Knowledge that Transforms

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of repetitions of past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventualitycase pairs, as follows. A memory is identified with a vector, counting the number of repetitions of each case. Multiplication of the matrix by a memory vector yields a numerical representation of the ordinal plausibility ranking given that memory. Interpreting this result for the ranking of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with their likelihood functions. 1 Introduction It is well known that inductive inference is not logically valid. As David Hume (1748) put it, "... The co...

In this paper, we propose a simple bias–reduced log–periodogram regression estimator, ^dr, of the long–memory parameter, d, that eliminates the first– and higher–order biases of the Geweke and Porter–Hudak (1983) (GPH) estimator. The bias–reduced estimator is the same as the GPH estimator except that one includes frequencies to the power 2k for k=1,…,r, for some positive integer r, as additional regressors in the pseudo–regression model that yields the GPH estimator. The reduction in bias is obtained using assumptions on the spectrum only in a neighborhood of the zero frequency. Following the work of Robinson (1995b) and Hurvich, Deo, and Brodsky (1998), we establish the asymptotic bias, variance, and mean–squared error (MSE) of ^dr, determine the asymptotic MSE optimal choice of the number of frequencies, m, to include in the regression, and establish the asymptotic normality of ^dr. These results show that the bias of ^dr goes to zero at a faster rate than that of the GPH estimator when the normalized spectrum at zero is sufficiently smooth, but that its variance only is increased by a multiplicative constant. We show that the bias–reduced estimator ^dr attains the optimal rate of convergence for a class of spectral densities that includes those that are smooth of order s≥1 at zero when r≥(s−2)/2 and m is chosen appropriately. For s>2, the GPH estimator does not attain this rate. The proof uses results of Giraitis, Robinson, and Samarov (1997). We specify a data–dependent plug–in method for selecting the number of frequencies m to minimize asymptotic MSE for a given value of r. Some Monte Carlo simulation results for stationary Gaussian ARFIMA (1, d, 1) and (2, d, 0) models show that the bias–reduced estimators perform well relative to the standard log–periodogram regression estimator.

We present estimators for nonparametric functions that are nonadditive in unobservable random terms. The distributions of the unobservable random terms are assumed to be unknown. We show that when a nonadditive, nonparametric function is strictly monotone in an unobservable random term, and it satisfies some other properties that may be implied by economic theory, such as homogeneity of degree one or separability, the function and the distribution of the unobservable random term are identified. We also present convenient normalizations, to use when the properties of the function, other than strict monotonicity in the unobservable random term, are unknown. The estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal. We extend the results to functions that depend on a multivariate random term. The results of a limited simulation study are presented.

I characterize the implications of the common prior assumption for finite orders of beliefs about beliefs at a state and show that in finite models, the only such implications are those stemming from the weaker assumption of a common support. More precisely, given any finite N and any finite partitions model where priors have the same support, there is another finite partitions model with common priors that has the same nth order beliefs and knowledge for all n≤N.

We introduce a game of complete information with multiple principals and multiple common agents. Each agent makes a decision that can affect the payoffs of all principals. Each principal offers monetary transfers to each agent conditional on the action taken by the agent. We characterize pure-strategy equilibria and we provide conditions—in terms of game balancedness—for the existence of an equilibrium with an efficient outcome. Games played through agents display a type of strategic inefficiency that is absent when either there is a unique principal or there is a unique agent.

We study the problem of the existence and uniqueness of solutions to the Bellman equation in the presence of unbounded returns. We introduce a new approach based both on consideration of a metric on the space of all continuous functions over the state space, and on the application of some metric fixed point theorems. With appropriate conditions we prove uniqueness of solutions with respect to the whole space of continuous functions. Furthermore, the paper provides new sufficient conditions for the existence of solutions that can be applied to fairly general models. It is also proven that the fixed point coincides with the value function and that it can be approached by successive iterations of the Bellman operator.

In this paper we estimate a bargaining model of government formation in parliamentary democracies. We use the estimated structural model to conduct constitutional experiments aimed at evaluating the impact of institutional features of the political environment on the duration of the government formation process, the type of coalitions that form, and their relative stability.

Cointegrated bivariate nonstationary time series are considered in a fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (2001, 2003) have justified least squares estimates of the cointegrating vector, as well as narrow-band frequency-domain estimates, which may be less biased. While consistent, these estimates do not always have optimal convergence rates, and they have nonstandard limit distributional behavior. We consider estimates formulated in the frequency domain, that consequently allow for a wide variety of (parametric) autocorrelation in the short memory input series, as well as time-domain estimates based on autoregressive transformation. Both can be interpreted as approximating generalized least squares and Gaussian maximum likelihood estimates. The estimates share the same limiting distribution, having mixed normal asymptotics (yielding Wald test statistics with χ2 null limit distributions), irrespective of whether the integration orders are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. The parameters describing the short memory stationary input series are √n-consistently estimable, but the assumptions imposed on these series are much more general than ones of autoregressive moving average type. A Monte Carlo study of finite-sample performance is included.

This paper develops new econometric methods to infer hospital quality in a model with discrete dependent variables and nonrandom selection. Mortality rates in patient discharge records are widely used to infer hospital quality. However, hospital admission is not random and some hospitals may attract patients with greater unobserved severity of illness than others. In this situation the assumption of random admission leads to spurious inference about hospital quality. This study controls for hospital selection using a model in which distance between the patient's residence and alternative hospitals are key exogenous variables. Bayesian inference in this model is feasible using a Markov chain Monte Carlo posterior simulator, and attaches posterior probabilities to quality comparisons between individual hospitals and groups of hospitals. The study uses data on 74,848 Medicare patients admitted to 114 hospitals in Los Angeles County from 1989 through 1992 with a diagnosis of pneumonia. It finds the smallest and largest hospitals to be of the highest quality. There is strong evidence of dependence between the unobserved severity of illness and the assignment of patients to hospitals, whereby patients with a high unobserved severity of illness are disproportionately admitted to high quality hospitals. Consequently a conventional probit model leads to inferences about quality that are markedly different from those in this study's selection model.