Knowledge that Transforms

E| Jhhuw

This paper characterizes empirically achievable limits for time series econometric modeling and forecasting. The approach involves the concept of minimal information loss in time series regression and the paper shows how to derive bounds that delimit the proximity of empirical measures to the true probability measure (the DGP) in models that are of econometric interest. The approach utilizes joint probability measures over the combined space of parameters and observables and the results apply for models with stationary, integrated, and cointegrated data. A theorem due to Rissanen is extended so that it applies directly to probabilities about the relative likelihood (rather than averages), a new way of proving results of the Rissanen type is demonstrated, and the Rissanen theory is extended to nonstationary time series with unit roots, near unit roots, and cointegration of unknown order. The corresponding bound for the minimal information loss in empirical work is shown not to be a constant, in general, but to be proportional to the logarithm of the determinant of the (possibility stochastic) Fisher–information matrix. In fact, the bound that determines proximity to the DGP is generally path dependent, and it depends specifically on the type as well as the number of regressors. For practical purposes, the proximity bound has the asymptotic form (K/2)log n, where K is a new dimensionality factor that depends on the nature of the data as well as the number of parameters in the model. When ‘good’ model selection principles are employed in modeling time series data, we are able to show that our proximity bound quantifies empirical limits even in situations where the models may be incorrectly specified. One of the main implications of the new result is that time trends are more costly than stochastic trends, which are more costly in turn than stationary regressors in achieving proximity to the true density. Thus, in a very real sense and quantifiable manner, the DGP is more elusive when there is nonstationarity in the data. The implications for prediction are explored and a second proximity theorem is given, which provides a bound that measures how close feasible predictors can come to the optimal predictor. Again, the bound has the asymptotic form (K/2)log n, showing that forecasting trends is fundamentally more difficult than forecasting stationary time series, even when the correct form of the model for the trends is known.

It has been known that, in aggregating infinite utility streams, there does not exist any social welfare function, which satisfies the axioms of Pareto, intergenerational equity, and continuity. We show that the impossibility result persists even without imposing the continuity axiom, and in frameworks allowing for more general domains of utilities than those used in the existing literature.

IN A SIMPLE DEBT CONTRACT the investor seizes all of a firm's assets when the project return is below some threshold and receives a constant payment when the return is higher. Krasa and Villamil (2000) show that simple debt contracts that are optimal (ie., give the investor the highest payoff) among the class of deterministic contracts in the costly state verification model, and that satisfy technical conditions (Al), (A2), and a reservation utility constraint, are optimal in a more general costly enforcement model even when stochastic monitoring is possible.2 The italicized segment of this statement was not made explicit in Theorem 1 in Krasa and Villamil (2000). As Sharma points out, this restriction is necessary for the result to hold. Sharma also points out that assumption (A2) had a typographical error. Assumption (A2) in Krasa and Villamil (2000) should have appeared

Recent theoretical advances have brought income and wealth distributions back into a prominent position in growth and development theories, and as determinants of specific socio-economic outcomes, such as health or levels of violence. Empirical investigation of the importance of these relationships, however, has been held back by the lack of sufficiently detailed high quality data on distributions. Household surveys that include reasonable measures of income or consumption can be used to calculate distributional measures but at low levels of aggregation these samples are rarely representative or of sufficient size to yield statistically reliable estimates. At the same time, census (or other large sample) data of sufficient size to allow disaggregation either have no information about income or consumption, or measure these variables poorly. This note outlines a statistical procedure to combine these types of data to take advantage of the detail in household sample surveys and the co...

We consider an infinite-horizon exchange economy with incomplete markets and collateral constraints.As in the two-period model of Geanakoplos and Zame (2002), households can default on their liabilities at any time, and financial securities are only traded if the promises associated with these securities are backed by collateral.We examine an economy with a single perishable consumption good, where the only collateral available consists of productive assets.In this model, competitive equilibria always exist and we show that, under the assumption that all exogenous variables follow a Markov chain, there also exist stationary equilibria.These equilibria can be characterized by a mapping from the exogenous shock and the current distribution of financial wealth to prices and portfolio choices.We develop an algorithm to approximate this mapping numerically and discuss ways to implement the algorithm in practice.A computational example demonstrates the performance of the algorithm and shows some quantitative features of equilibria in a model with collateral and default.

An isotone pure strategy equilibrium exists in any game of incomplete information in which (1) each player i's action set is a finite sublattice of multi-dimensional Euclidean space, (2) types are multidimensional and atomless, and each player's interim expected payoff function satisfies two "non-primitive conditions" whenever others adopt isotone pure strategies: (3) single-crossing in own action and type and (4) quasisupermodularity in own action.Similarly, given that ( 134) and (2') types are multi-dimensional (with atoms) an isotone mixed strategy equilibrium exists.Conditions (34) are satisfied in supermodular and log-supermodular games given affiliated types, and in games with independent types in which each player's ex post payoff satisfies (a) supermodularity in own action and (b) non-decreasing differences in own action and type.These results also extend to games with a continuum action space when each player's ex post payoff is also continuous in his and others' actions.

This paper applies revealed preference theory to the nonparametric statistical analysis of consumer demand. Knowledge of expansion paths is shown to improve the power of nonparametric tests of revealed preference. The tightest bounds on indifference surfaces and welfare measures are derived using an algorithm for which revealed preference conditions are shown to guarantee convergence. Nonparametric Engel curves are used to estimate expansion paths and provide a stochastic structure within which to examine the consistency of household level data and revealed preference theory. An application is made to a long time series of repeated cross-sections from the Family Expenditure Survey for Britain. The consistency of these data with revealed preference theory is examined. For periods of consistency with revealed preference, tight bounds are placed on true cost of living indices.

This paper develops an inferential theory for factor models of large dimensions. The principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator (if normality is assumed). We derive the rate of convergence and the limiting distributions of the estimated factors, factor loadings, and common components. The theory is developed within the framework of large cross sections ("N") and a large time dimension ("T"), to which classical factor analysis does not apply.We show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of "N" and "T". The estimated factors and their loadings are generally normal, although not always so. The convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components. These results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions. Stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic. A necessary and sufficient condition for consistency is derived for large "N" but fixed "T". Copyright The Econometric Society 2003.

In certain auction, search, and related models, the boundary of the support of the observed data depends on some of the parameters of interest. For such nonregular models, standard asymptotic distribution theory does not apply. Previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models. In contrast, we study the problem of constructing efficient point estimators. We show that the maximum likelihood estimator is generally inefficient, but that the Bayes estimator is efficient according to the local asymptotic minmax criterion for conventional loss functions. We provide intuition for this result using Le Cam's limits of experiments framework. Copyright The Econometric Society 2003.