Knowledge that Transforms

T HE purpose of this paper is to point out how the efficient instrumental-variables technique discussed by Brundy and Jorgenson (1971) can be modified to take into account auto-regressive properties of the error terms. The limited-information and full-information estimators proposed in this paper are consistent and have the same asymptotic distributions as the limited-information and full-information maximum likelihood estimators, respectively. The full-information estimation of simultaneous equations models with auto-regressive errors has been discussed by Sargan (1961), Hendry (1971), Chow and Fair (1973), and Dhrymes (1971). Sargan originally proposed the full-information maximum likelihood estimation of such models, and Hendry and Chow and Fair have recently developed computationally feasible methods for obtaining the maximum likelihood estimates. Hendry considered only the case of completely unrestricted auto-regressive coefficient matrices (i.e., no zero elements), whereas Chow and Fair considered the case of restricted auto-regressive coefficient matrices as well. Dhrymes has recently proposed the three-stage least squares estimator of simultaneous equations models with auto-regressive errors. Dhrymes also considered only the case of completely unrestricted auto-regressive coefficient matrices. The limited-information estimation of simultaneous equations models with auto-regressive errors has been discussed by Sargan (1961), Amemiya (1966), and Fair (1970), among others. Sargan proposed the limited-information maximum likelihood estimation of such models, and Amemiya and Fair considered various two-stage least souares estimators of such models. Most of the work on limited-information estimators has been concerned with the case of diagonal auto-regressive coefficient matrices. Brundy and Jorgenson's criticism of the twoand three-stage least squares estimators, namely, that the first stage involves estimating reduced form equations with a very large number of variables included in them, holds even more so for models with auto-regressive errors. For these models, the reduced form equations include not only all of the predetermined variables in the system but also all of the lagged endogenous and lagged predetermined variables. In fact, one of the main purposes of the work by Fair (1970) was to suggest ways in which the number of variables used in the first stage regressions of two-stage least squares might be decreased with perhaps small loss of asymptotic efficiency. The advantage of the instrumental-variables techniques proposed in the Brundy-Jorgenson paper and in this paper is that the first stage regressions need not be run.

PpT HE issue is stated that after Phase II the United States faces or competition. Leading economists Charls Walker, Charles Schultze, Murray Weidenbaum and others who oppose controls in principle nevertheless caution (forecast?) against expecting an early return to free markets. The general prescription comes to something like Weidenbaum's: Basically, we need to deal with those concentrations of private economic power which have become insulated from the influences of aggregate monetary and fiscal policy. 1 Charls Walker, Undersecretary of the Treasury, recently predicted voluntary controls for Phase III in a talk before the Manufacturing Chemists Association.2 Walker said this will require what Paul McCracken, former Chairman of the President's Council of Economic Advisers, called a 'social compact'a consensus among business and labor that substantial gains in real economic growth must be paid for by wage and price stability. Arguments supporting such a definition of the issue are grounded in believed about concentration of economic power and concern derived from accepted interpretations of these facts. The evidence concerning these facts will be reviewed in a moment.

FEW economic magnitudes have commanded as much attention from economists as the earnings of capital. Despite this emphasis, it is interesting that there exists scant empirical evidence concerning the determinants of capital income over the relatively long run. This is rather surprising since the short-term behavior of profits has come under considerable scrutiny by econometric model builders. Existing evidence concerning long-run behavior stems primarily from recent studies of the incidence of the corporation income tax.' In order to isolate the effects of the tax, investigators have had to identify and eliminate the effects of the nontax determinants of profit. As would be expected, conclusions regarding tax incidence have turned out to be extremely sensitive to the underlying model of profit. It is the purpose of this paper to ascertain the extent to which a model based upon standard competitive behavior is capable of explaining the time path of corporation earnings over a period of almost forty years. Since most incidence studies have been based upon models which explicitly or implicitly assume nonprofit maximizing behavior, such a study will provide a useful extension of the empirical evidence concerning the behavior of profit as well as a test of the relative efficacy of standard economic theory. Furthermore, unlike existing studies, the model will be tested in such a way that the contribution of such determinants of profit as technological change, capital intensity and aggregate demand can be isolated. Since indirect evidence on such factors exists from studies of aggregate production functions and business cycle behavior, the plausibility of the estimates can be determined. Finally, the model can be used to provide additional evidence concerning the shifting of the corporation income tax. If the model is specified correctly, the introduction of a corporation income tax variable into the estimating equation should have little effect. In what follows, a model of corporation earnings is developed and tested for the manufacturing sector of the United States economy for the period 1930-1968. The model is based upon the hypothesis that the return to capital depends upon its marginal productivity and short-run fluctuations in output. It is found that the model does quite well in explaining the time path of manufacturing earnings over the sample period; all coefficients are statistically significant, have the right sign, and are of reasonable magnitude. These estimates also provide evidence concerning the underlying aggregate production function. Specifically, the estimates imply an elasticity of factor substitution of less than one, and technical progress which is not solely of the Harrod-neutral variety. At this point the question of short-run corporation tax shifting is taken up. A suitably defined tax variable is introduced into the statistical model. It is found that the tax variable does not significantly add to the explanatory power of the model; its coefficient is small in absolute value and is statistically insignificant. It is concluded, therefore, that corporations bear the full burden of the corporation income tax in the short run.

A recent paper by Baumol, Heim, Malkiel and Quandt (1970) (hereafter referred to as BHMQ), estimated the relative rates of return on retained earnings, debt, and equity financing in United States corporations. The present paper summarises some results of my recent study (chapter 5, 1971) which investigates the effect of external financing on the future profitability of British quoted companies. The results of this study, which differs both in methodology and data used, are then compared with the BHMQ results. The comparison yields two important insights into the interpretation of the BHMQ results, whilst confirming the general conclusion that retained earnings seem to be used less profitably than external finance.

T HE most frequently used estimating technique for applied economic research has been ordinary least squares (OLS). There are two theoretical justifications for its use. First, the Gauss-Markov theorem suggests that OLS estimators will outperform all other techniques in the class of linear unbiased estimators.1 Secondly, under the assumption that the error terms are normally distributed, OLS estimators can be derived as the maximum likelihood estimates. Frequently when OLS is introduced in elementary texts, the method of minimizing the sum of absolute deviations (MAD) is presented for comparison purposes, but rarely is it given serious consideration for applied uses.) Certainly one reason for such behavior stems from previous evaluations of OLS versus MAD estimators. Asher and Wallace (1963) found that the use of MAD meant one should be prepared to give up considerable efficiency 3 More recently Glahe and Hunt (1970), suggested several estimators derived under the general minimization criterion. In contrast to the Asher-Wallace study, the Glahe-Hunt model was a two-equation linear simultaneous system. Their results show that neither form of absolute deviation estimator outperformed either OLS or two-stage least squares.4 The purpose of this paper is to suggest that in at least one aspect these comparisons have given OLS a differential advantage. That is, both of these studies employed errors for their hypothesized models which were drawn from normal distributions. Consequently the OLS estimators are both maximum likelihood and best linear unbiased estimators (BLUE) under such circumstances. Since recently published works by Zeckhauser and Thompson (1970), Fama (1965) and others have called into question the assumption of normally distributed error terms, attention has begun to shift to other alternatives.5 Blattberg and Sargent (1971) have examined three techniques including both OLS and MAD when the errors are drawn from a stable Paretian distribution. Their findings indicate that the MAD estimator . performs sufficiently well that it deserves further study and elaboration. G Accordingly we have chosen to explore the relative merits of OLS and MAD for a single equation model whose errors are drawn from a double exponential parent distribution. This distribution was chosen because both estimators will exhibit theoretically desirable properties. OLS remains the BLUE estimator, while MAD is the maximum likelihood estimator. Furthermore, this distribution is one member of the power distribution suggested by Zeckhauser and Thompson as an alternative to the normal. This paper is divided into, three sections. The first describes the design of the experiments. Section II presents the empirical results and the last summarizes the primary findings of the paper.

where X1 represents a series of T observations (t = 1, . .. , T). This ratio is not appropriate for testing the independence of residuals from least squares regression; its purpose is to test for autocorrelation among observed variables. The Durbin-Watson development (1950, 1951) of the von Neumann ratio was concerned with testing residuals from regression for serial correlation. They test the null hypothesis H,, that there is no serial correlation between the residuals (Ut) against the alternative hypothesis H1 that the Ut are positively correlated. The Durbin-Watson test statistic is

M ANY cross-section studies exist in the literature attempting to explain variations in per capita state and local expenditures on such services as highways, municipal services, health, and education. Differences in per capita expenditures across states are explained in terms of such factors as differences in population densities, urban-rural distributions, average income levels, age distributions, and numbers of school-age children.' In most of these studies, however, the underlying theory has not been carefully spelled out and, in particular, it is never made clear whether the demographic variables are thought to enter on the demand side or on the supply side of the market for state and local services. In the first part of this paper we look at the theory underlying such regression studies of the determinants of state and local expenditures. We attempt to distinguish between the demand side of the market for such services and the supply (cost) side. In the second part of the paper we obtain empirical estimates of price and income elasticities of demand for state and local services for three broad classifications of services. Finally we discuss a number of interesting applications of our results.

T HE geographic extent of the market has long been recognized as an important element of industry structure. For lack of systematic and direct measures, however, previous studies have relied either on rough classifications of geographical market size (local, regional or national) (Comanor and Wilson, 1967, p. 433; Kaysen and Turner, 1959, appendixes, pp. 283-285; Stigler, 1963, pp. 265-269 and 56-57) or on output dispersion indexes such as the number of states needed to account for 75 per cent of total shipments (Collins and Preston, 1968, 1969; Fuchs, 1962). This paper develops an alternative index of market size based on the Census of Transportation. Some attempts are made to evaluate various measures of market extent by comparisons with indexes of output dispersion and with an element of transport cost. It ends with a brief summary of the geographic market sizes of United States manufacturing industries.