A NY econometric equation representing a complex behavioral or technical relationship is, of necessity, an approximation of reality. As such, it is subject to errors in specification and structural change over time. This problem is well recognized by econometricians. Duesenberry and Klein (1965) point out that *'. . . as technology, institutional arrangements, tastes and managerial techniques change over time, the relationships represented by our equations inevitably change. Furthermore, when statistical tests are applied to econometric relationships, the hypothesis of structural stability is frequently rejected.' Some methods for dealing with structural change have evolved. Quandt (1957) has developed a maximum likelihood technique for estimating a point of structural change within a sample.2 Klein and Evans (1967) adjust the intercepts of the Wharton Model to account for structural change.3 The purpose of this paper is to test the robustness of Adaptive Regression (1973) to specification errors causing structural change over time, relative to ordinary least squares analysis with and without the autoregressive correction.4 Since econometricians are inevitably faced with structural change and errors in specification, they should use a technique which is robust rela-tive to such problems. The device most commonly used is to assume that the disturbances are subject to an autoregressive process. The autoregressive correction may frequently ameliorate the effects of misspecification and structural change, but it is doubtful whether such processes, except in rare instances, describe the true distribution of the disturbances. The economics literature seldom gives any justification for this scheme except that omitted variables may be subject to an autoregressive process or the structure of the model may be changing.5 We suspect the reasons for the widespread use of the autoregressive correction are that it is a simple hypothesis, explains serial correlation in the disturbances, and can be dealt with efficiently. The adaptive regression model considered in this paper is equally simple but more general, explains serial correlation, and can also be dealt with efficiently.6 In the next section the adaptive regression model is presented and the Bayesian estimators are developed. In section II the results of a Monte Carlo Study are presented. Two models are considered for which data are generated by eleven different schemes. The estimation and forecasting efficiency of adaptive regression, and ordinary least squares with and without the autoregressive correction are compared. Section III contains an analysis of the role of time trends in econometric relationships. In section IV the relative forecasting ability of the three estimation techniques is tested on real data. The three models suggested by Received for publication February 10, 1972. Revision accepted for publication November 30, 1972. *The authors acknowledge helpful comments of Professors F. G. Adams, R. Roll and R. Summers and the participants of the NBER conference on Bayesian Statistical Inference in Economics. Computations were executed on the University of Pennsylvania computer. 'Examples of such tests include Brown (1966), Goldfield (1969) and Howrey (19-70). One of the most extensive studies was done by Duffy (1969). 'The Quandt technique is limited by the fact that it is mainly useful for finding stable subsamples. If structural change occurs often, it is not very useful. Rosenberg (1968) has used stepwise composition to develop the computationally efficient Aitken estimates of a model subject to structural change over time. His procedure, however, requires that the true covariance matrix of the disturbances be known up to a constant scale factor. 'Adjusting the intercepts is an ad hoc method for keeping the model on track for ex ante forecasting. The intercepts are not assumed to change over the sample period which is always much longer than the forecasting period. 'The autoregressive correction assumes the error is subject to a first or second order autoregressive scheme. See Dhrymes (1969) for the maximum likelihood approach and Zellner and Tiao (1965) for the Bayesian development. The latter approach is used in this paper. 'In fact, if omitted variables are subject to an autoregressive process, the disturbances will, in general, be subject to a more complicated process. 6 A test with sufficient power to differentiate betweer these two models (or others which result in serial correlation) using sample sizes generally available to econometricians does not appear to exist. Further, if one did, its usefulness would be limited as neither structure is likely to be an exact representation of reality. That one structure is more likely on the basis of the data does not imply thai it will forecast better if, in fact, a third structure is generating the data.

CONTROVERSIES involving inflation, particularly inflation in developing countries, have usually focused on Latin America.1 One major point which emerges from these controversies is the distinction between a fully anticipated, fully adjusted inflation and an inflation which proceeds with such irregularity that economic agents are able neither to anticipate nor to adjust completely. To the extent that individuals can anticipate and adjust to inflation, a higher rate of inflation will cause the income velocity of money to rise, as attempts are made to exchange money for hedges against inflation.' The influence of inflation on monetary velocity is less clear, however, under the conditions of imperfect anticipation and adjustment which prevail in Latin America. Not only are the rates of inflation in most Latin American countries high, but they also tend to be highly variable. In addition, most Latin American countries have less than perfect markets for hedging against inflation, and these are further restricted by the regulations often imposed on interest rates, prices and international trade in the wake of inflationary conditions.' The present paper examines the impact of inflation on the income velocity of money for sixteen Latin American countries over the period 1950-1969. Such an examination not only indicates the sensitivity of demand for real cash balances to changes in the price level, but also reflects the extent to which economic agents under conditions prevailing in Latin America can anticipate inflation and adjust by hedging. Aside from Cagan's well-known work on hyperinflation (Friedman, 1956, pp. 25117), most empirical studies of the demand for money in individual countries conclude that inflation does not have a significant impact on velocity.4 These studies generally argue that the small changes in the price level usually observed cannot be adequately anticipated or are not large enough to cover the costs of adjustment. A recent article by Melitz and Correa (1970) on international differences in income velocity, like most studies of individual countries (but contrary to theoretical expectations), also concludes that inflation does not influence velocity. This article, like the present study, uses international comparisons, but the findings differ substantially. Melitz and Correa find that the coefficient for the impact of inflation on velocity does not have the expected sign and therefore omit the inflation variable from further consideration. They argue that price changes are important only in cases of hyperinflation and that adjusting to mild inflation is too costly and difficult to be worthwhile. Having excluded inflation as an explanatory variable, Melitz and Received for publication May 24, 1972. Revision accepted for publication January 30, 1973. * The authors wish to thank Michael C. Lovell for many helpful comments and suggestions, Francisco Chaves for assistance with data collection and computational work, and the Wesleyan Computer Center for generous use of its facilities. ' Best known is the monetarist-structuralist controversy over the causes of inflation and the impact of inflation on economic development. See, for example, Baer and Kerstenetzky (1964), Johnson (1967, pp. 281-291) and Baer (1967). 2-Johnson (1967, pp. 104-142) identifies the tax on real cash balances as the essence of the quantity theory approach to inflation, and it is the efforts to escape this tax which cause monetary velocity to rise with inflation. 'In discussions of inflation and economic growth, more costs and benefits of inflation are attributed to structural imperfections rather than to the tax on real cash balances. Structuralists emphasize the benefits of inflation in circumventing market imperfections, while monetarists focus on the costs of inflation in conjunction with inappropriate government regulations. See Johnson (1967, pp. 281-291) and Baer (1967). 4 However, some studies in a collection edited by Meiselman (1970) provide limited support for a positive influence of inflation on velocity in several less-developed countries. Deaver (Meiselman, 1970, pp. 7-67), finds the rate of inflation to be a significant variable in explaining velocity changes in Chile during the period 1932-1955, while Campbell (Meiselman, 1970, pp. 339-386) finds a positive correlation between velocity and changes in the rate of inflation in a comparative study of South Korea and Brazil. In a cross-country study Perlman (Meiselman, 1970, pp. 297337) finds nominal interest rates or inflation rates (as proxies for the opportunity cost of holding money) to be significant in explaining international differences in liquid asset portfolios.

Over the years there has been a growing interest in the over-the-counter (OTC) trading of exchange-listed securities (known as the third market). Although the third market has flourished and its advantages have been expounded, it has not been possible to compare accurately the third market with organized exchanges because of an incomplete quotation system. On April 5, 1971, the National Association of Security Dealers Automatic Quotation (NASDAQ) system began including bid-and-ask quotations for 30 stocks listed on the New York Stock Exchange (NYSE); see Table 1.

In their provocative article that discusses risk as the probability of an investment's worth falling below some specified minimal value, Machol and Lerner observe that by this definition investments may be risky over a short time horizon but not over a long one [5, p. 484], and that a person who could invest in the stock market over a relatively long period of time without needing to withdraw capital during the period could invest with “relatively little worry” [5, p. 488]. The purpose of this comment is to examine the foregoing position rather more closely insofar as the time path of investment values is concerned. To this end, we model the value of an investment in the New York Stock Exchange Index, relative to its initial value, as a Markov chain. We assume that no part of the initial investment or dividends received on it is withdrawn before termination of the process, at which point the entire amount accumulated (which may be less than the initial investment) is realized. Values taken from a record of annual percentage changes in the New York Stock Exchange Index over the period 1940–1968 are then used to define a representative matrix of transition probabilities which describes the manner in which investment values can change from one period to the next. The probability distributions of relative investment values over differing lengths of time for which the investment may be held are then investigated using the Markov chain model.

Abstract The article examines the usefulness of financial ratios to investors in common stock. It was assumed that the formation of expectations about future rate of return rankings was significant to investors. Thus, the explanatory relationships found to exist between financial ratios and rate of return on investment in common stock were tested for ability to predict rate of return rankings. By moving from unadjusted rate of return to market adjusted rate of return, strong evidence of a market effect on the rate of return yielded by a common stock was found.