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Online Econometrics Textbook - Regression Extensions - Distributed Lags

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Sometimes the econometrician wishes to model the dynamic properties of economic time series data. The distributed lag theory tries to introduce these dynamics, in an intelligent way (i.e. without the loss of many degrees of freedom). The underlying principle can be formulated as

distributed lags


from which it is obvious that it is impossible to estimate an infinite amount of parameters from a finite sample.

In general a distinction is made between finite and infinite distributed lags.

It should be noted that distributed lags can be used for sequential observations as in eq. (III.VI-1) but also for seasonal or periodic data

seasonally distributed lags


where s is the seasonal period (e.g. s = 12 for monthly data).

Of course combinations of sequential and seasonal distributed lags are also possible.

In each case, the distributed lag model should be parsimonious (i.e. the model should explain as much as possible with the smallest number of parameters as possible).

Distinction should also be made between distributed lags in classical econometrics and time series analysis. The reason for this distinction will become clear in the chapters about time series analysis.

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Assumption Violations
Restricted LS
Distributed Lags
Finite DL
Infinite DL
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