In regression analysis involving time series data, if the regression model includes not only the current but also the lagged (past) values of the explanatory variables (the X's), it is called a distributed-lag model. If the model includes one or more lagged values of the dependent variable among its explanatory variables, it is called an autoregressive model. Thus,
Yt = a + ft Xt + 0i X— + ft Xt-2 + ut represents a distributed-lag model, whereas
Yt = a + 0 Xt + y Yt-i + ut is an example of an autoregressive model. The latter are also known as dynamic models since they portray the time path of the dependent variable in relation to its past value(s).
Autoregressive and distributed-lag models are used extensively in econometric analysis, and in this chapter we take a close look at such models with a view to finding out the following:
1. What is the role of lags in economics?
2. What are the reasons for the lags?
3. Is there any theoretical justification for the commonly used lagged models in empirical econometrics?
4. What is the relationship, if any, between autoregressive and distributed-lag models? Can one be derived from the other?
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
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5. What are some of the statistical problems involved in estimating such models?
6. Does a lead-lag relationship between variables imply causality? If so, how does one measure it?
17.1 THE ROLE OF "TIME," OR "LAG," IN ECONOMICS
In economics the dependence of a variable Y (the dependent variable) on another variable(s) X (the explanatory variable) is rarely instantaneous. Very often, Y responds to X with a lapse of time. Such a lapse of time is called a lag. To illustrate the nature of the lag, we consider several examples.
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