Knowledge that Transforms

S. R. Johnson, Peter A. Haigh, Agricultural Land Price Differentials and Their Relationship to Potentially Modifiable Aspects of the Climate, The Review of Economics and Statistics, Vol. 52, No. 2 (May, 1970), pp. 173-180

T HE geographical distribution and mobility of the labor force have received considerable attention in the literature. However, while various factors have been proposed to explain these phenomena, a satisfactory formal theory of the migration and subsequent location of the labor force, susceptible to empirical verification, has not yet evolved. With this study, we hope to contribute to this evolution by developing and empirically testing a more refined theoretical model through the use of a rich but seldom exploited body of statistical data. One dominant emphasis in the existing literature is on the wage or income differential thesis. Raimon [1], in an analysis of the patterns of interstate migration in the United States from 1950 to 1958, found significant rank correlations between percentage changes in population arising from migration and (1) levels of average per capita income (r = .75), and (2) average earnings of employed workers (r = .85). His results are supported by Gallaway, Gilbert and Smith [21], who in a study of interstate migration for a later period, suggest that income differentials are statistically significant in explaining interstate migratory patterns over the interval 1955-1960. On the other hand, Nelson's study [31] of interstate migration during the periods 1935-1940 and 1949-1950 shows no relationship between migration and income differentials; and Easterlin's European emigration study [4] concludes that per capita income, used by itself, was a poor predictor of migration rates. Finally, Fleischer's analysis [51] of postwar Puerto Rican migration to the United States shows that the ratio of gross hourly earnings in the source and receiving areas was, by itself, a very poor predictor. A second emphasis in the literature concerns what one might loosely call the job vacancy thesis. Except for Nelson, there is general agreement about the importance of this variable, whether it is expressed in terms of percentage changes in employment over states (Raimon), unemployment differentials (Gallaway, et al.), the ratio of unemployment levels in source and receiving areas (Fleischer), or cycles in economic activity (Easterlin). Along similar lines, Bjork [6] introduced an index of demand for migrant labor 1 based on the belief that the economic growth of the United States during the period 1880-1950 was accompanied by a dramatic differential growth in demand for agricultural as opposed to nonagricultural labor and by differential rates of natural increase of the population over states. Although their evidence is circumstantial and indirect, both Nelson and Fleischer hypothesize that the role of information afforded by the presence of friends and relatives is a significant variable affecting the magnitude of migratory movements. This opinion is shared by Kirk and Huyck [7], who assert that, . . in the choice of alternative overseas destinations the emigrant will almost always forego theoretical maximum opportunity for the practical advantages of locating among relatives, friends, and countrymen overseas. The interpretation of the results recorded above is rendered difficult not only because of differing definitions of the variables, but also because of the identification problem implicit in some of the models. We contend that the apparently contradictory findings with respect

T HE present study applies the two-stage least squares principle to a nonlinear least squares estimation method; the nonlinear least squares method is based on Marquardt's maximum neighborhood method. The method is applied to the CES production functions of the Canadian manufacturing industries. Section II explains the application of the nonlinear least squares method to the CES production functions; in section III the estimated results are presented; section IV gives some qualifications to the results obtained in the present study.

M OST recent studies of the demand for assets (real or financial) restrict themselves to the examination of the market for a single asset or small group of similar assets. This approach contrasts with the usual treatment of the demand for consumer goods in which complete systems of equations are estimated. This paper reports an attempt to develop a complete set of asset-demand functions for the household sector and to present estimates of the parameters derived from postwar United States data.

where S2 is the usual unbiased estimator of (X2. This procedure in effect defines a new composite estimator which is a probabilistic mixture of bi and b1* and which has corresponding performance characteristics: its MSE is a weighted average (for given parameter values) of MSE bi and MSE bl*, the weights being given by the probabilities that inequality (13) will or will not be realized. We do not wish to suggest that time and effort be devoted to consideration of principal component estimators in every regression study. Benefits in terms of MSE reduction will often be nonexistent or outweighed by the additional computational costs. But in cases such that (i) data augmentation is impossible or very costly, (ii) multicollinearity is severe, and (iii) there exists a well-defined estimation objective, the principal component procedure appears to offer one route for improving upon conventional estimation techniques. FIGURE 1. BREAK-EVEN CORRELATION VALUES r 9

INCOME velocity studies have centered thus far on a few countries, mostly the United States. The present effort deals with international differences in income velocity. While there have been a number of far-reaching international monetary studies of hyperinflation,' to our knowledge only limited work has been done on international differences in income velocity.2 Our approach is to try to explain international differences in income velocity on the basis of a simple demand for money equation, and thus to view the money supply as determined exogenously. This accords with the usual econometric treatment of income velocities.3 The approach may seem rather naive at present, in the light of institutional differences in world monetary environments and statistical discrepancies in national accounts. However, our aim is not to produce structural estimates of income velocity, but to isolate some major influences on income velocity. Accordingly, we have included as many countries as possible in the study, spanning 1958 through 1965 51 at some points and 45 for the rest. We find three statistically significant variables, all operating with the theoretically appropriate sign: the rate of interest, the currency-money ratio, and the degree of monetization. The favorable outcome regarding the interest rate, despite other variables in the equations reflecting inter-country differences in structural environment, is particularly noteworthy. Another important result is that the level of economic development is not an independent influence on income velocity.

FIRMS determine their demands for factors of production by finding the combination of factor inputs that will maximize profits or minimize costs, subject to a technological constraint the production function. Because the production function is common to decisions for all factors, the factor demands must be interrelated; each factor demand function contains parameters from the underlying production function which also appear in other demand functions. Yet factor demand equations are commonly estimated independently, with the consequence that production function parameters implied by the different equation estimates may well be inconsistent. If the demand functions are to be included in a complete model of an economy, it is certainly desirable, if not essential, that they be consistent, i.e., that they imply a single set of parameters for the underlying production function. The authors are currently engaged in constructing a medium-term macro-model of the United States economy, an important subsector of which consists of aggregative labor and investment demand functions. This paper summarizes our efforts at estimating these two demand functions with data extending back to the early 1920's, treating relative prices and financial variables as exogenous. To illuminate the methodological issue just raised, we present results for three estimation procedures: (1) independent estimation of both relations, (2) a two-step approach in which production function parameters implied by independent estimates of one function are imposed in estimating the other relation, (3) joint estimation of both functions. By the nature of our approach, we obtain estimates of the production function from estimates of the factor demand relations. Indirect estimation of the production function in this way has also been suggested, though not carried out, by Dhrymes [7] and Nerlove [15]. It seems to us to be preferable to several alternatives. The production function is a constraint relating desired or expected (long-run equilibrium) output to desired (long-run equilibrium) factor inputs, and these are generally not observable variables. Expected output may be related to current and past levels of output, and observed factor inputs are likely to be disequilibrium values associated with lagged adjustment to desired levels. Use of actual current output and actual current inputs to estimate the production function directly is objectionable for these reasons. The frequent practice of correcting measured capital stock for its utilization (usually by assuming that capital is unemployed to the same extent as labor) recognizes that the observed capital stock is not the equilibrium quantity to which the production function refers, but it seems an inadequate way of accounting for expectations and adjustment lags in capital stock decisions. Also, if lagged adjustment characterizes the labor input so that labor, like capital, is a partially fixed factor, then labor input (employment) should also be corrected for utilization. The procyclical behavior of labor productivity suggests that this is the case. A second shortcoming of many direct estimates of the production function is that they ignore information contained in marginal productivity conditions. This information can usually be summarized in a so-called expansion path equation, i.e., an equation relating the ratio of desired factor inputs to the ratio of their prices. If the production function is estimated independently of the expansion path equation, the estimates will be statistically inconsistent. For this reason, among others, the expansion path is sometimes estimated first, and the information so obtained is then used in *This research was supported by National Science Foundation Grant No. GS1686. The authors wish to acknowledge the assistance of Richard Freeman, Margaret Simms, and Robert Willig on much of the computational work. A preliminary version of the paper was read at the Winter Meetings of the Econometric Society, December 28, 1968. We are indebted to Sherwin Rosen for his constructive suggestions, especially as concerns the clarification of our hypotheses on the adjustment process.

W ITH a number of recent empirical studies presenting evidence in support of the embodiment hypothesis, the vintage aggregate production function appears to be a well established alternative to the aggregate production function which has only disembodied technical progress.' However, this evidence is not wholly satisfactory since the estimation methods used relied upon the conditional estimation of certain crucial parameters of the production function given the values of other (equally important) parameters. It is shown in this paper that for the Cobb-Douglas vintage production function an identification problem arises that may cause serious biases in the estimated parameters if conditional estimation techniques are used with the wrong values of the parameters that are given. A further disquieting aspect of this evidence is that sometimes the parameter that is given is the rate of embodied technical progress which is usually the parameter through which the embodied hypothesis is expressed. In these cases no standard error may be attached to the rate of embodied technical progress and so no direct test of the embodiment hypothesis may be made. A more reliable test of the embodiment hypothesis would be one that is based upon unconditional estimates of the parameters of the vintage production functions and their standard errors. In this paper an attempt is made to obtain such estimates using nonlinear estimation methods. Although the estimates derived are not completely free from conditioning assumptions they do indicate that once cyclical movements in output are adequately treated their evidence alone is not sufficient to support the embodiment hypothesis. Put another way, annual time series data for the United States 1900-1960 do not permit us to distinguish between a vintage Cobb-Douglas production function with a rather high rate of embodied technical progress and one with a very low rate.