Applied Microeconometrics Assignment 2

Assignment Task

1. You are given the following statement

The forward orthogonal transformation has the advantage that it does not remove time-constant regressors.

Do you agree or disagree? Support your answer mathematically.

2. Suppose you are given country level data and estimate the following gasoline demand equation

G _it = α + β ₁ Inc _it + β ₂ PG _it + β ₃ Cars _it + c _i + u _it (1)

where

• G _it : Gasoline consumption of country i in year t
• Inc _it : Total income of country i in year t
• PG _it : Gasoline price in country i in year t
• Cars _it : Number of cars in country i in year t

Your sample consists of 120 countries over 5 years.

You estimate equation (1) with the random effects estimator and the fixed effects estimator. Furthermore, you calculate the residuals using the fixed effects estimator and plot them against the variable Income.

How can you assess which one of the two estimators is appropriate in the given set up? Describe and motivate your procedure.

Hint: From your description your procedure should be clear. However, you do not have to derive any estimators or test statistics formally.

3. Using the data set dta , we aim at estimating the following model for the log of wag it

lwage _i,t = lwage _i,t — 1 α + x ^r β + δ _t + c _i + u _it , (2) where lwage _i,t denotes the wage (measured in logs) of individual i in time period t . The vector

x _it encompasses the following variables: exper _it , expersq _it , union _it , married _it .

The variable expersq _it is the squared experience of individual i in time period t . We assume that x _it are strictly exogenous variables but possibly correlated with the individual effect c _i . We include a full set of year dummies and δ _t is the corresponding year dummy coefficient for time period t . The idiosyncratic error term u _it is assumed to be serially uncorrelated over time.

• Estimate equation (2) by means of pooled OLS (POLS). Is the estimate of α consistent?
• Estimate equation (2) by means of fixed effects (FE). Is the estimate of α consistent?

From the lecture, you know the Anderson-Hsiao estimator, which proposes two different in- struments.

• Estimate equation (2) where you use the instruments separately. Compare the two esti- mates of α .
• Estimate equation (2) where you use both
• Is there a way to check whether the chosen approach in (d) is appropriate? If not, explain. If yes, then conduct the respective tests. Interpret the test outcomes. What do you conclude about the consistency of the estimate for α ?

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