Q1. As you may recall from class, Dehejia and Wahba showed that matching methods are able to estimate treatment effects close to those obtained from experimental data. They used a subset of the experimental data set used by Lalondet. Subjects in the experiment were randomly assigned to either a Treatment group, and received on-the-job training, or to a Control group, in which case they were untreated. In this problem you will use a placebo data set. The data set "Placebo.dta" was constructed in the following way. As the "Control" group, we use all observations in PSID. As the "Treatment" group, we use all the observations in the Dehejia and Wahba who were in the Control group - you can examine how the data set was put together in the do file "Placebo.do". Very importantly, in this data set neither the observations in "Control" (those in PSID), nor the observations in "Treatment" (those who were in the Control group originally) were actually treated - no observations in the data set have received on-the-job treatment. Thus, the true treatment effect (the effect of being called "Treated" but not actually receiving on-the-job training) is zero.

(a) Use the command teffects nnmatch to match on the following covariates: black, hispanic, and married. Estimate the treatment on the treated effect. Is this effect close to the true effect? Is it statistically significant?

(b) Compare the matching estimate to the estimate from a regression using the same covariates as control variables. What accounts for this discrepancy?

(c) Now match on all the covariates in the sample. Estimate the treatment on the treated effect. Is this effect close to the true effect? Is it statistically significant?

(d) Now match on all the covariates in the sample using a propensity score. Are all the covariates balanced? Does it matter in this context if the covariates are balanced? Why or why not?

(e) Are the propensity scores balanced between the Treatment and the Control group? Use an overlapping histogram or two side-by-side histograms of the propensity scores in each group to test the balance.

(f) Calculate the treatment on the treated effect by matching on the propensity score using all the covariates. Is this effect close to the true effect? Is it statistically significant?

(g) Write down a brief conclusion. Do matching methods seem suitable to estimate treatment on the treated effects?

Q2. In this problem you will use the data set "HealthStatus.dta" which surveys people on their health status (coded 0 for poor, 1 for fair, 2 for good, and 3 for excellent). The survey also asks a number of demographic and socio-economic variables. We are interested in the effect these variables have on one's health status.

(a) Estimate a model that would allow you to predict the health status of a black 30 year old woman, using a version of the logistic model.

(b) Using the output of the previous model, calculate by hand the predicted probability that a black 30 year old woman is in good health. Show your work. You may use any STATA commands such as display, except the command that directly calculates the predicted probability.

(c) Calculate by hand the marginal effect of age on the probability of being in good health for a black 30 year old woman. Show your work. You may use any STATA commands such as display, except the command that directly calculates the marginal effect.

(d) Add to the model above the log of one's income, the number of people in the family, and one's schooling. Test by hand whether these variables, jointly, belong to the model. You may use any STATA commands such as display, except the command which automatically tests the hypothesis.

(e) Do people get better over time? Modify the model in the previous part to answer this question. What is your conclusion?

(f) Does the variable you added to the model last belong to the model? Use a STATA command that answers this question by likelihood ratio test.

Q3. In this question you will have to use the data set "GDP.dta", which contains a time series of US GDP between 1947 and 2016.

(a) Estimate a linear trend of GDP over time. Interpret the slope coefficient of this regression.

(b) Examine the residual plot. What does this tell you?

(c) Are the residuals auto-correlated? Use two tests for this question. Use a partial auto-correlations graph to determine how many lags are statistically significant.

(d) For the rest of the questions we will examine the log of the GDP. Run a regression of log of GDP on year. Interpret the slope coefficient of this regression.

(e) Examine the residual plot. What does this tell you?

(f) Are the residuals auto-correlated? Use two tests for this question. Use a auto-correlations graphs to determine how many lags seem to be significant.

(g) Are the residuals homoskedastic? Use two tests for this question.

(h) Run a feasible weighted least squares model. What do you expect to happen to the standard errors of your estimates? Does that happen in this case?

Q4. You have been asked by a consulting firm to evaluate the effect of individual student tutoring (conducted after school) during middle school (grades 6 to 8) on subsequent high school academic performance in grades 9 to 12. In your data set you have the GPA in grades 9-12 as the outcome variable and total hours of tutoring during the 6th through 8th grades as the treatment variable.

Your data set also contains the following variables:

a) GPA 6th to 8th grade

b) IQ in 10th grade

c) Levels of class taken (basic, average, or advanced placement) in 9th to 12th grade (1.5 points, 60 words maximum)

d) Socio-economic status of parents

e) Extracurricular activities in 6th to 12th grade

Consider the above candidate control variables a) through e) individually (as opposed to using multiple control variables at the same time). For each variable, discuss whether you would, or would not add it to a short regression of the response variable on the explanatory variable of interest.

Attachment:- Assignment Files.zip