Notes: PCON = private consumption expenditure.

GDP = gross domestic product. Source: See footnote 47.

Notes: PCON = private consumption expenditure.

GDP = gross domestic product. Source: See footnote 47.


47The data are obtained from the data disk in Chandan Mukherjee, Howard White, and Marc Wuyts, Econometrics and Data Analysis for Developing Countries, Routledge, New York, 1998. The original data is from World Bank's World Tables.

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



EXAMPLE 17.10 (Continued)

Now suppose that our consumption function were

In this formulation permanent or long-run consumption Ct is a linear function of the current or observed income. Since Ct is not directly observable, let us invoke the partial adjustment model (17.6.2). Using this model, and after algebraic manipulations, we obtain

In appearance, this model is indistinguishable from the adaptive expectations model (17.12.3). Therefore, the regression results given in (17.12.4) are equally applicable here. However, there is a major difference in the interpretation of the two models, not to mention the estimation problem associated with the autoregressive and possibly serially correlated model (17.12.3). The model (17.12.5) is the long-run, or equilibrium, consumption function, whereas (17.12.6) is the short-run consumption function. ß2 measures the long-run MPC, whereas a2 ( = Sß2) gives the short-run MPC; the former can be obtained from the latter by dividing it by S, the coefficient of adjustment.

Returning to (17.12.4), we can now interpret 0.4043 as the short-run MPC. Since S = 0.4991, the long-run MPC is 0.81. Note that the adjustment coefficient of about 0.50 suggests that in any given time period consumers only adjust their consumption one-half of the way toward its desired or long-run level.

This example brings out the crucial point that in appearance the adaptive expectations and the partial adjustment models, or the Koyck model for that matter, are so similar that by just looking at the estimated regression, such as (17.12.4), one cannot tell which is the correct specification. That is why it is so vital that one specify the theoretical underpinning of the model chosen for empirical analysis and then proceed appropriately. If habit or inertia characterizes consumption behavior, then the partial adjustment model is appropriate. On the other hand, if consumption behavior is forward-looking in the sense that it is based on expected future income, then the adaptive expectations model is appropriate. If it is the latter, then, one will have to pay close attention to the estimation problem to obtain consistent estimators. In the former case, the OLS will provide consistent estimators, provided the usual OLS assumptions are fulfilled.

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