Skip to main content

22.05.2024

Local spatial difference-in-differences models: treatment correlations, response interactions, and expanded local models

verfasst von: Shanxia Sun, Michael S. Delgado

Erschienen in: Empirical Economics

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We propose spatial difference-in-differences (DID) models that are able to incorporate treatment effect spillovers through modeling spatial interactions in the response and spatial correlations in treatment status among individuals. We first explore the ways in which combinations of spatial interaction and spatial correlation bias the conventional DID estimator, and then we develop spatial DID models, estimators, and specification tests that allow for a flexible order of local spatial structures. We consider both simultaneous and dynamic treatment. The local spatial DID models with a flexible order of spatial structure allow for different types of heterogeneity in the treatment effects. Monte Carlo simulations support our discussions of the bias in the conventional DID model under spatial interaction and correlation, and demonstrate the finite sample performance of our proposed models, estimators, and tests.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
An alternative approach that is applicable to cases of local spatial interaction is to define multiple treatment groups depending on both own treatment and the number of neighbors treated, and apply a difference-in-difference-in-differences technique (Imbens and Wooldridge 2009). However, with this approach, the number of treatment and control groups quickly becomes cumbersome, which is inefficient in small samples.
 
2
See Durlauf and Ioannides (2010).
 
3
See, also, Brock and Durlauf (2001), Durlauf and Ioannides (2010), Blume et al. (2011), Blume et al. (2015) and Graham (2015) for overviews on the economics and econometrics of social interaction.
 
4
Besides γ, the exact value of δ is also determined by the correlation between (WD∘T) and X, the correlation between D and X, and the correlation among the different covariates in X if X is multivariate.
 
5
For example, if we assume \(D\) and \(X\) are not correlated and only consider the correlations between \(D\) and \(DT\), \(WDT\) and \(D\), \(WDT\) and \(DT\), the bias of conventional DID estimator will be.
\(Bias\left\{{{a}_{4}}_{did}|Z\right\}={\alpha }_{4}\rho \frac{\left({\gamma }_{DT,WDT}-{\gamma }_{DT,D}{\gamma }_{WDT,D}\right)}{1-{\gamma }_{DT,D}^{2}}\sqrt{\frac{{V}_{WDT}}{{V}_{DT}}},\) where \({\gamma }_{DT,WDT}\) represents the correlation between \(DT\) and \(WD\circ T\), \({\gamma }_{DT,D}\) represents the correlation between \(D\) and \(DT\), \({\gamma }_{WDT,D}\) represents the correlation between \(D\) and \(WD \circ T\), \(V_{WDT}\) represents the variance of \(WD \circ T\), \(V_{DT}\) represents the variance of \(DT\).
 
6
Typically, spatial correlation between the covariates in the model (the X variables) does not affect parameter estimation, and so we focus primarily on simulations with \(\lambda { } = 0\). To confirm, we also run simulations with \(\lambda { } = 0\) and report results in the Supplemental Appendix (SA Tables 1-2); these auxiliary results confirm that \(\lambda\) does not affect estimation of the treatment effects
 
7
In our case, because \(D_{i}\) is binary, defining spatial correlation in \(D\) is difficult since binary \(D\) only indicates location of spatial units (either points or areas) and is not measured continuously. Join count statistics provide a way to measure spatial correlation in binary variables (Cliff and Ord 1981).
 
8
This structure is different from a global spatial process, in which the spillovers percolate throughout the entire spatial system. In a typical, stable spatial system, the strength of the spatial interaction decays as the distance from the treated individual increases. Regardless of the decay structure, formulating a global spatial DID requires more careful consideration than does the limited local processes, so we leave that setup for further research.
 
9
A threshold model of this type could be defined at any threshold of treated neighbors, not simply one treated neighbor.
 
Literatur
Zurück zum Zitat Angrist J, Imbens GW, Rubin DB (1996) Identification of causal effects using instrumental variables. J Am Stat Assoc 91:444–472CrossRef Angrist J, Imbens GW, Rubin DB (1996) Identification of causal effects using instrumental variables. J Am Stat Assoc 91:444–472CrossRef
Zurück zum Zitat Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic PublishersCrossRef Anselin L (1988) Spatial econometrics: methods and models. Kluwer Academic PublishersCrossRef
Zurück zum Zitat Arduini T, Patacchini E, Rainone E (2014) Identification and estimation of outcome response with heterogeneous treatment externalities. Working paper Arduini T, Patacchini E, Rainone E (2014) Identification and estimation of outcome response with heterogeneous treatment externalities. Working paper
Zurück zum Zitat Ashenfelter O (1978) Estimating the effect of training programs on earnings. Rev Econ Stat 60:47–57CrossRef Ashenfelter O (1978) Estimating the effect of training programs on earnings. Rev Econ Stat 60:47–57CrossRef
Zurück zum Zitat Ashenfelter O, Card D (1985) Using the longitudinal structure of earnings to estimate the effect of training programs. Rev Econ Stat 67:648–660CrossRef Ashenfelter O, Card D (1985) Using the longitudinal structure of earnings to estimate the effect of training programs. Rev Econ Stat 67:648–660CrossRef
Zurück zum Zitat Athey S, Imbens G (2022) Design-based analysis in difference-in-differences settings with staggered adoption. J Econometrics 226(1):62–79CrossRef Athey S, Imbens G (2022) Design-based analysis in difference-in-differences settings with staggered adoption. J Econometrics 226(1):62–79CrossRef
Zurück zum Zitat Bardaka E, Delgado MS, Florax RJGM (2019) A spatial multiple treatment/multiple outcome difference-indifferences model with an application to urban rail infrastructure and gentrification. Transp Res Part A 121:325–345 Bardaka E, Delgado MS, Florax RJGM (2019) A spatial multiple treatment/multiple outcome difference-indifferences model with an application to urban rail infrastructure and gentrification. Transp Res Part A 121:325–345
Zurück zum Zitat Blume LE, Brock WA, Durlauf SN, Ioannides YM (2011) Identification of social interactions, Volume 1B of Handbook of Social Economics, Chapter 18. Elsevier, pp 853–964 Blume LE, Brock WA, Durlauf SN, Ioannides YM (2011) Identification of social interactions, Volume 1B of Handbook of Social Economics, Chapter 18. Elsevier, pp 853–964
Zurück zum Zitat Blume LE, Brock WA, Durlauf SN, Jayaraman R (2015) Linear social interactions models. J Polit Econ 123:444–496CrossRef Blume LE, Brock WA, Durlauf SN, Jayaraman R (2015) Linear social interactions models. J Polit Econ 123:444–496CrossRef
Zurück zum Zitat Bramoulle Y, Djebbari H, Fortin B (2009) Identification of peer effects through social networks. J Econom 150:41–55CrossRef Bramoulle Y, Djebbari H, Fortin B (2009) Identification of peer effects through social networks. J Econom 150:41–55CrossRef
Zurück zum Zitat Brock WA, Durlauf SN (2001) Interaction-based models, Volume 5 of Handbook of Econometrics, Chapter 54. Elsevier, pp 3297–3380 Brock WA, Durlauf SN (2001) Interaction-based models, Volume 5 of Handbook of Econometrics, Chapter 54. Elsevier, pp 3297–3380
Zurück zum Zitat Borusyak K, Jaravel X, Spiess J (2024) Revisiting event-study designs: robust and efficient estimation. Rev Econ Stud, forthcoming Borusyak K, Jaravel X, Spiess J (2024) Revisiting event-study designs: robust and efficient estimation. Rev Econ Stud, forthcoming
Zurück zum Zitat Callaway B, Sant’Anna PHC (2021) Difference-in-differences with multiple time periods. J Econom 225(2):200–230CrossRef Callaway B, Sant’Anna PHC (2021) Difference-in-differences with multiple time periods. J Econom 225(2):200–230CrossRef
Zurück zum Zitat Chagas ALS, Azzoni CR, Almeida A (2016) A spatial difference-in-differences analysis of the impact of sugarcane production on respiratory diseases. Reg Sci Urban Econ 59:24–36CrossRef Chagas ALS, Azzoni CR, Almeida A (2016) A spatial difference-in-differences analysis of the impact of sugarcane production on respiratory diseases. Reg Sci Urban Econ 59:24–36CrossRef
Zurück zum Zitat Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, London Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, London
Zurück zum Zitat de Chaisemartin C, D’Haultfoeuille X (2020) Two-way fixed effects estimators with heterogeneous treatment effects. Amer Econ Rev 110(9):2964–2996CrossRef de Chaisemartin C, D’Haultfoeuille X (2020) Two-way fixed effects estimators with heterogeneous treatment effects. Amer Econ Rev 110(9):2964–2996CrossRef
Zurück zum Zitat Delgado MS, Florax RJGM (2015) Difference-in-difference techniques for spatial data: local autocorrelation and spatial interaction. Econ Lett 137:123–126CrossRef Delgado MS, Florax RJGM (2015) Difference-in-difference techniques for spatial data: local autocorrelation and spatial interaction. Econ Lett 137:123–126CrossRef
Zurück zum Zitat Diao M, Leonard D, Sing TF (2017) Spatial-difference-in-differences models for impact of new mass rapid transit line on private housing values. Reg Sci Urban Econ 67:64–77CrossRef Diao M, Leonard D, Sing TF (2017) Spatial-difference-in-differences models for impact of new mass rapid transit line on private housing values. Reg Sci Urban Econ 67:64–77CrossRef
Zurück zum Zitat Dubé J, Legros D, Thériault M, Rosiers FD (2014) A spatial Difference-in-Differences estimator to evaluate the effect of change in public mass transit systems on house prices. Transp Res Part b Methodol 64:24–40CrossRef Dubé J, Legros D, Thériault M, Rosiers FD (2014) A spatial Difference-in-Differences estimator to evaluate the effect of change in public mass transit systems on house prices. Transp Res Part b Methodol 64:24–40CrossRef
Zurück zum Zitat Durlauf SN, Ioannides YM (2010) Social interactions. Annu Rev Econom 2:451–478CrossRef Durlauf SN, Ioannides YM (2010) Social interactions. Annu Rev Econom 2:451–478CrossRef
Zurück zum Zitat Feser E (2013) Isserman’s impact: quasi-experimental comparison group designs in regional research. Int Reg Sci Rev 36:44–68CrossRef Feser E (2013) Isserman’s impact: quasi-experimental comparison group designs in regional research. Int Reg Sci Rev 36:44–68CrossRef
Zurück zum Zitat Goodman-Bacon A (2021) Difference-in-differences with variation in treatment timing. J Econom 225:254–277CrossRef Goodman-Bacon A (2021) Difference-in-differences with variation in treatment timing. J Econom 225:254–277CrossRef
Zurück zum Zitat Gerber AS, Green DP (2012) Field experiments: design, analysis, and interpretation. W. W Norton and Company Gerber AS, Green DP (2012) Field experiments: design, analysis, and interpretation. W. W Norton and Company
Zurück zum Zitat Gibbons S, Overman HG, Patacchini E (2015) Spatial methods. In: Duranton G, Henderson V, Strange W (eds) Handbook of regional and urban economics, Volume 5a, Chapter 3. Elsevier Gibbons S, Overman HG, Patacchini E (2015) Spatial methods. In: Duranton G, Henderson V, Strange W (eds) Handbook of regional and urban economics, Volume 5a, Chapter 3. Elsevier
Zurück zum Zitat Goldsmith-Pinkham P, Imbens GW (2013) Social networks and the identification of peer effects. J Bus Econ Stat 31:253–264CrossRef Goldsmith-Pinkham P, Imbens GW (2013) Social networks and the identification of peer effects. J Bus Econ Stat 31:253–264CrossRef
Zurück zum Zitat Graham BS (2015) Methods of identification of social networks. Annu Rev Econ 7:465–485CrossRef Graham BS (2015) Methods of identification of social networks. Annu Rev Econ 7:465–485CrossRef
Zurück zum Zitat Greene WH (2017) Econometric analysis, 8th edn. Pearson Greene WH (2017) Econometric analysis, 8th edn. Pearson
Zurück zum Zitat Han X, Lee L (2016) Bayesian analysis of spatial panel autoregressive models with time-varying endogenous spatial weight matrices, common factors, and random coefficients. J Bus Econ Stat 34(4):642–660CrossRef Han X, Lee L (2016) Bayesian analysis of spatial panel autoregressive models with time-varying endogenous spatial weight matrices, common factors, and random coefficients. J Bus Econ Stat 34(4):642–660CrossRef
Zurück zum Zitat Hsieh C, Lee L (2016) A social interactions model with endogenous friendship formation and selectivity. J Appl Economet 31(2):301–319CrossRef Hsieh C, Lee L (2016) A social interactions model with endogenous friendship formation and selectivity. J Appl Economet 31(2):301–319CrossRef
Zurück zum Zitat Imbens GW, Wooldridge JM (2009) Recent developments in the econometrics of program evaluation. J Econ Lit 47:5–86CrossRef Imbens GW, Wooldridge JM (2009) Recent developments in the econometrics of program evaluation. J Econ Lit 47:5–86CrossRef
Zurück zum Zitat Lee L (2007) Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. J Econom 140:333–374CrossRef Lee L (2007) Identification and estimation of econometric models with group interactions, contextual factors and fixed effects. J Econom 140:333–374CrossRef
Zurück zum Zitat Lee L, Liu X, Lin X (2010) Specification and estimation of social interaction models with network structures. Econom J 13:145–176CrossRef Lee L, Liu X, Lin X (2010) Specification and estimation of social interaction models with network structures. Econom J 13:145–176CrossRef
Zurück zum Zitat LeSage J, Pace RK (2009) Introduction to spatial econometrics. CRC PressCrossRef LeSage J, Pace RK (2009) Introduction to spatial econometrics. CRC PressCrossRef
Zurück zum Zitat Lin X (2010) Identifying peer effects in student academic achievement by spatial autoregressive models with group unobservables. J Law Econ 28:825–860 Lin X (2010) Identifying peer effects in student academic achievement by spatial autoregressive models with group unobservables. J Law Econ 28:825–860
Zurück zum Zitat Manski CF (2000) Economic analysis of social interactions. J Econ Persp 14:115–136CrossRef Manski CF (2000) Economic analysis of social interactions. J Econ Persp 14:115–136CrossRef
Zurück zum Zitat Manski CF (2013) Identification of treatment response with social interactions. Economet J 16:S1–S23CrossRef Manski CF (2013) Identification of treatment response with social interactions. Economet J 16:S1–S23CrossRef
Zurück zum Zitat Millo G (2014) Maximum likelihood estimation of spatially and serially correlated panels with random effects. Comput Stat Data Anal 71:914–933CrossRef Millo G (2014) Maximum likelihood estimation of spatially and serially correlated panels with random effects. Comput Stat Data Anal 71:914–933CrossRef
Zurück zum Zitat Qiu F, Tong Q (2021) A spatial difference-in-differences approach to evaluate the impact of light rail transit on property values. Econ Model 99:105496CrossRef Qiu F, Tong Q (2021) A spatial difference-in-differences approach to evaluate the impact of light rail transit on property values. Econ Model 99:105496CrossRef
Zurück zum Zitat Rubin DB (1978) Bayesian inference for causal effects: the role of randomization. Ann Stat 6:34–58CrossRef Rubin DB (1978) Bayesian inference for causal effects: the role of randomization. Ann Stat 6:34–58CrossRef
Zurück zum Zitat Rubin DB (1990) Formal modes of statistical inference for causal effects. J Stat Plan Inference 25:279–292CrossRef Rubin DB (1990) Formal modes of statistical inference for causal effects. J Stat Plan Inference 25:279–292CrossRef
Zurück zum Zitat Sun L, Abraham S (2021) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects. J Econom 225(2):175–199CrossRef Sun L, Abraham S (2021) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects. J Econom 225(2):175–199CrossRef
Zurück zum Zitat Verbitsky-Savitz N, Raudenbush SW (2012) Causal inference under interference in spatial settings: a case study evaluating community policing program in Chicago. Epidemiol Methods 1(1):6CrossRef Verbitsky-Savitz N, Raudenbush SW (2012) Causal inference under interference in spatial settings: a case study evaluating community policing program in Chicago. Epidemiol Methods 1(1):6CrossRef
Metadaten
Titel
Local spatial difference-in-differences models: treatment correlations, response interactions, and expanded local models
verfasst von
Shanxia Sun
Michael S. Delgado
Publikationsdatum
22.05.2024
Verlag
Springer Berlin Heidelberg
Erschienen in
Empirical Economics
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-024-02610-2

Premium Partner