# 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

• I have answered the linked question now. Apr 23, 2015 at 18:18
• I guess an error term is missing in your initial specification. As it stands now, your model is a deterministic equation, some kind of definition used in accountancy rather than a regression model. Apr 23, 2015 at 20:01

• (+1) Interesting interpretation. The Central Bank probably does not react immediately after a change in CPI. There may a lag between the changes in CPI and the decision to change the interest rate, $r_t$. In that case, CPI and $r_t$ are not independent of each other but they are contemporaneously uncorrelated, that is, given a time point $t$, $E(\hbox{error}_t r_t)=0$ (the shocks at time $t$ do no affect the interest rate at time $t$ because the Central Bank has not yet reacted). In this case, OLS will be biased but will at least be consistent and inference will be valid in large samples. Apr 23, 2015 at 20:03
• @javlacalle, The central bank may be forward looking rather than backward looking. If the central bank is able to predict CPI, it will not wait for the CPI to realize but will try to affect it before that. Even if the information flow may be messy (CPI $\rightarrow$ interest rate, vice versa or both ways), I suspect endogeneity may be a worry nevertheless. Apr 23, 2015 at 20:09