In both corporate finance and asset pricing empirical work, researchers are often confronted with panel data. In these data sets, the residuals may be correlated across firms and across time, and OLS standard errors can be biased. Historically, the two literatures have used different solutions to this problem. Corporate finance has relied on clustered standard errors, while asset pricing has used the Fama-MacBeth procedure to estimate standard errors. This paper examines the different methods used in the literature and explains when the different methods yield the same (and correct) standard errors and when they diverge. The intent is to provide intuition as to why the different approaches sometimes give different answers and give researchers guidance for their use.

/pdf/estimating-standard-errors-in-finance-panel-data-sets-1rry6mh9tl.pdf

Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches

The present historical moment may seem a particularly inopportune time to review Bowling Alone, Robert Putnam's latest exploration of civic decline in America. After all, the outpouring of volunteerism, solidarity, patriotism, and self-sacrifice displayed by Americans in the wake of the September 11 terrorist attacks appears to fly in the face of Putnam's central argument: that \"social capital\" -defined as \"social networks and the norms of reciprocity and trustworthiness that arise from them\" (p. 19)'has declined to dangerously low levels in America over the last three decades. However, Putnam is not fazed in the least by the recent effusion of solidarity. Quite the contrary, he sees in it the potential to \"reverse what has been a 30to 40-year steady decline in most measures of connectedness or community.\"' As an example of how the current \"war on terrorism\" could generate a durable civic renewal, Putnam points to the burst in civic practices that occurred during and after World War II, which he says \"permanently marked\" the generation that lived through it and had a \"terrific effect on American public life over the last half-century.\" 3 If Americans can follow this example and channel their current civic

Bowling alone: The collapse and revival of American community

A Treatise on the Family. G. S. Becker. Cambridge, MA: Harvard University Press. 1981. Gary Becker is one of the most famous and influential economists of the second half of the 20th century, a fervent contributor to and expounder of the University of Chicago free-market philosophy, and winner of the 1992 Nobel Prize in economics. Although any book with the word "treatise" in its title is clearly intended to have an impact, one coming from someone as brilliant and controversial as Becker certainly had such a lofty goal. It has received many article-length reviews in several disciplines (Ben-Porath, 1982; Bergmann, 1995; Foster, 1993; Hannan, 1982), which is one measure of its scholarly importance, and yet its impact is, I think, less than it may have initially appeared, especially for scholars with substantive interests in the family. This book is, its title notwithstanding, more about economics and the economic approach to behavior than about the family. In the first sentence of the preface, Becker writes "In this book, I develop an economic or rational choice approach to the family." Lest anyone accuse him of focusing on traditional (i.e., material) economics topics, such as family income, poverty, and labor supply, he immediately emphasizes that those topics are not his focus. "My intent is more ambitious: to analyze marriage, births, divorce, division of labor in households, prestige, and other non-material behavior with the tools and framework developed for material behavior." Indeed, the book includes chapters on many of these issues. One chapter examines the principles of the efficient division of labor in households, three analyze marriage and divorce, three analyze various child-related issues (fertility and intergenerational mobility), and others focus on broader family issues, such as intrafamily resource allocation. His analysis is not, he believes, constrained by time or place. His intention is "to present a comprehensive analysis that is applicable, at least in part, to families in the past as well as the present, in primitive as well as modern societies, and in Eastern as well as Western cultures." His tone is profoundly conservative and utterly skeptical of any constructive role for government programs. There is a clear sense of how much better things were in the old days of a genderbased division of labor and low market-work rates for married women. Indeed, Becker is ready and able to show in Chapter 2 that such a state of affairs was efficient and induced not by market or societal discrimination (although he allows that it might exist) but by small underlying household productivity differences that arise primarily from what he refers to as "complementarities" between caring for young children while carrying another to term. Most family scholars would probably find that an unconvincingly simple explanation for a profound and complex phenomenon. What, then, is the salient contribution of Treatise on the Family? It is not literally the idea that economics could be applied to the nonmarket sector and to family life because Becker had already established that with considerable success and influence. At its core, microeconomics is simple, characterized by a belief in the importance of prices and markets, the role of self-interested or rational behavior, and, somewhat less centrally, the stability of preferences. It was Becker's singular and invaluable contribution to appreciate that the behaviors potentially amenable to the economic approach were not limited to phenomenon with explicit monetary prices and formal markets. Indeed, during the late 1950s and throughout the 1960s, he did undeniably important and pioneering work extending the domain of economics to such topics as labor market discrimination, fertility, crime, human capital, household production, and the allocation of time. Nor is Becker's contribution the detailed analyses themselves. Many of them are, frankly, odd, idiosyncratic, and off-putting. …

A Treatise on the Family

We investigated the differential diffusion of all of the verified true and false news stories distributed on Twitter from 2006 to 2017. The data comprise ~126,000 stories tweeted by ~3 million people more than 4.5 million times. We classified news as true or false using information from six independent fact-checking organizations that exhibited 95 to 98% agreement on the classifications. Falsehood diffused significantly farther, faster, deeper, and more broadly than the truth in all categories of information, and the effects were more pronounced for false political news than for false news about terrorism, natural disasters, science, urban legends, or financial information. We found that false news was more novel than true news, which suggests that people were more likely to share novel information. Whereas false stories inspired fear, disgust, and surprise in replies, true stories inspired anticipation, sadness, joy, and trust. Contrary to conventional wisdom, robots accelerated the spread of true and false news at the same rate, implying that false news spreads more than the truth because humans, not robots, are more likely to spread it.

The spread of true and false news online

This paper provides an introduction and "user guide" to Regression Discontinuity (RD) designs for empirical researchers. It presents the basic theory behind the research design, details when RD is likely to be valid or invalid given economic incentives, explains why it is considered a "quasi-experimental" design, and summarizes different ways (with their advantages and disadvantages) of estimating RD designs and the limitations of interpreting these estimates. Concepts are discussed using examples drawn from the growing body of empirical research using RD.

Regression Discontinuity Designs in Economics

We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.

/pdf/a-practitioner-s-guide-to-cluster-robust-inference-1xbcejtio0.pdf

A Practitioner’s Guide to Cluster-Robust Inference

In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g., Liang and Zeger 1986; Arellano 1987) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state–year effects example of Bertrand, Duflo, and Mullainathan (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present.

/pdf/robust-inference-with-multi-way-clustering-buxopcmamj.pdf

Robust Inference with Multi-way Clustering

Researchers have increasingly realized the need to account for within-group dependence in estimating standard errors of regression parameter estimates. The usual solution is to calculate cluster-robust standard errors that permit heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. Standard asymptotic tests can over-reject, however, with few (five to thirty) clusters. We investigate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the example of Bertrand, Duflo, and Mullainathan (2004). Rejection rates of 10% using standard methods can be reduced to the nominal size of 5% using our methods.

/pdf/bootstrap-based-improvements-for-inference-with-clustered-1m8x7cabov.pdf

Bootstrap-Based Improvements for Inference with Clustered Errors

In this paper we propose a new variance estimator for OLS as well as for nonlinear estimators such as logit, probit and GMM, that provcides cluster-robust inference when there is two-way or multi-way clustering that is non-nested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g. Liang and Zeger (1986), Arellano (1987)) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand et al. (2004) to two dimensions; and by application to two studies in the empirical public/labor literature where two-way clustering is present.

https://papers.ssrn.com/sol3/Delivery.cfm/nber_t0327.pdf?abstractid=927374&mirid=4

Robust Inference with Multi-Way Clustering

Microeconometrics researchers have increasingly realized the essential need to account for any within-group dependence in estimating standard errors of regression parameter estimates. The typical preferred solution is to calculate cluster-robust or sandwich standard errors that permit quite general heteroskedasticity and within-cluster error correlation, but presume that the number of clusters is large. In applications with few (5-30) clusters, standard asymptotic tests can over-reject considerably. We investigate more accurate inference using cluster bootstrap-t procedures that provide asymptotic refinement. These procedures are evaluated using Monte Carlos, including the much-cited di¤erences-in-di¤erences example of Bertrand, Mullainathan and Duflo (2004). In situations where standard methods lead to rejection rates in excess of ten percent (or more) for tests of nominal size 0:05, our methods can reduce this to five percent. In principle a pairs cluster bootstrap should work well, but in practice a Wild cluster bootstrap performs better.

/pdf/bootstrap-based-improvements-for-inference-with-clustered-2rr1liz8yy.pdf

Douglas L. Miller

Papers

A Practitioner’s Guide to Cluster-Robust Inference

Robust Inference with Multi-way Clustering

Bootstrap-Based Improvements for Inference with Clustered Errors

Robust Inference with Multi-Way Clustering

Bootstrap-Based Improvements for Inference with Clustered Errors