Knowledge that Transforms

Much attention has been devoted to the peculiar behavior of the unemployment rate from 1969 to 1973.

Thomas F. Morrisey, A Model of Federal Home Loan Bank System and Federal National Mortgage Association Behavior--A Comment, The Review of Economics and Statistics, Vol. 57, No. 1 (Feb., 1975), pp. 121-123

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Herriott, R. E., and A. I. Kohen, On the Pooling of Mental Ability Measures for Different Tests: A Pragmatic Approach (unpublished paper which appears in Appendix A of Kohen, 1973).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A. I., Determinants of Early Labor Market Success Among Young Men: Race, Ability, Quantity and Quality of Schooling (unpublished Ph.D. thesis, Ohio State University, 1973).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).