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* Y = family heads under 65 years old X = dollars

*X4 = percent of civilian labor force unemployed

Source: Census Tracts: New York, Bureau of the Census, U.S. Department of Commerce, 1970.

* Y = family heads under 65 years old X = dollars

*X4 = percent of civilian labor force unemployed

Source: Census Tracts: New York, Bureau of the Census, U.S. Department of Commerce, 1970.

c. How would you test the hypothesis that the overall unemployment rate has no effect on the labor force participation of the urban poor in the census tracts given in the accompanying table?

d. Should any variables be dropped from the preceding model? Why?

e. What other variables would you consider for inclusion in the model?

C.11. In an application of the Cobb-Douglas production function the following results were obtained:

lnY = 2.3542 + 0.9576 ln X2i + 0.8242 ln X3i (0.3022) (0.3571)

where Y = output, X2 = labor input, and X3 = capital input, and where the figures in parentheses are the estimated standard errors.

a. As noted in Chapter 7, the coefficients of the labor and capital inputs in the preceding equation give the elasticities of output with respect to labor and capital. Test the hypothesis that these elasticities are individually equal to unity.

b. Test the hypothesis that the labor and capital elasticities are equal, assuming (i) the covariance between the estimated labor and capital coefficients is zero, and (ii) it is -0.0972.

c. How would you test the overall significance of the preceding regression equation?

954 APPENDIX C: THE MATRIX APPROACH TO LINEAR REGRESSION MODEL

*C.12. Express the likelihood function for the &-variable regression model in matrix notation and show that (3, the vector of maximum likelihood estimators, is identical to (3, the vector of OLS estimators of the &-variable regression model.

C.13. Regression using standardized variables. Consider the following sample regression functions (SRFs):

where

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