Category Springer Texts in Business and Economics

A Lagged Dependent Variable Model with AR(1) Disturbances

Подпись: Yt = a + вYt-l + Yxt + ut Подпись: t = 2,...,T Подпись: (6.20)

A model with a lagged dependent variable and an autoregressive error term is estimated using instrumental variables (IV). This method will be studied extensively in Chapter 11. In short, the IV method corrects for the correlation between Yt-i and the error term by replacing Yt-i with its predicted value Yt-i. The latter is obtained by regressing Yt-i on some exogenous variables, say a set of Z’s, which are called a set of instruments for Yt-i. Since these variables are exogenous and uncorrelated with ut, YYt-i will not be correlated with ut. Suppose the regression equation is

and that at least one exogenous variable Zt exists which will be our instrument for Yt_1. Re­gressing Yt-i on Xt, Zt and a constant, we get

Yt_1 = Yt-l + = a1 + Cb2Zt + 0-3Xt + vt – (6.21)

Then Yt-1 = Y1 ...

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