A Description Of The FE-IV Model

Another reason for choosing the FE model12 is that it can solve the endogeneity problem through using the FE-IV model; the variable GDP per capita-used as a proxy of income-could be an endogenous variable. An endogenous variables are variables that correlated with the error term (ε௜௧ ), while the variables that uncorrelated with the error term are called exogenous variables. The description of these terms explains that an endogenous variable is determined within the model itself while an exogenous variable is determined outside the model. To understand the endogeneity, we will use the classic regression equations that show the relationship between prices and wages:
Price = ߚ0 + ߚ1Wage + ε௜௧ ………………………… (11)
Wage = ߚ0௔ + ߚ1௕Price + u௜௧ ……………………... (12)
From equation (11) and (12) we can see that prices can affect wages and also wages can affect prices, in this case we can say that both wages and prices are interdependent variables and to run our regression we can‟t use the OLS technique because using OLS will give us biased estimates because of endogeneity13. From equation (11), the variable Wage is an endogenous variable and to solve the endogeneity we need an instrument that correlated with Wage but not correlated with the error term. To solve the endogeneity problem we will use FE- panel IV model, after identifying a set of instruments, ܼ௜ , which are explanatory for the endogenous variables in ܺ but which are logically uncorrelated with the error term. The FE-IV procedure is (1) regress the endogenous elements of ܺ on ܼ௜ ; then (2) regress on the predicted value of ܺ. We mentioned previously that a good instrument is the one that uncorrelated with the error term, in other words, is an exog...

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...an instrument is required. The test can be represented by the following equations:
ܺ1௜௧ = ߚ0 + ߚ2ܺ2௜௧ + ߚ௭ Z௜௧ + ε௜௧ ……... .. (13)
Y௜௧ = ߚ0 + ߚ1ܺ1௜௧ + λݒ௜௧ + ε௜௧ ………... ... (14)
Where Z௜௧ is the instrument, ܺ1௜௧ is the variable to be tested for endogeneity, ܺ2௜௧ is any other exogenous variable, and ݒ௜௧ is the residuals from the regression in

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Chapter 3 Empirical Evidence equation (13). Equation (14) means that if ܺ௜௧ is uncorrelated with ε௜௧ then λ = 0; for ܺ௜௧ to be endogenous we need to reject the null hypothesis that λ = 0, or in other words, for ܺ௜௧ to be endogenous, coefficient λ should be significant. The results are shown in table (5) which shows that the residuals are highly significant, indicating that RGD per capita is endogenous, and running the regression without using the instrument, will produce inconsistent estimates.