Two-step Estimation Procedure Research Articles

Tariff liberalization and firm-level markups in Indian manufacturing

Tariff liberalization has a significant bearing on firm performance. Existing theoretical studies predict that input tariff liberalization would raise firm-level markups while final goods tariff liberalization would lower markups. This paper examines whether this two-sided effect holds for Indian manufacturing firms and the role of size and classification. It employs fixed effects models and Heckman's two-step estimation procedure to estimate the impact of input and final goods tariff liberalization under India's Export-Import Policy of 1997–2003 and 2004-09 for large versus Micro, Small and Medium Enterprise (MSME) firms. It confirms the two-sided effect and finds that the input channel is stronger, with large rather than MSME firms experiencing higher markups following input tariff reduction. Further, using a semiparametric Difference-in-Difference model it finds that relaxed size limits in 2006 resulted in higher markups for importing MSMEs. This study highlights the importance of firm size, liberalization channel, and policy framework for firm-level markups.

Nonparametric expected shortfall forecasting incorporating weighted quantiles

A new semi-parametric expected shortfall (ES) estimation and forecasting framework is proposed. The proposed approach is based on a two-step estimation procedure. The first step involves the estimation of value at risk (VaR) at different quantile levels through a set of quantile time series regressions. Then, the ES is computed as a weighted average of the estimated quantiles. The quantile weighting structure is parsimoniously parameterized by means of a beta weight function whose coefficients are optimized by minimizing a joint VaR and ES loss function of the Fissler–Ziegel class. The properties of the proposed approach are first evaluated with an extensive simulation study using two data generating processes. Two forecasting studies with different out-of-sample sizes are then conducted, one of which focuses on the 2008 Global Financial Crisis period. The proposed models are applied to seven stock market indices, and their forecasting performances are compared to those of a range of parametric, non-parametric, and semi-parametric models, including GARCH, conditional autoregressive expectile (CARE), joint VaR and ES quantile regression models, and a simple average of quantiles. The results of the forecasting experiments provide clear evidence in support of the proposed models.

Inverse optimization with kernel regression: Application to the power forecasting and bidding of a fleet of electric vehicles

This paper considers an aggregator of Electric Vehicles (EVs) who aims to learn the aggregate power of his/her fleet while also participating in the electricity market. The proposed approach is based on a data-driven inverse optimization (IO) method, which is highly nonlinear. To overcome such a caveat, we use a two-step estimation procedure which requires solving two convex programs. Both programs depend on penalty parameters that can be adjusted by using grid search. In addition, we propose the use of kernel regression to account for the nonlinear relationship between the behavior of the pool of EVs and the explanatory variables, i.e., the past electricity prices and EV fleet’s driving patterns. Unlike any other forecasting method, the proposed IO framework also allows the aggregator to derive a bid/offer curve, i.e. the tuple of price-quantity to be submitted to the electricity market, according to the market rules. We show the benefits of the proposed method against the machine-learning techniques that are reported to exhibit the best forecasting performance for this application in the technical literature.

Quantile Regression with Generated Regressors

This paper studies estimation and inference for linear quantile regression models with generated regressors. We suggest a practical two-step estimation procedure, where the generated regressors are computed in the first step. The asymptotic properties of the two-step estimator, namely, consistency and asymptotic normality are established. We show that the asymptotic variance-covariance matrix needs to be adjusted to account for the first-step estimation error. We propose a general estimator for the asymptotic variance-covariance, establish its consistency, and develop testing procedures for linear hypotheses in these models. Monte Carlo simulations to evaluate the finite-sample performance of the estimation and inference procedures are provided. Finally, we apply the proposed methods to study Engel curves for various commodities using data from the UK Family Expenditure Survey. We document strong heterogeneity in the estimated Engel curves along the conditional distribution of the budget share of each commodity. The empirical application also emphasizes that correctly estimating confidence intervals for the estimated Engel curves by the proposed estimator is of importance for inference.

Age estimation from the biometric information of hand bones: Development of new formulas

IntroductionIn the judicial context of the age estimation of living individuals, a new method was recently proposed, based on the collection of biometric information on hand bones radiographs. The aim of this study was to apply this method to a large French sample to provide new tools for age estimation Materials and methodsThe study sample consisted of metacarpals and proximal phalanges measurements of 1003 individuals aged less than 21 years. This sample was divided into two subgroups 1–12 and 13–21 years as the age of 13 is a relevant legal threshold for most European countries. A quadratic discriminant analysis was performed to identify the group to which an individual was most likely to belong. Age estimation formulas were also constructed from linear models: for each subgroup and the total sample. ResultsThe belonging of an individual to the 1–12 or 13–21 subgroup was determined with a correct classification rate of 89.8%. Age estimation formulas became less precise with age, with a mean absolute error ranging between 11 and 21 months. ConclusionWe proposed a two-step procedure for age estimation: firstly, the identification of the age group to which the individual is most likely to belong, and secondly, the age estimation of this individual by applying the appropriate formula.

Identifiability of causal effects with multiple causes and a binary outcome.

Unobserved confounding presents a major threat to causal inference in observational studies. Recently, several authors have suggested that this problem could be overcome in a shared confounding setting where multiple treatments are independent given a common latent confounder. It has been shown that under a linear Gaussian model for the treatments,the causal effect is not identifiable without parametric assumptions on the outcome model. In this note, we show that the causal effect is indeed identifiable if we assume a general binary choice model for the outcome with a non-probit link. Our identification approach is based on the incongruence between Gaussianity of the treatments and latent confounder and non-Gaussianity of a latent outcome variable. We further develop a two-step likelihood-based estimation procedure.

Generalized Additive Poisson Models for Quantifying Geological Factors Effect on The Earthquake Risk Mapping

Cluster-type point process models are the popular model for modeling the arrangement of locations of earthquake occurrences. When a spatial trend is presence due to e.g. geological factors, the log-linear intensity of the point process is often considered to exploit inhomogeneity due to such factors. However, this could be a major drawback, especially in seismology when the relation between the intensity of earthquake occurrences and environmental covariates is not log-linear. In this paper, we consider the Cauchy cluster process with a log-additive intensity model to quantify two effects in modeling the distribution of locations of major earthquakes in Sulawesi-Maluku: (1) spatial trend due to geological covariates such as subduction zones, faults, and volcanoes and (2) clustering effect due to seismic activities. The Cauchy cluster process could detect the clustering effect even when the aftershocks are extremely distant to the mainshocks while log-additive intensity is a more flexible model to study inhomogeneity due to the environment. To estimate the parameters, we apply two-step estimation procedure, in the first step, we estimate the regression parameter corresponding to effects of the geological variables by maximum composite likelihood by involving penalized iteratively re-weighted least squares (PIRLS) technique, and in the second step, we obtain the cluster estimates by maximum second order composite likelihood. The results show that the active faults and volcanoes are significant covariates that trigger earthquakes, the estimated mainshock intensity is around 78, and the aftershocks are distributed around it with a distance of 15.2 km due to mainshock activity.

Variable selection for partially linear models via Bayesian subset modeling with diffusing prior

Most existing methods of variable selection in partially linear models (PLM) with ultrahigh dimensional covariates are based on partial residuals, which involve a two-step estimation procedure. While the estimation error produced in the first step may have an impact on the second step, multicollinearity among predictors adds additional challenges in the model selection procedure. In this paper, we propose a new Bayesian variable selection approach for PLM. This new proposal addresses those two issues simultaneously as (1) it is a one-step method which selects variables in PLM, even when the dimension of covariates increases at an exponential rate with the sample size, and (2) the method retains model selection consistency, and outperforms existing ones in the setting of highly correlated predictors. Distinguished from existing ones, our proposed procedure employs the difference-based method to reduce the impact from the estimation of the nonparametric component, and incorporates Bayesian subset modeling with diffusing prior (BSM-DP) to shrink the corresponding estimator in the linear component. The estimation is implemented by Gibbs sampling, and we prove that the posterior probability of the true model being selected converges to one asymptotically. Simulation studies support the theory and the efficiency of our methods as compared to other existing ones, followed by an application in a study of supermarket data.

Statistical inference on shape and size indexes for counting processes.

Single-index models have gained increased popularity in time-to-event analysis owing to their model flexibility and advantage in dimension reduction. We propose a semiparametric framework for the rate function of a recurrent event counting process by modelling its size and shape components with single-index models. With additional monotone constraints on the two link functions for the size and shape components, the proposed model possesses the desired directional interpretability of covariate effects and encompasses many commonly used models as special cases. To tackle the analytical challenges arising from leaving the two link functions unspecified, we develop a two-step rank-based estimation procedure to estimate the regression parameters with or without informative censoring. The proposed estimators are asymptotically normal, with a root- convergence rate. To guide model selection, we develop hypothesis testing procedures for checking shape and size independence. Simulation studies and a data example on a hematopoietic stem cell transplantation study are presented to illustrate the proposed methodology.

Semiparametric analysis of case K interval-censored failure time data in the presence of a cured subgroup and informative censoring

Interval censoring and the existence of a cured subgroup occur quite often in survival studies and many procedures have been developed for dealing with each of the two issues individually or them together. In this paper, we discuss the situation where both issues exist and furthermore, interval censoring may be informative, for which there exists relatively much less literature. For the problem, we present a frailty-based joint model approach in which a frailty term is employed to describe the correlation between the failure time of interest and the censoring mechanism. For inference, a two-step estimation procedure is developed and in particular, the sieve maximum-likelihood estimation approach is used for estimation of the unknown function. The proposed estimators of regression parameters are shown to be consistent and asymptotically normal, and an extensive simulation study conducted suggests that the proposed procedure works well for practical situations. In addition, an application is provided.

Conditional Quantile Analysis for Realized GARCH Models

This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ conditional standard deviation, realized volatility, realized quantile, and absolute overnight return as innovations in the proposed dynamic quantile models. We devise a two-step estimation procedure to estimate the conditional quantile parameters. The first step applies a quasi-maximum likelihood estimation procedure, with the realized volatility as a proxy for the volatility proxy, to estimate the conditional standard deviation parameters. The second step utilizes a quantile regression estimation procedure with the estimated conditional standard deviation in the first step. Asymptotic theory is established for the proposed estimation methods, and a simulation study is conducted to check their finite-sample performance. Finally, we apply the proposed methodology to calculate the value at risk (VaR) of 20 individual assets and compare its performance with existing competitors.

Bayesian inference for a single factor copula stochastic volatility model using Hamiltonian Monte Carlo

For modeling multivariate financial time series a single factor copula model with stochastic volatility margins is proposed. It generalizes single factor models based on the multivariate normal distribution by allowing for symmetric and asymmetric tail dependence. A joint Bayesian approach using Hamiltonian Monte Carlo (HMC) within Gibbs sampling is developed. Thus, the information loss caused by the two-step approach for margins and dependence is avoided. Further, the Bayesian approach is tractable in high dimensional parameter spaces in addition to uncertainty quantification through credible intervals. By introducing indicators for different copula families the copula families are selected automatically in the Bayesian framework. In a first simulation study the performance of HMC for the copula part is compared to a procedure based on adaptive rejection Metropolis sampling within Gibbs sampling. It is shown that HMC considerably outperforms this alternative approach in terms of effective sample size per minute. In a second simulation study satisfactory performance is seen for the full HMC within Gibbs procedure. The approach is illustrated for a portfolio of financial assets with respect to one-day ahead value at risk forecasts. Comparison to a two-step estimation procedure and to relevant benchmark models, such as a multivariate factor stochastic volatility model, shows superior performance of the proposed approach.

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.

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.

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.

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.

Estimation of semi- and nonparametric stochastic frontier models with endogenous regressors

This paper considers the problem of estimating a nonparametric stochastic frontier model with shape restrictions and when some or all regressors are endogenous. We discuss three estimation strategies based on constructing a likelihood with unknown components. One approach is a three-step constrained semiparametric limited information maximum likelihood, where the first two steps provide local polynomial estimators of the reduced form and frontier equation. This approach imposes the shape restrictions on the frontier equation explicitly. As an alternative, we consider a local limited information maximum likelihood, where we replace the constrained estimation from the first approach with a kernel-based method. This means the shape constraints are satisfied locally by construction. Finally, we consider a smooth-coefficient stochastic frontier model, for which we propose a two-step estimation procedure based on local GMM and MLE. Our Monte Carlo simulations demonstrate attractive finite sample properties of all the proposed estimators. An empirical application to the US banking sector illustrates empirical relevance of these methods.

Construction of leading economic index for recession prediction using vine copulas

Abstract This paper constructs a composite leading index for business cycle prediction based on vine copulas that capture the complex pattern of dependence among individual predictors. This approach is optimal in the sense that the resulting index possesses the highest discriminatory power as measured by the receiver operating characteristic (ROC) curve. The model specification is semi-parametric in nature, suggesting a two-step estimation procedure, with the second-step finite dimensional parameter being estimated by QMLE given the first-step non-parametric estimate. To illustrate its usefulness, we apply this methodology to optimally aggregate the 10 leading indicators selected by The Conference Board (TCB) to predict economic recessions in the United States. In terms of the discriminatory power, our method is significantly better than the Index used by TCB.