What would be an appropriate statistical test to determine the best model for two competing linear models?
Both models use the same independent variables (IVs); however, some independent variables are measured at different times. In the first model, the IVs lag the dependent variable (DV) by one period of time, and in the second model, the IVs lag the DV by a longer period of time. I'm interested in determining which lagged period is more appropriate to use. The DV for both models is measured at the same time period. In symbols:
$$ y_{i,t} = x_{i,t-1} + y_{i,t-1} + z_{i,t-1} + \epsilon_i $$
versus
$$ y_{i,t} = x_{i,t-2} + y_{i,t-2} + z_{i,t-2} + \epsilon_i $$
Are AIC, BIC, etc. appropriate for this?