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.

翻译：气候变化影响研究为政策制定者提供了未来气候变化对经济、健康及其他方面造成的预估损失信息。在大多数研究中，观测变量为年度结果变量（如农业产量），并伴随高频解释变量（如日温度）。应用研究者随后面临模型选择问题，即如何刻画结果变量与高频解释变量之间的非线性关系，以基于模型隐含的损害函数提出政策建议。我们证明，现有模型选择准则仅在候选模型中包含真实模型时适用于政策目标。若将所有模型视为对真实非线性关系的不完美近似，则在正常气候条件下表现良好的模型，无法保证在偏离历史常态的预估气候下同样表现优异。为此，我们提出新准则——邻近加权均方误差（PWMSE），该准则直接瞄准预估未来气候下损害函数的精度。为使准则可行，在利用PWMSE评估竞争模型时，我们对可作为预估未来气候天气模拟的早年数据赋予更高权重。研究表明，该方法能选出对预估未来气候下预测影响加权误差最小的最优近似回归模型。一项仿真研究及重新审视气候变化对农业生产影响的实证分析，验证了我们理论分析的经验相关性。