Question

First-differenced estimation in a panel data analysis is subject to serious biases if _____.

Select one:

a. the explanatory variables do not change by the same unit in each time period

b. one or more of the explanatory variables are measured incorrectly

c. the regression model exhibits homoscedasticity

d. key explanatory variables vary significantly over time

Answer 1

First differencing is a technique which is used in panel data models for getting rid of the unobserved time independent effect.This is important to be gotten rid of because this effect is correlated with the explanantory variables, causing endogeneity in the model.

As we know, if the model is endogeneous, we can't apply OLS because the estimates will be biased. Hence we need to get rid of that unobserved term in order for usto run OLS and estimate the parameters.

As the term is time independent, we can difference the data across the years, to get what is known as the first difference equation. Running OLS on this equation gives us the first difference estimator.

Suppose we have these two equations for t=2 and t=1 respectively:

(for t=2)

(for t=1)

where ai represents the time independent unobserved term.

If we subtract the second equation from the first one, we have:

or,

, ........(1)

(1) is the first difference equation.

denotes the change from t=1 to t=2 and the unobserved time independent term has been differenced away.

To get the first difference estimators, run OLS on (1).

Now, first-differenced estimation in a panel data analysis has to have some key assumptions to satisfy.

Firstly, should be uncorrelated with , which means that there shouldn't be any endogeneity in the model. This is required because unless the exogeneity condition is satisfied, we can't apply OLS.

Next, should have some variations over i. Hence, key explanatory variables should vary significantly over time. Moreover, the explanatory variables should not change by the same unit in each time period.

We should also have the homoskedasticity assumption holding. Thus,  the regression model should exhibit homoscedasticity.

Thus,

First-differenced estimation in a panel data analysis is subject to serious biases if one or more of the explanatory variables are measured incorrectly

Hence option (b) is the correct answer.