## Ns

Sig

Sig: Significant; NS: Not significant.

Note: Growth is real per capita GDP growth at 1985 international prices.

Source: World Bank, The East Asian Miracle: Economic Growth and Public Policy, Oxford University Press, New York, 1993, p. 244, (Table A5-2). The original source is Robert Summers and Alan Heston, "The Penn World Tables (Mark 5): An Expanded Set of International Comparisons, 1950-88," Quarterly Journal of Economics, vol. 105, no. 2, 1991.

Sig: Significant; NS: Not significant.

Note: Growth is real per capita GDP growth at 1985 international prices.

Source: World Bank, The East Asian Miracle: Economic Growth and Public Policy, Oxford University Press, New York, 1993, p. 244, (Table A5-2). The original source is Robert Summers and Alan Heston, "The Penn World Tables (Mark 5): An Expanded Set of International Comparisons, 1950-88," Quarterly Journal of Economics, vol. 105, no. 2, 1991.

59These results are obtained from The East Asian Miracle: Economic Growth and Public Policy, published for the World Bank by Oxford University Press, 1993, p. 244.

Models: Autoregressive and Distributed-Lag Models

CHAPTER SEVENTEEN: DYNAMIC ECONOMETRIC MODELS 701

*A Note on Causality and Exogeneity

As we will study in the chapters on simultaneous equation model in Part IV of this text, economic variables are often classified into two broad categories, endogenous and exogenous. Loosely speaking, endogenous variables are the equivalent of the dependent variable in the single-equation regression model and exogenous variables are the equivalent of the X variables, or regressors, in such a model, provided the X variables are uncorrelated with the error term in that equation.60

Now we raise an interesting question: Suppose in a Granger causality test we find that an X variable (Granger) causes a Y variable without being caused by the latter (i.e., no bilateral causality). Can we then treat the X variable as exogenous? In other words, can we use Granger causality (or non-causality) to establish exogeneity?

To answer this question, we need to distinguish three types of exogeneity: (1) weak, (2) strong, and (3) super. To keep the exposition simple, suppose we consider only two variables, Yt and Xt, and further suppose we regress Yt on Xt. We say that Xt is weakly exogenous if Yt also does not explain Xt. In this case estimation and testing of the regression model can be done, conditional on the values of Xt. As a matter of fact, going back to Chapter 2, you will realize that our regression modeling was conditional on the values of the X variables. Xt is said to be strongly exogenous if current and lagged Y values do not explain it (i.e., no feedback relationship). And Xt is super-exogenous if the parameters in the regression of Y and X do not change even if the X values change; that is, the parameter values are invariant to changes in the value(s) of X. If that is in fact the case, then, the famous "Lucas critique" may lose its force.61

The reason for distinguishing the three types of exogeneity is that, "In general, weak exogeneity is all that is needed for estimating and testing, strong exogeneity is necessary for forecasting and super exogeneity for policy analysis."62

Returning to Granger causality, if a variable, say Y, does not cause another variable, say X, can we then assume that the latter is exogenous? Unfortunately, the answer is not straightforward. If we are talking about weak exogeneity, it can be shown that Granger causality is neither necessary nor sufficient to establish exogeneity. On the other hand, Granger causality is necessary (but not sufficient) for strong exogeneity. The proofs of these

60Of course, if the explanatory variables include one or more lagged terms of the endogenous variable, this requirement may not be fulfilled.

61The Nobel laureate Robert Lucas put forth the proposition that existing relations between economic variables may change when policy changes, in which case the estimated parameters from a regression model will be of little value for prediction. On this, see Oliver Blanchard, Macroeconomics, Prentice Hall, 1997, pp. 371-372.

62Keith Cuthbertson, Stephen G. Hall, and Mark P. Taylor, Applied Econometric Techniques, University of Michigan Press, 1992, p. 100.

Optional.

Models: Autoregressive and Distributed-Lag Models

702 PART THREE: TOPICS IN ECONOMETRICS

statements are beyond the scope of this book.63 For our purpose, then, it is better to keep the concepts of Granger causality and exogeneity separate and treat the former as a useful descriptive tool for time series data. In Chapter 19 we will discuss a test to find out if a variable can be treated as exogenous.

1. For psychological, technological, and institutional reasons, a regres-sand may respond to a regressor(s) with a time lag. Regression models that take into account time lags are known as dynamic or lagged regression models.

2. There are two types of lagged models: distributed-lag and autoregressive. In the former, the current and lagged values of regressors are explanatory variables. In the latter, the lagged value(s) of the regressand appear as explanatory variables.

3. A purely distributed-lag model can be estimated by OLS, but in that case there is the problem of multicollinearity since successive lagged values of a regressor tend to be correlated.

4. As a result, some shortcut methods have been devised. These include the Koyck, the adaptive expectations, and partial adjustment mechanisms, the first being a purely algebraic approach and the other two being based on economic principles.

5. But a unique feature of the Koyck, adaptive expectations, and partial adjustment models is that they all are autoregressive in nature in that the lagged value(s) of the regressand appear as one of the explanatory variables.

6. Autoregressiveness poses estimation challenges; if the lagged regres-sand is correlated with the error term, OLS estimators of such models are not only biased but also are inconsistent. Bias and inconsistency are the case with the Koyck and the adaptive expectations models; the partial adjustment model is different in that it can be consistently estimated by OLS despite the presence of the lagged regressand.

7. To estimate the Koyck and adaptive expectations models consistently, the most popular method is the method of instrumental variable. The instrumental variable is a proxy variable for the lagged regressand but with the property that it is uncorrelated with the error term.

8. An alternative to the lagged regression models just discussed is the Almon polynomial distributed-lag model, which avoids the estimation problems associated with the autoregressive models. The major problem with the Almon approach, however, is that one must prespecify both the lag length and the degree of the polynomial. There are both formal and informal methods of resolving the choice of the lag length and the degree of the polynomial.

63For a comparatively simple discussion, see G. S. Maddala, Introduction to Econometrics, 2d ed., Macmillan, New York, 1992, pp. 394-395, and also David F. Hendry, Dynamic Econometrics, Oxford University Press, New York, 1995, Chap. 5. 