter and longer lags. Based on these criteria, the ten-lag structure has been found to be appropriate.(6)

Furthermore, cointegration and the Almon lag technique will be used to investigate whether an equilibrium (long-run) relationship exists between the variables and the range of lags (short-run or distant lags) over which the independent variables affect the dependent variables in an attempt to distinguish between short-run and long-run effects of demand-pull and cost-push inflation. There is, more or less, a consensus that the influence of demand factors on inflation is continuous (long-run); and that demand factors tend to initiate as well as perpetuate inflation. However, monetarist (Cagan, 1979) tend to think of cost-push factors as exerting a perpetuating (short-run) effect on inflation, because there is an implicit presumption that prices tend to "cause" changes in wages (and other costs) without continuous feedbacks. Through the Almon lag technique, we should be able to isolate the impact of the different variables on each other at different time periods, and also acknowledge whether the cumulative effect is significant (continuous) or insignificant (short-run). Note that cointegration (unlike the Almon lag) does not trace out the relationship between the variables at each and every specific lag. The Almon lag has also been commended over the Cagan-Koych (adaptive expectations) method because it requires less stringent restrictions and is more consistent with perfectly rational expectations (Muth 1961) which considers only supply side exogenous shocks, and with partially rational (Sargent 1973) models subject to both supply and demand shocks.(7) To avoid spurious results due to improper choice of the lag of the polynomial functions of the Almon technique, Theil's criterion together with stability tests of the different functions will be adopted. Stability tests are used to detect whether demand-pull and/or cost-push are typically characteristic of certain important sub-periods where structural shifts in the economy are suspected. Three sub-periods were though to be critical: (1) 1947-1959; the period immediately following the end of World War II which included the Korean War. Inflation during this period was persistent at an annual rate of about 2-4% in industrial countries. (2) 1960-1974; during the first half of the sixties the U.S. enjoyed relatively lower rates of inflation (about 2%), but by the early 1970's worldwide inflation was imminent. (3) 1975-1982; this period experienced two major OPEC price shocks when double-digit inflation hit the U.S. economy in 1974-1975 and returned again during the 1979-1981 period. The Chow-test for stability reflects no undue cause for concern about structural shifts over the sample period.(8)

U.S. quarterly data covering the period 1947.1-1986.4 have been used. The data for M1 has been taken from the Federal Reserve Bulletin (various issues). All other variables have been taken from The Handbook of Cyclical Indicators (1984) and Business Conditions Digest (various issues). All variables are stationary after differencing and are transformed into natural logarithmic forms to give percentage (growth rates) changes directly and to help alleviate trend and serial correlation. Indeed, none of the subsequent regressions experienced any significant serial correlation.(9) The different variables are defined as follows:

NY = percentage change in nominal

CPI = percentage change in consumer

price index;

PPI = percentage change in producer

WN = percentage change in nominal

wage rates.

III. Causality (Exogeneity) Results

In Table I, the series are identified and estimated using the Box-Jenkins' method. The autocorrelations of the changes in the original series are non-stationary. For almost all series autocorrelations range from .55 to .00 until the 20th lag. With first differencing, we were able to find stationary series for the change in the CPI and the change in real GNP. All other series were stationary after they were differenced a second time. The ARIMA models that were chosen are found in Table 1. The chosen models have minimum standard errors and Q statistics. [Tabular Data I Omitted]

Using the white-noise series we proceeded to test for causality utilizing both Sims' and Granger's tests of causality. Using Sims' test, causality is indicated by the insignificance of the F-values on future-lagged variables. For Granger's method, causality is indicated by the significance of the F-values on the sum of lagged independent variables. The results shown in Table II, III and IV affirm the monetarist claim that monetary expansion leads to demand-pull inflation. That is, unidirectional causality runs from money supply to prices (and not the reverse) such that money supply is truly exogenous to prices. Nevertheless, our empirical investigations lends some support to the two-way endogeneity of money supply and the Keynesian aggregate demand (real GNP). There is bidirectional causality effects between money supply and both nominal and real incomes. The results so far are not inconsistent with Keynesian theory which applauds the monetarist belief that monetary expansion causes demand-pull inflation. Yet, the results also emphasize the influence of aggregate demand on inflation; hence, the importance of demand-management policies to curb inflation. These results are further supported by the unidirectional causality going from real GNP (aggregate demand) to the CPI; whereas the PPI and the GNP deflator show and independent relationship with real GNP. This casts some doubt on Cagan's contention that demand is not related to prices in the short-run. Cagan's assertion is based on manufacturing prices (PPI) only.(10) It is true that manufacturing prices may not be responsive to short-run shifts in demand, but consumer prices are. In congruence with this, Thornton (1988) reports a positive relationship between the CPI and real output for some developed countries.

[Tabular Data III Omitted]

Causality linkages examined in this paper also reveal that the simultaneous existence of both cost-push and demand-pull inflation is possible. Nominal wages show a bidirectional (wage-price spiral) causality with all prices in the economy.(11) The endogeneity of prices and nominal wages to each other offers strong support to the wage-price spiral theory. Thus firms cannot base price expectations only on excess demand; cost considerations are also important. That is, the impact of cost-push inflation is continuous. Hence, breaking down of labor unions may temporarily interrupt the wage-price spiral, but the bidirectional causality existing between wages and prices raises the possibility of an independent cost-push inflation, regardless of unions' actions.

IV. Cointegration Results

The causality results between prices, money, and income are reported in Table IV. Such causal inferences may gain more insight if the causally linked variables possess an equilibrium (long-run) relationship, and if the causally independent variables lack a significant equilibrium relation. Recently, it has been demonstrated by Engle and Granger (1987), and Granger (1986), among others, that cointegration (common trends) can be used to test for the presence of a equilibrium relationship between variables containing unit roots.

To test for the presence of a unit-root, we regress the first difference of, for example, the CPI on its lagged value, in addition to a constant, a time trend, and a lagged dependent variable which will approximate short-run dynamics and yield white-noise residuals. If the coefficient (of the CPI) is significant, then we reject the null hypothesis that the variable, in level form, contains a unit-root. The test statistic is calculated by dividing the estimated coefficient by the standard error, and the critical values are modified t-values reported in Fuller (1976).

Each of the series reported in Table IV, was examined for the possible order of difference stationarity. As reported in Table V, the null-hypothesis that non-stationarity (unit-roots availability) could not be rejected for the levels of all variables. The next step is to see whether the series have the same unit-roots (cointegrated) or have different unit-roots. After differencing, the series were found to be stationary.

To test for cointegration, we regress the different variables against each other (plus a constant term). The resulting equation is called the cointegrating (equilibrium) regression. The absence (presence) of cointegration is indicated by the nonstationarity (stationarity) of the residuals. We followed Darrat and Suliman (1990), Engle and Yoo (1987), and Miller and Russek (1990) to test the hypothesis of no cointegration. As such, we performed a Dickney-Fuller test (DF), an Augmented Dickney-Fuller test (ADF), and a modified Durbin-Watson test (DW).

The DF test requires regressing the first differences of the estimated residuals from the cointegrating regressions on their lagged values, and then testing the significance of the estimated coefficient. The t-ratios are compared against modified critical values reported by Engle and Yoo. The ADF test adds to the DF test a lagged dependent variable (to alleviate any autocorrelation). For the DW test, the resulting DW statistics from the cointegration regressions are compared against some critical values given by Engle and Yoo.

Except for the case of the CPI and real income (Y), the three tests are consistent with our causality results reported in Table IV. As shown in Table V, the tests could not reject the hypotheses of no cointegration for money and the three price indices, for money and income, and for wages and prices. Not surprisingly, however, no cointegration was found to exist between real income and the three price indices.

V. Distributed Lags and the Time-path

This study has also envisaged the long-run effects of demand-pull and cost-push inflations by tracing out the time-path of the estimated distributed lag coefficient, using both Almon's lags and OLS unrestricted lags. It is important to note that when Almon technique is used the resulting t-statistics may end up being high. This is because they are testing whether coefficients can be made zero while maintaining the shape restriction, which is almost impossible.(12) The Almon lags are shown in Table VI.(13) The significance of the distributed lag is determined if most of the individual lags are significant, and also the sum of the coefficients must be significant. The use of distributed lags at this point is quite legitimate as supported by the above exogeneity tests of Sims and Granger, One, first, must be clear about exogeneity; thereafter one can ponder long-term and short-term effects.

Both Almon and unrestricted lag techniques were used to avoid spurious results from uncertain Almon restrictions on the shape of the coefficients. However, Almon's technique does a superb job in measuring the accumulated weight-impact (weighted average) of the exogenous variable on the endogenous variable. Moreover, the Almon lag technique alleviates multicollinearity. The results of both methods are consistent with each other. These distributed lag investigations indicate the co-existence of both demand-pull and cost-push inflations at different time periods. Besides, demand-pull inflation appears to be more explicable through exogeneity of money supply rather than the traditional Keynesian aggregate demand. Even though our causality (exogeneity) tests suggest that real income (aggregate demand) may cause a change in the CPI, the weighted-average Almon technique gives very weak support for this result where only the first two lags (short-run) results are significant at the 10% level. This finding is consistent with Leon's (1986) results indicating the absence of a long-run relationship between output growth and inflation. Furthermore, the existence of feedback causality between money and real income (aggregate demand) indicates that changes in aggregate demand affect prices mainly through their impact on money supply. The distributed lag results show that the cumulative impacts of changes in money supply on nominal income, real income, and prices vary significantly over time. The heaviest positive impact on all three variables occurs during the initial five lags, with negative impacts coming after that on nominal and real income. The negative impact on nominal income dies out as time goes on; whereas the negative impact on real income gets stronger with time. The positive impact of monetary expansion on prices also gets weaker over time. The results have some appealing intuitive implications: that the division of nominal income into real income (quantity) and prices is revealed by observing that the impact of money on nominal income seems to follow an average conflicting force of its two components. Although the impact on both prices and real income is stronger in the first few lags, the negative impact on nominal income seems to die out exponentially following the same pattern as prices where their positive coefficients are also dying-out exponentially. These results, though not inconsistent with the monetarist belief of no money-illusion, are not indicative of any permanent impact of money on nominal variables since inflation dies exponentially. This type of evidence is probably in disagreement with Mehra's (1978) result that the effect on the price level is negligible during the time when real and nominal income are increasing due to monetary expansion.(13)

Furthermore, our bivariate distributed lag analysis indicates a cost-push (wage-price spiral) over time. The regressions of wages and prices against each other indicate that the sums of the coefficients as well as most of the individual coefficients are significant at the 5% level. For the GNP deflator and the CPI regressions, the cumulative sums of coefficients are definitively significant at the 5% level. However, the impact of wages on the PPI is only significant during the initial time periods. By intuition, any increase in producer prices through higher wages is passed immediately to consumer prices. These arguments are congruous with cost-push theory in that money wages cause a push in prices with a feedback (spiral) to wages from prices. The results, moreover, tend to suggest that empirical findings about the inflationary process are contingent on the price index used. Different indexes may interact with wages differently at different time periods. Furthermore, the wage-price bidirectional causation elucidates the Phillips curve formulation of a relationship between the rate of wage change (inflation) and unemployment; implying that the specification of a wage equation in the estimation of the natural rate of unemployment is probably not irrelevant.

VI. Summary and Concluding Remarks

This paper has re-examined the cost-push and demand-pull theories of inflation. Recent investigations by Cushing and McGarvey (1990), Gordon (1988), Gutherie (1981), and Silver and Wallace (1980), among others, have produced diverse results. However, these studies have generally tended to consider cost-push inflation in isolation of demand-pull; with cost-push proponents contending a one-way causality from the wholesale price to the CPI, and derived demand (perfectly flexible prices) adherents indicating the reverse causality as well. Moreover, there is no clear consensus as to whether money is a more appropriate proxy for aggregate demand than real income (total expenditure).

To make ends meet, we tried having (in isolation) both money and real income as proxies for aggregate demand. We also considered the three price indices together with nominal wages to test for cost-push. Bivariate causality testing has been carried out in both directions for all variables (taken two at a time). To cater to robustness, both Sims and Granger methods have been utilized. Further support of causality (or non-causality) is derived from cointegration tests, which (together with the Almon lag) is used to examine the existence of long-run relationships. Adjustments have also been made for the possibility of a structural break in relatively high inflation periods (1947-1959 and 1975-1982) and relatively low inflation periods (1960-1974), and, moreover, the Box Jenkins' procedure has been used to test for stationarity.

Contrary to pure markup pricing supporters and derived demand adherents, this study stands neutral. Our results do not refute either the cost-push or demand-pull theories. Both inflation theories are coexistent over time, and it is almost impossible to identify the existence of any of them with time-length, a finding consistent with imperfect foresight formulations. However, demand inflation appears to be more definitive with monetary growth than the Keynesian aggregate demand (real income). Of course, this does not preclude the possibility that real income ad inflation are jointly determined in a simultaneous equation system.(14) Cost-push (wage-prices) inflation is also significant and continuous, suggesting that firms are apt to form their price expectations based on costs together with excess demand. Furthermore, the bidirectional causality between wages and prices enunciates the possibility of an independent cost-push inflation, regardless of labor-unions' actions; implying that breaking down unions may interrupt the wage-price spiral only temporarily.

Clearly, our results, though not inconsistent with the monetary theory of demand-side inflation, is at odds with the accelerationists model of perfect foresight (absence of money illusion) where laborers fully realize any anticipated changes in prices that they, presumably, bargain for real rather than money wages. Such a contention is, obviously, inconsistent with our adduced wage/price feedback results. In addition, this two-way causality upholds the inclusion of a wage (Phillips curve) equation in the estimation of the natural rate of unemployment. Thus, both restrictive (but steady) monetary policy as well as government policies designed to stabilize wages and prices are probably desirable.

Notes

(1)Milton Friedman (1970) p. 24. (2)Our intention is to test the direct causality linkages between each two variables separately in isolation of indirect relationships. Hence, we performed bivariate causality testing rather than multivariate methods such as the vector autoregression (VAR) model. (3)Sims' model is specified as: [Mathematical Expression Omitted] where [e.sub.t] and [[Mu].sub.t] are white-noise error terms; n indicates past lags; m indicates future lags. The null hypothesis is: [H.sub.o]: Y does not cause X in equation (1); and [H.sub.o]: X does not cause Y in equation (2). The null hypothesis is accepted if the estimated coefficients on future lags are significant. The F-statistic used is: [Mathematical Expression Omitted] [RRS.sub.a] = residual sum of squares obtained from the regression involving past values of the independent variables only; [RRS.sub.b] = residual sum of squares from the regression involving both past lags and future lags of the independent variables; [df.sub.1] = future-lags' degrees of freedom; [df.sub.2] = past-lags + future-lags' degrees of freedom. (4)Granger's model is specified as: [Mathematical Expression Omitted] Note that Granger's approach utilizes only past values of the dependent and independent variables. [V.sub.t] and [E.sub.t] are white-noise error terms; [H.sub.o]: X does not cause Y in (i), and Y does not cause X in (ii). [H.sub.o] is accepted if the coefficients of the lagged independent variables are insignificant. A similar F-test to that of Sims' is used. (5)See for example, Barth and Bennett (1975). (6)We chose not to use the final prediction error (FPE) technique to specify the lag length because in our bivariate causality testing context the number of variables is relatively few and the common lag is simpler. For more on this see Akaike (1969). (7)See Gordon (1977b). (8)The F-values are respectively 1.57, 1.85, and 1.90. (9)Traditional Durbin-Watson statistics are biased in the presence of lagged dependent variables. Hence, for the Granger method tests, the Durbin h-tests have been used. No significant serial correlation exists. The results are available from the authors upon request. (10)Philip Cagan, Persistent Inflation, 1979, p. 19. (11)We realize the existence of simultaneity between wages and prices. We, therefore, ran the tests without contemporaneous lags such that all variables became predetermined (exogenous). (12)We are indebted to a referee for pointing this out to us. (13)End-point constraints are not necessary for the Almon-Lag regressions, as pointed out by Peter Schmidt and Roger N. Waud, "The Almon Lag Technique and the Monetary versus Fiscal Policy Debate." Journal of the American Statistical Association, March 1973, vol. 68, no. 341, p. 12. The unrestricted lags results are not reported but are available from the authors upon request. (14)Clearly this is a topic for future research.

References

Akaike, H. "Statistical Predictor Identification." Annals of the Institute of Statistical Mathematics, 21 (1969), 203-217. Barth, J. and Bennett, J. "Cost-push versus Demand-pull Inflation: Some Empirical Evidence." Journal of Money, Credit, and Banking, (August, 1975), 391-397. Berman, P. Inflation and the Money Supply in the United States, 1956-1977. Lexington, Mass., D.C. Heath and Company, 1978. Box, G. and Pierce, D. "Distribution of Residual Autocorrelation in autoregression Moving Average Time Series." Journal of the U.S. Statistical Association, 65 (1970), 1509-1526. Cagan, P. Persistent Inflation. New York, Columbia University Press, 1979. Cushing, M. McGarvey, M. "Feedback Between Wholesale and Consumer Price Inflation: A Re-examination of the Evidence." Southern Economic Journal, 56, (April 1990), 1059-1072. Darrat, A., and Suliman, O. "Volatility of Money Growth and the [M.sub.1] Velocity Puzzle: Some Further Results." Unpublished Manuscript, (1990). Dickey, D., and Fuller, W. "Distribution of Estimates for Autoregressive Time Series with a Unit Root." Journal of American Statistical Association, (June 1979), 427-559. Engle, R. and Granger, C. "Co-integration and Error Correction: Representation, Estimation, and Testing." Econometrica, (March 1987), 251-276. Engle, R., and Yoo, B. "Forecasting and Testing in Co-integrated Systems." Journal of Econometrics, (1987), 143-159. Feige, E. and Pearce, D. "The Causal Relationship Between Money and Income: Some Caveats for Time Series Analysis." Review of Economics and Statistics, 51 (4, 1979), 521-533. Friedman, M. "The Counter Revolution in Monetary Theory." Occasional paper 33, Institute of Economic Affairs for Wincott Foundation, London, 1970. Fuller, W. Introduction to Statistical Time Series. New York: John Wiley and Sons, (1976). Gordon, R. "Can Inflation of the 1970's be Explained?" Brooking Paper on Economic Activity, (1, 1977a), 256-276. Gordon, R. "World Inflation and Monetary Accommodation in Eight Countries." Brooking Paper on Economic Activity, (2, 1977b), 409-468. Gordon, R. "The Role of Wages in the Inflation Process." The American Economic Review, 78 (May 1988), 276-283. Granger, C. "Developments in the Study of Co-integrated Economic Variables." Oxford Bulletin of Economics and Statistics, (November 1986), 213-228. Granger, C. "Investigating Causal Relationships by Econometric Models and Cross-Spectral Methods." Econometrica, 37 (July, 1969), 424-438. Guilkey, D. and Schmidt, P. "Extended Tabulations for Dickney-Fuller Tests." Economic Letters, (December 1989), 355-357. Leon, H. "Inflation and Growth: An Empirical Note." Economic Letters, (1986), 23-26. Mehra, Y. "An Empirical Note on Some Monetarist Propositions." Southern Economic Journal, 45 (July, 1978), 154-167. Miller, S. "Co-integration and Error-Correction Models: The Temporal Causality Between Government Taxes and Spending." Southern Economic Journal, 57, (July 1990), 221-229. Samuelson, P. and Solow, R. "Analytical Aspects of Anti-Inflation Policy." American Economic Review, 50, (May, 1960). Sargent, T. "Rational Expectations, the Real Rate of Interest, and the National Rate of Unemployment." Brooking Paper on Economic Activity, (2, 1973), 429-472. Sargent, T. "A Classical Macroeconomic Model for the United States." Journal of Political Economy, 84, (2, 1976), 207-237. Schmidt, P. and Waud, R. "The Almon Lag Technique and the Monetary versus Fiscal Policy Debate." Journal of the American Statistical Association, 68 (March, 1973), 11-18. Sims, C. "Money, Income, and Causality." American Economic Review, 62 (September, 1972), 540-552. Stephens, J. "An Empirical Note on Some Monetarist Propositions: Comment." Southern Economic Journal, 46 (44, 1980), 1237-1243. Thornton, J. "Inflation and Output Growth: Some Time Series Evidence, a Note." The American Economist, 32 (Fall 1988), 55-58. Trevithick, J. and Mulvey, C. The Economics of Inflation, Glasgow Social & Economic Research Studies 3, Martin Robertson and Co., London. 1975. M. Osman Suliman Grambling State University, Grambling, LA 71245. Kevin McCann Illinois Department of Public Aid, Springfield, Illinois 62704. The authors which to

thank participants in the Missouri Valley Economic Association Meeting (March 1988) and A. F. Darrat for helpful comments on an earlier version of this paper. Thanks also go to an anonymous referee of this Journal for many helpful comments and suggestions. All remaining errors are our own.

A great part of the post-Keynesian/monetarist debate arose from disagreement about the causal routes of inflation. In this respect, the question of whether it is possible to implement a test which will distinguish between cost-push and demand-pull inflation has a direct relevance to the selection of policies designed to avoid inflation. The extreme cost-push position advocates that only institutional factors are responsible for causing inflation; therefore, an institutional reform through, for example, prices and incomes polices is called for. Demand-pull adherents propose that long-run solutions to inflation must be based on demand restraint policies. Here, both the monetarist model and the Keynesian inflationary gap model are in agreement. Monetarists, however, claim that "inflation is always and everywhere a monetary phenomenon"(1) and, as such, prefer a regime of monetary control in which the growth rates of money and nominal income are compatible. In other words, monetarists contend that money supply |causes' prices without feedback. By contrast, neo-Keynesians hold that through the inflationary gap, changes in real income (aggregate demand) are expected to cause changes in prices. The endogeneity of income and prices in a simultaneous Keynesian system also implies that income and prices exhibit bidirectional causality.

Conventionally inflation was mainly explained through the wage/price (Phillips curve) approach which has been claimed to explain both demand-pull and cost-push inflation. Samuelson and Solow (1960) argued that if costs and prices are insignificantly sensitive to demand-restraint policies such that unemployment significantly increases, then cost-push inflation is dominant; and likewise the reverse is true for demand-pull inflation. Up to the 1970's markup models dominated inflation theory, but since that time monetarist models have taken over. Gordon (1988) argued that inflation (changes in the GNP deflator) do not statistically explain the behavior of each other; indicating that markup pricing hypothesis is dead. Notwithstanding, one of the by-products of this paper is to signify that such conclusions are probably sensitive to the type of price index used. Furthermore, reduced-form regressions are more indicative of correlation relationships than causal linkages. Of course, a bidirectional causality between wages and prices is supportive of cost-push theory in which case firms are bound to adjust any price expectation by the average costs, indicating that markup pricing may still be alive.

Numerous other studies by, for example, Cushing and McGarvey (1990), Gutherie (1981), Silver and Wallace (1980), and Engle (1978), among others, have examined the causal linkages between the CPI and the producer price index (PPI). Using one-way distributed lags, Gutherie, Silver and Wallace, and Engle found a unidirectional causality going from wholesale prices to consumer prices, a result which is consistent with markup pricing (cost-push) theory. Cushing and McGarvey are supportive of the perfectly flexible price (derived demand) and strong demand elements theory. However, it should be pointed out that using one-way causality testing from producer prices to the CPI to support markup pricing implies a fixed wage rate postulation (as in traditional Keynesian models). Likewise, the perfect (foresight) flexible prices (or the full-employment model) assumes away money illusion such that money wages perfectly adjust with any price changes, indicating a unidirectional causality from prices to money wages. Under imperfect foresight, however, money wages and prices may possess feedback causal links. Moreover, almost all previous studies emphasized mainly the role of money as a measure of aggregate demand, with no reference to the Keynesian aggregate demand (output). On the other hand, studies, such as Leon (1986), which concentrate only on inflation and output growth (without considering the potential effect of money) are probably flawed.

Clearly, the diversity of the results together with the profound importance of the issue of inflation requires further examination.

This paper provides further empirical evidence on wages, income (Keynesian demand), and money (classical demand). Besides being a direct component of costs, the inclusion of wages permits the investigation of their possible spiral influences with prices. To mitigate the inherent simultaneity in the wages and prices process, the contemporaneous lags were dropped such that the regressions were run only on exogenous (predetermined) variables. Note that Granger (1969) recommends dropping the contemporaneous lags for proper causality testing. In addition, adjustment is also made for the possibility of a structural breakdown in the relationship during periods of relatively high inflation (1947-1959 and 1975-1982) and those of relatively low inflation (1960-1974), and the variables are tested for the presence of unit roots. Another point of departure from previous studies in this area is that in this study stationarity tests (to perform Granger and Sims' causality methods) are done using Box-Jenkins' procedure instead of using Sims' filter or simple time trends.

The paper is organized as follows: In section II we described the data and the methodology. In section III we identify and estimate the different series using Box-Jenkins' method to ensure that the series are white-noise. Then we proceed to conduct causality testing using both Sims' and Granger's approaches.(2) Section IV examines the possibility of equilibrium (long-run) relationship between the variables using cointegration tests. In section V we discuss the results of Almon's distributed lags in an attempt to give further insight into the long-run and short-run properties of the cost-push and demand-pull inflations. Section VI concludes the paper.

II. Data and Methodology

The paper envisages the proclaimed monetarist exogeneity of money supply to prices, nominal income, and to real income. The neo-Keynesian inflationary gap theory will be examined by studying the causality linkages of aggregate demand (real income) and prices. The cost-push relationship of wages to prices will also be investigated. Both two-sided distributed-lag (Sims 1972)(3) and one-sided distributed-lag methods (Granger 1969)(4) of causality testing will be employed. Although Sims' approach has been widely used, Granger's method is probably superior. Granger's inclusion of the lagged dependent variable is more likely to purge residual autocorrelation. Furthermore, Granger's method of using only past values of the dependent and independent variables exhausts less degree of freedom; unlike Sims' approach which uses past as well as future values of the independent variable. Using both methods could, therefore, shed some light on the validity (or lack thereof) of previous studies and, moreover, provide some evidence on the robustness of the obtained results (see Feige and Pearce, 1979). In addition, we used Box-Jenkins' procedure to prewhiten each series separately instead of imposing a priori Sims' filter as commonly done in previous work(5). To assume a white-noise series, we selected the ARIMA models (Table I) with insignificant autoregressive and moving-average portions, and with the smallest Box-Pierce Q statistics.

Robust results are also to be maintained through a search for the optimum lag structure of the equations using Theil's minimum residual-variance criterion. In addition, we adopted Berman's (1978) sensitivity tests by selecting forward and backward lengthening procedures and then testing for a candidate lag by "straddling" with other shorter and longer lags. Based on these criteria, the ten-lag structure has been found to be appropriate.(6)

Furthermore, cointegration and the Almon lag technique will be used to investigate whether an equilibrium (long-run) relationship exists between the variables and the range of lags (short-run or distant lags) over which the independent variables affect the dependent variables in an attempt to distinguish between short-run and long-run effects of demand-pull and cost-push inflation. There is, more or less, a consensus that the influence of demand factors on inflation is continuous (long-run); and that demand factors tend to initiate as well as perpetuate inflation. However, monetarist (Cagan, 1979) tend to think of cost-push factors as exerting a perpetuating (short-run) effect on inflation, because there is an implicit presumption that prices tend to "cause" changes in wages (and other costs) without continuous feedbacks. Through the Almon lag technique, we should be able to isolate the impact of the different variables on each other at different time periods, and also acknowledge whether the cumulative effect is significant (continuous) or insignificant (short-run). Note that cointegration (unlike the Almon lag) does not trace out the relationship between the variables at each and every specific lag. The Almon lag has also been commended over the Cagan-Koych (adaptive expectations) method because it requires less stringent restrictions and is more consistent with perfectly rational expectations (Muth 1961) which considers only supply side exogenous shocks, and with partially rational (Sargent 1973) models subject to both supply and demand shocks.(7) To avoid spurious results due to improper choice of the lag of the polynomial functions of the Almon technique, Theil's criterion together with stability tests of the different functions will be adopted. Stability tests are used to detect whether demand-pull and/or cost-push are typically characteristic of certain important sub-periods where structural shifts in the economy are suspected. Three sub-periods were though to be critical: (1) 1947-1959; the period immediately following the end of World War II which included the Korean War. Inflation during this period was persistent at an annual rate of about 2-4% in industrial countries. (2) 1960-1974; during the first half of the sixties the U.S. enjoyed relatively lower rates of inflation (about 2%), but by the early 1970's worldwide inflation was imminent. (3) 1975-1982; this period experienced two major OPEC price shocks when double-digit inflation hit the U.S. economy in 1974-1975 and returned again during the 1979-1981 period. The Chow-test for stability reflects no undue cause for concern about structural shifts over the sample period.(8)

U.S. quarterly data covering the period 1947.1-1986.4 have been used. The data for M1 has been taken from the Federal Reserve Bulletin (various issues). All other variables have been taken from The Handbook of Cyclical Indicators (1984) and Business Conditions Digest (various issues). All variables are stationary after differencing and are transformed into natural logarithmic forms to give percentage (growth rates) changes directly and to help alleviate trend and serial correlation. Indeed, none of the subsequent regressions experienced any significant serial correlation.(9) The different variables are defined as follows:

M = percentage change in money supply M1;

NY = percentage change in nominal

GNP; Y = percentage change in real GNP;

CPI = percentage change in consumer

price index;

PPI = percentage change in producer

price index; G = percentage change in GNP price deflator;

WN = percentage change in nominal

wage rates.

III. Causality (Exogeneity) Results

In Table I, the series are identified and estimated using the Box-Jenkins' method. The autocorrelations of the changes in the original series are non-stationary. For almost all series autocorrelations range from .55 to .00 until the 20th lag. With first differencing, we were able to find stationary series for the change in the CPI and the change in real GNP. All other series were stationary after they were differenced a second time. The ARIMA models that were chosen are found in Table 1. The chosen models have minimum standard errors and Q statistics. [Tabular Data I Omitted]

Using the white-noise series we proceeded to test for causality utilizing both Sims' and Granger's tests of causality. Using Sims' test, causality is indicated by the insignificance of the F-values on future-lagged variables. For Granger's method, causality is indicated by the significance of the F-values on the sum of lagged independent variables. The results shown in Table II, III and IV affirm the monetarist claim that monetary expansion leads to demand-pull inflation. That is, unidirectional causality runs from money supply to prices (and not the reverse) such that money supply is truly exogenous to prices. Nevertheless, our empirical investigations lends some support to the two-way endogeneity of money supply and the Keynesian aggregate demand (real GNP). There is bidirectional causality effects between money supply and both nominal and real incomes. The results so far are not inconsistent with Keynesian theory which applauds the monetarist belief that monetary expansion causes demand-pull inflation. Yet, the results also emphasize the influence of aggregate demand on inflation; hence, the importance of demand-management policies to curb inflation. These results are further supported by the unidirectional causality going from real GNP (aggregate demand) to the CPI; whereas the PPI and the GNP deflator show and independent relationship with real GNP. This casts some doubt on Cagan's contention that demand is not related to prices in the short-run. Cagan's assertion is based on manufacturing prices (PPI) only.(10) It is true that manufacturing prices may not be responsive to short-run shifts in demand, but consumer prices are. In congruence with this, Thornton (1988) reports a positive relationship between the CPI and real output for some developed countries.

TABLE II Sim's Model F-statistics on Future Coefficients for Sims' Test Causality Regression Equation F-ratios patterns(*) 1. G = F(M, 10 Future Values) 1.15 Yes 2. M = F(G, 10 Future Values) 1.35 No 3. CPI = F(M, 10 Future Values) .96 Yes 4. M = F(CPI, 10 Future Values) 2.16 No 5. PPI = F(M, 10 Future Values) 1.29 Yes 6. M = F(PPI, 10 Future Values) 1.44 No 7. Y = F(M, 10 Future Values) 1.27 Yes 8. M = F(Y, 10 Future Values) 1.58 Yes 9. NY = F(M, 10 Future Values 1.21 Yes 10. M = F(NY, 10 Future Values) 1.24 Yes 11. Y = F(G, 10 Future Values) 1.58(*) No 12. G = F(Y, 10 Future Values) 1.08 No 13. Y = F(CPI, 10 Future Values) 1.82(*) No 14. CPI = F(Y, 10 Future Values) .89 Yes 15. Y = F(PPI, 10 Future Values) 1.10 No 16. PPI = F(Y, 10 Future Values) .87 No 17. G = F(WN, 10 Future Values) .77 Yes 18. WN = F(G, 10 Future Values) 1.50 Yes 19. CPI = F(WN, 10 Future Values) 1.22 Yes 20. WN = F(CPI, 10 Future Values) 1.09 Yes 21. PPI = F(WN, 10 Future Values) 1.69 Yes 22. WN = F(PPI, 10 Future Values) 1.22 Yes (*)Yes indicates existence of causality. No indicates no causality. (**)Significant at the 10% level. (***)Significant at the 5% level.

[Tabular Data III Omitted]

Causality linkages examined in this paper also reveal that the simultaneous existence of both cost-push and demand-pull inflation is possible. Nominal wages show a bidirectional (wage-price spiral) causality with all prices in the economy.(11) The endogeneity of prices and nominal wages to each other offers strong support to the wage-price spiral theory. Thus firms cannot base price expectations only on excess demand; cost considerations are also important. That is, the impact of cost-push inflation is continuous. Hence, breaking down of labor unions may temporarily interrupt the wage-price spiral, but the bidirectional causality existing between wages and prices raises the possibility of an independent cost-push inflation, regardless of unions' actions.

IV. Cointegration Results

The causality results between prices, money, and income are reported in Table IV. Such causal inferences may gain more insight if the causally linked variables possess an equilibrium (long-run) relationship, and if the causally independent variables lack a significant equilibrium relation. Recently, it has been demonstrated by Engle and Granger (1987), and Granger (1986), among others, that cointegration (common trends) can be used to test for the presence of a equilibrium relationship between variables containing unit roots.

To test for the presence of a unit-root, we regress the first difference of, for example, the CPI on its lagged value, in addition to a constant, a time trend, and a lagged dependent variable which will approximate short-run dynamics and yield white-noise residuals. If the coefficient (of the CPI) is significant, then we reject the null hypothesis that the variable, in level form, contains a unit-root. The test statistic is calculated by dividing the estimated coefficient by the standard error, and the critical values are modified t-values reported in Fuller (1976).

Each of the series reported in Table IV, was examined for the possible order of difference stationarity. As reported in Table V, the null-hypothesis that non-stationarity (unit-roots availability) could not be rejected for the levels of all variables. The next step is to see whether the series have the same unit-roots (cointegrated) or have different unit-roots. After differencing, the series were found to be stationary.

To test for cointegration, we regress the different variables against each other (plus a constant term). The resulting equation is called the cointegrating (equilibrium) regression. The absence (presence) of cointegration is indicated by the nonstationarity (stationarity) of the residuals. We followed Darrat and Suliman (1990), Engle and Yoo (1987), and Miller and Russek (1990) to test the hypothesis of no cointegration. As such, we performed a Dickney-Fuller test (DF), an Augmented Dickney-Fuller test (ADF), and a modified Durbin-Watson test (DW).

The DF test requires regressing the first differences of the estimated residuals from the cointegrating regressions on their lagged values, and then testing the significance of the estimated coefficient. The t-ratios are compared against modified critical values reported by Engle and Yoo. The ADF test adds to the DF test a lagged dependent variable (to alleviate any autocorrelation). For the DW test, the resulting DW statistics from the cointegration regressions are compared against some critical values given by Engle and Yoo.

Except for the case of the CPI and real income (Y), the three tests are consistent with our causality results reported in Table IV. As shown in Table V, the tests could not reject the hypotheses of no cointegration for money and the three price indices, for money and income, and for wages and prices. Not surprisingly, however, no cointegration was found to exist between real income and the three price indices.

TABLE IV Summary: Causality Directions Unidirectional Bidirectional Independent 1. M to G 1. WN and G 1. Y and G 2. M to CPI 2. WN and CPI 2. Y and PPI 3. M to PPI 3. WN and PPI 4. Y to CPI 4. M to Y 5. M to NY TABLE V Cointegration Regressions DF ADF D-W M = f(G) 4.02(*) 4.23(*) 1.24 M = f(CPI) 3.82(*) 5.17(*) 2.20 M = f(PPI) 3.90(*) 4.08(*) 2.20 M = f(Y) 3.06(**) 3.30(**) 1.30 M =f(NY) 3.67(*) 3.91(*) 2.12 WN = f(G) 3.16(**) 3.09(**) 1.27 WN = f(PPI) 4.14(*) 3.92(*) 1.28 Y =f(G) -2.15 -1.89 0.14 Y = f(CPI) -2.87 -3.00 0.27 Y =f(PPI) -1.95 -2.12 0.09 (*)Significant at the 5 percent level (critical value 3.37). (**)Significant at the 10 percent level (critical value 3.03).

V. Distributed Lags and the Time-path

This study has also envisaged the long-run effects of demand-pull and cost-push inflations by tracing out the time-path of the estimated distributed lag coefficient, using both Almon's lags and OLS unrestricted lags. It is important to note that when Almon technique is used the resulting t-statistics may end up being high. This is because they are testing whether coefficients can be made zero while maintaining the shape restriction, which is almost impossible.(12) The Almon lags are shown in Table VI.(13) The significance of the distributed lag is determined if most of the individual lags are significant, and also the sum of the coefficients must be significant. The use of distributed lags at this point is quite legitimate as supported by the above exogeneity tests of Sims and Granger, One, first, must be clear about exogeneity; thereafter one can ponder long-term and short-term effects.

Both Almon and unrestricted lag techniques were used to avoid spurious results from uncertain Almon restrictions on the shape of the coefficients. However, Almon's technique does a superb job in measuring the accumulated weight-impact (weighted average) of the exogenous variable on the endogenous variable. Moreover, the Almon lag technique alleviates multicollinearity. The results of both methods are consistent with each other. These distributed lag investigations indicate the co-existence of both demand-pull and cost-push inflations at different time periods. Besides, demand-pull inflation appears to be more explicable through exogeneity of money supply rather than the traditional Keynesian aggregate demand. Even though our causality (exogeneity) tests suggest that real income (aggregate demand) may cause a change in the CPI, the weighted-average Almon technique gives very weak support for this result where only the first two lags (short-run) results are significant at the 10% level. This finding is consistent with Leon's (1986) results indicating the absence of a long-run relationship between output growth and inflation. Furthermore, the existence of feedback causality between money and real income (aggregate demand) indicates that changes in aggregate demand affect prices mainly through their impact on money supply. The distributed lag results show that the cumulative impacts of changes in money supply on nominal income, real income, and prices vary significantly over time. The heaviest positive impact on all three variables occurs during the initial five lags, with negative impacts coming after that on nominal and real income. The negative impact on nominal income dies out as time goes on; whereas the negative impact on real income gets stronger with time. The positive impact of monetary expansion on prices also gets weaker over time. The results have some appealing intuitive implications: that the division of nominal income into real income (quantity) and prices is revealed by observing that the impact of money on nominal income seems to follow an average conflicting force of its two components. Although the impact on both prices and real income is stronger in the first few lags, the negative impact on nominal income seems to die out exponentially following the same pattern as prices where their positive coefficients are also dying-out exponentially. These results, though not inconsistent with the monetarist belief of no money-illusion, are not indicative of any permanent impact of money on nominal variables since inflation dies exponentially. This type of evidence is probably in disagreement with Mehra's (1978) result that the effect on the price level is negligible during the time when real and nominal income are increasing due to monetary expansion.(13)

Furthermore, our bivariate distributed lag analysis indicates a cost-push (wage-price spiral) over time. The regressions of wages and prices against each other indicate that the sums of the coefficients as well as most of the individual coefficients are significant at the 5% level. For the GNP deflator and the CPI regressions, the cumulative sums of coefficients are definitively significant at the 5% level. However, the impact of wages on the PPI is only significant during the initial time periods. By intuition, any increase in producer prices through higher wages is passed immediately to consumer prices. These arguments are congruous with cost-push theory in that money wages cause a push in prices with a feedback (spiral) to wages from prices. The results, moreover, tend to suggest that empirical findings about the inflationary process are contingent on the price index used. Different indexes may interact with wages differently at different time periods. Furthermore, the wage-price bidirectional causation elucidates the Phillips curve formulation of a relationship between the rate of wage change (inflation) and unemployment; implying that the specification of a wage equation in the estimation of the natural rate of unemployment is probably not irrelevant.

VI. Summary and Concluding Remarks

This paper has re-examined the cost-push and demand-pull theories of inflation. Recent investigations by Cushing and McGarvey (1990), Gordon (1988), Gutherie (1981), and Silver and Wallace (1980), among others, have produced diverse results. However, these studies have generally tended to consider cost-push inflation in isolation of demand-pull; with cost-push proponents contending a one-way causality from the wholesale price to the CPI, and derived demand (perfectly flexible prices) adherents indicating the reverse causality as well. Moreover, there is no clear consensus as to whether money is a more appropriate proxy for aggregate demand than real income (total expenditure).

To make ends meet, we tried having (in isolation) both money and real income as proxies for aggregate demand. We also considered the three price indices together with nominal wages to test for cost-push. Bivariate causality testing has been carried out in both directions for all variables (taken two at a time). To cater to robustness, both Sims and Granger methods have been utilized. Further support of causality (or non-causality) is derived from cointegration tests, which (together with the Almon lag) is used to examine the existence of long-run relationships. Adjustments have also been made for the possibility of a structural break in relatively high inflation periods (1947-1959 and 1975-1982) and relatively low inflation periods (1960-1974), and, moreover, the Box Jenkins' procedure has been used to test for stationarity.

Contrary to pure markup pricing supporters and derived demand adherents, this study stands neutral. Our results do not refute either the cost-push or demand-pull theories. Both inflation theories are coexistent over time, and it is almost impossible to identify the existence of any of them with time-length, a finding consistent with imperfect foresight formulations. However, demand inflation appears to be more definitive with monetary growth than the Keynesian aggregate demand (real income). Of course, this does not preclude the possibility that real income ad inflation are jointly determined in a simultaneous equation system.(14) Cost-push (wage-prices) inflation is also significant and continuous, suggesting that firms are apt to form their price expectations based on costs together with excess demand. Furthermore, the bidirectional causality between wages and prices enunciates the possibility of an independent cost-push inflation, regardless of labor-unions' actions; implying that breaking down unions may interrupt the wage-price spiral only temporarily.

Clearly, our results, though not inconsistent with the monetary theory of demand-side inflation, is at odds with the accelerationists model of perfect foresight (absence of money illusion) where laborers fully realize any anticipated changes in prices that they, presumably, bargain for real rather than money wages. Such a contention is, obviously, inconsistent with our adduced wage/price feedback results. In addition, this two-way causality upholds the inclusion of a wage (Phillips curve) equation in the estimation of the natural rate of unemployment. Thus, both restrictive (but steady) monetary policy as well as government policies designed to stabilize wages and prices are probably desirable.

Notes

(1)Milton Friedman (1970) p. 24. (2)Our intention is to test the direct causality linkages between each two variables separately in isolation of indirect relationships. Hence, we performed bivariate causality testing rather than multivariate methods such as the vector autoregression (VAR) model. (3)Sims' model is specified as: [Mathematical Expression Omitted] where [e.sub.t] and [[Mu].sub.t] are white-noise error terms; n indicates past lags; m indicates future lags. The null hypothesis is: [H.sub.o]: Y does not cause X in equation (1); and [H.sub.o]: X does not cause Y in equation (2). The null hypothesis is accepted if the estimated coefficients on future lags are significant. The F-statistic used is: [Mathematical Expression Omitted] [RRS.sub.a] = residual sum of squares obtained from the regression involving past values of the independent variables only; [RRS.sub.b] = residual sum of squares from the regression involving both past lags and future lags of the independent variables; [df.sub.1] = future-lags' degrees of freedom; [df.sub.2] = past-lags + future-lags' degrees of freedom. (4)Granger's model is specified as: [Mathematical Expression Omitted] Note that Granger's approach utilizes only past values of the dependent and independent variables. [V.sub.t] and [E.sub.t] are white-noise error terms; [H.sub.o]: X does not cause Y in (i), and Y does not cause X in (ii). [H.sub.o] is accepted if the coefficients of the lagged independent variables are insignificant. A similar F-test to that of Sims' is used. (5)See for example, Barth and Bennett (1975). (6)We chose not to use the final prediction error (FPE) technique to specify the lag length because in our bivariate causality testing context the number of variables is relatively few and the common lag is simpler. For more on this see Akaike (1969). (7)See Gordon (1977b). (8)The F-values are respectively 1.57, 1.85, and 1.90. (9)Traditional Durbin-Watson statistics are biased in the presence of lagged dependent variables. Hence, for the Granger method tests, the Durbin h-tests have been used. No significant serial correlation exists. The results are available from the authors upon request. (10)Philip Cagan, Persistent Inflation, 1979, p. 19. (11)We realize the existence of simultaneity between wages and prices. We, therefore, ran the tests without contemporaneous lags such that all variables became predetermined (exogenous). (12)We are indebted to a referee for pointing this out to us. (13)End-point constraints are not necessary for the Almon-Lag regressions, as pointed out by Peter Schmidt and Roger N. Waud, "The Almon Lag Technique and the Monetary versus Fiscal Policy Debate." Journal of the American Statistical Association, March 1973, vol. 68, no. 341, p. 12. The unrestricted lags results are not reported but are available from the authors upon request. (14)Clearly this is a topic for future research.

References

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thank participants in the Missouri Valley Economic Association Meeting (March 1988) and A. F. Darrat for helpful comments on an earlier version of this paper. Thanks also go to an anonymous referee of this Journal for many helpful comments and suggestions. All remaining errors are our own.

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Author: | Suliman, M. Osman; McCann, Kevin |
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Publication: | American Economist |

Date: | Sep 22, 1991 |

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