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on Econometrics |
| By: | Jahar L. Bhowmik; Maxwell L. King |
| Abstract: | In this paper, we consider the problem of estimation of semi-linear regression models. Using invariance arguments, Bhowmik and King (2001) have derived the probability density functions of the maximal invariant statistic for the nonlinear component of these models. Using these density functions as likelihood functions allows us to estimate these models in a two-step process. First the nonlinear component parameters are estimated by maximising the maximal invariant likelihood function. Then the nonlinear component, with the parameter values replaced by estimates, is treated as a regressor and ordinary least squares is used to estimate the remaining parameters. We report the results of a simulation study conducted to compare the accuracy of this approach with full maximum likelihood estimation. We find maximising the maximal invariant likelihood function typically results in less biased and lower variance estimates than those from full maximum likelihood. |
| Keywords: | Maximum likelihood estimation, nonlinear modelling, simulation experiment, two-step estimation. |
| JEL: | C2 C12 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2005-18&r=ecm |
| By: | Jahar L. Bhowmik; Maxwell L. King |
| Abstract: | In the context of a general regression model in which some regression coefficients are of interest and others are purely nuisance parameters, we derive the density function of a maximal invariant statistic with the aim of testing for the inclusion of regressors (either linear or non-linear) in linear or semi-linear models. This allows the construction of the locally best invariant test, which in two important cases is equivalent to the one-sided t-test for a regression coefficient in an artificial linear regression model. |
| Keywords: | Invariance; linear regression model; locally best invariant test; non-linear regression model; nuisance parameters; t-test. |
| JEL: | C2 C12 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:msh:ebswps:2005-19&r=ecm |
| By: | David I. Stern (Department of Economics, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA) |
| Abstract: | Time series models of global climate change have tended to estimate a low climate sensitivity and a fast adjustment rate to equilibrium. These results appear to be biased by omission of a key variable - heat stored in the ocean. I develop a time series model of the ocean atmosphere climate system where atmospheric temperature moves towards a long-run equilibrium with both radiative forcing and ocean heat content, which is distributed between upper ocean and deep ocean components. The time series model utilizes the notion of multicointegration to impose energy balance relations on an autoregressive model. As there are only around fifty years of observations on ocean heat content I use the Kalman filter to estimate heat content as a latent state variable constrained by the available observations. The estimate of the equilibrium climate sensitivity is 8.4K with a confidence interval of 5.0 to 11.7K. Temperature takes centuries to adjust to an increase in radiative forcing. The transient climate sensitivity at the point of carbon dioxide doubling is 1.7K. |
| JEL: | Q53 Q54 |
| Date: | 2005–07 |
| URL: | http://d.repec.org/n?u=RePEc:rpi:rpiwpe:0510&r=ecm |
| By: | Maarten Dossche (National Bank of Belgium, Research Department); Gerdie Everaert (Ghent University, Study Hive for Economic Research and Public Policy Analysis (SHERPPA)) |
| Abstract: | Time series estimates of inflation persistence incur an upward bias if shifts in the inflation target of the central bank remain unaccounted for. Using a structural time series approach we measure different sorts of inflation persistence allowing for an unobserved timevarying inflation target. Unobserved components are identified using Kalman filtering and smoothing techniques. Posterior densities of the model parameters and the unobserved components are obtained in a Bayesian framework based on importance sampling. We find that inflation persistence, expressed by the halflife of a shock, can range from 1 quarter in case of a costpush shock to several years for a shock to longrun inflation expectations or the output gap. |
| Keywords: | Inflation persistence, inflation target, Kalman filter, Bayesian analysis. |
| JEL: | C11 C13 C22 C32 E31 |
| Date: | 2005–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbb:reswpp:200506-1&r=ecm |
| By: | Harvey, David I; Leybourne, Stephen J; Taylor, A.M. Robert |
| Abstract: | In this paper we build upon the robust procedures proposed in Vogelsang (1998) for testing hypotheses concerning the deterministric trend function of a univariate time series. Vogelsang proposes statistics formed from taking the product of a (normalised) Wald statistic for the trend function hypothesis under test with a specific function of a separate variable addition Wald statistic. The function of the second statistic is explicitly chosen such that the resultant product statistic has pivotal limiting null distributions, coincident at a chosen level, under I(0) or I(1) errors. The variable addition statistic in question has also been suggested as a unit root statistic, and we propose corresponding tests based on other well-known unit root statistics. We find that, in the case of the linear trend model, a test formed using the familiar augmented Dickey-Fuller [ADF] statistic provides a useful complement to Vogelsang's original tests, demonstrating generally superior power when the errors display strong serial correlation with this pattern tending to reverse as the degree of serial correlation in the errors lessens. Importantly for practical considerations, the ADF-based tests also display significantly less finite sample over-size in the presence of weakly dependent errors than the original tests. |
| Keywords: | Wald tests; trend function hypotheses; unit root statistics |
| JEL: | C22 |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:05-07&r=ecm |
| By: | Bailey, Ralph |
| Keywords: | Complex ARMA processes; cycles; reciprocal polynomials; palindromic polynomials |
| JEL: | C32 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:05-09&r=ecm |
| By: | EVA RAQUEL PORRAS (Instituto de Empresa) |
| Abstract: | In the financial field much of the data available is in panel form. The objective of this paper is to analyze the long run equilibrium relationship between prices and fundamentals while proposing a very simple method of extending time series models to panel data. This method has several characteristics that make it appealing. First, it is simple to implement. Second, it is general in scope. Third, it takes into account arbitrary correlations. Fourth, it does not require making unrealistic assumptions. Our results are supportive of Han´s (1996) in that we do not find cointegration between fundamentals and prices. |
| Keywords: | Panel data, Time series, Fundamentals, Prices |
| Date: | 2004–06 |
| URL: | http://d.repec.org/n?u=RePEc:emp:wpaper:wp04-18&r=ecm |
| By: | ALBERTO MAYDEU (Instituto de Empresa) |
| Abstract: | We introduce a multidimensional latent trait model for binary data with non-monotone item response functions. We assume that the conditional probability of endorsing an item is a normal probability density function, and that the latent traits are normally distributed. The model yields closed form expressions for the moments of the multivariate Bernoulli (MVB) distribution. As a result, cell probabilities can be computed also in closed form, regardless of the dimensionality of the latent traits. The model is an ideal point model in the sense that a respondent -precisely at the ideal point (the mode of the item response function)- endorses the item with probability one. |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:emp:wpaper:wp05-11&r=ecm |
| By: | ALBERTO MAYDEU (Instituto de Empresa) |
| Abstract: | We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables of arbitrary dimensions. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any consistent and asymptotically normal estimator. We show that when r is small (r = 2) the proposed statistics have more accurate empirical Type I errors and are more powerful than Pearson´s X2 for a widely used item response model. Also, we show that the proposed statistics are asymptotically chi-squared under the null hypothesis when applied to subtables. |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:emp:wpaper:wp05-12&r=ecm |