Dynamic Panel Equation

[Truong Quoc Phan]

Hello
I am trying to build a Dynamic Panel Equation with the following information
- Variables: Y, X, and C (controlling variable)
- Time t1, t2, t3, ..., tn

At any time t, I propose the following possible relationships. Let t=t2
X(t2) → Y(t2)
Y(t1) → Y(t2)
Y(t1) → X(t2)



Taking the information above, the mode is:

Y(t) = a + b*Y(t-1) + c*X(t) + d*X(t-1) + Σθ*C(t)

Where:
- C(t): are controlling variables at time t

I have two questions:
1. Does the model above correct?
2. If the model above is correct then the Instrument Variables (according to Anderson and Hisao 1981) is:
- IV1: Y(t-1) - Y(t-2)
- IV2: X(t-1) - X(t-2)

Is this correct?

Thank you
Phan

[Sebastian Kripfganz]

Given the dynamic nature of your model, Y(t) is a function of Y(t-1) and X(t). Thus, X(t-1) is not necessarily needed in the regression model, even though you can keep it in and then test whether its coefficient is indeed equal to zero.

Furthermore, X(t) is a function of Y(t-1). Thus, X(t) is a predetermined (weakly exogenous) regressor.

Anderson and Hsiao (1981, Journal of the American Statistical Association) propose estimating the model in first differences to remove unobserved fixed effects. For the first-differenced model, they propose instruments Y(t-2) - Y(t-3). Note the time subscripts! For predetermined regressors in the first-differenced model, the instrument would be indeed X(t-1) - X(t-2).

For more information on the instrumental-variables based estimation of such dynamic panel data models in Stata, please see:

• Kripfganz, S. (2019). Generalized method of moments estimation of linear dynamic panel data models. Proceedings of the 2019 London Stata Conference.