Nonlinear Panel Data Models Research Articles

Identification of Average Marginal Effects in Fixed Effects Dynamic Discrete Choice Models

Abstract In nonlinear panel data models, fixed-effects methods are often criticized because they cannot identify average marginal effects (AMEs) in short panels. In contrast with that criticism, we prove the point identification of different AMEs, including causal effects of changes in the lagged dependent variable or the last choice's duration, in a panel dynamic logit model for T as small as three. Our proofs are constructive and provide simple closed-form expressions for the AMEs in terms of probabilities of choice histories. We illustrate our results using Monte Carlo experiments and with an empirical application of a dynamic model of consumer brand choice.

GMM estimation for high-dimensional panel data models

In this paper, we study a class of high dimensional moment restriction panel data models with interactive effects, where the factors are unobserved and these factor loadings are nonparametrically unknown smooth functions of individual characteristic variables. We allow the dimension of the parameter vector and the number of moment conditions to diverge with the sample size. This is a very general framework and is closely related to many existing linear and nonlinear panel data models. In order to estimate the unknown parameters, factors and factor loadings, we propose a sieve-based generalized method of moments estimation method and we show that under a set of simple identification conditions, all those unknown quantities can be consistently estimated. Further we establish asymptotic distributions of the proposed estimators. In addition, we propose tests for over-identification, specification of factor loading functions, and establish their large sample properties. Moreover, a number of simulation studies are conducted to examine the performance of the proposed estimators and test statistics in finite samples. An empirical example on stock return prediction is studied to demonstrate both the empirical relevance and the applicability of the proposed framework and corresponding estimation and testing methods.

Green innovation and corporate financial performance: Insights from operating risks

Green innovation endeavors are of utmost importance for China's green transformation, and the precondition for corporations to undertake green innovation is whether it can enhance their financial performance. Additionally, corporations must utilize leverage to stabilize funding for green innovation. However, it is uncertain how financial leverage affects the relationship between green innovation and corporate financial performance. This study examines the impact mechanism of green innovation on corporate financial performance, as well as its interaction with leverage ratio, using data from listed companies with green patents in the Shanghai and Shenzhen A-share markets spanning the period from 2000 to 2020. Employing a nonlinear panel data model, the findings reveal a U-shaped relationship between green innovation and corporate financial performance. Furthermore, the impact of green strategic innovation and green substantive innovation on corporate financial performance exhibits heterogeneity. The study also highlights the negative impact of the risk accumulation effect resulting from the combination of leverage ratio and green innovation on corporate financial performance. Conversely, the interaction between deleveraging measures and green innovation proves beneficial in promoting corporate financial performance. Therefore, decision-makers in corporations and governments should make rational use of financial leverage when formulating green innovation development strategies.

Bootstrap Inference for Fixed‐Effect Models

The maximum‐likelihood estimator of nonlinear panel data models with fixed effects is asymptotically biased under rectangular‐array asymptotics. The literature has devoted substantial effort to devising methods that correct for this bias as a means to salvage standard inferential procedures. The chief purpose of this paper is to show that the (recursive, parametric) bootstrap replicates the asymptotic distribution of the (uncorrected) maximum‐likelihood estimator and of the likelihood‐ratio statistic. This justifies the use of confidence sets and decision rules for hypothesis testing constructed via conventional bootstrap methods. No modification for the presence of bias needs to be made.

Extended Mundlak Device for Heterogeneity in Nonlinear Panel Data Models with Positive Response Variables

Extended Mundlak Device for Heterogeneity in Nonlinear Panel Data Models with Positive Response Variables

Do Financial Crises Matter for Nonlinear Exchange Rate and Stock Market Cointegration? A Heterogeneous Nonlinear Panel Data Model with PMG Approach

The existing literature has explained the causality flow from the exchange rates toward the stock market without explaining the role of the economic crisis in effecting this nexus. This study examines the role of the financial crisis in affecting the nonlinear causality flowing from the exchange rates toward the stock market indexes of the ASEAN-5 region. The precrisis, postcrisis, and overall sample duration comprised 365, 650, and 1085 observations over the periods from January 2002 to January 2008, January 2010 to January 2020, and January 2002 to January 2020, respectively. The results showed that the conventional symmetrical panel ARDL (PARDL) model was not able to formulate long-run cointegration between currency value fluctuations and stock market indexes for both regimes, i.e., the post recessionary and pre recessionary periods. However, asymmetrical cointegration was established between the currency values and stock market indexes for the pre recessionary period and the overall sampling time frame by utilizing the panel-based NARDL framework (PNARDL). The study suggests practical implications for the exporters and importers to consider the regime as well as both the negative and positive shocks in the international dollar values while making forward contractual agreements.

SECOND-ORDER BIAS REDUCTION FOR NONLINEAR PANEL DATA MODELS WITH FIXED EFFECTS BASED ON EXPECTED QUANTITIES

In many nonlinear panel data models with fixed effects maximum likelihood estimators suffer from the incidental parameters problem, which often entails that point estimates are markedly biased. While the recent literature has mostly generated methods that yield a first-order bias reduction relative to maximum likelihood, we derive a first- and second-order bias correction of the profile likelihood based on “expected quantities” which differs from the corresponding correction based on “sample averages” derived in Dhaene and Sun (2021,Journal of Econometrics220, 227–252). While consistency and asymptotic normality of our estimator are derived in a setting where both the number of individuals and the number of time periods grow to infinity, we illustrate in a simulation study that our second-order bias reduction indeed yields an estimator with substantially improved small sample properties relative to its first-order unbiased counterpart, especially when less than 10 time periods are available.

On the Estimation of True State Dependence in the Persistence of Innovation*

AbstractThis paper explores the persistence often found in firms’ innovation and advances current research by investigating its actual nature. Previous studies have aimed at disentangling true state dependence from spurious state dependence by using a random effects (RE) dynamic panel probit approach, thereby imposing strong conditions on the underlying structure of the unobserved heterogeneity. Building on recent advances in the econometric literature, which allows for true fixed effects estimation of dynamic nonlinear panel data models, we demonstrate that relaxing the assumptions on the unobserved heterogeneity can have a considerable effect on the estimates of true state dependence. While we confirm the existence of a strong persistence of innovation in firms, we however find that true state dependence only explains about half of the persistent behaviour displayed by firms; this is in contrast to the popular RE methodology that attributes 70% to 100% of persistence to true state dependence. Our results suggest that policy programs aimed at encouraging initial innovations alone are useful but may not possess a long‐term stimulating effect on innovation activity.

Partial effects in non-linear panel data models with correlated random effects

Summary Nonlinearity and heterogeneity are known to cause difficulties in estimating and interpreting partial effects. This paper provides a systematic characterization of the various partial effects in nonlinear panel data models that might be of interest to empirical researchers. The interpretation of the partial effects depends upon (i) whether the distribution of unobserved heterogeneity is treated as fixed or allowed to vary with covariates, and (ii) whether one is interested in particular covariate values or an average over such values. The characterization covers partial-effects concepts already in the literature but also includes new concepts for partial effects. A simple panel probit design highlights that the different partial effects can be quantitatively very different.

NONLINEAR PANEL DATA MODELS WITH DISTRIBUTION-FREE CORRELATED RANDOM EFFECTS

Under a Mundlak-type correlated random effect (CRE) specification, we first show that the average likelihood of a parametric nonlinear panel data model is the convolution of the conditional distribution of the model and the distribution of the unobserved heterogeneity. Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a semiparametric family of average likelihood functions of observables by combining the conditional distribution of the model and the recovered distribution of the unobserved heterogeneity, and show that the parameters in the nonlinear panel data model and in the CRE specification are identifiable. Based on the identification result, we propose a sieve maximum likelihood estimator. Compared with the conventional parametric CRE approaches, the advantage of our method is that it is not subject to misspecification on the distribution of the CRE. Furthermore, we show that the average partial effects are identifiable and extend our results to dynamic nonlinear panel data models.

Integrated likelihood based inference for nonlinear panel data models with unobserved effects

We propose a new integrated likelihood based approach for estimating panel data models when the unobserved individual effects enter the model nonlinearly. Unlike existing integrated likelihoods in the literature, the one we propose is closer to a genuine likelihood. Although the statistical theory for the proposed estimator is developed in an asymptotic setting where the number of individuals and the number of time periods both approach infinity, results from a simulation study suggest that our methodology can work very well even in moderately sized panels of short duration in both static and dynamic models.

How to promote energy transition in China: From the perspectives of interregional relocation and environmental regulation

Abstract This study investigates the impacts of interregional clean energy relocation and environmental regulation on energy transition with panel data of 30 provinces in China from 1997 to 2015. Instead of applying the production data of clean energy directly as prior studies did, we calculate the actual consumption of clean energy in each region to get more accurate and reliable conclusion. Applying linear, and further, non-linear panel data models, we derive the following conclusions: (1) Interregional electricity relocation (IRET) projects transmit electricity from sending areas to landing areas and have different impacts on energy transition in different areas. Specifically, in landing areas, IRET promotes energy transition but not as significantly as expected, which implies landing areas should try to be more self-sufficient in clean energy instead of relying on interregional relocation completely. In sending areas, IRET has a negative effect on energy transition. Furthermore, IRET impedes energy transition when energy intensity is higher than the threshold value. This suggests that energy efficiency improvement should be paid particular attention, especially in sending regions. (2) Energy-specific environmental regulation has a significant positive impact on energy transition in China. Meanwhile, environmental regulation's impact on energy transition is weakened by high energy intensity.

Heterogeneous Variable Selection in Nonlinear Panel Data Models: A Semi-Parametric Bayesian Approach

In this paper, we develop a general method for heterogeneous variable selection in Bayesian nonlinear panel data models. Heterogeneous variable selection refers to the possibility that subsets of units are unaffected by certain variables. It may be present in applications as diverse as health treatments, consumer choice-making, macroeconomics, and operations research. Our method additionally allows for other forms of cross-sectional heterogeneity. We consider a two-group approach for the model's unit-specific parameters: each unit-specific parameter is either equal to zero (heterogeneous variable selection) or comes from a Dirichlet process (DP) mixture of multivariate normals (other cross-sectional heterogeneity). We develop our approach for general nonlinear panel data models, encompassing multinomial logit and probit models, poisson and negative binomial count models, exponential models, among many others. For inference, we develop an efficient Bayesian MCMC sampler. In a Monte Carlo study, we find that our approach is able to capture heterogeneous variable selection whereas a standard'' DP mixture is not. In an empirical application, we find that accounting for heterogeneous variable selection and non-normality of the continuous heterogeneity leads to an improved in-sample and out-of-sample performance and interesting insights. These findings illustrate the usefulness of our approach.

Identifying latent group structures in nonlinear panels

We propose a procedure to identify latent group structures in nonlinear panel data models where some regression coefficients are heterogeneous across groups but homogeneous within a group and the group number and membership are unknown. To identify the group structures, we consider the order statistics for the preliminary unconstrained consistent estimators of the regression coefficients and translate the problem of classification into the problem of break detection. Then we extend the sequential binary segmentation algorithm of Bai (1997) for break detection from the time series setup to the panel data framework. We demonstrate that our method is able to identify the true latent group structures with probability approaching one and the post-classification estimators are oracle-efficient. The method has the advantage of more convenient implementation compared with some alternative methods, which is a desirable feature in nonlinear panel applications. To improve the finite sample performance, we also consider an alternative version based on the spectral decomposition of certain estimated matrix and link the group identification issue to the community detection problem in the network literature. Simulations show that our method has good finite sample performance. We apply this method to explore how individuals’ portfolio choices respond to their financial status and other characteristics using the Netherlands household panel data from year 1993 to 2015, and find three latent groups.

On the unbiased asymptotic normality of quantile regression with fixed effects

Nonlinear panel data models with fixed individual effects provide an important set of tools for describing microeconometric data. In a large class of such models (including probit, proportional hazard and quantile regression to name just a few) it is impossible to difference out the individual effects, and inference is usually justified in a ‘large n large T’ asymptotic framework. However, there is a considerable gap in the type of assumptions that are currently imposed in models with smooth score functions (such as probit, and proportional hazard) and quantile regression. In the present paper we show that this gap can be bridged and establish unbiased asymptotic normality for fixed effects quantile regression panels under conditions on n,T that are very close to what is typically assumed in standard nonlinear panels. Our results considerably improve upon existing theory and show that quantile regression is applicable to the same type of panel data (in terms of n,T) as other commonly used nonlinear panel data models. Thorough numerical experiments confirm our theoretical findings.

Single Currency in ECOWAS: Is the Proposed Fiscal Convergence Criterion Pro‐Growth?

AbstractTo facilitate the introduction of a single currency in Economic Community of West African States (ECOWAS), the fiscal convergence criterion currently proposed by countries limits the public deficit to 3 per cent of GDP. According to the literature, the limitation of the public deficit to a given threshold is the most fundamental norm of the various convergence pacts existing and needed for monetary integration. Through a nonlinear panel data model, this paper tests the validity of the threshold by determining the public deficit threshold not to be exceeded so that fiscal policy has a positive effect on economic growth. Over the decade 2007–2016, this threshold is estimated at 4.74 per cent of GDP. Thus, the paper concludes that the proposed convergence criterion of 3 per cent of GDP is pro‐growth. However, in relation to the estimated threshold, there is a room for manoeuvre that can be used for supporting economic growth. Thus, the proposed threshold could be readjusted upward. The analysis also reveals that only four countries in ECOWAS are on the track to respect in the future, the proposed fiscal criterion and therefore are taking an important step toward the adoption of the future currency. The other countries need to make significant fiscal consolidation operations before hoping to adopt the single currency on the basis of fiscal discipline.

What drives the banks' diversification decision? A dynamic nonlinear panel data approach

This paper empirically determines the drivers of functional diversification decision for 365 banks set in selected Middle East and North Africa (MENA) countries over 1988–2015. For this purpose, we use a dynamic nonlinear panel data model. Our findings reveal that both market share and financial intermediation stratify the diversification decision for the whole MENA sample. Splitting the sample shows that the risk‐adjusted profitability and the loan loss provision ratio exert a major influence over the diversification indicator for Gulf Cooperation Council (GCC) banks, whereas the net interest margin ratio, the bank market share, and financial intermediation are the major drivers of the strategic decision for the remaining non‐GCC banks.

Determinants of voluntary online local budget transparency

This article analyses the determinants of the voluntary online local budget transparency (OLBT) of Croatian local governments. Budget transparency is one of preconditions for enabling citizens’ participation and improving public sector outcomes; however, the previous empirical results are ambiguous and inconclusive, with particular gaps for ex-socialist, fiscally centralized countries. To contribute to the existing literature, this article uses the principal-agent and legitimacy theories and non-linear panel data models for the 2015-2017 period to analyse 128 cities and 428 municipalities in Croatia. The findings show that local governments with higher residents’ per capita income, population, Internet access, and administrative and fi scal capacity voluntarily publish more budget documents online. Policy recommendations point to the urge for the reform of the country’s territorial and fi scal organisation, the promotion of budget transparency in less developed cities/ municipalities and for education of citizens about budgets. The main study limitation is the absence of a qualitative analysis of observed documents.

Regional heterogeneity among non-operating earnings quality, stock returns, and firm value in biotech industry

This paper analyses regional heterogeneity under the discretionary measures of non-operating earnings quality and stock returns on firm value in Taiwan’s biotech industry during 2008–2015. An econometric framework based on panel smooth transition regression models is employed in a non-linear panel data model. The results show that biotech firms near the bottom threshold for operating income have low-quality non-operating earnings and those near the upper threshold demonstrate the opposite. Investors who exclusively focus on stock returns are thus likely to miss important information about the quality of earnings.

An Analysis on Household Consumption-Fueled Borrowing in China

In recent years, the size of household debt in China has grown rapidly, accompanied by many typical economic and social phenomena in which households are heavily affected by liabilities, such as house slaves” and car slaves”. That is, the borrowing behavior may have brought tremendous pressure on Chinese households. These phenomena caused by household debt seem to be consistent with household decision-making affected by traditional culture: under the traditional culture led by Chinese Confucianism, households tend to make ends meet, and borrowing is a last resort. However, the classic theory of intertemporal consumption asserts that household borrowing is used to smooth consumption, and predicts that the increase in liabilities will better smooth intertemporal consumption and help to improve family welfare. The inconsistency between the above observation and the prediction of the classical theory motivates us to ask the following questions: What are the driving factors and the consequences of the Chinese household borrowing behavior? What is the economic mechanism behind it? This paper uses the China Family Panel Studies （CFPS） 2010−2014 panel data to empirically examine the borrowing behavior of Chinese households. Motivated by the observation that China’s household consumption debt constitutes the main part of household debt, we employ the analytical framework where household borrowing is driven by expenditures, and linear and nonlinear panel data models to identify the driving factors and impacts of the borrowing of urban and rural residents, and explore the underlying economic mechanism. We find that the borrowing behavior exhibits an inverted U-shaped pattern over the family life cycle, and the highest debt occurs in households with a family head of 30−34 years old. The ownership of housing and the durable consumption significantly increase household debt whereas the education consumption and/or health care consumption significantly decrease household debt. Further examinations demonstrate the heterogeneity of the household borrowing behavior: on the one hand, the borrowing exhibits conservative propensity in that households with higher medical consumption and education consumption have stronger saving motivation, which is consistent with the prediction that household borrowing is affected by Chinese traditional culture; on the other hand, households tend to smoothen durable consumption through borrowing, which is consistent with the prediction of the classical theory. There is no evidence that household borrowing faces significant financial exclusion. Further tests find that borrowing harms the welfare of households measured by the depression level of the head of households while housing consumption significantly reduces the welfare. This result suggests that the pressure of house slaves” is prominent. The sum of the negative welfare effect of household borrowing driven by purchasing cars and the direct positive welfare effect of owning cars is not significantly different from zero, suggesting that the pressure of car slaves” is not significant in the sample family of the CFPS survey. These findings deliver an important policy implication that depending on the types of household consumption, different credit policies should be employed. Specifically, it is desirable to implement policies to strengthen housing price supervision and tighten real estate credit; the relevant credit policies and micro-market mechanisms should be used to stimulate the consumption of durable goods; and public education and related support policies should be used to change the consumption ideas of Chinese households. We contribute to the literature in two aspects. Firstly, we identify the heterogeneity of the Chinese household borrowing behavior in the main driving factors and the consequences. Secondly, and more importantly, rooted in the Chinese cultural background, this paper is among the first to explore the economic mechanism behind the household borrowing behavior in China.