Orthogonal Locally Ancillary Estimating Functions with Application to Stratified Clustered Data

We propose an orthogonal locally ancillary estimating function that provides first-order bias correction of inferences. It requires the specification of merely the first two moments of the observations when applying to analysis of stratified clustered (continuous or binary) data with the parameters of interest in both the first and second joint moments of dependent data. Simulation results confirm that the estimators obtained using the proposed method are substantially improved over those using regular profile estimating functions.     

Specification analysis in mixed hazard models and a test of crossing survival functions

The paper investigates diagnostic procedures for the specification of common hazard models in duration analysis. It is shown that under mixed hazard specifications the survival functions of different subgroups cannot cross. A nonparametric test for the crossing of two survival functions is provided and its applications in duration analysis are discussed. In particular, the proportional hazard model with unobserved heterogeneity (PHU) is investigated, and procedures are developed to test whether given data are consistent with the PHU model and whether they contain unobserved heterogeneity within the PHU specification. Examples in which crossing survivals are of substantive concern are discussed, including the dynamics of infectious diseases and the demand for vaccination.     

Econometric Reviews

This paper considers the problem of estimating a nonlinear statistical model subject to stochastic linear constraints among unknown parameters. These constraints represent prior information which originates from a previous estimation of the same model using an alternative database. One feature of this specification allows for the disign matrix of stochastic linear restrictions to be estimated. The mixed regression technique and the maximum likelihood approach are used to derive the estimator for both the model coefficients and the unknown elements of this design matrix. The proposed estimator whose asymptotic properties are studied, contains as a special case the conventional mixed regression estimator based on a fixed design matrix. A new test of compatibility between prior and sample information is also introduced. Thesuggested estimator is tested empirically with both simulated and actual marketing data.     

Generalized mixed estimator for nonlinear models: a maximum likelihood approach

This paper considers the problem of estimating a nonlinear statistical model subject to stochastic linear constraints among unknown parameters. These constraints represent prior information which originates from a previous estimation of the same model using an alternative database. One feature of this specification allows for the disign matrix of stochastic linear restrictions to be estimated. The mixed regression technique and the maximum likelihood approach are used to derive the estimator for both the model coefficients and the unknown elements of this design matrix. The proposed estimator whose asymptotic properties are studied, contains as a special case the conventional mixed regression estimator based on a fixed design matrix. A new test of compatibility between prior and sample information is also introduced. Thesuggested estimator is tested empirically with both simulated and actual marketing data.     

Estimation of systems of equations subject to curvature constraints

Two computationally manageable estimation procedures for maintaining curvature constraints are compared. Using an efficient nonlinear optimizing algorithm, the well-known Cholesky factorization is compared with the eigenvalue decomposition method for estimating a system of input demand and output supply equations. Statistical tests are provided. The Cholesky factorization is superior when efficient optimizers are used. The eigenvalue decomposition may become a better choice when the user is limited to less efficient algorithms.     

The Effects of Price Aggregation Bias in Systems of Demand Equations

This article illustrates the importance of maintaining consistent levels of aggregation between prices and quantities when estimating consumer demand functions. The impact of violating this condition is quantified by using summary performance measures and estimates of demand elasticity biases. Results derived from an application of 1972–1973 Consumer Expenditure Survey data and supported with a quasi-Monte Carlo experiment consistently indicate that the point estimates of demand elasticities are significantly biased. Thus the study indicates the importance of developing and maintaining price indexes disaggregated to the same level as the expenditure data in consumer expenditure and budget surveys.     

潜在流动性约束与城镇家庭消费

笔者认为,收入不平等与家庭消费的关系与信贷约束程度以及家庭社会地位偏好有关。住房是典型的地位性商品,收入差距扩大时,人们为了维持或提高现有的相对地位会努力改善居住条件,住房攀比最终会导致全社会住房面积标准提高和房价上涨。在信贷缺乏的环境中,购房标准提高和房价上涨意味着家庭未来遭遇流动性约束的风险加大,为此,家庭在增加购房预算的同时会抑制日常消费。利用2010年、2012年和2014年的微观跟踪调查数据所做的实证分析支持了我们的观点：（1）周围人群的住房面积的扩大,会促使家庭选择购买更大的房子。并且,攀比效应对住房需求的刺激作用明显大于房价上涨对住房需求的抑制作用。（2）家庭平均住房面积扩大和房价上涨都与收入不平等引发的住房攀比有关。（3）收入不平等对城镇家庭消费皆有拉动作用和抑制作用。（4）潜在流动性约束对家庭消费的抑制作用与家庭地位等级的高低有关。     

An Analysis of Nonlinearities,Heteroscedasticity, and Functional Form in the Market Model

Using a generalized specification of the single-index market model, this study examines the sources of statistical anomalies previously found in estimating the market model. Two generalized models are developed for juxtaposition with the traditional linear specification. The most general model is a Box–Cox model with different λ's and heteroscedastic errors. The empirical results indicate that previous findings of significant “nonlinearities” are primarily attributable to nonnormalities and unequal variance.     

A Note on Forecaster Discord and Consensus Prediction Error

In using survey data, the cross-sectional dispersion of forecasts is commonly used as a proxy for uncertainty. This article proposes a test for the validity of this practice that is a modification of Amemiya's (1977) procedure for estimating heteroscedasticity functions. To deal with the common practical problem of overlapping forecasts, a moving average specification is employed. The technique is applied to the Livingston forecasts of several variables, and the results suggest a significant positive relationship between cross-forecaster dispersion (a measure of forecaster discord) and the variance of ex post prediction errors.     

Age,Trend, and Cohort Effects in a Macro Model of Canadian Expenditure Patterns

A quadratic almost ideal demand system allowing for age, cohort, and trend effects is developed at the macro level. The model is estimated by maximum likelihood, using a three-tier iterative/search method applied to pooled 1961–1992 time series for five regions of Canada and six categories of expenditure. Hypothesis tests indicate support for the model specification. Elasticities are compared with those reported in other studies, with special attention to food. Effects of demographic and trend variables on elasticities and expenditure shares are investigated. An overall conclusion is that such effects can be very important in a macro demand system.     

A local likelihood method for estimating relative risk functions in case-control studies

A local likelihood method with constraints is developed for the case-control sample for estimating the unknown relative risk function and odds ratio. Our estimates can be reduced to simply solving two systems of estimating equations. One system of estimating equations is for estimating the relative risk function, and is identical to that based on the locally weighted logistic regression analysis under prospective sampling. Another system of estimating equations is for estimating the odds ratio, and is identical to that used in the traditional linear logistic regression analysis. Asymptotic properties of the estimators are presented. Two real examples and simulations are given to illustrate our method. The results confirm that our approach is useful for estimating the relative risk function and odds ratio in case-control studies.     

Frontier estimation using kernel smoothing estimators with data transformation

In economics, a production frontier function is a graph that shows the maximum output of production units such as firms, industries, or economies, as a function of their inputs. Practically, estimating production frontiers often requires imposition of constraints such as monotonicity or monotone concavity. However, few constrained estimators of production frontier have been proposed in the literature. They are based on simple envelopment techniques which often suffer from lack of precision and smoothness. Motivated by this observation, we propose a smooth constrained nonparametric frontier estimator respecting constraints by considering kernel smoothing estimators from a transformed data. It is particularly appealing to practitioners who would like to use smooth estimates that, in addition, satisfy theoretical axioms of production. The utility of this method is illustrated through application to one real dataset and simulation evidences are also presented to show its superiority over the most known methods.     

A new REML (parameter expanded) EM algorithm for linear mixed models

Linear mixed models are regularly applied to animal and plant breeding data to evaluate genetic potential. Residual maximum likelihood (REML) is the preferred method for estimating variance parameters associated with this type of model. Typically an iterative algorithm is required for the estimation of variance parameters. Two algorithms which can be used for this purpose are the expectation‐maximisation (EM) algorithm and the parameter expanded EM (PX‐EM) algorithm. Both, particularly the EM algorithm, can be slow to converge when compared to a Newton‐Raphson type scheme such as the average information (AI) algorithm. The EM and PX‐EM algorithms require specification of the complete data, including the incomplete and missing data. We consider a new incomplete data specification based on a conditional derivation of REML. We illustrate the use of the resulting new algorithm through two examples: a sire model for lamb weight data and a balanced incomplete block soybean variety trial. In the cases where the AI algorithm failed, a REML PX‐EM based on the new incomplete data specification converged in 28% to 30% fewer iterations than the alternative REML PX‐EM specification. For the soybean example a REML EM algorithm using the new specification converged in fewer iterations than the current standard specification of a REML PX‐EM algorithm. The new specification integrates linear mixed models, Henderson's mixed model equations, REML and the REML EM algorithm into a cohesive framework.     

Specification of household engel curves by nonparametric regression

This paper demonstrates the usefulness of nonparametric regression analysis for functional specfication of houshold Engel curves.

After a brief review in section 2 of the literature on demand functions and equivalence scales and the functional specifications used, we first discuss in section 3 the issues of using income versus total expenditure, the origin and nature of the error terms in the light of utility theroy, and the interpretation of empirical demand functions. we shall reach the unorthodox view that household demand functions should be interpreted as conditional expectations relative to prices, household composition and either income or the conditional expectation of total expenditure (rather that total expenditure itself), where the latter conditional expectation is taken relative to income, prices and household composition. these two forms appear to be equivalent. this result also solves the simultaneity problem: the error variance matrix is no longer singular. Moreover, the errors are in general heteroskedastic.

In section 4 we discuss the model and the data, and in section 5 we review the nonparametric kernal regression approach.

In section 6 we derive the functional form of our household engel curves from nonparametric regression results, using the 1980 budget survey for the netherlands, in order to avoid model misspecification. thus the modl is derived directly from the data, without restricting its functional form. the nonparametric regression results are then translated to suitable parametric functional specifications, i.e., we choose parametric functional forms in accordance with the nanparametric regression results. these parametric specification are estimated by least squares, and various parameter restrictions are tested in order to simplify the models. this yields very simple final specifications of the household engel curves involved, namely linear functions of income and the number of children in two age groups.     

Specification of household engel curves by nonparametric regression

This paper demonstrates the usefulness of nonparametric regression analysis for functional specfication of houshold Engel curves.

After a brief review in section 2 of the literature on demand functions and equivalence scales and the functional specifications used, we first discuss in section 3 the issues of using income versus total expenditure, the origin and nature of the error terms in the light of utility theroy, and the interpretation of empirical demand functions. we shall reach the unorthodox view that household demand functions should be interpreted as conditional expectations relative to prices, household composition and either income or the conditional expectation of total expenditure (rather that total expenditure itself), where the latter conditional expectation is taken relative to income, prices and household composition. these two forms appear to be equivalent. this result also solves the simultaneity problem: the error variance matrix is no longer singular. Moreover, the errors are in general heteroskedastic.

In section 4 we discuss the model and the data, and in section 5 we review the nonparametric kernal regression approach.

In section 6 we derive the functional form of our household engel curves from nonparametric regression results, using the 1980 budget survey for the netherlands, in order to avoid model misspecification. thus the modl is derived directly from the data, without restricting its functional form. the nonparametric regression results are then translated to suitable parametric functional specifications, i.e., we choose parametric functional forms in accordance with the nanparametric regression results. these parametric specification are estimated by least squares, and various parameter restrictions are tested in order to simplify the models. this yields very simple final specifications of the household engel curves involved, namely linear functions of income and the number of children in two age groups.     

The misspecification of dynamic regression models

This paper investigates some of the hazards of estimating dynamic regression relationships with misspecified models. It is argued that, whenever the dynamic specification is in doubt, we should do well to adopt models which attribute separate sets of parameters to the systematic and disturbance parts of the regression relationship. Some of the models which are commonly adopted in applied econometrics attempt to capture the basic dynamic properties of the two parts of the relationship with the same set of parameters. If the properties of these two parts differ radically, then they are bound to be misrepresented by such models which can give rise to very misleading estimates.     

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.     

Empirical likelihood ratio test for or against a set of inequality constraints

We use the empirical likelihood ratio approach introduced by Owen (Biometrika 75 (1988), 237–249) to test for or against a set of inequality constraints when the parameters are defined by estimating functions. Our objective in this paper is to show that under fairly general conditions, the limiting distributions of the empirical likelihood ratio test statistics are of chi-bar square type (as in the parametric case) and give the expression of the weighting values. The results obtained here are similar to those in El Barmi and Dykstra (1995) where a full distributional model is assumed. This work presents also an extension of the results in Qin and Lawless (1995).     

Semiparametric ARCH Models: An Estimating Function Approach

We introduce the method of estimating functions to study the class of autoregressive conditional heteroscedasticity (ARCH) models. We derive the optimal estimating functions by combining linear and quadratic estimating functions. The resultant estimators are more efficient than the quasi-maximum likelihood estimator. If the assumption of conditional normality is imposed, the estimator obtained by using the theory of estimating functions is identical to that obtained by using the maximum likelihood method in finite samples. The relative efficiencies of the estimating function (EF) approach in comparison with the quasi-maximum likelihood estimator are developed. We illustrate the EF approach using a univariate GARCH(1,1) model with conditional normal, Student-t, and gamma distributions. The efficiency benefits of the EF approach relative to the quasi-maximum likelihood approach are substantial for the gamma distribution with large skewness. Simulation analysis shows that the finite-sample properties of the estimators from the EF approach are attractive. EF estimators tend to display less bias and root mean squared error than the quasi-maximum likelihood estimator. The efficiency gains are substantial for highly nonnormal distributions. An example demonstrates that implementation of the method is straightforward.     

The Estimation of Short-Run Household Electricity Demand Using Pooled Aggregate Data

Short-run household electricity demand has been estimated with conditional demand models by a variety of authors using both aggregate data and disaggregate data. Disaggregate data are most desirable for estimating these models. However, in many cases, available disaggregate data may be inappropriate. Furthermore, disaggregate data may be unavailable altogether. In these cases, readily available aggregate data may be more appropriate. This article develops and evaluates an econometric technique to generate unbiased estimates of household electricity demand using such aggregate data.