  Climate change impact studies inform policymakers on the estimated damages of
future climate change on economic, health and other outcomes. In most studies,
an annual outcome variable is observed, e.g. agricultural yield, along with a
higher-frequency regressor, e.g. daily temperature. Applied researchers then
face a problem of selecting a model to characterize the nonlinear relationship
between the outcome and the high-frequency regressor to make a policy
recommendation based on the model-implied damage function. We show that
existing model selection criteria are only suitable for the policy objective if
one of the models under consideration nests the true model. If all models are
seen as imperfect approximations to the true nonlinear relationship, the model
that performs well in the normal climate conditions is not guaranteed to
perform well at the projected climate that is different from the historical
norm. We therefore propose a new criterion, the proximity-weighted mean-squared
error (PWMSE), that directly targets precision of the damage function at the
projected future climate. To make this criterion feasible, we assign higher
weights to prior years that can serve as weather analogs to the projected
future climate when evaluating competing models using the PWMSE. We show that
our approach selects the best approximate regression model that has the
smallest weighted error of predicted impacts for a projected future climate. A
simulation study and an application revisiting the impact of climate change on
agricultural production illustrate the empirical relevance of our theoretical
analysis.
