Study fits Cobb-Douglas production function to the bituminous coal industry. Author concludes that increase in productivity is due almost entirely to increase in horsepower per worker, with residual due to work force quality changes.

G. S. Maddala, R. Blaine Roberts; Statistical Cost Analysis Re-Revisited, The Quarterly Journal of Economics, Volume 96, Issue 1, 1 February 1981, Pages 177–181

Journal Article “The Demand for Money: A Cross-Section Study of Business Firms”: Comment Get access G. S. Maddala, G. S. Maddala Stanford University Search for other works by this author on: Oxford Academic Google Scholar Robert C. Vogel Robert C. Vogel Stanford University Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 79, Issue 1, February 1965, Pages 153–159, https://doi.org/10.2307/1880521 Published: 01 February 1965

[The paper derives a function that describes the size distribution of incomes. The two functions most often used are the Pareto and the lognormal. The Pareto function fits the data fairly well towards the higher levels but the fit is poor towards the lower income levels. The lognormal fits the lower income levels better but its fit towards the upper end is far from satisfactory. There have been other distributions suggested by Champernowne, Rutherford, and others, but even these do not result in any considerable improvement. The present paper derives a distribution that is a generalization of the Pareto distribution and the Weibull distribution used in analyses of equipment failures. The distribution fits actual data remarkably well compared with the Pareto and the lognormal.]

[The paper presents maximum likelihood methods for estimating four types of disequilibrium models. In each case the model includes three equations: the demand equation, the supply equation, and the condition that quantity observed is the minimum of quantity demanded and quantity supplied. The first model consists of just these equations. In the second model one knows whether one is on the demand function or the supply function by looking at the direction of the change in price. In the third model the price change is assumed to be proportional to excess demand. In the fourth model the price change is a stochastic function of excess demand and possibly other exogenous variables. Some illustrative calculations are presented using the housing starts model considered by Fair and Jaffee in an earlier issue of this journal.]

The presence of farm programs should directly affect the expectations of producers. This paper analyzes the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We first investigate what the expected price would be if the usual rational expectations formula is used. This leads to a relationship that is not estimable. We suggest two alternatives -one based on a tobit approximation and the other based on a perfect prediction of when the support is going to be effective. Using a simplified model of the U.S. corn market, the methodology is demonstrated and compared to an alternative method of using futures prices as the expectation of harvest price. The analysis of supply response for the major U.S. field crops is made difficult due to government intervention in these markets. This intervention has been characterized by the use of price supports, acreage diversion, storage incentives, etc. during the last thirty years. Many studies have analyzed producer behavior in the presence of governmental involvement. Such studies have typically been concerned with modeling the effect of supports and diversions in an ex post sense rather than with how producers used the knowledge of farm programs to form their expectations. If producers are rational economic agents, their expectations of harvest prices should be conditioned both by free market forces and the type and degree of governmental intervention in the market. Of course, farm programs have varied in nature and extent during the past thirty years and it is doubtful that any structural model could capture their complexities. In this paper we attempt to introduce rational expectations in a simplified model of the U.S. corn market. In essence we focus on the formation of price expectations when price supports constitute an effective lower bound on the distribution of the expectations. We proceed by developing a theoretical model that connects the rational expectations model with a model of bounded price variation. It is shown that one representation that may characterize the corn market is a triangular structural system with endogenous switching. A full information maximum likelihood estimator is proposed for the system. Next an empirical model is specified and estimated. The model is evaluated in comparison to an augmented model that contains a futures price so that some inferences may be made concerning the rational expectations model's success in summarizing relevant market information. Expectations Under Bounded Prices Consider a market that may be represented by a simple supply and demand system Q= a,Pt* + a2W, + el, Supply Function Pt= b,Qt + b2Xt + e2t Demand Function (1) where P and Q represent market price and quantity, W and X represent supply and demand shifters, and P,* represents the rational expectation of product price at the time production decisions are made. Note that this system has a familiar recursive structure when the expected price variable is specified in terms of one or more lagged prices. When the restricted reduced form of the structural system is solved for in terms of the expected price and this expression is used to replace Pj* (Wallis (1980)) then models similar to those of Goodwin and Sheifrin (1982) and Shonkwiler and Emerson (1982)

7 The F-statistic for the first test is F(4,107) = 0.50 while for the second test it is F(4,11 1) = 0.81. Both of these values are well below the critical-F at conventional levels of significance. 8 Further experimentation showed that one additional parameter could be eliminated by, for example, disposing of the last join point (setting d2 = 0.). However, since the purpose here was simply to show that fewer than 12 parameters are required, the equation has been left in the present form.

HE most important motivation for T current study investigating lagged relationships in corporate demand for liquid assets is current controversy over lags in monetary policy. The literature is so wellknown that it need not be recapitulated here. The evidence that has been presented is of two kinds: analysis based on turning points in different series, i.e., that by Friedman; and an analysis based on estimation of distributed lag relationships, i.e., by Karaken and Solow. The latter authors estimate distributed lag relationships in different sectors and simply add these up. However, as Tucker [12] has pointed out, in a general equilibrium context summing lags in various sectors to measure lag in monetary policy is not a valid procedure. This implies that estimation of distributed lags should be done in a simultaneous equations context. But we feel that there are still several unresolved problems connected with estimation of single equations. The present study, therefore, concentrates on estimating distributed lags in a single equation context, with a specific view of analyzing merits and demerits of various alternative estimation techniques proposed till now for estimation of distributed lag models. We recognize that controversy over lags in monetary policy must be resolved in a general equilibrium context, with additional evidence on interactions among all variables, and especially on lags in each component function. For manufacturing corporations there is little evidence on lags in liquid asset demand, since most studies do not focus explicitly on this problem. Only Heston [7] and Anderson [2] enter lagged dependent variables in their regressions to examine adjustment. However, neither study discusses various problems of statistical estimation and interpretation. Anderson finds that approximately one-third of adjustment to equilibrium occurs in one quarter for cash while figure is about onefourth for government securities.' On other hand, Heston discovers that cash adjusts less than two-thirds of way to equilibrium in one year, and government securities less than one-half.2 The number of aggregate time-series studies of money demand dealing explicitly with lags is also not large, nor are statistical procedures particularly sophisticated. In one of earliest studies using a lagged model, Bronfenbrenner and Mayer [3] find that implied speed of adjustment toward equilibrium is onefourth to one-half per year. Treating money supply as an endogenous variable and using technique of two-stage least squares, Teigen [11] observes that during postwar period, one-third of adjustment to equilibrium occurs in a quarter, while for interwar period about one-half of adjustment takes place in a year.3 A study of money demand by Chow [4] also considers question of lagged adjustment at length, both by contrasting permanent income and wealth with current income and by including lagged dependent variables.4 Chow finds that speed of adjustment is less than one-half in first year. In a Federal Reserve study, De Leeuw [5] employs alternative estimation techniques in an attempt to deal with problems of serial correlation and lagged adjustment. He concludes his analysis saying the long lag hypothesis emerges from tests against post-war data