Modeling different lag structures I know there are various information criteria that can be used to compare model specifications, including those with different lag structures.  I can easily compare the Akaike Information Criterion (AIC) of two models.
My question is how to develop models of different lag structures for comparison?
Example problem:
Dependent variable:
consumer price index (CPI)
Independent variables:
money supply (M),
interest rates (r,)
exchange rate (XR)
My initial specification is:
CPIt=a0+a1Mt+a2rt+a3XRt.
How would a one period lag structure be specified?  And how would a two period lag structure be specified?  Is the specification in the following link correct?  It was unanswered.
Testing between two competing linear models with different lagged independent variables
 A: This is not really an answer, but I hope it will be helpful.
First, your "initial specification" is rather problematic. For the model to be estimable by OLS you would need the regressors (the right-hand-side variables) to be exogenous with respect to the regressand (the left-hand-side variable). Here you have interest rates that are anything but exogenous with respect to CPI. Central banks normally follow the development of CPI closely and try to affect CPI using the main instrument they have, i.e. the interest rates. That is, the interest rate depends on CPI due to the actions of the central bank. Moreover, exchange rate and money supply could also be argued to be endogenous. Thus there is very little chance that the regressors are uncorrelated with errors. In presence of correlation between regressors and the error term, the OLS estimates will not have their nice properties of unbiasedness and consistency. Therefore you should rethink the model specification. But perhaps you are analyzing a country where the central bank has some other target than inflation stability, that does not have a free-floating currency or is peculiar in some other way. Then my remarks may not apply.
Second, I suppose it depends on the definition of what a "one period lag structure" is. Have you looked carefully into the source you are following (textbook, lecture notes, slides, research paper) to find the definition? Or are you asking for the definition here so that What is a one period lag structure? actually is you question?
