Question

TRUE OR FALSE: JUSTIFY THE ANSWER TO GET FULL CREDIT

a). One can add time fixed effects if the regressor of interest varies across time for the same entity and across entities for the same point in time.

b). In the fixed effects regression model, you should exclude one of the binary variables for entities when an intercept is present in the equation because one of the entities in the analysis is always excluded from the regression.

c). The condition mean assumption required for panel data is satisfied if u_it does not depend on X_it.

Answer 1

One can add time fixed effects if the regressor of interest varies across time for the same entity and across entities for the same point in time.

A panel data set contains observations on multiple entities (individuals, states, companies…), where each entity is observed at two or more points in time. N different entities are observed at T different time periods .

For examples: Data on 420 California school districts in 1999 and again in 2000, for 840 observations total.

Time Fixed Effects control for omitted variables that are constant across entities but vary over time.

ex. national level anti-crime policy or safety standard each year.

Entity Fixed Effects control for omitted variables that are constant within the entity and do not vary over time.

ex. gender, race, or cultural and religious characteristics of each State.

This is a false statement. If one can fixed time effect so as per assumption of panel data is  Time Fixed Effects control for omitted variables that are constant across entities but vary over time.

b). In the fixed effects regression model, you should exclude one of the binary variables for entities when an intercept is present in the equation because one of the entities in the analysis is always excluded from the regression.

False statement. In the fixed effects regression model, you should exclude one of the binary variables for entities when an intercept is present in the equation because  to avoid perfect multicollinearity.

A fixed effects regression is an estimation technique employed in a panel data setting that allows one to control for time-invariant unobserved individual characteristics that can be correlated with the observed independent variables.

c). The condition mean assumption required for panel data is satisfied if u_it does not depend on X_it.

uit is idiosyncratic error or time-varying error and represents unobserved factors that change over time and effect yit.

yit = β0 + δ0d2t + β1xit + ai + uit, t = 1, 2

Lets start with the regression model Yit = X 0 itβ + uit

We still maintain Assumption 2 that E(uitXit) = 0

Yit depends on Xit.

Panel data consist of observations on the same n entities at two or more time periods T. If the data set contains observations on the independent variables X1, X2, . . . , Xk and the dependent variable Y , then we denote the data by (X1,it, X2,it, . . . , Xk,it, Yit), i = 1, . .

But uit does depend on Xit. So the statement is false.