Essays on Time Inconsistency

Abstract

Time inconsistency is of primary concern in dynamic economic environments. People with time-inconsistent preferences have difficulty saving for retirement or avoid accumulating too much debt. Hence, interactions with time-inconsistent agents differ from predictions made by classical economics with time-consistent agents. If agents are time inconsistent, government policies that encourage retirement savings would have to account for this behavior. Contracts in the credit market between creditors and debtors would also be different if debtors are time inconsistent. The first two chapters in the thesis analyze these interactions. Institutions may also display time inconsistency. In the final chapter, my coauthor, Radek Paluszynski, and I document an empirical phenomenon in the pricing of life-insurance. We find that prices are extremely rigid over time, even though the marginal cost is nonstationary and volatile. We show that such pricing can occur when firms have time-inconsistency problem in setting its price. In Chapter 1, I explore the optimal tax policies with time-inconsistent agents. People with time-inconsistent preferences tend to make intertemporal choices different from their original intentions. In particular, time-inconsistent agents make sub-optimal saving decisions. This chapter studies the optimal savings and insurance policy in an economy with time-inconsistent agents who privately observe their skill. I introduce a mechanism that can elicit private information at zero cost by threatening sophisticated time-inconsistent agents with off-equilibrium path policies that can undo commitments, and fooling naively time-inconsistent agents with empty promises. The government can implement the full information efficient optimum, which is better than the constrained optimum obtained with traditional proposals to increase savings, like linear savings subsidies or mandatory savings rules. I show that welfare increases monotonically with the population of time-inconsistent agents. In essence, the presence of time-inconsistent agents improves the government's ability to provide insurance. I characterize the tax policies for decentralization, and also discuss its implications on the design of social security and retirement plans. In Chapter 2, I analyze price discrimination by firms offering credit contracts in a sequential screening model with sophisticated time-inconsistent consumers. Consumers choose a credit contract after learning about their likely future taste for consumption and proceed to make consumption decisions after realizing their tastes. I show that a credit company price discriminates by providing immediate gratification combined with large payment penalties to time-inconsistent consumers with high taste shocks, while consumers with lower taste shocks are provided with commitment contracts. This may cause time-inconsistent consumers to experience large welfare losses ex-post without being naive about their preference reversal. I show that policies, such as the Credit Card Accountability, Responsibility and Disclosure act, aimed at avoiding ex-post welfare loss may induce ex-ante deadweight loss. In Chapter 3, I explore an interesting price phenomenon exhibited in life insurance contracts. Life insurance premiums have displayed a significant degree of rigidity over the past two decades. On average, prices took over 3 years to adjust and the magnitude of these one-time jumps exceeded 10%. This stands in sharp contrast with the dynamics of the corresponding marginal cost which exhibited considerable volatility since 1990 due to the movements in the interest and mortality rates. We build a model with consumer hold-up problem that captures these empirical findings. Price rigidity arises as an optimal response to the relationship-specific investment the consumers need to make before buying. The optimal contract takes the form of a simple cutoff rule: premiums are rigid for all cost realizations smaller than the threshold, and adjustments must be large and are only possible when cost realizations exceed it.