Networked instrumental variable estimation: The case of Hausman-style instruments

Shi, Xiangyu (2024): Networked instrumental variable estimation: The case of Hausman-style instruments.

Abstract

In this paper, I argue that in situations of complex network dependence, the traditional and widely used Hausman-style instrumental variable estimation may not be valid for causal identification. This is the case for inter-regional migration networks when evaluating place-based labor market policies, and for correlated unobserved consumer tastes in the product and geographic space in demand estimation. I build an economic model for these two cases, respectively, to derive the estimating equation and to shed light on the fallacy---omitted variable bias and the resulting violation of exclusion restriction---of the traditional econometric framework. I then build an alternative econometric framework and propose a new approach to estimation that exploits higher-order network neighbors and, then, I establish its desirable properties. I conduct Monte Carlo simulations and two empirical analyses that each correspond to the two economic models to validate this new approach of estimation.

• Item Type: MPRA Paper
• Language: English
• Keywords: treatment effect; network; instrumental variable; Hausman IV; spatial linkages; migration network; demand estimation
• Subjects: C - Mathematical and Quantitative Methods > C0 - General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables

References

@article{graham2020dyadic, title={Dyadic regression}, author={Graham, Bryan S}, journal={The Econometric Analysis of Network Data}, pages={23--40}, year={2020}, publisher={Elsevier} }

@incollection{graham2020network, title={Network data}, author={Graham, Bryan S}, booktitle={Handbook of Econometrics}, volume={7}, pages={111--218}, year={2020}, publisher={Elsevier} }

@techreport{graham2021minimax, title={Minimax risk and uniform convergence rates for nonparametric dyadic regression}, author={Graham, Bryan S and Niu, Fengshi and Powell, James L}, year={2021}, institution={National Bureau of Economic Research} }

@article{fafchamps2007formation, title={The formation of risk sharing networks}, author={Fafchamps, Marcel and Gubert, Flore}, journal={Journal of development Economics}, volume={83}, number={2}, pages={326--350}, year={2007}, publisher={Elsevier} }

@article{cameron2014robust, title={Robust inference for dyadic data}, author={Cameron, A Colin and Miller, Douglas L}, journal={Unpublished manuscript, University of California-Davis}, year={2014} }

@article{aronow2015cluster, title={Cluster--robust variance estimation for dyadic data}, author={Aronow, Peter M and Samii, Cyrus and Assenova, Valentina A}, journal={Political Analysis}, volume={23}, number={4}, pages={564--577}, year={2015}, publisher={Cambridge University Press} }

@article{tabord2019inference, title={Inference with dyadic data: Asymptotic behavior of the dyadic-robust t-statistic}, author={Tabord-Meehan, Max}, journal={Journal of Business \& Economic Statistics}, volume={37}, number={4}, pages={671--680}, year={2019}, publisher={Taylor \& Francis} }

@article{conley1999gmm, title={GMM estimation with cross sectional dependence}, author={Conley, Timothy G}, journal={Journal of econometrics}, volume={92}, number={1}, pages={1--45}, year={1999}, publisher={Elsevier} }

@article{lee2010estimation, title={Estimation of spatial autoregressive panel data models with fixed effects}, author={Lee, Lung-fei and Yu, Jihai}, journal={Journal of econometrics}, volume={154}, number={2}, pages={165--185}, year={2010}, publisher={Elsevier} }

@article{hu2022average, title={Average direct and indirect causal effects under interference}, author={Hu, Yuchen and Li, Shuangning and Wager, Stefan}, journal={Biometrika}, year={2022} }

@article{egami2022identification, title={Identification of Causal Diffusion Effects Using Placebo Outcomes Under Structural Stationarity}, author={Egami, Naoki}, year={2022} }

@article{egami2021identification, title={Identification and estimation of causal peer effects using double negative controls for unmeasured network confounding}, author={Egami, Naoki and Tchetgen, Eric J Tchetgen}, journal={arXiv preprint arXiv:2109.01933}, year={2021} }

@article{pesaran2021general, title={General diagnostic tests for cross-sectional dependence in panels}, author={Pesaran, M Hashem}, journal={Empirical Economics}, volume={60}, number={1}, pages={13--50}, year={2021}, publisher={Springer} }

@article{aronow2020design, title={Design-based inference for spatial experiments with interference}, author={Aronow, Peter M and Samii, Cyrus and Wang, Ye}, journal={arXiv preprint arXiv:2010.13599}, year={2020} }

@article{wang2021causal, title={Causal Inference under Temporal and Spatial Interference}, author={Wang, Ye}, journal={arXiv preprint arXiv:2106.15074}, year={2021} }

@article{imbens1994identification, title={Identification and Estimation of Local Average Treatment Effects}, author={Imbens, Guido W and Angrist, Joshua D}, journal={Econometrica: Journal of the Econometric Society}, pages={467--475}, year={1994}, publisher={JSTOR} }

@article{heckman2005structural, title={Structural equations, treatment effects, and econometric policy evaluation 1}, author={Heckman, James J and Vytlacil, Edward}, journal={Econometrica}, volume={73}, number={3}, pages={669--738}, year={2005}, publisher={Wiley Online Library} }

@article{heckman2001policy, title={Policy-relevant treatment effects}, author={Heckman, James J and Vytlacil, Edward}, journal={American Economic Review}, volume={91}, number={2}, pages={107--111}, year={2001} }

@article{imbens2009recent, title={Recent developments in the econometrics of program evaluation}, author={Imbens, Guido W and Wooldridge, Jeffrey M}, journal={Journal of economic literature}, volume={47}, number={1}, pages={5--86}, year={2009} }

@article{rubin1974estimating, title={Estimating causal effects of treatments in randomized and nonrandomized studies.}, author={Rubin, Donald B}, journal={Journal of educational Psychology}, volume={66}, number={5}, pages={688}, year={1974}, publisher={American Psychological Association} }

@article{rosenbaum1983central, title={The central role of the propensity score in observational studies for causal effects}, author={Rosenbaum, Paul R and Rubin, Donald B}, journal={Biometrika}, volume={70}, number={1}, pages={41--55}, year={1983}, publisher={Oxford University Press} }

@article{card1993minimum, title={Minimum Wages And Employment: A Case Study Of The Fast Food Industry In New Jersey And Pennsylvania}, author={Card, David and Krueger, Alan B}, year={1993} }

@article{rubin1997estimating, title={Estimating causal effects from large data sets using propensity scores}, author={Rubin, Donald B}, journal={Annals of internal medicine}, volume={127}, number={8\_Part\_2}, pages={757--763}, year={1997}, publisher={American College of Physicians} }

@article{imbens2008regression, title={Regression discontinuity designs: A guide to practice}, author={Imbens, Guido W and Lemieux, Thomas}, journal={Journal of econometrics}, volume={142}, number={2}, pages={615--635}, year={2008}, publisher={Elsevier} }

@book{anselin1988spatial, title={Spatial econometrics: methods and models}, author={Anselin, Luc}, volume={4}, year={1988}, publisher={Springer Science \& Business Media} }

@article{yu2008quasi, title={Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large}, author={Yu, Jihai and De Jong, Robert and Lee, Lung-fei}, journal={Journal of Econometrics}, volume={146}, number={1}, pages={118--134}, year={2008}, publisher={Elsevier} }

@article{lee2010spatial, title={A spatial dynamic panel data model with both time and individual fixed effects}, author={Lee, Lung-fei and Yu, Jihai}, journal={Econometric Theory}, volume={26}, number={2}, pages={564--597}, year={2010}, publisher={Cambridge University Press} }

@article{lee2014efficient, title={Efficient GMM estimation of spatial dynamic panel data models with fixed effects}, author={Lee, Lung-fei and Yu, Jihai}, journal={Journal of Econometrics}, volume={180}, number={2}, pages={174--197}, year={2014}, publisher={Elsevier} }

@article{shi2021hometown, title={Hometown Favoritism and Intercity Investment Networks in China}, author={Shi, Xiangyu}, journal={Available at SSRN 3745064}, year={2021} }

@article{shi2021moving, title={“Moving Umbrella”: Bureaucratic transfers and the comovement of interregional investments in China}, author={Shi, Xiangyu and Xi, Tianyang and Zhang, Xiaobo and Zhang, Yifan}, journal={Journal of Development Economics}, volume={153}, pages={102717}, year={2021}, publisher={Elsevier} }

@article{liu2022reciprocity, title={Reciprocity in Political Network: Hometown Ties and Intercity Investment in China}, author={Liu, Yu and Shi, Xiangyu}, journal={Available at SSRN 4174390}, year={2022} }

@article{hausman1978specification, title={Specification tests in econometrics}, author={Hausman, Jerry A}, journal={Econometrica: Journal of the econometric society}, pages={1251--1271}, year={1978}, publisher={JSTOR} }

@article{berry1992, title = {Estimation of a Model of Entry in the Airline Industry}, volume = {60}, abstract = {This paper considers the effect of an airline's scale of operation at an airport on the profitability of routes flown out of that airport. The empirical methodology uses the entry decisions of airlines as indicators of underlying profitability; the results extend the empirical literature on airport presence by providing a new set of estimates of the determinants of city pair profitability. The literature on empirical models of oligopoly entry is also extended, particularly via a focus on the important (and difficult) role of differences between firms.}, pages = {889--917}, number = {4}, journaltitle = {Econometrica}, author = {Berry, Steven T.}, urldate = {2023-01-25}, year = {1992} }

@article{cilibertomurrytamer2021, title = {Market Structure and Competition in Airline Markets}, volume = {129}, issn = {0022-3808}, abstract = {We provide an econometric framework for estimating a game of simultaneous entry and pricing decisions while allowing for correlations between unobserved cost and demand shocks. We use our framework to account for selection in the pricing stage. We estimate the model using data from the {US} airline industry and find that not accounting for endogenous entry leads to biased estimation of demand elasticities. We simulate a merger between American and {US} Airways and find that product repositioning and postmerger outcomes depend on how we model the characteristics of the merged firm as a function of the premerger firms’ characteristics.}, pages = {2995--3038}, number = {11}, journaltitle = {Journal of Political Economy}, author = {Ciliberto, Federico and Murry, Charles and Tamer, Elie}, urldate = {2023-01-31}, year = {2021} }

@article{bai2009panel, title={Panel data models with interactive fixed effects}, author={Bai, Jushan}, journal={Econometrica}, volume={77}, number={4}, pages={1229--1279}, year={2009}, publisher={Wiley Online Library} }

@article{holtz1988estimating, title={Estimating vector autoregressions with panel data}, author={Holtz-Eakin, Douglas and Newey, Whitney and Rosen, Harvey S}, journal={Econometrica: Journal of the econometric society}, pages={1371--1395}, year={1988}, publisher={JSTOR} }

@book{imbens2015causal, title={Causal inference in statistics, social, and biomedical sciences}, author={Imbens, Guido W and Rubin, Donald B}, year={2015}, publisher={Cambridge University Press} }

@article{nickell1981biases, title={Biases in dynamic models with fixed effects}, author={Nickell, Stephen}, journal={Econometrica: Journal of the econometric society}, pages={1417--1426}, year={1981}, publisher={JSTOR} }

@article{yu2012estimation, title={Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration}, author={Yu, Jihai and de Jong, Robert and Lee, Lung-fei}, journal={Journal of Econometrics}, volume={167}, number={1}, pages={16--37}, year={2012}, publisher={Elsevier} }

@article{de2020two, title={Two-way fixed effects estimators with heterogeneous treatment effects}, author={De Chaisemartin, Cl{\'e}ment and d’Haultfoeuille, Xavier}, journal={American Economic Review}, volume={110}, number={9}, pages={2964--2996}, year={2020}, publisher={American Economic Association 2014 Broadway, Suite 305, Nashville, TN 37203} }

@article{banerjee2013diffusion, title={The diffusion of microfinance}, author={Banerjee, Abhijit and Chandrasekhar, Arun G and Duflo, Esther and Jackson, Matthew O}, journal={Science}, volume={341}, number={6144}, pages={1236498}, year={2013}, publisher={American Association for the Advancement of Science} }

@article{shi2023treatment, title={Treatment Effects with Dyadic Data in the Presence of Spatial Dependence}, author={Shi, Xiangyu}, journal={Available at SSRN 4490775}, year={2023} }

@article{goodman2021difference, title={Difference-in-differences with variation in treatment timing}, author={Goodman-Bacon, Andrew}, journal={Journal of Econometrics}, volume={225}, number={2}, pages={254--277}, year={2021}, publisher={Elsevier} }

@article{sun2021estimating, title={Estimating dynamic treatment effects in event studies with heterogeneous treatment effects}, author={Sun, Liyang and Abraham, Sarah}, journal={Journal of Econometrics}, volume={225}, number={2}, pages={175--199}, year={2021}, publisher={Elsevier} }

@article{borusyak2021revisiting, title={Revisiting event study designs: Robust and efficient estimation}, author={Borusyak, Kirill and Jaravel, Xavier and Spiess, Jann}, journal={arXiv preprint arXiv:2108.12419}, year={2021} }

@article{nevo2001measuring, title={Measuring market power in the ready-to-eat cereal industry}, author={Nevo, Aviv}, journal={Econometrica}, volume={69}, number={2}, pages={307--342}, year={2001}, publisher={Wiley Online Library} }

@article{lanoie2011environmental, title={Environmental policy, innovation and performance: new insights on the Porter hypothesis}, author={Lanoie, Paul and Laurent-Lucchetti, J{\'e}r{\'e}my and Johnstone, Nick and Ambec, Stefan}, journal={Journal of Economics \& Management Strategy}, volume={20}, number={3}, pages={803--842}, year={2011}, publisher={Wiley Online Library} }

@techreport{azar2022estimating, title={Estimating labor market power}, author={Azar, Jos{\'e} A and Berry, Steven T and Marinescu, Ioana}, year={2022}, institution={National Bureau of Economic Research} }

@article{crawford2012welfare, title={The welfare effects of bundling in multichannel television markets}, author={Crawford, Gregory S and Yurukoglu, Ali}, journal={American Economic Review}, volume={102}, number={2}, pages={643--685}, year={2012}, publisher={American Economic Association} }

@article{houde2012spatial, title={Spatial differentiation and vertical mergers in retail markets for gasoline}, author={Houde, Jean-Fran{\c{c}}ois}, journal={American Economic Review}, volume={102}, number={5}, pages={2147--2182}, year={2012}, publisher={American Economic Association} }

@article{hausman1994competitive, title={Competitive analysis with differenciated products}, author={Hausman, Jerry and Leonard, Gregory and Zona, J Douglas}, journal={Annales d'Economie et de Statistique}, pages={159--180}, year={1994}, publisher={JSTOR} }

@article{caliendo2019trade, title={Trade and labor market dynamics: General equilibrium analysis of the china trade shock}, author={Caliendo, Lorenzo and Dvorkin, Maximiliano and Parro, Fernando}, journal={Econometrica}, volume={87}, number={3}, pages={741--835}, year={2019}, publisher={Wiley Online Library} }

@article{berry1994estimating, title={Estimating discrete-choice models of product differentiation}, author={Berry, Steven T}, journal={The RAND Journal of Economics}, pages={242--262}, year={1994}, publisher={JSTOR} }

@article{bramoulle2009identification, title={Identification of peer effects through social networks}, author={Bramoull{\'e}, Yann and Djebbari, Habiba and Fortin, Bernard}, journal={Journal of econometrics}, volume={150}, number={1}, pages={41--55}, year={2009}, publisher={Elsevier} }

@article{ciliberto2021market, title={Market structure and competition in airline markets}, author={Ciliberto, Federico and Murry, Charles and Tamer, Elie}, journal={Journal of Political Economy}, volume={129}, number={11}, pages={2995--3038}, year={2021}, publisher={The University of Chicago Press Chicago, IL} }

@article{nevo2001measuring, title={Measuring market power in the ready-to-eat cereal industry}, author={Nevo, Aviv}, journal={Econometrica}, volume={69}, number={2}, pages={307--342}, year={2001}, publisher={Wiley Online Library} }

@article{igami2017estimating, title={Estimating the innovator’s dilemma: Structural analysis of creative destruction in the hard disk drive industry, 1981--1998}, author={Igami, Mitsuru}, journal={Journal of Political Economy}, volume={125}, number={3}, pages={798--847}, year={2017}, publisher={University of Chicago Press Chicago, IL} }

@article{atkin2021we, title={How do we choose our identity? a revealed preference approach using food consumption}, author={Atkin, David and Colson-Sihra, Eve and Shayo, Moses}, journal={Journal of Political Economy}, volume={129}, number={4}, pages={1193--1251}, year={2021}, publisher={The University of Chicago Press Chicago, IL} }

@article{sanderson2016weak, title={A weak instrument F-test in linear IV models with multiple endogenous variables}, author={Sanderson, Eleanor and Windmeijer, Frank}, journal={Journal of econometrics}, volume={190}, number={2}, pages={212--221}, year={2016}, publisher={Elsevier} }

@article{berry2013connected, title={Connected substitutes and invertibility of demand}, author={Berry, Steven and Gandhi, Amit and Haile, Philip}, journal={Econometrica}, volume={81}, number={5}, pages={2087--2111}, year={2013}, publisher={Wiley Online Library} }

@article{sargan1958estimation, title={The estimation of economic relationships using instrumental variables}, author={Sargan, John D}, journal={Econometrica: Journal of the econometric society}, pages={393--415}, year={1958}, publisher={JSTOR} }

@article{hansen1982large, title={Large sample properties of generalized method of moments estimators}, author={Hansen, Lars Peter}, journal={Econometrica: Journal of the econometric society}, pages={1029--1054}, year={1982}, publisher={JSTOR} }

@article{cragg1993testing, title={Testing identifiability and specification in instrumental variable models}, author={Cragg, John G and Donald, Stephen G}, journal={Econometric Theory}, volume={9}, number={2}, pages={222--240}, year={1993}, publisher={Cambridge University Press} }