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Use the data in WAGE2 for this exercise.(i) In Example $15.2,$ if sibs is used as an instrument for educ, the IV estimate of the return toeducation is $122 .$ To convince yourself that using sibs as an IV for educ is not the same as justplugging sibs in for educ and running an OLS regression, run the regression of log(wage) onsibs and explain your findings.(ii) The variable brthord is birth order (brthord is one for a first-born child, two for a second-bornchild, and so on). Explain why educ and brthord might be negatively correlated. Regress educon brthord to determine whether there is a statistically significant negative correlation.(iii) Use brthord as an IV for educ in equation $(15.1) .$ Report and interpret the results.(iv) Now, suppose that we include number of siblings as an explanatory variable in the wageequation; this controls for family background, to some extent:$$\log (w a g e)=\beta_{0}+\beta_{1} e d u c+\beta_{2} s i b s+u$$Suppose that we want to use brthord as an IV for educ, assuming that sibs is exogenous. Thereduced form for educ is$$e d u c=\pi_{0}+\pi_{1} \operatorname{sibs}+\pi_{2} \text { brthord }+v$$State and test the identification assumption.(v) Estimate the equation from part (iv) using brthord as an IV for educ (and sibs as its own IV).Comment on the standard errors for $\hat{\boldsymbol{\beta}}_{\text {educ}}$ and $\hat{\boldsymbol{\beta}}_{\text {sibs}}$(vi) Using the fitted values from part (iv), $\overline{e d u c}$ compute the correlation between $\overline{e d u c}$ and sibs. Use this result to explain your findings from part (v).

(i) The coefficient of $\operatorname{sibs}$ is $-0.028$ It is interpreted as an increase of an additional sibling reduces the monthly wage by 2.78$\%$. The variable sibs could be correlated with the error term of this model as the error may account for omitted variable such as educ with which sibs is stated to have certain degree of correlation. (ii) The coefficient of brthord is-0.283. The sign of the coefficient of brthord is negative indicating a negative relationship between educand brthord. The p-value of the coefficient of brthord is 0.00 indicating that there is statistically significant negative correlation between brthord and educ (iii) See video (iv) since the coefficient of brthord is $-0.152$ with the p-value 0.01, indicating that $\pi_{2} \neq 0$ and the identification assumption is evident (v) The standard errors for $\hat{\beta}_{educ}$ is 0.075 and that for $\hat{\beta}_{sibs}$ is 0.0174 (vi) See video

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Chapter 15

Instrumental Variables Estimation and Two Stage Least Squares

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part one. This is the regression result of log a wage on siblings. This is a reduced form, simple regression equation. It shows that controlling for no other factors, one more sibling in the family is associated with multi celery. That is about 2.8% lower. Let me write that down. Oh, yeah, The T statistic Armed siblings is about minus 4.7, meaning this variable is highly significant. Siblings can be correlated with many things that should have an effect on wage, including years of education. That's for sure. Hard to it's possible that older Children are given priority for higher education. Families may hit budget constraint and may not be able to afford as much education for Children born later. This is the regression result of education on birth order. This equation predicts everyone unit increase in birth order reduces predicted education by about 0.28 years. Our three when we use birth order as an instrument for education in the simple wage equation, this is what we get. This estimate is much higher than the old L s, which is point oh six and even higher than the estimate when siblings is used as an instrument for education, which is 0.1 to you too hard, for we have their reduced form equation. In order for data sub j to be identified, we need hi to you not equal zero We take the null hypothesis to be all right by two equals zero and we look to rejection of there's no hypothesis the regression of education on siblings and birth order yields Yeah, hi to hat yeah equals minus 0.153 with a standard error of point Oh 57 And that gives a T statistic of minus 2.7, which strongly rejects the null hypothesis. Mhm. This is the identification assumption appears to hold Part five. The equation estimated by instrumental variable is lage wage equals to have 4.94 plus 0.14 education plus point oh two siblings. The standard error on the estimate on education is much larger than we obtain In part three. The 95% confidence interval for beta education is roughly minus 0.1 two 0.28 which is very wide and includes the value zero. The standard error of the estimate on sibling is very large relative to the coefficient. Estimates making siblings highly insignificant. Uh huh. Yeah, yeah, yeah, right. Art six. Education had represents the first stage fitted values. The correlation between that and siblings is about minus 0.93 which is a very strong negative correlation. This means, for the purposes of using instrumental variable Monte culinary T is a serious problem. Yeah, we can still estimate the effect of education, but we would not get to estimate with much precision. Mhm, Yeah.

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