Below is an estimated cross-country regression of a Cobb-Douglas production function based upon the manufacturing sector of 60 countries in 2009 where t-ratios are given in brackets:
where Y denotes the natural logarithm of value added output in thousands of dollars, X1 is the natural logarithm of labour input in thousands of worker hours and X2 is the natural logarithm of capital expenditure in thousands of dollars.
a. Interpret the coefficients.
b. The following auxiliary regression is used to conduct White's test for heteroskedasticity given the diversity of countries used in the cross-sectional regression:
where ui denotes the residuals of the estimated Cobb-Douglas production function. Using this information, apply White's LM test for heteroskedasticity at the 5% and the 10% significance level. Be careful to clearly specify the hypotheses of the test and explain how you draw your inference.