A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.

It is generally believed that market power is an important determinant of profits. Although market power is not observable directly, theories of and industry behavior suggest that it may be correlated with easily measurable variables like size, market share and/or industry concentration, and recent growth. If true, these several associations imply a correlation between observable variables, S, which measure size, market share, and recent growth, and (observable) variables, H, which index profitability. These correlations have been demonstrated in empirical literature and have been adduced as evidence of an underlying (casual) correlation between market power (M) and profitability. In fact, it has been claimed that the predicted profitability of each firm, based on models of type under consideration, provides a single integrated estimator of market power held by firm (Shepherd, 1972, p. 35). Such interpretations of S::fl correlations, however, have been questioned seriously on a number of grounds. On one hand, it has been argued that large size, market share and industry concentration should be attributed primarily to efficiency and superior competitive performance rather than to collusion.' The second major line of attack, on other hand, suggests that S::f1 correlations could result from stochastic processes which, of course, do not imply a correlation between market power, or efficiency, and profitability (Mancke, 1974). Our principal concern in present paper is with possible stochastic determinants of profitability. We argue essentially that while ex ante investment opportunities can be randomly distributed, realized rates of return may not generally be specified as fully determined by stochastic processes (cf. Caves, Gale, and Porter, 1977, pp. 668-669). The implications of this argument are explored in a simulation study based on a rudimentary, but representative, model of and industry behavior. The evidence drawn from this experiment does not support view that empirical relationships between profitability and market structure are likely to be result of random processes. The paper is divided into two parts. The principal section develops a simulation model of behavior that incorporates reasonable market features, and examines effects of randomly distributed ex ante investment opportunities in such a setting. A final section contains concluding remarks and suggestions for further research.

The composite measures of investment performance: the reward-to-variability index, by Sharpe ([29], [30]) and Lintner [23], and the reward-to-volatility index, by Treynor [33], were developed after Markowitz ([24], [25]) and Tobin [32] popularized the mean-variance framework of analyzing the problems of certain investments. Since these are ex ante measures they are not directly applicable to the evaluation of ex post performance. A theoretical basis for doing so has been provided by Jensen ([17], [18]) who also developed another composite performance measure, the predictability index. In practice, these composite measures have been found to have problems. Foremost, they have been observed to exhibit systematic biases. Various causes of the biases have been proposed. These are: the existence of unequal lending and borrowing rates, the failure to consider higher moments of return distributions, and the elusive “true” holding period.