Estimating climate damages Suppose that you observe data on agricultural yields Yand temperature T, for a set of counties i

Estimating climate damages Suppose that you observe data on agricultural yields Yand temperature T, for a set of counties i. You estimate the econometric model Y = a +17+ over all i to obtain an ordinary least squares (OLS) estimate of &;. (a) Argue that if T, is randomly assigned (so that T is independently distributed from e), then your estimate of âu will give the average causal effect of temperature on agricultural yields. (b) Explain why, when e, is not independent of T.--for example, due to an omitted variable like farmers' investments in better technology to adapt to higher temperatures your estimate of 1 will not necessarily reflect the causal effect of temperature on agricultural yields. (c) Now suppose you observe also controls X, for each county i. If & is independent of T, conditional on X, then will your estimate of an in the following equation, Y; = 00 + T. + B'X, +6 correspond to the average causal effect of temperature on yields? (a) Suppose that there are 1,000 counties and each unit Y of agricultural output is worth $100 million in social surplus. 'If you interpret âj as the true causal relationship between temperature and yields, and you estimate âu = -0.3, then what is the lost social surplus due to the effects of a temperature increase of 2°C on the agricultural industry?