Two-step Estimation Research Articles

A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data.

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

Regression analysis of censored data with nonignorable missing covariates and application to Alzheimer Disease

In this paper, we discuss regression analysis of censored failure time data when there exist missing covariates and more specifically, we will consider interval-censored data, a general form of censored data, and the nonignorable missing. Although many methods have been proposed in the literature for censored data with missing covariates, they only apply to limited situations and it does not seem to exist an established procedure for the situation discussed here. For the analysis, we employ the semiparametric linear transformation model and develop a two-step estimation procedure. In addition, the asymptotic properties of the resulting estimators are established and a Poisson variable-based EM algorithm is provided for the implementation of the proposed estimation procedure. Finally the proposed approach is applied to an Alzheimer Disease study that motivated this investigation.

Effect of exchange rate uncertainty on bilateral trade performance in SAARC countries: a gravity model analysis

PurposeExchange rate uncertainty leads to an indecisive environment for imports and exports that would condense international trade, foreign direct investment, trade earnings, trade volumes, economic growth and welfare. This study aims to examine, empirically, the effect of exchange rate uncertainty on bilateral trade performance, focusing on eight SAARC member economies using the popular modified gravity model of trade.Design/methodology/approachThe paper includes eight SAARC members – Afghanistan, Bangladesh, Bhutan, Maldives, Nepal, Pakistan and Sri Lanka panel data set over the period 2005–2018. The authors consider both standardized value (standard deviation) and conditional variance model to determine volatility of exchange rate. Primarily, ordinary least squares, random effects and fixed effects estimation techniques are employed to investigate the impact of exchange rate volatility. Endogeneity and robustness of the findings have been tested using the simultaneity-adjusted model and dynamic panel data two-step system GMM estimation techniques.FindingsEmpirical findings endorse the view that exchange rate volatility lowers trade flows in the SAARC regions. However, this adverse effect of exchange rate uncertainty on trade is pretty small. The negative correlation between exchange rate volatility and bilateral trade remains consistent and significant after controlling of simultaneous causality, autocorrelation, year effects, country-pair heterogeneity and endogeneity irrespective of panel data estimation techniques and different measures of volatility.Originality/valueThe present paper is original work.

A Faster Procedure for Estimating CFA Models Applying Minimum Distance Estimators with a Fixed Weight Matrix

ABSTRACT This paper presents a numerically more efficient implementation of the quadratic form minimum distance (MD) estimator with a fixed weight matrix for confirmatory factor analysis (CFA) models. In structural equation modeling (SEM) computer software, such as EQS, lavaan, LISREL and Mplus, various MD estimators are available to the user. Standard procedures for implementing MD estimators involve a one-step approach applying non-linear optimization techniques. Our implementation differs from the standard approach by utilizing a two-step estimation procedure. In the first step, only a subset of the parameters are estimated using non-linear optimization. In the second step, the remaining parameters are obtained using numerically efficient linear least squares (LLS) methods. Through examples, it is demonstrated that the proposed implementation of MD estimators may be considerably faster than what the standard implementation offer. The proposed procedure will be of particular interest in computationally intensive applications such as simulation, bootstrapping, and other procedures involving re-sampling.

Dynamic Factor Models with Clustered Loadings: Forecasting Education Flows using Unemployment Data

We propose a dynamic factor model which we use to analyze the relationship between education participation and national unemployment, as well as to forecast the number of students across the many different types of education. By clustering the factor loadings associated with the dynamic macroeconomic factor, we can measure to what extent the different types of education exhibit similarities in their relationship with macroeconomic cycles. Since unemployment data is available for a longer time period than our detailed education data panel, we propose a twostep estimation procedure. First, we consider a score-driven model which filters the conditional expectation of the unemployment rate. Second, we consider a multivariate regression model for the number of students featuring the dynamic macroeconomic factor as a regressor, and we further apply the k-means method to estimate the clustered loading matrix. In a Monte Carlo study we analyze the performance of the proposed procedure in its ability to accurately capture clusters and preserve or enhance forecasting accuracy. For a high-dimensional, nation-wide data set from The Netherlands, we empirically investigate the impact of the rate of unemployment on choices in education over time. Our analysis confirms that the number of students in part-time education covaries more strongly with unemployment than those in full-time education.

Measuring timeliness of annual reports filing by jump additive models

Foreign public issuers (FPIs) are required by the Securities and Exchanges Commission (SEC) to file Form 20-F as comprehensive annual reports. In an effort to increase the usefulness of 20-Fs, the SEC recently enacted a regulation to accelerate the deadline of 20-F filing from six months to four months after the fiscal year-end. The rationale is that the shortened reporting lag would improve the informational relevance of 20-Fs. In this work we propose a jump additive model to evaluate the SEC’s rationale by investigating the relationship between the timeliness of 20-F filing and its decision usefulness using the market data. The proposed model extends the conventional additive models to allow possible discontinuities in the regression functions. We suggest a two-step jump-preserving estimation procedure and show that it is statistically consistent. By applying the procedure to the 20-F study, we find a moderate positive association between the magnitude of the market reaction and the filing timeliness when the acceleration is less than $17$ days. We also find that the market considers the filings significantly more informative when the acceleration is more than $18$ days and such reaction tapers off when the acceleration exceeds $40$ days.

Two-stage physics-based Wiener process models for online RUL prediction in field vibration data

Due to most failure mechanisms, such as fatigue crack growth and fatigue spall, the degradation process of rotating machinery commonly exhibits two-stage features in engineering practice. Other minor factors are also the key issues affecting the health evolution process, including the component structure, assembly accuracy, and working environment. Ignoring such a mechanism may lead to imprecise in degradation modeling, life prognostic, and ultimately lead to safety risk. Besides, achieving high accuracy of prognostic emphasizes the influence of random effect in the degradation process. The contribution of this study lies in addressing this issue by proposing two-stage physics-based Wiener process models integrating: (a) fatigue crack mechanism and crack growth law, and (b) other minor factors. A general prognostic framework is formulated by jointly employing the online change point detection, parameter estimation, and remaining useful life (RUL) prediction, which has good statistic inference and applicability in two general nonlinear systems, i.e., power-law and exponential-law. A joint implement of offline two-step parameter estimation method and the online Bayesian update method is executed, making full advantage of historical and in-service data, based on which the RUL prediction transcends into an imperative PHM module. A practical case study on the vibration dataset of wheel treads demonstrates the practically implement ability of the proposed method in achieving high accuracy of RUL prediction.

Estimation of a binary dependent variable sample selection model with endogeneity under a nonparametric selection mechanism

In this paper, we consider an estimation of a sample selection model with a binary dependent variable and possible endogenous regressors. Under the semiparametric framework, we impose neither the parametric specification of the error distribution nor the functional form of the selection equation, which largely reduces the risk of model misspecification. Throughout this paper, we present the identification 条件 and propose a two-step semiparametric maximum likelihood estimator with the first step being a nonparametric regression for the selection variable. A control function approach is used to control for the possible endogeneity. The proposed estimator is shown to be consistent and asymptotically normal. In the simulation studies, we compare the finite sample properties of our estimator with those of existing alternatives, demonstrating the significant advantages of our approach especially in robustness to the model misspecification. Finally, an economic application on labor economics is carried out to illustrate the usefulness of our estimator.

Portfolio Risk Assessment under Dynamic (Equi)Correlation and Semi-Nonparametric Estimation: An Application to Cryptocurrencies

The semi-nonparametric (SNP) modeling of the return distribution has been proved to be a flexible and accurate methodology for portfolio risk management that allows two-step estimation of the dynamic conditional correlation (DCC) matrix. For this SNP-DCC model, we propose a stepwise procedure to compute pairwise conditional correlations under bivariate marginal SNP distributions, overcoming the curse of dimensionality. The procedure is compared to the assumption of dynamic equicorrelation (DECO), which is a parsimonious model when correlations among the assets are not significantly different but requires joint estimation of the multivariate SNP model. The risk assessment of both methodologies is tested for a portfolio of cryptocurrencies by implementing backtesting techniques and for different risk measures: value-at-risk, expected shortfall and median shortfall. The results support our proposal showing that the SNP-DCC model has better performance for lower confidence levels than the SNP-DECO model and is more appropriate for portfolio diversification purposes.

Does early tracking affect learning inequalities? Revisiting difference-in-differences modeling strategies with international assessments

The development of international surveys on children’s learning like PISA, PIRLS and TIMSS—delivering comparable achievement measures across educational systems—has revealed large cross-country variability in average performance and in the degree of inequality across social groups. A key question is whether and how institutional differences affect the level and distribution of educational outcomes. In this contribution, we discuss the difference-in-differences strategies employed in the existing literature to evaluate the effect of early tracking on learning inequalities exploiting international assessments administered at different age/grades. In their seminal paper, Hanushek and Woessmann (Econ J 116:C63–C76, 2006) analyze with two-step estimation the effect of early tracking on overall inequalities, measured by test scores’ variability indexes. Later work of other scholars in the economics and sociology of education focuses instead on inequalities among children of different family background, using individual-level models on pooled data from different countries and assessments. In this contribution, we show that individual pooled difference-in-differences models are quite restrictive and that in essence they estimate the effect of tracking by double differentiating the estimated cross-sectional family background regression coefficients between tracking regimes and learning assessments. Starting from a simple learning growth model, we show that if test scores at different surveys are not measured on the same scale, as occurs for international learning assessments, pooled individual models may deliver severely biased results. Instead, the scaling problem does not affect the two-step approach. For this reason, we suggest using two-step estimation also to analyze family-background achievement inequalities. Against this background, using PIRLS-2006 and PISA-2012 we conduct two-step analyses, finding new evidence that early tracking fosters both overall inequalities and family background differentials in reading literacy.

Bank Competition in Africa: Do Institutional Quality and Cross-border Banking Matter?

ABSTRACT This paper analyses the implications of cross-border banking (CBB) and institutional quality (IQ) for bank competition in Africa. It applies a two-step estimation procedure using bank-level panel data for 29 African countries. In step one, the Boone indicator and the Lerner index are used to gauge bank competition in a given country in Africa. In the second step, it analyzes the sources of bank competition placing emphasis on the impact of CBB and IQ. The results suggest that competition increased in the period of 2002–2005, before decreasing somewhat between 2006 and 2007 and increasing again thereafter. The results also show that cross-border banking enhances bank competition in African countries with stronger governance structures and institutional quality. These results are robust to an array of controls including an alternative methodology, variable specifications, and the regulatory environments that banks operate in.

The Effect of Financial Sector Development on Economic Growth of Selected Sub-Saharan African Countries

Finance-growth nexus is among the main debatable issue in economics and policymaking. So, this research tried to look at the effect of financial sector development on the economic growth of 25 sub-Saharan Africa countries by using panel data for time 2010-2017. Precisely, three dynamic panel data models which look the effect of financial sector depth, access and efficiency on economic growth were estimated by two-step system GMM estimation. In this research, credit extended to the private sector per GDP, commercial bank branch per 100,000 adult population, and Return to assets were used as a proxy for financial sector depth, access, and efficiency, respectively. Accordingly, the results revealed financial sector depth, access, and efficiency have a positive and statistically significant effect on the economic growth of these countries. It is therefore recommended for the concerned bodies that broadening the depth of financial institutions by giving more credit for the private sector is essential. Besides, the financial institutions will have to be expanded to increase their accessibility to the mass and have to take some measures which promote their efficiency.

Estimating Fuel Loads and Structural Characteristics of Shrub Communities by Using Terrestrial Laser Scanning

Forest fuel loads and structural characteristics strongly affect fire behavior, regulating the rate of spread, fireline intensity, and flame length. Accurate fuel characterization, including disaggregation of the fuel load by size classes, is therefore essential to obtain reliable predictions from fire behavior simulators and to support decision-making in fuel management and fire hazard prediction. A total of 55 sample plots of four of the main non-tree covered shrub communities in NW Spain were non-destructively sampled to estimate litter depth and shrub cover and height for species. Fuel loads were estimated from species-specific equations. Moreover, a single terrestrial laser scanning (TLS) scan was collected in each sample plot and features related to the vertical and horizontal distribution of the cloud points were calculated. Two alternative approaches for estimating size-disaggregated fuel loads and live/dead fractions from TLS data were compared: (i) a two-steps indirect estimation approach (IE) based on fitting three equations to estimate shrub height and cover and litter depth from TLS data and then use those estimates as inputs of the existing species-specific fuel load equations by size fractions based on these three variables; and (ii) a direct estimation approach (DE), consisting of fitting seven equations, one for each fuel fraction, to relate the fuel load estimates to TLS data. Overall, the direct approach produced more balanced goodness-of-fit statistics for the seven fractions considered jointly, suggesting that it performed better than the indirect approach, with equations explaining more than 80% of the observed variability for all species and fractions, except the litter loads.

Logistics Performance, Ratings, and its impact on Customer Purchasing Behavior and Sales in E-commerce Platforms

Problem Definition: We examine the impact of logistics performance metrics such as delivery time, and customer’s requested delivery speed on logistics service ratings and third-party sellers’ sales on an e-commerce platform. Academic/Practical Relevance: While e-commerce retailers like Amazon have recently invested heavily in their logistics networks to provide faster delivery to customers, there is scant academic literature that tests and quantifies the premise that convenient and fast delivery will drive sales. In this paper, we provide empirical evidence on whether this relationship holds in practice by analyzing a mechanism that connects delivery performance to sales through logistics ratings. Prior academic work on online ratings in ecommerce platforms has mostly analyzed customers’ response to product functional performance and biases that exist within. Our study contributes to this stream of literature by examining customer experience from a service quality perspective by analyzing logistics service performance, logistics ratings, and its impact on customer purchase probability and sales. Methodology: Using an extensive data set of more than 15 million customer orders on the Tmall platform and Cainiao network (logistics arm of Alibaba), we employ the Heckman ordered regression model to explain the variation in customers’ rating of logistics performance, as well as the likelihood of customers posting a logistics rating. Next, we develop a generic customer choice model that links the customer’s likelihood of making a purchase to the logistics ratings provided by prior customers. We implement a two-step estimation of the choice model to quantify the impact of logistics ratings on customer purchase probability and third-party seller sales. Results: We surprisingly find that even customers with no promise on delivery speed are likely to post lower logistics ratings for delivery times longer than two days. Although these customers are not promised an explicit delivery deadline, they seem to have a mental threshold of two days and expect deliveries to be made within that time. Similarly, we find that priority customers (those with two-day and one-day promise speed) provide lower logistics ratings for delivery times longer than their anticipated delivery date. We estimate that reducing the delivery time of all three-day delivered orders on this platform (which makeup approximately 35% of the total orders) to two days would improve the average daily third-party seller sales by 13.3% on this platform. The impact of delivery time performance on sales is more significant for sellers with a higher percentage of three-day delivered orders and a higher spend per order. Managerial Implications: Our study emphasizes that delivery performance and logistics ratings, which measure service quality, are essential drivers of the customer purchase decision on e-commerce platforms. Further, by quantifying the impact of delivery time performance on sales, our study also provides a framework for online retailers to assess if the increase in sales due to improved logistics performance can offset the increase in additional infrastructure costs required for faster deliveries. Our study’s insights are relevant to third-party sellers and e-commerce platform managers who aim to improve long-term online customer traffic and sales.

Reliability analysis of face stability for tunnel excavation in a dependent system

From a practical perspective, it is necessary to consider multivariate failure mechanisms in reliability analysis. The multivariate in a system may be dependent on each other, which should be considered in reliability analysis. To investigate the reliability of a structural system, this study develops a copula-based approach to construct dependence structures of different failure mechanisms. Herein, a novel two-step parameter estimation method based on a hybrid-evolution Markov chain Monte Carlo (MCMC) algorithm has been developed to estimate copula parameters with high accuracy and less bias. To verify the validity and robustness of proposed method, the face stability issue in shield tunneling has been used as an illustrative example. Results indicate that: (1) the novel two-step parameter estimation method yields reasonable parameter values; (2) the calculated values based on copula model are more accurate than Nataf model in practical engineering; (3) the failure probability pf calculated by copula model is obviously different (almost over 50% in both examples) from Independent scenario. The proposed reliability analysis using the copula model provides guidelines for face stability control under uncertainty and randomness, which can reduce the failure probability ahead of time and mitigate risk magnitudes to some degree after failure occurrence.

LIMIT THEOREMS FOR FACTOR MODELS

This paper establishes central limit theorems (CLTs) and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global parameter includes aggregation of a cross-section of heterogeneous microparameters estimated separately for each entity. The CLT applies for quantities involving both cross-sectional and time series aggregation, as well as for quadratic forms in time-aggregated errors. This paper studies the conditions when one can consistently estimate the asymptotic variance, and proposes a bootstrap scheme for cases when one cannot. A small simulation study illustrates performance of the asymptotic and bootstrap procedures. The results are useful for making inferences in two-step estimation procedures related to factor models, as well as in other related contexts. Our treatment avoids structural modeling of cross-sectional dependence but imposes time-series independence.

On the direct and indirect effects of the Great East Japan earthquake on self rated health through social connections: Mediation analysis

The Great East Japan Earthquake created health hazards for many people. Using Panel Data gathered in Iwanuma city, Japan, at two points in time (in 2010 before the quake, and in 2013 after the quake), we found that the high degree of housing damage negatively affected victims’ self rated health (SRH) (direct effect), and decreased the levels of their social connections, which in turn also had a harmful effect on their SRH (indirect effect). We also found that although the direct impacts of earthquakes disappear relatively quickly, the harmful indirect effects associated with a decrease in social connections are slower to dissipate. We conducted a first-difference two-step GMM estimation to consider the possible problem of endogeneity. The results support the above conclusion, and show that in the short-term, the indirect impacts of the earthquake accounted for 55 % of all the impacts experienced.

Simultaneous confidence bands for comparing variance functions of two samples based on deterministic designs

Asymptotically correct simultaneous confidence bands (SCBs) are proposed in both multiplicative and additive form to compare variance functions of two samples in the nonparametric regression model based on deterministic designs. The multiplicative SCB is based on two-step estimation of ratio of the variance functions, which is as efficient, up to order $$n^{-1/2}$$ , as an infeasible estimator if the two mean functions are known a priori. The additive SCB, which is the log transform of the multiplicative SCB, is location and scale invariant in the sense that the width of SCB is free of the unknown mean and variance functions of both samples. Simulation experiments provide strong evidence that corroborates the asymptotic theory. The proposed SCBs are used to analyze several strata pressure data sets from the Bullianta Coal Mine in Erdos City, Inner Mongolia, China.

A Two-Step Parameter Optimization Method for Low-Order Model-Based State-of-Charge Estimation

The state-of-charge (SOC) estimation is an enabling technique for the efficient management and control of lithium-ion batteries (LIBs). This article proposes a novel method for online SOC estimation, which manifests itself with both high accuracy and low complexity. Particularly, the particle swarm optimization (PSO) algorithm is exploited to optimize the model parameters to ensure high modeling accuracy. Following this endeavor, the PSO algorithm is used to tune the error covariances of extended Kalman filter (EKF) leveraging the early stage segmental data of LIB utilization. Within this PSO-based tuning framework, the searching boundary is derived by scrutinizing the error transition property of the system. Experiments are performed to validate the proposed two-step PSO-optimized SOC estimation method. Results show that even by using a simple first-order model, the proposed method can give rise to a high SOC accuracy, which is comparative to those using complex high-order models. The proposed method is validated to excavate fully the potential of model-based estimators so that the computationally expensive model upgrade can be avoided.

Predicting with Proxies: Transfer Learning in High Dimension

Predictive analytics is increasingly used to guide decision making in many applications. However, in practice, we often have limited data on the true predictive task of interest and must instead rely on more abundant data on a closely related proxy predictive task. For example, e-commerce platforms use abundant customer click data (proxy) to make product recommendations rather than the relatively sparse customer purchase data (true outcome of interest); alternatively, hospitals often rely on medical risk scores trained on a different patient population (proxy) rather than their own patient population (true cohort of interest) to assign interventions. Yet, not accounting for the bias in the proxy can lead to suboptimal decisions. Using real data sets, we find that this bias can often be captured by a sparse function of the features. Thus, we propose a novel two-step estimator that uses techniques from high-dimensional statistics to efficiently combine a large amount of proxy data and a small amount of true data. We prove upper bounds on the error of our proposed estimator and lower bounds on several heuristics used by data scientists; in particular, our proposed estimator can achieve the same accuracy with exponentially less true data (in the number of features d). Finally, we demonstrate the effectiveness of our approach on e-commerce and healthcare data sets; in both cases, we achieve significantly better predictive accuracy as well as managerial insights into the nature of the bias in the proxy data. This paper was accepted by George Shanthikumar, big data and analytics.