Suppose you are tasked with investigating if whether there is a causal effect of exclusive golf club membership, or even playing golf more generally, on CEO salaries. You want to estimate the following:

salaryi = Bo + Bimemberi + B2playsi + Ui , where salaryi is the salary (in $m) of the ith CEO in the sample, memberi is a dummy variable taking the value 1 if CEO i is a member of an exclusive golf club and 0 otherwise, plays, is a dummy variable taking the value 1 if CEO i plays golf regularly and 0 otherwise, and B1 and 32 are the causal effects you wish to estimate. You are worried that CEOs' unobserved professional networks might be correlated with their membership or golfing behavior and also related to their salary (say, though being more likely to be offered high-paying CEO jobs), causing Assumption 1 to be violated. (a) Would OLS regression of salary on member and plays produce consistent estimates of B1, and B2? (b) Would OLS regression of salary on member and plays produce consistent estimates of the BLP coefficients for predicting a CEO's salary having observed their values of member and plays? salaryi = Bo + Bimemberi + B2playsi + Ui , where salaryi is the salary (in $m) of the ith CEO in the sample, memberi is a dummy variable taking the value 1 if CEO i is a member of an exclusive golf club and 0 otherwise, plays, is a dummy variable taking the value 1 if CEO i plays golf regularly and 0 otherwise, and B1 and 32 are the causal effects you wish to estimate. You are worried that CEOs' unobserved professional networks might be correlated with their membership or golfing behavior and also related to their salary (say, though being more likely to be offered high-paying CEO jobs), causing Assumption 1 to be violated. (a) Would OLS regression of salary on member and plays produce consistent estimates of B1, and B2? (b) Would OLS regression of salary on member and plays produce consistent estimates of the BLP coefficients for predicting a CEO's salary having observed their values of member and plays