Quantile Regression Analysis of the Rational Addiction Model: Making unobservable heterogeneity observable
The Rational Addiction (RA) model assumes that individual decisions about the consumption of harmful and addictive commodities are made on a rational basis (Becker and Murphy, 1988). In this context, rational means forward looking, i.e. a tendency to take account of future consequences of current consumption decisions. Different individuals may well attach different weights to the present relative to the future. The degree to which an individual is forward looking in her consumption decisions is revealed not by her current consumption level but rather by the time path of her consumption of an addictive commodity. Hence, the need to estimate a forward looking second order difference equation (SODE) as part of the process of testing the RA model. Most studies using micro level data estimate a single SODE for the whole sample. This involves estimating an average propensity to be forward looking for the entire sample, even when it is believed that different fully rational individuals in the same sample may have different propensities to be forward looking. Forward looking behaviour is an aspect of treating the consumption of an addictive commodity as part of an inter-temporal optimization problem. Inter-temporal optimization is characterized by what are known as saddle point dynamics and the information about an individual’s propensity to be forward looking is contained in what are known as the characteristic roots of the equation (Ferguson, 2003). In a sample of heterogeneous individuals we expect propensity to be forward looking to differ across individuals and the best way to identify these differences is by looking at the dynamic behaviour of the individual consumption paths. Estimating a common SODE for everyone hides this key difference. In this paper, we make the argument that the best place to look for differences in individual propensities to be forward looking is in dynamic behaviour considered at different points in the distribution of the consumption of an addictive commodity. To do this we adopt techniques of Quantile Regression, (QR) estimating RA type difference equations in consumption across quantiles of cigarette consumption. We use panel data to ensure that we are examining the behaviour of individuals across time. Our hypothesis is that we will find differences in the degree of forward looking behaviour characterizing the time paths of consumption across quantiles in the micro-level data.
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