But, in fact, we do not measure the present discounted value of utility, only happiness at a point in time. This makes interpretation of the results somewhat more complicated. For a time consistent consumer, the effect of taxes on today’s utility is clearly negative, but the effect on future happiness can be positive. This is because reducing smoking today can raise future utility. Put another way, the tax inducing him to reduce smoking is analogous to an investment in which he bears a cost today (immediate pain of withdrawal) and reaps a benefit in the future (higher utility tomorrow). Even though the net effect of this investment on utility is negative, when appropriately discounted, the long-run effect will be positive. On the other hand, the sophisticated hyperbolic consumer is made immediately better off by a tax, since they are pleased to have this commitment device made available.
The problem is that our existing test does not measure the immediate impacts of the tax, but rather the average impacts over time. Since we are regressing current happiness on current taxes, our estimated coefficients include the immediate effect of taxes on happiness. But if taxes are correlated over time, they will also include the lagged effect. Specifically, the more auto-correlated are cigarette taxes, the more the estimated effect in equation includes the effect of lagged taxes. Thus, our test cannot rule out that time consistent smokers are being made better off in the long run, which through serially correlated tobacco taxes appears as an effect of the current tax on happiness. add comment
This discussion suggests a stricter test to distinguish these models: examine the immediate, rather than long run, impact of taxes on happiness. But doing so increases our data requirements dramatically. To measure the average effect over time, all we require is that, summed over all periods before and after a tax changes in a state, we have sufficient observations to identify an impact of a tax change. But, to examine an immediate impact requires having data in one period on enough observations to distinguish the impact of taxation. This is impossible in the U.S. GSS. That data has the advantage of many years of data, but the typical sample size in any year is fewer than 2000 observations, which is then divided over 50 states. When years are pooled, our state specific sample sizes are sufficient to identify average tax effects. But identifying immediate effects is impossible.
The Canadian GSS, however, does permit this comparison. Our Canadian GSS data have between 9300 and 27,600 observations per year. Moreover, these are divided over only 10 provinces, so that the average province/year cell size is over 2000 observations. Thus, we can aggregate these data to the province/year level and estimate changes regressions that allow us to examine immediate impacts of tax changes.
To do so, we divide our Canadian GSS sample into those likely and unlikely to smoke; the former group is composed of those above the 75th percentile of the predicted smoker distribution (a 41% chance of smoking or greater), while the latter is composed of those below the 25th percentile (a 19% chance of smoking or smaller).