Maximum likelihood estimation of sum-constrained linear models with insufficient observations

A maximum likelihood procedure for estimating sum-constrained linear models is presented, which seems to provide a good balance between excessive observational requirements on the one hand and an unduly restrictive specification of the contemporaneous covariance matrix on the other.     

Maximum likelihood estimation of search costs

In a recent paper Hong and Shum [2006. Using price distributions to estimate search costs. Rand Journal of Economics 37, 257-275] present a structural method to estimate search cost distributions. We extend their approach to the case of oligopoly and present a new maximum likelihood method to estimate search costs. We apply our method to a data set of online prices for different computer memory chips. The estimates suggest that the consumer population can be roughly split into two groups which either have quite high or quite low search costs. Search frictions confer a significant amount of market power to the firms: Despite more than 20 firms operating in each of the markets, we estimate price-cost margins to be around 25%. The paper also illustrates how the structural method can be employed to simulate the effects of the introduction of a sales tax.     

Maximum likelihood estimation of time-varying parameters: an application to the Athens Stock Exchange index

The problem of maximum likelihood estimation of time-varying parameters is considered. A hierarchical approach is proposed that involves, first, the estimation of the model order and parameters when they are assumed time-invariant. Second, for each parameter, an autoregressive (AR) model, with constant coefficients, is developed. This allows the parameters to change over time. Finally, the estimates of the AR coefficients for each parameter are used as initial conditions to a time-varying model with AR coefficients, which are allowed to change over time subject to some regularity constraints. This approach is then applied to the Athens Stock Exchange index, where the dominant forces affecting this index are analysed.     

Maximum likelihood estimation for vector autoregressions with multivariate stochastic volatility

This paper analyzes the maximum likelihood estimation for vector autoregressions with stochastic volatility. The stochastic volatility is modeled following Uhlig (1997). The asymptotic distribution of the maximum likelihood estimate is discussed under mild regularity conditions. The maximum likelihood estimate can be obtained via an iterative method. In that case, the maximum likelihood estimate becomes the iteratively reweighted least squares estimate analyzed in Rubin (1983). The iteratively reweighted least squares estimate is computationally much simpler than the Bayesian method offered by Uhlig (1997).     

Consistency ofs 2 in the linear regression model with correlated errors

We give a simple sufficient condition for consistency of the standard OLS-based estimate of the disturbance variance in the linear regression model with autocorrelated disturbances.Research supported by Deutsche Forschungsgemeinschaft (DFG). We are grateful to B. M. Poetscher for a generous supply of counterexamples.     

Stochastic unit root processes: Maximum likelihood estimation,and new Lagrange multiplier and likelihood ratio tests

We show in this study that the maximum likelihood estimators of stochastic unit root (STUR) processes are consistent and asymptotically normally distributed. We also present two new tests for STUR. We first propose a Lagrange multiplier test and show that it has a standard χ² distribution asymptotically. We also propose a likelihood ratio test and show that it has an asymptotic distribution of 50–50 mixture of χ² and a point mass at 0. As an empirical example, we test the existence of STUR in the Canadian real exchange rate and explore the implication of STUR on the validity of purchasing power parity.     

Maximum likelihood estimation of the Rotterdam model under two different conditions

This letter describes maximum likelihood (ML) procedures for the Rotterdam model (1) when the model is formulated in relative prices and (2) under the constraints of the theory of rational random behavior.     

The effect of measurement errors on the estimation of demand systems

Statistical inference in complete demand systems is usually based on imperfect data. This letter explores some of the implications of these imperfections, in particular for the estimates of income elasticities.     

The estimation of British local government expenditure decisions under a piecewise linear budget constraint

In the light of the reforms that have affected local government finance in Britain, the empirical analysis of local government responses to the changes in the grant system has become a topical subject because of its policy implications. Barnett et al.proposed different models to predict the likely impact of the reforms on local government expenditure but never tested ofr the validity of the functional form used in their model. The main reason for this omission is related to the piecewise nature of the budget constraint faced by local authorities which complicated the estimation techniques and restricted the choice of the functional forms that could be used. The presented here tests for the validity of the functional form using data for the three fiscal years that preceded the poll tax reform, namely 1986–87 to 1988–89 and suggests specific tests to compare the parameters obtained using different models. The main conclusion of the analysis is that only the behaviour of metropolitan districts is consistent with utility maximization.     

Feles: The functionalized extended linear expenditure system: Theory,estimation procedures and application to individual household consumption expenditures involving socioeconomic and sociodemographic characteristics

This article introduces the Functionalized Extended Linear Expenditure System, FELES, a new extension on Lluch's familiar Extended Linear Expenditure System. Household individual expenditures with respect to ‘subsistence expenditures’ and ‘partial marginal propensities to consume’ are made explicitly dependent on socioeconomic and sociodemographic characteristics in a system-wide approach. A restricted maximum likelihood estimator for relatively small systems with few explanatory variables and an iterative estimation procedure for larger systems with an extensive set of explanatory variables are proposed. The complete FELES then is applied to cross-sectional data with more than 47,000 German households. Stone's LES and Lluch's ELES are first quantified too on a German data base of this extent.     

Delimitation of the class of budget-constrained utility maximizing partially linear consumer expenditure functions: An alternative approach

Zusammenfassung Dieser Aufsatz behandelt eine alternative Herleitung notwendiger und hinreichender Bedingungen, denen Nachfragefunktionen, die linear im Einkommen jedoch nicht notwendigerweise linear in den Preisen sind, genügen müssen, um zu sichern, daß bei gegebenem Einkommen ein Nutzenmaximum realisiert wird. Diese Bedingungen erscheinen weniger einschränkend als jene, die Gorman (1953, 1961) abgeleitet hat. Beispiele für derartige Funktionen werden im dritten Abschnitt angeführt. Einige kritische Anmerkungen beschließen den Aufsatz.

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The author is indebted to Mr. P. M. C. de Boer, Dr. J. van Daal, and Mr. W. J. Keller, staff members of the Netherlands School of Economics, Erasmus University Rotterdam, for their helpful criticisms and suggestions.     

Bartlett adjustments for systems of linear equations with linear restrictions

Simple matrix formulae are derived for calculating a Bartlett adjustment to the likelihood ratio test statistic for testing linear parameter restrictions in a system of linear equations. For the special case of column and/or row restrictions on the matrix of coefficients the adjustment is a simple function of matrix dimensions being invariant to sample observations and the error covariance matrix. An example of testing for homogeneity and symmetry in a demand system is given.     

Bayesian estimation of duration models: An application of the multiperiod probit model

The multiperiod probit model is presented and Bayesian estimation using the Gibbs sampler with data augmentation is described. As an empirical illustration, the multiperiod probit model is then used to estimate a duration model using employment duration data for the Canadian province of New Brunswick. Bayesian estimation with unobserved heterogeneity is shown to be a simple extension of estimation of a duration model with no unobserved heterogeneity. More importantly, perhaps, some numerical problems encountered by other authors using Maximum Likelihood are avoided.I would like to thank M. Baker, G. Koop, A. Melino and D. Poirier for helpful comments and discussions. I would also like to thank M. Baker for providing his data.     

Testing for linear Engel curves: An application of NLES to cross-country data

The demand system, NLES, proposed recently by Blundell and Ray (1982), is shown to aggregate consistently across households. It is then used to analyse time series expenditure data of Korea, Greece, Israel and Puerto Rico. The empirical results reject linear Engel curves for each country.     

An incremental budgeting model of local public expenditure setting in the presence of piecewise linear budget constraints

This Paper develops and tests an incremental budgeting model of local government expenditure decisions using data on British local government. The model introduces two distinctive feautures into the incremental budegeting literature. Firstly, it takes explicit account of the availability of an independent source of revenue for jurisdictions (in this example, a local property tax). And secondly it shows how it is possible to develop satisfactory emperical models when budget constraints are only piecewise linear. The model is shown to perform well, both in explaining within-year variability in budgeting decisions, and in predicting subsequent budgets under revised budget constraints.     

Randomization of commodity taxes: An expenditure minimization approach

Using an expenditure minimization approach, necessary and sufficient conditions for local random taxation are obtained in terms of the curvature of the compensated demand function, so that intuition from excess burden analysis can be applied. Major findings include: (1) random taxation is locally optimal if the compensated demand function is sufficiently convex; (2) horizontally equitable taxation is locally optimal if the compensated demand function is concave, and (3) local randomization is not optimal if the tax revenue requirement is sufficiently close to zero or to any local maximum. We also derive an inverse elasticity characterization of the optimal random tax structure.     

An extension of mixed estimation,with an application to forecasting new product growth

This paper extends the mixed estimation technique to handle a case in which the coefficients of a set of linear constraints are known nonlinear functions of an unknown parameter vector for which an extraneous unbiased estimate is available. This novel form of the mixed estimation technique is illustrated by applying it to the Bass innovation/diffusion model of new product growth. It is suggested that this is superior to the traditional method whereby managerial intuition is incorporated into this type of model, and is an attractive alternative to recently-suggested Bayesian methods.I thank an anonymous referee for helpful comments and references.     

An alternative semiparametric estimate of the base-independence equivalence scale: an application to US consumer expenditure survey data

The deficit debate is a recurring theme in academic and political circles. The controversy is over the effect of deficits on inflation and interest rates. The existing body of empirical evidence does not resolve the controversy. This paper focuses on the inflationary impact of deficits. The model used is derived from a comprehensive IS-LM analysis which incorporates a foreign trade sector and a general price (adoptive expectation) adjustment mechanism. We test the model using time series data for the United states. From our results we conclude that NIA deficits have no significant bearing on the rate of inflation.