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Mostly Harmless Econometrics: An Empiricist's Companion
Abstract
The core methods in today's econometric toolkit are linear regression for statistical control, instrumental variables methods for the analysis of natural experiments, and differences-in-differences methods that exploit policy changes. In the modern experimentalist paradigm, these techniques address clear causal questions such as: Do smaller classes increase learning? Should wife batterers be arrested? How much does education raise wages?Mostly Harmless Econometricsshows how the basic tools of applied econometrics allow the data to speak.In addition to econometric essentials,Mostly Harmless Econometricscovers important new extensions--regression-discontinuity designs and quantile regression--as well as how to get standard errors right. Joshua Angrist and J rn-Steffen Pischke explain why fancier econometric techniques are typically unnecessary and even dangerous. The applied econometric methods emphasized in this book are easy to use and relevant for many areas of contemporary social science.An irreverent review of econometric essentialsA focus on tools that applied researchers use mostChapters on regression-discontinuity designs, quantile regression, and standard errorsMany empirical examplesA clear and concise resource with wide applications.
... Our statistical analysis pipeline comprises logit regression [7] and Analysis of Variance (ANOVA) [27]. These methods provide complementary insights into the impact of the studied attributes on fairness. ...
... Logit regression [7] models the relation between attributes and the binary outcome of a model. It is a generalized linear model that estimates the probability of a binary outcome based on one or more independent variables using: ...
Face recognition and verification are two computer vision tasks whose performances have advanced with the introduction of deep representations. However, ethical, legal, and technical challenges due to the sensitive nature of face data and biases in real-world training datasets hinder their development. Generative AI addresses privacy by creating fictitious identities, but fairness problems remain. Using the existing DCFace SOTA framework, we introduce a new controlled generation pipeline that improves fairness. Through classical fairness metrics and a proposed in-depth statistical analysis based on logit models and ANOVA, we show that our generation pipeline improves fairness more than other bias mitigation approaches while slightly improving raw performance.
... Therefore, fixed-effect regression is generally employed to estimate the causal effects of entity-and time-specific effects (e.g. Bertrand et al. 2004;Angrist and Pischke 2009). The fixed effect model allows controlling for time-invariant heterogeneities among households. ...
The world population has experienced several challenges due to different measures, including complete lockdowns, which were taken to contain the 2019 Coronavirus Disease (COVID-19) pandemic. This paper assessed the impact of the COVID-19 pandemic on rural household livelihoods in sub-Saharan Africa. Data were collected from 2705 rice smallholder producers in five countries (Cote d’Ivoire, Togo, Sierra Leone, Senegal, and Madagascar) and analyzed using fixed-effect regression models. The results showed that 81% of respondents perceived that their income had decreased due to the COVID-19 pandemic. Access to production inputs such as seeds, fertilizers, and herbicides has become more difficult and expensive. Approximately 45% of the rice farmers reported having difficulty obtaining agricultural extension services. Although the short-term impact on food security was not significant, we found evidence that the pandemic decreased the income of rice farmers by approximately US$ 240 per month. To support smallholder producers against the effects of future pandemics, income-enhancing actions, such as increasing access to credit and subsidies for agricultural inputs, should be prioritized.
... This reasoning explains why many researchers opt for static panel regressions; in their contexts, treatment is random, so although past outcomes affect current outcomes, they are not correlated with the treatment and, therefore, are not classic confounders [Angrist and Pischke, 2009]. Due to fixed effects estimation, a past outcome is a generated confounder and generates bias if it is correlated with either the treatment or the outcome. ...
This paper identifies an important bias - termed dynamic bias - in fixed effects panel estimators that arises when dynamic feedback is ignored in the estimating equation. Dynamic feedback occurs if past outcomes impact current outcomes, a feature of many settings ranging from economic growth to agricultural and labor markets. When estimating equations omit past outcomes, dynamic bias can lead to significantly inaccurate treatment effect estimates, even with randomly assigned treatments. This dynamic bias in simulations is larger than Nickell bias. I show that dynamic bias stems from the estimation of fixed effects, as their estimation generates confounding in the data. To recover consistent treatment effects, I develop a flexible estimator that provides fixed-T bias correction. I apply this approach to study the impact of temperature shocks on GDP, a canonical example where economic theory points to an important feedback from past to future outcomes. Accounting for dynamic bias lowers the estimated effects of higher yearly temperatures on GDP growth by 10% and GDP levels by 120%.
... Within the realm of public policy, they inform the design and evaluation of interventions, from education reforms to social welfare programs Rubin, 2015, Hill, 2011]. In economics, ATE and CATE estimations are crucial for understanding the impacts of economic policies, labor market interventions, and consumer behavior [Angrist andPischke, 2008, Heckman andVytlacil, 2007]. ...
Causal inference is a critical task across fields such as healthcare, economics, and the social sciences. While recent advances in machine learning, especially those based on the deep-learning architectures, have shown potential in estimating causal effects, existing approaches often fall short in handling complex causal structures and lack adaptability across various causal scenarios. In this paper, we present a novel transformer-based method for causal inference that overcomes these challenges. The core innovation of our model lies in its integration of causal Directed Acyclic Graphs (DAGs) directly into the attention mechanism, enabling it to accurately model the underlying causal structure. This allows for flexible estimation of both average treatment effects (ATE) and conditional average treatment effects (CATE). Extensive experiments on both synthetic and real-world datasets demonstrate that our approach surpasses existing methods in estimating causal effects across a wide range of scenarios. The flexibility and robustness of our model make it a valuable tool for researchers and practitioners tackling complex causal inference problems.
... Here we provide a very brief introduction to the theory of instrumental variables; see the sources [AP09,NM94] for more details. Section 2.1 introduces the standard instrumental variable setup, whereas Section 2.2 introduces the notion of exogeneous covariates. ...
We provide a non-asymptotic analysis of the linear instrumental variable estimator allowing for the presence of exogeneous covariates. In addition, we introduce a novel measure of the strength of an instrument that can be used to derive non-asymptotic confidence intervals. For strong instruments, these non-asymptotic intervals match the asymptotic ones exactly up to higher order corrections; for weaker instruments, our intervals involve adaptive adjustments to the instrument strength, and thus remain valid even when asymptotic predictions break down. We illustrate our results via an analysis of the effect of PM2.5 pollution on various health conditions, using wildfire smoke exposure as an instrument. Our analysis shows that exposure to PM2.5 pollution leads to statistically significant increases in incidence of health conditions such as asthma, heart disease, and strokes.
Understanding the causes and consequences of corporate risk-taking has remained a crucial topic for organizational scholars. Using the case of U.S. banks and one dimension of their risk-taking behavior around the 2008 financial crisis, we offer a theory of how the diverse experiences of corporate leaders can shape their risk-taking behavior. Building on the imprinting literature, we theorize how different types of experiences that bank CEOs had in the past interact to shape current risk-taking behavior, resulting in risk moderation under crisis conditions. We focus on two imprinting experiences with particular relevance for bank CEOs’ risk-taking behavior—MBA education and past crisis experience. We argue that the latter played a pronounced role during the crisis because of greater imprint-environment fit. Our analysis using data from 170 large banks between 2001 and 2019 shows that bank CEOs’ firsthand experience of a prior banking crisis not only directly tempered bank risk-taking but also did so indirectly by limiting the risk-taking tendencies of CEOs with an MBA, particularly during the crisis period. Our study contributes to the sociological literature about organizational risk-taking by emphasizing the crucial role of organizational leaders’ biographies and exploring how earlier institutional conditions shape their risk-taking behavior later.
The proliferation of social media platforms has afforded social scientists unprecedented access to vast troves of data on human interactions, facilitating the study of online behavior at an unparalleled scale. These platforms typically structure conversations as threads, forming tree-like structures known as ''discussion trees.'' This paper examines the structural properties of online discussions on Reddit by analyzing both global (community-level) and local (post-level) attributes of these discussion trees. We conduct a comprehensive statistical analysis of a year's worth of Reddit data, encompassing a quarter of a million posts and several million comments. Our primary objective is to disentangle the relative impacts of global and local properties and evaluate how specific features shape discussion tree structures. The results reveal that both local and global features contribute significantly to explaining structural variation in discussion trees. However, local features, such as post content and sentiment, collectively have a greater impact, accounting for a larger proportion of variation in the width, depth, and size of discussion trees. Our analysis also uncovers considerable heterogeneity in the impact of various features on discussion structures. Notably, certain global features play crucial roles in determining specific discussion tree properties. These features include the subreddit's topic, age, popularity, and content redundancy. For instance, posts in subreddits focused on politics, sports, and current events tend to generate deeper and wider discussion trees. This research enhances our understanding of online conversation dynamics and offers valuable insights for both content creators and platform designers. By elucidating the factors that shape online discussions, our work contributes to ongoing efforts to improve the quality and effectiveness of digital discourse.
This thesis comprises three essays that relate to tax innovations that occurred in Rio Grande do Sul State from 2019 to 2022. The State's main revenue is an indirect tax on consumption, which has the characteristics of regressivity and fiscal anesthesia. The innovations presented and evaluated in this thesis comprise solutions for these issues. Thus, in the first essay we present a study that aims to verify the impact of the COVID-19 pandemic on the use of the Menor Preço Brasil app service. To this end, it investigates both the correlation between confirmed cases of COVID-19 in Brazil and the changes in the application’s functionalities with the variation in citizens’ queries to the application. For this purpose, the method of identifying multiple structural breaks and regression models are employed. The results indicate that a 1% increase in COVID-19 cases led to a 0.2% increase in queries. The results confirm also that user behavior related to application was influenced by the change in the app’s feature and by inflation rates. In the second essay, we study the program (the Devolve-ICMS Program) that refunds consumption tax to low-income citizens (cashback). This study aims to evaluate the impacts of this Program using a differences-in-differences model and having, as response variables, the monthly sum of electronic invoices issued to the Program’s beneficiaries, as well as their value. The results show that the Program is effective, as it has reduced tax pressure on poor people and increased both the number of invoices issued and their value. Finally, the last essay is about the use of monetary incentives through Receita Certa project. Targeted at the commerce sector, this initiative offers cashback rewards, refunding a portion of the consumption tax to citizens. This study evaluates the impacts of Receita Certa using a difference-in-differences model. The response variables are the monthly number and value of electronic invoices issued to beneficiaries. Refunds are contingent on certain conditions, such as revenue exceeding inflation. The results show that the Receita Certa is ineffective, as it decreased the number of tax documents issued and it is not significant about variable value of the documents. Additionally, the initiative’s cost was high, highlighting the need for reevaluation and refinement. States that have a large tax gap need to improve their control systems. Initiatives such as those presented in this thesis seek to engage taxpayers in combating evasion, some more successfully than others. The objective of these studies was to contribute to better public policies in tax administration.
The relevance of center defensive midfielders (CDM) in football cannot be overemphasized. During football games, they are the interlocutor between defense and attack and can be tasked with huge responsibilities. Given the high cost of acquiring an efficient and readily available CDM, we designed this study to use multivariate analysis techniques to determine the correlation between attributes (variables) of a center defensive midfielder such as crossing, short passing, volleys, dribbling, long passing, ball control, and others. With the nonexistence of a multivariate analysis of CDM attributes, we have used canonical correlation analysis (CCA) to investigate these correlations. The study produced four statistically significant (p < 0.05) canonical functions (CF), that showed that attributes such as dribbling, sprint speed, agility, and stamina should be considered more when football clubs are considering a central defensive midfielder. Principal component analysis (PCA) was conducted to discover the most important variables for a CDM. The PCA generated three components. The first component was optimal and highlighted short passing, composure, ball control, interceptions, long passing, vision, and dribbling as the most relevant attributes of a CDM.
Financial institutions are crucial players in the Bhutanese economy. However, little to no research has been conducted on the determinants of the performance of financial institutions in Bhutan to date, especially the COVID-19 pandemic (Yangchen et al., 2022). This research aims to address this gap by studying the impact of COVID-19, financial variables, and macroeconomic factors on the profitability of financial institutions in Bhutan. The panel data is collected from seven leading financial institutions (five commercial banks and two insurance companies) in Bhutan from 2018 to 2022. Random effects generalized least squares (GLS) regression was employed to conduct the empirical analysis focusing on dependent profitability indicators namely return on assets (ROA), return on equity (ROE), and net profit margin (NPM) and indicators of both financial and macroeconomic independent variables. The empirical results showed that Bhutanese financial institutions were resilient and were not significantly affected by COVID-19. The findings also revealed that non-performing loans (NPLs) and cost-to-income ratio (CIR) have a significant negative impact on the profitability of financial institutions in Bhutan, similar to previous research (Bhowmik & Sarker, 2024). The capital adequacy ratio (CAR) has a mixed relationship with profitability. Additionally, earnings per share (EPS) and statutory liquidity ratio (SLR) are found to have a marginal impact on profitability. On the other hand, asset size (LnTA), gross domestic product (GDP) growth rate, and inflation rate (INFL) are found to have insignificant effects on the profitability of financial institutions. The findings from this research provide useful recommendations and strategies to improve the profitability of financial institutions in Bhutan.
We evaluate Angrist and Krueger (1991) and Bound, Jaeger, and Baker (1995) by constructing reliable confidence regions around the 2SLS and LIML estimators for returns-to-schooling regardless of the quality of the instruments. The results indicate that the returns-to-schooling were between 8 and 25 percent in 1970 and between 4 and 14 percent in 1980. Although the estimates are less accurate than previously thought, most specifications by Angrist and Krueger (1991) are informative for returns-to-schooling. In particular, concern about the reliability of the model with 178 instruments is unfounded despite the low first-stage F-statistic. Finally, we briefly discuss bias-adjustment of estimators and pretesting procedures as solutions to the weak-instrument problem.
For a quarter century, American education researchers have tended to favour qualitative and descriptive analyses over quantitative studies using random assignment or featuring credible quasi-experimental research designs. This has now changed. In 2002 and 2003, the US Department of Education funded a dozen randomized trials to evaluate the efficacy of pre-school programmes, up from one in 2000. In this essay, I explore the intellectual and legislative roots of this change, beginning with the story of how contemporary education research fell out of step with other social sciences. I then use a study in which low-achieving high-school students were randomly offered incentives to learn to show how recent developments in research methods answer ethical and practical objections to the use of random assignment for research on schools. Finally, I offer a few cautionary notes based on results from the recent effort to cut class size in California.
S ummary
Bounds for matrix weighted averages of pairs of vectors are presented. The weight matrices are constrained to certain classes suggested by the Bayesian analysis of the linear regression model and the multivariate normal model. The bounds identify the region within which the posterior location vector must lie if the prior comes from a certain class of priors.
The paper examines two approaches to the omitted variable problem. Both of them try to correct for the omitted variable bias by specifying several equations in which the unobservable appears. The first approach assumes that the common left out variable is the only thing connecting the residuals from these equations, making it possible to extract this common factor and control for it. The second approach relies on building a model of the unobservable, by specifying observable variables which are causally related to it. A combination of these two methods is applied to the 1964 CPS-NORC veterans sample in order to evaluate the bias in income- schooling regressions caused by the omission of an unobservable initial ‘ability’ variable.
When several candidate tests are available for a given testing problem, and each has nice properties with respect to different criteria such as efficiency and robustness, it is desirable to combine them. We discuss various combined tests based on asymptotically normal tests. When the means of two standardized tests under contiguous alternatives are close, we show that the maximum of the two tests appears to have an overall best performance compared with other forms of combined tests considered, and that it retains most power compared with the better one of the two tests combined. As an application, for testing zero location shift between two groups, we studied the normal, Wilcoxon, median tests and their combined tests. Because of their structural differences, the joint convergence and the asymptotic correlation of the tests are not easily derived from the usual asymptotic arguments of the tests. We developed a novel application of martingale theory to obtain the asymptotic correlations and their estimators. Simulation studies were also performed to examine the small sample properties of these combined tests. Finally we illustrate the methods by a real data example.