Parameter Restrictions Research Articles

Groseclose and Snyder in finite legislatures

The Groseclose and Snyder (1996) model is one of the best-known models of vote buying in legislatures. Although the logic of the model is compelling, it is not clear that its key propositions, derived in a continuous set-up, hold in finite legislatures. This is an important issue because many real-world legislatures are small and should be modeled as finite in order to make predictions on coalition formation in them. This paper makes two contributions. The main one is to show with full generality that the key propositions in the Groseclose and Snyder model do carry through into finite legislatures. Secondly, it clarifies the role that parameter restrictions played in previous work on this question by Banks (2000) which was not fully general.

The conditional autoregressive Wishart model for multivariate stock market volatility

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes an autoregressive moving average structure for the scale matrix of the Wishart distribution. It accounts for positive definiteness of covariance matrices without imposing parametric restrictions, and can be estimated by Maximum Likelihood. We also propose extensions of the CAW model obtained by including a Mixed Data Sampling (MIDAS) component and Heterogeneous Autoregressive (HAR) dynamics for long-run fluctuations. The CAW models are applied to realized variances and covariances for five New York Stock Exchange stocks.

On the conditions eliciting a detailed structure in the hyperfine field distribution at 57Fe nuclei

A technique has been developed to extract a fine structure in the hyperfine field distribution (HFD) at Mössbauer resonating nuclei such as 57Fe. It has been shown that the NORMOS program package widely spread for fitting Mössbauer spectra may be used for this purpose under some restrictions for variable parameters. In a case of iron and its some alloys both as a bulk and aerosol nanoparticles, applying the technique has permitted to bring out a discrete structure in HFD at 57Fe nuclei caused with a set of weak magnetic interactions.

Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model

In this paper, we study a stochastic predator–prey model with Beddington–DeAngelis type functional response and logistic growth for predators. The deterministic model is already well-studied and we recall some important results here. We construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations. For the stochastic model, we show that the system admits unique positive global solution starting from the positive initial value. Then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes. Finally, we show that the system has a stationary distribution under certain parametric restrictions. Numerical simulations are carried out to substantiate the analytical results.

A class of distribution and association sensitive multidimensional welfare indices

This paper axiomatically characterizes a class of two-parameter generalized mean social welfare indices having two or more dimensions of well-being. These indices, under appropriate parametric restrictions, are sensitive to two distinct forms of inter-personal inequality. The first form of inequality is concerned with the dispersion of each dimensional achievement across the population. The second is concerned with the association or correlation across dimensions, reflecting the observation that the correlation of individual components of well-being across dimensions is relevant for social welfare evaluation. It is shown that many existing multidimensional welfare indices are closely related to this new class. Statistical tests are developed to verify the significance of the evaluations generated by these indices. Finally, the class of indices is applied to Indonesian data to analyze the impact on financial crisis on the country’s social welfare using two waves of Indonesian Family Life Surveys (IFLS).

On the Relation Between the Linear Factor Model and the Latent Profile Model.

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the unconditional covariances. In particular, a 2-class latent profile model with Gaussian components underestimates the observed covariances but not the variances, when the data are consistent with a unidimensional Gaussian factor model. In explanation of this phenomenon we provide some results relating the unconditional covariances to the goodness of fit of the latent profile model, and to its excess multivariate kurtosis. The analysis also leads to some useful parameter restrictions related to symmetry.

GEL CRITERIA FOR MOMENT CONDITION MODELS

GEL methods that generalize and extend previous contributions are defined and analyzed for moment condition models specified in terms of weakly dependent data. These procedures offer alternative one-step estimators and tests that are asymptotically equivalent to their efficient two-step GMM counterparts. The basis for GEL estimation is via a smoothed version of the moment indicators using kernel function weights that incorporate a bandwidth parameter. Examples for the choice of bandwidth parameter and kernel function are provided. Efficient moment estimators based on implied probabilities derived from the GEL method are proposed, a special case of which is estimation of the stationary distribution of the data. The paper also presents a unified set of test statistics for overidentifying moment restrictions and combinations of parametric and moment restriction hypotheses.

On the link between volatility and growth

A model of growth with endogenous innovation and distortionary taxes is presented. Since innovation is the only source of volatility, any variable that influences innovation directly affects volatility and growth. This joint endogeneity is illustrated by working out the effects through which economies with different tax levels differ in their volatility and growth process. We obtain analytical measures of macro volatility based on cyclical output and on output growth rates for plausible parametric restrictions. This analysis implies that controls for taxes should be included in the standard growth-volatility regressions. Our estimates show that the conventional Ramey–Ramey coefficient is affected sizeably. In addition, tax levels do indeed appear to affect volatility in our empirical application.

Generalized full-information item bifactor analysis.

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single-group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than 1 group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker's (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood requires only 2-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy.

Corruption in a model of vertical linkage between formal and informal credit sources and credit subsidy policy

The present note develops a model of vertical linkage between the formal and informal credit markets highlighting the presence of corruption in the distribution of formal credit. The existing dominant moneylender, the bank official and the new moneylenders move sequentially. The existing moneylender acts as a Stackelberg leader and unilaterally decides on the informal interest rate. We show that there may arise a case where an increase in the supply of formal credit results in an increase in the informal interest rate under reasonable parametric restrictions. This shows that apart from (i) asymmetric information on the part of informal sector lenders (Bose, 1998), (ii) an increase in the probability of default of all informal sector lenders (Hoff and Stiglitz 1997), and the (iii) possibility of informal lenders to collude (Floro and Ray 1997), the presence of corruption in the distribution of formal credit might be another factor responsible for the policy of vertical linkage to break down.

Semiparametric estimation of a bivariate Tobit model

The existing semiparametric estimation literature has mainly focused on univariate Tobit models and no semiparametric estimation has been considered for bivariate Tobit models. In this paper, we consider semiparametric estimation of the bivariate Tobit model proposed by Amemiya (1974), under the independence condition without imposing any parametric restriction on the error distribution. Our estimator is shown to be consistent and asymptotically normal, and simulation results show that our estimator performs well in finite samples. It is also worth noting that while Amemiya’s (1974) instrumental variables estimator (IV) requires the normality assumption, our semiparametric estimator actually outperforms his IV estimator even when normality holds. Our approach can be extended to higher dimensional multivariate Tobit models.

A new strategy for estimating two-locus recombination fractions under some natural inequality restrictions

Linkage analysis is now being widely used to map markers on each chromosome in the human genome, to map genetic diseases, and to identify genetic forms of common diseases. Two-locus linkage analysis and multi-locus analysis have been investigated comprehensively, and many computer programs have been developed to perform linkage analysis. Yet there exists a shortcoming in traditional methods, i.e., the parameter space of two-locus recombination fractions has not been emphasized sufficiently in the usual analyses. In this paper, we propose a new strategy for estimating the two-locus recombination fractions based on data of backcross family in the framework of some natural and necessary parameter restrictions. The new strategy is based on a restricted projection algorithm, which can provide fast reasonable estimates of recombination fraction, and can therefore serve as a superior alternative algorithm. Results obtained from both real and simulated data indicate that the new algorithm performs well in the estimation of recombination fractions and outperforms current methods.

On the Link Between Volatility and Growth

A model of growth with endogenous innovation and distortionary taxes is presented. Since innovation is the only source of volatility, any variable that influences innovation directly affects volatility and growth. This joint endogeneity is illustrated by working out the effects through which economies with different tax levels differ in their volatility and growth process. We obtain analytical measures of macro volatility based on cyclical output and on output growth rates for plausible parametric restrictions. This analysis implies that controls for taxes should be included in the standard growth-volatility regressions. Our estimates show that the conventional Ramey-Ramey coefficient is affected sizeably. In addition, tax levels do indeed appear to affect volatility in our empirical application.

Quantum isotonic nonlinear oscillator as a Hermitian counterpart of Swanson Hamiltonian and pseudo-supersymmetry

Within the ideas of pseudo-supersymmetry, we have studied a non-Hermitian Hamiltonian , where α ≠ β and ξ is a first-order differential operator, to obtain the partner potentials V+(x) and V−(x) which are new isotonic and isotonic nonlinear oscillators, respectively, as the Hermitian equivalents of the non-Hermitian partner Hamiltonians H±. We have provided an algebraic way to obtain the spectrum and wavefunctions of a nonlinear isotonic oscillator. The solutions of V−(x) which are Hermitian counterparts of Swanson Hamiltonian are obtained under some parameter restrictions that are found. Also, we have checked whether the intertwining operator satisfies η1H− = H+η1, where and is the first-order differential operator, which factorizes Hermitian equivalents of H±.

Household Income Uncertainties Over Three Decades

We study the trend in household income uncertainty using a novel approach that measures income uncertainty as the variance of forecast errors at each future horizon separately without imposing parametric restrictions on the underlying income shocks. We find that household income uncertainty has risen significantly and persistently since the early 1970s. For example, our measure of near-future uncertainty in total family non-capital income rose about 40 percent between 1971 and 2002. This rising uncertainty is likely due to the increase in variances of both persistent and transitory income shocks. Although the increase in uncertainty was widespread, the increase was most pronounced among single-earner households and high-income households. A parsimoniously calibrated Aiyagari (1994) model is solved to illustrate how rising income uncertainty affects aggregate saving.

Robustness to Parametric Assumptions in Missing Data Models

We consider estimation of population averages when data are missing at random. If some cells contain few observations, there can be substantial gains from imposing parametric restrictions on the cell means, but there is also a danger of misspecification. We develop a simple empirical Bayes estimator, which combines parametric and unadjusted estimates of cell means in a data-driven way. We also consider ways to use knowledge of the form of the propensity score to increase robustness. We develop an empirical Bayes extension of a double robust estimator. In a small simulation study, the empirical Bayes estimators perform well. They are similar to fully nonparametric methods and robust to misspecification when cells are moderate to large in size, and when cells are small they maintain the benefits of parametric methods and can have lower sampling variance.

Why suicide-terrorists get educated, and what to do about it

This paper tries to reconcile the observed fact that suicide-terrorists have a relatively high education level with rationality. It brings out the conditions under which potential students choose to acquire some education in a rational-choice model where this yields a non-zero probability of blowing up the resulting human capital in a terrorist attack. The comparative-statics of the rational expectations equilibrium of this model demonstrate how economic development, on the one hand, and repression, on the other hand, might reduce terrorism under some parameter restrictions.

Generalized Maximum Entropy Estimators: Applications to the Portland Cement Dataset

Consider the linear regression model y= X+ u in the usual notation. In many applications the design matrix X is frequently subject to severe multicollinearity. In this paper an alternative estimation methodology, maximum entropy is given and used to estimate the parameters in a linear regression model when the basic data are ill-conditioned. We de- scribed the generalized maximum entropy (GME) estimator, imposing sign restrictions of parameters and imposing cross parameter restrictions for GME. Mean squared error (mse) values of the estimators are estimated by the bootstrap method. We compared the generalized maximum entropy (GME) estimator, least squares and inequality restricted least squares (IRLS) estimator on the widely analyzed dataset on Portland cement.

MODELING THE SUNSPOT NUMBER DISTRIBUTION WITH A FOKKER-PLANCK EQUATION

Sunspot numbers exhibit large short-timescale (daily-monthly) variation in addition to longer timescale variation due to solar cycles. A formal statistical framework is presented for estimating and forecasting randomness in sunspot numbers on top of deterministic (including chaotic) models for solar cycles. The Fokker-Planck approach formulated assumes a specified long-term or secular variation in sunspot number over an underlying solar cycle via a driver function. The model then describes the observed randomness in sunspot number on top of this driver function. We consider a simple harmonic choice for the driver function, but the approach is general and can easily be extended to include other drivers which account for underlying physical processes and/or empirical features of the sunspot numbers. The framework is consistent during both solar maximum and minimum, and requires no parameter restrictions to ensure non-negative sunspot numbers. Model parameters are estimated using statistically optimal techniques. The model agrees both qualitatively and quantitatively with monthly sunspot data even with the simplistic representation of the periodic solar cycle. This framework should be particularly useful for solar cycle forecasters and is complementary to existing modeling techniques. An analytic approximation for the Fokker-Planck equation is presented, which is analogous to the Euler approximation, which which allows for efficient maximum likelihood estimation of large data sets and/or when using difficult to evaluate driver functions.

Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions

This article studies the minimum divergence (MD) class of estimators for econometric models specified through moment restrictions. We show that MD estimators can be obtained as solutions to a tractable lower dimensional optimization problem. This problem is similar to the one solved by the generalized empirical likelihood estimators of Newey and Smith (2004), but it is equivalent to it only for a subclass of divergences. The MD framework provides a coherent testing theory: tests for overidentification and parametric restrictions in this framework can be interpreted as semiparametric versions of Pearson-type goodness of fit tests. The higher order properties of MD estimators are also studied and it is shown that MD estimators that have the same higher order bias as the empirical likelihood (EL) estimator also share the same higher order mean square error and are all higher order efficient. We identify members of the MD class that are not only higher order efficient, but also, unlike the EL estimator, well behaved when the moment restrictions are misspecified.