Pages
Note: You need SAS/STAT® software to open the supporting data files.
PROBLEM SETS | SUPPORTING DATA FILES |
---|---|
Review problem set (PDF) | |
Problem set 1 (PDF) | |
Problem set 2 (PDF) |
March 1992 CPS (SAS7BDAT) Wine prices (SAS7BDAT) |
Problem set 3 (PDF) | |
Problem set 4 (PDF) |
GPA (SAS7BDAT) NBA salaries (SAS7BDAT) Part B (SAS7BDAT) |
Problem set 5 (PDF) |
October 1984 CPS extract (SAS7BDAT - 18.0 MB) October 1989 CPS extract (SAS7BDAT - 23.0 MB) For C8.5 (SAS7BDAT) For C10.5 (SAS7BDAT) For C12.10 (SAS7BDAT) |
Problem set 6 (PDF) |
Quarter of birth data (SAS7BDAT - 12.0 MB) Fish data (SAS7BDAT) |
Texts
Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 3rd ed. Mason, OH: Thomson/South-Western, 2006. ISBN: 9780324289787.
Goldberger, Arthur S. A Course in Econometrics. Cambridge, MA: Harvard University Press, 1991. ISBN: 9780674175440.
DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2001. ISBN: 9780201524888.
Wooldridge is the main text. The material in Goldberger is more advanced and optional. DeGroot and Schervish is a recommended text for statistics review. The lecture notes are unavailable.
The course consists of parts 1 (A, B, and C) and 2 (D, E, F, and G).
TOPIC # | TOPICS | Readings |
---|---|---|
A. Review of probability and statistics | ||
1 | Probability and distribution |
Lecture note 1: Probability and distribution Lecture note 2: Expectation and moments Wooldridge. Appendix B. Goldberger. Chapters 1-7. DeGroot. Chapters 1-5. Burtless, Gary. “Are Targeted Wage Subsidies Harmful? Evidence from a Wage Voucher Experiment.” Industrial and Labor Relations Review 39 (October 1985): 105-111. |
2 | Expectation and moments | |
B. Review of statistical inference | ||
3 | Sampling distributions and inference |
Lecture note 3: Sampling distributions and inference Lecture note 4: Approximate [asymptotic] distribution of the sample mean Lecture note 5: Confidence intervals Wooldridge. Appendix C. Goldberger. Chapters 8-10. DeGroot. Chapters 6-8. Woodbury, S. A., and R. Spiegelman. “Bonuses to Workers and Employers to Reduce Unemployment: Randomized Trials in Illinois.” American Economic Review 77, no. 4 (September 1987): 513-530. |
4 | The Central Limit theorem (Asymptotic distribution of the sample mean) | |
5 | Confidence intervals | |
C. Regression basics | ||
6 | Conditional expectation functions, bivariate regression |
Lecture note 6: Bivariate regression Lecture notes 7 and 8: Sampling distribution of regression estimates Lecture note 9: Residuals, fitted values, and goodness of fit Wooldridge. Chapters 1-5. Goldberger. Chapters 13-16. |
7 | Sampling distribution of regression estimates; Gauss-Markov theorem | |
8 | How Classical assumptions are used; asymptotic distribution of the sample slope | |
9 | Residuals, fitted values, and goodness of fit | |
D. Multivariate regression | ||
10 | Regression, causality, and control; anatomy of multivariate regression coefficients |
Lecture note 10: Introduction to multivariate regression Lecture note 11: Multivariate regression (cont.) Lecture note 12a: Using multivariate regression Lecture note 12b: Regression analysis of “Natural Experiments” - the minimum wage controversy Wooldridge. Chapters 6-7 and 19. Goldberger. Chapters 17-24. Krueger, A. “How Computers Have Changed the Wage Structure: Evidence from Micro Data.” Quarterly Journal of Economics 108, no. 1 (February 1993): 33-60. DiNardo, J., and J. S. Pischke. “The Returns to Computer Use Revisited: Have Pencils Changed the Wage Structure Too?” The Quarterly Journal of Economics 112, no. 1 (February 1997): 291-303. Krueger, A., and S. B. Dale. “Estimating the Payoff to Attending a More Selective College: An Application of Selection on Observables and Unobservables.” The Quarterly Journal of Economics 117 (November 2002): 1491-1529. Card, David E., and Alan B. Krueger. Myth and Measurement: The New Economics of the Minimum Wage. Princeton, NJ: Princeton University Press, 1995, chapters 1 to 4. ISBN: 9780691048239. |
11 | Omitted variables formula, short vs. long regressions | |
12a | Dummy variables and interactions; testing linear restrictions using F-tests | |
12b | Regression analysis of natural experiments, differences-in-differences | |
E. Inference problems - heteroscedasticity and autocorrelation | ||
13a | Heteroscedasticity, consequences of; weighted least squares; the linear probability model |
Lecture note 13a: Heteroscedasticity, linear probability models Lecture note 13b: Serial correlation Wooldridge. Chapters 8 and 12. Goldberger. Chapters 27-28. Freeman, R., and A. Castillo-Freeman. “When the Minimum Wage Really Bites: The Effect of the US-Level Minimum on Puerto Rico.” In Immigration and the Work Force: Economic Consequences for the United States and Source Areas. Edited by G. Borjas and R. Freeman. Chicago, IL: University of Chicago Press, 1992. ISBN: 9780226066332. Graddy, K. “Testing for Imperfect Competition at the Fulton Fish Market.” RAND Journal of Economics 26, no. 1 (Spring 1995): 75-92. |
13b | Serial correlation in time series, consequences of; quasi-differencing; common-factor restriction; Durbin-Watson test for serial correlation | |
F. Instrumental variables, simultaneous equations models, measurement error | ||
14a | Using IV to solve omitted-variables problems |
Lecture note 14: Instrumental variables for omitted-variables problems Wooldridge. Chapter 15. Goldberger. Chapter 31. Angrist, J. “Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records.” American Economic Review 80, no. 3 (June 1990): 313-336. Angrist, J., and A. Krueger. “Does Compulsory School Attendance Affect Schooling and Earnings?” Quarterly Journal of Economics 106, no. 4 (November 1991): 979-1014. Angrist, J., and W. E. Evans. “Children and Their Parents’ Labor Supply: Evidence from Exogenous Variation in Family Size.” American Economic Review 88 (June 1998): 450-477. Lecture note 14b: IV and measurement error Ashenfelter, O., and A. Krueger. “Estimates of the Economic Returns to Schooling from a New Sample of Twins.” American Economic Review 84, no. 5 (December 1994): 1157-1174. Lecture note 14c: Regression-discontinuity Angrist, J., and V. Lavy. “Using Maimonides Rule to estimate the Effects of Class Size on Scholastic Achievement.” Quarterly Journal of Economics 114, no. 2 (May 1999): 533-575. |
14b | Measurement error (Time-permitting) | |
14c | Regression-discontinuity designs (Time-permitting) | |
G. Simultaneous equation models | ||
15 |
Simultaneous equations models I
|
Lecture note 15: Simultaneous equations models - motivation and identification Lecture note 16: Simultaneous equations models - estimation Wooldridge. Chapter 16. Goldberger. Chapters 32-34. Angrist, J., G. Imbens, and K. Graddy. “The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish.” Review of Economic Studies 67, no. 3 (July 2000): 499-527. |
16 |
Simultaneous equations models II
|
These recitation notes are courtesy of Jim Berry. Used with permission.
More on Differences-in-Differences (PDF)
More on FGLS and How to Test for Heteroskedasticity (PDF)
Serial Correlation (PDF)
Implementation of IV and Two-stage Least Squares (PDF)
Additional Notes on 2SLS and Simultaneous Equations (PDF)
Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Recitations: 1 session / week, 1 hour / session
Description
This course covers the statistical tools needed to understand empirical economic research and to plan and execute independent research projects. Topics include statistical inference, regression, generalized least squares, instrumental variables, simultaneous equations models, and evaluation of government policies and programs.
Prerequisites
The prerequisite courses include Introduction to Statistical Methods in Economics (14.30) or equivalent. Students should be familiar with basic concepts in probability theory and statistical inference. The course includes a brief statistics review.
Course Requirements
Each week there are two lectures and a weekly recitation.
In addition to the readings, there are 6 graded problem sets and ungraded review problem sets at the beginning and end of the course. The problem sets have both analytical and computer-exercise components. The statistical analysis will be done using Stata or SAS on PCs or MIT workstations. Help for new Stata users will be given in recitation.
Texts
Wooldridge, Jeffrey M. Introductory Econometrics: A Modern Approach. 3rd ed. Mason, OH: Thomson/South-Western, 2006. ISBN: 9780324289787.
Goldberger, Arthur S. A Course in Econometrics. Cambridge, MA: Harvard University Press, 1991. ISBN: 9780674175440.
DeGroot, Morris H., and Mark J. Schervish. Probability and Statistics. 3rd ed. Boston, MA: Addison-Wesley, 2001. ISBN: 9780201524888.
Wooldridge is the main text. The material in Goldberger is more advanced and optional. DeGroot and Schervish is a recommended text for statistics review. Each unit also has readings from published journal articles.
Grading
ACTIVITIES | PERCENTAGES |
---|---|
Problem sets (5% each) | 30% |
Midterm exam | 30% |
Final exam | 40% |
Each review problem set is worth 1 bonus percentage point.
Graded problem sets are mandatory and solutions should be submitted on time to receive credit. Stata or SAS logs should be submitted with solution sets. A grade of 50% or better on at least 5 problem sets is required in order to be eligible to take the final. Consult with classmates on problem sets if you get stuck, but written solution sets should be your own work.
Course Outline
Part I
- A. Review of probability and statistics
- 1. Probability and distribution
- 2. Expectation and moments
- B. Review of statistical inference
- 3. Sampling distributions and inference
- 4. The Central Limit theorem (Asymptotic distribution of the sample mean)
- 5. Confidence intervals
- C. Regression basics
- 6. Conditional expectation functions, bivariate regression
- 7. Sampling distribution of regression estimates; Gauss-Markov theorem
- 8. How classical assumptions are used; asymptotic distribution of the sample slope
- 9. Residuals, fitted values, and goodness of fit
Part II
- D. Multivariate regression
- 10. Regression, causality, and control; anatomy of multivariate regression coefficients
- 11. Omitted variables formula, short vs. long regressions
- 12a. Dummy variables and interactions; testing linear restrictions using F-tests
- 12b. Regression analysis of natural experiments, differences-in-differences
- E. Inference problems - heteroscedasticity and autocorrelation
- 13a. Heteroscedasticity, consequences of; weighted least squares; the linear probability model
- 13b. Serial correlation in time series, consequences of; quasi-differencing; common-factor restriction; Durbin-Watson test for serial correlation
- F. Instrumental variables, simultaneous equations models, measurement error
- 14a. Using IV to solve omitted-variables problems
- 14b. Measurement error (Time-permitting)
- 14c. Regression-discontinuity designs (Time-permitting)
- G. Simultaneous equation models
- 15. Simultaneous equations models I
- a. The use of structural models
- b. Simultaneous equations bias
- c. The identification problem
- d. The structure and the reduced form
- e. Indirect least squares
- 16. Simultaneous equations models II
- a. IV for the SEM
- b. Two-stage least squares
- c. Sampling variance of 2SLS estimates
- 15. Simultaneous equations models I