Y o i X ut

- (1 - S)(1 - y)Yt-2 + [Sut - s(1 - Y)ut-1] (17.7.2) = ao + a1 Xt + a2Yt-1 + a3Yt-2 + vt

Optional.

Gujarati: Basic I III. Topics in Econometrics I 17. Dynamic Econometric I I © The McGraw-Hill

Econometrics, Fourth Models: Autoregressive Companies, 2004 Edition and Distributed-Lag

Models

676 PART THREE: TOPICS IN ECONOMETRICS

where vt = S[ut — (1 — y)ut—1]. This model too is autoregressive, the only difference from the purely adaptive expectations model being that Yt—2 appears along with Yt— 1 as an explanatory variable. Like Koyck and the AE models, the error term in (17.7.2) follows a moving average process. Another feature of this model is that although the model is linear in the as, it is nonlinear in the original parameters.

A celebrated application of (17.7.1) has been Friedman's permanent income hypothesis, which states that "permanent" or long-run consumption is a function of "permanent" or long-run income.27

The estimation of (17.7.2) presents the same estimation problems as the Koyck's or the AE model in that all these models are autoregressive with similar error structures. In addition, (17.7.2) involves some nonlinear estimation problems that we consider briefly in exercise 17.10, but do not delve into in this book.

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