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

The Becker and Murphy (1988)’s model of rational addiction is the benchmark model to investigate addictive behavior. It predicts that current and past consumption of addictive goods are positively correlated, and that demand is sensitive to current and future prices. Since the early empirical contributions of Chaloupka (1991) and Becker et al. (1994), the rational addiction model has been tested using a Euler equation which relates consumption in three adjacent periods.

Yet, this empirical strategy is potentially problematic because the Euler equation describes a necessary condition that describes consumption paths that explode as time advances. As illustrated in Laporte et al. (2017), estimating the parameters associated to the explosive solutions of the Euler Equation may lead to unreliable estimates.

As a better alternative, we propose to test the rational addiction model using a linear first-order difference equation in which current consumption depends on past consumption. Our empirical specification is simple and it is theoretically justified using a stochastic rational addiction model where individuals have uncertain lifetime. In contrast to the Euler equation, the solution guarantees that the estimates will be stable, and it allows for estimation strategies that would otherwise be unavailable using a second-order difference specification. Moreover, it produces the same policy implications described by Becker and Murphy (1988) and popularized by the subsequent literature (see, e.g., Cawley and Ruhm, 2012). In particular, it allows to directly test for adjacent complementarity and forward looking behavior, and to show that estimating the discount rate using the Euler equation, a typical exercise in the empirical literature, is not correct. This may explain the empirical difficulties in finding reasonable and significant estimates of the discount rate, and their large variability (see Baltagi and Griffin, 2001, and Baltagi, 2007, for a discussion).

As an empirical application, we estimate the demand for smoking in the US from 1970 to 2016, showing that the estimates are consistent with the rational addiction model, although with different short and long run elasticity to prices.