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Notes: COMP = index of real compensation per hour (1992 = 100). PRODUCT = index of output per hour (1992 = 100). UNRate = civilian unemployment rate, %. Source: Economic Report of the President, 2001, Table B-49, p. 332.

a. How would you decide whether it is wage compensation that determines labor productivity or the other way round?

b. Develop a suitable model to test your conjecture in a, providing the usual statistics.

c. Do you think the unemployment rate has any effect on wage compensation, and if so, how would you take that into account? Show the necessary statistical analysis.

17.31. Sims' test of causality.* In a twist of Granger causality, Sims exploits the fact that the future cannot cause the present. Suppose we want to find out if X causes Y. Now consider the following model:

Yt = a + PkXt-k + Pk-1 Xt-k-1 +• • • + P1 Xt-1 + Po Xt

This regression includes the lagged, current, and future, or lead, values of the regressor X; terms such as Xt+1 and Xt+2 are called lead terms. In the preceding regression, there are k lagged and m lead terms. If X is to

C. A. Sims, "Money, Income, and Causality," American Economic Review, vol. 62, 1972, pp. 540-552.

Gujarati: Basic I III. Topics in Econometrics I 17. Dynamic Econometric I I © The McGraw-Hill

Econometrics, Fourth Models: Autoregressive Companies, 2004 Edition and Distributed-Lag

Models

CHAPTER SEVENTEEN: DYNAMIC ECONOMETRIC MODELS 713

(Granger) cause Y, the sum of the coefficients of the lead X terms must be statistically equal to zero.*

Apply the Sims' test of causality to the data given in exercise 17.22 to determine whether sales (Granger) cause investment expenditure. Decide for yourself the appropriate lead and lag values of the regressor.

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