Curva de Engel para alimentos y bebidas no alcohólicas en Colombia: abordando los problemas de heteroscedasticidad y variable expresada como una proporción continua
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En este trabajo se estima la curva de Engel para alimentos y bebidas no alcohólicas en hogares urbanos colombianos. Para lo anterior, se realizan estimaciones paramétricas y semi-paramétricas de la curva de Engel usando métodos de regresión basados en distribuciones como normal, gamma, normal inversa y beta, con diversas funciones de enlace, usando los datos de la Encuesta Nacional de Presupuestos de los Hogares (2016-2017) y controlando por características socio-económicas como el estrato, la región, el nivel educativo del jefe de hogar, entre otras. Los modelos estimados se comparan mediante criterios de información, con lo cual se encuentra que el modelo de regresión beta con función de enlace probit y en el que el gasto total se describe de forma no paramétrica es el que describe de mejor manera los datos. Este modelo tiene la ventaja de que, al igual que los datos de la variable respuesta, la distribución considerada para describirla se restringe al intervalo (0,1) y es naturalmente heteroscedástica.
In this work the Engel Curve for food and non-alcoholic beverages for urban homes in Colombia is estimated. To achieve that, parametric and semi-parametric estimations for the curve are obtained by using regression methods based on normal, gama, inverse-normal and beta distributions, also considering many link functions. The data are obtained from the National Survey of Household Budgets (2016-2017), which include socio-economic characteristics such as stratum, region, education level of the head of household, among others. The fitted models are compared by using information criteria, and the beta regression model with probit link function, where the total expenditure is described non-parametrically, is found to be the best to describe the data. This model is appealing as, likewise the data on the response variable, the distribution used to describe its behavior is restricted to the (0,1) interval and is naturally heteroscedastic.
In this work the Engel Curve for food and non-alcoholic beverages for urban homes in Colombia is estimated. To achieve that, parametric and semi-parametric estimations for the curve are obtained by using regression methods based on normal, gama, inverse-normal and beta distributions, also considering many link functions. The data are obtained from the National Survey of Household Budgets (2016-2017), which include socio-economic characteristics such as stratum, region, education level of the head of household, among others. The fitted models are compared by using information criteria, and the beta regression model with probit link function, where the total expenditure is described non-parametrically, is found to be the best to describe the data. This model is appealing as, likewise the data on the response variable, the distribution used to describe its behavior is restricted to the (0,1) interval and is naturally heteroscedastic.
Abstract
Palabras clave propuestas
Ley de Engel; Engel's Law; Gasto de Hogares; Household expenditure; Engel Curve; Curva de Engel; Generalized Linear Models; Modelos Lineales Generalizados; Beta Regression; Regresión Beta; Máxima verosimilitud penalizada; Penalized Maximum Likelihood; Modelos Lineales Generalizados Semi-paramétricos; Semi-parametric Generalized Linear Models; Regresión Beta Semi-paramétrica; Semi-parametric Beta Regression