Congestion and Penalization in Optimal Transport - Under review Marcelo Gallardo, Manuel Loaiza, and Jorge Chávez.
Abstract | Pre-print
In this paper we introduce two novel models derived from the discrete optimal transport problem. The first model extends the traditional transport problem by adding a quadratic congestion factor directly into the cost function, while the second model replaces conventional constraints with weighted penalization terms. We present theoretical results, for the characterization of interior and corner solution for some specific cases, and we perform smooth comparative statics analysis. We also propose an O((N+L)(NL)2) algorithm for computing the optimal plan for the penalized model assuming interior solutions. Pre-print in arXiv differs slightly from the last version in SSRN.
Heterogenous Quadratic Regularization in Optimal Transport - Under review Marcelo Gallardo, Manuel Loaiza and Jorge Chávez.
Abstract | Pre-print
In this paper, we build upon the optimal transport quadratic regularization model to develop a framework that incorporates congestion costs, particularly in matching within the healthcare and education sectors. Specifically, we introduce a model with heterogeneous quadratic costs. We analyze the model's properties under specific cases, extending the existing literature. Furthermore, we explore key structural characteristics of the model and provide numerical examples illustrating why this formulation more accurately captures real-world phenomena, particularly in the Peruvian context. The main result consists of identifying a specific type of corner solution when matching the same number of clusters, i.e., N=L.
Irregular wave dynamics driven by a random force within the Burgers equation - Submitted
Marcelo Gallardo and Marcelo Flamarion.
Abstract | Pre-print under request
In this article, we study the classical Burgers equation as a model for random fields. First, we consider initial data defined as a sum of harmonics with random phases and compute the blow-up time. Several simulations are performed, revealing that, while the critical blow-up time is approximately distributed according to a Gaussian law, the statistical tests reject the normality hypothesis. For the viscous case, we analyze waves driven by a random force. Using the Cole-Hopf transformation, the averaged wave field is computed numerically. Through a change of variables, we demonstrate that randomness primarily affects the phase of the wave field. Assuming the phase follows a uniform distribution, we show that the averaged field spreads and diminishes over time.
Working Papers
Political and economic uncertainty indicator for Peru based on Twitter and GPT-3.5 Turbo - New version coming soon Manuel Loaiza, Marcelo Gallardo, and Gabriel Rodriguez.
Abstract | Draft available under request
This paper develops a new political-economic uncertainty index based on tweets from influential figures in Peruvian politics and economics. Tweets are analyzed using GPT-3.5 Turbo, generating a time series of political-economic uncertainty.
Price Information and Duopolistic Competition with Seller Cost Uncertainty and Advertising - New version coming soon Marcelo GallardoAbstract | Draft available under request
We build on Martinelli and Xiao (2024) by introducing a new model of duopolistic competition that incorporates seller cost uncertainty and advertising. Unlike Martinelli and Xiao (2024), our model explicitly includes advertising as a decision variable, leading to a more intricate yet realistic formulation of expected demand. This extension captures the impact of advertising expenditures by each firm, adding a crucial strategic dimension to the analysis. Although our model is formulated for an arbitrary positive integer number of firms, most of our analysis focuses on the case of two firms, placing it within the framework of a duopoly. This choice is driven by the algebraic complexity introduced by advertising, which significantly complicates the transition to a more general setting. We examine two scenarios: one where advertising is exogenous, limiting the optimization to pricing decisions, and another where advertising is treated as an endogenous strategic variable. For the exogenous case with J=2, we derive analytical results, while for the more general cases, we rely on numerical analysis to explore the equilibrium outcomes.
Novel innovation indicator for Peruvian universities
Marcelo Gallardo and Juan Leon Jara-Almonte.
Abstract | Draft available under request
This paper proposes an innovation indicator for Peruvian universities, focusing on scientific innovation in fields such as engineering and pure sciences. The indicator is constructed using a selected dataset (Scopus, TUNI, Sunedu) and confirmatory factor analysis (CFA) to ensure robust measurement, with Tucker-Lewis Index (TLI) and Comparative Fit Index (CFI) used to validate the model fit. K-means clustering is applied to identify innovation clusters among universities. The validity of the indicator is examined through standard correlation with university rankings and econometric analysis linking the indicator with wage per hour and simple overeducation. To address potential sample selection bias, we implement a Heckman two-step correction, incorporating the inverse Mills ratio (IMR) into the wage equation. Additionally, we correct for heteroscedasticity by employing heteroscedasticity-robust standard errors (HC3). For this work, we used ENAHO modules 200-500.