Knowledge that Transforms

OCCASIONALLY IN EMPIRICAL WORK, a highly insignificant test statistic is encountered. A rule that the null hypothesis not be rejected when the value of a statistic falls below a threshold which is given by the tester's desired Type I error probability 8 < implies a fortiori that the null is not rejected when the probability that the statistic is smaller than the realized value is less than 8. We suggest an interpretation of this outcome in time series problems. For ease of exposition we focus on the usual F-ratio which tests that an intercept or a slope coefficient of a trending explanatory variable is zero, though similar results hold more generally. Conditions are given such that the F-ratio converges in probability to zero when the disturbances are I(d) for some d <0. A covariance stationary I(d) process is defined to have spectral density f(A) = 11 - eiA 2dg(A), where 0 <g(O) < oo. The I(d), d < 0, processes include noninvertible ones (that is, ones for which d S due possibly to misguided differencing of a stationary I(d + 1) series, where d < The I(d), d < 0, processes also include invertible ones (when - 2 <d < 0) which integrate to nonstationary series. With a suitable regression specification, the F-ratio will be seen to provide a consistent diagnostic for departures from unit root behavior in the direction of stationarity or less-nonstationarity. It has less power than many unit root tests, but has attractive features not all shared by these: it is exact in the Gaussian case and approximately valid more generally; it is a diagnostic which a regression package may automatically print out; it is compared with a null distribution of standard type; its critical regions are independent of explanatory variables. Like the usual unit root tests it can be robustified in large samples to permit short- or long-memory parametric or nonparametric autocorrelation under the null. It has a Lagrange multiplier (LM) interpretation against stationary autoregressive alternatives. The zero at the origin of the disturbance spectrum can be of fractional, as well as unit, order. To provide greater generality we go beyond the I(d) class by allowing for the presence of a slowly varying function, and quite general behavior of the spectrum away from the origin. The slowly varying function is reflected in a simple way in the results. Section 2 contains preliminary results on the variance of unweighted and weighted partial sums. In Section 3 these are applied to obtain either an exact rate or an upper bound for the F-ratio, and unit root testing implications are explored. The proofs are in appendices.

This paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function, where this function can be characterized by an index. The estimator is shown to be consistent, asymptotically normally distributed, and to achieve the semiparametric efficiency bound. Monte-Carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known, and that the small-sample behavior of the estimator in other cases is good.

This paper specifies and empirically analyzes a continuous-time, linear-quadratic, representative consumer model wit h time-nonseparable preferences of several forms. Within this framewor k, the author shows how time aggregation and time nonseparabilities in preferences over consumption streams can interact. The behavior of b oth seasonally adjusted and unadjusted consumption data is consistent wi th time-nonseparable preferences if consumption goods are durable and i f individuals develop habit over the flow of services from the good. T he data do not support a version of the model that ignores time nonseparabilities in preferences and focuses solely upon time aggregation. Copyright 1993 by The Econometric Society.

This paper reports estimates of the primitive parameters of a stochastic control model describing the labor decisions of West African small farmers. Maximum likelihood estimates are computed although optimal labor decision rules cannot be derived analytically. Vuong's non-nested model specification test shows that this method yields estimates superior to those derived by assuming that farmers solve a deterministic control problem. Low levels of labor effort are shown to be a consequence of low labor productivity in archaic rain-fed agriculture and of farmers' awareness that, in the absence of a labor market, overly ambitious production plans lead to seasonal manpower shortages.

Stefan Mittnik, Peter A. Zadrozny, Asymptotic Distributions of Impulse Responses, Step Responses, and Variance Decompositions of Estimated Linear Dynamic Models, Econometrica, Vol. 61, No. 4 (Jul., 1993), pp. 857-870

This paper discusses the dynamic implications of learning in a large population coordination game, focusing on the structure of the matching process which describes how players meet.As in Kandori, Mailath, and Rob (1993) a combination of experimentation and myopia creates "evolutionary" forces which lead players to coordinate on the risk dominant equilibrium.To describe play with finite time horizons it is necessary to consider the rates at which the dynamic systems converge.In large populations with uniform matching, play is determined largely by historical factors.In contrast, when players interact with small sets of neighbors it is more reasonable to assume that evolutionary forces may determine the outcome.

In a decision-theoretic model of a firm, the author represents managers as information processors of limited capacity; efficiency is measured in terms of (1) the number of processors and (2) the delay between the receipt of information by the organization and the implementation of the decision. The author characterizes efficient networks for both one-shot and repeated regimes, as well as the corresponding 'production function' relating the number of items processed to the number of processors and the delay. He sketches some applications to common decision paradigms, and implications for decentralization and organizational returns to scale. Copyright 1993 by The Econometric Society.

A system of consumer expenditure functions is estimated from Norwegian household budget data. Specific features o f our approach are: (I) Panel data on individual households are used, which offer far richer opportunities for identification, estimation and testing than usual cross section data. (II) Measurement errors are carefully modelled. Total consumption expenditure is modelled as a latent variable, purchase expenditures on different goods and two income measures are used as indicators of this basic latent variable. (III) The distribution of latent total expenditure across households, and its evolution over time, is estimated and important properties tested. (IV) Individual differences in preferences, represented by individual, time invariant latent variables, are modelled, identified, estimated, and tested. (V) We test the hypothesis that preferences are uncorrelated with total consumption expenditure, which is basic to all cross section estimation of consumer demand functions. (VI) The model can be formalized as a special case of the LISREL model, and the maximum likelihood algorithm of the computer program LISREL VI is applied.

The authors design and study an OLG experimental economy where the government finances a fixed real deficit through seigniorage. The economy has continua of nonstationary rational expectations equilibria and two stationary rational expectations equilibria. The authors do not observe nonstationary rational expectations paths. Observed paths tend to converge close to, or somewhat below, the low inflation stationary state. The adaptive learning hypothesis is consistent with the data in selecting the low inflation stationary state rational expectations equilibrium as a long-run stationary equilibrium. Nevertheless, simple adaptive learning models do not capture the market uncertainty or the biases observed in the data. Copyright 1993 by The Econometric Society.

We analyze an evolutionary model with a finite number of players and with noise or mutations.The expansion and contraction of strategies is linked-as usual-to their current relative success, but mutations-which perturb the system away from its deterministic evolution-are present as well.Mutations can occur in every period, so the focus is on the implications of ongoing mutations, not a one-shot mutation.The effect of these mutations is to drastically reduce the set of equilibria to what we term "long-run equilibria."For 2 x 2 symmetric games with two symmetric strict Nash equilibria the equilibrium selected satisfies (for large populations) Harsanyi and Selten's (1988) criterion of risk-dominance.In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium.