Quasi-maximum Likelihood Approach Research Articles

Community influence analysis in social networks

Heterogeneous influence detection across network nodes is an important task in network analysis. A community influence model (CIM) is proposed to allow nodes to be classified into different communities (i.e., clusters or groups) such that the nodes within the same community share the common influence parameter. Employing the quasi-maximum likelihood approach, together with the fused lasso-type penalty, both the number of communities and the influence parameters can be estimated without imposing any specific distribution assumption on the error terms. The resulting estimators are shown to enjoy the oracle property; namely, they perform as well as if the true underlying network structure were known in advance. The proposed approach is also applicable for identifying influential nodes in a homogeneous setting. The performance of our method is illustrated via simulation studies and two empirical examples using stock data and coauthor citation data, respectively.

Bipartite network influence analysis of a two-mode network

A two-mode network contains two types of nodes, and edges exist only between any two nodes that are associated with different entities. Owing to the network connections (i.e., edges) between the two types of network nodes, nodal responses are unlikely to be independently and identically distributed, resulting in possible nodal heterogeneity across the two types of nodes. This study proposes a novel bipartite network influence model (BNIM) to evaluate nodal heterogeneity from the perspective of nodal influence. To make the model estimable, we parameterize the influence indices with a set of nodal attributes through a prespecified link function, and employ the quasi-maximum likelihood approach to estimate the unknown parameters. Score tests are presented to examine the heterogeneity of nodal influences across the two types of nodes. To assess the adequacy of the link function, we carry out a quasi-likelihood ratio test and establish its asymptotic properties under the appropriate conditions. Simulation studies and the real data analysis of a fund-stock network are studied to assess the finite-sample performance of BNIM.

Semi-nonparametric estimation of secret reserve prices in auctions

This letter proposes an estimation method for the distribution of unobservable secret seller reserve prices in auctions. Within the symmetric affiliated private values model, I construct a density estimator using the semi-nonparametric quasi maximum likelihood approach developed by Gallant and Nychka (1987). I then use Monte Carlo experiments to demonstrate its performance in relatively small samples. A discussion on applying this method to structurally similar identification problems is provided. • This letter offers an approach to identify the distribution of secret reserve prices. • The model allows for affiliated private values among buyers and sellers. • Input data include the auction’s paying bid and whether the item sold at said bid. • A semi-nonparametric estimator identifies the distribution of secret reserve prices. • This method works well in relatively small samples ( ∼ 100 ).

Empirical likelihood for spatial dynamic panel data models.

Spatial dynamic panel data (SDPD) models have received great attention in economics in recent 10 years. Existing approaches for the estimation and test of SDPD models are quasi-maximum likelihood (QML) approach and generalized method of moments (GMM). In this article, we introduce the empirical likelihood (EL) method to the statistical inference for SDPD models. The EL ratio statistics are constructed for the parameters of spatial dynamic panel data models. It is shown that the limiting distributions of the empirical likelihood ratio statistics are chi-squared distributions, which are used to construct confidence regions for the parameters of the models. Simulation results show that the EL based confidence regions outperform the normal approximation based confidence regions.

Inward and Outward Network Influence Analysis

Measuring heterogeneous influence across nodes in a network is critical in network analysis. This article proposes an inward and outward network influence (IONI) model to assess nodal heterogeneity. Specifically, we allow for two types of influence parameters; one measures the magnitude of influence that each node exerts on others (outward influence), while we introduce a new parameter to quantify the receptivity of each node to being influenced by others (inward influence). Accordingly, these two types of influence measures naturally classify all nodes into four quadrants (high inward and high outward, low inward and high outward, low inward and low outward, and high inward and low outward). To demonstrate our four-quadrant clustering method in practice, we apply the quasi-maximum likelihood approach to estimate the influence parameters, and we show the asymptotic properties of the resulting estimators. In addition, score tests are proposed to examine the homogeneity of the two types of influence parameters. To improve the accuracy of inferences about nodal influences, we introduce a Bayesian information criterion that selects the optimal influence model. The usefulness of the IONI model and the four-quadrant clustering method is illustrated via simulation studies and an empirical example involving customer segmentation.

Marginal Propensities to Consume Before and After the Great Recession

Using a quasi maximum likelihood approach for a semi-structural model, we find highly precise and distinct estimates of consumption responses to idiosyncratic income shocks for different groups of households. Homeowners stratified by liquid wealth exhibit the most dispersion in their marginal propensities to consume. Time-varying estimates support strong patterns of heterogeneity by homeownership status and balance sheet liquidity, with economically and statistically significant increases in the sensitivity of transitory consumption for homeowners, especially those with lower liquid wealth, following the collapse in house prices with the Great Recession. These findings support consumption theories that include housing as an illiquid asset.

Dealing with Markov-switching parameters in quantile regression models

Quantile regression has become a standard modern econometric method because of its capability to investigate the relationship between economic variables at various quantiles. The econometric method of Markov-switching regression is also considered important because it can deal with structural models or time-varying parameter models flexibly. A combination of these two methods, known as “Markov-switching quantile regression (MSQR),” has recently been proposed. Liu and, Liu and Luger propose MSQR models using the Bayesian approach whereas Ye et al.’s proposal for MSQR models is based on the classical approach. In our study, we extend the results of Ye et al. First, we propose an efficient estimation method based on the expectation-maximization algorithm. In our second extension, we adopt the quasi-maximum likelihood approach to estimate the proposed MSQR models unlike the maximum likelihood approach that Ye et al. use. Our simulation results confirm that the proposed expectation-maximization (EM) estimation method for MSQR models works quite well.

A replication of “A quasi-maximum likelihood approach for large, approximate dynamic factor models” (Review of Economics and Statistics, 2012)

Abstract The authors replicate and extend the Monte Carlo experiment presented in Doz, Giannone and Reichlin (A Quasi-Maximum Likelihood Approach For Large, Approximate Dynamic Factor Models, Review of Economics and Statistics, 2012) on alternative (time-domain based) methods for extracting dynamic factors from large datasets; they employ open source software and consider a larger number of replications and a wider set of scenarios. Their narrow sense replication exercise fully confirms the results in the original article. As for their extended replication experiment, the authors examine the relative performance of competing estimators under a wider array of cases, including richer dynamics, and find that maximum likelihood (ML) is often the dominant method; moreover, the persistence characteristics of the observable series play a crucial role and correct specification of the underlying dynamics is of paramount importance.

Robust estimation and inference of spatial panel data models with fixed effects

It is well established that the quasi maximum likelihood (QML) estimation of the spatial regression models is generally inconsistent under unknown cross-sectional heteroskedasticity (CH) and the CH-robust methods have been developed. The same issue remains for the spatial panel data (SPD) models but the similar studies based on QML approach do not seem to have been carried out. This paper focuses on the SPD model with fixed effects (FE). We argue that under unknown CH the QML estimator for the SPD-FE model is inconsistent in general, but there are ‘special cases’ where it may remain consistent although the exact conditions may not be possible to check, as in practice the type of CH is generally unknown. Thus, we introduce a new set of estimation and inference methods based on the adjusted quasi scores (AQS), which are fully robust against unknown CH. Consistency and asymptotic normality of the proposed AQS estimators are established. Robust standard error estimates are provided and their consistency is proved. To improve the finite sample performance, a set of AQS methods based on concentrated quasi scores is also introduced and its asymptotic properties examined. Extensive Monte Carlo results show that the new estimator outperforms the QML estimator even when the latter seems robust.

First difference estimation of spatial dynamic panel data models with fixed effects

This paper investigates the first difference (FD) estimation of spatial dynamic panel data (SDPD) models with fixed effects using quasi-maximum likelihood (QML) approach, where both n and T are large. We show that the QML estimation for the SDPD with FD can be reduced to the direct estimation of individual effects, except for the estimation of variance parameter. After bias correction, these two approaches would yield asymptotically equivalent estimates for all parameters including the variance parameter. Our results extend the equivalence of LSDV estimate and GLS estimate of FD equation in the panel regression model to the spatial dynamic panel model, which includes the conventional dynamic panel as a special case. Our analysis highlights the importance of initial values rather than the many fixed effects in spatial panel models.

Affine Pricing and Hedging of Collateralized Debt Obligations

This study deals with the pricing and hedging of single-tranche collateralized debt obligations (STCDOs). We specify an affine two-factor model in which a catastrophic risk component is incorporated. Apart from being analytically tractable, this model has the feature that it captures the dynamics of super-senior tranches, thanks to the catastrophic component. We estimate the factor model based on the iTraxx Europe data with six tranches and four different maturities, using a quasi-maximum likelihood (QML) approach in conjunction with the Kalman filter. We derive the model-based variance-minimizing strategy for the hedging of STCDOs with a dynamically rebalanced portfolio on the underlying swap index. We analyze the actual performance of the variance-minimizing hedge on the iTraxx Europe data. In order to assess the hedging performance further, we run a simulation analysis where normal and extreme loss scenarios are generated via the method of importance sampling. Both in-sample hedging and simulation analysis suggest that the variance-minimizing strategy is most effective for mezzanine tranches in terms of yielding less riskier hedging portfolios and it fails to provide adequate hedge performance regarding equity tranches.

Fixed Effects Spatial Panel Data Model with Time-Varying Spatial Dependence: An Application to Regional Expenditure Competition in China

To analyze the variation of spatial spillover effects over time as well as control unobserved individual-specific features, we extend the fixed effects spatial panel data model by introducing time-varying spatial dependence. For estimation, we propose a two-stage least squares method and the quasi-maximum likelihood approach. Finite sample properties of these two methods are investigated through Monte Carlo simulations. We apply the model to study the expenditure competition among county-level governments in China from 2002 to 2016. Our empirical findings show that the downward pressure of the economy in 2007-2008 and 2015 may lead to stronger competition. Central government regulation on official assessment after 2013 may cause weaker competition.

Quasi-maximum-Likelihood Estimator of PPS on the Uniform Linear Array

In this paper, an idea from the quasi-maximum-likelihood (QML) algorithm has been applied to estimation of the direction of arrival (DOA) and parameters of the polynomial phase signals (PPS) impinging on the uniform linear array. The algorithm uses a search over a set of possible DOA values. For considered value, the DOA is compensated and resulted signal parameters are estimated using the original QML approach. In this way, several sets of potential estimates are obtained. Optimal DOA and PPS parameters belong to set that maximizes the proposed cost function. In the proposed approach, parameters are estimated using 2-D search over DOA and window widths used for calculation of the short Fourier transform in the QML that is an important advantage with respect to existing strategies like, for example, the polynomial beamformer requiring multi-dimensional or metaheuristic search strategies. Numerical validation of the proposed approach for both mono- and multi-component signals is provided in the paper. Both far- and near-field scenarios are considered.

The Effects of WTO and Preferential Trade Agreements on Trade Flows: Count Data Models With Dual Endogenous Binary Treatments

The World Trade Organization (WTO) and preferential trade agreements (PTA) are key factors in international trade liberalization. However, their relative effects on trade flows are controversial (ranging from 16 percent to 277 percent), depending on whether the endogeneity of these two variables is taken into account. Surprisingly, there is no paper estimating the endogenous trade effects of WTO and PTAs simultaneously, thus the existing findings about these variables might be questioned. To fill the gap of the trade literature, we thus extend the econometric model of Terza (1998) and empirical works of Egger et al. (2011) by proposing a count data models with dual endogenous binary regressors. A two-step quasi-maximum likelihood approach to estimation and inference is introduced. Since we derive the analytic gradient and hessian matrices of the log likelihood function of the proposed model, we can easily conduct the Monte Carlo simulations where the data observation is over 10,000 and the parameters to be estimated are over several hundreds, as is typically found in the empirical studies of international economics. Indeed, the simulation results are promising under various configurations considered in this paper. We then apply our approach to the data of Egger et al. (2011) who only investigate the trade effects of PTA. Our results show that both WTO and PTA membership have huge impacts on bilateral trade flows, increasing the value by 926 percent and 218 percent respectively. On the contrary, their partial trade effects are much smaller (13 percent and 74 percent) if the endogeneity is totally ignored.

Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading

Estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading. In this paper we develop a multivariate realised quasi maximum likelihood (QML) approach, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Under stochastic volatility the resulting realised QML estimator is positive definite, uses all available data, is consistent and asymptotically mixed normal. The quasi-likelihood is computed using a Kalman filter and optimised using a relatively simple EM algorithm. We also propose an alternative estimator using a factor model, which scales well with the number of assets. We derive the theoretical properties of these estimators and prove that they achieve the efficient rate of convergence. Our estimators are also analysed using Monte Carlo methods and applied to equity data with varying levels of liquidity.

Statistical inference of partially linear varying coefficient spatial autoregressive models

This paper proposes a semiparametric partially linear varying coefficient spatial autoregressive model, which is a generalization of standard spatial autoregressive model and partially linear spatial autoregressive model. To estimate the unknown spatial lag parameter, constant coefficients and coefficient functions, a profile quasi-maximum likelihood approach based on the local-linear method is introduced. To test the existence of the spatial effects, a generalized likelihood ratio test statistic is proposed, and a residual-based bootstrap procedure is used to derive the p-value of the test. Some simulations are conducted to examine the performance of our proposed procedures and the results are satisfactory. Furthermore, a real-world example is given to demonstrate the application of the proposed procedures.

Estimating a model of sportfishing trip expenditures using a quasi-maximum likelihood approach

This article presents an exponential model of tourist expenditures estimated by a quasi-maximum likelihood (QML) technique. The advantage of this approach is that, unlike conventional OLS and Tobit estimators, it produces consistent parameter estimates under conditions of a corner solution at zero and heteroscedasticity. An application to sportfishing evaluates the role of socioeconomic demographics and species preferences on trip spending. The bias from an inappropriate estimator is illustrated by comparing the results from QML and OLS estimation, which shows that OLS significantly overstates the impact of trip duration on trip expenditures compared with the QML estimator. Both sets of estimates imply that trout and bass anglers spend significantly more on their fishing trips compared with other anglers.

Peer effects, fast food consumption and adolescent weight gain

This paper aims at opening the black box of peer effects in adolescent weight gain. Using Add Health data on secondary schools in the U.S., we investigate whether these effects partly flow through the eating habits channel. Adolescents are assumed to interact through a friendship social network. We propose a two-equation model. The first equation provides a social interaction model of fast food consumption. To estimate this equation we use a quasi maximum likelihood approach that allows us to control for common environment at the network level and to solve the simultaneity (reflection) problem. Our second equation is a panel dynamic weight production function relating an individual's Body Mass Index z-score (zBMI) to his fast food consumption and his lagged zBMI, and allowing for irregular intervals in the data. Results show that there are positive but small peer effects in fast food consumption among adolescents belonging to a same friendship school network. Based on our preferred specification, the estimated social multiplier is 1.15. Our results also suggest that, in the long run, an extra day of weekly fast food restaurant visits increases zBMI by 4.45% when ignoring peer effects and by 5.11%, when they are taken into account.

Peer Effects, Fast Food Consumption and Adolescent Weight Gain

This paper aims at opening the black box of peer effects in adolescent weight gain. Using Add Health data on secondary schools in the U.S., we investigate whether these partly flow through the eating habits channel. Adolescents are assumed to interact through a friendship social network. We propose a two-equation model. The first equation provides a social interaction model of fast food consumption. To estimate this equation we use a quasi maximum likelihood approach that allows us to control for common environment at the network level and to solve the simultaneity (reflection) problem. Our second equation is a panel dynamic weight production function relating an individual's Body Mass Index z-score (zBMI) to his fast food consumption and his lagged zBMI, and allowing for irregular intervals in the data. Results show that there are positive but small peer effects in fast food consumption among adolescents belonging to a same friendship school network. Based on our preferred specification, the estimated social multiplier is 1.15. Our results also suggest that, in the long run, an extra day of weekly fast food restaurant visits increases zBMI by 4.45% when ignoring peer effects and by 5.11%, when they are taken into account.

Two Cholesky-log-GARCH models for multivariate volatilities

Parsimonious estimation of high-dimensional covariance matrices is of fundamental importance in multivariate statistics. Typical examples occur in finance, where the instantaneous dependence among several asset returns should be taken into account. Multivariate GARCH processes have been established as a standard approach for modelling such data. However, the majority of GARCH-type models are either based on strong assumptions that may not be realistic or require restrictions that are often too hard to be satisfied in practice. We consider two alternative decompositions of time-varying covariance matrices [Formula: see text]. The first is based on the modified Cholesky decomposition of the covariance matrices and second relies on the hyperspherical parametrization of the standard Cholesky factor of their correlation matrices [Formula: see text]. Then, we combine each Cholesky factor with the log-GARCH models for the corresponding time–varying volatilities and use a quasi maximum likelihood approach to estimate the parameters. Using log-GARCH models is quite natural for achieving the positive definiteness of [Formula: see text] and this is a novelty of this work. Application of the proposed methodologies to two real financial datasets reveals their usefulness in terms of parsimony, ease of implementation and stresses the choice of the appropriate models using familiar data-driven processes such as various forms of the exploratory data analysis and regression.