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In the growing literature of factor analysis, little is done to understand the finite sample properties of an approximate factor model solution. In empirical applications with relatively small samples, the asymptotic theory might be a poor approximation and the resulting distortions might affect the estimation (bias in the point estimate and the standard errors) and the statistical inference. The present paper uses the estimation method of Bai and Ng [Bai, J. and Ng, S., 2002, Determining the number of factors in approximate factor models. Econometrica , 70, 191–221.] and assesses the sampling behavior of the estimated common components, common factors and factor loadings. The study compares the empirical distributions to the asymptotic theory of Bai [Bai, J., 2003, Inference on factor models of large dimension. Econometrica , 71, 135–171.]. Simulation results suggest that the point estimates have a Gaussian distribution for panels with relatively small dimensions. However, these estimates have a significant finite sample bias and the dispersion of their sampling distribution is severely underestimated by the asymptotic theory. [ABSTRACT FROM AUTHOR]

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale contaminated compound normal distribution and the sample sizes are less than thirty. [ABSTRACT FROM AUTHOR]