Research

Working Papers

1. Bardóczy, B., and M. Velásquez-Giraldo. (2024): “HANK Comes of Age,” Finance and Economics Discussion Series, Federal Reserve Board. Submitted.
2. Barth, D., N. W. Papageorge, K. Thom, and M. Velásquez-Giraldo. (2022): “Genetic Endowments, Income Dynamics, and Wealth Accumulation Over the Lifecycle,” Working Paper Series, National Bureau of Economic Research. Submitted.

   We develop and estimate a life-cycle consumption savings model in which observed genetic variation is allowed to affect wealth accumulation through several distinct channels. We focus on genetic markers that predict educational attainment, aggregated into a predictive index called a polygenic score. Based on substantial descriptive evidence, we allow variation in these endowments to affect earnings, the disutility of labor, stock market participation costs, and idiosyncratic rates of return on risky investments. The model also incorporates endogenous retirement and a realistic social security system. Parameter estimates suggest that, in addition to earnings, genetic differences are significantly associated with risky asset returns, both of which contribute to wealth inequality. Counterfactual policy exercises indicate that two ways to lower costs of an aging population (extending the age of retirement or cutting social security benefits) have similar magnitudes and distributions of welfare costs even though the latter policy appears to reduce wealth differences between agents with different genetic endowments. This illustrates the importance of welfare calculations when evaluating how genes interact with policy, which is possible to do if we incorporate genetic data into structural models.
3. Velásquez-Giraldo, M. (2024): “Life-Cycle Portfolio Choices and Heterogeneous Stock Market Expectations,” SSRN Scholarly Paper, SSRN Scholarly Paper.

   Survey measurements of households’ expectations about U.S. equity returns show substantial heterogeneity and large departures from the historical distribution of actual returns. The average household perceives a lower probability of positive returns and a greater probability of extreme returns than history has exhibited. I build a life-cycle model of saving and portfolio choices that incorporates beliefs estimated to match these survey measurements of expectations. This modification enables the model to greatly reduce a tension in the literature in which models that have aimed to match risky portfolio investment choices by age have required much higher estimates of the coefficient of relative risk aversion than models that have aimed to match wealth age-profiles. The tension is reduced because beliefs that are more pessimistic than the historical experience reduce people’s willingness to invest in stocks.

Work in Progress

1. Barth, D., N. W. Papageorge, K. Thom, P. Rakheja, and M. Velásquez-Giraldo. “Using Subjective Beliefs Data to Characterize Heterogeneity: A Machine Learning Approach,”
2. Carroll, C. D., and M. Velásquez-Giraldo. “Fading Memory, Disagreement, and Asset Price Dynamics,”
3. Carroll, C. D., A. Lujan, A. Shanker, and M. Velásquez-Giraldo. “Portfolio Choice with Risky Housing,”

Publications

1. Álvarez-Franco, S. I., D. A. Restrepo-Tobón, and M. Velásquez-Giraldo. (2017): “Medición del valor en riesgo de portafolios de renta fija usando modelos multifactoriales dinámicos de tasas de interés,” Estudios Gerenciales, 33, 52–63.

   Resumen En este trabajo se evalúa el desempeño de tres modelos dinámicos de la estructura a plazos de tasas de interés para estimar el valor en riesgo (VaR, por su traducción de Value at Risk) de portafolios de renta fija. De esta forma, se encuentra que el modelo de Diebold, Rudebusch y Aruoba se desempeña adecuadamente respecto a las pruebas de backtesting del VaR, mientras que el modelo de Diebold y Li y un modelo afín de no arbitraje exhiben un pobre desempeño. Los tres modelos asumen que la matriz de varianzas y covarianzas de los factores latentes a cada modelo es constante, lo cual limita su utilidad en el cálculo del VaR. Por lo tanto, modelos que relajen este supuesto deberían ofrecer un mejor desempeño y ser más adecuados para la gestión del riesgo de portafolios de renta fija. In this article we assess the performance of three interest rate dynamic term structure models in order to estimate the Value at Risk (VaR) of fixed-income portfolios. We find that that the model proposed by Diebold, Rudebusch and Aruoba performs appropriately in VaR backtesting statistical tests, while the model from Diebold and Li and a no-arbitrage akin term structure model display serious problems. The three models assume that the variance-covariance matrix for their underlying factors is constant, which limits their usefulness in estimating the VaR. Therefore, those models that relax this assumption should perform better and be more adequate for risk-management of fixed-income portfolios. Resumo Neste artigo, o desempenho de três modelos dinâmicos da estrutura a prazos das taxas de juros para estimar o valor em risco (VaR, por sua tradução de Value at Risk) de carteiras de renda fixa é avaliado. Assim, verificou-se que o modelo de Diebold, Rudebusch e Aruoba funciona adequadamente respeitar no que se refere ao backtesting do VaR; enquanto o modelo de Diebold e Li e um modelo relacionado de não arbitragem apresentam um mau desempenho. Os três modelos assumem que a matriz de variâncias e covariâncias dos fatores latentes em cada modelo é constante, o que limita a sua utilidade no cálculo do Valor em Risco. Portanto, os modelos que relaxam esta hipótese devem proporcionar melhor desempenho e ser mais adequados para a gestão de risco das carteiras de renda fixa.
2. Velásquez-Giraldo, M., and D. Restrepo-Tobón. (2016): “Affine Term Structure Models: Forecasting the Yield Curve for Colombia,” Lecturas de Economía, , 53–90.

   Superior modeling of the yield curve is useful for asset pricing, financial planning, and risk management. In this article, we estimate five affine term str...
3. Velásquez-Giraldo, M., G. Canavire-Bacarreza, and A. Lundberg. (2023): “Crime Variability, Peer Effects, and Economic Inequality in Social Networks,” Journal of Economic Criminology, 1, 100011.

   A large fraction of the variance in aggregate crime rates cannot be explained by observable socioeconomic conditions. Social determinants of crime may drive the unexplained variation, but economic models of social influence so far emphasize the intensity of criminal effort, not the decision of whether to participate in crime. This article develops a model of criminal participation as a supermodular game, based on the theory of differential association. Simulations relate the structural characteristics of social networks to supportable patterns of crime in equilibrium. Denser and more unevenly connected networks show wider variation in aggregate crimes, but wage inequality in the formal sector reduces the variance. Additionally, average crimes rates are a single-peaked function of wage inequality. This feature suggests future cross-sectional studies of crime rates and income inequality should treat inequality as a quadratic function within a regression model.
4. Velásquez-Giraldo, M., G. Canavire-Bacarreza, K. P. Huynh, and D. T. Jacho-Chavez. (2018): “Flexible Estimation of Demand Systems: A Copula Approach,” Journal of Applied Econometrics, 33, 1109–16.

   In this paper we study the own-price elasticity for gasoline in demand systems involving three expenditure categories in the transportation sector in Canada: gasoline, local transportation, and intercity transportation for Canadian households from 1997 to 2009. In particular, we conduct a replication of Chang and Serletis, (The demand for gasoline: Evidence from household survey data, Journal of Applied Econometrics, 2014, 29, 291–343) hereafter CS, who—using TSP version 5.1—estimated Deaton and Muellbauer, ’s Almost Ideal Demand System (AIDS) (American Economic Review, 1980, 70, 312–326), Banks et al., ’s Quadratic AIDS (Review of Economics and Statistics, 1997, 79, 527–539), and Barnett, ’s Minflex Laurent (ML) (Journal of Business and Economic Statistics, 1983, 1, 7–23) models to demand systems consisting of these three goods, analyzing and enforcing theoretical economic regularity—that is, the compliance of estimates with positivity, monotonicity, and curvature. Using the R statistical language instead, we found that our estimates are similar to those of CS using data for single-member households and married couples without children, but differ for households with one child. (All replicated estimation tables in CS, as well as our full implementation, are available as supplementary material in the online version of this paper.) However, using a more flexible copula model, a total of 168 possible specifications for each type of household and their resulting gasoline own-price elasticities are also estimated. We find that allowing for skewness in the marginal distributions of local transportation budget shares greatly improves the Bayesian information criterion (BIC) of our models.
5. Velásquez Giraldo, M., J. C. Gutiérrez Betancur, and P. M. Almonacid Hurtado. (2016): “Calibración de parámetros de los modelos de tasas de interés NS y NSS para Colombia: una nota técnica,” Journal of Economics, Finance and Administrative Science, 21, 73–80.

   Resumen La calibración del modelo Nelson-Siegel para ajustarse a curvas de rendimientos soberanas se ha encontrado problemática, pues presenta correlación entre sus factores y genera funciones objetivas con múltiples óptimos locales. Estos problemas no han sido profundizados en el contexto colombiano, dándole poca importancia al proceso de calibración. En el presente trabajo se evalúan dos métodos diferentes del gradiente para resolver el problema de ajuste por mínimos cuadrados no lineales: el metaheurístico de evolución diferencial y el método de búsquedas incrementales sobre los parámetros no lineales. Se realizan comparaciones entre los resultados en términos del ajuste logrado, consistencia en los resultados (para el metaheurístico) y formas obtenidas para la curva. El mismo procedimiento es realizado para el modelo Nelson-Siegel-Svensson, evaluando la pertinencia de su uso dentro del mercado local. Calibration of the Nelson-Siegel (NS) model to adjust to sovereign yield curves has been found to be problematic since the model exhibits a correlation between its factors, and generates objective functions with local multiple optima. These problems are often disregarded in the Colombian market, enough importance is not being given to the calibration process. This study aims to evaluate two non-gradient based methods for solving the non-linear least squares problem: the differential evolution metaheuristic and an incremental search procedure on the non-linear parameters. Comparisons of the results are made in terms of the achieved fit, consistency (for the metaheuristic) and the shapes obtained for the curves. The same procedure is carried out on the Nelson-Siegel-Svensson (NSS) model, evaluating the advisability of its use in the local market.

Other Working Documents and Software

1. Velásquez-Giraldo, M. (2021): “Mv77/RiskyContrib: A Two-Asset Savings Model with an Income-Contribution Scheme,”Zenodo.

   This paper develops a two-asset consumption-savings model and serves as the documentation of an open-source implementation of methods to solve and simulate it in the HARK toolkit (Carroll, Kaufman, Kazil, Palmer, and White, 2018). The model represents an agent who can save using two different assets—one risky and the other risk-free—to insure against fluctuations in his income, but faces frictions to transferring funds between assets. The flexibility of its implementation and its inclusion in the HARK toolkit will allow users to adapt the model to realistic life-cycle calibrations, and also to embedded it in heterogeneous-agents macroeconomic models.