In an earlier paper [1] a model of securities markets was introduced which implies that the ratio of transaction volume to price change is greater for transactions on which price rises than for those on which price falls. Examination of individual transactions data for a sample of corporate bonds showed that price changes and transaction volumes for those securities appears to behave in a manner consistent with the theory. However, the paper raised the question of whether the same is true for stocks. The positive dependence on share price of broker commissions for stocks could easily eliminate, or even reverse the sign of, the predicted positive difference between the absolute values of slopes of buyers' and sellers' reservation demand functions; and it is this difference which leads the model to predict the inequality of the ratios of volume to price change on upticks and downticks. This note records the results of tests of the model with stock data, using volumes and price changes pertaining both to individual transactions and to trading days. The tests indicate that the ratios of volume to price change exhibit the predicted relationship, when one of the two possible measures of volume is employed.

This paper provides an analysis of the choice of method for raising additional equity capital by listed firms. Examination of expenses reported to the SEC indicates that rights offerings involve significantly lower costs; yet underwriter are employed in over 90 percent of the offerings. The underwriting industry, finance textbooks, and corporate proxy statements offer several justifications for the use of underwriters. However, estimates of the magnitudes of these arguments indicate that they are insufficient to justify the additional costs of the use of underwriters. The use of underwriters thus appears to be inconsistent with rational, wealth-maximizing behavior by the owners of the firm. The paper concludes with an examination of alternate explanations of the observed choice of financing method.

Annual earnings, Time-series, Random walk, Predictive ability

is misleading if o-2 $ o-2 and n, and n2 are both small, where Y, and Xi are ni x 1 and ni x k observation matrices, ,li is a k x 1 coefficient matrix, and ei is an n, x 1 error matrix for i=1,2. A valid asymptotic test may easily be obtained by regarding (1) and (2) as seemingly unrelated regression equations. In this paper we establish a small sample test which may readily be extended to a test of some of the coefficients in the two regressions.

The distributions of the LIML and TSLS estimates of the coefficient of an endogenous variable in a single equation can be approximated by asymptotic expansions. This paper relates the expansions in terms of the noncentrality parameter and the sample size going to infinity, the noncentrality parameter going to infinity with the sample size held fixed, and the standard deviation of the disturbance going to zero (small-o). 1. INTRODUCriON RECENTLY, ASYMPTOTIC EXPANSIONS of the distributions of estimates of coefficients of a single equation in a system of simultaneous equations have been made by Anderson [1], Anderson and Sawa [2], Mariano [6 and 7], and Sargan and Mikhail [11]. The expansions have usually been carried out on the basis that the sample size increases and that the effect of the exogenous variables (the noncentrality parameter) increases along with the sample size. In this paper we consider the case of the covariance matrix of the disturbances known and alternatively the case of the sample size fixed. We relate these three cases to the approach of letting the disturbance decrease (the small-o- approach). The estimates treated are two-stage least squares (TSLS) and limited information maximum likelihood (LIML).

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