The Department for Health wishes to understand the effect of health on wages. You are commissioned to examine data on a group of individuals born in 1970, which has been followed from birth to age 40. You run four OLS regressions and get the following results: Constant Health at 40 Health at 10 Education Health at 10* Education N R-squared Dependent variable: In(wages at 40) (1) (2) 2.252 1.653 (0.052) 0.126 (0.042) (0.043) 0.165 (0.051) 5000 0.123 0.195 (0.088) 5000 0.158 (3) 1.682 (0.065) 0.082 (0.041) 0.102 (0.006) 5000 0.146 (4) 1.823 (0.256) -0.368 (0.124) 0.063 (0.023) 0.052 (0.025) 5000 0.151 where Health at 40 and Health at 10 are dummies that take the value 1 if the individual self-reports being in good health and 0 otherwise at age 40 and at age 10, respectively; Education measures the number of years of schooling completed, and Health at 10* Education is an interaction term between the variables Health at 10 and Education. In indicates the natural logarithm. Numbers in parentheses are standard errors. (a) What might be the economic reasons for health to affect wages? Comment on the effect of health on wages in regression (1). Can we claim there is a causal effect of health on wages? Explain. (b) The coefficient on Health at 40 is lower in regression (2) than it is in regression (1). Why do you think this is the case? What can you infer about the correlation between health and education? Show the derivation in detail and explain the intuition. (c) Your colleague argues that regression (3), in which health is measured at age 10, provides more conclusive evidence of a causal effect than regression (2), in which health is measured at age 40. What concern about measuring health at 40 do you think she has (d) In regression (4), you include Health at 10*Education, an interaction term between Health at 10 and Education. How do you interpret the coefficient on the interaction term? Should you be worried that the main coefficient on Health 10 is negative (-0.368)? In the sample, the least educated individuals have 11 years of schooling.