The Excess Smoothness Puzzle
– An Experimental Investigation of Consumption
Marcus Giamattei
Johann Graf Lambsdorff 
Abstract
We run an experiment where groups of six subjects determine their level of
consumption with a target-level that is proportional to income. All known reasons for
the existence of smoothed levels of consumption have been abandoned, such as
financial reserves or borrowing at the aggregate level, habit persistence, sluggish
arrival of information, current income deviating from permanent income or selfcontrol problems. Nonetheless our consumption varies less than its equilibrium
prediction. While mathematically simple, the challenge of our game arises from, first,
income being determined endogenously, second, subjects failing to observe that
savings are not scarce at the aggregate level, third, equilibrium being driven by nonstationary investments and, fourth, depending on treatment the payoff-dominant
solution might not be a dominant-strategy equilibrium. We find theoretical reasons
for this behavior but suspect that our findings may also relate to sticky reasoning, the
sluggish convergence towards equilibrium due to subjects being cognitively (rather
than habitually) anchored by past data.
JEL Classification: E20, E50, E12
Keywords: Beauty contest, absolute consumption hypothesis, permanent income hypothesis

Marcus Giamattei is Research Assistants at the University of Passau, Germany,
[email protected]. Johann Graf Lambsdorff is chair in economic theory at the University of
Passau, [email protected]. Contact address: Innstrasse 27, D-94032 Passau. The authors are grateful to
Lisa Einhaus for helpful comments.
1
1 Introduction
In his General Theory Keynes (1936: 96-97) stated reasons for consumption to vary less than
income, thus revealing excess smoothness relative to current income:
“…men are disposed, as a rule and on the average, to increase their consumption as
their income increases, but not by as much as the increase in their income… a decline
in income due to a decline in the level of employment, if it goes far, may even cause
consumption to exceed income not only by some individuals and institutions using up
the financial reserves which they have accumulated in better times, but also by the
government, which will be liable, willingly or unwillingly, to run into a budgetary
deficit or will provide unemployment relief; for example, out of borrowed money.”
Keynes relates this to government’s willingness to dampen fluctuations and to individual
habits, standards of life that require time to adapt to new circumstances. This property has
found widespread empirical support for the short term. Longer time horizons repeatedly
revealed evidence in favor of a constant ratio between consumption and income, contrary to
the Keynesian hypothesis. One proposal to explain the data has been proposed by Friedman
(1956). He claims that the ratio is constant between consumption and permanent income. He
relates short-term observations of excess smoothing to a statistical artifact: Households
observe the ups and downs of current income but determine consumption proportionally to
the expected, stable long-run level of their income. This implies that fluctuations of current
income translate to less than proportional changes of permanent income and, thus,
consumption. A less than proportional reaction of consumption to income is then a statistical
illusion, because current income is an excessively volatile proxy for permanent income.
The permanent income hypothesis has experienced various challenges. One criticism was
raised by empirical studies which showed that consumers do not smooth out consumption as
much as predicted by the permanent income hypothesis, (Hall and Mishkin 1982). There
exists an excess reaction to permanent income, while consumption is smooth relative to
current income. Flavin (1981) pointed to an excess dependence of consumption on past
income. Campbell and Deaton (1989) and Deaton (1992) have thus advanced the term
“excess smoothness puzzle”, the excess being in relation to current income. This puzzle has
also become known as the Deaton paradox. Deaton (1992) suggests that habit persistence
may explain a good deal of the puzzle. Habitual levels of consumption are seen to impact the
marginal utility of consumption. A new steady state would not be approached immediately
but rather smoothly as old habits fade out. For a review of theoretical and empirical
approaches that include habits in the determination of consumption see Fuhrer (2000),
Seckin (2001) and Attanasio (1999).1 Goodfriend (1992) observes that sluggish arrival and
inattention to information can also account for explaining the puzzle. Aggregate shocks are
imperfectly perceived such that consumption reacts only slowly to aggregate income. Deaton
(1992: 171-174) observes that such lags in the arrival of information generate consumption
patterns similar to those with habit persistence.
Anomalies in the determination of consumption have recently been observed by reference to
psychological elements (Shefrin and Thaler 1988) or neuroeconomics, (Brocas and Carillo
1
The life-cycle permanent income hypothesis has been criticized on further grounds, such as due to a bequest
motive or market imperfections. These are not further discussed here as they contribute more to reasons why
current income may retain some significance. Their contribution to the excess smoothing puzzle relative to
current income is less clear.
2
2008). Consumers are seen to face a self-control problem. Discounting is steeper in the
immediate future than in the further future. For a review of recent field experiments see
DellaVigna (2009). This has been employed to depart from the permanent income
hypothesis and restate the importance of current income, (Thaler 1990). This strand of
research may also contribute to explaining the excess smoothing puzzle, (Akerlof 2007: 17).
Households may impose discipline on themselves by following the rule that they need to
work more if they want to consume more. Consumption would be tied to costly effort and
subjects suffer from a psychological penalty when they finance consumption from current
assets or future income (Shefrin and Thaler 1988). During a boom, households may obtain
windfall profits. But these windfalls are effortless and little motivate households to increase
consumption. A recession may go along with substantial efforts to resist deprivation but little
income. These efforts may be seen as an entitlement to sustain a high level of consumption.
But what might happen if all these reasons for smoothed consumption are absent? We
conjecture that the puzzle might still survive. Smoothed consumption may also be caused by
limited rationality. Subjects may fail in calculating the equilibrium or may expect others to
fail. Finding equilibria can become cognitively demanding when income is unknown a-priori
and must be forecasted from the behavior expected by all other subjects. This is the type of
complexity already assumed by Keynes (1936: 44) when he notes for the level of income:
“net income is what we suppose the ordinary man to reckon his available income to be when
he is deciding how much to spend on current consumption.”
The task of setting consumption thus requires first to forecast income. Forecast errors may
then account for disequilibrium consumption levels. Such a forecast error was not considered
by Keynes. He notes (1936: 122): “the logical theory of the multiplier [...] holds good
continuously, without time-lag, at all moments of time” . As reviewed by Hoover (1997),
Keynes failed in particular in presenting a consistent approach to the formation of
expectations, treating short-term expectations as fulfilled or deviations to be negligible.
Keynes assumed expected and realized income to be equal. He did not assume unplanned
savings that might result from forecast errors. This was in contrast to adherents to the
Stockholm school, who regarded income forecast errors to be important drivers of unplanned
savings.
Lindahl (1983: 235) criticizes Keynes from the perspective of the Stockholm school and
describes how demanding the task of determining consumption can be: “If consumers plan to
spend a certain fraction of their income during the period, but the income is determined only
after the consumption purchases are finished, the only possibility of avoiding the distinction
between the expected income, which is the basis of the consumption plans, and the realized
income, which is the result of the carrying through of plans […] is to make them equal, i.e.
implicitly to assume that individuals correctly anticipate their income.” In his lecture notes
Keynes (1973: 181) deplored his approach: “I now feel that if I were writing the book again I
should […] have a subsequent chapter showing the difference it makes when short-period
expectations are disappointed.”
This issue, unfortunately, has received little attention since. Extensive research was devoted
to expectation formation, its capacity to explain short run deviations from long-run equilibria
and whether policy can exploit these for its goals. But whether short-run equilibria are
rationally determined in the Keynesian sense has, to the best of our knowledge, been less of
a focus.
A second difficulty for setting consumption arises from the question whether savings will
suffice for the level of investment. If consumption is too high and savings fall short of
3
investment, costly borrowing must be arranged on imperfect markets. Likewise, excess
savings that result from under-consumption must be transferred across imperfect markets to
those in need of finance, producing similar frictional losses. The task to equilibrate savings
and investments may be relevant for individual households that also engage in investments.
If investors are separated from households, this task still arises at the regional level of an
economy, if regions seek to balance their current account and capital markets that transfer
savings from one region to another are imperfect. While this concern is relevant at the
individual (or regional) level, a core contribution by Keynes (1936) has been that savings are
never scarce at the aggregate level. In chapter 6, section II of the General Theory he argues:
“Thus the act of investment in itself cannot help causing the residual or margin, which we
call saving, to increase by a corresponding amount.” Chapter 14 is devoted completely to
explain the equivalence of savings and investments and concludes: “the level of income must
be the factor which brings the amount saved to equality with the amount invested.”
Investments require additional financial means, but these are automatically created if banks
hand out loans, investors use these means to make purchases and a multiplier process forces
an increase in income that subsequently increases savings to an extent equal to the initial
increase in investments. For a recent review of the debate see Lambsdorff (2011).
We model an economy where this Keynesian assumption holds at aggregate level. But we
hypothesize that subjects may fail to reason through this logic. The theoretically advanced
will observe that sufficient aggregate savings are always generated, suggesting that frictional
costs for excess or scarce savings can be disregarded. But others may fail to observe this
logic. They might fear that increased consumption reduces their individual savings without
recognizing positive feedback loops that arise from increased consumption by others and a
multiplier process that raises income. Responding to increased investments they are thus
tempted to reduce rather than increase consumption. This postpones convergence towards
equilibrium.
2
Previous Experimental Evidence
Laboratory macroeconomic experiments have gained prominence lately, as evidenced in the
comprehensive survey by Duffy (2008). Quite a number of experiments have focused on
commodity prices. The main challenge in these experiments is to learn to forecast correctly.
These experiments have thus been labeled Learning to Forecast Experiments (LtFEs),
(Hommes 2011). Subjects are not provided complete information on the quantitative
structure of the underlying model. At the core of these experiments lies the question of
whether equilibria can be approached by help of adaptive learning. For a more extensive
review see Lambsdorff et al. (2011).
Another branch of experimental research, which acts under limited information as well, deals
with inflation forecasting in complex New Keynesian Dynamic Stochastic General
Equilibrium (DSGE) Models, (Adam 2007; Pfajfar and Zakelj 2009; Assenza et al. 2011).
Other experiments provide players with complete information and find evidence against
monetary neutrality, (Fehr and Tyran 2001; 2008; Sutan and Willinger 2009).
More complex models require subjects to determine prices and quantities simultaneously,
(Noussair et al. 2011; Petersen 2011; Davis and Korenok 2011; Roos and Luhan 2010),
considering different types of menu costs and their potential impact on quantities. A result
that is close to our study is reported by Petersen (2011). She observes under-consumption by
households, particularly when these have negative bank balances. This allows Petersen to
trace under-consumption to debt-aversion. In reaction to decreased nominal interest rates
4
only slightly more than half of the subjects increased consumption, while almost a fifth even
lowered it. She observes that “even with multiple repetitions subjects had considerable
difficulty forming rational expectations.”
Laboratory beauty contests have been employed to investigate the cognition of reasoning
processes, and they reveal some similarity to our study. Nagel (1995) and Stahl and Wilson
(1995) report the results from such a laboratory guessing game. In this experiment subjects
are asked to pick a number between 0 and 100. The player whose number is closest to p
(0<p<1) times the average of all numbers chosen wins a fixed prize while all other players
earn nothing. The iterated elimination of (weakly) dominated strategies implies that only 0
survives as the equilibrium number. However, subjects substantially deviate from this
equilibrium point. Average numbers are usually between 20 and 30 for p=2/3 and
distributions of number choices show prominent spikes at 33 and 22. In order to explain
these findings, both studies propose some boundedly rational refinements to the process of
iterated application of dominance: First, level-0-players are defined to randomly select
numbers between 0 and 100, the average value being 50. This value then serves as a focal
point for more sophisticated players. Level-1 players best respond to level-0 players, thus
choosing 33. Level-k players best respond to the assumption that all others are level-(k-1)
players. With these adjustments, participants are found to obey two to three steps of iterated
dominance rather than an infinite number (Nagel 1995; Ho, Camerer and Weigelt 1998).
When being played repeatedly, in higher rounds level-0 players stop picking randomly, but
employ the previous round’s average number as a starting value instead. This implies that
repeated play generates convergence towards equilibrium. But this convergence can be
particularly slow and strongly dependent on how the game is framed, (Ho, Camerer and
Weigelt 1998: 950; Duffy and Nagel 1997: 1699). These findings, observed for interaction
among subjects, reveal some similarities to heuristics that can be found at the individual
psychological level. Tversky and Kahnemann (1974) observe how subjects start with
acquainted pieces of information (anchor) when estimating unknown quantities. They then
adjust the estimates until a satisfactory result is achieved. This adjustment is seen to remain
incomplete as subjects test only whether the outcome is plausible but not whether it is
perfect, (Epley and Gilovich 2006).
We believe that subjects are limited in their capacity to find an equilibrium level of
consumption, either because they have limited computational skills or because they do not
belief that other subjects can calculate the equilibrium. For our experiment we prefer models
with complete information. Departure from equilibrium in LtFEs may arise when the true
model has not yet been detected and an efficient rule for forecasting has not yet been found.
The same may be true for complex models where subjects need longer to learn.
Our experiment is almost as simple as the above mentioned guessing games. But we let
subjects determine consumption across many rounds and confront them with a nonstationary, exogenously given level of investments. To the best of our knowledge, while
non-stationary data are standard to macroeconometrics, they represent a novelty in
experimental macroeconomics. A non-stationary shock is cognitively demanding to subjects
and allows us to observe how incentives to approach equilibrium are overshadowed by the
arrival of news. While limits to rationality have already been widely observed in behavioral
macroeconomics, it remains unclear whether they would disappear over time as subjects
improve their understanding of the underlying model. We design a very simple model to test
whether and when deviations from rationality can be observed in spite of its simplicity, this
way not being caused by subjects’ failure to initially understand the given task.
5
3
Experimental Design
We build on a very simple consumption model based on a Keynesian multiplier process with
consumption , investment I and savings , where consumption together with investment
determines income
, which again determines consumption defined by
with marginal and average propensity to consume being set to
. Solving this simple model
yields
and
. This implies automatically that
and that total
savings equal total investment.
We implemented this model in the laboratory with the following design. An experimental
economy consisted of 6 subjects
who played rounds of the game. Each player was
instructed to act as an adviser to a household in an economy consisting of 6 regions. His
advisory task was to decide the level of consumption
for the region’s single household
in a range between and
in every period.
was the experimental currency
used throughout the whole experiment. In each of the 6 regions a computerized investor
determined levels of investments , identical across all regions. The value was announced
prior to the consumption decision.
While making the decision on consumption the household’s current level of income
was
unknown to the subjects. Income in each period was calculated as the sum over all
consumption decisions and the total sum of investment divided by the number of players.
That means that income was distributed equally across all households2 and given by
∑
̂
, where ̂
.
Subjects were incentivized to meet up to two different goals to maximize their payoff. First
consumption should equal a target level on consumption ̅
, so that they aimed to
minimize |
̅ |. This was explained by the fact that less consumptions does not satisfy
the current lifestyle while excess consumption renders savings being short of their desired
level. This goal implements the Keynesian multiplier process in our experimental economy.
The second goal was to balance out savings
and investment . This means
|, which was motivated by the fact that cost similar to a use of the
to minimize |
capital market would occur. For the investor in a region it is easy to access the savings of the
household of the same region , while organizing extra savings from other regions would be
costly. The same holds true, if investments are higher than savings and additional savings
have to be collected from other regions. As is known at least since Hanson (1949: 220), even
in disequilibrium aggregate savings will necessarily be equal to aggregate investments. To
see this, assume n subjects picking arbitrary values for consumption,
with
.
∑
Aggregate income then amounts to
. But aggregate savings are determined
by
-∑
such that they must always equal investment. But they may differ in percapita-terms thereby causing costly deviations.
Both deviations decreased the adviser’s payoff per round. Subjects were provided with an
initial payoff
at the beginning of all rounds and an endowment for every
round . That means their overall payoff was given by
∑
|
̅|
|
|
(1)
2
As we only used integer values a remaining part of income could not be distributed equally. Subjects thus
took turns in getting one unit of the rest.
6
where
is a weighting factor for sanctioning the savings deviation.
The level of investment was given by a non-stationary random walk
with
and
. We used a version of this time series, where an ADFtest,
, produced insignificant coefficients and
close to
zero. These made sure that the process did not, by random selection, turn out to be stationary
or characterized by serial correlation. We used the same sequence of in all treatments.
The theoretical solution can be derived by maximizing (1) with respect to
. Given that all
subjects do the same calculus (i.e.
) it can be shown that the maximization
(
) as |
| is always zero in equilibrium, since by
problem is solved by
construction
and
. This yields the payoff-dominant equilibrium
of
. Whether this is a dominant-strategy equilibrium is discussed below. Both the
levels of investment as well as the equilibrium solution are displayed in figure 1.
Figure 1 - Investment and Payoff-Dominant Equilibrium Level of Consumption
But what about the adjustment process towards equilibrium? As in the beauty contest by
Nagel (1995) this can be described by iterated elimination of (weakly) dominated strategies.
Thereby player
takes the average decision of all other player
into account and
maximizes (1) in order to calculate his best response. Inserting for consumption and income
we obtain a minimization problem for both deviations:
|
(
|
)|
(
|(
)|
)
|
|
(2)
|
7
Figure 2 - Reaction Function for Different  for
For
equation (2) can be solved easily and yields (3). In figure 2 this reaction function
is depicted with a red line for an investment level of
.
(3)
Given this investment of
and player
assuming that all other players
will
choose their consumption level
it is not optimal for m to choose
, but to set consumption according to
(
)
(see the dotted lines and arrows in figure 2). As player plays best response we label him
level-1-player in contrast to all other players not doing best response and therefore being
labeled level-0-player. Suppose now all other players – make the same calculus as player
. It would then be optimal for player
to set
(
)
and act as a superior level-2-player in contrast to all other players being level-1. Now again
all other players may act as level-2-players as well. Iterative deletion of strictly dominated
strategies brings about the dominant-strategy Nash-equilibrium with
.
For
the decision is more complicated. The first absolute term could be solved by the
same calculus according to (3) as for
, but the second absolute term incentivizes player
to choose consumption as close as possible to the consumption of all others
and
|
|.
thereby minimizing
This creates a trade-off between playing a response rule
like (3) (and thereby ignoring the second deviation) versus “follow-the-crowd”. For the
given set of consumption possibilities in the interval [0;100] with
the second deviation
is important enough so that best response is given by just setting
. There is no
incentive to deviate from the decisions of all other players. This reaction function is marked
with a blue line in figure 2. As there are no incentives to deviate from other players’
8
decisions a single player has no incentive to initiate a reasoning process towards equilibrium
as described above. Disequilibrium values equally chosen by all subjects are not weakly
dominated and iterated elimination of weakly dominated strategies will fail to converge
strategy choices towards the payoff-dominant equilibrium. This equilibrium is thus not a
dominant-strategy equilibrium. Still, the payoff-dominant equilibrium might be approached
if enough subjects are capable of calculating it and believe others to do the same.
With
equation (2) implies that the first term should always be more important than the
⁄ , while the
second term. Variations of
by 1 imply changes in the first term of
second term varies by ⁄ . Thus, even if a change in the second term counters the one of
the first term, it never outbalances it. It then suffices to recognize the first term for
minimizing deviations. The payoff-dominant solution is thus obtained by elimination of
strictly dominated strategies. However, given that the game was only played with integers,
the minor difference in changes between the two terms often does not materialize. We thus
argue more carefully that elimination of weakly dominated strategies still brings about the
payoff-dominant solution. We thus depict best response behavior by the green, shaded area
in figure 2. This means that can also be seen as an inverse indicator on how strong the
forces are that push subjects towards equilibrium. While
indicates rational herding
towards the equilibrium that affects all subjects, with
some subjects in this area may
feel comfortable with not moving towards the payoff-dominant solution (and thereby
disregarding that they can make others better off). With
there is no automatic driver at
all but only the captaincy of single subjects may guide the group towards equilibrium.
4
Treatments
We implemented three different treatments, see table 1. As treatment variable we changed
the parameter  in order to vary the importance of savings deviating from investment, S-I. In
order to ensure a fair reimbursement of our subjects we increased the endowment with a
rise in the parameter . In every treatment subjects played 24 rounds of the game, where the
first four rounds were used for practicing purposes.
Treatment

Importance of S-I
0: Baseline
1: Normal Savings
2: Double Saving
0
1
2
None
Normal
Double
Endowment
round
10
20
22
per
Rounds
(practice/with
payoff)
4/20
4/20
4/20
Table 1 - Treatment Overview
In the baseline treatment subjects just had to focus to meet their consumption target, which
was equal to 80% of income. With
the fact that savings should match investment was
irrelevant in this context. This design is similar to a beauty contest with an inner solution and
can be solved by iterated elimination of dominated strategy as shown above. We expected
that subjects may succumb to similar cognitive limitations as in the beauty contest and may
fail to approach equilibrium.
We then increased the cognitive challenge by letting subjects also consider a target for
savings. With
subjects were sanctioned for their savings deviating from investment.
In order to avoid ordering effects we varied the order in which both deviations were
9
reported. This permutation revealed no significant differences, which may also act as an
additional robustness check for our design.
We hypothesize that adding this additional target may detract subjects from equilibrium. An
exogenous increase in investments implies that savings must be increased. Savings are
commonly increased at the individual level by reducing consumption. This logic may serve
as a salient anchor to guide subjects’ behavior. They may observe that increased investment
also increases income, such that a reduction of consumption is unnecessary. But few will be
as sophisticated as to observe that aggregate savings are always generated to a sufficient
amount, such that their task can be simplified to setting consumption to its target value.
Due to this we hypothesize that increasing the penalty for missing the saving’s target may
drive away the game from equilibrium. We thus implement a second treatment with
.
Under this regime we expected deviations of savings from investment were sanctioned very
extensively. This should minimize any attempt by a single player to raise consumption to its
target value because deviation from the others consumption level would mean large payoff
losses due to the savings deviation. We think that subjects still may be capable of
coordinating their decisions but may largely fail in approaching the payoff-dominant
equilibrium. Still the theoretical solutions would predict that herd behavior should be larger
under these circumstances as “follow-the-crowd” is optimal considering best response. That
means that the only forces which push in the direction of the payoff-dominant equilibrium
are players who understood the model. As their presence may vary we expected a larger
variation in the third treatment.
5
Experimental Procedures
The experiment was conducted computer-based at the Passau University Experimental
Laboratory (PAULA) using z-Tree (Fischbacher 2007).
Figure 3 –English Translation of one Instruction Screen – Baseline Treatment
10
Upon arrival, subjects were randomly seated in the laboratory and publicly instructed 3 about
the purpose of the game, its expected length, dos and don'ts and about (standard) payment
and blindness procedures. In order to increase overall understanding of the rules, the first
screens explained the game in a detailed manner using a step-by-step approach that was
found to be perceived as intuitively appealing by pilot subjects (see figure 3 for an example).
Through the whole experiments a graph visualized the functionality of the economy and
displayed the values of the previous period. Subjects were provided with a calculator.
The first four rounds (1*, 2*, 3* and 4*) in each treatment were reserved for learning, thus
payoffs in these rounds were hypothetical. Actual payoffs were achieved in the following 20
rounds. Each subject participated in only one treatment (between-subjects design).
After the experiment subjects had to fill out a questionnaire on demographic variables. In all
but the baseline treatment they were asked as well on how they evaluated the deviation of
savings and target consumption for their decision process. Subjects should classify the
importance of both savings and target consumption on a scale from 1 (not important at all) to
5 (very important). Unsurprisingly, a rise in induced subjects to increase their importance
of savings. But despite high importance of savings some groups kept importance of target
consumption on a high level.
Throughout the entire experiment we provided feedback on all relevant information (see
figure 4). At the end of the experiment, each subject received the sum of
earned at an
exchange rate of 1 Taler = 4 Eurocent. Total payoffs were rounded to 5 Eurocent. Payments
were disbursed by a third person.
Figure 4 – Decision Screen for Round 7 – English translation – Baseline Treatment
3
Instructions are available upon request.
11
6
Descriptive Results
The experiment was conducted in seven sessions of 12 to 18 students from the University of
Passau at February 9th 2012, 26th 2012 and March 6th. In total, 114 subjects participated and
formed 19 autonomous laboratory economies. Total payoffs to the 114 participants
amounted to 1186.20 €. Altogether 2/3 of the participants were female with an average age
of 23.63. Participants were students of different field of studies, predominantly social
sciences, business, economics and law, where only 15% had taken a lecture in
macroeconomics. For payoffs and durations of all treatments see table 2.
Baseline
Treatment 1
Treatment 2
All
Time (in min.)
Payoff
Number of
economies
Total
Instructions
Average
Min4
Max
Average
per Hour
6
10
3
19
52.96
71.19
91.46
71.87
17.28
24.67
34.39
25.45
7.42 €
12.57 €
9.09 €
9.70 €
2.00 €
3.00 €
3.00 €
2.00 €
9.00 €
15.96 €
13.40 €
15.96 €
8.41 €
10.60 €
5.96 €
8.32 €
Table 2 - Payoff and Time for Different Treatments
A first grasp of the results is presented in figures 5-7. The first four rounds for learning are
separated by a vertical line. The figures depict the median values of chosen consumption,
alongside with the equilibrium prediction and upper and lower quintiles of individual
choices. Figure 5 depicts values for the baseline treatment. As can be seen, while
consumption is too high initially it over time converges to equilibrium. While the upper and
lower quintiles denote some heterogeneity, subjects seem to react to investments according
to theoretical predictions. Our hypothesis that subjects may fail to approach equilibrium, as
they do in one-shot beauty contests or in Lambsdorff, Schubert and Giamattei (2011) in
repeated, non-stationary play, was not confirmed.
4
The payoff was restricted downwards not to be lower than 2€ (baseline treatment) or 3€ (first and second
treatment). Negative payoffs and payoff less than these amounts were rounded up to these minimum payoffs.
12
Figure 5 - Individual Consumption - Baseline Treatment
Figure 6 - Individual Consumption - Treatment 1
Figure 6 depicts values for the first treatment where subjects are additionally confronted with
targeting savings. As can be seen, consumption varies less than its equilibrium prediction.
Only the upper and lower quintiles are partly capable of coming close to equilibrium values.
Heterogeneity appears to be larger than in the baseline treatment.
13
Figure 7 - Individual Consumption - Treatment 2
Figure 7 depicts values for the second treatment where deviations from the savings target
were more severely penalized. Subjects revealed severe limitations in identifying the
equilibrium. One group was able to come close to equilibrium, being denoted by data for the
upper quintile. The two other groups remained stuck in disequilibrium with strong underconsumption. Heterogeneity increased over time.
7
Regression Analysis
We focus on average group levels of consumption ̂ and regress this variable on the
announced level of investments:
̂
The baseline treatment shows that subjects were able to approach the equilibrium. The
constant is close to zero. Thus, there is no autonomous consumption in line with our
equilibrium prediction. Investments enter with a coefficient of 4.2, which is close to the
equilibrium prediction of 4.
14
Method: Ordinary Least Squares and ADF-test.a)
Dependent
Average Group Consumption,
Variable
Independent
Baseline
1. Treatment 2. Treatment
Variable
-2.68
23.2
18.6
 1 Constant
(-2.7)
(19.5)
(3.6)
4.2
2.17
1.31
 2 Investment, it
(52.4)
(22.5)
(3.1)
Rounds
1-20
1-20
1-20
Total Obs.
120
200
60
2
R
0.96
0.72
0.14
Dependent
Change in residuals from above regression,
Variable
 t
 1 Constant
0.45
(1.7)
-0.33
(-4.97)
 2 lagged
residual,  t 1
0.09
 3 lagged change
(0.9)
of residual,  t 1
Total Obs.
108
2
R
0.19
a) t-statistics in parenthesis.
-0.03
(-0.1)
-0.08
(-1.97)
-0.15
(-0.3)
0.03
(0.93)
-0.18
(-2.3)
-0.02
(-0.1)
180
0.07
54
0.02
Table 3 - Time Series Regressions for Average Group Consumption
A positive constant would depict autonomous consumption, even if the equilibrium predicts
this term to be zero. We carry out an ADF-test on the residuals, t, of the type
 t   1   2 t 1 3  t 1  t and report the respective values. The critical McKinnon values
for the coefficient  2 are -2.57 (10% error level) and -2.88 (5% error level). A note of
caution is required. With only 20 observations per group convergence is not very strong and
error levels may be measured with imprecision.
In the baseline treatment the ADF-statistic reveals a t-statistic of the lagged residuals of 4.97, which denotes significance at the 1-percent level. The variables thus cointegrate. The
first treatment reveals some considerable deviations from equilibrium. The constant signifies
autonomous consumption and the impact of investment is too low. The ADF-test fails to be
significant at the 10% level. Subjects thus maintained difficulties in finding equilibrium
values and heterogeneity remained strong throughout the game.
The second treatment reveals how strongly this confusion can be amplified. Investment still
exerts a significant positive impact, but with a coefficient of 1.31 the magnitude is only
about a third of the equilibrium prediction. With an R2 of 0.14 the explanatory power of the
regression is poor and there is no cointegration of the variables. This mirrors our previous
description of the data. For some groups we were able to crash the economy.
15
8
Conclusions and Outlook
Our experiment revealed how limited reasoning may contribute to smoothed consumption.
The endogeneity of income was manageable by subjects, bringing about payoff-dominant
equilibrium levels of consumption. But an additional savings target turned out to be
troubling to subjects. In line with theoretical predictions, equilibria can no longer be
determined by iterated elimination of dominated strategies. But we hypothesize that also the
task may have cognitively overburdened subjects. When investments must be financed by
own savings, subjects may be tempted to reduce consumption in response to increased
investments, failing to recognize the Keynesian logic that savings are never scarce at the
aggregate level.
While our findings thus cast a first light on limited reasoning in consumption decisions,
much remains to be done. Are deviations from equilibrium well described by theory or are
framing effects contributing to their emergence? As shown theoretically, rather than
targeting savings an equivalent task can be framed by targeting average consumption. It is up
to future research to identify whether this simpler task induces subjects to equilibrium play,
even when theory suggests that the payoff-dominant equilibrium can no longer be
approached by iterated deletion of dominated strategies. If not, this would suggest that the
savings target involves non-trivial framing effects.
Other treatments are equally promising and can provide extensions to our model. Would
original sin, the asymmetric penalizing of insufficient savings but not excess savings,
contribute to global underconsumption? Can this be remedied if a hegemon, such as the
United States, is exempt from this restriction? Would overconsumption result if debtor
nations are not fully responsible for their excessive consumption, for example due to their
hopes to be bailed out? Our model provides a workhorse to tackle these issues for
experimental subjects that face cognitive limitations.
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