Question

1. Suppose you are interested in investigating how the crime rate (crmte) would affect a city's GDP (a) Soppose you randomly selected 50 cities in China and collected data on the crime rates and GDP's of these cities, you set up the following model GDP po Pierm te,+ u Explain why the OLS estimator for the above model is likely to be biased (b) Suppose now you have the data of the 50 cities from the year 2000 to 2010. Clearly state under which situation, use fixed effect model analyze the panel data would allow you to obtain unbiased estimator of B. What is the first-differenced equation?

Answer 1

1)

a) The bias is the difference in the expected value of an estimator and the true value.

The bias can occur as the error term in the given equation is being affected by various other factors that in turn is affecting the dependent variable. In this way we are not able to capture the rue impact of crime rates on the GDP. The error term may be correlated with the independent variable causing a problem leading to the problem of bias.

b) When we set up a panel data fixed effects model we get the following equation:

GDP_it = a_i + b₀+ b₁Crmte_it+ u_it

Here a_i denotes the fixed component variable. The situation which are needed to obtain unbiased estimator of b₁ are as follows:

1) E[ u_it| Crmte_is, a_i ] = 0

2) There shall be no perfect collinearity among the variables.

3) There shall be time variation in explanatory variables.

4) Cov ( a_i , Crmte_is) = 0

The first difference equation is an approach to address the problem of omitted variables in panel data. By using this method we estimate the first difference of the equation and then take the difference of the two to arrive at the difference equation form which eliminates the fixed effect component from the equation.

The first difference of the equation will be:

GDP_it-1 = a_i + b₀+ b₁Crmte_it-1+ u_it-1

Thus the differenced equation will be:

△GDP_it = △b₁Crmte_it+ △u_it