Regression Discontinuity Design

Abstract

We estimate the effect of new unionization on firms’ equity value over the 1961-1999 period using a newly
assembled sample of National Labor Relations Board (NLRB) representation elections matched to stock market
data. Event-study estimates show an average union effect on the equity value of the firm eq uivalent to a cost of at
least $40,500 per unionized worker. At the same time, point estimates from a regression-discontinuity design –
comparing the stock market impact of close union election wins to close losses – are considerably smaller and close
to zero. We find a negative relationship between the cumulative abnormal returns and the vote share in support of
the union, allowing us to reconcile these seemingly contradictory findings. Using the magnitudes from the analysis,
we calibrate a structural “median voter” model of endogenous union determination in order to conduct
counterfactual policy simulations of policies that would marginally increase the ease of unionization.

Year of Publication
2009
Number
547
Date Published
01/2009
Publication Language
eng
Citation Key
8336
Mas, A., & Lee, D. (2009). Long-Run Impacts of Unions on Firms: New Evidence from Financial Markets, 1961-1999. Retrieved from http://arks.princeton.edu/ark:/88435/dsp011c18df784 (Original work published 01/2009AD)
Working Papers
Abstract

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 using examples drawn from the growing body of empirical research using RD.

Year of Publication
2009
Number
548
Date Published
02/2009
Publication Language
eng
Citation Key
8366
Lee, D., & Lemieux, T. (2009). Regression Discontinuity Designs in Economics. Retrieved from http://arks.princeton.edu/ark:/88435/dsp015138jd866 (Original work published 02/2009AD)
Working Papers
Abstract

It has become standard practice to use local linear regressions in regression discontinuity designs.
This paper highlights that the same theoretical arguments used to justify local linear regression suggest
that alternative local polynomials could be preferred. We show in simulations that the local linear estimator
is often dominated by alternative polynomial specifications. Additionally, we provide guidance on the
selection of the polynomial order. The Monte Carlo evidence shows that the order-selection procedure
(which is also readily adapted to fuzzy regression discontinuity and regression kink designs) performs
well, particularly with large sample sizes typically found in empirical applications.

Year of Publication
2018
Number
622
Date Published
08/2018
Publication Language
eng
Citation Key
10656
Pei, Z., Card, D., Lee, D., & Weber, A. (2018). Local Polynomial Order in Regression Discontinuity Designs. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01v118rh27h (Original work published 08/2018AD)
Working Papers
Abstract

Despite the widespread use of graphs in empirical research, little is known about readers’ ability to
process the statistical information they are meant to convey (“visual inference”). In this paper, we evaluate
several key aspects of visual inference in regression discontinuity (RD) designs by measuring how
well readers can identify discontinuities in graphs. First, we assess the effects of graphical representation
methods on visual inference, using randomized experiments crowdsourcing discontinuity classifications
with graphs produced from data generating processes calibrated on datasets from 11 published papers.
Second, we evaluate visual inference by both experts and non-experts and study experts’ ability to predict
our experimental results. We find that experts perform comparably to non-experts and partly anticipate
the effects of graphical methods. Third, we compare experts’ visual inference to commonly used econometric
procedures in RD designs and observe that it achieves similar or lower type I error rates. Fourth,
we conduct an eyetracking study to further understand RD visual inference, but it does not reveal gaze
patterns that robustly predict successful inference. We also evaluate visual inference in the closely related regression kink design.

Year of Publication
2020
Number
638
Date Published
02/2020
Publication Language
eng
Citation Key
11631
Pei, Z., Shen, Y., Korting, C., Lieberman, C., & Matsudaira, J. (2020). Visual Inference and Graphical Representation in Regression Discontinuity Designs. Retrieved from http://arks.princeton.edu/ark:/88435/dsp013j3335157 (Original work published 02/2020AD)
Working Papers