Consider the following two periods panel data model: Wageit = Bo + do D2 + BEducit...

 

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Consider the following two periods panel data model: Wageit = Bo + do D2 + B₁Educit + B₂ Expit +B3Female; + ai + uit, t = {1,2}, where D2 is a dummy variable which equals to one in period 2 and zero in period 1. (a) Can we estimate the above model by OLS? Explain why. (b) Explain whether the OLS regression controls for individual-specific unobserved heterogeneity (i.e., a fixed effect a;)? (c) Write down the first differenced model. State which coefficients can be esti- mated by OLS? (d) Explain whether the first differenced model controls for individual-specific un- observed heterogeneity (i.e., a fixed effect a;)? (e) Write down the demeaned model. State which coefficients can be estimated by OLS? (f) Show that the models in (c) and (e) are actually equivalent. Consider the following two periods panel data model: Wageit = Bo + do D2 + B₁Educit + B₂ Expit +B3Female; + ai + uit, t = {1,2}, where D2 is a dummy variable which equals to one in period 2 and zero in period 1. (a) Can we estimate the above model by OLS? Explain why. (b) Explain whether the OLS regression controls for individual-specific unobserved heterogeneity (i.e., a fixed effect a;)? (c) Write down the first differenced model. State which coefficients can be esti- mated by OLS? (d) Explain whether the first differenced model controls for individual-specific un- observed heterogeneity (i.e., a fixed effect a;)? (e) Write down the demeaned model. State which coefficients can be estimated by OLS? (f) Show that the models in (c) and (e) are actually equivalent.