# Instrumental variable for panel data

I am trying to quantify the effect of financial sanctions on cross-border capital flows. I have built a dyadic dataset of sanctions and capital flows by country pair and year. My sample period spans 20 years.

I conducted a fixed effects regression where the explanatory variable for sanctions is a dummy variable that takes the value 1 in each year in which a sanction is imposed between a given country pair. I include fixed effects for each country pair and each year in the sample.

$$\begin{equation*} \text{Capital_flows}_{c1, c2, t} = \beta_0 + \beta_1 \text{sanction}_{c1, c2, t} + \eta_{c1, c2} + \varphi_t + \varepsilon_{c1, c2, t} \end{equation*}$$

(where $$\eta_{c1, c2}$$ is a set of country-combination specific fixed effects and $$\varphi_{t}$$ is a set of time-specific fixed effects.)

As I understand, my fixed effects will remove all the time-invariant factors determining capital flows that were previously included in my error term. As such, I am now stuck with the various time-variant factors determining capital flows.

Having done some reading, the main problem with my approach seems to be endogeneity, i.e., my sanctions dummy will be correlated with my error term. I was planning on addressing this issue by carefully adding additional (time-variant) control variables to my model.

However, having spoken to one of my professors, he mentioned that the way to resolve this is through an instrumental variable approach and a Generalised Method of Moments estimator.

I have several questions regarding all this, and would really appreciate any advice:

• Is my idea to address endogeneity through additional (time-variant) control variables wrong?
• What exactly would an instrumental variable approach with a GMM estimator require me to do? As far as I understand, it is often very hard to find adequate instrumental variables.
• From my reading it seems that researchers sometimes use lagged dependent variables as instrumental variables. Would something like this apply to my case?
• Is there another way of getting a consistent estimator?

Thank you!

## 1 Answer

This question is very broad. To do instrumental variable estimation, you will need to find a variable, say $$Z_{c_1,c_2,t}$$, that is time varying, correlated with a sanctions, but not correlated with your error term. These are usually difficult to find. Now including additional control variables works when they are the ones causing endogeneity concerns. If you are dealing with unobserved omitted variables such as those you have no data for, then IV is the only other option. Sometimes lags of independent variables can be used as instruments, though I am not sure that this will work with sanctions. Your Profs. mentioned GMM because IV is simply a special case of GMM: you are imposing the moment condition $$E[z\epsilon]=0$$.

Without an IV, you have some other options. For example if sanctions are sufficiently rare, you may want to consider difference-in-difference estimation. You may have a hard time justifying the necessary parallel trends assumption but it's a start.