Fast quantum subroutines for the simplex method

We propose quantum subroutines for the simplex method that avoid classical computation of the basis inverse. For an $m \times n$ constraint matrix with at most $d_c$ nonzero elements per column, at most $d$ nonzero elements per column or row of the basis, basis condition number $\kappa$, and optimality tolerance $\epsilon$, we show that pricing can be performed in $\tilde{O}(\frac{1}{\epsilon}\kappa d \sqrt{n}(d_c n + d m))$ time, where the $\tilde{O}$ notation hides polylogarithmic factors. If the ratio $n/m$ is larger than a certain threshold, the running time of the quantum subroutine can be reduced to $\tilde{O}(\frac{1}{\epsilon}\kappa d^{1.5} \sqrt{d_c} n \sqrt{m})$. The steepest edge pivoting rule also admits a quantum implementation, increasing the running time by a factor $\kappa^2$. Classically, pricing requires $O(d_c^{0.7} m^{1.9} + m^{2 + o(1)} + d_c n)$ time in the worst case using the fastest known algorithm for sparse matrix multiplication, and $O(d_c^{0.7} m^{1.9} + m^{2 + o(1)} + m^2n)$ with steepest edge. Furthermore, we show that the ratio test can be performed in $\tilde{O}(\frac{t}{\delta} \kappa d^2 m^{1.5})$ time, where $t, \delta$ determine a feasibility tolerance; classically, this requires $O(m^2)$ time in the worst case. For well-conditioned sparse problems the quantum subroutines scale better in $m$ and $n$, and may therefore have a worst-case asymptotic advantage. An important feature of our paper is that this asymptotic speedup does not depend on the data being available in some "quantum form": the input of our quantum subroutines is the natural classical description of the problem, and the output is the index of the variables that should leave or enter the basis.Comment: Added discussion on condition number and infeasibilitie

A simulation-based sensitivity analysis for matching estimators

In this paper, I present a Stata program (sensatt) that implements the sensitivity analysis for matching estimators proposed by Ichino, Mealli, and Nannicini (2008). The analysis simulates a potential confounder to assess the robustness of the estimated treatment effects with respect to deviations from the Conditional Independence Assumption (CIA). The program uses the commands for propensity-score matching (att*) developed by Becker and Ichino (2002). I provide an example using the National Supported Work (NSW) demonstration, widely known in the program evaluation literature.

Do Better Paid Politicians Perform Better? Disentangling Incentives from Selection

The wage paid to politicians affects both the choice of citizens to run for an elective office and the performance of those who are appointed. First, if skilled individuals shy away from politics because of higher opportunities in the private sector, an increase in politicians' pay may change their mind. Second, if the reelection prospects of incumbents depend on their in-office deeds, a higher wage may foster performance. We use data on all Italian municipal governments from 1993 to 2001 and test these hypotheses in a quasi-experimental framework. In Italy, the wage of the mayor depends on population size and sharply rises at different thresholds. We apply a regression discontinuity design to the only threshold that uniquely identifies a wage increase – 5,000 inhabitants – to control for unobservable town characteristics. Exploiting the existence of a two-term limit, we further disentangle the composition from the incentive component of the effect of the wage on performance. Our results show that a higher wage attracts more educated candidates, and that better paid politicians size down the government machinery by improving internal efficiency. Importantly, most of this performance effect is driven by the selection of competent politicians, rather than by the incentive to be reelected.political selection, efficiency wage, term limit, local finance, regression discontinuity design

Tying Your Enemy’s Hands in Close Races: The Politics of Federal Transfers in Brazil

This paper uses a quasi-experimental strategy to disclose utterly political reasons behind the allocation of intergovernmental transfers in a federal state. We apply a regression discontinuity design in close elections to identify the effect of political alignment on federal transfers to municipal governments in Brazil. We find that municipalities where the mayor is affiliated with the coalition of the Brazilian President receive larger (discretionary) infrastructure transfers by about 40% in pre-election years. This effect is mainly driven by the fact that the federal government penalizes municipalities run by mayors from the opposition coalition who won by a narrow margin, thereby tying their hands for the next election.federal transfers, political alignment, regression discontinuity

Generalized metallic pseudo-Riemannian structures

We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We construct a metallic natural connection recovering as particular case the Ganchev and Mihova connection, which we extend to a metallic natural connection on the generalized tangent bundle. Moreover, we construct metallic pseudo-Riemannian structures on the tangent and cotangent bundles.Comment: 16 page

Competing on Good Politicians

Is electoral competition good for political selection? To address this issue, we introduce a theoretical model in which ideological parties select candidates between party loyalists and experts, and allocate them into the electoral districts. Non-ideological voters, who care about national and local policies, strongly prefer experts. We show that parties compete on good politicians by allocating them to the most contestable districts. Empirical evidence on Italian members of parliament confirms this prediction. We find that politicians with higher ex-ante quality − as measured by years of schooling, previous market income, and local government experience − are more likely to run in a contestable district. Indeed, despite being different on average, the characteristics of politicians belonging to opposite parties converge to high-quality levels in close races. Furthermore, politicians elected in contestable districts make fewer absences in parliament; this is shown to be driven more by a selection effect than by reelection incentives.political competition, political selection, probabilistic voting

Autocratic Transitions and Growth

In this paper we use a transparent statistical methodology – synthetic control methods – to implement data-driven comparative studies about the impact of autocratic transition on real per capita GDP. The applied methodology compares the growth of countries that experienced a transition to autocracy with the growth of a convex combination of similar countries that remained democratic, and it accommodates for the time-varying impact of unobservable heterogeneity. To implement this statistical framework, in a panel of 160 countries, we focus on 14 episodes of transition from democracy to autocracy. We find that the effects of autocratic transitions come in all shapes and sizes, since our data are split in almost equal parts between insignificant, negative, and positive effects. We also find that negative effects tend to get worse over time, and that African countries are badly affected by the autocratic transition possibly because of a resource curse.autocracy, democracy, growth, synthetic control methods