Session summary
Researching on Weak IVs
1 Session Introduction
- See slide with browser1: slide-weak-instruments.html.
This Session will focus on the weak Instrumental Variables (IVs).
We will learn some important papers and resources about the weak IVs.
Also, we will use the data and code to replicate the example in theses paper.
2 Useful Learning Resources
Causal Inference: The Mixtape online free book and github repo here. Chapter 7 Instrumental Variables. notes: Throughly explained this example, but not supply the data and code.
(Cunningham 2021) Cunningham, S. Causal Inference: The Mixtape[M]. Yale University Press, 2021.
Useful slides for the textbook companion by Prof Scott Cunningham: chapter 7 Instrumental Variables. see here.
Dive into Advanced IV topic with Prof Peter Hull. see here. notes: slides and R code.
Econometric Replication Paper Project of “Does Compulsory School Attendance Affect Schooling and Earning?” github repo. notes: Stata code and Latex pdf files; also all tables and figures in the paper are provided.
R Code for Mastering ’Metrics online free book. Chapter 9: Quarter of Birth and Returns to Schooling. notes: useful Figures with R code.
- (Angrist and Pischke 2015) Angrist, J. D., and J. S. Pischke. Mastering “Metrics”: The Path from Cause to Effect[M]. Princeton, Oxford: Princeton University Press, 2015.
chapter 13 Instrumental Variables Regression. by (Muller, Winship, and Morgan 2014) Muller, C., C. Winship, and S. Morgan. Instrumental Variables Regression[A]. The SAGE Handbook of Regression Analysis and Causal Inference[C]. SAGE Publications Ltd, 2014. notes: Another useful example which may supply R code.
- See the book of (Best and Wolf 2015). Best, H., and C. Wolf. The SAGE Handbook of Regression Analysis and Causal Inference[M]. Los Angeles: Sage, 2015. we may find more resources in this book’s website with permission by subscription.
3 Replication Articles
3.1 (Angrist and Krueger 1991) Does Compulsory School Attendance Affect Schooling and Earnings?
3.1.1 Class Reading Material
See html page with browser: click here
See or download pdf file: click here
Source (AK1991): Angrist, J. D., and A. B. Krueger. Does Compulsory School Attendance Affect Schooling and Earnings?[J]. The Quarterly Journal of Economics, 1991, 106(4):979-1014.
Abstract: We establish that season of birth is related to educational attainment because of school start age policy and compulsory school attendance laws. Individuals born in the beginning of the year start school at an older age, and can therefore drop out after completing less schooling than individuals born near the end of the year. Roughly 25 percent of potential dropouts remain in school because of compulsory schooling laws. We estimate the impact of compulsory schooling on earnings by using quarter of birth as an instrument for education. The instrumental variables estimate of the return to education is close to the ordinary least squares estimate, suggesting that there is little bias in conventional estimates.
3.1.2 Replication Code and Data
We will use the data and code to replicate the example in the paper (Angrist and Krueger 1991).
Statacode and data are provided as following2:
3 Based on the github repo.
- Data set:
ak91.dta - Stata code:
Table_I.do - Stata code:
Table_II.do - Stata code:
Table_III.do - Stata code:
Table_IV.do - Stata code:
Table_V.do - Stata code:
Table_VI.do - Stata code:
Table_VII.do - Stata code:
Table_VIII.do
Rcode for replication:
The R code is not yet available.
3.2 (Bound, Jaeger, and Baker 1995) Many Weak Instruments
3.2.1 Class Reading Material
See html page with browser： click here
See or download pdf file: click here
Source (BKB1995): Bound, J., D. A. Jaeger, and R. M. Baker. Problems with Instrumental Variables Estimation When the Correlation between the Instruments and the Endogenous Explanatory Variable Is Weak[J]. Journal of the American Statistical Association, 1995.
Abstract: We draw attention to two problems associated with the use of instrumental variables (IV), the importance of which for empirical work has not been fully appreciated. First, the use of instruments that explain little of the variation in the endogenous explanatory variables can lead to large inconsistencies in the IV estimates even if only a weak relationship exists between the instruments and the error in the structural equation. Second, in finite samples, IV estimates are biased in the same direction as ordinary least squares (OLS) estimates. The magnitude of the bias of IV estimates approaches that of OLS estimates as the R 2 between the instruments and the endogenous explanatory variable approaches 0. To illustrate these problems, we reexamine the results of a recent paper by Angrist and Krueger, who used large samples from the U.S. Census to estimate wage equations in which quarter of birth is used as an instrument for educational attainment. We find evidence that, despite huge sample sizes, their IV estimates may suffer from finite-sample bias and may be inconsistent as well. These findings suggest that valid instruments may be more difficult to find than previously imagined. They also indicate that the use of large data sets does not necessarily insulate researchers from quantitatively important finite-sample biases. We suggest that the partial R 2 and the F statistic of the identifying instruments in the first-stage estimation are useful indicators of the quality of the IV estimates and should be routinely reported.
3.3 (Andrews, Stock, and Sun 2019) Weak Instruments Theory and Practice
3.3.1 Class Reading Material
- See or download pdf file: click here
Source (Andrews2019): Andrews, I., J. H. Stock, and L. Sun. Weak Instruments in Instrumental Variables Regression: Theory and Practice[J]. Annual Review of Economics, 2019, 11:727-753.
Abstract: When instruments are weakly correlated with endogenous regressors, conventional methods for instrumental variables (IV) estimation and inference become unreliable. A large literature in econometrics has developed procedures for detecting weak instruments and constructing robust confidence sets, but many of the results in this literature are limited to settings with independent and homoskedastic data, while data encountered in practice frequently violate these assumptions. We review the literature on weak instruments in linear IV regression with an emphasis on results for nonhomoskedastic (heteroskedastic, serially correlated, or clustered) data. To assess the practical importance of weak instruments, we also report tabulations and simulations based on a survey of papers published in the American Economic Review from 2014 to 2018 that use IV. These results suggest that weak instruments remain an important issue for empirical practice, and that there are simple steps that researchers can take to better handle weak instruments in applications.
3.4 (Keane and Neal 2024) A Practical Guide to Weak Instruments
3.4.1 Class Reading Material
- See or download pdf file: click here
Source (Keane2024): Keane, M. P., and T. Neal. A Practical Guide to Weak Instruments[J]. Annual Review of Economics, 2024, 16:185-212.
Abstract: We survey the weak instrumental variables (IV) literature with the aim of giving simple advice to applied researchers. This literature focuses heavily on the problem of size inflation in two-stage least squares (2SLS) two-tailed t-tests that arises if instruments are weak. A common standard for acceptable instrument strength is a first-stage F of 10, which renders this size inflation modest. However, 2SLS suffers from other important problems that exist at much higher levels of instrument strength. In particular, 2SLS standard errors tend to be artificially small in samples where the 2SLS estimate is close to ordinary least squares (OLS). This power asymmetry means the t-test has inflated power to detect false positive effects when the OLS bias is positive. The Anderson-Rubin (AR) test avoids this problem and should be used in lieu of the t-test even with strong instruments. We illustrate the practical importance of this issue in IV papers published in the American Economic Review from 2011 to 2023. Use of the AR test often reverses t-test results. In particular, IV estimates that are close to OLS and significant according to the t-test are often insignificant according to AR. We also show that for first-stage F in the 10–20 range there is a high probability that OLS estimates will be closer to the truth than 2SLS. Hence we advocate a higher standard of instrument strength in applied work.