The preceding equation was based on the assumption that the desired level of employment Et* is a function of output, time, and time squared and on the hypothesis that Et — Et-1 = S(E* — Et-1), where S, the coefficient of adjustment, lies between 0 and 1.

F. P. R. Brechling, "The Relationship between Output and Employment in British Manufacturing Industries," Review of Economic Studies, vol. 32, July 1965.

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 707

a. Interpret the preceding regression.

c. Derive the long-run demand function for labor from the estimated short-run demand function.

d. How would you test for serial correlation in the preceding model?

17.15. In studying the farm demand for tractors, Griliches used the following model*:

where T* = desired stock of tractors X1 = relative price of tractors X2 = interest rate

Using the stock adjustment model, he obtained the following results for the period 1921-1957:

logTt = constant - 0.218log XU-1 - 0.855log X2,t-1 + 0.864 log Tt-1 (0.051) (0.170) (0.035)

where the figures in the parentheses are the estimated standard errors.

a. What is the estimated coefficient of adjustment?

b. What are the short- and long-run price elasticities?

c. What are the corresponding interest elasticities?

d. What are the reasons for high or low rate of adjustment in the present model?

17.16. Whenever the lagged dependent variable appears as an explanatory variable, the R2 is usually much higher than when it is not included. What are the reasons for this observation?

17.17. Consider the lag patterns in Figure 17.10. What degree polynomials would you fit to the lag structures and why?

To obtain the variance of 2i from the variances of ai, we use the following formula:

var (f)i) = var (ao + â 1 i + â2i2 + ■■■ + amim)

= ^2 i2' var (âj) + 2 ^ i('+p)cov (atap) j=0 j<p

Zvi Griliches, "The Demand for a Durable Input: Farm Tractors in the United States, 1921-1957," in Arnold C. Harberger, ed., The Demand for Durable Goods, University of Chicago Press, Chicago, 1960.

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

708 PART THREE: TOPICS IN ECONOMETRICS

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