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For my thesis I am studying the impact that economic sanctions can have on the GDP per capita growth rate of targeted countries. I am using panel data for 56 countries spanning a period of 23 years. I have also chosen to use a two-way fixed effects model. My dependant variable is GDP per capita growth rate, but one of my key independent variables is lagged GDP per capita. However I have read that because I am using a fixed effects method, having a 'GDP' term on both the LHS and RHS is innacurate?

Can anyone please explain why this might be the case, and if it is infact a problem, how it can be circumvented?

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  • $\begingroup$ can you give a brief description of other Independent variables including the computation or measurement procedures. $\endgroup$ – Subhash C. Davar Apr 4 '18 at 9:14
  • $\begingroup$ what is your two way fixed efects model ? $\endgroup$ – Subhash C. Davar Apr 4 '18 at 9:16
  • $\begingroup$ Y_it= a_i+ β_1 〖Sanction〗_(it )+ β_2 X_it+δ_t+ ε_it - The independent variable would be the sanction variable, and then the other control variables in x, are lagged gdp growth rate, lagged population and a lagged trade openness term which is calculated by the sum of imports + exports /GDP. I also have included controls for the level of democracy in the nation, and a dummy varible coded for 1 if the country was involved in a civil/interstate war at time t. The two way fixed effects model, includes country-fixed effects and year-fixed effects $\endgroup$ – Sam Jacobs Apr 7 '18 at 16:04
  • $\begingroup$ Do you find any problems with the results for your fixed effects model ? $\endgroup$ – Subhash C. Davar Apr 7 '18 at 17:14
  • $\begingroup$ You can edit your question - body text to show your model $\endgroup$ – Subhash C. Davar Apr 7 '18 at 17:16
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Consider a simple version of the model without regressors, which is enough to highlight the problem with fixed effects: \begin{equation} y_{im}=\alpha_i+\rho y_{i,m-1}+\eta_{im}\quad(m=1,\ldots,M;\;i=1,\ldots,n) \end{equation} Further assume that $E(\alpha_i\eta_{im})=0$ and $E(y_{i0}\eta_{im})=0$ for all $m$, as well as $E(\eta_{i,m}\eta_{i,h})=0$ as well as $E(\eta_{i,m}^2)=\sigma_{\eta}^2$.

Recursive substitution yields \begin{eqnarray*} y_{im}&=&\alpha_i+\rho(\alpha_i+\rho y_{i,m-2}+\eta_{i,m-1})+\eta_{i,m}\\ &=&\eta_{i,m}+\rho\eta_{i,m-1}+\rho^2\eta_{i,m-2}+\rho^3 y_{i,m-3}+\alpha_i+\rho\alpha_i+\rho^2\alpha_i\\ &=&\ldots\\ &=&\eta_{i,m}+\rho\eta_{i,m-1}+\rho^2\eta_{i,m-2}+\ldots+\rho^{m-1}\eta_{i,1}+\frac{1-\rho^m}{1-\rho}\alpha_i+\rho^my_{i0} \end{eqnarray*} Multiplying through with $\eta_{ih}$ and taking expectations on both sides gives \begin{eqnarray} E(y_{im}\eta_{ih})&=&E(\eta_{im}\eta_{ih})+\rho E(\eta_{i,m-1}\eta_{ih})+\rho^2E(\eta_{i,m-2}\eta_{ih})+\ldots\notag\\ &&\quad+\rho^{m-1}E(\eta_{i,1}\eta_{ih})+\frac{1-\rho^m}{1-\rho}E(\alpha_i\eta_{ih})+\rho^mE(y_{i0}\eta_{ih})\notag\\ &=&\begin{cases} 0 &\text{for }h>m\\ \rho^{m-h}\sigma_{\eta}^2&\text{for }h=1,\ldots,m\end{cases}\label{yeta} \end{eqnarray} Hence, the regressor $y_{i,m-1}$ will not be uncorrelated with all idiosyncratic errors $\eta_{ih}$, which is the key orthogonality condition for consistency of fixed effects.

Have a look for the Arellano-Bond estimator as an alternative estimation strategy.

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The use of lagged GDP per capita as an independent variable can not be justified. You should excude it frrom your model. However, the justification can not be traced to the fixed effects modelling. The GDP growth rate for current year depends heavily on the terms of trade, economic sanctions and population etc. The lagged GDP growth rate is almost perfectly related to the current growth rate and hence; nothing is likely to be left out that needs explanatory variables.

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