Interactive Fixed Effects Research Articles

Moment-Based Estimation of Linear Panel Data Models with Factor-Augmented Errors

Abstract I compare two popular methods of estimation for linear panel data models with unobserved factors: the first eliminates the factors with a parameterized quasi-long-differencing (QLD) transformation. The other, referred to as common correlated effects (CCE), uses cross-sectional averages of the data to proxy for the factor space. I show that the CCE assumptions imply unused moment conditions that can be exploited by the QLD transformation. I also derive new linear estimators that weaken identifying assumptions and have desirable theoretical properties. Unlike CCE, these estimators do not require the number of covariates to be less than the number of time periods. I provide the first proof of a fixed-T consistent mean group estimator for heterogeneous linear models with interactive fixed effects. I investigate the effects of per-student expenditure on standardized test performance using data from the state of Michigan.

Causal models for longitudinal and panel data: a survey

Summary In this survey we discuss the recent causal panel data literature. This recent literature has focused on credibly estimating causal effects of binary interventions in settings with longitudinal data, emphasising practical advice for empirical researchers. It pays particular attention to heterogeneity in the causal effects, often in situations where few units are treated and with particular structures on the assignment pattern. The literature has extended earlier work on difference-in-differences or two-way fixed effect estimators. It has more generally incorporated factor models or interactive fixed effects. It has also developed novel methods using synthetic control approaches.

Robust inference of panel data models with interactive fixed effects under long memory: A frequency domain approach

This paper studies a linear panel data model with interactive fixed effects wherein regressors, factors and idiosyncratic error terms are all stationary but with potential long memory. The setup involves a new formulation of panel data models, where weakly dependent regressors, factors and idiosyncratic errors are embedded as a special case. Standard methods based on principal component decomposition and least squares estimation, as in Bai (2009), are found to be biased and distorted in inference. To cope with this failure and to provide a simple implementable estimation procedure, a frequency domain least squares estimation is proposed. The limit distribution of the frequency domain estimator is established and a self-normalized approach to inference without the need for plug-in estimation of memory parameters is developed. Simulations show that the frequency domain estimator performs robustly under short memory and outperforms the time domain estimator when long range dependence is present. An empirical illustration is provided, examining the long-run relationship between stock returns and realized volatility.

Terms‐of‐trade effects of productivity shocks in developing economies

AbstractThis paper studies the terms‐of‐trade effects of economy‐specific shocks to productivity in developing economies using a panel vector autoregression model with interactive fixed effects and the “max‐share” approach. We find that the terms of trade after unanticipated changes in economy‐specific productivity mostly exhibit insignificant dynamics in the developing economies. However, we present evidence that they can significantly deteriorate in a particular set of developing countries, namely the ones with a high score on technological deepening and upgrading.

Do consumers try to solve the air pollution problem themselves? the effects of air pollution on purchase of hybrid and electric cars

Using a unique panel dataset on air pollution and car sales from thirty major cities in China across three years, we estimate the impact of air pollution on the adoption of hybrid and electric vehicles. To identify the causal effect, we use three sets of interactive fixed effects to control for a large group of potential confounders and an instrument for the air pollution variable. Our results show that worse air quality leads consumers to purchase more hybrid and electric cars, and the effect is larger in cities with higher incomes. These findings are consistent with predictions from the social preferences theory and point out new directions for strategies to promote the adoption of hybrid and electric cars.

Improved inference for interactive fixed effects model under cross-sectional dependence

Improved inference for interactive fixed effects model under cross-sectional dependence

Policy Analysis Using Multilevel Regression Models with Group Interactive Fixed Effects

The use of multilevel regression models is prevalent in policy analysis to estimate the effect of group level policies on individual outcomes. In order to allow for the time varying effect of group heterogeneity and the group specific impact of time effects, we propose a group interactive fixed effects approach that employs interaction terms of group factor loadings and common factors in this model. For this approach, we consider the least squares estimator and associated inference procedure. We examine their properties under the large n and fixed T asymptotics. The number of groups, G, is allowed to grow but at a slower rate. We also propose a test for the level of grouping to specify group factor loadings, and a GMM approach to address policy endogeneity with respect to idiosyncratic errors. Finally, we provide empirical illustrations of the proposed approach using two empirical examples.

INFERENCE IN PARTIALLY IDENTIFIED PANEL DATA MODELS WITH INTERACTIVE FIXED EFFECTS

In this paper, we develop methods for statistical inferences in a partially identified nonparametric panel data model with endogeneity and interactive fixed effects. Under some normalization rules, we can concentrate out the large-dimensional parameter vector of factor loadings and specify a set of conditional moment restrictions that are involved with only the finite-dimensional factor parameters along with the infinite-dimensional nonparametric component. For a conjectured restriction on the parameter, we consider testing the null hypothesis that the restriction is satisfied by at least one element in the identified set and propose a test statistic based on a novel martingale difference divergence measure for the distance between a conditional expectation object and zero. We derive a tight asymptotic distributional upper bound for the resultant test statistic under the null and show that it is divergent at rate-N under the global alternative. To obtain the critical values for our test, we propose a version of multiplier bootstrap and establish its asymptotic validity. Simulations demonstrate the finite sample properties of our inference procedure. We apply our method to study Engel curves for major nondurable expenditures in China by using a panel dataset from the China Family Panel Studies.

Oracle Efficient Estimation of Heterogeneous Dynamic Panel Data Models with Interactive Fixed Effects

We propose a two-step procedure to estimate a heterogeneous dynamic panel data model with interactive fixed effects. We establish the asymptotic properties of the estimators and show that the final estimator is oracle efficient. We also propose a specification test for the null hypothesis of homogeneous slopes and study the asymptotic properties of the test statistic under both local and global alternatives. Simulations demonstrate the fine performance of the estimator and test statistic. The new estimation and inference methods are applied to study the heterogeneous effects of minimum wage on employment across different counties in the United States. Our dynamic model suggests that the changes of employment range from about–1% to 1% when the minimum wage increases by 1%.

Is peer-to-peer demand cointegrated at the listing level?

In this paper, we analyse the long-run equilibrium demand of the peer-to-peer sharing economy. Our panel data demand model relates occupancy rates to relative prices of Airbnb and HomeAway listings, prices of competitors (hotels and apartments) and a proxy for income of tourists visiting the Canary Islands (Spain). We use a fractional heterogeneous panel data model which allows for a more general persistence and cointegration relationship and incorporates individual and interactive fixed effects. We find some evidence for (fractional) cointegration in P2P at the listing level. Regarding elasticities, classic cointegration methods give larger estimates for individual slopes and mean group coefficients than the fractional integrated heterogeneous model. Finally, own-price elasticities are inelastic, and the cross-price elasticity indicates that P2P listings and hotels are substitute goods. Income elasticity is lower than 1 and is not statistically significant, indicating that the demand for tourism in the Canary Islands is not sensitive to the economic conditions in the origin countries.

Frontier markets sovereign risk: New evidence from spatial econometric models

This paper considers spatial linkages of bilateral trade, financial correlation, and bilateral distance to study the macroeconomic determinants of sovereign risk for frontier markets. It applies (Shi and Lee, 2017) dynamic spatial Durbin model with interactive fixed effects. Analysis confirms the existence of spillover effects stemming from the explanatory variables’ movement towards the Credit default swaps (CDSs) premium of itself and neighboring countries. Bilateral distance and trade are the most significant spatial linkages. All macroeconomics except reserves impact CDS spreads directly and through feedback effects. Spatial dependence strengthens during recessions. Findings suggest policymakers should account for regional contagion channels that transmit sovereign risk.

NONPARAMETRIC TIME-VARYING PANEL DATA MODELS WITH HETEROGENEITY

Abstract Since Bai (2009, Econometrica 77, 1229–1279), considerable extensions have been made to panel data models with interactive fixed effects (IFEs). However, little work has been conducted to understand the associated iterative algorithm, which, to the best of our knowledge, is the most commonly adopted approach in this line of research. In this paper, we refine the algorithm of panel data models with IFEs using the nuclear-norm penalization method and duple least-squares (DLS) iterations. Meanwhile, we allow the regression coefficients to be individual-specific and evolve over time. Accordingly, asymptotic properties are established to demonstrate the theoretical validity of the proposed approach. Furthermore, we show that the proposed methodology exhibits good finite-sample performance using simulation and real data examples.

Digital finance and performance in innovation: Evidence from universities.

This study evaluated 72 universities' performance innovation during 2011 to 2019 of panel data, using the data envelopment analysis-Malmquist method. The study used benchmark regression to analyse the relationship between digital finance and the universities' innovation performance. The aim was to improve innovation performance and promote national innovation across countries. According to the results of the empirical analysis, digital finance positively affects innovation performance. That finding was confirmed through advanced robustness test evaluation, such as limited information maximum likelihood, two-stage least squares, and interactive fixed effects. Moreover, based on information theory, the digital finance influence mechanism improves credit demand and financial efficiency. Additionally, innovation performance survived spatial overflow effects. Lastly, the paper concludes with some implications for improving digital financial coverage and constructing innovation networks among universities.

Can the green credit policy reduce carbon emission intensity of “high-polluting and high-energy-consuming” enterprises? Insight from a quasi-natural experiment in China

Previous studies have examined the effect of green credit policy (GCP) on innovation, the environment, and corporate performance. However, few studies have focused on GCP's impact on carbon reduction of high-polluting and high-energy-consuming (“two high”) enterprises. Based on millions of unbalanced panel data from the China Taxation Survey database from 2009 to 2016, this study considers the most acclaimed GCP (“Green Credit Guideline” in 2012) as a quasi-natural experiment and adopts a difference-in-difference (DID) method along with interactive fixed effects to study the impact of GCP on the carbon emission intensity of “two high” enterprises. In general, we find that GCP significantly reduces the carbon emission intensity of “two high” enterprises. This effect is achieved by optimizing the energy structure, promoting technology transformation, and increasing the intensity of innovation input. A heterogeneous analysis shows that the GCP has a significant suppression effect on “two high” enterprises in eastern and western regions, although its impact is less evident in central areas. Moreover, it shows that non-state-owned, unsubsidized, medium-scale, and large-scale “two high” enterprises are more significantly negatively impacted by the GCP. Finally, to further address the endogeneity problem, the propensity score matching–difference-in-difference (PSM-DID) estimation is conducted and pragmatic policy implications are proposed to improve the development and effectiveness of the GCP.

Can rural e-commerce narrow the urban–rural income gap? Evidence from coverage of Taobao villages in China

PurposeThe digital economy is expected to revive the countryside and reduce the current level of urban–rural inequality. Nevertheless, whether rural e-commerce can narrow the urban–rural income gap still requires further analysis. The purpose of this paper is to clarify whether this goal is, in fact, being achieved.Design/methodology/approachTaobao villages have become the epitome of rural e-commerce development in China. Therefore, this paper matches the data of Taobao villages and the data of prefecture-level cities from 2014 to 2019, and employs a two-way fixed effect model, nonlinear model, instrumental variable model and interactive fixed effects model to explore the impact of rural e-commerce on the urban–rural income gap.FindingsFirstly, the ability of urban residents to share rural e-commerce development is higher than that of rural residents, which actually widens the urban–rural income gap. Secondly, the migration to cities of rural families that have profited from e-commerce, and the return of working-class people to the countryside, are two factors that are contributing to the widening of the urban–rural income gap. Thirdly, the farther the distance from the urban area and the higher the spatial agglomeration of the rural e-commerce cluster is, the weaker the impact on widening the urban–rural income gap will be. Finally, while industrial-led rural e-commerce is responsible for widening the urban–rural income gap, agricultural-led rural e-commerce has no significant impact on the urban–rural income gap.Originality/valueTo the best of the authors' knowledge, this paper is the first to analyze the impact of rural e-commerce on the urban–rural income gap from the perspective of the coverage of Taobao villages. This empirical study will enrich existing theoretical perspectives on urban–rural integration under the backdrop of the digital economy.

How does fintech affect energy transition: Evidence from Chinese industrial firms

This article constructs a dataset of Chinese industrial firms between 2005 and 2010 to investigate the influence of fintech developments on the coal consumption of Chinese firms. Results reveal a significant negative correlation between Fintech and firms' coal consumption. By addressing the potential endogeneity, controlling city-level variables and interactive fixed effects, and testing the unobservable bias, the benchmark results are robust to the above alternative identification strategies. Furthermore, this article investigates the potential mechanisms and finds that Fintech can be negatively connected with coal consumption at firms by elevating export and innovation performance. Finally, this article examines the heterogeneous effects of fintech development and discovers the reduction effect of fintech development on the coal consumption of firms, which is greater for young firms located in the central and eastern regions as well as for those located in regions with lower GDP growth, lower development of the tertiary sector, and a higher level of financial development. The results may contribute to China's carbon neutrality goal by 2060 and help policymakers make policies in the energy sector.

How does urbanisation affect the evolution of territorial space composite function?

Under the background of drastic global changes and the widespread urbanisation process, the problems of urban-rural imbalance, food security and ecosystem degradation arising from land use changes have attracted widespread attention. By constructing an analysis framework for the driving mechanism of the territorial spatial composite function, taking 199 county-level units in the Beijing-Tianjin-Hebei region as samples, based on panel data, the influence mechanism of population-land urbanisation on the territorial spatial functions evolution was discussed by using the spatio-temporal interactive fixed effects model and spatial econometric models. It was found that land urbanisation did not contribute as significantly as population urbanisation to the composite level of territorial spatial functions, and this difference stemmed from the substitution effect between population urbanisation and land urbanisation. Population-land urbanisation had a complementary effect on urban space development and a substitution effect on agricultural production and ecological maintenance. And urban space development did not offset the weakening effect on agricultural production and ecological maintenance functions. The agglomeration of population to cities and towns and rural construction could alleviate the negative effects of the urban construction space expansion, which was conducive to the sustainable development of territorial space. Therefore, it makes up for the shortcomings of existing research on the evolution mechanism of territorial spatial composite function, and has reference significance for the improvement of territorial space development mode and the optimization of territorial space planning system in urban agglomeration areas.

NUCLEAR NORM REGULARIZED QUANTILE REGRESSION WITH INTERACTIVE FIXED EFFECTS

This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.

Social R&D: Does academic freedom contribute to improved societal outcomes?

The economics literature views R&D as an important conduit for growth because it generates new ideas that can be translated into technological innovations. Some of this R&D occurs in universities, making academic freedom an important part of this process. This literature ignores the potential role that academic research in the social sciences plays toward achieving non-commercial societal outcomes. We bridge this gap by proposing that academia generates social R&D. We posit that greater degrees of academic freedom allow for social R&D to flourish and be transformed into policies that improve societal conditions. We test our hypothesis by studying the relationship between academic freedom and inequality using panel data of 132 countries over the 1967–2018 period. We measure academic freedom using an index developed by the V-Dem Institute. Our econometric analysis suggests that an increase in the index is associated with a decrease in inequality. We employ instrumental variable and interactive fixed effects techniques to try to lend support to the causal relationship between academic freedom and inequality. We argue that this negative relationship can be explained by academia, predominantly the social sciences, exerting pressure on governments to enact policies that redistribute wealth. We find evidence in support of this mechanism using data from other sources.

Does the Belt and Road Initiative affect the energy intensity of countries along the route? An analysis of the direct and indirect effects

We empirically evaluate the effect of China’s Belt and Road Initiative (BRI) on the energy intensity of countries along the route. Furthermore, we decompose this overall effect into direct effects via connectivity and indirect effects through development. We apply a relatively new synthetic control method based on interactive fixed effects to identify the causal effects of the BRI. Our main results include: (1) the overall effect of the BRI reduces the energy intensity of countries along the route by 0.0152 toes per thousand dollars, of which the direct effect is 0.0125 (82%); (2) the indirect effect in the current status is limited, mainly through the contradictory effects of economic growth and industrial structural change; and (3) countries along the route with a lower level of development, higher levels of energy technology, more abundant energy endowments, and less stringent carbon regulations experience a greater reduction in energy intensity after the BRI.