# Lag regression independent variables in dynamic panel: which Explanation of the signs? [Resolved]

In the famous paper " Richard Blundell & Stephen Bond (2000): GMM Estimation with persistent panel data: an application to production functions, Econometric Reviews, 19:3, 321-34" the authors report in table III two independent variables with lag 0 and lag 1 (respectively $$t_0$$ and $$t_{-1}$$). The value of the regressors is positive in $$t_0$$ and negative in $$t_{-1}$$. Why these values have opposite signs? Does exist a theoretical explanation for $$K_{t_0}$$ and $$K_{t_1}$$ in production function? Thanks a lot for the explanation.

• The process that is defined by $Y_t = \alpha_1 Y_{t-1} + \alpha_2 Y_{t-2}$ where $\alpha_1 > 0$ and $\alpha_2 < 0$ will follow a sinusoidal trend. I think you can prove this by finding the (imaginary) eigenvalues of the transition/coefficient matrix. – AdamO Jan 17 at 16:03

After deepening the subject I think I found the solution after listening to the advice of a scholar (of which I omit the name but is very prestigious).

"This sign pattern is as it should be IF the dynamics are generated from a static production function with an AR(1) error component. For example, if we have (dropping I subscripts):

$$y_{t} = bx_{t} + u_{t}$$

and

$$u_{t} = au_{t-1} + e_{t-1}$$

then we have

$$[y_t - bx_t] = a[y_{t-1} - bx_{t-1}] + e_{t}$$

or equivalently

$$y_t = bx_t - abx_{t-1} + ay_{t-1} + e_{t}$$

So if a is positive, $$x_t$$ and $$x_{t-1}$$ appear in the dynamic specification with opposite signs."