Knowledge that Transforms

Duncan, 0. D., Socioeconomic Index for All and Properties and Characteristics of the Socioeconomic Index, in Occupations and Status, A. J. Reiss, et al. (eds.), (New York: Free Press of Glencoe, 1961). Hansen, W. L., B. A. Weisbrod, and W. J. Scanlon, and Earnings of Low Achievers, American Economic Review (June 1970), 409-418. Herriott, R. E., and A. I. Kohen, On the Pooling of Mental Ability Measures for Different Tests: A Pragmatic Approach (unpublished paper which appears in Appendix A of Kohen, 1973). Johnson, E., and F. P. Stafford, Social Returns to Quantity and Quality of Schooling, Journal of Human Resources (Spring 1973), 139-155. Kohen, A. I., Determinants of Early Labor Market Success Among Young Men: Race, Ability, Quantity and Quality of Schooling (unpublished Ph.D. thesis, Ohio State University, 1973). Link, C. R., Graduate Education, School Quality, Experience, Student Ability, and Earnings, Journal of Business, University of Chicago (forthcoming). O'Neill, D. M., The Effect of Discrimination on Earnings: Evidence From Military Test Scores, Journal of Human Resources (Fall 1970), 475-486. Parnes, H. S., et al., Career Thresholds: A Longitudinal Study of the Educational and Labor Market Experience of Male Youth, vol. I, U.S. Department of Labor Manpower Research Monograph no. 16 (U.S. Government Printing Office, Washington, D.C., 1970). Reiss, A. J., et al. (eds.), Occupations and Status (New York: Free Press of Glencoe, 1961). Weiss, R. D., The Effect of Education on the Earnings of Blacks and Whites, this REVIEW, LII (May 1970), 150-159. Welch, F., Black-White Differences in Returns to Schooling, American Economic Review (Dec. 1973), 893-907.

The Problem Many discrete time series are generated by the observation of processes which are most naturally considered to be continuously changing with time, or (almost equivalently) which have a fundamental time interval of evolution which is very much smaller than the sampling interval.The case in which the sampling interval is constant has been studied at some 1ength,1 but for some important applications, the sampling intervals are not evenly spaced, and this factor adds considerable complication to analysis of the data.Consider a continuous random process X(t) which is covariance stationary, that is: E(X(t)'X(t+s)) = R(s) is a function of s only.Further, assume that X(t) is "ergodic"; namelyCondition (1) assures that time averages converge to expectations when ca1culating sample autocovariances. 2 Finally, to help simplify the analysis and notation, assume E[X(t)] = 0 Then the discrete process ... , XeD) , X(l), X(2), .. has mean zero and is stationary and "ergodic" in the sense defined.It can be analyzed by standard statistical methods, although a "simple" X(t) in continuous time may give rise to a more "complicated" process in discrete time. 3

Houthakker, H. S., and S. P. Magee, and Price Elasticities in World Trade, this REVIEW, 51 (May 1969). Leamer, E. E., and R. M. Stern, Quantitative Economics (Boston: Allyn and Bacon, 1970). Magee, S. P., Prices, Income and Foreign Trade, a paper presented at the Conference on Research in Trade and Finance, Princeton, (March 1973), forthcoming in Peter B. Kenen, editor, Trade and Finance: Frontiers for Research (Cambridge: Cambridge University Press, 1974). Marston, R., Effects and Delivery Lags in British Import Demand: 1955-67, Journal of Economics, 1 (Nov. 1971). Polak, J. J., An Economic System (Chicago: University of Chicago Press, 1953). Turnovsky, S. J., International Trading Relationships for a Small Country: The Case of New Zealand, Canadian Journal of Economics, 1 (Nov. 1968).

In an interesting paper B. Singh and H. Drost (S-D) (1971) gave two iterative methods for estimating the parameters in two different specifications of Friedman's Permanent Income Hypothesis (PIH). As to their Method I comments have been given by Rao ( 1973, p. 261 ) and Pesaran ( 1973, pp. 259261), and this method will not be taken up in this paper. It has been shown by Pesaran and the present author (1974) that (S-D) 's iterative Method II is easily solved algebraically. The iterative procedures proposed by (S-D) are applications of WAold's NIPALS (nonlinear iterative partial least squares). Furthermore (S-D)'s alternative approach is a direct application of the NIPALS modelling of an errors-in-variables model given by Wold (1966, pp. 438-439). However, as should be clear from Wold (1966, p. 439) the NIPALS procedure designed by Wold rests upon an assumption, the importance of which has been overlooked by (S-D). The contribution by Pesaran (1973) is to show the necessity of this assumption for the estimate of the marginal propensity to consume to be consistent. As has been shown by the present author, the scope of the NIPALS procedure designed by Wold (1966) is easily broadened. Retaining the definition of variables made by (S-D) we have the following model

The principal problem with previous estimates of the effect of welfare programs on labor supply' is that the specification of the labor supply equation misrepresents the intercept and slope of the budget line for low-income individuals. Labor supply has typically been posited to be a function of the market wage rate unadjusted for the welfare tax rate and other income2 including actual welfare benefits.