Full-information estimates of a nonlinear macroeconometric model

Results of estimating a large-scale, nonlinear macroeconometric model by full-information maximum-likelihood, nonlinear three-stage least squares, and nonlinear two-stage least squares are reported in this paper. The computation of the estimates is first discussed, and then the differences among the estimates are examined.     

Almost unbiased estimation in multiplicative models

In the lognormal linear models the estimation of constant term presents problems. In this paper we use weighted jackknife procedure (suggested by Hinkley 1977) for reducing the bias of the maximum likelihood estimator. The resulting estimator is unbiased upto order (1/T),T being the number of observations, and has the same MSE as that of the MLE to the same order of approximation; moreover, being the jackknife estimator it enjoys all the desirable large sample properties like any other jackknife estimator. The research of this author is partially supported through a research grant from NSERC of Canada.     

Median unbiased estimates for M.L.R.-families

Summary Lehmann [p. 83] has shown that some families of probability measures with monotone likelihood ratios (m.l.r.) admit median unbiased estimates which are optimum in the sense that among all median unbiased estimates they minimize the expected loss for any loss function which assumes its minimal value zero for the “true” parameter value and is nondecreasing as the parameter moves away from the true value in either direction. This very strong optimum property was proved under the assumption that all probability measures of the m.l.r.-family have continuous distribution functions, that they are mutually absolutely continuous and that each element of the support is the median of somep-measure of the family. This result does therefore not cover important cases such as the binomial families or thePoisson family. The purpose of the present paper is to show the existence ofrandomized median unbiased estimates with the same optimum property for m.l.r.-families which are closed and connected with respect to the strong topology. Such families are always dominated. We do, however, neither assume that thep-measures are mutually absolutely continuous nor that the distribution functions are continuous. We remark that the use of randomized estimates is indispensable here because nonrandomized median unbiased estimates do not always exist in the general case.     

Differences in the properties of large-scale macroeconometric models: The role of labour market specifications

This paper examines important differences in simulation properties of four leading UK macroeconometric models that arise from features of their labour market specifications. Econometric evaluation of model equations and their subsequent re-specification, together with sensitivity analysis of simulation results, explains and resolves differences in overall model properties. The examples cover the determination of non-manufacturing employment, the modelling of employment, unemployment and the working population, and the effect of the retention ratio on wage determination. Increased attention to systematic comparison and testing leads to increased convergence of model simulation results or, as second best, increased understanding of the reasons for divergence.     

Automatic leading indicators versus macroeconometric structural models: A comparison of inflation and GDP growth forecasting

This paper compares the forecast performance of automatic leading indicators (ALIs) and macroeconometric structural models (MESMs) commonly used by non-academic macroeconomists. Inflation and GDP growth form the forecast objects for comparison, using data from China, Indonesia and the Philippines. ALIs are found to outperform MESMs for one-period-ahead forecasts, but this superiority disappears as the forecast horizon increases. It is also found that ALIs involve greater uncertainty in choosing indicators, mixing data frequencies and utilizing unrestricted VARs. Two ways of reducing the uncertainty are explored: (i) give theory priority in choosing indicators, and include theory-based disequilibrium shocks in the indicator sets; and (ii) reduce the VARs by means of the general-to-specific modeling procedure.     

Computing equilibria in dynamic models with occasionally binding constraints

We propose a method to compute equilibria in dynamic models with several continuous state variables and occasionally binding constraints. These constraints induce non-differentiabilities in policy functions. We develop an interpolation technique that addresses this problem directly: It locates the non-differentiabilities and adds interpolation nodes there. To handle this flexible grid, it uses Delaunay interpolation, a simplicial interpolation technique. Hence, we call this method Adaptive Simplicial Interpolation (ASI). We embed ASI into a time iteration algorithm to compute recursive equilibria in an infinite horizon endowment economy where heterogeneous agents trade in a bond and a stock subject to various trading constraints. We show that this method computes equilibria accurately and outperforms other grid schemes by far.     

Confidence statements for efficiency estimates from stochastic frontier models

This paper is an empirical study of the uncertainty associated with technical efficiency estimates from stochastic frontier models. We show how to construct confidence intervals for estimates of technical efficiency levels under different sets of assumptions ranging from the very strong to the relatively weak. We demonstrate empirically how the degree of uncertainty associated with these estimates relates to the strength of the assumptions made and to various features of the data.     

Two kinds of variance/covariance estimates in linear mixed models

For longitudinal data, the within-subject covariance matrix plays an important role in statistical inference and it is of great interest to investigate this. In the paper, two kinds of estimators are investigated for the random effect covariance matrix D ₁ and the error variance σ ² in linear mixed models. One is to estimate D ₁ first and then to estimate σ ²; the other kind is to estimate σ ² first and then for D ₁. Both kinds of estimators are consistent. The covariance matrices of these covariance estimators and the variances of these two error variance estimators are calculated. In particular, the mean square errors of these estimators are also derived for one dimensional random effects. Besides, a simulation study is conducted to investigate the performances of these estimators.     

A Monte Carlo study of ranked efficiency estimates from frontier models

Parametric stochastic frontier models yield firm-level conditional distributions of inefficiency that are truncated normal. Given these distributions, how should one assess and rank firm-level efficiency? This study compares the techniques of estimating (a) the conditional mean of inefficiency and (b) probabilities that firms are most or least efficient. Monte Carlo experiments suggest that the efficiency probabilities are easier to estimate (less noisy) in terms of mean absolute percent error when inefficiency has large variation across firms. Along the way we tackle some interesting problems associated with simulating and assessing estimator performance in the stochastic frontier model.     

On existence and uniqueness of maximum likelihood estimates in quantal and ordinal response models

Summary For quantal and ordinal response models, conditions on existence and uniqueness of maximum likelhood estimates are presented. Results are derived from general results on direction sets and spaces associated with a proper concave function. If each summand of the log likelihood is in any direction either strictly concave or affine, necessary and sufficient conditions are obtained. If all cell counts are strictly positive, then it is shown that estimates always exist, and that they are unique if all parameters are identifiable. If estimates exist without being unique, results on uniquely estimable linear functions are given, paralleling corresponding results in linear regression. An extension of the maximum likelihood principle is outlined yielding similar results even if the likelihood does not attain its supremum. The logit model, the linear probability model, cumulative and sequential models and binomial response models are considered in detail.     

The limit distribution of the estimates in cointegrated regression models with multiple structural changes

We study estimation and inference in cointegrated regression models with multiple structural changes allowing both stationary and integrated regressors. Both pure and partial structural change models are analyzed. We derive the consistency, rate of convergence and the limit distribution of the estimated break fractions. Our technical conditions are considerably less restrictive than those in Bai et al. [Bai, J., Lumsdaine, R.L., Stock, J.H., 1998. Testing for and dating breaks in multivariate time series. Review of Economic Studies 65, 395–432] who considered the single break case in a multi-equations system, and permit a wide class of practically relevant models. Our analysis is, however, restricted to a single equation framework. We show that if the coefficients of the integrated regressors are allowed to change, the estimated break fractions are asymptotically dependent so that confidence intervals need to be constructed jointly. If, however, only the intercept and/or the coefficients of the stationary regressors are allowed to change, the estimates of the break dates are asymptotically independent as in the stationary case analyzed by Bai and Perron [Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78]. We also show that our results remain valid, under very weak conditions, when the potential endogeneity of the non-stationary regressors is accounted for via an increasing sequence of leads and lags of their first-differences as additional regressors. Simulation evidence is presented to assess the adequacy of the asymptotic approximations in finite samples.     

On the existence of maximum likelihood estimates in random effects models for clustered multivariate binary data

We consider a class of random effects models for clustered multivariate binary data based on the threshold crossing technique of a latent random vector. Components of this latent vector are assumed to have a Laird–Ware structure. However, in place of their Gaussian assumptions, any specified class of multivariate distribution is allowed for the random effects, and the error vector is allowed to have any strictly positive pdf. A well known member of this class of models is the multivariate probit model with random effects. We investigate sufficient and necessary conditions for the existence of maximum likelihood estimates for the location and the association parameters. Implications of our results are illustrated through some hypothetical examples.     

A financial accelerator in the business sector of a macroeconometric model of a small open economy

We have incorporated a financial accelerator mechanism operating through investments in the business sector in a dynamic macroeconometric model of the Norwegian economy. In this new and amended model aggregated credit and equity prices are determined simultaneously in a system characterized by a two-directional contemporaneous causal link, which has been designed and estimated by a new procedure for simultaneous structural model design. Combined with a mechanism where credit and asset prices are mutually influenced by real investments, this creates a financial accelerator amplified by a credit-asset price spiral. Simulations illustrate how the introduction of a financial accelerator significantly reinforces and extends the economic cycles in projections and forecasts, in particular when confronted by a severe shock. Furthermore, monetary policy has a markedly stronger effect in the short and medium term, while the impact of fiscal policy is affected to a relatively small degree as it is more remotely linked to financial markets.     

Locally minimum variance unbiased estimator in a discontinuous density function

The exact forms of the locally minimum variance unbiased estimators and their variances are given in the case of a discontinuous density function.