We examine how social comparison within endogenously formed peer networks affects mental health among young adults. Using over 2 million smartphone-based communication records from the NetHealth Study – a dataset of university students with repeated mental-health assessments – we determine the network linking the subjects on the basis of objective measures of social interaction and estimate a structural model in which individuals form ties endogenously and mental health depends on the income of chosen peers. Under exogenous network assumptions, higher average peer income improves mental health, consistent with positive spillovers from a wealthier social environment. Once we model network formation endogenously, this relationship reverses: exposure to higher-income peers significantly worsens mental health outcomes, indicating that adverse social comparison effects dominate income spillovers. Decomposing peer income into upward and downward components reveals that income gaps harm mental health symmetrically regardless of direction, a pattern inconsistent with standard relative deprivation and consistent with inequality aversion. These findings demonstrate that endogenous peer selection is not a second-order econometric concern but a substantively important force shaping the mental-health consequences of social comparison, and that models ignoring network formation risk qualitatively misleading conclusions about the direction of peer effects.
This paper introduces a new econometric framework for modeling social interactions with heterogeneous peer responses, addressing endogenous link formation. Our Selection-corrected Heterogeneous Spatial Autoregressive (SCHSAR) approach jointly models link formation and outcome determination. We incorporate a finite mixture structure to capture heterogeneity in peer effects and account for unobserved individual-specific factors driving both network formation and outcome equations, addressing network endogeneity for credible estimation of heterogeneous spillover effects. We propose a fully Bayesian data augmentation approach for estimation and inference, overcoming challenges posed to standard likelihood-based methods. A simulation study validates our approach. Our empirical application to an innovation network among U.S. firms reveals significant positive, yet heterogeneous, peer effects on corporate R&D investments, after accounting for endogenous network formation. The findings highlight varying firm behaviors in response to exogenous R&D policy shocks and quantify firm-level direct and spillover effects, offering valuable insights for evidence-based and targeted policy design.
This paper develops a Bayesian implementation of the zero-inflated ordered probit model introduced in Harris and Zhao (2007), providing a broad replication of the frequentist method and extending the original paper with a Bayesian implementation. Posterior distributions naturally propagate parameter uncertainty to non-linear quantities of interest—participation, consumption intensity, and associated marginal effects—without relying on asymptotic approximations such as the delta method. Performance is assessed through Monte Carlo experiments compared against maximum likelihood estimation, with empirical applications to marijuana and tobacco consumption in Colombia. Results confirm the Bayesian approach reproduces original substantive findings while providing a coherent framework for structural inference.
We introduce heterogeneous R&D productivities into an endogenous R&D network formation model, generalizing the framework of Goyal and Moraga-González (2001). Heterogeneous productivities endogenously create asymmetric gains from collaboration: less productive firms benefit disproportionately from links, while more productive firms exert greater R&D effort and incur higher costs. When productivity gaps are sufficiently large, more productive firms experience lower profits from collaborating with less productive partners. As a result, the complete network – stable under homogeneity – becomes unstable, and the positive assortative (PA) network, in which firms cluster by R&D productivity, emerges as pairwise stable. Using simulations, we show that the clustered structure delivers higher welfare than the complete network; nevertheless, welfare under this formation follows an inverted U-shape as the fraction of high-productivity firms increases, reflecting crowding-out effects at high fractions. Altogether, we uncover an R&D productivity puzzle: economies with higher average R&D productivity may exhibit lower welfare through (i) the formation of alternative stable networks, or (ii) a crowding-out effect of high-productivity firms. Our findings show that productivity gaps shape the organization of innovation by altering equilibrium R&D alliances and effort. Productivity-enhancing policies must therefore account for these endogenous responses, as they may reverse intended welfare gains.
Medellín has undergone rapid urban transformation and is often cited as a model of inclusive urbanism. However, less is known about how these changes shape spatial inequalities and segregation. This study examines neighbourhood change between 2004 and 2019. First, we develop robust neighbourhood-level income estimates by leveraging Medellín’s household survey micro-data and sampling design. Second, we validate and re-weight the representativeness of our income metrics using reliable census and national survey benchmarks. Third, using these estimates we document spatial and temporal shifts in income in Medellín’s neighbourhoods, identifying clusters of time series income trajectories. Our taxonomy of neighbourhood change captures spatial sorting dynamics, emerging patterns of income mixing, and clear trends across time spent in the neighbourhood. This research moves beyond conventional gentrification frameworks, offering a multidimensional, data-driven approach to understanding socio-spatial inequalities and urban transformation in Medellín.
The response of illicit drug consumers to policy changes like legalization is mediated by demand behavior. Since individual drug use is driven by many unobservable factors, accounting for unobserved heterogeneity becomes crucial for designing targeted policies. This paper introduces a finite Gaussian mixture of EASI demand systems to estimate joint demand for marijuana, cocaine, and basuco (a low-purity cocaine paste) in Colombia, accounting for corner solutions and endogenous prices. Our method classifies users into two groups with distinct preferences over consumption: “soft” and “hard” users. Nationally representative survey estimates find drugs are unit-elastic, with marijuana and cocaine complementary. International marijuana legalization episodes along with Colombia’s low marijuana production cost suggest legalization is likely to drive prices down significantly. Legalization counterfactuals under the most likely scenario of a 50% marijuana price decrease reveal \$363/year welfare gains for consumers, \$120M in government revenue, and \$127M dealer losses.
We develop Probabilistic Targeted Factor Analysis (PTFA), a likelihood-based framework for constructing latent factors that are explicitly targeted to variables of economic interest. PTFA provides a probabilistic foundation for Partial Least Squares, allowing supervised factor extraction under uncertainty. The model is estimated via a fast expectation maximization algorithm and naturally accommodates missing data, mixed-frequency observations, stochastic volatility, and factor dynamics. Simulation evidence shows that PTFA improves recovery of economically relevant latent factors relative to standard PLS, particularly in noisy environments. Applications to financial conditions indices, macroeconomic forecasting, and equity premium prediction illustrate the measurement and forecasting gains delivered by targeted probabilistic factor extraction.
This paper provides a novel approach to identification and estimation of a network formation model using observed network data, where the model acknowledges possible externalities in agents’ utilities of forming connections with one another. The existence of externalities induces an issue of multiple equilibria. We first show that local point identification of the parameters of interest is possible under a mild assumption on the equilibrium selection process. We then propose a Bayesian estimation method to conduct statistical inference of structural payoff coefficients. Implementing the resulting MCMC algorithm requires sampling from the generalized inverse normal distribution, for which we found no efficient sampling algorithm in the literature. A by-product of this paper is to provide such efficient sampling algorithm for the regular and truncated variants of this distribution. Our method also allows us to estimate equilibrium selection probabilities, which requires knowledge on possible equilibrium configurations. We address this issue by proposing a composite likelihood function based on subgraphs of the observed network. We show that the use of a composite likelihood induces misspecification, characterize the Kullback-Leibler divergence that measures this misspecification error and show this measure can be used to tune the composite likelihood weights. We present an empirical application to model the network formation process of individuals creating social connections in villages in Karnataka, India and find strong evidence of homophily effects.
This paper expands the applied researcher’s toolkit for dealing with nonlinear panel data models with unobserved heterogeneity using multivariate fractional outcomes. It presents a wide range of methods that include maximum likelihood estimation for identifying the parameters of a conditional mean, a simple probit approach to identify average partial effects, and a Bayesian estimator from a latent dependent variable specification to account for corner outcomes. I then show how all these methods can be modified to handle continuous endogenous covariates. A range of simulation exercises showcase the comparative advantages of each method and how they might be used to approach different situations that arise in applied microeconomics.
This paper introduces a unified estimation methodology using copulas for multivariate fractional outcomes with a conditional mean specification. These outcomes are defined as vectors where each component is bounded to the unit interval and together they add up to 1. The methods satisfy the fractional and unit-sum constraints while allowing for cross-equation restrictions among the conditional mean parameters, which are crucial in applications to structural estimation. While ultimately Bayesian in nature, the paper rigorously examines the asymptotic properties of the arising frequentist estimators, as they are themselves additions to the literature. The methodology is augmented to handle variable selection using regularization in a Bayesian framework. A range of numerical exercises evaluate the properties of the estimators and showcase their flexibility in examples of both structural and reduced form models. An empirical application to transportation expenditures in Canada is also presented.