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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.

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  • $\begingroup$ 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. $\endgroup$ – AdamO Jan 17 at 16:03
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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."

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