5th Summer School in Advanced Economics

July 3-7, 2023

Causal Inference, Potential Outcomes, and Modern Difference-in-Differences

Distinguished Guest Professor:
Jeffrey M. Wooldridge (Michigan State University)

Description: This course covers causal inference for cross-section and panel data using the potential outcomes framework. We will cover identification of key treatment effects assuming unconfoundedness, and then study various estimators: regression adjustment, inverse probability weighting, combinations thereof (to achieve double robustness), and matching methods. More recent methods using covariate balancing to obtain the propensity score also will be covered. We will then study identification of the local average treatment effect (LATE) and the local average treatment effect on the treated (LATT) and cover recent doubly robust methods for estimating these parameters when one has covariates in the instrument propensity score. Control function methods can be used to allow heterogeneity when functional forms are imposed on the conditional mean functions.

We then turn to difference-in-differences methods for panel data, starting with a review of the two-period analysis. Regression-based methods, propensity score methods, and doubly robust estimators will be covered. With common timing but multiple control and treatment periods, different effects can be estimated using regression methods or combining regression with inverse probability weighting. We will also discuss how to test and correct for the parallel trends assumption.

For the general staggered intervention case, we will discuss how to allow full heterogeneity in treatment effects by treatment cohort and calendar time. Various estimators turn out to be equivalent, including an extended version of two-way fixed effects. Covariates are easily incorporated. Rolling methods and long differencing, where one can apply standard treatment effects, will also be covered. Testing and adjusting for violation of parallel trends in the staggered case will be covered. I will also present my recent work on nonlinear difference-in-differences for the general staggered case, with focus on binary, fractional, and nonnegative responses (including count variables and corner solution outcomes).

Additional special topics include allowing for exit from treatment, clustering standard errors, and inference when there are few control or treated groups. If time permits, I will show how the linear and nonlinear methods apply to repeated cross sections.

Participants should have good working knowledge of ordinary least squares estimation, fixed effects estimation, and basic nonlinear models such as logit, probit, and exponential conditional means. Sufficient background is provided by my introductory econometrics book, Introductory Econometrics: A Modern Approach, 7e, Cengage, 2020. My book Econometric Analysis of Cross Section and Panel Data, 2e, MIT Press, 2010, covers the background material at a higher level.

For some of the material I will rely on my 2010 MIT Press book and my recent working papers, “Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators” and “Simple Approaches to Nonlinear Difference-in-Differences with Panel Data.” I will make the course material, including slides and Stata data sets and code, available on a shared Dropbox prior to the course. In lecture, I will illustrate the methods using Stata, mentioning packages available in other platforms.

Course Timetable

Monday, July 3, 2023
09:00-10:30 Lecture 1
10:30-11:00 Break
11:00-12:30 Lecture 2
12:30-14:00 Lunch
14:00-15:30 Lab Session 1

Tuesday, July 4, 2023
09:00-10:30 Lecture 3
10:30-11:00 Break
11:00-12:30 Lecture 4
12:30-14:00 Lunch
14:00-15:30 Lab Session 2

Wednesday, July 5, 2023
09:00-10:30 Lecture 5
10:30-11:00 Break
11:00-12:30 Lecture 6
12:30-14:00 Lunch
14:00-15:30 Lab Session 3

Thursday, July 6, 2023
09:00-10:30 Lecture 7
10:30-11:00 Break
11:00-12:30 Lecture 8
12:30-14:00 Lunch
14:00-15:30 Lab Session 4

Friday, July 7, 2023
09:00-10:30 Lecture 9
10:30-11:00 Break
11:00-12:30 Lecture 10
12:30-14:00 Lunch
14:00-15:30 Lab Session 5

 

Daily Content

Day 1
Potential outcomes and parameters of interest. Randomization. Unconfoundedness and overlap. Identification. Regression adjustment, inverse probability weighting, normalized weights. Covariate balancing propensity score estimation. Matching and doubly robust estimators. Improved efficiency under randomized controlled trials. Multiple treatments.

Day 2
Potential treatment status. Constant effect model. Compliers and defiers. One-sided non-compliance. Identification of LATE and LATT. Including covariates for LATE and LATT estimation. Control function methods. Regression discontinuity (if time permits).

Day 3
Two-period difference-in-differences; no anticipation and parallel trends; controlling for covariates via regression adjustment and propensity score methods. General common timing case and heterogeneous effects.

Day 4
Staggered interventions. Parameters of interest. Parallel trends. Shortcomings of the constant effect model. Regression-based methods. Two-period difference-in-differences; no anticipation and parallel trends; controlling for covariates via regression adjustment and propensity score methods. Repeated cross sections.

Day 5
Parallel trends in nonlinear models. Nonlinear DiD with two periods. Staggered interventions. Adding covariates. Binary, fractional, and nonnegative responses (count, corner). Imputation estimates. Pooled quasi-maximum likelihood estimation. Estimation with a canonical link function. Repeated cross sections.

Partial Reading List

Day 1

Angrist, J.D. and J.-S. Pischke (2009), Mostly Harmless Econometrics. Princeton University Press. Chapters 1 through 3.

Cunningham, S. (2021), Causal Inference: The Mixtape. Yale University Press. Chapter 4.

Imai, K. and M. Ratkovic (2014), “Covariate Balancing Propensity Score,” Journal of the Royal Statistical Society: Series B 76, 243-263.

Imbens, G.W. and D.B. Rubin (2015), Causal Inference for Statistics, Social, and Behavioral Sciences. Cambridge University Press. Chapters 1-7, 12-13.

Negi, A. and J.M. Wooldridge (2021), “Revisiting Regression Adjustment in Experiments with Heterogeneous Treatment Effects,” Econometric Reviews 40, 504-534.

Słoczyński, T. (2022), “Interpreting Estimands when Treatment Effects are Heterogeneous: Smaller Groups Get Larger Weights,” Review of Economics and Statistics 104, 501-509.

Wooldridge, J.M. (2010), Econometric Analysis of Cross Section and Panel Data, MIT Press.Chapter 21.

Day 2

Abadie, A. (2003), “Semiparametric Instrumental Variable Estimation of Treatment
Response Models,” Journal of Econometrics 113 231-263.

Angrist and Pischke (2009), Chapter 4.

Cunningham (2021), Chapter 7.

Imbens, G.W. and J.D. Angrist (1994), “Identification and Estimation of Local Average Treatment Effects,” Econometrica 62, 467-475.

Imbens and Rubin (2015), Chapters 23-24.

Frölich, M. (2007), “Nonparametric IV Estimation of Local Average Treatment Effects with Covariates,” Journal of Econometrics 139, 35-75.

Heiler, P. (2022), “Efficient Covariate Balancing for the Local Average Treatment Effect,” forthcoming, Journal of Business & Economic Statistics.

Słoczyński, T., S.D. Uysal, and J.M. Wooldridge (2022), “Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment.”

Day 3

Abadie, A. (2005), “Semiparametric Difference-in-Differences Estimators,” Review of Economic Studies 72, 1-19.

Angrist and Pischke (2009), Chapter 5.

Cunningham (2021), Chapter 9.

Heckman, J.J., H. Ichimura, and P.E. Todd (1997), “Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme,” Review of Economic Studies 64, 605-654.

Sant'Anna, P.H.C. and J. Zhao (2020), “Doubly Robust Difference-in-Differences Estimators,” Journal of Econometrics 219, 101-122.

Wooldridge, J.M. (2021), “Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators,” unpublished. https://www.dropbox.com/sh/zj91darudf2fica/AADj_jaf5ZuS1muobgsnxS6Za?dl=0

Day 4

Borusyak, K., X. Jaravel, and J. Spiess (2021), “Revisiting Event Study Designs: Robust and Efficient Estimation,” working paper, University College London.

Callaway, B., and P.H.C. Sant'Anna (2021), “Difference-in-Differences with Multiple Time Periods,” Journal of Econometrics 225, 200-230.

de Chaisemartin, C., and X. D'Haultfœuille (2020), “Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects,” American Economic Review 110, 2964-2996.

Goodman-Bacon, A. (2021), “Difference-in-Differences with Variation in Treatment Timing,” Journal of Econometrics 225, 254-277.

Lee, S.J., and J.M. Wooldridge (2022), “A Simple Transformation Approach to Difference-in-Differences Estimation for Panel Data,” working paper, Michigan State University Department of Economics.

Day 5

Athey, S. and G.W. Imbens (2006), “Identification and Inference in Nonlinear Difference-in-Differences Models,” Econometrica 74, 431-497.

Wooldridge, J.M. (2022), “Simple Approaches to Nonlinear Difference-in-Differences with Panel Data,” unpublished. https://www.dropbox.com/sh/zj91darudf2fica/AADj_jaf5ZuS1muobgsnxS6Za?dl=0