ALTERNATIVE ASYMPTOTICS AND THE PARTIALLY LINEAR MODEL WITH MANY REGRESSORS

By M. D. Cattaneo, Michael Jansson, Whitney K. Newey. Econometric Theory, 2015

77 citations recorded by the source corpus.

Many empirical studies estimate the structural effect of some variable on an outcome of interest while allowing for many covariates. We present inference methods that account for many covariates. The methods are based on asymptotics where the number of covariates grows as fast as the sample size. We find a limiting normal distribution with variance that is larger than the standard one. We also find that with homoskedasticity this larger variance can be accounted for by using degrees-of-freedom-adjusted standard errors. We link this asymptotic theory to previous results for many instruments and for small bandwidth(s) distributional approximations.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6669079462c3bb259fe8778fdc814eabfc017d2d

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Citations in the corpus

Inference in Linear Regression Models with Many Covariates and Heteroscedasticity (2015, background): “For further technical details see, for example, Newey (1997), Chen (2007), Cattaneo and Farrell (2013), and Belloni, Chernozhukov, Chetverikov, and Kato (2015).”
High-dimensional econometrics and regularized GMM (2018, background): “[39] and [40] consider inference for a low-dimensional set of coefficients in a linear model with number of variables proportional to but smaller than the sample size in a framework allowing for the coefficients on the nuisance variables to be dense.”
Leave‐Out Estimation of Variance Components (2018, unknown): “Cattaneo et al. (2016) show that the estimation error in β̂ leads to first order biases in estimators of this type when k/n 9 0.”
The Risk of James–Stein and Lasso Shrinkage (2016, background): “Another related work is Cattaneo et al. (2012), which explores inference in regression models with p proportional to n This article does not contribute to the theory of shrinkage estimation.”