Question 16 (11 marks) This question consists of three parts, part (a) to (c). I am interested in studying the determinants of educational attainment, measured by years of schooling, E. In particular, I want to estimate the causal impact of an individual's mother's education on individual's educational attainment. Suppose that the correct model is the following and E(e, SM, SIB) = 0: E=B1+BSM + ASIB + e (3) where SM is an individual's mother's years of schooling and SIB is the number of siblings an individual has. I don't initially realise that SIB is an important factor that affects educational attainment, and so estimate the regression model without SIB. I then realise my mistake and estimate the regression model with both SM and SIB. The regression results (including the coefficients, standard errors, t-statistic, p-value, and 95% confidence interval) for both regressions are below. Some of the numbers in the results below have been left out intentionally and replaced by an *. Model 1 N=540, R2 = 0.1308 Coefficient Std.error t-statistic Prob. 95% Confidence Interval Constant 10.0469 SM 0.4147. 24.23 0.000 Model 2 N = 540, R2 = 0.1446 (9.2322, 10.8615) * Coefficient Std.error t-statistic Prob. 95% Confidence Interval Constant SM 10.9052 0.2781 0.5046 0.0365 21.61 7.61 0.000 0.000 (9.9140, 11.8964) SIB (0.2063, 0.3499) (-0.1435, -0.0532) 6 of 16 (a) (3 Marks) Based on the result provided, interpret the 95% confidence interval for g in model 2. What is your best guess of how an increase in the number of siblings affects expected educational attainment, keeping mother's education constant? (i.e. the sign of 3 in Model 2). (b) (5 Marks) Suppose that more educated women tend to have fewer children, and that this is true for the mothers of the individuals in the sample. Using the information you have so far and the relevant 11 Mark T