Originally, in statistics semi-parametric techniques were introduced as a way of circum-venting the curse of dimensionality of their non-parametric counterparts, still providing some sort of functional form flexibility. In econometrics they were quite welcome to avoid functional misspecification in nuisance parts of the model, but also because their out-comes were much easier to interpret than those of purely non-parametric models. In more recent literature, semi-parametric methods are also used in a so far less common way, relaxing the functional form in the interesting parts of the model but using stiff modeling approaches for the nuisance parameter.
In the first part of this chapter we recall that the non-parametric part of the model is unfortunately not free from the underlying model assumptions in the parametric part.
Along with the popular example of life-satisfaction analysis, we show how biases caused by a misspecification in the nuisance parameter transfer to the part of interest. Moreover, the flexibility of the non-parametric part in such a scenario becomes a disadvantage, as it tries to absorb the bias coming from the parametric part. We have shown in a simulation study on life-satisfaction, the concept of mid-life crisis could merely be a result of such a bias transfer.
We consider the recently published study of Wunder et al. [2013]. Applying a PLM
on SOEP data, they found a hollow at the age of 45 to 50, interpreted as mid-life crises.
We first replicate their numerical findings to afterwards critically discuss their conclusions making reference to our findings in the previous sections: this finding could be a conse-quence of their model specification. We show how an appropriate robustness check could be preformed and, if applicable, the model and empirical analysis be improved. We could verify that the mid-life crisis (the change in the curvature of the marginal effect of age) is observed over all our different models. That is, even though our simulations show that Wunder et al. [2013] were overconfident about their estimation outcome when concluding to have found empirical evidence for the mid-life crises, our robustness check confirms their conclusion.
Referring to the existing literature there are justifications provided by economists and sociologist regarding the existence of mid-life crisis. Blanchflower and Oswald [2008]
consider a U-Shape function of life-satisfaction in age, which is due to the underlying assumptions of the model, but the first argument that they provide is that individuals learn how to adopt to their environment and at mid-life they leave behind their infeasible dreams. This partially and for some time compensates the continuous negative effect of aging (e.g. health reduction) and create the hollow that is regarded as mid-life crisis. It is worth noting that it also confirmed that an identity link function (as it is usually assumed in such studies) is inappropriate.
Chapter 2
Robust analysis of wage distribution
1 In the empirical analysis there is a tendency to focus on the estimation of the marginal impacts at the mean or median of the outcome distribution. The reason is that these methods are well established and are mathematically much easier to handle. Consider the case of linear model E(Y | X) = X—. We can fit the model to the data by using OLS. The law of iterated expectations provides E(Y) = EX[E(Y | X)] = E(X)—. This allows for the unconditional mean interpretation of—, i.e. — is the effect of increase in the mean X on the unconditional mean of Y. If the data generating processes is Gaussian, then the least squares estimator is the most efficient, yet it is well known that such estimator is extremely sensitive to the presence of outliers. This makes such estimators very poor in many non-Gaussian, especially heavy-tailed situations, see Koenker and Bassett [1978]. Therefore, while it is very popular to look at the marginal effects for the variables of interest at the mean of the outcome, in many cases this is neither sufficient nor appropriate.
A robust alternative to least square error is the least absolute error that minimizes the sum of absolute values of the residuals and analyzes the results for the median. Moreover, in cases such as analyzing the income or expenditure data it can be of interest to study the effect of a particular variable at different quantiles of the outcome. These quantile marginal effects are non-linear parameters for which the unconditional interpretations are no more straightforward. For instance, the law of iterated expectations does not apply in the case of quantiles, i.e. Q· ”=EX[Q·(X)] =E(X)—·. Firpo et al. [2009] have proposed an alternative regression approach, based on the Re-centered Influence Function, that allows for computing the marginal effects on the unconditional functional statistics of interest, given that the closed form influence function is provided under some general assumptions.
This chapter presents empirical evidence for the impact of minimum wages on different quantiles of the wage distribution, in developing countries. We use conditional quantile regression, byKoenker and Bassett[1978], and unconditional quantile regression, byFirpo et al. [2009], on data from four developing countries, namely Brazil, India, Indonesia and Mexico. The findings of taking into consideration the institution impact for the conditional and unconditional quantile regressions are then discussed. The purpose of this analysis is to estimate the effect of the minimum wages on the wage distribution of those workers who are covered by minimum wage legislation. This study does not aim
1This chapter is based on joint work with Dr. Uma Rani Amara, Senior Development Economist, Research Department, International Labour Office Geneva. However, all possible errors or omissions in this script are merely my own responsibility.
at analyzing the total effect of minimum wages on different aspects of the labor market outcomes. Nevertheless, this is an attempt to evaluate the impact of the minimum wages on wage distribution in developing countries. The analysis is based on the rich vector of confounders available in the household or labor force surveys of these countries that are conditioned on in our regressions, in addition to taking into consideration the complex minimum wage settings in these countries.
2.1 The effect of minimum wages on wage distribu-tion and inequality
Since the 1980s there has been intense debate about the impact of minimum wages on dif-ferent aspects of labour market outcome. These effects can be briefly classified as positive effects on reducing the inequality and poverty or negative effects through employment loss by increase of labour cost or increase of product prices, which leads to reduction of the demand for the product and consequently for labour. See for instance, Card[1992], Katz and Krueger [1992], Card and Krueger [1994], Neumark and Wascher [1992, 1995a,b], Terrell and Gindling [2004] and Neumark and Wascher[2006] and Neumark et al. [2014]
for a comprehensive discussion of minimum wage effects on the wages and employment.
However, in the literature, there has been an overemphasis on the employment effects of minimum wages, which has to a large extent, overshadowed the re-distributive impacts and its effects on the wage distribution. The literature focusing on employment effects often also ignores the impact of minimum wages on the wage distribution, where in some of the low wage workers potentially earn better wages due to minimum wages or increase in minimum wages. In this regard, Dickens et al.[2012] recently have pointed out that “if the impact on wage inequality and not employment is the first-order effect of the minimum wage then the existing literature on the minimum wage has been poorly focused” (p.1).
In developing countries, the objective of minimum wage legislations is to redistribute wages to low paid workers so as to ensure that it meets their basic minimum needs.
For instance, in case of Latin American countries, it has been observed that a very high proportion of income among the urban poor comprises of wages of unskilled workersLustig and McLeod [1996]. Therefore, minimum wages could be an important tool for raising the wages of the unskilled workers. This aside, minimum wages can also have a strong spill-over effect affecting the entire wage distribution rather than just those around the minimum wages. There is also some evidence that minimum wages act as an anchor or numeraire for setting other wages or social security benefits, which could have an impact on the wage distribution.
In this context, the impact of minimum wages on the entire wage distribution in general and on the wage inequality more specifically is the main interest of this chapter. We provide a brief review of the literature and the methodological developments in estimating the impact of the minimum wage effect on wage distribution and inequality in Section 2.2.
Section 2.3 provides a brief description of the minimum wage setting mechanisms in the different countries under analysis and the data sources. This is followed by discussing the methodology adopted to look at the effects of minimum wages on the wage distribution.
Section (2.4) illustrates the empirical evidences in the four developing countries under study. Finally, Section 2.5 concludes.