Question

A researcher wants to understand how wildfire smoke affects the respiratory health of agricultural households. She finds a survey of households f rom throughout Indonesia that provides information on whether or not anyone in the household has experienced a respiratory illness in the year of some severe wildfires, the total time household members spent outside f or work, and a small set of household socio-economic characteristics ( e.g. household size, education, etc.). To understand how to use this information, she writes a simple model of household behavior. Let H be respiratory health, C be consumption, L be agricultural labor, A be household landholdings, X be household health endowments, P be outdoor air pollution, and M be household non-labor income. Suppose the household performs the following maximization problem: Max C,L U (C, H) = ln(C) + H subject to the budget constraint and biological relationship given by: C = AL + M H = K – (P²L)/X where K is some constant. Assume that X/ P² > M/A. Answer the following questions:

a. Holding consumption C and labor L constant, is there a nonlinear effect of pollution on health H? Is the magnitude of the marginal effect larger at higher or lower levels of pollution?

b. Find the optimal choices of C and L. If the household chooses these optimally, what is the resulting value of respiratory health H? What is the resulting value of utility U (referred to as “indirect utility”)?

c. Take the derivative of your expression for H from part (b) with respect to P . Does increasing exposure to pollution P reduce or increase respiratory health? How does the marginal effect of pollution on health change at higher levels of pollution? Explain why this is different from your answer in part (a).

d. Take the derivative of your expression for indirect utility from part (b) with respect to P.

e. Does increasing exposure to pollution P reduce or increase indirect utility? Explain why this is different from your answer regarding health status in part(c).

f. Suppose the researcher runs a regression of respiratory health on household income, household landholdings, household demographic characteristics, and local pollution levels (household consumption and labor supply are not included in the regression). She finds that the coefficient on local pollution levels is small but positive and statistically significant. Should she interpret this to mean that pollution does not have a negative effect on health and on wellbeing? Explain, using your results from above.

Answer 1