Strict Version Research Articles

The dichotomization theory for differential autonomic responsivity reconsidered.

ABSTRACTThe effect of the serial position of a relevant (chosen) stimulus on the differential skin conductance response evoked by it was investigated. One hundred and three subjects were tested in four experimental conditions in which they were presented with a verbal sequence of 8 numbers, one of which they had previously chosen. It was found that differential responsivity decreased as a function of the serial position of the chosen number. This finding contrasts with a strict version of the dichotomization theory. A modified version of this theory was suggested to account for the present finding, as well as for previously reported results. It focuses on the different attributes of the stimuli. It states that habituation to a stimulus is dependent on the frequency with which attributes of the stimulus were presented either as components of the stimulus or as components of other stimuli.

Structural Lags and Stability in International Macromodels

One of the features of many popular international macromodels that is troublesome is their apparent sensitivity to very slight changes in assumptions and intial conditions. This is especially the case for models with an asset sector in which hodlings depend on the instantaneous expected rate of change of a variable, such as the exchange rate, and in which asset holders are taken to exhibit "myopic perfect foresight" in making their forecasts. Typically these models are only conditionally stable -- i.e., if they are distrubed from equilibrium, some free variable (often the current exchange rate) must accomplish a discrete, exactly correct jump so as to put the system on its unique stable trajectory to the new equilibrium. In the strict version of these models, even the slightest deviation from this path or the smallest error in this jump will lead -- in the absence of the intervention or other bounds of the system -- to its collapse through an explosive movement of the exchange rate and other related variables.

Separatrices and solitary periodic solutions

A separatrix trajectory of a general solution to an ordinary differential equation is one which differs topologically from near by trajectories. Maximal regions of parallel flow are separated by a union of separatrices. The structure of these solutions has been a useful tool in the qualitative theory, especially in the plane (see, for example, [‘2, 6, 71). We will consider the separatrix structure of a flow near a solitary periodic solution in 3-space (cf. [Sj). A periodic orbit y is solitary if it has a compact neighborhood (neighborhood of solitude) G such that any negative (respectively, positive) semitrajectory contained in i? has its 4imit (resp., w-limit) at y. Within a neighborhood of solitude, trajectories are distinguished by their eventual behavior in time. For those sets of trajectories which are elhptic, that is, are contained in L’ and hence have CLand w-limit at y, an analysis of separatrix structure in a slightly different situation has already been set forth [a]. Our interest here will be primarily in the set &I+ of positively attracted trajectories, i.e.,. those which have w-limit at y, but leave U in the negative time direction. In contrast with the situation in two-dimensional settings, where each separatrix trajectory is thought of as separating two canonical regions, our analysis of separatrix structure must be concerned with connected components of the union of all separatrices. Thus, whereas a study of a planar flow is concerned with the geometry of individual trajectories, we must concern ourselves with the geometry of “surfaces” of separatrices. In general, these surfaces may be quite different from manifolds, even for C” flows. Our approach here is to restrict attention to those flows whose separatrix sets satisfy some kind of “manifold hypothesis.” We will also demand that no positive semitrajectory with initial state in the boundary of A !be internally tangent to the boundary of the neighborhood of solitude. Under a strict version of these hypotheses, a classification of regions of 9, is given by boundary type.

An Alternative Econometric Approach to the Permanent Income Hypothesis: An International Comparison

PpTHE theory of aggregative consumption function has undergone several developments since Kuznets' [27] saving-income estimates for the United States showed disagreement with Keynes' [ 2 1 ] fundamental psychological rule. Noteworthy among these developments are the Relative Income Hypothesis [10] the Life-Cycle Hypothesis [33] and the Permanent Income Hypothesis [ 13 ]. Although these different hypotheses are rather complementary yet the Permanent Income Hypothesis (PIH) has been more widely studied than the others. According to the PIH, measured income and consumption are composed of two components permanent and transitory. Under the assumption of zero correlation between transitory and permanent and also between the two transitory components, postulates that permanent consumption constitutes a constant proportion of permanent income. The basic concepts of permanent income and consumption, although theoretically attractive, involved considerable difficulties in regard to their measurability. This stimulated a number of debates and empirical researches. Some corroborated the PIH, while others showed a strong disagreement over some of its major assumptions. A close investigation of these debates and researches suggests that Friedman's own proposal to use Cagan's [7] distributed lag scheme, as one of the alternatives for constructing an estimate of permanent income in time series studies, has perhaps invited more troubles than actually solved. Clearly, does not allow for a separation of the permanent and transitory components from the observed data.' It is not surprising then that Laumas [28] and Choudhury [8] can obtain significant marginal propensities to consume transitory income for Canada and India respectively, and that Walters [41] can show a relationship between transitory and permanent income. A cursory look at such studies may sometimes shatter the faith in the strict version of the PIH but if one studies them more carefully one feels inclined to speak with Ovid it often happens that the material is better than the workmanship. The purpose of the present paper is two-fold: first, to improve upon the workmanship and second, to investigate whether the PIH is applicable to economies with different structures. The improvement in the 'workmanship' lies in the application of Nonlinear Iterative Least Squares (NILES) procedure 2 to estimate the coefficient of proportionality when both permanent income and consumption are unknown. The advantages of this method over the commonly used Ordinary Least Squares procedure are that overcomes the problem of identification in the consumption function arising from the nonlinearity of parameters and that yields individual estimates of the parameters with least squares properties. In addition to this, is computationally more convenient than other nonlinear procedures. This method has been applied on the one hand to the existing approach in which the estimate of permanent income has been defined in terms of Cagan's distributed lag scheme, and on the other hand to an alternative approach in which considers the PIH on the lines of the classical two-variables linear model where both variables are subject to errors of observation. In neither case do we violate any of Friedman's assumptions. The advantage of the second approach lies in the fact that the estimation of permanent income does not require any extraneous informa* The authors would like to express their gratitude to Professors A. R. Dobell, S. J. Turnovsky and T. A. Wilson for constructive criticism and encouragement, and to the referee for helpful comments on an earlier draft of this paper. Needless to say, the responsibility for any errors lies with the authors alone. 'Singh [38], pp. 3-6. 2For the NILES procedure see Wold [43], pp. 433-434 and 438-440.

Poincaré Recurrences

In connection with the tracing of the origin of the apparent irreversibility exhibited by a class of simple mechanical systems, namely all multiply or conditionally periodic Hamilton-Jacobi systems, estimates are obtained for the Poincar\'e recurrence time of such a system in terms of the preassigned limits of error of the mechanical recurrence, $\ensuremath{\epsilon}$. By applying the theory of diophantine approximations, the asymptotic fraction of the time a system spends in such recurrences is found exactly. These results allow further deductions concerning the fraction of time a given system obeys a strict version of the second law of thermodynamics, as well as the existence and order of magnitude of the average Poincar\'e recurrence time of a Gibbsian ensemble of such systems whose degrees of freedom are indistinguishable.The relation of the results obtained for this important class of mechanical systems and the resolution of the paradoxes of heat theory propounded by Zermelo, Loschmidt, etc., due to Boltzmann and von Smoluchowski, is discussed. An especially easily visualized model, the one-dimensional gas of hard spheres, is treated, in particular, in some detail.