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This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications.

AbstractDo minorities fare worse under direct democracy than under representative democracy? We provide new evidence by studying naturalization requests of immigrants in Switzerland that were typically decided with referendums in each municipality. Using panel data from about 1,400 municipalities for the 1991–2009 period, we exploit Federal Court rulings that forced municipalities to transfer the decisions to their elected municipality councils. We find that naturalization rates surged by about 60% once politicians rather than citizens began deciding on naturalization applications. Whereas voters in referendums face no cost of arbitrarily rejecting qualified applicants based on discriminatory preferences, politicians in the council are constrained to formally justify rejections and may be held accountable by judicial review. Consistent with this mechanism, the increase in naturalization rates caused by switching from direct to representative democracy is much stronger for more marginalized immigrant groups and in areas where voters are more xenophobic or where judicial review is more salient.

Do minorities fare worse under direct democracy than under representative democracy? We provide new evidence by studying naturalization requests of immigrants in Switzerland that were typically decided with referendums in each municipality. Using panel data from about 1,400 municipalities for the 1991–2009 period, we exploit Federal Court rulings that forced municipalities to transfer the decisions to their elected municipality councils. We find that naturalization rates surged by about 60% once politicians rather than citizens began deciding on naturalization applications. Whereas voters in referendums face no cost of arbitrarily rejecting qualified applicants based on discriminatory preferences, politicians in the council are constrained to formally justify rejections and may be held accountable by judicial review. Consistent with this mechanism, the increase in naturalization rates caused by switching from direct to representative democracy is much stronger for more marginalized immigrant groups and in areas where voters are more xenophobic or where judicial review is more salient.

Do minorities fare worse under direct democracy than under representative democracy? We provide new evidence by studying naturalization requests of immigrants in Switzerland that were typically decided with referendums in each municipality. Using panel data from about 1,400 municipalities for the 1991–2009 period, we exploit Federal Court rulings that forced municipalities to transfer the decisions to their elected municipality councils. We find that naturalization rates surged by about 60% once politicians rather than citizens began deciding on naturalization applications. Whereas voters in referendums face no cost of arbitrarily rejecting qualified applicants based on discriminatory preferences, politicians in the council are constrained to formally justify rejections and may be held accountable by judicial review. Consistent with this mechanism, the increase in naturalization rates caused by switching from direct to representative democracy is much stronger for more marginalized immigrant groups and in areas where voters are more xenophobic or where judicial review is more salient. ; ISSN:0092-5853 ; ISSN:1540-5907

We propose the use of Kernel Regularized Least Squares (KRLS) for social science modeling and inference problems. KRLS borrows from machine learning methods designed to solve regression and classification problems without relying on linearity or additivity assumptions. The method constructs a flexible hypothesis space that uses kernels as radial basis functions and finds the best-fitting surface in this space by minimizing a complexity-penalized least squares problem. We argue that the method is well-suited for social science inquiry because it avoids strong parametric assumptions, yet allows interpretation in ways analogous to generalized linear models while also permitting more complex interpretation to examine nonlinearities, interactions, and heterogeneous effects. We also extend the method in several directions to make it more effective for social inquiry, by (1) deriving estimators for the pointwise marginal effects and their variances, (2) establishing unbiasedness, consistency, and asymptotic normality of the KRLS estimator under fairly general conditions, (3) proposing a simple automated rule for choosing the kernel bandwidth, and (4) providing companion software. We illustrate the use of the method through simulations and empirical examples.

We study discrimination against immigrants using microlevel data from Switzerland, where, until recently, some municipalities used referendums to decide on the citizenship applications of foreign residents. We show that naturalization decisions vary dramatically with immigrants' attributes, which we collect from official applicant descriptions that voters received before each referendum. Country of origin determines naturalization success more than any other applicant characteristic, including language skills, integration status, and economic credentials. The average proportion of "no" votes is about 40% higher for applicants from (the former) Yugoslavia and Turkey compared to observably similar applicants from richer northern and western European countries. Statistical and taste-based discrimination contribute to varying naturalization success; the rewards for economic credentials are higher for applicants from disadvantaged origins, and origin-based discrimination is much stronger in more xenophobic municipalities. Moreover, discrimination against specific immigrant groups responds dynamically to changes in the groups' relative size.