A Logical Economist's Argument Against Hyperbolic Discounting
A Logical Economist's Argument Against Hyperbolic Discounting
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逻辑经济学家反对双曲线贴现的论证
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发表时间：
1998
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影响因子：
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通讯作者：
C. Mulligan
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作者：
C. Mulligan
尽管在心理学和经济学领域有大量且不断增长的文献使用实验证据来支持双曲折现假说，但本文首次提出了这样一个问题：“我们能否通过向参与市场的人提供未来不同日期的不同货币金额之间的选择来检测双曲折现？”如果答案是肯定的，那么市场将利用双曲折扣率，直到他们的财富为零。如果答案是否定的，那么心理学家和一些经济学家对各种货币实验结果的解释就不合逻辑了。这篇文章讨论的问题是“我们能否通过向参与市场的人提供未来不同日期的不同货币金额之间的选择来检测双曲线贴现？”如果答案是肯定的，那么市场将利用双曲折扣率，直到他们的财富为零。如果答案是否定的，那么心理学家和一些经济学家对各种货币实验结果的解释就不合逻辑了。第1节定义了双曲折现和指数折现。第2节概述了一个典型的实验，该实验可以在心理学和经济学文献中找到，并被一些经济学家解释为双曲折现的证据。在第三节中，我区分了两种类型的双曲折现，财富最大化者和非财富最大化者，并表明前者应该以与经济学文献中流行的“指数”折现者完全相同的方式对货币实验做出反应。第四节显示了非财富最大化双曲折扣在市场中被利用。I.双曲型和指数型贴现偏好的工作定义我采用Laibson（1994）的工作定义。考虑日期t消费者对于从日期t开始并持续到（可能无限的）未来的确定性消费序列的以下偏好：对于双曲折扣，< 1，而对于指数折扣，= 1。在萨缪尔森（Samuelson, 1937）、巴罗（Barro, 1974）和卢卡斯（Lucas, 1990）等众多经济模型中，指数贴现者都具有“时间一致的偏好”，也就是说，他的边际替代率不会随着时间的推移而改变。考虑一下，例如，日期t+1消费和日期t+2对双曲折现2之间的MRS。关于双曲折现的其他公式，参见Strotz（1955）、Pollak（1968）、Peleg和Yaari（1973）、Thaler和Shefrin（1981）和Simon（1990）。例如，在经济模型中，允许贴现率随时间变化是很常见的，但在某种程度上不会导致偏好逆转。对于时间一致的可变贴现率模型，请参见Koopmans (1960), Uzawa（1968）或Becker和Mulligan（1994）。消费。对于指数折现者，从日期t和日期t+1的角度来看，这个MRS是相同的：双曲折现者的MRS随着时间的推移而变化：因为它们的MRS随着时间的推移而变化，双曲折现者可以说表现出偏好逆转。截至日期t，日期t+1的消费对他们来说不是很紧急（相对于日期t+2的消费），但当日期t+1到来时。还有其他的“指数”和“双曲线”折现公式，但“偏好逆转”的存在与否是任何公式的重要区别。二世。考虑一个来自心理学文献的典型的“时间偏好”实验：问题1：你今天想要10美元还是明天想要15美元？问题2你想要100天后的10美元还是101天后的14美元？与上述金额相对应的实际金钱通常会支付给回答问题的人。经济学文献中引用的此类实验的例子包括Kurz et al (1973), Thaler (1981)， Kirby和Herrnstein(1995)，反对双曲贴现3受访者通常在问题1中拿10美元，在问题2中拿15美元，通常假设（在我看来是合理的，但这个想法的合理性对我的论点无关紧要），如果在100天内问问题1，他们会拿10美元。这篇文章提出的问题是“这个实验是否说明了偏好？”三世。双曲折现能使财富最大化吗？在这一点上，我向双曲折现的支持者提出一个简单的问题：“你的双曲折现能使财富最大化吗？”我只要求支持者对这个问题回答“是”或“否”，而不是“可能”。如果答案是“是”，并且双曲折现者可以在市场上交易，那么他们将回答问题1和问题2，以实现财富最大化。如果利率（包括所有相关交易成本）大于50%，财富最大化者选择今天的10美元，因为今天的10美元加上利息，明天可以产生超过15美元。如果利率低于50%，财富最大化者选择明天的15美元。请注意，许多经济模型中的“指数”折现代理也是财富最大化者，因此它们回答问题1和问题2的方式与财富最大化双曲折现相同；如果他是财富最大化的，问题1和问题2不允许我们发现双曲折现。非财富最大化双曲折扣？如果参与市场的双曲折现者不能使财富最大化，那么让我们假设（正如心理学文献所做的那样）双曲折现者在收到现金流时消耗现金流，而不是像财富最大化者那样将现金流交易出去。如果一些市场参与者是自私的，不进行双曲折现，那么参与市场的非财富最大化双曲折现者将失去他们所有的财富。这些双曲线折扣店的偏好反转使它们对“荷兰书”敞开大门。要了解如何创建自己的赚钱荷兰书，请向按照我的建议回答问题1和2的双曲折让者提供以下交易序列。交易一：要求双曲线贴现者承诺在100天内支付你10美元，以换取101天内的14美元。他会这样做，因为他不反对双曲贴现4，使财富最大化，根据他对问题2的回答，他希望在101天内获得14美元。交易2 100天后，收回你的10美元。今天（第100天）提供10美元的双曲折扣价，以换取明天（第101天）的15美元。他会接受这笔交易，因为他没有实现财富最大化，根据他对问题1的回答，他现在更喜欢10美元。付10美元。当第101天到来时，收取交易2中承诺的15美元，并支付交易1中承诺的14美元。你每次都能赚1美元！请注意，你和双曲线贴现者之间的承诺没有被打破。非财富最大化双曲贴现参与的荷兰书的数量和大小没有限制。此外，双曲折让不会使财富最大化，因此他不会“货比三家”，去买更便宜的“荷兰书”。换句话说，一个荷兰人不需要与另一个荷兰人竞争双曲折现者的注意力，因为双曲折现者不会使财富最大化。财富最大化者和非财富最大化者之间的交换只能导致后者的剥削。
Although there is a large and growing literature in psychology and economics that uses experimental evidence to support the hyperbolic discounting hypothesis, this note is the first to address the question "Can we detect hyperbolic discounting by offering choices between various monetary amounts at various dates in the future to people who also participate in markets?" If the answer is "yes," I show that the marketplace will exploit hyperbolic discounters to the point where their wealth is zero. If the answer is "no", then the interpretations of various monetary experimental results by psychologists and some economists are illogical. M This note addresses the question "Can we detect hyperbolic discounting by offering choices between various monetary amounts at various dates in the future to people who also participate in markets?" If the answer is "yes," I show that the marketplace will exploit hyperbolic discounters to the point where their wealth is zero. If the answer is "no", then the interpretations of various monetary experimental results by psychologists and some economists are illogical. Hyperbolic and exponential discounting are defined in Section I. Section II outlines a typical experiment that can be found in the psychology and economics literatures and is interpreted by several economists as evidence for hyperbolic discounting. I distinguish between two types of hyperbolic discounters in Section III wealth maximizers and nonwealth maximizers and show that the former should respond to the monetary experiments in exactly the same way as a the "exponential" discounters that populate the economics literature. Section IV shows that the nonwealth maximizing hyperbolic discounters are exploited in the marketplace. I. Working Definitions of Hyperbolic and Exponential Discount Preferences I adopt the working definitions of Laibson (1994). Consider the following preferences of a date t consumer for deterministic consumption sequences beginning at date t and continuing into the (potentially infinite) future: For the hyperbolic discounter, < 1 while = 1 for the exponential discounter. The exponential discounter, who populates a huge number of economic models including Samuelson (1937), Barro (1974), and Lucas (1990), has “time consistent preferences” in the sense that his marginal rates of substitution do not change with the passage of time. Consider, for example, the MRS between date t+1 consumption and date t+2 Against Hyperbolic Discounting 2 For other formulations of hyperbolic discounting, see Strotz (1955), Pollak 1 (1968), Peleg and Yaari (1973), Thaler and Shefrin (1981), and Simon (1990). For example, it is common in economic modeling to allow discount rates to 2 vary over time, but in a way that does not lead to preference reversals. For time consistent variable discount rate models, see Koopmans (1960), Uzawa (1968), or Becker and Mulligan (1994). consumption. For the exponential discounter, this MRS is the same from the point of view of date t and from the point of view of date t+1: The hyperbolic discounter's MRS changes with the passage of time: Because their MRSs change with the passage of time, hyperbolic discounters can be said to exhibit preference reversals. As of date t, date t+1 consumption is not very urgent for them (relative to date t+2 consumption), but it is when date t+1 arrives. There are other formulations of “exponential” and “hyperbolic” discounting , but the 1 presence or lack of “preference reversals” is the important distinction in any formulation. II. A Typical Monetary Experiment Consider a typical "time preference" experiment from the psychology literature: Question 1 Would you like $10 today or $15 tomorrow? Question 2 Would you like $10 in 100 days or $14 in 101 days? Actual money corresponding to the amounts above are often paid to the respondents to the questions. Examples of such experiments that have been cited in the economics literature include Kurz et al (1973), Thaler (1981), Kirby and Herrnstein (1995), Against Hyperbolic Discounting 3 Respondents often take the $10 in Question 1 and the $15 in Question 2 and it is usually assumed (and reasonably in my opinion but the reasonableness of this idea doesn't matter for my argument) that they would take the $10 if Question 1 were reasked in 100 days. The question posed by this note is "Does this experiment say anything about preferences?" III. Do Hyperbolic Discounters Maximize Wealth? At this point, I pose a simple question to proponents of hyperbolic discounting "Do your hyperbolic discounters maximize wealth?" I only require that proponents answer either yes or no to this question, but not "maybe." If the answer is "yes," and hyperbolic discounters can trade in a market, then they will answer Questions 1 and 2 in order to maximize wealth. If the interest rate (inclusive of all relevant transactions costs) is greater than 50%, the wealth maximizer chooses the $10 today because $10 today can, with interest, produce more than $15 tomorrow. If the interest rate is less than 50%, the wealth maximizer chooses the $15 tomorrow. Note that the "exponential" discounting agents that populate so many economic models are also wealth maximizers so they answer Question 1 and Question 2 in the same way as the wealth maximizing hyperbolic discounter; Questions 1 and 2 do not allow us to detect a hyperbolic discounter if he is wealth maximizing. IV. Nonwealth maximizing hyperbolic discounters? If hyperbolic discounters that participate in markets do not maximize wealth, then let's suppose (as the psychology literature does) that hyperbolic discounters consume cash flows when they receive them rather than trading them away as the wealth maximizers might. If some market participants are selfish and do not discount hyperbolically, nonwealth maximizing hyperbolic discounters that participate in markets will loose all their wealth. The preference reversals of these hyperbolic discounters leave them open to "Dutch books." To see how to create your own money-making Dutch book, offer the following sequence of deals to a hyperbolic discounter who answered Questions 1 and 2 as I suggested. Deal 1 Ask the hyperbolic discounter to promise to pay you $10 in 100 days in exchange for $14 in 101 days. He will do so because he does not Against Hyperbolic Discounting 4 maximize wealth and, according to his answer to Question 2, prefers $14 in 101 days. Deal 2 After 100 days have passed, collect your $10. Offer the hyperbolic discounter $10 today (the 100th day) in exchange for $15 tomorrow (the 101st day). He will take the deal because he does not maximize wealth and, according to his answer to Question 1, prefers $10 now. Pay the $10. When the 101st day arrives, collect the $15 promised in Deal 2 and pay the $14 promised in Deal 1. You'll make $1 every time! Notice that no promises made between you and the hyperbolic discounter were broken. There is no limit to the number or size of the Dutch books in which the nonwealth maximizing hyperbolic discounter will participate. Moreover, the hyperbolic discounter does not maximize wealth so he does not "shop around" for a cheaper "Dutch booker". In other words, one Dutch booker does not have to compete with another Dutch booker for the attention of a hyperbolic discounter because the hyperbolic discounter does not maximize wealth. Exchange between wealth maximizers and nonwealth maximizing hyperbolic discounters can only lead to the exploitation of the latter.