## Climate Econometrics

Climate $C_iτ$ and weather $c_iτ$ are vectors of $K$ parameters specifying respectively the probability and empirical distributions of atmosphere-ocean states (temperature, rainfall, humidity, etc.) at location $i$ during period $τ$. Climate may affect an outcome directly through weather or through individual decision (belief): $Y(C) = Y(c(C), b(C))$, with (marginal) direct effect $∂Y/∂c$ and belief effect $∂Y/∂b$. Adaptation refers to the belief effects and the interactions between belief and direct effects $∂^2Y/∂b∂c$. Average treatment effect for climate change under current climatic and non-climatic factors: $β = E[Y|C+ΔC, x] - E[Y|C, x]$.

Non-experimental research designs to estimate $β$:

1. Cross-sectional (CS): exploit spatial variation; adopts the unit homogeneity assumption; subject to omitted variables bias (Estimates are biased if the model omits relevant variables; there is no systematic method to detect such omission.);
2. Time-series (TS): exploit temporal variation, with unit-specific fixed effects and time trends; adopts the marginal treatment comparability assumption, i.e. the same marginal change in weather and climate have the same effect on outcome;
3. Long differences (LD): cross-sectional comparison of changes over time, primarily used to test effects of gradual changes; a trade-off for the two assumptions;

Frequency-identification trade-off: Low observation frequency might capture belief effects, but the unit gets less comparable to itself between observations.

A partial test of marginal treatment comparability: If the estimates are stable across all temporal frequencies from unfiltered time-series to long differences to cross section, the marginal treatment comparability assumption is more plausible.

The marginal effects of climate and weather are identical, if the agent adapts its belief/action to the climate to consistently maximize the outcome which is a differentiable function of beliefs/actions. The total effect of climate change is the integration of marginal effects of weather, which can be computed using time-series estimates.

Climate should be parameterized into variables/measures that most strongly influence social or economic outcomes.

Important aspects in reduced-form econometric models of climate effects (dose-response function, regression function): 1. nonlinear effects: nonlinear response functions at the resolution of weather data can be recovered despite aggregated outcome data; 2. spatial and temporal displacement: distribution of net effect in time (harvesting, advancing an expected event; delayed effect, effects dominate after the event) and space (transmit effect across locations; remote effect, effects dominate at other locations); 3. statistical uncertainty: estimates of standard error may be biased, due to spatial and temporal autocorrelation in climate data; 4. measurement of adaptation: - if the adaptive action is known and observed directly as an outcome, the climate effect on adaptation can be estimated; - for an outcome influenced by adaptation, cross-sectional estimate captures all belief effects along with all direct effects, while time-series estimates stratified by proxies of adaptive actions can measure the overall net effect of all adaptive actions; 5. meta-anlysis (cross-study comparison and synthesis): results across studies can be combined to fit a response function applicable to all populations;

Attribute historical impacts and project future impacts of climate change under different scenarios, typically using models of partial equilibrium responses. General equilibrium responses include factor reallocation and price change, but is rarely studied.

Climate can affect an outcome via many mechanisms/pathways, and a specific mechanism/pathway may be isolated and estimated in a structural model.

Note that adaptation costs are almost never measured.