Econ 500: Practice of Econometrics

Return a printout with your answers and an appendix with your do file

Problem

Download the datafile “fertil2.dta” from the Wooldridge directory in the Datasets section of Blackboard. This is a data set used for a few examples in two econometrics books by Jeffrey Wooldridge: Econometric Analysis of Cross-Section and Panel Data, (2 editions: 2002, 2010) and Introductory Econometrics: A Modern Approach (multiple editions). According to the Data Set Handbook of the latter, “These data were obtained by James Heakins, a former MSU undergraduate, for a term project. They come from Botswana’s 1988 Demographic and Health Survey.”

If you do describe _all, you see which variables are in the data set, and the variable labels are clear. This is a data set of women of childbearing age (you can confirm this by looking at the distributionof age in the data). Wooldridge is interested in the effect of education on fertility, a topic that is of great interest in the study of development. We will follow him and look at the effect of having at least seven years of schooling, as measured in the variable educ7, on the number of children a woman has, as measured in the variable children, so “education” and “fertility” are narrowly defined in this way.

(a) Suppose the treatment is “as good as” randomly assigned. What is then your estimate of the average treatment effect? Comment on whether it is large.

(b) Give an argument why the treatment may not be “as good as” randomly assigned. Study whether there is evidence for this by checking for balance in the variables age, evermarr, urban, electric, and catholic.

(c) One way to reduce bias in the estimated treatment effect is to control for potential confounders. Estimate the average treatment effect while controlling for age, agesq, evermarr, urban, electric, and the three religion dummies. Is your estimate very different from the one in 3(a)? Briefly comment on whether including these controls is a good or a bad thing. (Hint: Look at Lecture 2, Slide 18, and Lecture 8, Slide 6, for ways you may think about this.)

(d) Another way to deal with endogeneity is to use instrumental variables. Wooldridge suggests using the frsthalf variable as an instrument. This follows in a tradition (started by Angrist and Krueger) in which a relationship is shown between the time of year persons are born and their ultimate educational attainment; this having to do with timing of school years and how compulsory schooling laws operate.

For 3(d)–3(h), we look at treatment effects without using the controls. Run the firststage regression. Is the treatment related to the instrument?

(e) Estimate the ITT. What does it measure? Would this be useful information for policy makers? Comment on its statistical significance and the magnitude of the ITT.

(f) Compute the LATE. What does this estimate here? Comment on whether you think this is an interesting parameter in this context. What do you conclude about the size and significance of the estimate?

(g) Is the instrument weak or strong? (Hint: Use the F-test rule of thumb.)

(h) Test for endogeneity of the treatment variable. What is the conclusion from this test? How does this conclusion compare to the conclusion from 3(b)?

(i) Repeat 3(d)–3(h) with the controls from 3(c) added. Discuss whether any conclusions are different now.

(j) So far, the instrument we have used was a dummy for being born in the first half of the year. However, we know the month in which the woman was born, so we can expand on this by using a full set of month dummies as instruments instead of frsthalf. Estimate the modelwith the month dummies as instruments. Are these instruments weak or strong? Perform the overidentification test. What are your conclusions about the instruments and the treatment effect of interest?

Subject | Mathematics |

Due By (Pacific Time) | 10/28/2015 01:09 am |

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