On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments

References

• Andrews, D. W. K. (1999), “Consistent Moment Selection Procedures for Generalized Method of Moments Estimation,” Econometrica, 67, 543–564.
   Web of Science ®Google Scholar
• Angrist, J. D., and Krueger, A. B. (1991), “Does Compulsory School Attendance Affect Schooling and Earnings?” Quarterly Journal of Economics, 106, 979–1014.
   Web of Science ®Google Scholar
• Bekker, P. A. (1994), “Alternative Approximations to the Distributions of Instrumental Variable Estimators,” Econometrica, 62, 657–681.
   Web of Science ®Google Scholar
• Belloni, A., Chen, D., Chernozhukov, V., and Hansen, C. (2012), “Sparse Models and Methods for Optimal Instruments with an Application to Eminent Domain,” Econometrica, 80, 2369–2429.
   Web of Science ®Google Scholar
• Belloni, A., and Chernozhukov, V. (2013), “Least Squares After Model Selection in High-dimensional Sparse Models,” Bernoulli, 19, 521–547.
   Web of Science ®Google Scholar
• Belloni, A., Chernozhukov, V., and Hansen, C. (2014), “Inference on Treatment Effects after Selection among High-Dimensional Controls,” Review of Economic Studies, 81, 608–650.
   Web of Science ®Google Scholar
• Bowden, J., Smith, G. D., Burgess, S. (2015), “Mendelian Randomization with Invalid Instruments: Effect Estimation and Bias Detection through Egger Regression,” International Journal of Epidemiology, 44, 512–525.
   PubMed Web of Science ®Google Scholar
• Bühlmann, P., and van der Geer, S. (2011), Statistics for High-Dimensional Data. Methods Theory and Applications (Springer Series in Statistics), Heidelberg: Springer.
   Google Scholar
• Burgess, S., Small, D. S., and Thompson, S. G. (2017), “A Review of Instrumental Variable Estimators for Mendelian Randomization,” Statistical Methods in Medical Research, 26, 2333–2355.
   PubMed Web of Science ®Google Scholar
• Cheng, X., and Liao, Z. (2015), “Select the Valid and Relevant Moments: An Information-based LASSO for GMM with Many Moments,” Journal of Econometrics, 186, 443–464.
   Web of Science ®Google Scholar
• Chernozhukov, V., Hansen, C., and Spindler, M. (2015), “Post-Selection and Post-Regularization Inference in Linear Models with Many Controls and Instruments,” American Economic Review, 105, 486–490.
   Web of Science ®Google Scholar
• Clarke, P. S., and Windmeijer, F. (2012), “Instrumental Variable Estimators for Binary Outcomes,” Journal of the American Statistical Association, 107, 1638–1652.
   Web of Science ®Google Scholar
• Davey Smith, G., and Hemani, G. (2014), “Mendelian randomization: Genetic Anchors for Causal Inference in Epidemiological Studies,” Human Molecular Genetics, 23, R89–R98.
   PubMed Web of Science ®Google Scholar
• Davidson, R., and MacKinnon, J. G. (1993), Estimation and Inference in Econometrics, Oxford: Oxford University Press.
   Google Scholar
• Davies, N. M., von Hinke Kessler Scholder, S., Farbmacher, H., Burgess, S., Windmeijer, F., and Smith, G. D. (2015), “The Many Weak Instruments Problem and Mendelian Randomization,” Statistics in Medicine, 34, 454–468.
   PubMed Web of Science ®Google Scholar
• Efron, B., Hastie, T., Johnstone, I., and Tibshirani, R. (2004), “Least Angle Regression,” The Annals of Statistics, 32, 407–451.
   Web of Science ®Google Scholar
• Farbmacher, H. (2017), SIVREG: Stata Module to Perform Adaptive Lasso with Some Invalid Instruments, Statistical Software Components S458394, Boston College Department of Economics.
   Google Scholar
• Greenland, S. (2000), “An Introduction to Instrumental Variables for Epidemiologists,” International Journal of Epidemiology, 29, 722–729.
   PubMed Web of Science ®Google Scholar
• Guo, Z., Kang, H., Cai, T., and Small, D. (2018), “Confidence Intervals for Causal Effects with Invalid Instruments using Two-Stage Hard Thresholding with Voting,” Journal of the Royal Statistical Society, Series B, 80, 793–815.
   Google Scholar
• Han, C., (2008), “Detecting Invalid Instruments using L1-GMM, Economics Letters, 101, 285–287.
   Web of Science ®Google Scholar
• Hansen, C., Hausman, J., and Newey, W. K. (2008), “Estimation with Many Instrumental Variables,” Journal of Business & Economic Statistics, 26, 398–422.
   Web of Science ®Google Scholar
• Hansen, L. P. (1982), “Large Sample Properties of Generalized Method of Moments Estimators,” Econometrica, 50, 1029–1054.
   Web of Science ®Google Scholar
• Hastie, T., Tibshirani, R., and Friedman, J. (2009), The Elements of Statistical Learning. Data Mining, Inference, and Prediction (Springer Series in Statistics, 2nd ed.), New York: Springer Science and Business Media.
   Google Scholar
• Imbens, G. W. (2014), “Instrumental Variables: An Econometrician’s Perspective,” Statistical Science, 29, 323–358.
   Web of Science ®Google Scholar
• Kang, H., Zhang, A., Cai, T. T., and Small, D. S. (2016), “Instrumental Variables Estimation with some Invalid Instruments and its Application to Mendelian Randomization,” Journal of the American Statistical Association, 111, 132–144.
   Web of Science ®Google Scholar
• Kolesar, M., Chetty, R., Friedman, J., Glaeser, E., Imbens, G. W. (2015), “Identification and Inference with Many Invalid Instruments,” Journal of Business and Economic Statistics, 33, 474–484.
   Web of Science ®Google Scholar
• Lawlor, D. A., Harbord, R. M., Sterne, J. A. C., Timpson, N., and Davey Smith, G. (2008), “Mendelian Randomization: Using Genes as Instruments for Making Causal Inferences in Epidemiology,” Statistics in Medicine, 27, 1133–1163.
   PubMed Web of Science ®Google Scholar
• Liao, Z. (2013), “Adaptive GMM Shrinkage Estimation with Consistent Moment Selection,” Econometric Theory, 29, 857–904.
   Web of Science ®Google Scholar
• Lin, W., Feng, R., and Li, H. (2015), “Regularization Methods for High-Dimensional Instrumental Variables Regression With an Application to Genetical Genomics,” Journal of the American Statistical Association, 110, 270–288.
   PubMed Web of Science ®Google Scholar
• Locke, A. E. (2015), “Genetic Studies of Body Mass Index Yield New Insights for Obesity Biology,” Nature, 518, 197–206.
   PubMed Web of Science ®Google Scholar
• Meinshausen, N., and Bühlmann, P. (2006), “High-Dimensional Graphs and Variable Selection with the Lasso,” Annals of Statistics, 34, 1436–1462.
   Web of Science ®Google Scholar
• Newey, W. K., and Windmeijer, F. (2009), “Generalized Methods of Moments with Many Weak Moment Conditions,” Econometrica, 77, 687–719.
   Web of Science ®Google Scholar
• Rothenberg, T. J. (1984), “Approximating the Distributions of Econometric Estimators and Test Statistics,” in Handbook of Econometrics (Vol. 2), eds. Z. Griliches, and M. D. Intriligator, Amsterdam: North Holland, pp. 881–935.
   Google Scholar
• Sargan, J. D. (1958), “The Estimation of Economic Relationships Using Instrumental Variables,” Econometrica, 26, 393–415.
   Web of Science ®Google Scholar
• Staiger, D., and Stock, J. H. (1997), “Instrumental Variables Regression with Weak Instruments,” Econometrica, 65, 557–586.
   Web of Science ®Google Scholar
• Stock, J. H., and Yogo, M. (2005), “Testing for Weak Instruments in Linear IV Regression,” in Identification and Inference for Econometric Models, Essays in Honor of Thomas Rothenberg, eds. D. W. K. Andrews, and J. H. Stock, New York: Cambridge University Press, pp. 80–108.
   Google Scholar
• Sudlow, C., Gallacher, J., Allen, N., Beral, V., Burton, P., Danesh, J., Downey, P., Elliott, P., Green, J., Landray, M., Liu, B., Matthews, P., Ong, G., Pell, J., Silman, A., Young, A., Sprosen, T., Peakman, T., and Collins, R. (2015), “UK Biobank: An Open Access Resource for Identifying the Causes of a Wide Range of Complex Diseases of Middle and Old Age,” PLoS Medicine, 12, e1001779.
   PubMed Web of Science ®Google Scholar
• von Hinke, S., Smith, G. D., Lawlor, D. A., Propper, C., and Windmeijer, F. (2016), “Genetic Markers as Instrumental Variables,” Journal of Health Economics, 45, 131–148.
   PubMed Web of Science ®Google Scholar
• Wainwright, M. J. (2009), “Sharp Thresholds for High-Dimensional and Noisy Sparsity Recovery Using ℓ1-Constrained Quadratic Programming (Lasso), IEEE Transactions on Information Theory, 55, 2183–2202.
   Web of Science ®Google Scholar
• Zhao, P., and Yu, B. (2006), “On Model Selection Consistency of Lasso,” Journal of Machine Learning Research, 7, 2541–2563.
   Web of Science ®Google Scholar
• Zou, H. (2006), “The Adaptive Lasso and Its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429.
   Web of Science ®Google Scholar