Exogenous Covariates Research Articles

Revisiting Panel Data Binary Choice Models with Lagged Dependent Variables*

This paper revisits the identification and estimation of a class of semiparametric (distribution-free) panel data binary choice models with lagged dependent variables, exogenous covariates, and entity fixed effects. We provide a novel identification strategy, using an “identification at infinity” argument. In contrast with the celebrated Honoré and Kyriazidou (2000), our method permits time trends of any form and does not suffer from the “curse of dimensionality”. We propose an easily implementable conditional maximum score estimator. The asymptotic properties of the proposed estimator are fully characterized. A small-scale Monte Carlo study demonstrates that our approach performs satisfactorily in finite samples. We illustrate the usefulness of our method by presenting an empirical application to enrollment in private hospital insurance using the Household, Income and Labor Dynamics in Australia (HILDA) Survey data.

Regression‐based network‐flow and inner‐matrix reconstruction

AbstractNetwork or matrix reconstruction is a general problem that occurs if the row‐ and column sums of a matrix are given, and the matrix entries need to be predicted conditional on the aggregated information. In this paper, we show that the predictions obtained from the iterative proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can be obtained by restricted maximum likelihood estimation relying on augmented Lagrangian optimization. Based on this equivalence, we extend the framework of network reconstruction, conditional on row and column sums, toward regression, which allows the inclusion of exogenous covariates and bootstrap‐based uncertainty quantification. More specifically, the mean of the regression model leads to the observed row and column margins. To exemplify the approach, we provide a simulation study and investigate interbank lending data, provided by the Bank for International Settlement. This dataset provides full knowledge of the real network and is, therefore, suitable to evaluate the predictions of our approach. It is shown that the inclusion of exogenous information leads to superior predictions in terms of and errors.

A Stochastic Recurrent Encoder Decoder Network for Multistep Probabilistic Wind Power Predictions.

In this article, a stochastic recurrent encoder decoder neural network (SREDNN), which considers latent random variables in its recurrent structures, is developed for the first time for the generative multistep probabilistic wind power predictions (MPWPPs). The SREDNN enables the stochastic recurrent model under the encoder-decoder framework to engage exogenous covariates to produce better MPWPP. The SREDNN consists of five components, the prior network, the inference network, the generative network, the encoder recurrent network, and the decoder recurrent network. The SREDNN is equipped with two critical advantages compared with conventional RNN-based methods. First, the integration over the latent random variable builds an infinite Gaussian mixture model (IGMM) as the observation model, which drastically increases the expressiveness of the wind power distribution. Secondly, hidden states of the SREDNN are updated in a stochastic way, which builds an infinite mixture of the IGMM for describing the ultimate wind power distribution and enables the SREDNN to model complex patterns across wind speed and wind power sequences. Computational experiments are conducted on a dataset of a commercial wind farm having 25 wind turbines (WTs) and two publicly assessable WT datasets to verify the advantages and effectiveness of the SREDNN for MPWPP. Experimental results show that the SREDNN achieves a lower negative form of the continuously ranked probability score (CRPS*) as well as a superior sharpness and comparable reliability of prediction intervals by comparing against considered benchmarking models. Results also show the clear benefit gained from considering latent random variables in SREDNN.

Traffic flows time series in a flood-prone area: modeling and clustering on extreme values with a spatial constraint

Time series of traffic flows, extracted from mobile phone origin–destination data, are employed for monitoring people crowding and mobility in areas subject to flooding risk. By applying a vector autoregressive model with exogenous covariates combined with dynamic harmonic regression to such time series, we detected the presence of many extreme events in the residuals, which exhibit heavy-tailed distribution. For this reason, we propose a time series clustering procedure based on tail dependence which is suitable for data characterized by a spatial dimension, since objects’ geographical proximity is taken into account. The final aim is to obtain clusters of areas characterized by the common tendency to the manifestation of extreme events, that in this case study are represented by extremely high incoming traffic flows. The proposed method is applied to the Mandolossa, a strongly urbanized area located on the western outskirts of Brescia (northern Italy) which is subject to frequent flooding.

The Gender Well-Being Gap

Given recent controversies about the existence of a gender wellbeing gap we revisit the issue estimating gender differences across 55 SWB metrics—37 positive affect and 18 negative affect—contained in 8 cross-country surveys from 167 countries across the world, two US surveys covering multiple years and a survey for Canada. We find women score more highly than men on all negative affect measures and lower than men on all but three positive affect metrics, confirming a gender wellbeing gap. The gap is apparent across countries and time and is robust to the inclusion of exogenous covariates (age, age squared, time and location fixed effects). It is also robust to conditioning on a wider set of potentially endogenous variables. However, when one examines the three ‘global’ wellbeing metrics—happiness, life satisfaction and Cantril’s Ladder—women are either similar to or ‘happier’ than men. This finding is insensitive to which controls are included and varies little over time. The difference does not seem to arise from measurement or seasonality as the variables are taken from the same surveys and frequently measured in the same way. The concern here though is that this is inconsistent with objective data where men have lower life expectancy and are more likely to die from suicide, drug overdoses and other diseases. This is the true paradox—morbidity doesn’t match mortality by gender. Women say they are less cheerful and calm, more depressed, and lonely, but happier and more satisfied with their lives, than men.

First-stage analysis for instrumental-variables quantile regression

In this article, we develop a first-stage linear regression command, fsivqreg, for an instrumental-variables quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, that is, a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, at a given quantile. An empirical application illustrates its implementation.

Intraindividual time-varying dynamic network of affects: linear autoregressive mixed-effects models for ecological momentary assessment.

An interesting recent development in emotion research and clinical psychology is the discovery that affective states can be modeled as a network of temporally interacting moods or emotions. Additionally, external factors like stressors or treatments can influence the mood network by amplifying or dampening the activation of specific moods. Researchers have turned to multilevel autoregressive models to fit these affective networks using intensive longitudinal data gathered through ecological momentary assessment. Nonetheless, a more comprehensive examination of the performance of such models is warranted. In our study, we focus on simple directed intraindividual networks consisting of two interconnected mood nodes that mutually enhance or dampen each other. We also introduce a node representing external factors that affect both mood nodes unidirectionally. Importantly, we disregard the potential effects of a current mood/emotion on the perception of external factors. We then formalize the mathematical representation of such networks by exogenous linear autoregressive mixed-effects models. In this representation, the autoregressive coefficients signify the interactions between moods, while external factors are incorporated as exogenous covariates. We let the autoregressive and exogenous coefficients in the model have fixed and random components. Depending on the analysis, this leads to networks with variable structures over reasonable time units, such as days or weeks, which are captured by the variability of random effects. Furthermore, the fixed-effects parameters encapsulate a subject-specific network structure. Leveraging the well-established theoretical and computational foundation of linear mixed-effects models, we transform the autoregressive formulation to a classical one and utilize the existing methods and tools. To validate our approach, we perform simulations assuming our model as the true data-generating process. By manipulating a predefined set of parameters, we investigate the reliability and feasibility of our approach across varying numbers of observations, levels of noise intensity, compliance rates, and scalability to higher dimensions. Our findings underscore the challenges associated with estimating individualized parameters in the context of common longitudinal designs, where the required number of observations may often be unattainable. Moreover, our study highlights the sensitivity of autoregressive mixed-effect models to noise levels and the difficulty of scaling due to the substantial number of parameters.

Energy price shocks and stock market volatility in an energy-importing country

We examine volatility dynamics in the Korean market using heterogeneous autoregressive models with exogenous covariates. The COVID-19 pandemic and the Russia–Ukraine War have caused substantial fluctuations in energy prices. We assess how these energy shocks affect stock market-implied volatility in Korea, a representative energy-importing country. During the pre-pandemic period, domestic and U.S. market factors affect Korea's volatility dynamics, whereas crude oil and natural gas futures prices have little explanatory power for these dynamics. In contrast, during the pandemic (war), oil (natural gas) futures prices become the key explanatory variable, and other market factors lose their explanatory power.

A Ridge-Regularized Jackknifed Anderson-Rubin Test

We consider hypothesis testing in instrumental variable regression models with few included exogenous covariates but many instruments—possibly more than the number of observations. We show that a ridge-regularized version of the jackknifed Anderson and Rubin (henceforth AR) test controls asymptotic size in the presence of heteroscedasticity, and when the instruments may be arbitrarily weak. Asymptotic size control is established under weaker assumptions than those imposed for recently proposed jackknifed AR tests in the literature. Furthermore, ridge-regularization extends the scope of jackknifed AR tests to situations in which there are more instruments than observations. Monte Carlo simulations indicate that our method has favorable finite-sample size and power properties compared to recently proposed alternative approaches in the literature. An empirical application on the elasticity of substitution between immigrants and natives in the United States illustrates the usefulness of the proposed method for practitioners.

Consistent estimation of panel data sample selection models

The properties of classical panel data estimators including fixed effect, first-differences, random effects, and generalized method of moments-instrumental variables estimators in both static as well as dynamic panel data models are investigated under sample selection. The correlation of the unobserved errors is shown not to be sufficient for the inconsistency of these estimators. A necessary condition for this to arise is the presence of common (and/or non-independent) non-deterministic covariates in the selection and outcome equations. When both equations do not have covariates in common and independent of each other, the fixed effects, and random effects estimators in static models with exogenous covariates are consistent. Furthermore, the first-differenced generalized method of moments estimator uncorrected for sample selection as well as the instrumental variables estimator uncorrected for sample selection are both consistent for autoregressive models even with endogenous covariates. The same results hold when both equations have no covariates in common but are correlated once we account for such correlation. Under the same circumstances, the system generalized method of moments estimator adding more moments from the levels equation has moderate bias. Alternatively, when both equations have common covariates the appropriate correction method is suggested. Serial correlation of the errors being a key determinant for that choice. The finite sample properties of the proposed estimators are evaluated using a Monte Carlo study. Two empirical illustrations are provided.

Dependence matters: Statistical models to identify the drivers of tie formation in economic networks

Networks are ubiquitous in economic research on organizations, trade, and many other areas. However, while economic theory extensively considers networks, no general framework for their empirical modeling has yet emerged. We thus introduce two different statistical models for this purpose – the Exponential Random Graph Model (ERGM) and the Additive and Multiplicative Effects network model (AME). Both model classes can account for network interdependencies between observations, but differ in how they do so. The ERGM allows one to explicitly specify and test the influence of particular network structures, making it a natural choice if one is substantively interested in estimating endogenous network effects. In contrast, AME captures these effects by introducing actor-specific latent variables affecting their propensity to form ties. This makes the latter a good choice if the researcher is interested in capturing the effect of exogenous covariates on tie formation without having a specific theory on the endogenous dependence structures at play. After introducing the two model classes, we showcase them through real-world applications to networks stemming from international arms trade and foreign exchange activity. We further provide full replication materials to facilitate the adoption of these methods in empirical economic research.

Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates

Density Power Divergence Estimator for General Integer-Valued Time Series with Exogenous Covariates

Understanding networks with exponential-family random network models

The structure of many complex social networks is determined by nodal and dyadic covariates that are endogenous to the tie variables. While exponential-family random graph models (ERGMs) have been very successful in modeling social networks with exogenous covariates, they are often misspecified for networks where some covariates are stochastic. Exponential-family random network models (ERNMs) are an extension of ERGM that retain the desirable properties of ERGM, but allow the joint modeling of tie variables and covariates. We compare ERGM to ERNM to show how conclusions of ERGM modeling are improved by consideration of the ERNM framework. In particular, ERNM simultaneously represents the effects of social influence and social selection processes, while commonly used models do not.

A combined moment equation approach for spatial autoregressive models

AbstractExisting methods for fitting spatial autoregressive models have various strengths and weaknesses. For example, the maximum likelihood estimation (MLE) approach yields efficient estimates but is computationally burdensome. Computationally efficient methods, such as generalized method of moments (GMMs) and spatial two‐stage least squares (2SLS), typically require exogenous covariates to be significant, a restrictive assumption that may fail in practice. We propose a new estimating equation approach, termed combined moment equation (COME), which combines the first moment with covariance conditions on the residual terms. The proposed estimator is less computationally demanding than MLE and does not need the restrictive exogenous conditions as required by GMM and 2SLS. We show that the proposed estimator is consistent and establish its asymptotic distribution. Extensive simulations demonstrate that the proposed method outperforms the competitors in terms of bias, efficiency, and computation. We apply the proposed method to analyze an air pollution study, and obtain some interesting results about the spatial distribution of PM2.5 concentrations in Beijing.

Electricity price spike clustering: A zero-inflated GARX approach

Sudden dramatic rises in electricity prices, known as electricity “price spikes”, are ubiquitous in electricity spot markets worldwide. These price spikes often cluster. Energy retailers in many countries, including Australia, purchase electricity in an unregulated spot market and sell it to consumers at a heavily regulated price. As a result, the occurrence and clustering of spikes in the spot electricity price is particularly hazardous for retailers, and effective modelling and forecasting of these spikes is of foremost importance for effective risk management. This paper uses a data-dependent two-regime threshold autoregression to determine the electricity price spikes and proposes a zero-inflated generalized autoregression with exogenous covariates (ZIGARX) for modelling the time series count of price spikes. This model is shown to well capture the salient features of electricity price spikes, and can provide effective rolling probability forecasts of price spike occurrence. We apply the proposed approach to analyze the spot prices in four major regions in the Australian National Electricity Market (NEM) over the period April 2016 to February 2022. Results show that price spike clustering is captured very well using our model, and the persistence in price spike occurrence remains even after controlling for the relevant exogenous covariates. We also find that, in most of our sample period, the increasing use of renewable generation has mixed effects on the occurrence of price spikes.

Regression of binary network data with exchangeable latent errors

AbstractUndirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance.

A first-stage representation for instrumental variables quantile regression

Summary This paper develops a first-stage linear regression representation for an instrumental variables (IV) quantile regression (QR) model. The quantile first stage is analogous to the least-squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first stage. We then suggest procedures to evaluate the validity of instruments by evaluating their statistical significance using the first-stage representation. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power. An empirical application illustrates the methods.

Strong mixing properties of discrete-valued time series with exogenous covariates

We derive strong mixing conditions for many existing discrete-valued time series models that include exogenous covariates in the dynamic. Our main contribution is to study how a mixing condition on the covariate process transfers to a mixing condition for the response. Using a coupling method, we first derive mixing conditions for some Markov chains in random environments, which gives a first result for some autoregressive categorical processes with strictly exogenous regressors. Our result is then extended to some infinite memory categorical processes. In the second part of the paper, we study autoregressive models for which the covariates are sequentially exogenous. Using a general random mapping approach on finite sets, we get explicit mixing conditions that can be checked for many categorical time series found in the literature, including multinomial autoregressive processes, ordinal time series and dynamic multiple choice models. We also study some autoregressive count time series using a somewhat different contraction argument. Our contribution fills an important gap for such models, presented here under a more general form, since such a strong mixing condition is often assumed in some recent works but no general approach is available to check it.

Estimation and inference in factor copula models with exogenous covariates

A factor copula model is proposed in which factors are either simulable or estimable from exogenous information. Point estimation and inference are based on a simulated methods of moments (SMM) approach with non-overlapping simulation draws. Consistency and limiting normality of the estimator is established and the validity of bootstrap standard errors is shown. Doing so, previous results from the literature are verified under low-level conditions imposed on the individual components of the factor structure. Monte Carlo evidence confirms the accuracy of the asymptotic theory in finite samples and an empirical application illustrates the usefulness of the model to explain the cross-sectional dependence between stock returns.

Multivariate time series models for mixed data

We introduce a general approach which unifies some previous attempts for modeling the dynamic of multivariate time series or for regression analysis when the data are of mixed type (binary/count/continuous). Our approach is quite flexible since conditionally on past values, each coordinate at time t can have a distribution compatible with a standard univariate time series model such as GARCH, ARMA, INGARCH or logistic models whereas past values of the other coordinates play the role of exogenous covariates in the dynamic. The simultaneous dependence in the multivariate time series can be modeled with a copula. Additional exogenous covariates are also allowed in the dynamic. We first study some usual stability properties of these models and then show that autoregressive parameters can be consistently estimated equation-by-equation using a pseudo-maximum likelihood method, leading to a fast implementation even when the number of time series is large. Moreover, we prove consistency results when a parametric copula model is fitted to the time series and in the case of Gaussian copulas, we show that the likelihood estimator of the correlation matrix is strongly consistent. We carefully check all our assumptions for two prototypical examples: a GARCH/INGARCH model and logistic/log-linear INGARCH model. Our results are illustrated with numerical experiments as well as two real data sets.