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Revealed preference axioms provide a simple way of testing data from consumers or firms for consistency with optimizing behavior. The resulting non-parametric tests are very attractive, since they do not require any ad hoc functional form assumptions. A weakness of such tests, however, is that they are non-stochastic. In this paper, we provide a detailed analysis of two non-parametric approaches that can be used to derive statistical tests for utility maximization, which account for random measurement errors in the observed data. These same approaches can also be used to derive tests for separability of the utility function.

This chapter aims to quantify and compare inequalities of opportunity in health across European countries considering two alternative normative ways of treating the correlation between effort, as measured by lifestyles, and circumstances, as measured by parental and childhood characteristics, championed by Brian Barry and John Roemer. This study relies on regression analysis and proposes several measures of inequality of opportunity. Data from the Retrospective Survey of SHARELIFE, which focuses on life histories of European people aged 50 and over, are used.

In Europe at the whole, inequalities of opportunity stand for almost 50% of the health inequality due to circumstances and efforts in Barry scenario and 57.5% in Roemer scenario. The comparison of the magnitude of inequalities of opportunity in health across European countries shows considerable inequalities in Austria, France, Spain and Germany, whereas Sweden, Poland, Belgium, the Netherlands and Switzerland present the lowest inequalities of opportunity. The normative principle on the way to treat the correlation between circumstances and efforts makes little difference in Spain, Austria, Greece, France, Czech Republic, Sweden and Switzerland, whereas it would matter the most in Belgium, the Netherlands, Italy, Germany, Poland and Denmark.

In most countries, inequalities of opportunity in health are mainly driven by social background affecting adult health directly, and so would require policies compensating for poorer initial conditions. On the other hand, our results suggest a strong social and family determinism of lifestyles in Belgium, the Netherlands, Italy, Germany, Poland and Denmark, which emphasises the importance of inequalities of opportunity in health within those countries and calls for targeted prevention policies.

Prior to the passage of the 20th amendment to the US Constitution in 1920, several states had extended the suffrage to women. Helen Laura Sumner (later Woodbury), a student of John R. Commons at Wisconsin, undertook a statistical study of the political, economic, and social impacts of the granting of voting rights to women in the state of Colorado, and subsequently defended the results against numerous attacks. In this paper, we present a brief account of the struggle for women’s equality in the extension of the suffrage and examine Sumner’s critical analysis of the evidence as to its effects, as well as the counterarguments to which she responded.