- Email: [email protected]
Does money illusion matter in intertemporal decision making?
Accepted Manuscript Title: Does Money Illusion Matter in Intertemporal Decision Making? Authors: Tetsuo Yamamori, Kazuyuki Iwata, Akira Ogawa PII: DOI: Reference:
S0167-2681(17)30323-2 https://doi.org/10.1016/j.jebo.2017.11.019 JEBO 4201
To appear in:
Journal
Received date: Revised date: Accepted date:
10-2-2017 22-11-2017 23-11-2017
of
Economic
Behavior
&
Organization
Please cite this article as: Yamamori, Tetsuo, Iwata, Kazuyuki, Ogawa, Akira, Does Money Illusion Matter in Intertemporal Decision Making?.Journal of Economic Behavior and Organization https://doi.org/10.1016/j.jebo.2017.11.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Does Money Illusion Matter in Intertemporal Decision Making?
a
IP T
Tetsuo Yamamoria,§1, Kazuyuki Iwatab, Akira Ogawac Faculty of Economics, Dokkyo University, 1-1 Gakuen-cho, Soka, Saitama 340-0042,
b
SC R
Japan. Email: [email protected]
Faculty of Economics, Matsuyama University, 4-2 Bunkyo-cho, Matsuyama, Ehime
790-8578, Japan. Email: [email protected]
College of Liberal Arts, International Christian University, 3-10-2 Osawa, Mitaka, Tokyo
U
c
A
CC E
PT
ED
M
A
N
181-8585, Japan. Email: [email protected]
§1
Corresponding author: Tetsuo Yamamori, Faculty of Economics, Dokkyo University, 1-1,
Gakuen-cho, Soka, Saitama 340-0042, Japan. Phone: +81-48-943-2217, Fax: +81-48-943-2217, Email: [email protected]. 1
Highlights We conduct an experiment for an intertemporal consumption/savings problem.
We examine how price fluctuations affect an individual consumption behavior.
The misconsumption is significantly high if the commodity price is fluctuated.
The price fluctuations strengthen the oversaving behavior.
IP T
Abstract
SC R
To examine the degree to which price fluctuations affect how individuals approach an
intertemporal decision-making problem, we conduct a laboratory experiment in which
U
subjects spend their savings to purchase only one commodity over 20 periods. In the
A
N
control treatment, the commodity price is constant across all periods. In the small (large)
M
price-fluctuation treatment, the price rate of change is always 1% (20%). Regardless of
ED
the treatment, the commodity price and subjects’ savings change at the same rate over time. Therefore, the optimal amount of consumption is the same in all three treatments.
PT
Our main findings are twofold. First, the magnitude of misconsumption (i.e., the deviation
CC E
from optimal consumption) is significantly high, with the large price-fluctuation treatment being the highest, followed by the small price-fluctuation treatment and then
A
the control treatment. Second, regardless of the presence of price fluctuations, subjects exhibit underconsumption (oversaving) behavior, and price fluctuations strengthen this tendency.
2
Keywords: intertemporal decision making; money illusion; price fluctuations; economic experiment. JEL Classification: C91, D91, E31
IP T
Funding: This study was financially supported by JSPS KAKENHI [Grant Number
SC R
24730169].
U
1. Introduction
N
Much research has been devoted to examining how people approach intertemporal
M
A
decision-making (IDM) problems. IDM is a key formulation of dynamic models in financial theory, operations research, game theory, and micro- and macroeconomic theory,
ED
within which agents are usually assumed to be unboundedly rational and able to solve
PT
dynamic programming problems. However, the results of previous studies of experiments
CC E
on IDM suggest that individuals are unable to correctly identify the optimal strategy even though they try to solve complex decision problems rationally (Johnson et al., 1987; Hey
A
and Dardanoni, 1988; Anderhub et al., 2000; Carbone and Hey, 2001; Houser and Winter, 2004; Hey and Knoll, 2011). Furthermore, the mistakes made by subjects are systematic, and they seem to adopt some heuristics or rules-of-thumb for dynamic problems. For example, Johnson et al. (1987) conducted a series of experiments associated with a life
3
cycle model and found that most subjects exhibit oversaving behavior. Carbone and Hey (2001) found in their moderately easy dynamic decision problem that many subjects used
IP T
backward induction and ignored the fact they would be behaving optimally thereafter.1 In real life, people fail to optimize IDM not only because such problems are too
SC R
complex to solve (i.e., poor numeracy) but also because most transactions are in nominal
terms, and prices are not always constant; in other words, people may suffer from “money
U
illusion.” The concept of money illusion refers to the tendency for people to make
N
economic decisions based on nominal rather than real monetary values. Money illusion
M
A
has long been recognized (Fisher, 1928) and is often mentioned to explain economic phenomena such as the rigidity of nominal prices and wages. To date, substantial proof
ED
of the existence of money illusion has been reported by experimental studies (Kahneman
PT
et al., 1986; Shafir et al., 1997; Thaler et al., 1997; Fehr and Tyran, 2001, 2007; Noussair
CC E
et al., 2012), and its influence on the economy cannot therefore be disregarded. The purpose of this study is to investigate how price fluctuations influence individuals’
A
choices in an intertemporal consumption/savings problem. As the nominal terms that people face change over time in association with price fluctuations, it is necessary to
1
Some authors classify the types of strategies that seem to be applied in a dynamic decision
problem. For example, see Hey and Knoll (2011). 4
examine whether money illusion distorts their economic decisions. How do these changing nominal terms influence individuals’ consumption/savings behavior? Does the
IP T
volatility of price fluctuations affect individuals’ welfare? This study investigates these questions using a laboratory experiment.
SC R
Although experimental studies of money illusion have shown that nominal frames
often influence individuals’ decisions, the underlying decision problems in most of these
U
works are static, or a repetition of a static problem in which the nominal frame changes
N
only once. For example, Fehr and Tyran’s (2001) subjects repeatedly played a price-
M
A
setting game. They showed that the average price in the aftermath of a monetary shock converges to the equilibrium more slowly when the game is presented in a nominal frame
ED
than in a real frame. However, this difference does not emerge when all the opponents are
PT
computer programs; in other words, money illusion does not matter in a repeated static
CC E
problem without strategic interactions. Noussair et al.’s (2012) experiment, in which subjects repeatedly played a continuous double auction by trading shares, is an exception.
A
Further, subjects’ stock of shares was carried over from one trading period to the next implying that the situation intrinsically posed an IDM problem. However, their research focused on aggregate market behavior rather than on individual behavior, and they showed that real asset market prices increase after a monetary deflationary shock but
5
remain unaffected by a monetary inflationary shock. Moreover, as shown by Fehr and Tyran (2001), due to the indirect effect of money illusion, the effect of monetary shock on games with strategic interaction need not necessarily imply an effect on IDM
IP T
problems. 2 Thus, the question of how ongoing price fluctuations affect individual
SC R
behavior in IDM problems remains.
Our study is based on an economic experiment in which subjects face a simple IDM
U
problem with a lifetime of 20 periods. At the beginning, a subject possesses 40,000
N
points (experimental currency units) in his/her savings account to spend during these 20
M
A
periods (hereafter, we use “his” for simplicity). Additional money is not credited to a subject’s account. In each period, he can spend his savings to buy only one commodity.
ED
His overall payoff is the sum of an instantaneous payoff, which is given by the square
PT
root of the consumption amount. The commodity price in the first period is 80 points.
CC E
Over time, the subject’s savings and commodity price change at the same rate. In any period, subjects do not directly choose the amount of the commodity but only their
A
expenditure on it. In our experiment, price fluctuations are irrelevant to the budget set,
2
Fehr and Tyran (2001) divided the effects of money illusion into direct and indirect effects. The
former directly result from individual optimization mistakes whereas the latter arise because some agents behave differently based on their expectation that others would be prone to money illusion. Following this classification, our research focuses only on the direct effects of money illusion. 6
and there is no uncertainty in the payoffs. We conducted three treatments. In the control treatment, price is constant across all
IP T
periods. In the other two treatments, price and savings fluctuate over time. In both these treatments, price increases, decreases, or does not change at the beginning of each period.
SC R
Each of these events occurs with an equal probability. In the small and large pricefluctuation treatments, the rate of change is always 1% and 20%, respectively. Because
N
of consumption is the same in all three treatments.
U
the subject’s savings and commodity prices change at the same rate, the optimal amount
M
A
We first tested the hypothesis that money illusion does not matter. This hypothesis was rejected by the results of our experiment showing that the magnitude of misconsumption
ED
is large when price fluctuations are large. Shafir et al. (1997) stated that money illusion
PT
is observed even in highly inflationary environments despite expecting “to find greater
CC E
awareness of the difference between nominal and real values when inflation is high than when it is low.” The previous observation suggests that money illusion appears more
A
strongly when price fluctuations are larger, which seems to be a stronger claim than the statement by Shafir et al. (1997). Furthermore, it follows that the actual payoffs of subjects in the control treatment are significantly higher than those in the large pricefluctuation treatment.
7
The hypothesis is concerned with only the absolute values of misconsumption rather than its direction (i.e., over- or underconsumption). As mentioned above, previous studies
IP T
of IDM experiments have shown that subjects’ mistakes are not random but rather systematic. Therefore, we also examined the direction of misconsumption in our
SC R
experiment. The results showed that our subjects displayed underconsumption (oversaving) behavior. Furthermore, we found that price fluctuations strengthen the
U
tendency toward such behavior.
N
The rest of the paper is organized as follows. In Section 2, we describe our experimental
M
A
design. In Section 3, the experimental results are presented. In Section 4, we summarize
PT
2. Experiment
ED
our results and argue their implications.
CC E
2.1. Experimental design and procedure We consider a simple IDM problem with a lifetime of 20 periods. At the beginning, a
A
subject possesses 40,000 points (experimental currency units) in his savings account to spend during these 20 periods. Additional money is not credited to his account. In each period, he can spend his savings to buy only one commodity. Let 𝑥𝑡 be the amount of the commodity purchased in period 𝑡; then, his payoff function is given by
8
∑
20
√𝑥𝑡 .
𝑡=1
The instantaneous payoff √𝑥𝑡 is a constant-relative, risk-aversion utility function with a
IP T
coefficient of 1⁄2. The discount rate is always 1, and the money that remains after period 20 is irrelevant to his payoff. This setup is like the experimental design in Anderhub et al.
SC R
(2000); however, we eliminate uncertainty to reduce the “poor numeracy” effect. Their experiment was based on a dynamic decision problem with an uncertain time horizon:
U
subjects had to allocate a given monetary amount over an uncertain number of periods.
N
Such uncertainty complicates the optimization problem dramatically, and therefore, the
M
A
result of the experiment may contain both “poor numeracy” and “money illusion.” In our setting, the calculation for optimization is sufficiently simple for all subjects.
ED
The experimental design consists of three treatments. Regardless of the treatment, the
PT
commodity price in the first period is 80 points; both the subject’s savings remaining in
CC E
his account and the commodity price change at the same rate over time. In the control treatment, denoted by C, price is constant across all periods. In the large (small) price-
A
fluctuation treatment, denoted by L (S), price increases by 20% (1%), decreases by 20% (1%), or is unchanged at the beginning of each period. Each event occurs with an equal probability. Because price and savings always change at the same rate, price fluctuations are irrelevant to the budget of a subject and are therefore irrelevant to his optimal
9
consumption. Thus, all treatments differ only in their nominal terms, and actual consumption in L and S should be the same as that in C if a subject’s decisions are based
IP T
only on real monetary values. As there is no uncertainty in the payoffs, the risk attitude of subjects should not affect their decisions.
SC R
It is easy to see that the sequence (𝑥𝑡 )20 𝑡=1 of consumption, in which 𝑥𝑡 = 25 for any 𝑡, maximizes a subject’s overall payoff. However, once a subject’s consumption deviates
U
from such optimality, this consumption sequence is no longer optimal for the remaining
N
periods. Let 𝑝𝑡 and 𝑀𝑡 be the commodity price and amount of money remaining in his
M
A
savings account in period 𝑡 , respectively. Then, in any period 𝑇 , the payoff in the 20 remaining periods, that is, ∑20 𝑡=𝑇 √𝑥𝑡 , is maximized by the sequence (𝑥𝑡 )𝑡=𝑇 of
ED
consumption, in which
PT
𝑥𝑡 = 𝑥(𝑚 𝑇 ) =
𝑚𝑇 (20 − 𝑇 + 1)
CC E
for all 𝑡, where 𝑚 𝑇 = 𝑀𝑇 ⁄𝑝𝑇 is the real value of savings in period 𝑇. Thus, optimal consumption depends only on real terms, instead of any nominal variables, including
A
future prices.
Our experiment was conducted at Takasaki City University of Economics. We recruited
subjects by displaying posters and distributing fliers. They were undergraduate students from several faculties at the university that had not participated in any prior IDM
10
experiments; furthermore, each subject could only participate in one treatment. All treatments were conducted in the same laboratory, and each computer terminal in the
IP T
laboratory was assigned a computer program associated with one of the treatments. Subjects were seated in front of a computer terminal at random. Each desk had a
SC R
calculator and an envelope containing all the experimental materials, including the
instructions, and a recording sheet. During the experiment, subjects could use the
U
calculator on the desk at any time. The total number of subjects who participated in (i.e.,
N
was assigned a computer terminal with) treatments C, S, and L was 20, 21, and 23,
M
A
respectively.
Each subject was asked to carefully read the instructions, which provided all the
ED
information about the structure of the treatment to which they had been allocated,
PT
including the price distribution. Before the actual experiment began, subjects were told
CC E
to solve the practice problems to confirm they understood the instructions for the experiment. All practice problems were the same in the three treatments. The problem set
A
contained a simple IDM problem with two periods and without price fluctuations to suggest that consumption smoothing is always optimal for any remaining periods.3 No subject could begin the actual experiment unless all problems had been answered
3
The instructions and the practice problems are presented in the Appendix. 11
correctly. In each period of the actual experiment, each subject was asked to input his expenditure on the commodity for the current period. In other words, subjects did not choose the
IP T
amount of commodity 𝑥𝑡 directly, but rather chose expenditure on the commodity,
SC R
𝑝𝑡 𝑥𝑡 4. On the computer screen, each subject could always observe the amount of money he currently held in his savings account, the current commodity price, and the percentage
U
price change from the previous period. Past consumption and expenditure were also
A
M
the next period automatically began.
N
displayed on the screen.5 Once the expenditure for the current period had been entered,
Decision-making time was not restricted. Therefore, the session duration differed by
ED
participant but was approximately one hour for most subjects. After the experiment, each
PT
subject was asked to answer a questionnaire. The reward given to the subjects was a kind
CC E
of two-part tariff: the fixed participation fee was ¥500, and proportional payment was ¥14 × realized payoff shown at the beginning of this section. The reward was paid in cash to
While the nominal variables do not affect optimal consumption, they do affect optimal
A
4
expenditure, which is given by 𝑝𝑡 𝑥(𝑚𝑡 ) in period 𝑡. 5
The instantaneous payoff or the payoff at an instant was not displayed on the screen. However, if
subjects wanted to know the amount, they could get it using the displayed information and the calculator. 12
each subject privately after the session. Subjects earned on average ¥1,579. 2.2. Hypotheses Our analysis focuses on the difference between actual and optimal consumption (hereafter
IP T
misconsumption) in each treatment. For treatment A ∈ {𝐶, 𝐿, 𝑆} , let 𝐷𝑡𝐴 be the
SC R
misconsumption in period 𝑡 in treatment 𝐴 and let |𝐷𝑡𝐴 | be its absolute value. Because
optimal consumption 𝑥(𝑚𝑡 ) in period 𝑡 is the same for all treatments, 𝐷𝑡𝐴 can be
U
written as 𝐷𝑡𝐴 = 𝑥𝑡𝐴 − 𝑥(𝑚𝑡 ), where 𝑥𝑡𝐴 is actual consumption in period 𝑡 in
A
M
on 𝐷𝑡𝐴 when analyzing its direction.
N
treatment 𝐴. We focus on |𝐷𝑡𝐴 | when analyzing the magnitude of misconsumption and
The impact of price fluctuations throughout all periods can be measured by the
ED
difference in |𝐷𝑡𝐴 | in the entire study period between C and L, or between C and S. Thus,
CC E
on average:
PT
we test the following hypothesis that price fluctuations do not affect subjects’ behavior
Hypothesis 1: On average, money illusion does not matter.
A
∑
19
( |𝐷𝑡𝐿 | − |𝐷𝑡𝐶 |) = 0, 𝑎𝑛𝑑 ∑
𝑡=1
19
( |𝐷𝑡𝑆 | − |𝐷𝑡𝐶 |) = 0.
𝑡=1
Observations for the 20th period are excluded because subjects could easily choose to
consume their remaining points in the last period without considering or calculating their optimal consumption.
13
As mentioned in the introduction, previous studies of IDM experiments have shown that deviations from the optimal solution of subjects’ behavior are not random but rather
following hypothesis:
∑
19
SC R
Hypothesis 2: Deviations from the optimal solution are random.
IP T
systematic. Thus, we also test this observation in our experiment by formulating the
𝐷𝑡𝐴 = 0 for any 𝐴 ∈ {𝐶, 𝐿, 𝑆}.
𝑡=1
U
The subjects in our experiment can make mistakes in two ways, namely
N
underconsumption (oversaving), that is, 𝐷𝑡𝐴 < 0, or overconsumption (undersaving), that
M
A
is, 𝐷𝑡𝐴 > 0. In each treatment, if their misconsumption does not tend toward either
ED
mistake, this hypothesis should be supported.
PT
3. Results
CC E
This section discusses the experimental results. The total number of observations in our experiment is 1,280 (= (20+21+23) ×20) because each subject makes decisions over 20
A
periods and the number of subjects is 20, 21, and 23 in C, S, and L, respectively. Among the observations, some subjects always make extraordinary decisions because they may not understand the experiment. To avoid such extraordinary decisions potentially influencing the results, from the sample of 64 subjects, we drop two subjects whose
14
decisions were all in the 95th percentile.6 In addition, observations for the 20th period are excluded. Consequently, 1,178 observations are used for our analysis. 3.1. Tests for Hypothesis 1
IP T
We first focus on the magnitude of misconsumption |𝐷𝑡𝐴 |. To illustrate all results for
SC R
|𝐷𝑡𝐴 |, Figure 1 presents the distributions for each treatment, along with the number of
U
observations, means, and standard deviations for each treatment.
0
ED
.02
.04
M
S. D. = 25.07
Obs. = 399 Mean = 20.37 S. D. = 32.44
A
.06
Obs. = 361 Mean = 13.91
PT
.08
L (20% fluctuation)
Total
Obs. = 418 Mean = 27.23
Obs. = 1178 Mean = 20.82 S. D. = 31.13
S. D. = 33.26
0
.02
CC E
.04
.06
Density
S (1% fluctuation)
N
.08
C (constant price)
100
200
300
0
100
200
300
absolute value of the misconsumption
A
0
Figure 1. Distribution of the absolute value of misconsumption
6
Even when we do not drop the two subjects, the trend of the estimation results is the same as
before. 15
Note: “S.D.” means standard deviation.
It is found that many subjects have a small amount of misconsumption that approaches
IP T
0. However, in the comparison among the three treatments, the fractions of subjects with small amounts of misconsumption in C and S are larger than that in L. The order of the
SC R
magnitude of the means is mean (C) < mean (S) < mean (L), which implies that subjects
facing high price fluctuations are likely to mistake their decisions. We test these
U
observations using the following econometric analysis.
N
We regress the absolute value of misconsumption on the treatment dummies and other
M
A
control variables that may affect subjects’ intertemporal decisions, such as individual characteristics. Let |𝐷𝑖𝑡 | be the absolute value of misconsumption of subject 𝑖 at
ED
period 𝑡, and 𝑇𝑆𝑖 and 𝑇𝐿𝑖 be dummy variables that take a value of 1 if he is assigned to
PT
S and L, respectively. The period is denoted as 𝑅𝑡 , which is a scale variable that takes
CC E
values of 1 to 19. 𝑿𝑖 is a control variable vector for capturing subject 𝑖’s characteristics that affect misconsumption. To obtain the subjects’ characteristics, a questionnaire survey
A
was conducted at the end of the experiment. To control for unobserved heteroscedastic effects, the individual fixed effect, 𝜇𝑖 , is incorporated. The idiosyncratic error term is represented as 𝜀𝑖𝑡 . The model for testing Hypothesis 1 is written as follows: ln(|𝐷𝑖𝑡 |) = 𝑿𝒊 𝑨′ + 𝑎1 𝑇𝑆𝑖 + 𝑎2 𝑇𝐿𝑖 + 𝑎3 𝑅𝑡 +𝜇𝑖 + 𝜀𝑖𝑡 16
where vector 𝑨, and 𝑎𝑘 (𝑘 = 1,2,3) are the parameters to be estimated. If insignificant 𝑎̂1 and 𝑎̂2 (estimated coefficients) are observed by estimating this equation, Hypothesis
IP T
1 is supported. Otherwise, money illusion matters on average in terms of individual IDM. Figure 1 indicates that the absolute values of misconsumption are highly skewed. To
SC R
avoid such skewness, logarithmic transformation is frequently used. However, zero-value problem arises in performing the transformation because 135 observations (11.5%) have
U
a zero value. Therefore, we add 10-16 to the absolute value of misconsumption and then
N
convert it into a logged variable (i.e., ln(𝐷𝑖𝑡 + 10−16 )), similar to the approach adopted
M
A
by Kahn (2005).7
The descriptive statistics for the explanatory variables are shown in Table 1. The
ED
variables Male, Faculty, and Alone are dummies that take a value of 1 if subjects are men,
PT
if they are students of the Faculty of Economics, and if they live on their own,
CC E
respectively.8 Unlike most studies, instead of age, we use Grade to represent respondents’ grade, which takes a value of 1 to 4. In optimal decision making, rationality is a key issue.
Kahn (2005) added 1 to the dependent variables to avoid the zero-value problem. However, we
A
7
add 10-16 because a 1-value increment may drastically change the distribution of |𝐷𝑡𝐴 | (see Figure 1). 8
There are two faculties in the Takasaki City University of Economics: Faculty of Economics and
Faculty of Regional Policy. 17
People who are good at mathematics may be more likely to choose optimal consumption. We therefore ask them the extent to which they are good at mathematics (Favorite for Math), which is a scale variable with five levels (1 and 5 indicate “my favorite subject is
IP T
mathematics” and “my least favorite subject is mathematics,” respectively). Income is
SC R
also a scale variable that takes a value of 1 (no income) to 7 (more than ¥100,000 per month). In addition to the described control variables, the survey contained five question
U
items associated with knowledge about economics keywords: inflation, deflation,
N
nominal wage, long-term bonds, and the real exchange rate. Each subject responded to
M
A
all questions using five-point scales, with 1 and 5 representing “I know the word well”
ED
and “I do not know the word at all,” respectively.
Table 1. Descriptive statistics of the explanatory variables
A
CC E
PT
Variables Mean S. D. Min. Max. S (1%) dummy 0.34 0.47 0 1 L (20%) dummy 0.35 0.48 0 1 Period 10.00 5.48 1 19 Male 0.73 0.45 0 1 Grade 2.24 0.98 1 4 Faculty 0.68 0.47 0 1 Alone 0.76 0.43 0 1 Favorite for Math 3.66 1.11 1 5 Income 3.40 1.89 1 7 Knowledge: inflation 1.52 0.62 1 4 Knowledge: deflation 1.55 0.69 1 4 Knowledge: nominal wage 3.26 1.23 1 5 Knowledge: long-term bond 2.60 1.07 1 5 Knowledge: real exchange rate 2.97 1.05 1 5
18
The estimation results for the equation that tests Hypothesis 1 are presented in Columns (1) and (2) of Table 2. As a robustness check, two models (with and without individual
IP T
fixed effects, respectively) are employed. They show that subjects in the L treatment are likely to mistake their decisions at the 1% significance level relative to those in the C
SC R
treatment. This finding implies that people cannot make optimal consumption decisions
under large price fluctuations. The coefficients of the S dummy in Columns (1) and (2)
U
also suggest that subjects may make suboptimal intertemporal decisions relative to C.
N
Specifically, the magnitude of misconsumption in L is larger than that in S, suggesting
M
A
that subjects are likely to mistake their decisions as the fluctuation rate rises.9 Regarding the other variables, men may be likely to consume closer to the optimal level
ED
than women, although the coefficient in Column (2) is not significant. Students who study
PT
economics as their majors may optimally consume more compared with non-economics
CC E
students, while students living alone tend to have small misconsumption levels relative to those living with their families. Although the coefficients of grade are statistically
A
significant in both Columns (1) and (2), the signs are the opposite of each other (i.e., negative and positive signs are obtained in Columns (1) and (2), respectively). Moreover, Favorite for math is found to be statistically related to IDM only in Column (2). The 9
These results are also supported by the Wilcoxon–Mann–Whitney test and the t test. 19
positive sign indicates that students who are good at mathematics are likely to choose their consumption more rationally. The sign of the coefficients of income is also
IP T
significant and positive only in Column (2). The results may thus reflect that subjects in higher grades and with higher income levels aim to finish the experiment as quickly as
SC R
possible because their opportunity costs are larger than those of students with lower
grades and income levels. Additionally, it is found that knowledge of economics has a
U
significant influence on consumption. Knowledge of inflation and long-term bonds is
N
significant and negative, implying that knowledge of economics makes people choose
M
A
correctly with respect to the magnitude of misconsumption.
A
CC E
PT
ED
Table 2. Estimation results for testing Hypothesis 1
20
Alone Favorite for Math Income Knowledge: inflation Knowledge: deflation Knowledge: nominal wage Knowledge: long-term bond
no 27.42*** 0.239
yes 33.95*** 0.635
ED
Knowledge: real exchange rate
PT
Constant
CC E
Individual fixed effects F-value Adj. R-squared
IP T
Faculty
SC R
Grade
U
Male
4.531* (2.553) 12.61*** (1.314) -0.0868* (0.0518) -3.227 (2.117) 6.190*** (0.860) -5.461*** (2.103) -11.15*** (1.907) 3.169*** (0.574) 2.213*** (0.334) -14.96*** (3.635) 12.80*** (2.978) 2.077** (1.034) -1.254*** (0.314) 0.250 (1.162) -38.26*** (2.891)
N
Period
8.789*** (1.124) 9.548*** (0.909) -0.0868 (0.0665) -4.637*** (0.599) -1.584*** (0.457) -1.570** (0.778) -4.567*** (0.526) -0.340 (0.308) 0.119 (0.198) -1.079 (1.805) 2.567 (1.682) -0.469 (0.317) -1.176*** (0.421) -0.160 (0.405) 7.072** (3.115)
A
L (20%) dummy
(2)
M
S (1%) dummy
(1)
Note: Robust standard errors are in parentheses; ***, **, and * represent the 1%, 5%, and 10%
A
significance levels, respectively.
3.2. Tests for Hypothesis 2 To assess whether subjects’ misconsumption shows a trend toward under- or overconsumption, we next focus on the results for 𝐷𝑡𝐴 . Table 3 shows the descriptive 21
statistics of 𝐷𝑡𝐴 for each treatment, and the results of the t test for which the null hypothesis is that the mean equals zero. Their box plots are also illustrated in Figure 2.
IP T
We find that regardless of the presence of price fluctuations, subjects purchase only a small quantity compared with the optimal one, that is, they show underconsumption
SC R
(oversaving) behavior overall. Such a tendency for subjects to make mistakes was also
L (20% fluctuation) -9.83*** -12.28 41.87
A
S (1% fluctuation) -13.13*** -1.01 35.99
M
C (Control) mean -3.22** median 0.00 S.D. 28.50
N
Table 3. Descriptive statistics of misconsumption
U
reported by Johnson et al. (1987) and Anderhub et al. (2000).
Note: The null hypothesis under the t test is that the mean is equal to zero; ***, **, and * represent
A
CC E
PT
ED
the 1%, 5%, and 10% significance levels, respectively.
22
50
IP T
0
SC R
-50
U
-100
S (1% price fluctuation)
L (20% price fluctuation)
N
C (constant price)
A
Figure 2. Box plots of misconsumption
Note: The bold horizontal lines represent medians. Ranges between the 25th to 75th percentiles are
M
expressed as boxes drawn in gray. The upper and lower adjacent lines are obtained from the procedure defined by Tukey (1977). The maximum and minimum values, which are usually represented by the
PT
ED
line segments of the box, are omitted.
Furthermore, by comparing the box plot of C with those of the other treatments, we see
CC E
that the existence of price fluctuations seems to strengthen the over-saving behavior of subjects. This observation is confirmed by the Wilcoxon–Mann–Whitney test results in
A
Table 4.
Table 4. Wilcoxon–Mann–Whitney test for Hypothesis 2
23
X C (constant Price) Y S (1% flactuation)
S (1% flactuation) -2.41 ** -
L (20% flactuation) -5.20 *** -1.76 *
Note: The null hypothesis under the test is that the distribution of X is equal to that of Y. The Wilcoxon statistic, which is approximately a standard normal random variable, is calculated based on the sum of
IP T
the ranks of the observations of X; ***, **, and * represent the 1%, 5%, and 10% significance levels,
SC R
respectively.
3.3. Payoff comparison among treatments
U
Earlier, we found that, on average, the magnitude and tendencies of misconsumption
N
differ among treatments. In this subsection, we focus on the payoffs described in Section
M
A
2. Note that the number of observations here is 62 because each subject has only one payoff. Moreover, these payoffs are not the same as the rewards that subjects received
ED
after the experiment since the rewards include the participation fee.
PT
The distribution of the payoff for each treatment is presented in Figure 3. In this figure,
CC E
the mean, standard deviation, and median are also presented. The Wilcoxon–Mann– Whitney test results in Table 5 show that the payoff distributions between C and L, and S
A
and L are different at the 1% and 5% significance levels, respectively, whereas there is no significant gap between C and S.
24
S (1% price fluctuation) Obs. = 21 Mean = 78.31 S. D. = 29.44 Median = 90.41
Total
Obs. = 22
Obs. = 62 Mean = 78.57 S. D. = 24.33 Median = 83.99
Mean = 72.16 S. D. = 22.33
0
50
100 0
50
100
A
Payoff
N
0
U
Median = 75.82
SC R
.05
L (20% price fluctuation)
IP T
Obs. = 19 Mean = 86.28 S. D. = 18.66 Median = 92.75
0
Density
.05
C (constant price)
ED
Note: “S. D.” means standard deviation.
M
Figure 3. Distribution of the payoff by treatment
Table 5. Wilcoxon–Mann–Whitney test for payoffs among treatments
PT
C (constant Price) S (1% fluctuation)
CC E
Y
X
S (1% fluctuation) -0.66 -
L (20% fluctuation) -2.75 *** -2.04 **
Note: The null hypothesis under the test is that the distribution of X is equal to that of Y. The Wilcoxon statistic, which is approximately a standard normal random variable, is calculated based on the sum of the ranks of the observations of X; ***, **, and * represent the 1%, 5%, and 10% significance levels,
A
respectively.
4. Concluding remarks Previous studies have focused on how people approach dynamic consumption decision
25
problems because it is often observed that they fail to choose optimal consumption. One of the reasons is that the individual recognizes nominal term and price fluctuations, that
IP T
is, money illusion. To study how money illusion affects individual IDM, a laboratory experiment was conducted, in which subjects spent their savings on consumption over 20
SC R
periods, without interaction with other subjects. We compared three treatment groups: a
constant price (C) and 1% (S) and 20% (L) price-fluctuation treatments. In all treatments,
U
the optimal consumption is irrelevant to the price fluctuations, because commodity prices
N
and savings simultaneously change at the same rate. In other words, optimal consumption
M
A
depends only on real terms instead of nominal terms.
Findings based on our data are twofold. First, the magnitude of the deviation from
ED
optimal consumption in all periods is significantly high, with the large price-fluctuation
PT
treatment highest, followed by the small price-fluctuation treatment and then the control
CC E
treatment. Thus, regardless of their size, price fluctuations influence individuals’ optimization. In other words, money illusion matters in IDM problems, and this effect is
A
significant if price fluctuations are large. Then, the actual payoffs of subjects in the C treatment are significantly higher than those in the L treatment. Second, regardless of the presence of price fluctuations, subjects purchase only a small quantity compared with the optimal amount. In other words, subjects show underconsumption (oversaving) behavior.
26
Furthermore, we find that price fluctuations strengthen the tendency toward such behavior. Johnson et al. (1987) found in their IDM experiment that most subjects display over-
IP T
saving behavior because they underestimate the power of compound interest. Their experiment was based on a questionnaire in which the subjects choose annual
SC R
consumption under a hypothetical life scenario from the age of 35 until death at 75. Unlike our study, there is a fixed amount of income each year until the age of 65, and debt and
U
savings are possible with a real interest rate of 4%. Our experimental result shows that
N
even when the real interest rate is 0%, and hence, regardless of whether the subjects know
M
A
the power of compound interest or not, they display oversaving behavior. Why do our subjects save excessively even though there is no uncertainty and the real
ED
interest rate is 0%? One possible explanation is that they dislike decreasing a nominal
PT
amount of the savings account. There is plenty of evidence that people tend to prefer
CC E
avoiding loses to acquiring gains, i.e., people tend to “loss aversion.”10 However, it is not clear why price fluctuations strengthen oversaving behavior. Further experimental studies
A
are necessary to investigate how loss aversion affects individual behavior in IDM problems with and without price fluctuations. Our experiment examined the effects of the magnitude of stochastic price fluctuations 10
For example, see Tversky and Kahneman (1991). 27
on IDM. However, individuals’ choices in IDM may also be distorted by inflationary and deflationary trends in price fluctuations. Exploring how these trends affect an individual’s
SC R
IP T
IDM thus remains a task for future research.
Acknowledgments
A
N
U
We would like to thank Toshiji Kawagoe and Yoich Gokan for their helpful comments.
M
References
allocation
behavior.
Experimental
Economics
3,
137–152.
PT
intertemporal
ED
Anderhub, V., Güth, W., Müller, W., Strobel, N., 2000. An experimental analysis of
https://doi.org/10.1023/A:1026589319018
CC E
Carbone, E., Hey, J. D., 2001. A test of the principle of optimality. Theory and Decision 50, 263–281. https://doi.org/10.1023/A:1010342908638
A
Fehr, E., Tyran, J.R., 2001. Does money illusion matter? American Economic Review 91, 1239–1262. http://www.jstor.org/stable/2677924
Fehr, E., Tyran, J.R., 2007. Money illusion and coordination failure. Games and Economic Behavior 58, 246–268. https://doi.org/10.1016/j.geb.2006.04.005 28
Fisher, I., 1928. The Money Illusion. Longmans: Toronto. Hey, J. D., Dardanoni, V., 1988. Optimal consumption under uncertainly: An investigation.
Economic
Journal
98,
105–116.
IP T
experimental
http://www.jstor.org/stable/2233308
SC R
Hey, J. D., Knoll, J. A., 2011. Strategies in dynamic decision making—An experimental investigation of rationality of decision behavior. Journal of Economic Psychology 32,
U
399–409. https://doi.org/10.1016/j.joep.2011.02.011
N
Houser, D., Winter, J., 2004. How do behavioral assumptions affect structural inference?
M
A
Evidence from a laboratory experiment. Journal of Business and Economic Statistics 22, 64–79. https://doi.org/10.1198/073500103288619386
ED
Johnson, S., Kotlikoff, L., Samuelson, W., 1987. Can people compute? An experimental
PT
test of the life cycle consumption model. Working Paper, Harvard University.
CC E
Kahn, M. E., 2005. The death toll from natural disasters: The role of income, geography, and institutions. Review of Economics and Statistics 87, 271–284.
A
Kahneman, D, Knetsch, J. K., Thaler, R., 1986. Fairness as a constraint on profit seeking: entitlements
in
the market.
American Economic Review 76, 728–741.
http://www.jstor.org/stable/1806070 Noussair, C. N., Richter, G., Tyran, J.R., 2012. Money illusion and nominal inertia in
29
experimental
asset markets.
Journal
of
Behavioral
Finance
13,
27–37.
https://doi.org/10.1080/15427560.2012.654546
Economics 112, 341–374. https://doi.org/10.1162/003355397555208
IP T
Shafir, E., Diamond, P. A., Tversky, A., 1997. Money illusion. Quarterly Journal of
SC R
Thaler, R., Tversky, A., Kahneman, D., Schwartz, A., 1997. The effect of myopic loss aversion on risk taking: an experimental test. Quarterly Journal of Economics 112,
U
647–661. https://doi.org/10.1162/003355397555226
N
Tukey, J. W., 1977. Exploratory Data Analysis. Boston: Addison-Wesley Publishing..
model.
Quarterly
M
A
Tversky, A., Kahneman D., 1991. Loss aversion in riskless choice: A reference-dependent Journal
of
A
CC E
PT
ED
https://doi.org/10.2307/2937956
30
Economics
106,
1039–1061.
S0167-2681(17)30323-2 https://doi.org/10.1016/j.jebo.2017.11.019 JEBO 4201
To appear in:
Journal
Received date: Revised date: Accepted date:
10-2-2017 22-11-2017 23-11-2017
of
Economic
Behavior
&
Organization
Please cite this article as: Yamamori, Tetsuo, Iwata, Kazuyuki, Ogawa, Akira, Does Money Illusion Matter in Intertemporal Decision Making?.Journal of Economic Behavior and Organization https://doi.org/10.1016/j.jebo.2017.11.019 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Does Money Illusion Matter in Intertemporal Decision Making?
a
IP T
Tetsuo Yamamoria,§1, Kazuyuki Iwatab, Akira Ogawac Faculty of Economics, Dokkyo University, 1-1 Gakuen-cho, Soka, Saitama 340-0042,
b
SC R
Japan. Email: [email protected]
Faculty of Economics, Matsuyama University, 4-2 Bunkyo-cho, Matsuyama, Ehime
790-8578, Japan. Email: [email protected]
College of Liberal Arts, International Christian University, 3-10-2 Osawa, Mitaka, Tokyo
U
c
A
CC E
PT
ED
M
A
N
181-8585, Japan. Email: [email protected]
§1
Corresponding author: Tetsuo Yamamori, Faculty of Economics, Dokkyo University, 1-1,
Gakuen-cho, Soka, Saitama 340-0042, Japan. Phone: +81-48-943-2217, Fax: +81-48-943-2217, Email: [email protected]. 1
Highlights We conduct an experiment for an intertemporal consumption/savings problem.
We examine how price fluctuations affect an individual consumption behavior.
The misconsumption is significantly high if the commodity price is fluctuated.
The price fluctuations strengthen the oversaving behavior.
IP T
Abstract
SC R
To examine the degree to which price fluctuations affect how individuals approach an
intertemporal decision-making problem, we conduct a laboratory experiment in which
U
subjects spend their savings to purchase only one commodity over 20 periods. In the
A
N
control treatment, the commodity price is constant across all periods. In the small (large)
M
price-fluctuation treatment, the price rate of change is always 1% (20%). Regardless of
ED
the treatment, the commodity price and subjects’ savings change at the same rate over time. Therefore, the optimal amount of consumption is the same in all three treatments.
PT
Our main findings are twofold. First, the magnitude of misconsumption (i.e., the deviation
CC E
from optimal consumption) is significantly high, with the large price-fluctuation treatment being the highest, followed by the small price-fluctuation treatment and then
A
the control treatment. Second, regardless of the presence of price fluctuations, subjects exhibit underconsumption (oversaving) behavior, and price fluctuations strengthen this tendency.
2
Keywords: intertemporal decision making; money illusion; price fluctuations; economic experiment. JEL Classification: C91, D91, E31
IP T
Funding: This study was financially supported by JSPS KAKENHI [Grant Number
SC R
24730169].
U
1. Introduction
N
Much research has been devoted to examining how people approach intertemporal
M
A
decision-making (IDM) problems. IDM is a key formulation of dynamic models in financial theory, operations research, game theory, and micro- and macroeconomic theory,
ED
within which agents are usually assumed to be unboundedly rational and able to solve
PT
dynamic programming problems. However, the results of previous studies of experiments
CC E
on IDM suggest that individuals are unable to correctly identify the optimal strategy even though they try to solve complex decision problems rationally (Johnson et al., 1987; Hey
A
and Dardanoni, 1988; Anderhub et al., 2000; Carbone and Hey, 2001; Houser and Winter, 2004; Hey and Knoll, 2011). Furthermore, the mistakes made by subjects are systematic, and they seem to adopt some heuristics or rules-of-thumb for dynamic problems. For example, Johnson et al. (1987) conducted a series of experiments associated with a life
3
cycle model and found that most subjects exhibit oversaving behavior. Carbone and Hey (2001) found in their moderately easy dynamic decision problem that many subjects used
IP T
backward induction and ignored the fact they would be behaving optimally thereafter.1 In real life, people fail to optimize IDM not only because such problems are too
SC R
complex to solve (i.e., poor numeracy) but also because most transactions are in nominal
terms, and prices are not always constant; in other words, people may suffer from “money
U
illusion.” The concept of money illusion refers to the tendency for people to make
N
economic decisions based on nominal rather than real monetary values. Money illusion
M
A
has long been recognized (Fisher, 1928) and is often mentioned to explain economic phenomena such as the rigidity of nominal prices and wages. To date, substantial proof
ED
of the existence of money illusion has been reported by experimental studies (Kahneman
PT
et al., 1986; Shafir et al., 1997; Thaler et al., 1997; Fehr and Tyran, 2001, 2007; Noussair
CC E
et al., 2012), and its influence on the economy cannot therefore be disregarded. The purpose of this study is to investigate how price fluctuations influence individuals’
A
choices in an intertemporal consumption/savings problem. As the nominal terms that people face change over time in association with price fluctuations, it is necessary to
1
Some authors classify the types of strategies that seem to be applied in a dynamic decision
problem. For example, see Hey and Knoll (2011). 4
examine whether money illusion distorts their economic decisions. How do these changing nominal terms influence individuals’ consumption/savings behavior? Does the
IP T
volatility of price fluctuations affect individuals’ welfare? This study investigates these questions using a laboratory experiment.
SC R
Although experimental studies of money illusion have shown that nominal frames
often influence individuals’ decisions, the underlying decision problems in most of these
U
works are static, or a repetition of a static problem in which the nominal frame changes
N
only once. For example, Fehr and Tyran’s (2001) subjects repeatedly played a price-
M
A
setting game. They showed that the average price in the aftermath of a monetary shock converges to the equilibrium more slowly when the game is presented in a nominal frame
ED
than in a real frame. However, this difference does not emerge when all the opponents are
PT
computer programs; in other words, money illusion does not matter in a repeated static
CC E
problem without strategic interactions. Noussair et al.’s (2012) experiment, in which subjects repeatedly played a continuous double auction by trading shares, is an exception.
A
Further, subjects’ stock of shares was carried over from one trading period to the next implying that the situation intrinsically posed an IDM problem. However, their research focused on aggregate market behavior rather than on individual behavior, and they showed that real asset market prices increase after a monetary deflationary shock but
5
remain unaffected by a monetary inflationary shock. Moreover, as shown by Fehr and Tyran (2001), due to the indirect effect of money illusion, the effect of monetary shock on games with strategic interaction need not necessarily imply an effect on IDM
IP T
problems. 2 Thus, the question of how ongoing price fluctuations affect individual
SC R
behavior in IDM problems remains.
Our study is based on an economic experiment in which subjects face a simple IDM
U
problem with a lifetime of 20 periods. At the beginning, a subject possesses 40,000
N
points (experimental currency units) in his/her savings account to spend during these 20
M
A
periods (hereafter, we use “his” for simplicity). Additional money is not credited to a subject’s account. In each period, he can spend his savings to buy only one commodity.
ED
His overall payoff is the sum of an instantaneous payoff, which is given by the square
PT
root of the consumption amount. The commodity price in the first period is 80 points.
CC E
Over time, the subject’s savings and commodity price change at the same rate. In any period, subjects do not directly choose the amount of the commodity but only their
A
expenditure on it. In our experiment, price fluctuations are irrelevant to the budget set,
2
Fehr and Tyran (2001) divided the effects of money illusion into direct and indirect effects. The
former directly result from individual optimization mistakes whereas the latter arise because some agents behave differently based on their expectation that others would be prone to money illusion. Following this classification, our research focuses only on the direct effects of money illusion. 6
and there is no uncertainty in the payoffs. We conducted three treatments. In the control treatment, price is constant across all
IP T
periods. In the other two treatments, price and savings fluctuate over time. In both these treatments, price increases, decreases, or does not change at the beginning of each period.
SC R
Each of these events occurs with an equal probability. In the small and large pricefluctuation treatments, the rate of change is always 1% and 20%, respectively. Because
N
of consumption is the same in all three treatments.
U
the subject’s savings and commodity prices change at the same rate, the optimal amount
M
A
We first tested the hypothesis that money illusion does not matter. This hypothesis was rejected by the results of our experiment showing that the magnitude of misconsumption
ED
is large when price fluctuations are large. Shafir et al. (1997) stated that money illusion
PT
is observed even in highly inflationary environments despite expecting “to find greater
CC E
awareness of the difference between nominal and real values when inflation is high than when it is low.” The previous observation suggests that money illusion appears more
A
strongly when price fluctuations are larger, which seems to be a stronger claim than the statement by Shafir et al. (1997). Furthermore, it follows that the actual payoffs of subjects in the control treatment are significantly higher than those in the large pricefluctuation treatment.
7
The hypothesis is concerned with only the absolute values of misconsumption rather than its direction (i.e., over- or underconsumption). As mentioned above, previous studies
IP T
of IDM experiments have shown that subjects’ mistakes are not random but rather systematic. Therefore, we also examined the direction of misconsumption in our
SC R
experiment. The results showed that our subjects displayed underconsumption (oversaving) behavior. Furthermore, we found that price fluctuations strengthen the
U
tendency toward such behavior.
N
The rest of the paper is organized as follows. In Section 2, we describe our experimental
M
A
design. In Section 3, the experimental results are presented. In Section 4, we summarize
PT
2. Experiment
ED
our results and argue their implications.
CC E
2.1. Experimental design and procedure We consider a simple IDM problem with a lifetime of 20 periods. At the beginning, a
A
subject possesses 40,000 points (experimental currency units) in his savings account to spend during these 20 periods. Additional money is not credited to his account. In each period, he can spend his savings to buy only one commodity. Let 𝑥𝑡 be the amount of the commodity purchased in period 𝑡; then, his payoff function is given by
8
∑
20
√𝑥𝑡 .
𝑡=1
The instantaneous payoff √𝑥𝑡 is a constant-relative, risk-aversion utility function with a
IP T
coefficient of 1⁄2. The discount rate is always 1, and the money that remains after period 20 is irrelevant to his payoff. This setup is like the experimental design in Anderhub et al.
SC R
(2000); however, we eliminate uncertainty to reduce the “poor numeracy” effect. Their experiment was based on a dynamic decision problem with an uncertain time horizon:
U
subjects had to allocate a given monetary amount over an uncertain number of periods.
N
Such uncertainty complicates the optimization problem dramatically, and therefore, the
M
A
result of the experiment may contain both “poor numeracy” and “money illusion.” In our setting, the calculation for optimization is sufficiently simple for all subjects.
ED
The experimental design consists of three treatments. Regardless of the treatment, the
PT
commodity price in the first period is 80 points; both the subject’s savings remaining in
CC E
his account and the commodity price change at the same rate over time. In the control treatment, denoted by C, price is constant across all periods. In the large (small) price-
A
fluctuation treatment, denoted by L (S), price increases by 20% (1%), decreases by 20% (1%), or is unchanged at the beginning of each period. Each event occurs with an equal probability. Because price and savings always change at the same rate, price fluctuations are irrelevant to the budget of a subject and are therefore irrelevant to his optimal
9
consumption. Thus, all treatments differ only in their nominal terms, and actual consumption in L and S should be the same as that in C if a subject’s decisions are based
IP T
only on real monetary values. As there is no uncertainty in the payoffs, the risk attitude of subjects should not affect their decisions.
SC R
It is easy to see that the sequence (𝑥𝑡 )20 𝑡=1 of consumption, in which 𝑥𝑡 = 25 for any 𝑡, maximizes a subject’s overall payoff. However, once a subject’s consumption deviates
U
from such optimality, this consumption sequence is no longer optimal for the remaining
N
periods. Let 𝑝𝑡 and 𝑀𝑡 be the commodity price and amount of money remaining in his
M
A
savings account in period 𝑡 , respectively. Then, in any period 𝑇 , the payoff in the 20 remaining periods, that is, ∑20 𝑡=𝑇 √𝑥𝑡 , is maximized by the sequence (𝑥𝑡 )𝑡=𝑇 of
ED
consumption, in which
PT
𝑥𝑡 = 𝑥(𝑚 𝑇 ) =
𝑚𝑇 (20 − 𝑇 + 1)
CC E
for all 𝑡, where 𝑚 𝑇 = 𝑀𝑇 ⁄𝑝𝑇 is the real value of savings in period 𝑇. Thus, optimal consumption depends only on real terms, instead of any nominal variables, including
A
future prices.
Our experiment was conducted at Takasaki City University of Economics. We recruited
subjects by displaying posters and distributing fliers. They were undergraduate students from several faculties at the university that had not participated in any prior IDM
10
experiments; furthermore, each subject could only participate in one treatment. All treatments were conducted in the same laboratory, and each computer terminal in the
IP T
laboratory was assigned a computer program associated with one of the treatments. Subjects were seated in front of a computer terminal at random. Each desk had a
SC R
calculator and an envelope containing all the experimental materials, including the
instructions, and a recording sheet. During the experiment, subjects could use the
U
calculator on the desk at any time. The total number of subjects who participated in (i.e.,
N
was assigned a computer terminal with) treatments C, S, and L was 20, 21, and 23,
M
A
respectively.
Each subject was asked to carefully read the instructions, which provided all the
ED
information about the structure of the treatment to which they had been allocated,
PT
including the price distribution. Before the actual experiment began, subjects were told
CC E
to solve the practice problems to confirm they understood the instructions for the experiment. All practice problems were the same in the three treatments. The problem set
A
contained a simple IDM problem with two periods and without price fluctuations to suggest that consumption smoothing is always optimal for any remaining periods.3 No subject could begin the actual experiment unless all problems had been answered
3
The instructions and the practice problems are presented in the Appendix. 11
correctly. In each period of the actual experiment, each subject was asked to input his expenditure on the commodity for the current period. In other words, subjects did not choose the
IP T
amount of commodity 𝑥𝑡 directly, but rather chose expenditure on the commodity,
SC R
𝑝𝑡 𝑥𝑡 4. On the computer screen, each subject could always observe the amount of money he currently held in his savings account, the current commodity price, and the percentage
U
price change from the previous period. Past consumption and expenditure were also
A
M
the next period automatically began.
N
displayed on the screen.5 Once the expenditure for the current period had been entered,
Decision-making time was not restricted. Therefore, the session duration differed by
ED
participant but was approximately one hour for most subjects. After the experiment, each
PT
subject was asked to answer a questionnaire. The reward given to the subjects was a kind
CC E
of two-part tariff: the fixed participation fee was ¥500, and proportional payment was ¥14 × realized payoff shown at the beginning of this section. The reward was paid in cash to
While the nominal variables do not affect optimal consumption, they do affect optimal
A
4
expenditure, which is given by 𝑝𝑡 𝑥(𝑚𝑡 ) in period 𝑡. 5
The instantaneous payoff or the payoff at an instant was not displayed on the screen. However, if
subjects wanted to know the amount, they could get it using the displayed information and the calculator. 12
each subject privately after the session. Subjects earned on average ¥1,579. 2.2. Hypotheses Our analysis focuses on the difference between actual and optimal consumption (hereafter
IP T
misconsumption) in each treatment. For treatment A ∈ {𝐶, 𝐿, 𝑆} , let 𝐷𝑡𝐴 be the
SC R
misconsumption in period 𝑡 in treatment 𝐴 and let |𝐷𝑡𝐴 | be its absolute value. Because
optimal consumption 𝑥(𝑚𝑡 ) in period 𝑡 is the same for all treatments, 𝐷𝑡𝐴 can be
U
written as 𝐷𝑡𝐴 = 𝑥𝑡𝐴 − 𝑥(𝑚𝑡 ), where 𝑥𝑡𝐴 is actual consumption in period 𝑡 in
A
M
on 𝐷𝑡𝐴 when analyzing its direction.
N
treatment 𝐴. We focus on |𝐷𝑡𝐴 | when analyzing the magnitude of misconsumption and
The impact of price fluctuations throughout all periods can be measured by the
ED
difference in |𝐷𝑡𝐴 | in the entire study period between C and L, or between C and S. Thus,
CC E
on average:
PT
we test the following hypothesis that price fluctuations do not affect subjects’ behavior
Hypothesis 1: On average, money illusion does not matter.
A
∑
19
( |𝐷𝑡𝐿 | − |𝐷𝑡𝐶 |) = 0, 𝑎𝑛𝑑 ∑
𝑡=1
19
( |𝐷𝑡𝑆 | − |𝐷𝑡𝐶 |) = 0.
𝑡=1
Observations for the 20th period are excluded because subjects could easily choose to
consume their remaining points in the last period without considering or calculating their optimal consumption.
13
As mentioned in the introduction, previous studies of IDM experiments have shown that deviations from the optimal solution of subjects’ behavior are not random but rather
following hypothesis:
∑
19
SC R
Hypothesis 2: Deviations from the optimal solution are random.
IP T
systematic. Thus, we also test this observation in our experiment by formulating the
𝐷𝑡𝐴 = 0 for any 𝐴 ∈ {𝐶, 𝐿, 𝑆}.
𝑡=1
U
The subjects in our experiment can make mistakes in two ways, namely
N
underconsumption (oversaving), that is, 𝐷𝑡𝐴 < 0, or overconsumption (undersaving), that
M
A
is, 𝐷𝑡𝐴 > 0. In each treatment, if their misconsumption does not tend toward either
ED
mistake, this hypothesis should be supported.
PT
3. Results
CC E
This section discusses the experimental results. The total number of observations in our experiment is 1,280 (= (20+21+23) ×20) because each subject makes decisions over 20
A
periods and the number of subjects is 20, 21, and 23 in C, S, and L, respectively. Among the observations, some subjects always make extraordinary decisions because they may not understand the experiment. To avoid such extraordinary decisions potentially influencing the results, from the sample of 64 subjects, we drop two subjects whose
14
decisions were all in the 95th percentile.6 In addition, observations for the 20th period are excluded. Consequently, 1,178 observations are used for our analysis. 3.1. Tests for Hypothesis 1
IP T
We first focus on the magnitude of misconsumption |𝐷𝑡𝐴 |. To illustrate all results for
SC R
|𝐷𝑡𝐴 |, Figure 1 presents the distributions for each treatment, along with the number of
U
observations, means, and standard deviations for each treatment.
0
ED
.02
.04
M
S. D. = 25.07
Obs. = 399 Mean = 20.37 S. D. = 32.44
A
.06
Obs. = 361 Mean = 13.91
PT
.08
L (20% fluctuation)
Total
Obs. = 418 Mean = 27.23
Obs. = 1178 Mean = 20.82 S. D. = 31.13
S. D. = 33.26
0
.02
CC E
.04
.06
Density
S (1% fluctuation)
N
.08
C (constant price)
100
200
300
0
100
200
300
absolute value of the misconsumption
A
0
Figure 1. Distribution of the absolute value of misconsumption
6
Even when we do not drop the two subjects, the trend of the estimation results is the same as
before. 15
Note: “S.D.” means standard deviation.
It is found that many subjects have a small amount of misconsumption that approaches
IP T
0. However, in the comparison among the three treatments, the fractions of subjects with small amounts of misconsumption in C and S are larger than that in L. The order of the
SC R
magnitude of the means is mean (C) < mean (S) < mean (L), which implies that subjects
facing high price fluctuations are likely to mistake their decisions. We test these
U
observations using the following econometric analysis.
N
We regress the absolute value of misconsumption on the treatment dummies and other
M
A
control variables that may affect subjects’ intertemporal decisions, such as individual characteristics. Let |𝐷𝑖𝑡 | be the absolute value of misconsumption of subject 𝑖 at
ED
period 𝑡, and 𝑇𝑆𝑖 and 𝑇𝐿𝑖 be dummy variables that take a value of 1 if he is assigned to
PT
S and L, respectively. The period is denoted as 𝑅𝑡 , which is a scale variable that takes
CC E
values of 1 to 19. 𝑿𝑖 is a control variable vector for capturing subject 𝑖’s characteristics that affect misconsumption. To obtain the subjects’ characteristics, a questionnaire survey
A
was conducted at the end of the experiment. To control for unobserved heteroscedastic effects, the individual fixed effect, 𝜇𝑖 , is incorporated. The idiosyncratic error term is represented as 𝜀𝑖𝑡 . The model for testing Hypothesis 1 is written as follows: ln(|𝐷𝑖𝑡 |) = 𝑿𝒊 𝑨′ + 𝑎1 𝑇𝑆𝑖 + 𝑎2 𝑇𝐿𝑖 + 𝑎3 𝑅𝑡 +𝜇𝑖 + 𝜀𝑖𝑡 16
where vector 𝑨, and 𝑎𝑘 (𝑘 = 1,2,3) are the parameters to be estimated. If insignificant 𝑎̂1 and 𝑎̂2 (estimated coefficients) are observed by estimating this equation, Hypothesis
IP T
1 is supported. Otherwise, money illusion matters on average in terms of individual IDM. Figure 1 indicates that the absolute values of misconsumption are highly skewed. To
SC R
avoid such skewness, logarithmic transformation is frequently used. However, zero-value problem arises in performing the transformation because 135 observations (11.5%) have
U
a zero value. Therefore, we add 10-16 to the absolute value of misconsumption and then
N
convert it into a logged variable (i.e., ln(𝐷𝑖𝑡 + 10−16 )), similar to the approach adopted
M
A
by Kahn (2005).7
The descriptive statistics for the explanatory variables are shown in Table 1. The
ED
variables Male, Faculty, and Alone are dummies that take a value of 1 if subjects are men,
PT
if they are students of the Faculty of Economics, and if they live on their own,
CC E
respectively.8 Unlike most studies, instead of age, we use Grade to represent respondents’ grade, which takes a value of 1 to 4. In optimal decision making, rationality is a key issue.
Kahn (2005) added 1 to the dependent variables to avoid the zero-value problem. However, we
A
7
add 10-16 because a 1-value increment may drastically change the distribution of |𝐷𝑡𝐴 | (see Figure 1). 8
There are two faculties in the Takasaki City University of Economics: Faculty of Economics and
Faculty of Regional Policy. 17
People who are good at mathematics may be more likely to choose optimal consumption. We therefore ask them the extent to which they are good at mathematics (Favorite for Math), which is a scale variable with five levels (1 and 5 indicate “my favorite subject is
IP T
mathematics” and “my least favorite subject is mathematics,” respectively). Income is
SC R
also a scale variable that takes a value of 1 (no income) to 7 (more than ¥100,000 per month). In addition to the described control variables, the survey contained five question
U
items associated with knowledge about economics keywords: inflation, deflation,
N
nominal wage, long-term bonds, and the real exchange rate. Each subject responded to
M
A
all questions using five-point scales, with 1 and 5 representing “I know the word well”
ED
and “I do not know the word at all,” respectively.
Table 1. Descriptive statistics of the explanatory variables
A
CC E
PT
Variables Mean S. D. Min. Max. S (1%) dummy 0.34 0.47 0 1 L (20%) dummy 0.35 0.48 0 1 Period 10.00 5.48 1 19 Male 0.73 0.45 0 1 Grade 2.24 0.98 1 4 Faculty 0.68 0.47 0 1 Alone 0.76 0.43 0 1 Favorite for Math 3.66 1.11 1 5 Income 3.40 1.89 1 7 Knowledge: inflation 1.52 0.62 1 4 Knowledge: deflation 1.55 0.69 1 4 Knowledge: nominal wage 3.26 1.23 1 5 Knowledge: long-term bond 2.60 1.07 1 5 Knowledge: real exchange rate 2.97 1.05 1 5
18
The estimation results for the equation that tests Hypothesis 1 are presented in Columns (1) and (2) of Table 2. As a robustness check, two models (with and without individual
IP T
fixed effects, respectively) are employed. They show that subjects in the L treatment are likely to mistake their decisions at the 1% significance level relative to those in the C
SC R
treatment. This finding implies that people cannot make optimal consumption decisions
under large price fluctuations. The coefficients of the S dummy in Columns (1) and (2)
U
also suggest that subjects may make suboptimal intertemporal decisions relative to C.
N
Specifically, the magnitude of misconsumption in L is larger than that in S, suggesting
M
A
that subjects are likely to mistake their decisions as the fluctuation rate rises.9 Regarding the other variables, men may be likely to consume closer to the optimal level
ED
than women, although the coefficient in Column (2) is not significant. Students who study
PT
economics as their majors may optimally consume more compared with non-economics
CC E
students, while students living alone tend to have small misconsumption levels relative to those living with their families. Although the coefficients of grade are statistically
A
significant in both Columns (1) and (2), the signs are the opposite of each other (i.e., negative and positive signs are obtained in Columns (1) and (2), respectively). Moreover, Favorite for math is found to be statistically related to IDM only in Column (2). The 9
These results are also supported by the Wilcoxon–Mann–Whitney test and the t test. 19
positive sign indicates that students who are good at mathematics are likely to choose their consumption more rationally. The sign of the coefficients of income is also
IP T
significant and positive only in Column (2). The results may thus reflect that subjects in higher grades and with higher income levels aim to finish the experiment as quickly as
SC R
possible because their opportunity costs are larger than those of students with lower
grades and income levels. Additionally, it is found that knowledge of economics has a
U
significant influence on consumption. Knowledge of inflation and long-term bonds is
N
significant and negative, implying that knowledge of economics makes people choose
M
A
correctly with respect to the magnitude of misconsumption.
A
CC E
PT
ED
Table 2. Estimation results for testing Hypothesis 1
20
Alone Favorite for Math Income Knowledge: inflation Knowledge: deflation Knowledge: nominal wage Knowledge: long-term bond
no 27.42*** 0.239
yes 33.95*** 0.635
ED
Knowledge: real exchange rate
PT
Constant
CC E
Individual fixed effects F-value Adj. R-squared
IP T
Faculty
SC R
Grade
U
Male
4.531* (2.553) 12.61*** (1.314) -0.0868* (0.0518) -3.227 (2.117) 6.190*** (0.860) -5.461*** (2.103) -11.15*** (1.907) 3.169*** (0.574) 2.213*** (0.334) -14.96*** (3.635) 12.80*** (2.978) 2.077** (1.034) -1.254*** (0.314) 0.250 (1.162) -38.26*** (2.891)
N
Period
8.789*** (1.124) 9.548*** (0.909) -0.0868 (0.0665) -4.637*** (0.599) -1.584*** (0.457) -1.570** (0.778) -4.567*** (0.526) -0.340 (0.308) 0.119 (0.198) -1.079 (1.805) 2.567 (1.682) -0.469 (0.317) -1.176*** (0.421) -0.160 (0.405) 7.072** (3.115)
A
L (20%) dummy
(2)
M
S (1%) dummy
(1)
Note: Robust standard errors are in parentheses; ***, **, and * represent the 1%, 5%, and 10%
A
significance levels, respectively.
3.2. Tests for Hypothesis 2 To assess whether subjects’ misconsumption shows a trend toward under- or overconsumption, we next focus on the results for 𝐷𝑡𝐴 . Table 3 shows the descriptive 21
statistics of 𝐷𝑡𝐴 for each treatment, and the results of the t test for which the null hypothesis is that the mean equals zero. Their box plots are also illustrated in Figure 2.
IP T
We find that regardless of the presence of price fluctuations, subjects purchase only a small quantity compared with the optimal one, that is, they show underconsumption
SC R
(oversaving) behavior overall. Such a tendency for subjects to make mistakes was also
L (20% fluctuation) -9.83*** -12.28 41.87
A
S (1% fluctuation) -13.13*** -1.01 35.99
M
C (Control) mean -3.22** median 0.00 S.D. 28.50
N
Table 3. Descriptive statistics of misconsumption
U
reported by Johnson et al. (1987) and Anderhub et al. (2000).
Note: The null hypothesis under the t test is that the mean is equal to zero; ***, **, and * represent
A
CC E
PT
ED
the 1%, 5%, and 10% significance levels, respectively.
22
50
IP T
0
SC R
-50
U
-100
S (1% price fluctuation)
L (20% price fluctuation)
N
C (constant price)
A
Figure 2. Box plots of misconsumption
Note: The bold horizontal lines represent medians. Ranges between the 25th to 75th percentiles are
M
expressed as boxes drawn in gray. The upper and lower adjacent lines are obtained from the procedure defined by Tukey (1977). The maximum and minimum values, which are usually represented by the
PT
ED
line segments of the box, are omitted.
Furthermore, by comparing the box plot of C with those of the other treatments, we see
CC E
that the existence of price fluctuations seems to strengthen the over-saving behavior of subjects. This observation is confirmed by the Wilcoxon–Mann–Whitney test results in
A
Table 4.
Table 4. Wilcoxon–Mann–Whitney test for Hypothesis 2
23
X C (constant Price) Y S (1% flactuation)
S (1% flactuation) -2.41 ** -
L (20% flactuation) -5.20 *** -1.76 *
Note: The null hypothesis under the test is that the distribution of X is equal to that of Y. The Wilcoxon statistic, which is approximately a standard normal random variable, is calculated based on the sum of
IP T
the ranks of the observations of X; ***, **, and * represent the 1%, 5%, and 10% significance levels,
SC R
respectively.
3.3. Payoff comparison among treatments
U
Earlier, we found that, on average, the magnitude and tendencies of misconsumption
N
differ among treatments. In this subsection, we focus on the payoffs described in Section
M
A
2. Note that the number of observations here is 62 because each subject has only one payoff. Moreover, these payoffs are not the same as the rewards that subjects received
ED
after the experiment since the rewards include the participation fee.
PT
The distribution of the payoff for each treatment is presented in Figure 3. In this figure,
CC E
the mean, standard deviation, and median are also presented. The Wilcoxon–Mann– Whitney test results in Table 5 show that the payoff distributions between C and L, and S
A
and L are different at the 1% and 5% significance levels, respectively, whereas there is no significant gap between C and S.
24
S (1% price fluctuation) Obs. = 21 Mean = 78.31 S. D. = 29.44 Median = 90.41
Total
Obs. = 22
Obs. = 62 Mean = 78.57 S. D. = 24.33 Median = 83.99
Mean = 72.16 S. D. = 22.33
0
50
100 0
50
100
A
Payoff
N
0
U
Median = 75.82
SC R
.05
L (20% price fluctuation)
IP T
Obs. = 19 Mean = 86.28 S. D. = 18.66 Median = 92.75
0
Density
.05
C (constant price)
ED
Note: “S. D.” means standard deviation.
M
Figure 3. Distribution of the payoff by treatment
Table 5. Wilcoxon–Mann–Whitney test for payoffs among treatments
PT
C (constant Price) S (1% fluctuation)
CC E
Y
X
S (1% fluctuation) -0.66 -
L (20% fluctuation) -2.75 *** -2.04 **
Note: The null hypothesis under the test is that the distribution of X is equal to that of Y. The Wilcoxon statistic, which is approximately a standard normal random variable, is calculated based on the sum of the ranks of the observations of X; ***, **, and * represent the 1%, 5%, and 10% significance levels,
A
respectively.
4. Concluding remarks Previous studies have focused on how people approach dynamic consumption decision
25
problems because it is often observed that they fail to choose optimal consumption. One of the reasons is that the individual recognizes nominal term and price fluctuations, that
IP T
is, money illusion. To study how money illusion affects individual IDM, a laboratory experiment was conducted, in which subjects spent their savings on consumption over 20
SC R
periods, without interaction with other subjects. We compared three treatment groups: a
constant price (C) and 1% (S) and 20% (L) price-fluctuation treatments. In all treatments,
U
the optimal consumption is irrelevant to the price fluctuations, because commodity prices
N
and savings simultaneously change at the same rate. In other words, optimal consumption
M
A
depends only on real terms instead of nominal terms.
Findings based on our data are twofold. First, the magnitude of the deviation from
ED
optimal consumption in all periods is significantly high, with the large price-fluctuation
PT
treatment highest, followed by the small price-fluctuation treatment and then the control
CC E
treatment. Thus, regardless of their size, price fluctuations influence individuals’ optimization. In other words, money illusion matters in IDM problems, and this effect is
A
significant if price fluctuations are large. Then, the actual payoffs of subjects in the C treatment are significantly higher than those in the L treatment. Second, regardless of the presence of price fluctuations, subjects purchase only a small quantity compared with the optimal amount. In other words, subjects show underconsumption (oversaving) behavior.
26
Furthermore, we find that price fluctuations strengthen the tendency toward such behavior. Johnson et al. (1987) found in their IDM experiment that most subjects display over-
IP T
saving behavior because they underestimate the power of compound interest. Their experiment was based on a questionnaire in which the subjects choose annual
SC R
consumption under a hypothetical life scenario from the age of 35 until death at 75. Unlike our study, there is a fixed amount of income each year until the age of 65, and debt and
U
savings are possible with a real interest rate of 4%. Our experimental result shows that
N
even when the real interest rate is 0%, and hence, regardless of whether the subjects know
M
A
the power of compound interest or not, they display oversaving behavior. Why do our subjects save excessively even though there is no uncertainty and the real
ED
interest rate is 0%? One possible explanation is that they dislike decreasing a nominal
PT
amount of the savings account. There is plenty of evidence that people tend to prefer
CC E
avoiding loses to acquiring gains, i.e., people tend to “loss aversion.”10 However, it is not clear why price fluctuations strengthen oversaving behavior. Further experimental studies
A
are necessary to investigate how loss aversion affects individual behavior in IDM problems with and without price fluctuations. Our experiment examined the effects of the magnitude of stochastic price fluctuations 10
For example, see Tversky and Kahneman (1991). 27
on IDM. However, individuals’ choices in IDM may also be distorted by inflationary and deflationary trends in price fluctuations. Exploring how these trends affect an individual’s
SC R
IP T
IDM thus remains a task for future research.
Acknowledgments
A
N
U
We would like to thank Toshiji Kawagoe and Yoich Gokan for their helpful comments.
M
References
allocation
behavior.
Experimental
Economics
3,
137–152.
PT
intertemporal
ED
Anderhub, V., Güth, W., Müller, W., Strobel, N., 2000. An experimental analysis of
https://doi.org/10.1023/A:1026589319018
CC E
Carbone, E., Hey, J. D., 2001. A test of the principle of optimality. Theory and Decision 50, 263–281. https://doi.org/10.1023/A:1010342908638
A
Fehr, E., Tyran, J.R., 2001. Does money illusion matter? American Economic Review 91, 1239–1262. http://www.jstor.org/stable/2677924
Fehr, E., Tyran, J.R., 2007. Money illusion and coordination failure. Games and Economic Behavior 58, 246–268. https://doi.org/10.1016/j.geb.2006.04.005 28
Fisher, I., 1928. The Money Illusion. Longmans: Toronto. Hey, J. D., Dardanoni, V., 1988. Optimal consumption under uncertainly: An investigation.
Economic
Journal
98,
105–116.
IP T
experimental
http://www.jstor.org/stable/2233308
SC R
Hey, J. D., Knoll, J. A., 2011. Strategies in dynamic decision making—An experimental investigation of rationality of decision behavior. Journal of Economic Psychology 32,
U
399–409. https://doi.org/10.1016/j.joep.2011.02.011
N
Houser, D., Winter, J., 2004. How do behavioral assumptions affect structural inference?
M
A
Evidence from a laboratory experiment. Journal of Business and Economic Statistics 22, 64–79. https://doi.org/10.1198/073500103288619386
ED
Johnson, S., Kotlikoff, L., Samuelson, W., 1987. Can people compute? An experimental
PT
test of the life cycle consumption model. Working Paper, Harvard University.
CC E
Kahn, M. E., 2005. The death toll from natural disasters: The role of income, geography, and institutions. Review of Economics and Statistics 87, 271–284.
A
Kahneman, D, Knetsch, J. K., Thaler, R., 1986. Fairness as a constraint on profit seeking: entitlements
in
the market.
American Economic Review 76, 728–741.
http://www.jstor.org/stable/1806070 Noussair, C. N., Richter, G., Tyran, J.R., 2012. Money illusion and nominal inertia in
29
experimental
asset markets.
Journal
of
Behavioral
Finance
13,
27–37.
https://doi.org/10.1080/15427560.2012.654546
Economics 112, 341–374. https://doi.org/10.1162/003355397555208
IP T
Shafir, E., Diamond, P. A., Tversky, A., 1997. Money illusion. Quarterly Journal of
SC R
Thaler, R., Tversky, A., Kahneman, D., Schwartz, A., 1997. The effect of myopic loss aversion on risk taking: an experimental test. Quarterly Journal of Economics 112,
U
647–661. https://doi.org/10.1162/003355397555226
N
Tukey, J. W., 1977. Exploratory Data Analysis. Boston: Addison-Wesley Publishing..
model.
Quarterly
M
A
Tversky, A., Kahneman D., 1991. Loss aversion in riskless choice: A reference-dependent Journal
of
A
CC E
PT
ED
https://doi.org/10.2307/2937956
30
Economics
106,
1039–1061.