z-Transform and identification of linear econometric models with autocorrelated errors

The paper consists of two main parts. In the first part we derive the solution of systems of linear stochastic difference equations by means of thez-transform. In the second part thisz-transform is used to treat the problem of identification of linear econometric systems (the term econometric is used to stress the special aspects of the identification problem dealt with in econometrics). It is shown, that under suitable restrictions observationally equivalent structures are related by unimodular matrices. Using this result, we state (rank-) conditions which ensure, that the unimodular matrices are constant, such that the classical econometric identification theorems can be applied. These conditions are given for stationary errors in the general case as well as in the MA, AR and ARMA case.     

Estimating predictions,prediction errors and their standard deviations using constructed variables

Increasing use has been made of predictive tests for assessing model adequacy, but it is sometimes difficult to generate predictions and their standard errors in dynamic or simultaneous equation models. Following earlier suggestions by Salkever and Fuller, this paper shows how the requisite information may be obtained by the use of specially constructed variables in a regression framework. The main use of the method will be in those situations where prediction information is not available as a standard option in econometric packages.     

Polynomial operators and the asymptotic distribution of dynamic multipliers

This paper employs formal manipulations of polynomial operators with matrix coefficients to derive dynamic and long-run multipliers. The same technique is employed to derive the asymptotic distribution of these quantities in a very simple manner. Some recursion formulae are given which make the computation of the covariance matrix of the limiting distribution a relatively simple process. The Klein Model I is used to provide a numerical illustration.     

Estimating nonlinear time-series models using simulated vector autoregressions

This paper develops two new methods for conducting formal statistical inference in nonlinear dynamic economic models. The two methods require very little analytical tractability, relying instead on numerical simulation of the model's dynamic behaviour. Although one of the estimators is asymptotically more efficient than the other, a Monte Carlo study shows that, for a specific application, the less efficient estimator has smaller mean squared error in samples of the size typically encountered in macroeconomics. The estimator with superior small sample performance is used to estimate the parameters of a real business cycle model using observed US time-series data.     

Indirect inference in structural econometric models

This paper considers parametric inference in a wide range of structural econometric models. It illustrates how the indirect inference principle can be used in the inference of these models. Specifically, we show that an ordinary least squares (OLS) estimation can be used as an auxiliary model, which leads to a method that is similar in spirit to a two-stage least squares (2SLS) estimator. Monte Carlo studies and an empirical analysis of timber sale auctions held in Oregon illustrate the usefulness and feasibility of our approach.     

Forecasting economic time series using flexible versus fixed specification and linear versus nonlinear econometric models

Nine macroeconomic variables are forecast in a real-time scenario using a variety of flexible specification, fixed specification, linear, and nonlinear econometric models. All models are allowed to evolve through time, and our analysis focuses on model selection and performance. In the context of real-time forecasts, flexible specification models (including linear autoregressive models with exogenous variables and nonlinear artificial neural networks) appear to offer a useful and viable alternative to less flexible fixed specification linear models for a subset of the economic variables which we examine, particularly at forecast horizons greater than 1-step ahead. We speculate that one reason for this result is that the economy is evolving (rather slowly) over time. This feature cannot easily be captured by fixed specification linear models, however, and manifests itself in the form of evolving coefficient estimates. We also provide additional evidence supporting the claim that models which ‘win’ based on one model selection criterion (say a squared error measure) do not necessarily win when an alternative selection criterion is used (say a confusion rate measure), thus highlighting the importance of the particular cost function which is used by forecasters and ‘end-users’ to evaluate their models. A wide variety of different model selection criteria and statistical tests are used to illustrate our findings.     

An algorithm for the solution of stochastic optimal control problems for large nonlinear econometric models

This paper considers the problem of solving an optimal control problem for large dynamic economic models which are both nonlinear and stochastic. It proposes a technique which combines conventional deterministic optimal control algorithms with the procedure of stochastic simulation, which calculates a numerical approximation to the distribution of the models endogenous variables. The new technique is computationally feasible for even large nonlinear models and, as an illustration of this, the Bank of England's large quarterly forecasting model is used in an example.     

Monitoring structural change in dynamic econometric models

The classical approach to testing for structural change employs retrospective tests using a historical data set of a given length. Here we consider a wide array of fluctuation‐type tests in a monitoring situation—given a history period for which a regression relationship is known to be stable, we test whether incoming data are consistent with the previously established relationship. Procedures based on estimates of the regression coefficients are extended in three directions: we introduce (a) procedures based on OLS residuals, (b) rescaled statistics and (c) alternative asymptotic boundaries. Compared to the existing tests our extensions offer ease of computation, improved size in finite samples for dynamic models and better power against certain alternatives, respectively. We apply our methods to three data sets, German M1 money demand, US labour productivity and S&P 500 stock returns. Copyright © 2005 John Wiley & Sons, Ltd.     

The specification of multi-market disequilibrium econometric models

The specifications of multi-market disequilibrium econometric models are clouded with different notions of effective demand. This paper points out that the specification of such models for econometric analysis can be achieved from the basic concept of fixed-price equilibrium and without the use of the concepts of effective demand. The specifications of Ito and Gourieroux, Laffont and Monfort are justified within this framework. With proper stochastic elements introduced in the system, the derived likelihood function from our approach does not involve multiple integrals and is computationally tractable for models with many disequilibrium markets.     

The reconstruction of index data in aggregative econometric models

Index data become inconsistent over time when publishing agencies change the method of aggregation. However, when they do so, they often republish some previously published data using the new method. It is shown that such overlapping data can be exploited to reconstruct the data series in an ‘optimal’ manner to provide for consistent series, using results from the theory of aggregation.     

Estimation of econometric models of some discrete games

This paper discusses, estimates and compares some microeconometric models for simultaneous discrete endogenous variables. The models are based on the assumption that observed endogenous variables represent the outcome of a static discrete game. I discuss models based on non-cooperative equilibrium concepts (Nash, Stackelberg), as well as models which presume Pareto optimality of observed outcomes. The models are estimated using data on the joint labor force participation decisions of husbands and wives in a sample of Dutch households.     

The econometric analysis of models with risk terms

In this paper we have attempted to provide an integrated approach to the estimation of models with risk terms. It was argued that there exist orthogonality conditions between variables in the information set and higher-order moments of the unanticipated variable density. These could be exploited to provide consistent estimators of the parameters associated with the risk term. Specifically, it was recommended that an IV estimator should be applied, with instruments constructed from the information set. Four existing methods commonly used to estimate models with risk terms are examined, and applications of the techniques are made to the estimation of the risk term in the $US/$C exchange market, and the effects of price uncertainty upon production.     

Tourism forecasting: accuracy of alternative econometric models

This study evaluates the forecasting accuracy of six alternative econometric models in the context of the demand for international tourism in Denmark. These econometric models are special cases of a general autoregressive distributed lag specification. In addition, the forecasting accuracy of two univariate time series models is evaluated for benchmark comparison purposes. The forecasting competition is based on annual data on inbound tourism to Denmark. Individual models are estimated for each of the six major origin countries over the period 1969–93 and forecasting performance is assessed using data for the period 1994–97. Rankings of these forecasting models over different time horizons are established based on mean absolute percentage error and root mean square percentage error.     

The numerical values of some key parameters in econometric models

In the case of two endogenous variables, exogenous predetermined variables, and normally distributed disturbances, the distributions of the Two-Stage Least Squares (TSLS) and Limited Information Maximum Likelihood (LIML) estimators can be compared on the basis of three key parameters: the non-centrality parameter, a standardization of the structural coefficient, and the number of excluded exogenous variables. In this paper the values of these parameters are estimated in eleven structural equations from various actual econometric models. The distribution functions of the normalized TSLS and LIML estimators are given for the first two key parameters set at approximately their trimmed means, and the third at its median.     

Some applications for Basil's independence theorem in testing econometric models

Basu's Independence Theorem is used to show how tests of compound econometric hypotheses, involving two or more naturally ordered hypotheses, may be based upon mutually independent test statistics.     

Lagrange multipliers in infinite horizon discrete time optimal control models

We consider constrained optimization problems on the (non-reflexive) Banach Space of bounded sequences and derive sufficient conditions on the objective function and the constraints so that the Lagrangean can be represented by a summable sequence of multipliers. We apply our results to a discrete time infinite horizon control model of the type that arises in economics, and show how our methods can be applied to analyze the existence of bounded solutions.     

On univariate time series methods and simultaneous equation econometric models

Systematic testing of the implications of the structural assumptions for the properties of the final equations and transfer functions associated with a dynamic econometric model, as proposed by Zellner and Palm (1974–1975), proved to be useful in model building. This paper contains several remarks on the use of univariate time series methods to empirically check out the implications of a linear dynamic simultaneous equation model.