Since Mueller’s (1970) seminal study on the determinants of presidential popularity in the United States, more than 300 papers on (vote and) popularity functions have been written (see Paldam (2008, 533)). Popularity functions describe the functional relationship between political support for a politician or government and a number of economic and political determinants. Among other things, it has repeatedly (though not always) been found that two important economic variables, unemployment and inflation, have a significant negative impact on presidential approval ratings in the United States (e.g. Newman and Forcehimes (2010)) and other countries. Although there is a strong degree of methodological heterogeneity among these studies, almost all of them make a critical assumption: the relationship between the approval rating and economic variables is linear.
Interpreting estimated popularity functions as social welfare functions, as it is done by Smyth et al. (1989), implies a social preference map consisting of linear indifference curves between two goals, e.g. unemployment and inflation. This linearity, as they argue, is “inconsistent with standard utility theory” (Smyth et al. (1989, footnote 3)). Based on the common formulation of welfare (or loss) functions in many macroeconomic models (e.g. Nordhaus (1975), Sargent and Wallace (1975), Barro and Gordon (1983)), Smyth and his co-authors estimate a popularity function including quadratic terms of unemployment and inflation, which enables them to derive well-behaved, concave indifference curves as they are known from consumer theory.
Both the linear relationship in the popularity function literature and the quadratic formulation in theoretical macro models are not deducible from theoretic work. In many cases, specifications are chosen “ad hoc” (Sargent and Wallace (1975, 244)) or for the sake of analytical or mathematical convenience.
In this paper, we estimate a popularity (welfare) function for the United States based on popularity data covering the period from 1953 to 2011. Instead of choosing an a-priori functional form, we employ a semi-parametric approach (penalized splines smoothing) to let the data specify the concrete relationship between approval ratings (welfare) and two economic variables, unemployment and inflation.
The unpleasant news is that we find the functional form to be neither linear nor quadratic (although the empirical approach allows for both forms). Rather, the influence of economic variables turns out to be strongly non-linear. Moreover, the empirical results imply that voters do not react to changes in inflation and unemployment within certain intervals. However, when inflation and unemployment cross a lower (upper) bound, political support starts to increase (decrease) strongly and in a non-linear fashion. Our results indicate that former popularity functions have been misspecified in empirical work. They also do not support the welfare functions as they are typically used in theoretical work.
Keywords: welfare function, popularity function, non-linearity, penalized splines
JEL classification: C14, D60, D72, H11