Twentieth century shocks, trends and cycles in industrialized nations

Using annual data on real Gross Domestic Product per capita of seventeen industrialized nations in the twentieth century the empirical relevance of shocks, trends and cycles is investigated. A class of neural network models is specified as an extension of the class of vector autoregressive models in order to capture complex data patterns for different countries and subperiods. Empirical evidence indicates nonlinear positive trends in the levels of real GDP per capita, time varying growth rates, switching behavior of individual countries with respect to their position in the distribution of real GDP per capita levels over time and club behavior with respect to convergence. Such evidence presents great challenges for economic modelling, forecasting and policy analysis in the long run

On Bayesian structural inference in a simultaneous equation model

Econometric issues that are considered fundamental in the development of Bayesian structural inference within a Simultaneous Equation Model are surveyed. The difficulty of specifying prior information which is of interest to economists and which yields tractable posterior and predictive distributions has started this line of research. A major issue is the nonstandard shape of the likelihood due to reduced rank restrictions. It implies that existence of structural posterior moments under vague prior information is a nontrivial issue. The problem is illustrated through simple examples using artificially generated data in a so-called limited information framework where the connection with the problem of weak instruments in classical econometrics is also described. A positive development is Bayesian inference of implied characteristics, in particular, dynamic features of a Simultaneous Equation Model. The potential of Bayesian structural inference, using a predictive approach for prior specification and using Monte Carlo simulation techniques for computational purposes, is illustrated by means of a prior and posterior analysis of the US business cycle in the period of the depression. A structural prior is elicited through investigation of the implied predictive features

Tinbergen, Jan (1903-1994)

Jan Tinbergen was the first Nobel Laureate in economics in 1969. This article presents a brief survey of his many contributions to economics, in particular to macroeconometric modelling, business cycle analysis, economic policymaking, development economics, income distribution, international economic integration and the optimal regime. It further emphasizes his desire to contribute to the solution of urgent socio-economic problems and his passion for a more humane world

Jan Tinbergen (1903-1994)

Jan Tinbergen was the first Nobel Laureate in Economics in 1969. This paper presents a brief survey of his many contributions to economics, in particular to macro-econometric modelling, business cycle analysis, economic policy making, development economics, income distribution, international economic integration and the optimal regime. It further emphasizes his desire to contribute to the solution of urgent socio-economic problems and his passion for a more humane world

Evidence on a Real Business Cycle Model with Neutral and Investment-Specific Technology Shocks using Bayesian Model Averaging

The empirical support for a real business cycle model with two technology shocks is evaluated using a Bayesian model averaging procedure. This procedure makes use of a finite mixture of many models within the class of vector autoregressive (VAR) processes. The linear VAR model is extended to permit cointegration, a range of deterministic processes, equilibrium restrictions and restrictions on long-run responses to technology shocks. We find support for a number of the features implied by the real business cycle model. For example, restricting long run responses to identify technology shocks has reasonable support and important implications for the short run responses to these shocks. Further, there is evidence that savings and investment ratios form stable relationships, but technology shocks do not account for all stochastic trends in our system. There is uncertainty as to the most appropriate model for our data, with thirteen models receiving similar support, and the model or model set used has signficant implications for the results obtained

Testing for integration using evolving trend and seasonal models: A Bayesian approach

In this paper, we make use of state space models to investigate the presence of stochastic trends in economic time series. A model is specified where such a trend can enter either in the autoregressive representation or in a separate state equation. Tests based on the former are analogous to Dickey-Fuller tests of unit roots, while the latter are analogous to KPSS tests of trend-stationarity. We use Bayesian methods to survey the properties of the likelihood function in such models and to calculate posterior odds ratios comparing models with and without stochastic trends. We extend these ideas to the problem of testing for integration at seasonal frequencies and show how our techniques can be used to carry out Bayesian variants of either the HEGY or Canova-Hansen test. Stochastic integration rules, based on Markov Chain Monte Carlo, as well as deterministic integration rules are used. Strengths and weaknesses of each approach are indicated

A Bayesian analysis of the PPP puzzle using an unobserved components model

The failure to describe the time series behaviour of most real exchange rates as temporary deviations from fixed long-term means may be due to time variation of the equilibria themselves, see Engel (2000). We implement this idea using an unobserved components model and decompose the observations on real exchange rates in long-term components, which capture the time-variation of the mean and in medium and short-term components which measure temporary deviations. A simulation-based Bayesian analysis is introduced to compute the posterior distribution of (functions) of the model parameters. A stationarity test in this setup indicates that the mean is slowly time-varying. Subsequently, we use our flexible model to derive the implied distributions of some key features of real exchange rates. Most notably, the half-life of deviations from the mean, which is a measure of persistence, is lowered. This provides a possible explanation for the PPP puzzle

Divergent Priors and well Behaved Bayes Factors

Divergent priors are improper when defined on unbounded supports. Bartlett's paradox has been taken to imply that using improper priors results in ill-defined Bayes factors, preventing model comparison by posterior probabilities. However many improper priors have attractive properties that econometricians may wish to access and at the same time conduct model comparison. We present a method of computing well defined Bayes factors with divergent priors by setting rules on the rate of diffusion of prior certainty. The method is exact; no approximations are used. As a further result, we demonstrate that exceptions to Bartlett's paradox exist. That is, we show it is possible to construct improper priors that result in well defined Bayes factors. One important improper prior, the Shrinkage prior due to Stein (1956), is one such example. This example highlights pathologies with the resulting Bayes factors in such cases, and a simple solution is presented to this problem. A simple Monte Carlo experiment demonstrates the applicability of the approach developed in this paper

The value of structural information in the VAR model

Economic policy decisions are often informed by empirical economic analysis. While the decision-maker is usually only interested in good estimates of outcomes, the analyst is interested in estimating the model. Accurate inference on the structural features of a model, such as cointegration, can improve policy analysis as it can improve estimation, inference and forecast efficiency from using that model. However, using a model does not guarantee good estimates of the object of interest and, as it assigns a probability of one to a model and zero to near-by models, takes extreme zero-one account of the "weight of evidence" in the data and the resarcher's uncertainty. By using the uncertainty associated with the structural features in a model set, one obtains policy analysis that is not conditional on the structure of the model and can improve efficiency if the features are appropriately weighted. In this paper tools are presented to allow for unconditional inference on the vector autoregressive (VAR) model. In particular, we employ measures on manifolds to elicit priors on subspaces defined by particular features of the VAR model. The features considered are cointegration, exogeneity, deterministic processes and overidentification. Two applications -- money demand in Australia, and a macroeconomic model of the UK proposed by Garratt, Lee, Persaran, and Shin (2002) are used to illustrate the feasibility of the proposed methods

Efficient estimation of income distribution parameters

The parameters of several families of distributions are estimated by means of minimum χ2; use is made of random samples taken from Dutch income-earning groups in 1973. The numerical search routine used, is the Complex method due to Box. The χ2 function is evaluated by standard numerical integration procedures. The lognormal and the Gamma families are rejected because of a poor fit. The log t and the log Pearson IV families are introduced. This results in a considerable improvement of χ2 critical levels. The generalized Gamma and the Champernowne function describe the income distribution reasonably well in some cases