Knowledge that Transforms

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

In a recent article in this journal, Professors Sinai and Stokes (1972) presented a very interesting test of the hypothesis that money enters the production function, and they suggest that real balances could be a missing variable that has contributed to the unexplained 'residual' being attributed to technological The theory of induced innovation, as presented by Fellner (1961) and Schmookler (1966), suggests that market conditions affect the demand for innovation and the realized technological changes. Since money may be regarded as a proxy for short-run fluctuations in the aggregate demand, this theory suggests that money affects output and technological changes as a demand factor rather than as a factor of production. In this note, we suggest the appropriate tests to distinguish between the two alternative hypotheses, and present some empirical results.

Parts II-IV of [1] are concerned with the simple case where there is a one-to-one-to-one relationship between private goods, public goods and final goods. Section V attempts to generalize the analysis in this respect by allowing for the fact that it will typically be the case that a private or a public good enters into several production functions for final goods. Let there be n final goods, q private goods and t public goods, and consider the following two alternative versions of consumers' production functions for final goods:

K-equilibrium concept 3/ The existence of a K-equilibrium V -EFFICIENCY PROPERTIES OF K-EQUILIBRIUM 1/ The criterion 2/ Properties of a K-equilibrium 3/ Inefficiency and multiplier effects 4/ The cause of inefficiency VI -AM EXA/vlPLE 1/ The economy 2/ Computation of equilibrium transactions

Puerto Rico's transformation from a preindustrial to an industralized economy in the period 1948-63 provides an opportunity to measure the impact of technological change on several basic parameters in a Marxian economic framework. The rate of surplus value (estimated using the Morishima-Seton transformation) remains relatively stable at 0.97 in 1948 and 0.93 in 1963, while the organic composition falls from 2.75 to 2.09. The stability in the rate of surplus value results from a 63 percent average fall in labor values counterbalanced by a 143 percent rise in labor's consumption. The rate of surplus value, when adjusted for trade flows, jumps to 1.31 in 1948 and 1.18 in 1963, due to Puerto Rico's large balance-of-trade deficit and the relative import intensity of labor's consumption.

A reduced-form equation relating length of "formal schooling" to market, endowment, and ability parameters was derived for a life-cycle human capital accumulation model with alternative assumptions: (a) equal borrowing and lending rates and (b) no loans for human capital investment. Length of "formal schooling" increases when loans are unavailable. For both cases, length of "formal schooling" varies directly with length of work life, a Hicks-neutral "ability" index, and the ratio of the human capital rental rate to the price of associated inputs, and varies inversely with the discount rate, deterioration rate, and initial human capital stock.

The demand for index bonds by households is studied in an inter-temporal optimization model in which households can choose a portfolio consisting of equity, nominal bonds, and index bonds. The rate of inflation is uncertain. In a setting where all income is from capital gains, it is shown that index bonds command a premium over nominal bonds only if equity is not a hedge against inflation; it is also shown that, if there are homogeneous expectations and no outside bonds, all lending and borrowing will be through index bonds with no nominal bonds existing. These conclusions are modified when individuals have income from human capital. The very stringent conditions under which a single index bond provides the household with the same utility as a full set of futures markets are examined in a model with many consumption goods.

This paper develops a theoretical example of a business cycle, that is, a model economy in which real output undergoes serially correlated movements about trend which are not explainable by movements in the availability of factors of production. The mechanism generating these movements involves unsystematic monetary-fiscal shocks, the effects of which are distributed through time due to information lags and an accelerator effect. Associated with these output movements are procyclical movements in prices, procyclical movements in the share of output devoted to investment, and, in a somewhat limited sense, procyclical movements in nominal rates of interest.

Significance Tests of the Future and Past Lag Partitions for Regressions Based on Real GNP, Ml, M2, and MB 10 8 8. Tests of the Homogeneity of Coefficients for Regressions Based on Real GNP and Ml, M2, and MB 110 9. Summary of OLS and JLS Regressions Based on the GNP Price Deflator, Ml, M2, and MB ... .Ill 10.Significance Tests of the Future and Past Lag Partitions for Regressions Based on the GNP Price Deflator, Ml, M2, and MB 112 11.Tests of the Homogeneity of Coefficients for Regressions Based on the GNP Price Deflator and Ml, M2, and MB 113 V CHAPTER I