Inference in differences-in-differences with few treated groups and heteroskedasticity
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional do FGV (FGV Repositório Digital) |
Texto Completo: | http://hdl.handle.net/10438/14170 |
Resumo: | Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment periods. We extend our inference methods to linear factor models when there are few treated groups. We also derive conditions under which a permutation test for the synthetic control estimator proposed by Abadie et al. (2010) is robust to heteroskedasticity and propose a modification on the test statistic that provided a better heteroskedasticity correction in our simulations. |
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Ferman, BrunoPinto, Cristine Campos de XavierEscolas::EESP2015-10-27T17:27:14Z2015-10-27T17:27:14Z2015-10-27TD 406http://hdl.handle.net/10438/14170Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment periods. We extend our inference methods to linear factor models when there are few treated groups. We also derive conditions under which a permutation test for the synthetic control estimator proposed by Abadie et al. 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dc.title.eng.fl_str_mv |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
title |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
spellingShingle |
Inference in differences-in-differences with few treated groups and heteroskedasticity Ferman, Bruno Difference-in-difference Heteroskedasticity Inference Economia Economia |
title_short |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
title_full |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
title_fullStr |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
title_full_unstemmed |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
title_sort |
Inference in differences-in-differences with few treated groups and heteroskedasticity |
author |
Ferman, Bruno |
author_facet |
Ferman, Bruno Pinto, Cristine Campos de Xavier |
author_role |
author |
author2 |
Pinto, Cristine Campos de Xavier |
author2_role |
author |
dc.contributor.unidadefgv.por.fl_str_mv |
Escolas::EESP |
dc.contributor.author.fl_str_mv |
Ferman, Bruno Pinto, Cristine Campos de Xavier |
dc.subject.por.fl_str_mv |
Difference-in-difference Heteroskedasticity Inference |
topic |
Difference-in-difference Heteroskedasticity Inference Economia Economia |
dc.subject.area.por.fl_str_mv |
Economia |
dc.subject.bibliodata.por.fl_str_mv |
Economia |
description |
Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment periods. We extend our inference methods to linear factor models when there are few treated groups. We also derive conditions under which a permutation test for the synthetic control estimator proposed by Abadie et al. (2010) is robust to heteroskedasticity and propose a modification on the test statistic that provided a better heteroskedasticity correction in our simulations. |
publishDate |
2015 |
dc.date.accessioned.fl_str_mv |
2015-10-27T17:27:14Z |
dc.date.available.fl_str_mv |
2015-10-27T17:27:14Z |
dc.date.issued.fl_str_mv |
2015-10-27 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10438/14170 |
dc.identifier.sici.none.fl_str_mv |
TD 406 |
identifier_str_mv |
TD 406 |
url |
http://hdl.handle.net/10438/14170 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartofseries.por.fl_str_mv |
EESP- Textos para Discussão;TD 406 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional do FGV (FGV Repositório Digital) instname:Fundação Getulio Vargas (FGV) instacron:FGV |
instname_str |
Fundação Getulio Vargas (FGV) |
instacron_str |
FGV |
institution |
FGV |
reponame_str |
Repositório Institucional do FGV (FGV Repositório Digital) |
collection |
Repositório Institucional do FGV (FGV Repositório Digital) |
bitstream.url.fl_str_mv |
https://repositorio.fgv.br/bitstreams/277fd1da-f589-4d76-89d2-0374b6be2ace/download https://repositorio.fgv.br/bitstreams/96efcfa3-516d-4c8a-ba12-0905b3d037a1/download https://repositorio.fgv.br/bitstreams/a1d3068b-f980-4268-959c-961f4567cab7/download https://repositorio.fgv.br/bitstreams/790355ce-6656-4681-9e26-003f97d35cb2/download https://repositorio.fgv.br/bitstreams/61a43f43-6af7-4c4e-98b5-394244e9327a/download https://repositorio.fgv.br/bitstreams/40ae58f2-2bed-4a6d-8268-11fc91add021/download https://repositorio.fgv.br/bitstreams/dad39c62-982b-42b2-8dd1-78418c58a9be/download https://repositorio.fgv.br/bitstreams/4854701f-a4fc-4dbe-9ef9-ec8bc9246ec3/download |
bitstream.checksum.fl_str_mv |
dfb340242cced38a6cca06c627998fa1 6df18df082300361b79356a5579efe15 2c8905c52312a5c36446e6e650ae0e1b 8dbe8984e9263439227cffdbc2629c8f a84d31e78f641a2fba32022d9ce17d68 06c3f8e3a2c35672d5625e0ad5a240aa 602480a8bd5a3dd9e79fb03c109b5370 6a6c0d961ccb43ca35ad876414fae4c5 |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional do FGV (FGV Repositório Digital) - Fundação Getulio Vargas (FGV) |
repository.mail.fl_str_mv |
|
_version_ |
1810023798568648704 |