Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models
TL;DR: In this article, the synthetic control method is combined with linear fixed effects models for causal inference in time-series cross-sectional data, and a linear interactive fixed effects model that incorporates unit-specific intercepts interacted with time-varying coefficients is proposed.
Abstract: Difference-in-differences (DID) is commonly used for causal inference in time-series cross-sectional data. It requires the assumption that the average outcomes of treated and control units would have followed parallel paths in the absence of treatment. In this paper, we propose a method that not only relaxes this often-violated assumption, but also unifies the synthetic control method (Abadie, Diamond, and Hainmueller 2010) with linear fixed effects models under a simple framework, of which DID is a special case. It imputes counterfactuals for each treated unit using control group information based on a linear interactive fixed effects model that incorporates unit-specific intercepts interacted with time-varying coefficients. This method has several advantages. First, it allows the treatment to be correlated with unobserved unit and time heterogeneities under reasonable modeling assumptions. Second, it generalizes the synthetic control method to the case of multiple treated units and variable treatment periods, and improves efficiency and interpretability. Third, with a built-in cross-validation procedure, it avoids specification searches and thus is easy to implement. An empirical example of Election Day Registration and voter turnout in the United States is provided.
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TL;DR: Practical guidance is provided to researchers employing synthetic control methods and the advantages of the synthetic control framework as a research design, and the settings where synthetic controls provide reliable estimates and those where they may fail are described.
Abstract: Probably because of their interpretability and transparent nature, synthetic controls have become widely applied in empirical research in economics and the social sciences. This article aims to provide practical guidance to researchers employing synthetic control methods. The article starts with an overview and an introduction to synthetic control estimation. The main sections discuss the advantages of the synthetic control framework as a research design, and describe the settings where synthetic controls provide reliable estimates and those where they may fail. The article closes with a discussion of recent extensions, related methods, and avenues for future research.
486 citations
TL;DR: It is proved that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights, implying that in contrast to the popular belief, the 2FE estimation does not represent a design-based, nonparametric estimation strategy for causal inference.
Abstract: The two-way linear fixed effects regression (2FE) has become a default method for estimating causal effects from panel data. Many applied researchers use the 2FE estimator to adjust for unobserved unit-specific and time-specific confounders at the same time. Unfortunately, we demonstrate that the ability of the 2FE model to simultaneously adjust for these two types of unobserved confounders critically relies upon the assumption of linear additive effects. Another common justification for the use of the 2FE estimator is based on its equivalence to the difference-in-differences estimator under the simplest setting with two groups and two time periods. We show that this equivalence does not hold under more general settings commonly encountered in applied research. Instead, we prove that the multi-period difference-in-differences estimator is equivalent to the weighted 2FE estimator with some observations having negative weights. These analytical results imply that in contrast to the popular belief, the 2FE estimator does not represent a design-based, nonparametric estimation strategy for causal inference. Instead, its validity fundamentally rests on the modeling assumptions.
192 citations
TL;DR: It is found that the EU ETS, which initially regulated roughly 50% of EU carbon emissions from mainly energy production and large industrial polluters, saved more than 1 billion tons of CO2 between 2008 and 2016 compared to a world without carbon markets.
Abstract: International carbon markets are an appealing and increasingly popular tool to regulate carbon emissions. By putting a price on carbon, carbon markets reshape incentives faced by firms and reduce the value of emissions. How effective are carbon markets? Observers have tended to infer their effectiveness from market prices. The general belief is that a carbon market needs a high price in order to reduce emissions. As a result, many observers remain skeptical of initiatives such as the European Union Emissions Trading System (EU ETS), whose price remained low (compared to the social cost of carbon). In this paper, we assess whether the EU ETS reduced [Formula: see text] emissions despite low prices. We motivate our study by documenting that a carbon market can be effective if it is a credible institution that can plausibly become more stringent in the future. In such a case, firms might cut emissions even though market prices are low. In fact, low prices can be a signal that the demand for carbon permits weakens. Thus, low prices are compatible with successful carbon markets. To assess whether the EU ETS reduced carbon emissions even as permits were cheap, we estimate counterfactual carbon emissions using an original sectoral emissions dataset. We find that the EU ETS saved about 1.2 billion tons of [Formula: see text] between 2008 and 2016 (3.8%) relative to a world without carbon markets, or almost half of what EU governments promised to reduce under their Kyoto Protocol commitments. Emission reductions in sectors covered under the EU ETS were higher.
174 citations
TL;DR: The probit regression results give a different outcome, as rescon, FID, CO2, Human Development Index (HDI), and investment in the energy sector by the private sector that will likely have an impact on the green financing and climate change mitigation of the study countries.
Abstract: Green finance is inextricably linked to investment risk, particularly in emerging and developing economies (EMDE). This study uses the difference in differences (DID) method to evaluate the mean causal effects of a treatment on an outcome of the determinants of scaling up green financing and climate change mitigation in the N-11 countries from 2005 to 2019. After analyzing with a dummy for the treated countries, it was confirmed that the outcome covariates: rescon (renewable energy sources consumption), population, FDI, CO2, inflation, technical corporation grants, domestic credit to the private sector, and research and development are very significant in promoting green financing and climate change mitigation in the study countries. The probit regression results give a different outcome, as rescon, FID, CO2, Human Development Index (HDI), and investment in the energy sector by the private sector that will likely have an impact on the green financing and climate change mitigation of the study countries. Furthermore, after matching the analysis through the nearest neighbor matching, kernel matching, and radius matching, it produced mixed results for both the treated and the untreated countries. Either group experienced an improvement in green financing and climate change mitigation or a decrease. Overall, the DID showed no significant difference among the countries.
156 citations
TL;DR: It is asserted in this paper that CEPI could serve as strong external stimulus that help to overcome various root problems in environmental governance system and therefore engender long-term improvements for environmental performance.
136 citations
References
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Book•
01 Jan 1993TL;DR: This article presents bootstrap methods for estimation, using simple arguments, with Minitab macros for implementing these methods, as well as some examples of how these methods could be used for estimation purposes.
Abstract: This article presents bootstrap methods for estimation, using simple arguments. Minitab macros for implementing these methods are given.
37,183 citations
TL;DR: A discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation is presented in this paper, where the objective is to specify the benefits of randomization in estimating causal effects of treatments.
Abstract: A discussion of matching, randomization, random sampling, and other methods of controlling extraneous variation is presented. The objective is to specify the benefits of randomization in estimating causal effects of treatments. The basic conclusion is that randomization should be employed whenever possible but that the use of carefully controlled nonrandomized data to estimate causal effects is a reasonable and necessary procedure in many cases. Recent psychological and educational literature has included extensive criticism of the use of nonrandomized studies to estimate causal effects of treatments (e.g., Campbell & Erlebacher, 1970). The implication in much of this literature is that only properly randomized experiments can lead to useful estimates of causal effects. If taken as applying to all fields of study, this position is untenable. Since the extensive use of randomized experiments is limited to the last half century,8 and in fact is not used in much scientific investigation today,4 one is led to the conclusion that most scientific "truths" have been established without using randomized experiments. In addition, most of us successfully determine the causal effects of many of our everyday actions, even interpersonal behaviors, without the benefit of randomization. Even if the position that causal effects of treatments can only be well established from randomized experiments is taken as applying only to the social sciences in which
8,377 citations
Book•
01 Jan 1997TL;DR: In this paper, Campbell, Lo, and MacKinlay present an attempt by three well-known and well-respected scholars to fill an acknowledged void in the empirical finance literature, a text covering the burgeoning field of empirical finance.
Abstract: This book is an ambitious effort by three well-known and
well-respected scholars to fill an acknowledged void in the
literature—a text covering the burgeoning field of empirical finance.
As the authors note in the preface, there are several excellent books
covering financial theory at a level suitable for a Ph.D. class or as
a reference for academics and practitioners, but there is little or
nothing similar that covers econometric methods and applications.
Perhaps the closest existing text is the recent addition to the Wiley
Series in Financial and Quantitative Analysis. written by Cuthbertson
(1996). The major difference between the books is that Cuthbertson
focuses exclusively on asset pricing in the stock, bond, and foreign
exchange markets, whereas Campbell, Lo, and MacKinlay (henceforth CLM)
consider empirical applications throughout the field of finance,
including corporate finance, derivatives markets, and market
microstructure. The level of anticipation preceding publication
can be partly measured by the fact that at least three reviews
(including this one) have appeared since the book arrived. Moreover,
in their reviews, both Harvey (1998) and Tiso (1998) comment on the
need for such a text, a sentiment that has been echoed by numerous
finance academics.
7,169 citations
TL;DR: The generalized least squares approach of Parks produces standard errors that lead to extreme overconfidence, often underestimating variability by 50% or more, and a new method is offered that is both easier to implement and produces accurate standard errors.
Abstract: We examine some issues in the estimation of time-series cross-section models, calling into question the conclusions of many published studies, particularly in the field of comparative political economy. We show that the generalized least squares approach of Parks produces standard errors that lead to extreme overconfidence, often underestimating variability by 50% or more. We also provide an alternative estimator of the standard errors that is correct when the error structures show complications found in this type of model. Monte Carlo analysis shows that these “panel-corrected standard errors” perform well. The utility of our approach is demonstrated via a reanalysis of one “social democratic corporatist” model.
5,670 citations
TL;DR: In this article, the authors use a particular model for causal inference (Holland and Rubin 1983; Rubin 1974) to critique the discussions of other writers on causation and causal inference.
Abstract: Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is addressed by using a particular model for causal inference (Holland and Rubin 1983; Rubin 1974) to critique the discussions of other writers on causation and causal inference. These include selected philosophers, medical researchers, statisticians, econometricians, and proponents of causal modeling.
4,845 citations