1 General model with lagged variables Static model AR(1) model Model with lagged dependent variable Methodologically, in developing a regression specification that survives the tests to which it is subjected, we have followed what is described as a specific-to-general procedure for model selection, and it is open to serious criticism. DYNAMIC MODEL SPECIFICATION

2 General model with lagged variables Static model AR(1) model Model with lagged dependent variable If you start with a poorly specified model, in our case the static model, the various diagnostic test statistics are likely to be invalidated. Thus there is a risk that the model may survive the tests and appear to be satisfactory, even though it is misspecified. DYNAMIC MODEL SPECIFICATION

3 General model with lagged variables Static model AR(1) model Model with lagged dependent variable To avoid this danger, you should in principle adopt a general-to-specific approach. You should start with a model that is sufficiently general to avoid potential problems of underspecification, and then see if you can legitimately simplify it. DYNAMIC MODEL SPECIFICATION

4 General model with lagged variables Static model AR(1) model Model with lagged dependent variable In our case, the starting point should be the model with all the lagged variables. DYNAMIC MODEL SPECIFICATION

5 General model with lagged variables Static model AR(1) model Model with lagged dependent variable Having fitted it, we might be able to simplify it to the static model, if the lagged variables individually and as a group do not have significant explanatory power. DYNAMIC MODEL SPECIFICATION

6 General model with lagged variables Static model AR(1) model Model with lagged dependent variable If the lagged variables do have significant explanatory power, we could perform a common factor test and see if we could simplify the model to an AR(1) specification. DYNAMIC MODEL SPECIFICATION

7 General model with lagged variables Static model AR(1) model Model with lagged dependent variable Sometimes we may find that a model with a lagged dependent variable is an adequate dynamic specification, if the other lagged variables lack significant explanatory power. DYNAMIC MODEL SPECIFICATION

8 General model with lagged variables Static model AR(1) model Model with lagged dependent variable In the case of the housing regression, we have done exactly the opposite. We started with a crude static model. DYNAMIC MODEL SPECIFICATION

9 General model with lagged variables Static model AR(1) model Model with lagged dependent variable We switched to an AR(1) specification. DYNAMIC MODEL SPECIFICATION

10 General model with lagged variables Static model AR(1) model Model with lagged dependent variable We turned to the more general model when the common factor test revealed that the AR(1) specification was inadequate. DYNAMIC MODEL SPECIFICATION

11 General model with lagged variables Static model AR(1) model Model with lagged dependent variable Finally we ended up with a model with a lagged dependent variable, perhaps a little lucky to do so. DYNAMIC MODEL SPECIFICATION

Copyright Christopher Dougherty These slideshows may be downloaded by anyone, anywhere for personal use. Subject to respect for copyright and, where appropriate, attribution, they may be used as a resource for teaching an econometrics course. There is no need to refer to the author. The content of this slideshow comes from Section 12.5 of C. Dougherty, Introduction to Econometrics, fourth edition 2011, Oxford University Press. Additional (free) resources for both students and instructors may be downloaded from the OUP Online Resource Centre Individuals studying econometrics on their own and who feel that they might benefit from participation in a formal course should consider the London School of Economics summer school course EC212 Introduction to Econometrics or the University of London International Programmes distance learning course 20 Elements of Econometrics