Question 132 136

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Consider a panel data model Me = 248+ zy+ 1+on, 1=1,2..... n, t = 1,2.... T. where n is large and T is small. One wants to estimate S and y. 1. Explain how to efficiently estimate s and y under (a) fixed effects, (b) random effects, when- over it is possible. State clearly all assumptions that you will need. 2. Consider the following proposal to estimate y. At the first step, estimate the model yy = r'8+ *, + by by the least squares dummy variables approach. At the second step, take these estimates *, and estimate the coefficient of the regression of *, on 2;. Investigate the resulting estimator of y for consistency. Can you suggest a better estimator of ~?We know (see Problem 9.3) that the NLLS estimator of a and A = arg min (uit a)' - bri) a,b in the nonlinear model (uto) = Bx+ e, where e is independent of r, is in general inconsistent. Suppose that there is a panel (ex,)" -1 1, where n is large and T is small, so that there is an opportunity to control individual heterogencity. Write out a one-way error component model assuming the same functional form but allowing for individual heterogencity in the form of random effects. Using an analogy with the theory of a linear panel regression, propose a multistep procedure of estimating a and / adapting the estimator you used in Problem 9.3 to a panel data environment