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    • Menezes et al also test the median

    2018-10-25

    Menezes et al. (2011) also test the median voter model for the Brazilian municipalities and find evidence that it seems to be valid. They estimate the demand for local public services in order to obtain a measure of misperception of candidates to reelection regarding the median local demand. The expenditures effectively made by the candidates during their first terms are taken as the bundle of public services they offer. They then evaluate whether this misperception affects the electoral performance of incumbents, measured by their vote share or probability of election, using selection models. Finally, there is evidence that the median voter model provides a better explanation for certain public programs than the interest group models. For example, Congleton and Bennet (1995) explore the extent to which public demand for roads and/or power of special interest groups determines road expenditures at the state level using an extension of the methodology developed in Congleton and Shughart (1990). They use reduced form models of median voter demand, special interest group equilibria, and a combined model and find support for the hypothesis that voting matters for American states. Pure median voter models show a better fit than pure special interest group models. Moreover, based on their combined model, they find evidence that variables from the median-voter model cannot be dropped without significantly reducing the fit of the combined model. The standard equation generally used to analyze the demand for local public goods is:where: is the health expenditures per capita of each municipality; , in which is the total tax you can look here and is the municipality population size; is the tax base of the median voter; is the median voter’s income plus the median voter’s share in intergovernmental transfers per capita; is a vector of explanatory variables (control variables); is the price elasticity of demand for public health services; is the income elasticity of demand for public health services; is a parameter vector related to explanatory variables; is the population elasticity; is the error term, and its estimate contains information about the inability of local governments to meet the demand of the median voter, as argued by Menezes et al. (2011). We estimate the median voter model using quantile regressions—QR (Koenker and Bassett, 1978). This method allows us to evaluate the impact of the explanatory variables not only on the dependent variable conditional distribution mean but also on different points along this distribution. Constant coefficient regression models, such as Ordinary Least Squares (OLS), have been extensively applied in empirical studies, providing, however, only the central distribution measurement of the dependent variable. Unfortunately, these models fail to address the behavior of the dependent variable in the tail regions. To address this issue, various random coefficient models emerged as viable alternatives in the field of statistical application. The Conditional Quantile Regression (QR) Model, proposed by Koenker and Bassett (1978), is one of these alternative models. This approach allows estimating various conditional distribution quantile functions. Among them, the median (0.5th quantile) function is a special case. Each quantile regression characterizes a particular (center or tail) point of the conditional distribution, and putting different quantile regressions together provides a more complete description of the underlying conditional distribution. This analysis is particularly useful when the conditional distribution is heterogeneous and does not have a standard shape, such as in an asymmetric, fat-tailed, or truncated distributions. Conditional quantile regression can serve as (i) an alternative to least squares when the normality assumption does not hold and (ii) a complement to least squares, allowing one to look beyond mean effects and obtain a more complete picture of the problem (Koenker, 2005). Quantile regression is desired if conditional quantile functions are of interest. One advantage of quantile regression compared to ordinary least squares regression is that quantile regression estimates are more robust against outliers. Different measures of central tendency and statistical dispersion may also be useful to obtain a more comprehensive analysis of the relation between variables. While OLS can be inefficient if errors are highly non-normal, QR is more robust to non-normal errors and outliers. QR also provides a richer data characterization, as Genomic (chromosomal) DNA clone allows one to measure the impact of a covariate on the entire distribution of the dependent variable, not merely on its conditional mean.