Moment Conditions Research Articles

Estimating multinomial logit models with endogenous variables: Control function versus two adapted approaches

It is shown that the control function (CF) method’s estimates of the modal constants in a multinomial logit model (MNL) with endogenous explanatory variables are biased. This has not previously been reported in the literature, and has consequences in demand analysis, transportation policy design and project evaluation. Two adaptations of existing approaches are proposed as alternatives to CF for deriving estimators of parameters in MNL models with endogenous explanatory variables that evidence good consistency properties. The first approach is based on moment conditions while the second one combines parameters obtained in two consecutive estimation stages. Both approaches employ instrumental variables. These two adapted approaches are implemented using simulated data from a transport mode choice problem. The results are compared with those obtained using the classic control-function method, typically used by practitioners for estimating transport demand models with endogenous variables and making quantitative evaluations of transport policies and projects. All three approaches generate similar estimates for the parameters of the explanatory variables, but the two proposed adaptations produce considerably more accurate estimates of the modal constants. This greater accuracy has potentially significant consequences for multinomial logit models’ predictive ability and estimates of marginal effects, elasticities and the social benefits of projects based on consumer surplus calculations.

Predicting conditional probability distributions of redshifts of Active Galactic Nuclei using Hierarchical Correlation Reconstruction

ABSTRACT The Large Area Telescope (LAT) onboard the Fermi gamma-ray observatory continuously scans the sky in an energy range from 50 MeV to 1 TeV. The telescope has identified over 6000 gamma-ray emitting sources, approximately half of which are classified as active galactic nuclei (AGN). However, not all of these gamma-ray sources have known redshift values for the reason that redshift estimation following traditional methods can be an expensive, challenging task. Alternatively, as an effort to robustly predict the AGN redshift values, many researchers have recently turned to machine learning methods. However, while the focus has primarily been on predicting specific values, real-world data often allows us only to predict conditional probability distributions, constrained by conditional entropy [H(Y|X)]. In our study, we employ the Hierarchical Correlation Reconstruction approach to inexpensively predict complex conditional probability distributions, including multimodal ones. This is achieved through independent Mean Squared Error estimation of multiple moment-like parameters, combined into reconstruction of the conditional distribution. By employing linear regression for this purpose, we can develop interpretable models where coefficients describe the contributions of features to conditional moments. This article extends the original approach by incorporating Canonical Correlation Analysis for feature optimization and l1 ‘lasso’ regularization. Our primary focus is on the practical problem of predicting the redshift of AGN using data from the Fourth Fermi-LAT Data Release 3 (4LAC-DR3) data set.

Conditional Moment Matching and Stratified Approximation for Pricing and Hedging Periodic-Premium Variable Annuities

Conditional Moment Matching and Stratified Approximation for Pricing and Hedging Periodic-Premium Variable Annuities

Identification and estimation of panel semiparametric conditional heteroskedastic frontiers with dynamic inefficiency

We study a semiparametric panel stochastic frontier model with nonseparable unobserved heterogeneity, which allows for time-varying conditional heteroskedastic productivity components. It does not require distributional assumptions on random noise except conditional symmetry. We utilize conditional characteristic functions from Kotlarski’s Lemma to derive new moment conditions that yield the identification of the heteroskedastic variance parameters of inefficiency and random noise. Identification only requires a panel with three periods for serially correlated inefficiency. A nonparametric estimation procedure is also developed for the conditional variance of inefficiency, and its convergence rate is established. Monte Carlo simulation shows that the estimator is robust to misspecification of inefficiency distributions.

Factor IV Estimation in Conditional Moment Models with an Application to Inflation Dynamics

Abstract In a conditional moment model, we develop a new integrated conditional moment (ICM) estimator which directly exploits factor-based conditional moment restrictions without having to first parametrize, or estimate such restrictions. We focus on a time series framework where the large number of available instruments and associated lags is driven by a relatively small number of unobserved factors. We build on the ICM principle originally proposed by Bierens (1982) and combine it with information reduction methods to handle the large number of potential instruments which may exceed the sample size. Under the maintained validity of the true factors, but not that of observed instruments, and standard regularity assumptions, our estimator is consistent, asymptotically normally distributed, and easy to compute. In our simulation studies, we document its reliability and power in cases where the underlying relationship between the endogenous variables and the instruments may be heterogeneous, non-linear, or even unstable over time. Our estimation of the New Keynesian Phillips curve with U.S. data reveals that forward- and backward-looking behaviors are quantitatively equally as important, while the driver’s role is nil.

An extreme worst-case risk measure by expectile

Abstract Expectiles have received increasing attention as a risk measure in risk management because of their coherency and elicitability at the level $\alpha\geq1/2$ . With a view to practical risk assessments, this paper delves into the worst-case expectile, where only partial information on the underlying distribution is available and there is no closed-form representation. We explore the asymptotic behavior of the worst-case expectile on two specified ambiguity sets: one is through the Wasserstein distance from a reference distribution and transforms this problem into a convex optimization problem via the well-known Kusuoka representation, and the other is induced by higher moment constraints. We obtain precise results in some special cases; nevertheless, there are no unified closed-form solutions. We aim to fully characterize the extreme behaviors; that is, we pursue an approximate solution as the level $\alpha $ tends to 1, which is aesthetically pleasing. As an application of our technique, we investigate the ambiguity set induced by higher moment conditions. Finally, we compare our worst-case expectile approach with a more conservative method based on stochastic order, which is referred to as ‘model aggregation’.

Exact perturbation approximations for the conditional moments of a multifactor CIR term structure model with a weak mean-reversion influence

In this paper, we derive exact series expressions for the conditional moments of a multivariate Cox-Ingersoll-Ross term structure model with a weak mean-reversion effect assumption. First, we construct the perturbation solution for the system of Riccati equations, which illustrates the conditional characteristic function of this term structure model. Second, we derive the power series expression for the perturbation solution. Via the power series solutions, we establish the exact series expressions for conditional moments. Furthermore, we demonstrate the error bounds for these perturbation approximations of the conditional moments. Numerical analysis indicates that our method is more efficient, accurate and superior to the Monte Carlo approach with the Euler scheme for computing the conditional moments.

Covariate adjustment in experiments with matched pairs

This paper studies inference for the average treatment effect (ATE) in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates, and finally, within each pair, one unit is selected at random for treatment. Importantly, we presume that not all observed, baseline covariates are used in determining treatment assignment. We study a broad class of estimators based on a “doubly robust” moment condition that permits us to study estimators with both finite-dimensional and high-dimensional forms of covariate adjustment. We find that estimators with finite-dimensional, linear adjustments need not lead to improvements in precision relative to the unadjusted difference-in-means estimator. This phenomenon persists even if the adjustments interact with treatment; in fact, doing so leads to no changes in precision. However, gains in precision can be ensured by including fixed effects for each of the pairs. Indeed, we show that this adjustment leads to the minimum asymptotic variance of the corresponding ATE estimator among all finite-dimensional, linear adjustments. We additionally study an estimator with a regularized adjustment, which can accommodate high-dimensional covariates. We show that this estimator leads to improvements in precision relative to the unadjusted difference-in-means estimator and also provides conditions under which it leads to the “optimal” nonparametric, covariate adjustment. A simulation study confirms the practical relevance of our theoretical analysis, and the methods are employed to reanalyze data from an experiment using a “matched pairs” design to study the effect of macroinsurance on microenterprise.

Improved estimation of drift coefficients using optimal local bandwidths

Stochastic differential equations (SDEs) are commonly used to model various systems. Data-driven methods have been widely used to estimate the drift and diffusion terms of a Langevin equation. Among the most commonly used estimation methods is the Nadaraya–Watson estimator, which is a non-parametric data-driven approach. In this study, we propose a method to improve the estimation of the drift coefficient of a stochastic process using optimal local bandwidths that minimize the error of the approximation of the first conditional moments of a univariate system. This approach is compared to a global bandwidth estimation and an estimation based on a fixed number of nearest neighbors. The proposed method has the potential to reduce the error of the drift estimation, thereby improving the accuracy of the model.

Empirical Evidence on the Validity of the Conditional Higher Moment Capm in the Bombay Stock Exchange

Various researchers criticized the assumption of a normal distribution of returns in the traditional Capital Asset Pricing Model (CAPM), leading to the recognition of the non-normal distribution of returns and the mean and variance were insufficient to characterize the distribution of returns completely which led the researchers to look for higher order moments. The present study investigated empirical validity of the conditional higher order moment Capital Asset Pricing Model (CAPM) in the context of the Indian stock market, specifically the Bombay Stock Exchange utilizing the data from sectoral indices for the period from April 2011 to March 2021. To test the four moment CAPM empirically, the specification derived from Bollerslev et al. (1988) has been used in the study. The study's findings reveals that the higher moment i.e. conditional coskewness and cokurtosis hold significant pricing implications and do have an impact on returns in the Indian stock market. The explanatory power of the model showed an increase as compared to the unconditional CAPM as the R-square value obtained was greater than the latter model. The results of the study were found to be mixed and inconclusive. Hence, the conditional higher moment CAPM cannot be validated in the Indian context.

BOUNDED SUPPORT IN LINEAR RANDOM COEFFICIENT MODELS: IDENTIFICATION AND VARIABLE SELECTION

We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identification, and show that the means and the variances and covariances of the random coefficients are identified from the first two conditional moments of the response given the covariates if the support of the covariates, excluding the intercept, contains a Cartesian product with at least three points in each coordinate. We also discuss identification of higher-order mixed moments, as well as partial identification in the presence of a binary regressor. Next, we show the variable selection consistency of the adaptive LASSO for the variances and covariances of the random coefficients in finite and moderately high dimensions. This implies that the estimated covariance matrix will actually be positive semidefinite and hence a valid covariance matrix, in contrast to the estimate arising from a simple least squares fit. We illustrate the proposed method in a simulation study.

Natural frequencies and modal shapes of folded sandwich plates made of porous core and FG-CNTRC coating layers resting on two parameters elastic foundation

Folded structures hold significant importance in aerospace technology due to their distinct design, effectively reconciling strength with a lightweight framework. Within aerospace applications, these structures fulfill diverse roles, serving as pivotal elements in aircraft wings, fuselage sections, and essential components of spacecraft and satellites. This study delves into the free vibration behavior of folded sandwich plates composed of a porous core and functionally graded carbon nanotube-reinforced composite (FG-CNTRC) coatings, resting on a two-parameter elastic foundation. Leveraging first-order shear deformation plate theory (FSDT), elasto-dynamic equations are established for each individual plate segment. Utilizing the two-dimensional generalized differential quadrature method (2D-GDQM), these equations are discretized. Subsequently, by applying boundary conditions to all six edges, including traditional clamped, simply supported, and free configurations, and incorporating continuity conditions for displacements, forces, and moments at the joint borders, natural frequencies and modal shapes are extracted for the folded plate structure. The validity of the proposed formulation and results is demonstrated by comparing them with numerical examples for both composite flat and folded plates. This comparison provides strong support for the accuracy and reliability of the present study. The study comprehensively examines the influence of various parameters on natural frequencies, including modal shape visualizations under different boundary configurations, plate thickness, crank angle, porosity parameter, core thickness, foundation stiffness, and CNTs distribution type.

On the variance estimator and its bounds in general linear models under linear restrictions

In the article, the error variance estimator σ ^ 2 and its finite sample size bounds are investigated in the framework of a general linear model under linear restrictions (gLMLR) where no distributions are assumed except for some moment conditions and the covariance matrix of the response may be singular, which extends the results in Lindholm and Wahl (2020). In particular, we overcome the difficulty that the matrix of quadratic form in σ ^ 2 is not idempotent. The estimator is obtained by the proposed restricted and proxy-type generalized least square procedure. Meanwhile, the estimable function of the regression coefficient β is estimated, too. Besides, the finite sample properties of these estimators and their consistency are also established. In the end, a simulation study and a real data analysis are done to examine the finite performance of these estimators.

GMM weighting matrices in cross-sectional asset pricing tests

When estimating misspecified linear factor models for the cross-section of expected returns using GMM, the explanatory power of these models can be spuriously high when the estimated factor means are allowed to deviate substantially from the sample averages. In fact, by shifting the weights on the moment conditions, any level of cross-sectional fit can be attained. The mathematically correct global minimum of the GMM objective function can be obtained at a parameter vector that is far from the true parameters of the data-generating process. This property is not restricted to small samples, but rather holds in population. It is a feature of the GMM estimation design and applies to both strong and weak factors, as well as to all types of test assets.

Medical application with an extended Ailamujia inverted Weibull model: Properties, estimation and simulation

In this article, we propose a new lifetime model called Kavya-Manoharan Ailanujia inverted Weibull distribution, which is obtained from the Kavya-Manoharan (KM) transformation family and Ailanujia inverted Weibull distribution. Various statistical properties are obtained, involving moments, incomplete moments, conditional moments, mean deviations, mean residual lifetime and mean past lifetime and entropy. Moreover, the newly proposed distribution, characterized by two parameters, proves to be remarkably versatile, as demonstrated in the application results. Several statistical properties of the KMAIW distribution are deduced, and the estimation of its parameters is accomplished through three distinct techniques. To assess the effectiveness of these approaches, a comprehensive simulation study is conducted. The significance and applicability of the proposed model are underscored through the analysis of a real-world dataset. In comparative evaluations against well-known distributions featuring two, three, and four parameters, the suggested model consistently outperforms them all. This highlights the superior fitting capability and adaptability of the proposed model in comparison to established distributions with varying parameter complexities.

Moment conditions for random coefficient AR(∞) under non-negativity assumptions

Moment conditions for random coefficient AR(∞) under non-negativity assumptions

Complete convergence for arrays of rowwise m n -extended negatively dependent random variables and its application

. In this article, under some proper and sufficient conditions, we gave complete convergence for weighted sums and maximal weighted sums of arrays of rowwise m n -extended negatively dependent (rowwise m n -END) random variables, which is a new dependent structure. In addition, a relationship between { m n , n ≥ 1 } and moment condition for convergence is revealed in a sense. The results obtained in the article generalize some corresponding ones for independent and some dependent random variables. As an application, the strong consistency for the weighted estimator in a non parametric regression model is established.

Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative

Focusing on the redshift space observations with plane-parallel approximation and relying on the rotational dependency of the general definition of excursion sets, we introduce the so-called conditional moments of the first derivative (cmd) measures for the smoothed matter density field in three dimensions. We derive the perturbative expansion of cmd for the real space and redshift space where peculiar velocity disturbs the galaxies’ observed locations. Our criteria can successfully recognize the contribution of linear Kaiser and Finger-of-God effects. Our results demonstrate that the cmd measure has significant sensitivity for pristine constraining the redshift space distortion parameter β = f/b and interestingly, the associated normalized quantity in the Gaussian linear Kaiser limit has only β dependency. Implementation of the synthetic anisotropic Gaussian field approves the consistency between the theoretical and numerical results. Including the first-order contribution of non-Gaussianity perturbatively in the cmd criterion implies that the N-body simulations for the Quijote suite in the redshift space have been mildly skewed with a higher value for the threshold greater than zero. The non-Gaussianity for the perpendicular direction to the line of sight in the redshift space for smoothing scales R ≳ 20 Mpc h −1 is almost the same as in the real space. In contrast, the non-Gaussianity along the line-of-sight direction in the redshift space is magnified. The Fisher forecasts indicate a significant enhancement in constraining the cosmological parameters Ω m , σ 8, and n s when using cmd + cr jointly.

The Type II Exponentiated Half Logistic-Gompertz-G Power Series Class of Distributions: Properties and Applications

We propose and study a new generalized class of distributions called the Type II Exponentiated Half Logistic-Gompertz-G Power Series (TIIEHL-Gom-GPS) distribution. Some structural properties including expansion of density,ordinary and conditional moments, generating function, order statistics and entropy are derived. We present some specialcases of the proposed distribution. The maximum likelihood method is used for estimating the model parameters. Theimportance of the new class of distributions are illustrated by means of two applications to real data sets.

TRILINEAR FOURIER MULTIPLIERS ON HARDY SPACES

Abstract In this paper, we obtain the $H^{p_1}\times H^{p_2}\times H^{p_3}\to H^p$ boundedness for trilinear Fourier multiplier operators, which is a trilinear analogue of the multiplier theorem of Calderón and Torchinsky [4]. Our result improves the trilinear estimate in [22] by additionally assuming an appropriate vanishing moment condition, which is natural in the boundedness into the Hardy space $H^p$ for $0<p\le 1$ .