Xycoon logo
Distributed Lags
Home    Site Map    Site Search    Free Online Software    
horizontal divider
vertical whitespace

Online Econometrics Textbook - Regression Extensions - Infinite distributed lags

[Home] [Up] [Finite DL] [Infinite DL]

III.VI.2 Infinite distributed lags

There exist different specifications for infinite distributed lags. Some of them are based on economic theory, others are of a more inductive nature.

The Koyck lags are frequently used in econometric practice. Formally this means that

Online Econometrics Textbook - Regression Extensions - Infinite distributed lags


for which


Note that the Koyck lag is sometimes also called the geometric distributed lag due to the fact that the regression parameters are exponentially decreasing.

The statistical model is, when using Koyck lags, assumed to be of the form


such that (III.VI.2-2) can be substituted into (III.VI.2-3) yielding


Sometimes it is suggested in econometric literature that Koyck lags can be estimated by OLS, using a mathematical trick.


or simply


which can be used in OLS estimation.

If we rewrite (III.VI.2-4) as


and if et is normally distributed with zero mean and constant variance then MLE can be applied to







Also, it is remarked that the Koyck distributed lags do not have to start from lag zero. It is possible to set the starting point to some specified lag, and capture the early lags by a finite distributed lag method such as the Almon lag. This way great flexibility can be obtained by combining finite distributed lags with postponed infinite distributed lags.

Another way of combining, say, Almon lags and Koyck lags is the following


such that the model becomes




Another method of distributing parameters over time is the Pascal distributed lag or formally


which are the weights of time. Hence the complete model is


If for instance r = 3 then the Pascal distributed lag becomes


from which it can be seen that this is a special case of (III.VI.2-12).

Define Jorgenson's rational distributed lag as the ratio of two polynomials


which may be illustrated by a simple example


The same remarks as with the Koyck lags hold for estimation of Jorgenson lags.

Finally we define the (adapted) gamma distributed lags by



The complete model is written as


for which it can be shown that the deletion of the truncation remainder does not affect the asymptotic properties.

We furthermore remark that the omission of important variables in the regression equation can have devastating effects on the estimation of distributed lag parameters (c.q. the UVB).

One of the most important inductive distributed lag models will be considered later (see Box-Jenkins Transfer Function Analysis).

vertical whitespace

Finite DL
Infinite DL
horizontal divider
horizontal divider

© 2000-2022 All rights reserved. All Photographs (jpg files) are the property of Corel Corporation, Microsoft and their licensors. We acquired a non-transferable license to use these pictures in this website.
The free use of the scientific content in this website is granted for non commercial use only. In any case, the source (url) should always be clearly displayed. Under no circumstances are you allowed to reproduce, copy or redistribute the design, layout, or any content of this website (for commercial use) including any materials contained herein without the express written permission.

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically updates the information without notice. However, we make no warranties or representations as to the accuracy or completeness of such information, and it assumes no liability or responsibility for errors or omissions in the content of this web site. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Contributions and Scientific Research: Prof. Dr. E. Borghers, Prof. Dr. P. Wessa
Please, cite this website when used in publications: Xycoon (or Authors), Statistics - Econometrics - Forecasting (Title), Office for Research Development and Education (Publisher), http://www.xycoon.com/ (URL), (access or printout date).

Comments, Feedback, Bugs, Errors | Privacy Policy