The Concept of Time Inconsistency
In economics, time-inconsistency is the problem that arises when a decision maker, especially a policymaker, prefers one policy in advance but later enacts a different one. Deciding among alternative policies at different points in time can vary depending on expected utility anomalies; thus people sometimes make time-inconsistent decisions.
We face this issue every day. Consider, for example, a smoker: there is a conflict between the pleasure of cigarette and the preservation of good health. When the promise of a cigarette is substantially delayed, say one year from now, a rational person will choose to preserve his health; but if one’s reward is imminent, it will be difficult for him to restrain.
Similarly, we can apply the same logic to the time value of money.
Would you rather be given $500 today or $505 in one week?
Now, would you rather be give $500 in one year or $505 in one year and one week?
Chances are that you prefer to receive $505 in one year and one week, whereas in the first case your choice was not that definitive. A rational person would choose the same option for both questions; nonetheless, we see that delaying the outcomes leads to different choices (Stephen Hoch and George Loewenstein).
Theory says that investors only care about delays in payoff in terms of interest gained or lost— is this realistic? Although there is no evidence in support of this, it is mathematically convenient. Standard economics assumes that a decision maker discounts future cash flows by a constant fraction in each time period, called the discount factor (delta). When computing a measure of utility, we use delta in order to discount the utility of future periods. Delta is less than 1, which means that we care more about today than the future.
Suppose you have two alternatives: receiving $100 at this moment or receiving the money in two weeks. How much money would it take for you not to take the $100 now?
Suppose you say “$110”. Your delta should be equal to = 0.909, using two weeks as the time period.
If the standard model is true, you should be indifferent between $100 now and = $1,191 in one year, which represents an annual interest rate which is higher than 1,000 % (a 10 % interest rate, compounded every two weeks, that is 26 times in a year).
What could be the reason of this inconsistency?
- Miscalculation: we do not realize, when asking $10 more over a two-week period, that this represents a 1,191% interest rate over one year.
- Competition for limited resources: when several people are competing for a common objective, it is better to act now because the opportunity may not be available tomorrow; this can lead to inconsistent behavior.
- Impatience, or present-biased: in the future, willpower is irrelevant— we always do the right thing. In conducting their study, Read and van Leeuwen asked a group of people whether they would prefer to to eat snacks or fruits during their lunch break one week before meeting them: 75% chose the fruits. During the actual meeting a week later, twenty minutes before the break people were given the choice to change their minds, and 75% switched their choice to the chocolate bars.
Richard Thaler and Shlomo Benartzi have conducted a study to check whether committing people to save more money for their retirement would be an efficient way to change their habits. Their first finding was that a vast majority of people offered to join the plan effectually joined it, showing a willingness to avoid the time inconsistency problem.
Second, they found that the majority of people did not leave the plan, and their third result was that the average savings rate of the participants rose from 3.5% to 13.6% over the long-term. Thaler and Benartzi concluded: “The results suggest that behavioral economics can be used to design effective prescriptive programs for important economic decisions.”
Time inconsistency can be met everywhere in finance, but we are going to focus on two issues which are created by this bias.
In 2004, Finn E. Kydland and Edward C. Prescott were awarded the Nobel Prize in Economics for their work on the time inconsistency of economic policies.
They showed that time inconsistency was causing excessive inflation. The central bank has two core goals: trying to keep inflation close to some target level, and keep unemployment close to the natural rate. However, markets are not perfect, and unemployment is usually higher than its natural rate. The central bank’s desire to reduce unemployment to the natural rate leads to time-inconsistent behavior.
The central bank will announce that it will set monetary policy such that inflation equals 2%, and then let the labor market clear at the market-clearing level; it means, the level at which there is no leftover supply or demand. Nonetheless, if workers believe inflation will effectively be 2%, they will bargain a 2% wage increase, which will shift the supply curve to the left. Thus, the central bank has an incentive to create an inflation surprise and meet its goal of reducing unemployment at a cost of higher inflation than first announced. This illustrates the idea of time inconsistency, since the first announcement has changed expectations and the central bank was better off not following what it first proclaimed.
To put it in a nutshell, the pattern is the following: A target level for inflation is announced -> People try to counter the effect of the announcement -> The central bank outbids, leading to an inflation rate which is not optimal.
Another instance of this trend is the discretionary inflation bias. When workers realize that the central’s bank announcements are not credible, they will expect higher inflation. This may prevent unemployment to drop, and thus the inflation will be set at an inefficient rate.
Generally, we assume that at first, we would be better off with discretionary measures than with fixed policies. Discretion should allow more flexibility and be more convenient in responding to changing conditions. However, we have seen that decision makers are tempted to not see through their original announcement and instead take advantage of expectations to implement another policy. Therefore, we should apply a fixed policy rule amid discretion. Policymakers can sometimes achieve better results without exercising their free will.
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