Two-step Estimation Procedure Research Articles

Valid instrumental variable selection method using negative control outcomes and constructing efficient estimator.

In observational studies, instrumental variable (IV) methods are commonly applied when there are unmeasured covariates. In Mendelian randomization, constructing an allele score using many single nucleotide polymorphisms is often implemented; however, estimating biased causal effects by including some invalid IVs poses some risks. Invalid IVs are those IV candidates that are associated with unobserved variables. To solve this problem, we developed a novel strategy using negative control outcomes (NCOs) as auxiliary variables. Using NCOs, we are able to select only valid IVs and exclude invalid IVs without knowing which of the instruments are invalid. We also developed a new two-step estimation procedure and proved the semiparametric efficiency of our estimator. The performance of our proposed method was superior to some previous methods through simulations. Subsequently, we applied the proposed method to the UK Biobank dataset. Our results demonstrate that the use of an auxiliary variable, such as an NCO, enables the selection of valid IVs with assumptions different from those used in previousmethods.

Impact of Trade Liberalisation and MSME Classification on Productivity of Indian Manufacturing Firms

This article examines the effects of tariff and non-tariff reductions on firm-level productivity of large as well as Micro, Small and Medium Enterprises (MSMEs) in India’s manufacturing sector for the 1999–2009 period. We calculate input and final goods tariffs, effective rates of protection and non-tariff barriers (NTBs) for broad product groups using information from India’s Exim Policy of 1997–2003 and 2004–2009 to examine this impact. We use a balanced as well as unbalanced firm-level panel data set, while accounting for firm, industry, state and time-specific factors. By using fixed effect models and Heckman’s two-step estimation procedure, we find that trade liberalisation is associated with improved firm-level productivity for large firms but not in the case of MSMEs. We posit that this might be due to the relative disadvantages that Indian MSMEs face which prevent them from benefiting from trade liberalisation. We also find that productivity gains arising from the sourcing of imported inputs have been greater than those arising from increased product competition and that NTB liberalisation has had a greater impact compared to tariff liberalisation on firm-level productivity. Changes in MSME legislation and the classification of firms are also found to have a bearing on firm performance. Our study contributes to the literature by confirming the need to focus specifically on constraints faced by MSMEs if they are to benefit from trade liberalisation. It highlights the importance of liberalising trade in intermediates as well as the role of MSME classification in enabling productivity gains. JEL Codes: L6, D24, L1, F13

Empirical Asset Pricing with Score-Driven Conditional Betas

Abstract We develop a novel empirical asset pricing framework to estimate time-varying risk premia, building upon score-driven conditional betas models. First, we extend the theory by establishing the asymptotic distribution of standard test statistics, allowing us to assess the significance of a given factor in the regression. Additionally, we introduce a bootstrap procedure and establish its validity. Second, we propose a two-step estimation procedure to recover time-varying risk premia. We illustrate the performance of our tests and risk premia estimation through simulations. Third, we estimate a time-varying premium associated with a carbon risk factor in the cross-section of U.S. industry portfolios.

Improved estimation of semiparametric dynamic copula models with filtered nonstationarity

This paper considers estimation of short-run dynamics in time series that contain a nonstationary component. We assume that appropriate preliminary methods can be applied to the observed time series to separate short-run elements from long-run slowly evolving secular components, and focus on estimation of the short-run dynamics based on the filtered data. We use a flexible copula-generated Markov model to capture the nonlinear temporal dependence in the short-run component and study estimation of the copula model. Using the rescaled empirical distribution of the filtered data as an estimator of the marginal distribution, Chen et al. (2022) proposed a simple, yet flexible, two-step estimation procedure for the copula model. The two-step estimator works well when the tail dependence is small. However, simulations reveal that the two-step estimator may be biased in finite samples in the presence of tail dependence. To improve the performance of short-term dynamic analysis in the presence of tail dependence, we propose in this paper a pseudo sieve maximum likelihood (PSML) procedure to jointly estimate the residual copula parameter and the invariant density of the filtered residuals. We establish the root-n consistency and asymptotic distribution of the PSML estimator of any smooth functional of the residual copula parameter and invariant residual density. We further show that the PSML estimator of the residual copula parameter is asymptotically normal, with the limiting distribution independent of the filtration. Simulations reveal that in the presence of strong tail dependence, compared to the two-step estimates of Chen et al. (2022), the proposed PSML estimates have smaller biases and smaller mean squared errors even in small samples. Applications to nonstationary macro-finance and climate time series are presented.

Two-Step Parameter Estimation for Read Feature Models

AbstractOver the last two decades, the field of molecular biology has witnessed a revolution due to the development of next generation sequencing (NGS) technologies. NGS enables researchers to routinely generate huge amounts of data that can be used to pursue a large variety of questions in diverse biological systems. The development of these techniques has propelled the emergence of a sub-discipline within computational biology that is concerned with developing methods and statistical models to derive quantitative information from the complex and often indirect data that are generated by NGS. Often, NGS analysis results in particular patterns per biological entity that can be exploited to estimate quantitative parameters of biological interest. Here, I define read feature models (RFMs) as a general framework for such data. RFMs entail global, genome-wide parameters as well as parameters per biological entity, suggesting a two-step procedure for parameter estimation. I describe the analysis of metabolic RNA labeling data as an example of an RFM and analyze and discuss the merits and shortcomings of the two-step estimation.

Regression analysis of longitudinal data with mixed synchronous and asynchronous longitudinal covariates

In linear models, omitting a covariate that is orthogonal to covariates in the model does not result in biased coefficient estimation. This generally does not hold for longitudinal data, where additional assumptions are needed to get an unbiased coefficient estimation in addition to the orthogonality between omitted longitudinal covariates and longitudinal covariates in the model. We propose methods to mitigate the omitted variable bias under weaker assumptions. A two-step estimation procedure is proposed to infer the asynchronous longitudinal covariates when such covariates are observed. For mixed synchronous and asynchronous longitudinal covariates, we get a parametric convergence rate for the coefficient estimation of the synchronous longitudinal covariates by the two-step method. Extensive simulation studies provide numerical support for the theoretical findings. We illustrate the performance of our method on a dataset from the Alzheimer’s Disease Neuroimaging Initiative study.

Estimation of complier expected shortfall treatment effects with a binary instrumental variable

Estimating the causal effect of a treatment or exposure for a subpopulation is of great interest in many biomedical and economical studies. Expected shortfall, also referred to as the super-quantile, is an attractive effect-size measure that can accommodate data heterogeneity and aggregate local information of effect over a certain region of interest of the outcome distribution. In this article, we propose the ComplieRExpected Shortfall Treatment Effect (CRESTE) model under an instrumental variable framework to quantity the CRESTE for a binary endogenous treatment variable. By utilizing the special characteristics of a binary instrumental variable and a specific formulation of Neyman-orthogonalization, we propose a two-step estimation procedure, which can be implemented by simply solving weighted least-squares regression and weighted quantile regression with estimated weights. We develop the asymptotic properties for the proposed estimator and use numerical simulations to confirm its validity and robust finite-sample performance. An illustrative analysis of a National Job Training Partnership Act study is presented to show the practical utility of the proposed method.

Regression analysis of multivariate interval-censored failure time data with a cured subgroup and informative censoring

Multivariate interval-censored failure time data occur when a failure time study involves several related failure times of interest and only interval-censored observations are available for each of them. Although a great deal of literature has been established for their regression analysis, there does not seem to exist an approach that applies to the situation where there exist both a cured subgroup and informative censoring, the focus of this paper. For the problem, a class of semiparametric transformation non-mixture cure models is presented and a two-step estimation procedure is proposed. For the implementation of the proposed method, an EM algorithm is developed. Numerical results suggest that the proposed method works well for practical situations and an application is provided.

Multivariate degradation system reliability analysis with multiple sources of uncertainty

As the industrial Internet of Things evolves, multi-sensor monitoring becomes increasingly prevalent, resulting in degrading systems frequently exhibiting multivariate degradation characteristics. Multiple performance characteristics are frequently interdependent due to the consistency of the operating environment, operating conditions, and internal structure of the system. On the other hand, performance characteristic detection is also affected by numerous uncertainties. A multivariate stochastic degradation model that takes dependencies with multiple sources of uncertainty into account is developed for the analysis of multivariately dependent degradation systems. To represent linear or nonlinear degradation qualities, the marginal degradation process is referred to as a generalized stochastic degradation model. By using the D-vine copula function and pair-copula construction, dependencies between numerous variables are formed. The marginal and joint distribution parameters of the degradation model are derived using a two-step parameter estimation procedure. Lastly, the C-MAPSS dataset is used to analyze the applicability of the proposed model for bivariate and multivariate instances. The effectiveness of the proposed method is verified by experiments.

Channel Estimation for Reconfigurable Intelligent Surface Aided Multi-User mmWave MIMO Systems

Channel acquisition is one of the main challenges for the deployment of reconfigurable intelligent surface (RIS) aided communication systems. This is because an RIS has a large number of reflective elements, which are passive devices with no active transmitting/receiving abilities. In this paper, we study the channel estimation problem for the RIS aided multi-user millimeter-wave (mmWave) multi-input multi-output (MIMO) system. Specifically, we propose a novel channel estimation protocol for the above system to estimate the cascaded channels, which are the products of the channels from the base station (BS) to the RIS and from the RIS to the users. Further, since the cascaded channels are typically sparse, this allows us to formulate the channel estimation problem as a sparse recovery problem using compressive sensing (CS) techniques, thereby allowing the channels to be estimated with less training overhead. Moreover, the sparse channel matrices of the cascaded channels of all users have a common block sparsity structure due to the common channel between the BS and the RIS. To take advantage of the common sparsity pattern, we propose a two-step multi-user joint channel estimation procedure. In the first step, we make use of the common column-block sparsity and project the received signals onto the common column subspace. In the second step, we make use of the row-block sparsity of the projected signals and propose a multi-user joint sparse matrix recovery algorithm that takes into account the common channel between the BS and the RIS.

On the transmission of oil supply and demand shocks to CO2 emissions in the US by considering uncertainty: A time-varying perspective

In an economic context increasingly governed by structural changes, crises, and uncertainty, our understanding of the transmission of oil price shocks to real economic activity and the resulting effects on CO2 emissions is found to evolve over time. Our understanding is also found to evolve when considering the sources of oil price fluctuations as emanating from the supply or demand side. So far, there is still few answers provided by the literature on how economic and policy uncertainty influences the response of CO2 emissions to different sources of oil price shocks. This paper tries to investigate this ‘missing link’ by estimating the time-varying transmission of oil supply and demand shocks to CO2 emissions in the US, while considering the simultaneous effect of uncertainty. Using monthly data covering a period including the Covid-19 health crisis, a two-step estimation procedure is adopted: before constructing a time-varying parameter structural vector autoregression model with stochastic volatility (TVP-SVAR-SV), a structural VAR model (SVAR) is implemented to decompose oil price shocks in four structural shocks namely: oil supply shock, aggregate demand shock, domestic demand shock and oil-specific demand shock. Estimation results and robustness tests show that the level of uncertainty shapes the transmission of oil price shocks to CO2 emissions. Oil supply and oil-specific demand shocks impact negatively CO2 emissions mostly when uncertainty is low. A high uncertainty level leads to a perverse positive impact of aggregate demand shocks on CO2 emissions. Interestingly, CO2 emissions are found to increase during low levels of uncertainty in response to domestic demand driven oil price shocks. This finding may be due to the expansive economic policies enforced to decrease uncertainty and increase consumption in reaction to domestic demand shocks. These results imply that workable solutions targeting an optimal level of CO2 emissions should not only consider different sources of oil price fluctuations but also the level of uncertainty. Discarding the level of uncertainty may lead to a sub-optimal calibration of the regulatory and fiscal measures aiming to protect the environment against different sources of oil price shocks and to adapt these measures to the time horizon of carbon emissions responses.

Asset Pricing via the Conditional Quantile Variational Autoencoder

We propose a new asset pricing model that is applicable to the big panel of return data. The main idea of this model is to learn the conditional distribution of the return, which is approximated by a step distribution function constructed from conditional quantiles of the return. To study conditional quantiles of the return, we propose a new conditional quantile variational autoencoder (CQVAE) network. The CQVAE network specifies a factor structure for conditional quantiles with latent factors learned from a VAE network and nonlinear factor loadings learned from a “multi-head” network. Under the CQVAE network, we allow the observed covariates such as asset characteristics to guide the structure of latent factors and factor loadings. Furthermore, we provide a two-step estimation procedure for the CQVAE network. Using the learned conditional distribution of return from the CQVAE network, we propose our asset pricing model from the mean of this distribution, and additionally, we use both the mean and variance of this distribution to select portfolios. Finally, we apply our CQVAE asset pricing model to analyze a large 60-year US equity return dataset. Compared with the benchmark conditional autoencoder model, the CQVAE model not only delivers much larger values of out-of-sample total and predictive R 2’s, but also earns at least 30.9% higher values of Sharpe ratios for both long-short and long-only portfolios.

Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation.

This work considers targeted maximum likelihood estimation (TMLE) of treatment effects on absolute risk and survival probabilities in classical time-to-event settings characterized by right-censoring and competing risks. TMLE is a general methodology combining flexible ensemble learning and semiparametric efficiency theory in a two-step procedure for substitution estimation of causal parameters. We specialize and extend the continuous-time TMLE methods for competing risks settings, proposing a targeting algorithm that iteratively updates cause-specific hazards to solve the efficient influence curve equationfor the target parameter. As part of the work, we further detail and implement the recently proposed highly adaptive lasso estimator for continuous-time conditional hazards with L1 -penalized Poisson regression. The resulting estimation procedure benefits from relying solely on very mild nonparametric restrictions on the statistical model, thus providing a novel tool for machine-learning-based semiparametric causal inference for continuous-time time-to-event data. We apply the methods to a publicly available dataset on follicular cell lymphoma where subjects are followed over time until disease relapse or death without relapse. The data display important time-varying effects that can be captured by the highly adaptive lasso. In our simulations that are designed to imitate the data, we compare our methods to a similar approach based on random survival forests and to the discrete-timeTMLE.

Approach for Identifying Cartesian Stiffness of a 5-Degree-of-Freedom Hybrid Robot for Machining

Abstract This article presents a systematic approach for identifying the Cartesian stiffness of a 5-degree-of-freedom (DOF) hybrid robot for machining that includes a parallel mechanism and an A/C wrist. The novelty of this approach is that the elasticities of both links and joints in the parallel mechanism are integrated into the compliance (inverse of stiffness) parameters at the limb level. By identifying the compliance parameters at the limb level rather than at the joint/link level, the number of parameters to be identified is significantly reduced and the complexity of the identification problem is decreased. Based on screw theory, the Cartesian stiffness model of this hybrid robot is established first. Then, by reconstructing this stiffness model, a linear regression model suitable for estimating the compliance parameter is derived. In addition, a two-step systematic procedure for parameter estimation is introduced, including the reconstruction of the design matrix and robust ridge estimation. Finally, both computer simulations and experiments are carried out to demonstrate the validity of the proposed approach. The simulation results show that the predictive deviations of the end-effector deflections identified by ridge estimation are less than those estimated by linear least squares, confirming its greater robustness. The experimental results indicate that the developed method has potential in industrial settings.

Rebundling Institutions: How property rights and contracting institutions combine for growth

This study provides empirical evidence for the joint workings of property rights and contracting institutions as fundamental causes of growth. In a two-step panel estimation procedure that uses data from 130 countries over the period 2005–2015, I find that the income effects of legal reforms in property rights institutions vary with the prevalent quality of legal contracting institutions and vice versa. Decomposing the interaction effects for groups of countries with different quality combinations reveals that the quality fit of the two types of institutions matters for not only the size but also the direction of the interaction effects. In countries with absent or bad legal institutions, legal reforms considering only one type can even reduce income. Piecemeal reforms work best when they close quality gaps and they can backfire when the gap widens. The findings remain robust after tackling endogeneity issues, extending the period of analysis, estimating alternative models, and using alternative estimators. The findings imply that legal reforms have to be coordinated across different types of institutions and consider possible interferences with extra-legal rules and practices.

A two-step estimation procedure for locally stationary ARMA processes with tempered stable innovations

A two-step estimation procedure for locally stationary ARMA processes with tempered stable innovations

Ranking of average treatment effects with generalized random forests for time-to-event outcomes.

Linkage between drug claims data and clinical outcome allows a data-driven experimental approach to drug repurposing. We develop an estimation procedure based on generalized random forests for estimation of time-point specific average treatment effects in a time-to-event setting with competing risks. To handle right-censoring, we propose a two-step procedure for estimation, applying inverse probability weighting to construct time-point specific weighted outcomes as input for the generalized random forest. The generalized random forests adaptively handle covariate effects on the treatment assignment by applying a splitting rule that targets a causal parameter. Using simulated data we demonstrate that the method is effective for a causal search through a list of treatments to be ranked according to the magnitude of their effect on clinical outcome. We illustrate the method using the Danish national health registries where it is of interest to discover drugs with an unexpected protective effect against relapse of severe depression.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly.

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

Tensor response quantile regression with neuroimaging data.

Collecting neuroimaging data in the form of tensors (i.e. multidimensional arrays) has become more common in mental health studies, driven by an increasing interest in studying the associations between neuroimaging phenotypes and clinical disease manifestation. Motivated by a neuroimaging study of post-traumatic stress disorder (PTSD) from the Grady Trauma Project, we study a tensor response quantile regression framework, which enables novel analyses that confer a detailed view of the potentially heterogeneous association between a neuroimaging phenotype and relevant clinical predictors. We adopt a sensible low-rank structure to represent the association of interest, and propose a simple two-step estimation procedure which is easy to implement with existing software. We provide rigorous theoretical justifications for the intuitive two-step procedure. Simulation studies demonstrate good performance of the proposed method with realistic sample sizes in neuroimaging studies. We conduct the proposed tensor response quantile regression analysis of the motivating PTSD study to investigate the association between fMRI resting-state functional connectivity and PTSD symptom severity. Our results uncover non-homogeneous effects of PTSD symptoms on brain functional connectivity, which cannot be captured by existing tensor responsemethods.

Estimation of linear transformation cure models with informatively interval-censored failure time data

Linear transformation models have been one type of models commonly used for regression analysis of failure time data partly due to their flexibility. More recently they have been generalised to the case where there may exist a cured subgroup or the censoring may be informative. In this paper, we consider a more complicated and general situation where both a cured subgroup and informative censoring, or more specifically informative interval censoring, exist. As pointed out in the literature, the analysis that fails to take into account either the cured subgroup or the informative censoring can yield biased estimation or misleading conclusions. For the problem, a three-component mixture cure model is presented and we develop a two-step estimation procedure with the use of B-splines to approximate unknown functions. The proposed approach is quite flexible and can be easily implemented. Also the proposed estimators of regression parameters are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and suggests that the method works well for practical situations. Furthermore a real application is provided to illustrate the proposed methodology.