Distributed Lags Analysis - General Purpose
Distributed lags analysis is a specialized technique for examining the relationships between variables that involve some delay. For example, suppose that you are a manufacturer of computer software, and you want to determine the relationship between the number of inquiries that are received, and the number of orders that are placed by your customers. You could record those numbers monthly for a one year period, and then correlate the two variables. However, obviously inquiries will precede actual orders, and one can expect that the number of orders will follow the number of inquiries with some delay. Put another way, there will be a (time) lagged correlation between the number of inquiries and the number of orders that are received (see also autocorrelation and crosscorrelation).
Time-lagged correlations are particularly common in econometrics. For example, the benefits of investments in new machinery usually only become evident after some time. Higher income will change people's choice of rental apartments, however, this relationship will be lagged because it will take some time for people to terminate their current leases, find new apartments, and move. In general, the relationship between capital appropriations and capital expenditures will be lagged, because it will require some time before investment decisions are actually acted upon.
In all of these cases, we have an independent or explanatory variable that affects the dependent variables with some lag. The distributed lags method allows you to investigate those lags.
Detailed discussions of distributed lags correlation can be found in most econometrics textbooks, for example, in Judge, Griffith, Hill, Luetkepohl, and Lee (1985), Maddala (1977), and Fomby, Hill, and Johnson (1984). In the following paragraphs we will present a brief description of these methods. We will assume that you are familiar with the concept of correlation (see Basic Statistics), lagged cross-correlation, and the basic ideas of multiple regression (see Multiple Regression).