Testing Rational Addiction: When Lifetime is Uncertain, One Lag is Enough

Solving the Milk Addiction Paradox

“…where p (t) is the price of the addictive good at time t, M (t) is income and A (0) = A 0 . 2 Dragone and Raggi (2018) show that the solution of the rational addiction model is the saddle path leading to a steady state of consumption and addiction. Using a quadratic utility function, the saddle path can be conveniently written as the following linear AR(1) equation,…”

“…which implies that the Euler equation is in general explosive, the only exception being the saddle path (Dragone and Raggi, 2018).…”

“…In fact, it formally resembles the solution of a myopic habit or taste formation model in which current consumption only depends on current and past variables (see, e.g. Pollak, 1970;Becker et al, 1994;Gilleskie and Strumpf, 2005;Dragone and Raggi, 2018). In the following we refer to 8 as to the non-addiction DGP.…”

“…In this paper we show that the rational addiction theory can be tested, provided one considers the AR(1) addiction model derived in Dragone and Raggi (2018), instead of the canonical AR(2) specification. Using both simulated and real data, we show that the AR(1) model is able to correctly discriminate rational addiction from simple persistence in the data, and to provide unbiased estimates of the short and long-run elasticity of demand, irrespective of whether individual or aggregated data are used.…”

“…To introduce the reader to the theoretical background, in section 2 we briefly present the rational addition model and the two specifications used in the empirical literature: the AR(1) equation representing the saddle path solution of the model (Dragone and Raggi, 2018), and the canonical AR(2) equation. The latter equation represents the Euler equation of the rational addiction model and it is the empirical specification typically used to test the theory on the data (Becker et al, 1991;Chaloupka, 1991;Grossman, 1993;Chaloupka, 1996;Chaloupka and Warner, 2000;Cawley and Ruhm, 2012).…”