Solved – First-difference instrumental variables (FDIV)

instrumental-variablespanel data

I want to estimate a panel data model (not yet decided if FE, RE or an alternative that is not yet known to me). The equation is:

$$ {y_{it}} = \alpha_{i} + \lambda_{t} + \beta_{1} X_{{it}} + \beta_{2} Z_{{it}} + \epsilon_{{it}}$$

I am mainly interested in X, but I suspect that might be endogenous. I investigate some options to deal with this problem, and I came up with the FDIV solution that involves:

  1. Take the first differences of all variables in the model;

  2. Instrument the "troublesome" $ {\Delta}X_i$ with $ {X_{{it-1}}} $ and use the $ \hat{{\Delta}X_i}$ in order to estimate the first-differences FD model:

    $$ {\Delta y_{i}} = \lambda_{t} + \alpha_{1} \hat{{\Delta}X_i} + \alpha_{2} \Delta Z_{{i}} + \Delta \epsilon_{{i}}$$

My question is: is this procedure valid, provided that I count only with two waves of the panel (so $t=2$)? I have more or less 300 observations per wave, so $i=600$ (roughly). My panel is balanced.

Your orientation and hints would be greatly appreciated.

Best Answer

It depends on why you think Delta x is endogenous. It is a very special kind of endogeneity if you think that x_it-1 is exogenous. Because in a sense, you already have x_it-1 in your equation (namely inside Delta x_it). I have a hard time thinking of any situation like that.

But sometimes you may be willing to assume that x_it-2 is exogenous as an instrument for Delta x_it.

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