Hypothesis testing in linear regression when k/n is large
This paper derives the asymptotic distribution of the F-test for the significance of linear regression coefficients as both the number of regressors, k, and the number of observations, n, increase together so that their ratio remains positive in the limit. The conventional critical values for this test statistic are too small, and the standard version of the F-test is invalid under this asymptotic theory. This paper provides a correction to the F statistic that gives correctly-sized tests both under this paper’s limit theory and also under conventional asymptotic theory that keeps k finite. This paper also presents simulations that indicate the new statistic can perform better in small samples than the conventional test. The statistic is then used to reexamine Olivei and Tenreyro’s results from [Olivei, G., Tenreyro, S., 2007. The timing of monetary policy shocks. The American Economic Review 97, 636–663] and Sala-i-Martin’s results from [Sala-i-Martin, X.X., 1997. I just ran two million regressions. The American Economic Review 87 (2), 178–183].
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- Giovanni P. Olivei & Silvana Tenreyro, 2004. "The timing of monetary policy shocks," Working Papers 04-1, Federal Reserve Bank of Boston.
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- Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, 07.
- Jerry Hausman & Whitney Newey & Tiemen Woutersen & John Chao & Norman Swanson, 2007. "Instrumental variable estimation with heteroskedasticity and many instruments," CeMMAP working papers CWP22/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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- Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
- Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000.
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- Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
- Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," NBER Working Papers 7750, National Bureau of Economic Research, Inc.
- Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
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