Commitments

People that have large commitments of expenditures (like mortgage payments) are more risk averse on small gambles than big ones (gated pdf). According to Chety and Szeidl, this might explain why people play the lottery:

Intuitively, an agent who earns an extra dollar can spend it only on food; but buying a lottery ticket gives him an opportunity to buy a better house or car, which can have higher expected utility than another dollar of food.

Agents only pursue gambles which have payoffs that would make it optimal to drop prior commitments. To see why such gambles can be attractive, consider an individual who is deciding whether to buy a candy bar that costs $1 or a fair lottery ticket for $1 that will pay $1 million if he wins. A one-good (no commitments) model assumes that the agent will buy one million candy bars if he wins the lottery (or one million units of the composite commodity). In this case, buying the lottery ticket is not optimal because the marginal utility of candy is diminishing, and the agent would be better off getting one candy bar with certainty. However, with commitments, the agent will buy more than just candy if he wins the lottery. While the $1 in hand cannot be spent to buy a better house or car, the $1 million can. Consequently, the expected utility of the skewed lottery may exceed the utility of the candy bar.

BTW, their theory also predicts people with higher percentages of their income tied up in commitments are more likely to play the lottery. Does this seem right? Do poorer people, who play the lottery more often, have more of their incomes tied up in commitments?

Anyway, there model also gives an explanation for the seemingly contradictory facts that in the long run families tend not to adjust their labor supply much to changes in wages (or taxes on wages), but they respond a lot, by adding spouses or teens to the work force, to short term changes in income.

To understand the intuition for this result, suppose the primary earner is temporarily unemployed. If the household has commitments that it wishes to maintain, there is a strong incentive for spouses to enter the labor force to help pay the mortgage and other bills, especially in the presence of liquidity constraints. In contrast, a household that experiences a large, permanent change in wealth will reoptimize on all margins of consumption in the long run, reducing the pressure to make large adjustments on [the number of family members in the labor force].

Studies of behavioral responses to taxation generally find small [effects of the tax on the number hours worked] in households with incomes below $100,000 [e.g., Saez 2004]. The inability to fully re-optimize consumption in the short run may dampen responses to tax reforms because of temporarily amplified income effects. In the short run, households may be reluctant to cut labor supply in response to a tax increase if they have made prior commitments. However, taxes may still have significant effects on labor supply in the long run, when short-run income needs due to commitments are diminished. Hence, empirical studies that focus on short-run changes in behavior could understate the distortionary effects of taxation.