Economics Letters 8 (I %I) 73-77 North-Holland Publishing Company 13 EFFICIENT ESTIMATION OF TAIL-AREA PROBABILITIES IN SAMPLING EXPERIMENTS Russell DAVIDSON and James G. MacKINNON Queen’s zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Unioersrty, Kingston, Ontario, Cmudu K7L 3N6 Received 27 July 1981 A technique based on the use of control variates is proposed for the efficient estimation, in Monte Carlo experiments, of tail-area probabilities of test statistics whose small-sample properties are unknown. Significant variance reduction can be achieved in some cases. 1. Introduction It is frequently of interest in both theoretical and applied econometrics to study the small-sample distributions of test statistics whose asymptotic distributions are known. Since the difficulty of doing so analytically is often formidable [see, e.g., Phillips (1980)], the most common way to proceed is to perform a sampling experiment. What will often be of most interest in such experiments, especially to applied workers concerned about the inferences they are drawing, is the fraction of the time, say q, that a given test statistic, say Y, exceeds a fixed critical value, Y”. For example, if Y is the drawing on the ith trial of a test statistic which is known to be asymptotically N(O,l), we may be most interested in how often Y exceeds 1.96 in absolute value. Ideally, it should do so exactly five percent of the time; if it does so much more than that, the test statistic should clearly be used with caution in cases similar to the experimental one. The results of sampling experiments are of course themselves random variables. We do not want to conclude that Y exceeds Y” more often than it should unless we can be confident that this result is not due to experimental error; neither do we want to draw the opposite conclusion unless our estimates of q are quite precise. Unfortunately, the event Y > Y” will usually not occur very often over the course of the experi- 01651765/81/0000-0000/$02.75 0 1981 North-Holland