Homework 2 Introduction to Metrics,Fall 2021 Zhaopeng Qu 11/06/2021 ?? 1 Learning Objectives 2 2 Due Date and Formats 2 3 Theory and Application Exercises 4 3.1 Exercises in SW textbooks(Third Edition,English version)(30 points) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.2 Practical Exercise(I): Instrumental Variable and Heckman Selection Model(50 points) . . . . . . . . . . . . . . . . . . . . . 4 3.3 Practical Exercise(II): Replicates results using Chinese data.(20 points) . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 1 LEARNING OBJECTIVES 2 1 Learning Objectives Better understanding of the concept of Internal Validity, IV and Sample Selection methods 2 Due Date and Formats Due to Nov.21 24:00. Late sending will lower your scores by a standard 10% per hour deduction Required forms. 1. The forms of report can be either MS Word or PDF,other forms will not accepted. 2. All files have to be generated by either Rmarkdown in RStudio or Stata Markdown in Stata. You must upload your homework on both two platforms.(????? ???????,???????????????) 1. Upload your report(only for PDF or docx files) to the mita system. ?? mita ????????? ????:??? 2. Send a email with an attachment including all files(may be compressed in .zip or .RAR format) of your homework to: intrometrics@gmail.com as follows Email Subject: ?? _ ?? _ ?? _HW1 Rename your file with ID_Name_Major_HW1 (eg. 151090001_ ??? _ ?? _HW1.zip) 2 DUE DATE AND FORMATS 3 Wrong filename or no subject emails may not be archived and scored it properly. All files may include Formal report in Word or PDF, Rmarkdown(.Rmd for R users) or stmd(.stmd for Stata users) to generate the final report, as well as Rscript(.R for R users) or dofile(.do for Stata users) to clean the survey data for the last question. Language English or Chinese(Writing in English will receive a small bonus) Important Rule: Plagiarism Will Be NOT Tolerant!. If TAs have enough evidence to make me believe that your homework is very very similar with another finished by one of your classmates, then both of you will score ZERO! 3 THEORY AND APPLICATION EXERCISES 4 3 Theory and Application Exercises 3.1 Exercises in SW textbooks(Third Edition,English version)(30 points) 8.4(pp341) 9.10(pp385) 11.1-11.7(pp450) 12.9(pp500) 13.9(pp551) Please try to prove the following formula of IV estimator when there is population heterogeneity in the treatment effect and in the influence of the instrument on the receipt of treatment. ??^ 2?????? ?? -? ??????(???? ) ??????(????) = ??(??1????1??) ??(??1??) 3.2 Practical Exercise(I): Instrumental Variable and Heckman Selection Model(50 points) Research Question: How education affect earnings for married women? Specifically, how much does a womans earnings increase when she obtains an additional schooling year? The file mroz.dta (in Stata format) from T.A. Mroz (1987), The Sensitivity of an Empirical Model of Married Womens Hours of Work to Economic and Statistical Assumptions, Econometrica 55, 765-799. 3 THEORY AND APPLICATION EXERCISES 5 1. OLS for return to education for working women Suppose we estimate the Mincer wage equation for women as follows: ?????????????? = ??0 + ??1 ?????????? + ??2 ???????????? + ??3 ??????????2 ?? + ???? 1) Which parameter is the most of interest for our question? explain the economic meaning of it. 2) Please use the concept of internal validity to assessing our OLS estimation in the case(Hint: list potential threatens to the validity and explain them specifically) 2. Instrumental Variable to return to education for working women To eliminate some potential biases, we use two variables fatheduc and motheduc, which are fathers and mothers education as instruments for the own education. 1) Using the content you learned in the class to assessing whether fatheduc and mothereduc can be valid instruments for the estimation of return to education for working women or not. Which one (or both or neither)should be chosen as our instrument(s)? 2) Report the all regressions you run for your assessment in tables(one or two), which should include all results of (1) the Simple OLS regression (2) the OLS with covariates (3) the first stage regression of 2SLS (4) the reduced form regression 3 THEORY AND APPLICATION EXERCISES 6 (5) the second regression of 2SLS (6) Addtional regressions may be useful you think Note that standard errors should be shown in parenthesis. 3. Heckman Selection Model to return to education for working women To eliminate the potential bias, we use Heckman selection model with 2 steps methods to estimate the regression again. 1) Explain why we may need heckman selection model to estimate the regression? Why instrumental variable method may not eliminate the bias from sample selection if it exists 2) Estimate the model in two individual steps without exclusion restrictions, by predicting the inverse mills ratios and including this as a control variable in the wage equation. 3) Estimate the model in two individual steps with exclusion restrictions which includes the variables nwifeinc, age, kidslt6, and kidsge6 in the selection model. 4) Reestimate two models using Stata command(heckman) or R Package(sampleSelection or others) to see if there a difference between the result here and above. 5) Can you tell if there is evidence of sample selection base on the last estimation above(thus using command to estimate it with exclusion restrictions) 4. Bonus Question(10 points) 3 THEORY AND APPLICATION EXERCISES 7 How to estimate the return to education for working women taking both endogenous variable of education and sample selection? (Hint: which means we have to combine IV and sample selection methods to estimate the regression) 3.3 Practical Exercise(II): Replicates results using Chinese data.(20 points) Research Question: The returns to schooling for women in the Chinese labor market In this exercise, please try to use the data you had cleaned by yourself in HW1 to replicate the main results in the Exercise(I) to estimate the returns to schooling for Chinese women. (Hint: you might have to choose some different covariates, instrumental variables and variables in exclusion restrictions from mroz.dta) Reference: ???????,????????????,??? ?,2009 ?? 7 ??

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hw2-2021-2-.pdf