Anom(in)alies : the interaction between money illusion and loss aversion

The interaction between money illusion and loss

aversion

by

Tobias Andres Frieder 11597399

Supervisor: dr. G. Romagnoli

Master of Science in Economics Behavioral Economics and Game Theory

University of Amsterdam

July, 2018

A particular interaction between money illusion and loss aversion was tested. 365 subjects participated in an online incentivized experiment, in which they had to make several binary choices between options that differed in their involved risk, real and nominal gains and losses. There is significant evidence of nominal loss aversion. In contexts with inflation, participants preferred options with larger nominal gains con-siderably more, although they may have been equivalent or even stochastically domi-nated by their counterparts. In addition, the effect of surpassing the nominal status-quo and avoiding the loss of money was crucial in the determination of participants´ preferences.

Abstract ii

Table of Contents v

1 Introduction 1

1.1 Research Question . . . 2

1.2 Relevance . . . 3

1.3 Organization and main results . . . 4

2 Related Literature 5 2.1 Loss Aversion . . . 5

2.2 Money Illusion . . . 6

2.3 Nominal Loss Aversion . . . 8

3 Methodology 11 3.1 First part . . . 11 3.2 Second part . . . 12 3.2.1 Hypothesis A . . . 15 3.2.2 Hypothesis B . . . 16 3.2.3 Hypothesis C . . . 17 3.2.4 Hypothesis D . . . 18 3.2.5 Hypothesis E . . . 19 3.2.6 Hypothesis F . . . 20 3.3 Third part . . . 21 3.4 Fourth part . . . 23 iii

4 Results 25

4.1 Difference of proportions tests . . . 25

4.1.1 Within-subjects analysis . . . 25

4.1.2 Between-subjects analysis . . . 32

4.2 Money illusion . . . 34

4.3 Loss aversion . . . 37

4.4 Rational behavior . . . 40

4.5 Interaction between money illusion and loss aversion . . . 42

4.6 Self-reported data . . . 46

5 Discussion 48 A Appendix 54 A.1 Group division of problems . . . 54

A.2 Instructions . . . 55

A.2.1 Welcome . . . 55

A.2.2 Part 1 . . . 56

A.2.2.1 Questions Part 1 . . . 56

A.2.3 Part 2 . . . 58

A.2.3.1 Review questions . . . 60

A.2.4 Part 3 . . . 61

A.2.5 Part 4 . . . 62

A.3 Subject pool composition . . . 62

A.4 Between-subjects difference of proportions tests . . . 63

A.5 Variables used for probit analysis . . . 65 A.6 Probit regressions for money illusion, loss aversion and rational behavior 65

A.8 Difference of proportions tests for subjects with loss aversion . . . 68 A.9 Difference of proportions tests for subjects with perfect review score . 70 A.10 Self-reported focus test . . . 71

Bibliography 71

Loss aversion and money illusion are two psychological effects, essential to un-derstand and describe individual decision-making. The former captures the fact that decision-makers evaluate situations as deviations from a subjective reference point and that the disutility of losses is larger than the utility of equivalent gains. The latter implies that people fail to internalize that the value of money is not stable over time. In fact, in economies with inflation, nominal gains do not necessarily imply a higher purchasing power. Although both effects have been extensively studied sep-arately, previous research about their interaction is scarce. If losses and gains are evaluated just in a nominal sphere, inflation can lead to larger nominal magnitudes and eliminate the loss domain from a particular decision. Consequently, a situation that makes an individual choose between mixed prospects in real terms, could be also postulated as a problem with strictly positive prospects if there is sufficient inflation.

Within the expected utility theory framework, presenting prospects as gains or losses should not modify decision-makers´ choices, since if only the utility of the final outcome is evaluated, it is irrelevant whether it is perceived as a gain or a loss. In contrast, prospect theory argues that decision-makers perceive differently positive or negative deviations from an initial reference point and sensitivity for losses is larger than for gains. Although there is extensive literature demonstrating how framing situations as gains or losses can shape decisions, most of the investigated techniques are artificially introduced in the decision-making problems. For instance, it has been proved with field experiments that punishments are more effective than rewards as incentives to motivate workers (Hossain and List, 2012). Another example of the

framing effect can be found in the insurance market. It has been demonstrated that charging extra deductibles when a sinister occurs is less preferred than charging a higher fee and giving back a rebate if a sinister does not materialize (Johnson et al., 1993). In this case, in contrast, the framing is naturally modified. First, people unconsciously think in nominal terms, “due to the ease, universality and salience of the nominal representation” (Shafir et al., 1997). Second, inflation automatically leads to higher nominal magnitudes, although the purchasing power may remain unchanged. Considering that loss aversion implies that options with large potential losses might be less preferred than options with both lower expected value and potential losses, the role of inflation as a natural way to make potential real losses unnoticeable becomes crucial. Indeed, in economies with inflation, there are several situations in which options are automatically presented to people in nominal terms, and real losses are hidden by nominal gains. Therefore, this natural framing might be dramatically modifying people preferences, by shifting all the decisions to the gain domain and creating, in the prospect theory framework, a completely different situation.

1.1

Research Question

The research question of this thesis is how the effects of money illusion on losses perceptions modify decision-makers´ preferences and choices. This research will aim to elucidate how inflation modifies individual decision-making, by masking real losses behind nominal gains. If money illusion suggests that people mostly evaluate their wealth and income in nominal terms and loss aversion implies that losses loom larger than gains, then the interaction of these two psychological effects probably entails several provocative consequences that will be analyzed during this research. First, people failure to separate real outcomes from their nominal coverage might generate

a decrease in loss aversion when there is inflation, and consequently an increase of the attractiveness of options with high potential real losses. In other words, the pre-sentation of the decision-making problem in a way that real losses are salient may produce significant different choices than the presentation of the same problem but with nominal gains masking the real losses. Second, if the reference point is the nominal status-quo, it is possible that only inflation levels that manage to transform real losers into nominal winners will produce significant changes in preferences. Par-ticularly, if inflation is not large enough to transform a real mixed prospect into a nominal strictly positive prospect, it is plausible that the magnitude shift will not produce as considerable changes in preferences as a situation in which potential losses are completely eliminated.

1.2

Relevance

Researching how nominal loss aversion influences people decisions is relevant both for behavioral economics research and public policy. From a theoretical point of view, nominal loss aversion represents the conjunction of two well-known and abundantly studied psychological effects. Therefore, research on this topic can help to understand how loss aversion and money illusion boost or constrain each other. Furthermore, considering that inflation is an existent attribute of actual economies and the fact that it can be partially manipulated by monetary policy, it is virtually possible for policy makers to use inflation as a way to modify the nominal magnitudes of costs and benefits. Consequently, if it is proved the existence of nominal loss aversion, inflation can be strategically used by policy makers as an additional tool to nudge people towards better decisions. In addition, policy makers can intentionally decide when to present a situation in real or nominal terms, in order to induce people to

choose the best options for themselves and their community.

1.3

Organization and main results

The rest of the thesis is organized as follows: section two analyzes the related literature about loss aversion, money illusion and nominal loss aversion. Section three explains the experimental design and the hypotheses. Section four consists on a complete analysis of the experimental results, with their respective interpre-tations. Finally, section five discusses the main conclusions, limitations and future research opportunities. As it is extensively discussed in the next sections, this re-search demonstrates the existence of a particular interaction between money illusion and loss aversion. Specifically, this research´s main result is that when inflation levels are large enough to completely cover potential real losses behind nominal gains, there is a significant shift in preferences produced by nominal loss aversion. In other words, it is proved that neither money illusion nor loss aversion can independently explain specific inconsistent behavior, while a combination of both effects can successfully justify it. In addition, there is evidence that money illusion and nominal loss aversion also produce significantly larger than zero choices of stochastically dominated options.

2.1

Loss Aversion

Prospect theory introduced the feature that outcomes are not evaluated in terms of their final states, as expected utility theory postulates. Daniel Kahneman and Amos Tversky developed an S-shaped value function that is described in terms of deviations from an initial reference point, and which is usually concave for gains and convex for losses. Moreover, it is steeper for losses than for gains (Kanehman and Tversky, 1979).

Figure 2.1: Prospect theory´s hypothetical value function

One of the most relevant corollaries of prospect theory´s value function is the concept of loss aversion, which implies that losses loom larger than gains. In other words, Daniel Kahneman and Amos Tversky found that negative deviations from a subjective reference point are suffered more than the pleasure provided by equivalent

positive deviations. Since its introduction, the concept of loss aversion has been extensively studied with experimental, field and neuroeconomics research (Schmidt and Traub, 2002; Rabin, 2000; Camerer, 1998; Tom et al., 2007) and it has been proved to be an extremely robust effect. Research demonstrates that loss aversion operates both in riskless (Tversky and Kahneman, 1991) and risky choices (Thaler et al., 1997). The importance of loss aversion lies in the fact that it clearly describes people preferences and can be used to clarify some phenomena that could not be explained by standard economics, namely the status-quo bias (Kahneman et al., 1991), the equity premium puzzle (Benartzi and Thaler, 1995) and the Saint Petersburg paradox (Camerer, 2005). In fact, loss aversion is in Kahneman´s viewpoint “the most significant contribution of psychology to behavioral economics” (Kahneman, 2011). In addition, the reference point used to define whether an outcome represents a gain or a loss is subjectively determined and can be based either on the status-quo, an expectation, a cognitive norm or an anchor (Kahneman, 1992; Kühberger, 1998; Heath et al., 1999).

2.2

Money Illusion

Another topic that has been extensively discussed by economics research during the last decades is money illusion. The concept of money illusion was initially intro-duced by Irving Fisher in 1928 and suggests that people fail to internalize that the value of money is not stable over time. In fact, in economies with inflation, nomi-nal gains do not necessarily imply a higher purchasing power. In this context, Don Patinkin stated that “an individual will be said to be suffering from such an illusion if his excess-demand functions for commodities do not depend [...] solely on relative prices and real wealth” (Patinkin, 1965). Until the emergence of behavioral economics

and the theoretical acceptance that decision-makers do not behave rationally, money illusion had been discarded from economic research. Indeed, James Tobin mentioned that “an economic theorist can, of course, commit no greater crime than to assume money illusion” (Tobin, 1972). However, during the last decades, field and experi-mental research have proved that money illusion is also a robust psychological effect that influences economic decision-making, and might have large macroeconomic con-sequences, since it can explain the short-run non-neutrality of money. Noussair et al. (2012) created a laboratory asset market which suffered exogenous nominal shocks. They found modifications in real relative prices due to money illusion, since there was inertia in the cognitive representations of the real prices. Additionally, Fehr and Tyran (2001) got to similar conclusions with a pricing game. They also found real price distortions caused by money illusion, and proved that nominal inertia was larger for negative than for positive shocks. Furthermore, Svedsäter et al. (2007) found that the nominal representation of assets modifies intuitive financial judgements. Particularly, in their experiments participants were asked to predict future prices of shares after an exogenous shock, and they found that shares with lower prices were predicted to suffer larger percentage changes. The consequences of money illusion in actual economies are considerable. As an illustration, Brunnermeier and Julliard (2008) used housing price series of the United States and United Kingdom to demonstrate that changes in inflation rates produced modifications of nominal interest rates that, due to money illusion, generated a mispricing of the relative cost of renting or buying a property that influenced investors´ decisions over time.

2.3

Nominal Loss Aversion

Loss aversion and money illusion have been extensively studied independently but research about their interaction is still scarce. The concept of nominal loss aver-sion has been first indirectly researched, by a focus on the evolution and rigidity of wages. Although it was rarely explicitly named as nominal loss aversion, the stickiness of nominal wages can be explained by the practical incapacity of firms to decrease nominal wages, sometimes even prohibited by law (Kahn, 1997; Fehr and Goette, 2005). Surveys have demonstrated that a nominal wage decrease in a context without inflation is considered much more unfair than a small wage increase in a context of high inflation (Kahneman et al., 1991). In this regard, Loewenstein and Sicherman (1991) demonstrated that workers prefer a nominally increasing wage profile than a nominally decreasing one, although the discounted present-value maximization might predict the opposite.

The few articles directly studying the concept of nominal loss aversion have fo-cused on the price evolution of houses, which has been used to analyze this phe-nomenon for several reasons. First, there is a lot of available data about the housing market, which makes it possible to use field data to test research hypotheses. Sec-ond, houses usually represent a big portion of people wealth, so decisions about their buying and selling prices are not made without careful consideration. Finally, people usually keep their houses for several years, in which macroeconomic shocks can pro-duce considerable nominal price modifications. In this regard, Genesove and Mayer (2001), used data from Boston in the 1990s to prove that nominal loss aversion was influencing the seller behavior in the housing market. In their analysis, they found that asking prices were usually higher than the nominal purchase prices and that sellers were averse to accept a nominal loss from the selling operation. In fact, sellers

were using their purchase price as a reference point and were willing to hold longer a nominal loser, while accepting to sell a nominal winner. In this context, Anenberg (2011) used data from the San Francisco Bay Area from 1988 to 2005 to amplify the results obtained by Genesove and Mayer. Anenberg demonstrated that the effect of nominal loss aversion had also implications for actual transaction prices, and not just for asking prices. In his analysis, he found that sellers facing larger nominal losses compared to their purchase price received on average higher prices, at the cost of staying in the market for a longer time. Similarly, Engelhardt (2003) used 1985-1996 data from the NLSY79 of the United States to study the effect of nominal loss aver-sion and equity constraints in housing mobility. He found that housing mobility was much more influenced by nominal loss aversion than by equity constraints.

In addition, some experiments have been made to test whether loss aversion is an important factor in the housing market transactions and if the usual reference point is on the real or nominal domain. Stephens and Tyran (2012) developed a survey in which subjects were faced with several housing transaction scenarios and had to grade the attractiveness of the operations in a scale from 1 (not advantageous at all) to 15 (very advantageous). In all the cases, the previous buying price of the house was the same but the selling prices and the accumulated inflation during the period changed. Their main finding was that there is a direct correlation between positive scenarios´ evaluations and the involvement of a nominal gain, while there is an incapacity to realize hidden real losses. They also remarked that socioeconomic factors and subjects´ cognitive abilities produce significant differences in the extent to which participants´ responses depend on winning or losing money. Finally, Shafir et al. (1997) made a similar survey in which subjects had to rank several housing transactions, each of them with different selling prices and accumulated inflation rates. They found that the respondents were mostly focusing on nominal selling prices to

determine their rankings, while ignoring real outcomes.

As it can be noticed, previous literature on the topic is still scarce and all the available research has been made either with field data or non-incentivized surveys. The purpose of this research is to contribute to this field´s literature, but developing an experiment in which subjects´ payoffs depend on their decisions. This approach would be a novel way to investigate the effects of nominal loss aversion and it is particularly interesting, because if people fail to realize that their real gains do not necessarily correlate with their nominal outcome, they may eventually choose suboptimal options or make inconsistent decisions in the experimental environment.

The research question and hypotheses were tested with an experiment, which was designed in Qualtrics and distributed online. The experiment was divided into four parts.

3.1

First part

In the first part, participants had to answer ten questions that required logical thinking. The objective of this section was to make subjects exert effort to gain the e20 endowment that they would need in the second part. Subjects were not told what was the minimum requirement of correct answers to earn the full endowment, so their incentive was to try to answer everything correctly and put effort in every single question. Actually, the minimum requirement was set in three correct answers, while a pilot version of this part of the experiment had shown that the minimum score was six out of ten. In summary, participants had to answer all the questions of the first part, that was designed to make them exert effort but succeed in winning their endowment. Information about the number of correct answers was also used to develop a proxy for individual cognitive abilities, which was used later in the analysis. The ten questions of this part of the experiment can be found in the Appendix 2.

3.2

Second part

In the second part, subjects had to use the previously earnede20. They were told that with those e20 they bought a house in an economy with an artificial currency called “$”. At the moment of the purchase, $10,000=e1, so the house they had bought was worth $200,000. In this part of the experiment, they had to choose ten times between two options that represented selling opportunities of their house some years later. In all the cases, the purchase price was $200,000 but the accumulated inflation during their ownership of the property and the selling prices differed. Subjects were told that their final payoff would be made in euros, so the selling price in $ would be transformed into euros, taking into account the $ accumulated inflation at the moment of the selling operation. After the instructions and before starting with the incentivized questions, subjects had to answer three review questions, intended to measure their understanding of the instructions. Participants were not told whether their answers were correct or not, but information about their understanding of the inflation mechanisms was used in the posterior analysis.

Participants were randomly divided into two treatments in a between-subjects design. The division was made by asking the participants the last digit of their mo-bile phone number. Even numbers were assigned to Treatment A and odd numbers to Treatment B. Both treatments were faced against the same problems but, in the Treatment B, the saliency of the deviation from the nominal status-quo was inten-tionally enhanced. Subjects of the Treatment A saw the options like in Figure 3.1, while subjects of the Treatment B saw the options like in Figure 3.2.

Figure 3.1: Example of an option, as it was presented to subjects of the Treatment A

Figure 3.2: Example of an option, as it was presented to subjects of the Treatment B

Considering that participants of both treatments were faced against the same economic problems, predictions about their responses did not differ. Nevertheless, in Treatment A participants faced the problems in a more transparent frame that allowed them to decide where to position their reference point independently. In Treatment B, in contrast, participants were nudged to use the nominal status-quo as a reference point. Therefore, results from Treatment A were used for the main analysis about the existence of nominal loss aversion in a transparent environment. On the other hand, results from Treatment B were used to elucidate whether a simple modification of the provided information could produce an increased influence of nominal loss aversion in decision-making.

All the subjects were faced against all the problems. However, in order to avoid confounding factors caused by order effects, another between-subjects design was em-bedded into this part of the experiment. The ten problems were divided into two groups, separating the related questions. There was randomization within these two groups but half of the subjects answered group A questions first and the other half, group B questions first. Therefore, the results had the statistical power of a within-subjects design and where counterbalanced, reducing the possibility of order effects affecting the aggregate results. Moreover, the experimental design provided the pos-sibility to analyze just the first or second group´s answers of all subjects. A detail about the group division of questions can be found in the Appendix 1. The following table presents a summary of the ten problems of the second part of the experiment:

Table 3.1: Summary of the problems of the second part of the experiment

Hypothesis Problem Option Nominal Outcomes Inflation Nominal Expected Gain in % Real Expected Gain in % Nominal Difference

50% 50% 100% A 1 1 $246,000 $275,520 23% 30% 6% $29,520 2 $216,240 2% 8% 6% $0 2 3 $204,000 $228,480 2% 8% 6% $24,480 4 $216,240 2% 8% 6% $0 B 3 5 $150,000 $250,000 0% 0% 0% $100,000 6 $200,000 0% 0% 0% $0 4 7 $205,500 $342,500 37% 37% 0% $137,000 8 $200,000 0% 0% 0% $0 C 5 9 $150,000 $250,000 0% 0% 0% $100,000 10 $175,000 $225,000 0% 0% 0% $50,000 6 11 $201,000 $335,000 34% 34% 0% $134,000 12 $180,250 $231,750 3% 3% 0% $51,500 D 7 13 $177,480 $246,840 2% 6% 4% $69,360 14 $210,800 $285,200 24% 24% 0% $74,400 E 8 15 $210,140 $236,740 33% 12% -16% $26,600 16 $165,640 $183,820 1% -13% -13% $18,180 F 9 17 $208,000 $312,000 30% 30% 0% $104,000 18 $164,800 $247,200 3% 3% 0% $82,400 10 19 $184,000 $276,000 15% 15% 0% $92,000 20 $164,800 $247,200 3% 3% 0% $82,400

Notes: subjects were faced against ten problems, each of them with two options. This table shows all the options, with their accumulated inflation, nominal and real expected gain in % and the nominal difference between the potential outcomes.

As it is shown in the Table 3.1, the ten questions that participants had to answer in this part of the experiment were used to formulate six hypotheses, which were designed to extract different conclusions.

3.2.1

Hypothesis A

Figure 3.3: Hypothesis A

Problem 1 and Problem 2 shared a safe option with a 6% real gain and equivalent inflation. However, they differed in the other options, which were prospects with the same potential outcomes in real terms but different nominal magnitudes. In Problem 1, both potential outcomes of Option 1 were nominally larger than the safe outcome of Option 2. In contrast, in Problem 2 the outcome of Option 4 was nominally contained between the two potential outcomes of Option 3. Statistically significant more choices of Option 1 in Problem 1 than choices of Option 3 in Problem 2 would provide evidence of money illusion. This was the expected outcome, taking into account the previous literature conclusions. It is necessary to explain why this expected behavior could not be explained by risk aversion. In real terms, the risk of both problems remained unchanged and, in nominal terms, the perceived risk was larger in Option 1 than in Option 3. Therefore, risk aversion could not be a potential explanation for statistically significant more choices of Option 1 in Problem 1 than Option 3 in Problem 2.

3.2.2

Hypothesis B

Figure 3.4: Hypothesis B

Problem 3 and Problem 4 shared a safe option with a 0% real gain and equivalent inflation. However, they differed in the other options, which were prospects with the same potential outcomes in real terms but different nominal magnitudes. In contrast with hypothesis A, in this case the other options included a potential real loss. Option 5 of Problem 3 introduced a potential nominal loss, while in Option 7 of Problem 4, potential real losses were completely hidden behind nominal gains. It was expected to find statistically significant more choices of Option 7 in Problem 4 than choices of Option 5 in Problem 3, which could be explained by nominal loss aversion and money illusion. For the same reason as in Hypothesis A, risk aversion could not be an explanation for the expected behavior, since the real risk was equivalent in both cases but the nominal risk was larger in Option 7 of Problem 4 than in Option 5 of Problem 3.

3.2.3

Hypothesis C

Figure 3.5: Hypothesis C

Problem 5 and Problem 6 were equivalent in real terms but differed nominally. For the same reasons as in hypothesis B, in this case it was expected to find more choices of Option 11 in Problem 6 than Option 9 in Problem 5, which would provide evidence in favor of nominal loss aversion and money illusion. In addition, in this case Option 12 of Problem 6 was not nominally equivalent to Option 10 of Problem 5 but, in both cases there still was a potential nominal loss.

3.2.4

Hypothesis D

Figure 3.6: Hypothesis D

In Problem 7, Option 13 first-order stochastically dominated Option 14. In real terms, Option 13 implied a potential loss of 13% or a potential gain of 21%. On the other hand, Option 14 implied a potential loss or gain of 15%. Both in the good or the bad state of the prospects, real outcomes were larger for Option 13 than for Option 14. However, taking into account that in Option 14 the real losses were completely covered by nominal gains, it was expected that participants would choose this option. Considering that Option 14 was first-order stochastically dominated by Option 13, choices of Option 14 significantly higher than zero would provide evidence of nominal loss aversion and money illusion.

3.2.5

Hypothesis E

Figure 3.7: Hypothesis E

In Problem 8, Option 16 second-order stochastically dominated Option 15. In real terms, Option 15 implied a potential loss of 21% or 11% while Option 16 implied a potential loss of 18% or 9%. In both possible states of the prospects, real outcomes were larger for Option 16 than for Option 15. In addition, in this case Option 16 was more predictable, which means that it involved less risk, both in nominal and real terms. Therefore, significantly higher than zero choices of Option 15 would be evidence in favor of nominal loss aversion and money illusion, since Option 15 was second-order stochastically dominated by Option 16 but, due to inflation, its real losses were completely hidden behind nominal gains.

3.2.6

Hypothesis F

Figure 3.8: Hypothesis F

In Problem 9 and Problem 10, all the options implied the same potential outcomes in real terms. Furthermore, Option 18 of Problem 9 and Option 20 of Problem 10 shared the same inflation, and therefore equivalent nominal potential outcomes. However, in Option 19 of Problem 10, the accumulated inflation was not sufficient to fully cover the potential real loss. In contrast, in Option 17 of Problem 9, real losses were completely hidden by nominal gains. Considering that real outcomes in both problems were equivalent, money illusion would predict significantly larger choices of Option 17 in Problem 9 and Option 19 in Problem 10 than their respective counterparts. Nevertheless, taking into account that in Option 19 there still were potential nominal losses, it was expected that in Problem 10 there would not be significant deviations from the random choice. In contrast, in Problem 9, it was expected to find significantly more choices of Option 17 than Option 18. If this was the case, it would be possible to state that money illusion was not the unique

mechanism involved and that breaking the nominal status-quo significantly influenced participants preferences. It is crucial to notice that without the confirmation of this hypothesis it would not be possible to conclude that all the previous predictions were caused by nominal loss aversion and not exclusively by money illusion.

3.3

Third part

The objective of this section was to determine to what extent was loss aversion influencing decisions in this experiment´s subject pool. Rabin (2000) demonstrated that people behave as virtually risk neutrals when stakes are low, because rejecting a gamble with a potential gain or loss of e20 would theoretically require excessively large coefficients in order to be explained by risk aversion. He argued that reject-ing risky gambles that involve small losses could be only explained by loss aversion. Nevertheless, this part of the experiment was added for two reasons. First, it was designed to empirically measure and distinguish loss and risk aversion. Second, it was used to create a proxy for loss averse subjects, which served as additional data in the results´ analysis.

Subjects had to decide six times between two options. There were three pair of questions and differences in the preferences within the pairs could be used as evidence of loss aversion.

Table 3.2: Summary of the problems of the third part of the experiment

Hypothesis Problem Option Initial endowment Outcomes Deviations

50% 50% 100%

G

11 21 e5 e5 e25 (+/-)e0 / (+)e20

22 e5 e15 (+)e10

12 23 e15 e5 e25 (-)e10 / (+)e10

24 e15 e15 (+/-)e0

H

13 25 e13 e13 e25 (+/-)e0 / (+)e12

26 e13 e20 (+)e7

14 27 e20 e13 e25 (-)e7 / (+)e5

28 e20 e20 (+/-)e0

I

15 29 e8 e8 e18 (+/-)e0 / (+)e10

30 e8 e12 (+)e4

16 31 e12 e8 e18 (-)e4 / (+)e6

32 e12 e12 (+/-)e0

Notes: subjects were faced against six problems, each of them with two options. This table shows all the options, with their initial endowment, potential outcomes and deviations from the status-quo.

As an illustration, hypothesis G compared participants´ responses to Problem 11 and Problem 12, that were formulated in the following way:

Problem 11:

You are given e5. What do you prefer?

Option 21: Keep the e5 with 50% probability or win additional e20 with 50% prob-ability (e5 or e25, each with 50% probability)

Option 22: Win additional e10 (e15 for sure)

Problem 12:

You are given e15. What do you prefer?

Option 23: Losee10 with 50% probability or win additional e10 with 50% probability (e5 or e25, each with 50% probability)

Option 24: Reject the lottery and keep mye15

As it can be clearly noticed, both problems included the same potential outcomes and risk, but they differed in their initial endowment. Expected utility theory pre-dicts that choices in Problem 11 and Problem 12 should not be different and that

they would depend on the subjects´ risk aversion. However, prospect theory adds that if participants are loss averse, preference for Option 24 in Problem 12 should be larger than for Option 22 in Problem 11. Therefore, considering the robustness of loss aversion in previous research, it was expected to find significantly different choices in these two problems. Again, in order to eliminate confounding factors caused by order effects, related problems were separated into two groups and each group of questions was presented to one half of the subjects first, counterbalancing the results. Con-sequently, results had the statistical power of a within-subjects design but provided the possibility to be analyzed as a between-subjects too. A detail about the group division can be found in the Appendix 1.

3.4

Fourth part

Finally, the fourth part of the experiment consisted on a short survey, which tried to capture subjects´ socioeconomic and background information. Also, in this part subjects were asked about how they chose among the available options in the different parts of the experiment.

3.5

Incentives

As it was previously mentioned, one of the key ingredients of this research is that it was the first time that nominal loss aversion was tested with an incentivized experiment. In the instructions (which can be found in the Appendix 2), participants were mentioned that five randomly chosen subjects would be paid (three according to their outcome in the second part and two according to their outcome in the third part), and that their earnings would depend on their choices in one randomly drawn

problem of the experiment. The last question of the survey asked for the participant´s email. They were mentioned that it was not compulsory to fill it, but it was necessary if they wanted to be considered for payment.

The experiment was online for one week, and participants were contacted by email and social media to participate. In the diffusion messages, prospective partici-pants were mentioned that they would have to make several choices among different options and were provided information about the potential earnings and the length of the experiment. 365 subjects completed the experiment. Based on the last digit of their mobile phone number, 189 participants were assigned to Treatment A and 176 to Treatment B. The Appendix 3 provides extra information about the sample´s background and socioeconomic factors.

4.1

Difference of proportions tests

4.1.1

Within-subjects analysis

The first set of results consists on general tests about the statistical difference of proportions between options, in order to provide a first analysis of the hypotheses presented in the previous section. Several difference of proportion tests (prtest in Stata) were performed to analyze the results. Taking into account that in all cases the alternative hypotheses predicted differences in a particular direction, the one-tailed p-values are considered to measure the statistical significance of these results. Hypothesis A predicted more choices of Option 1 in Problem 1 than Option 3 in Problem 2 and stated that a confirmation of the hypothesis would be prove of money illusion. In Treatment A there was not difference in choices, while in Treatment B a

48% of the subjects chose Option 1 and 40% Option 3. In Treatment B, it is possible to reject the null hypothesis, which postulated equality of proportions, with p<.10.

Table 4.1: Difference of proportions in hypothesis A Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z) Treatment A Option 1 38.62% 3.54% 189 31.68% 45.57% Option 3 38.10% 3.53% 189 31.17% 45.02% difference 0.53% 5.00% -9.27% 10.33% 0.11 0.4579 Treatment B Option 1 47.73% 3.77% 176 40.35% 55.11% Option 3 40.34% 3.70% 176 33.09% 47.59% difference 7.39% 5.28% -2.96% 17.73% 1.40 0.0814 Notes: difference: prop(Option 1) - prop(Option 3)

H0: difference = 0 Ha: difference > 0

Hypothesis B predicted more choices of Option 7 in Problem 4 than Option 5 in Problem 3. A confirmation of this hypothesis could be explained both by money illusion, nominal loss aversion or a combination of both effects. Indeed, in both treatments more subjects selected Option 7 in Problem 4 than Option 5 in Problem 3. In Treatment A, 29% of the subjects chose Option 7 and 23% Option 5, and the difference is significant with p<.10. In Treatment B, 43% of the participants chose Option 7 and 30% Option 5, and the results are significant with p<.01.

Table 4.2: Difference of proportions in hypothesis B Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z) Treatment A Option 7 29.10% 3.30% 189 22.62% 35.58% Option 5 23.28% 3.07% 189 17.26% 29.31% difference 5.82% 4.51% -3.02% 14.67% 1.29 0.0991 Treatment B Option 7 42.61% 3.73% 176 35.31% 49.92% Option 5 30.11% 3.46% 176 23.34% 36.89% difference 12.50% 5.08% 2.53% 22.47% 2.44 0.0074 Notes: difference: prop(Option 7) - prop(Option 5)

Hypothesis C predicted more choices of Option 11 in Problem 6 than Option 9 in Problem 5. An empirical verification of this hypothesis could also be explained both by money illusion, nominal loss aversion or a combination of both effects. In fact, the predicted results were observed in both treatments. In Treatment A, 30% of the subjects chose Option 11 and 25% Option 9. However, the difference is not significant with p<.10 and it is not possible to reject the null hypothesis. In Treatment B, 38% of the subjects chose Option 11 while 27% Option 9. In this case, the difference is significant with p<.05.

Table 4.3: Difference of proportions in hypothesis C Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z) Treatment A Option 11 30.16% 3.34% 189 23.62% 36.70% Option 9 25.40% 3.17% 189 19.19% 31.60% difference 4.76% 4.60% -4.26% 13.78% 1.03 0.1507 Treatment B Option 11 37.50% 3.65% 176 30.35% 44.65% Option 9 27.27% 3.36% 176 20.69% 33.85% difference 10.23% 4.96% 0.51% 19.95% 2.05 0.0202 Notes: difference: prop(Option 11) - prop(Option 9)

H0: difference = 0 Ha: difference > 0

In hypothesis D, choices of Option 14 significantly larger than zero would imply that at least some subjects preferred first-order stochastically dominated options, something completely unacceptable by standard economics. However, 25% of subjects of Treatment A and 37% of Treatment B selected the stochastically dominated option. Before testing if the proportion of choices of the stochastically dominated option was significantly larger than zero, it is necessary to solve a technical issue. Considering that under the null hypothesis, the choice of Option 14 should have been zero in all the cases, then its average would not have a normal distribution and the central limit theorem would not apply. Technically, the proportion could be considered different to zero with just one choice of Option 14. However, it would be mathematically possible

to test whether the proportion of choices of Option 14 was larger than 0.1% and the intuition of the result would not suffer considerable consequences. Proceeding as it was just explained, in both treatments results are statistically significant with p<.01.

Table 4.4: Difference of proportions in hypothesis D Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z) Treatment A Option 14 24.87% 3.14% 189 18.71% 31.03% 107.73 0.0000 Treatment B Option 14 36.93% 3.64% 176 29.80% 44.06% 154.60 0.0000 Notes: p: prop(Option 14) H0: p = 0.001 Ha: p > 0.001

Predictions and potential conclusions were similar for hypothesis E and, in fact, 30% of participants of Treatment A and 44% of Treatment B selected the second-order stochastically dominated option. Again, in both cases the proportion is significantly larger than zero with p<.01.

Table 4.5: Difference of proportions in hypothesis E Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z) Treatment A Option 15 29.63% 3.32% 189 23.12% 36.14% 128.44 0.0000 Treatment B Option 15 43.75% 3.74% 176 36.42% 51.08% 183.21 0.0000 Notes: p: prop(Option 15) H0: p = 0.001 Ha: p > 0.001

Hypothesis F was designed to distinguish the effects of money illusion and nomi-nal loss aversion. If, as predicted, money illusion was not sufficient to explain the shift in preferences, it was expected to find random choice in Problem 10 and a proportion larger than 50% in choices of Option 17 in Problem 9. Contrary to the predictions, evidence did not reflect random choice in Problem 10. In fact, the option with high accumulated inflation was chosen less than 50% of the times in Problem 10. This

unexpected effect could have been caused by an inherent dislike for inflation, an ef-fect that had not been predicted in the experimental design. Although the expected results of hypothesis F were not found in the evidence, it is still possible to draw interesting results that will serve as insights for several interpretations and conclu-sions. The comparison between Option 17 of Problem 9 (in which the real losses were completely hidden) and Option 19 of Problem 10 (in which there were still potential nominal losses) reflects significant more choices of Option 17 than Option 19 in both treatments. In Treatment A, 32% of the subjects chose Option 17 and 22% Option 19. The difference is significant with p<.05. In Treatment B, 57% of the participants selected Option 17 and 40% Option 19, and the difference is significant with p<.01.

Table 4.6: Difference of proportions in hypothesis F Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z) Treatment A Option 17 32.28% 3.40% 189 25.61% 38.94% Option 19 22.22% 3.02% 189 16.30% 28.15% difference 10.05% 4.55% 1.13% 18.97% 2.19 0.0141 Treatment B Option 17 57.39% 3.73% 176 50.08% 64.69% Option 19 40.34% 3.70% 176 33.09% 47.59% difference 17.05% 5.25% 6.75% 27.34% 3.20 0.0007 Notes: difference: prop(Option 17) - prop(Option 19)

H0: difference = 0 Ha: difference > 0

The first set of results provides significant evidence to confirm that money illusion is not neutral in the determination of people preferences in the aggregate. As it was shown in the previous difference of proportions tests, when the same situation in real terms is nominally modified, results can be considerably different. Furthermore, some initial patterns must be highlighted. Firstly, there is an important distinction be-tween treatments. In all the hypotheses, differences were larger in Treatment B than in Treatment A. Although the most interesting analysis will be made with Treatment A data because it is where situations were transparently presented to subjects, the fact

that a simple addition in the provided information generated an enlargement of the differences, implies that it is straightforward to nudge people to think in terms of devi-ations from the nominal status-quo. The implicdevi-ations of this conclusion will be deeply analyzed in the Discussion section. Secondly, against standard economics predictions, a statistically significant larger than zero proportion of subjects chose stochastically dominated options in hypotheses D and E. This result is curious, because it does not reflect a shift in preferences between two problems presented separately, but a choice of a suboptimal option in a unique problem. What makes this result even more interesting, is that choices of the suboptimal option were larger in hypothesis E than in hypothesis D, while in the first case the suboptimal option was second-order stochastically dominated and in the latter case it was just first-order stochastically dominated. The main difference between the two situations is that in hypothesis E both potential outcomes of the dominating option implied a nominal loss while, in hypothesis D, one potential outcome already contained a nominal gain. Thirdly, it is also insightful that the weakest differences are found in hypothesis A, in which there were no potential real losses and money illusion was the only possible effect that could explain a shift in preferences. In Treatment A, there is no difference between choices of Option 1 and Option 3 in hypothesis A, while all the other tests show a difference of proportions significant with a confidence of at least 85%. In Treatment B, hypothesis A is significant with a confidence of 90% while all the other differences of proportions tests have a minimum statistical confidence of 95%. This pattern automatically leads to the necessary question about what can be the reasons for the weaker outcome in hypothesis A. The only difference between this hypothesis and the other ones, it that in hypothesis A there were no losses involved, neither real nor nominal. The fact that money illusion produces larger shifts in preferences between a nominally mixed prospect and a nominally strictly positive one than among two strictly positive

prospects, provides further evidence to support the idea that breaking the nominal status-quo has an effect in the aggregate preferences.

Finally, considering that the two previous results imply that money illusion is more powerful in shifting preferences when nominal losses are transformed into nomi-nal gains, it is interesting to specifically anomi-nalyze the results of hypothesis F, since it is the only case in which both related problems included options with high inflation but just one of them completely eliminated the loss domain. As a reminder, hypothesis F compared choices between Option 17 in Problem 9 and Option 19 in Problem 10. Both cases represented prospects with a potential real gain or loss of 20%, but Option 19 included just a 15% accumulated inflation against a 30% of Option 17. Therefore, in Option 17 real losses were completely hidden behind nominal gains while in Option 19 the nominal coverage was not sufficient to eliminate the potential nominal losses. The differences of proportions in hypothesis F were extremely significant, much larger than the expected effect due to just a 15% nominal increase. As an illustration, hypotheses B and C incorporated nominal increases of 37% and 34% respectively be-tween compared options and the differences of proportions were less significant than the ones generated by a 15% in hypothesis F. This result is curious, since it pro-vides strong evidence about something special happening in the nominal status-quo. In particular, this result suggests that when subjects have to choose between mixed prospects, they negatively evaluate the option with high inflation. But, on the other hand, when inflation is sufficiently high to transform a mixed prospect into a strictly positive one, the valuable feeling of not losing money surpass the negative perception about high inflation.

4.1.2

Between-subjects analysis

As it was explained in the Methodology section, participants were faced against all the problems but, in order to avoid potential order effects caused by a strategic response to related questions, there was a between-subjects design embedded in the second part of the experiment. Considering that problems were divided into two groups and half of the subjects answered one group of questions first, aggregate results were counterbalanced. Nevertheless, the experimental design also allows to inspect what would have been the results if the participants would have had to answer just half of the questions, by analyzing just the first five problems presented to each subject. In general terms, however, the examination of the data assuming the between-subjects design do not provide considerably new conclusions. Hypotheses B, C, D and E do not show new patterns when the results are analyzed with the between-subject design. In some cases, the effect goes in different directions depending on the treatment and in others the difference of proportions remains statistically unchanged. However, results in hypotheses A and F should be highlighted. An analysis of hypothesis A shows relatively larger differences of proportions for both treatments when the between-subjects design is considered. In Treatment A, the difference of proportions is slightly larger but still not significant, and in Treatment B there is much stronger evidence of money illusion. In hypothesis F, it is possible to find a relatively smaller difference of proportions in both treatments. Detailed tables with the results of the between-subjects analysis can be found in the Appendix 4.

The combination of these results of hypotheses A and F imply that when just the first five answers of every subject are being taken into consideration, there is slightly more money illusion than when the whole set of answers is evaluated. In order to deepen this discovery, hypotheses A and F were compared again, but now

considering just the participants´ last five answers. It is plausible to believe that subjects may have improved their choices during the experiment, since the repetition of ten similar rounds gave them the opportunity to think the problems from different perspectives and progressively incorporate to their computations factors that they had been previously ignoring. Therefore, modifications of results in participants´ last five answers provide insights about their learning mechanisms. The following table shows that in hypothesis A, differences are reversed in both treatments when just the last five answers are considered. The largest effect can be found in Treatment B, in which the within-subjects analysis had provided evidence of a significant preference for options with larger nominal magnitudes, but this analysis concludes the opposite. In opposition, in hypothesis F differences of proportions are relatively larger when only participants´ last five answers are considered.

Table 4.7: Differences comparison in hypotheses A and F Treatment Hypothesis Analysis Mean St. Dev. |z| Pr(Z>|z|)

A

HA Difference all answers 0.53% 5.00% 0.11 0.4579 Difference last 5 answers -1.56% 7.16% 0.22 0.5860 HF Difference all answers 10.05% 4.55% 2.19 0.0141 Difference last 5 answers 12.47% 6.76% 1.87 0.0308

B

HA Difference all answers 7.39% 5.28% 1.40 0.0814 Difference last 5 answers -2.57% 7.50% 0.34 0.6341 HF Difference all answers 17.05% 5.25% 3.20 0.0007 Difference last 5 answers 22.68% 7.36% 3.00 0.0030 Notes: HA makes reference to hypothesis A and HF to hypothesis F. Difference all answers evaluate

the difference of proportions in the within-subjects analysis, while Difference last 5 answers contains the difference of proportions in the last half of questions that every subject had to answer.

Therefore, it is possible to conclude that during the experiment subjects progres-sively learned about the mechanisms of inflation and the effects of money illusion, but there was not learning regarding nominal loss aversion. In other words, people can easily learn that when nominal gains are accompanied by inflation, they are not nec-essarily in a better final state. However, the evidence also suggests that this learning

does not occur when inflation leads to the transformation of a nominal loss into a nominal gain. In these cases, even after some rounds of learning, subjects still signif-icantly preferred to avoid nominal losses, which supports the hypothesis of nominal loss aversion.

4.2

Money illusion

The first set of results confirms the existence of money illusion within the ex-perimental environment and states that its effect is weaker when it raises an already positive option than when it transforms a previously negative option into a positive one. Previous results also suggest that money illusion decreases with learning and experience. This section examines the qualitative determinants of money illusion. To do so, it is first necessary to determine which are the subjects that most suffered from money illusion. Only the Treatment A subjects are being considered in this part of the study, since it is the treatment in which options were presented transparently and there were no confounding factors that could bias the conclusions. The subjects´ discrimination is made by creating a subgroup – Money Illusion TA – which is inte-grated by the participants that chose Option 1 in Problem 1 and Option 4 in Problem 2. 34 out of 189 subjects were incorporated to the Money Illusion TA subgroup. The idea behind this criterion of discrimination is that the only plausible reason that could explain that a subject that preferred Option 4 in Problem 2 also chose Option 1 in Problem 1 is money illusion. Considering that the objective of this section is to analyze the qualitative determinants of money illusion, a probit model is used for the analysis, since it provides insights about how particular individual attributes modify the likelihood of a person suffering from money illusion. The potential explanatory variables are detailed in the Appendix 5.

As it can be seen in the first probit model of Appendix 6, the regression confirms that most of the indicator variables did not significantly affect the likelihood of suf-fering from money illusion. The only qualitative factor that clearly affected money illusion was the nationality. Relative to the baseline group (EMEA region), subjects from the LATAM region were less likely to suffer from money illusion, significant with p<.01. In order to correctly calculate the size of the effect it is necessary to perform an extra computation: considering that nationality is an indicator variable in this model, its marginal effect as an explanatory variable can be calculated as the difference in the cumulative distributive function of the normal distribution when the indicator goes from zero to one. This computation implies that subjects from Latin Amer-ica were 31.9% less likely to suffer from money illusion than subjects from Europe, Middle East and Africa. Taking into account that most of the Nationality LATAM subjects were actually from Argentina and that Nationality EMEA was mostly com-posed by participants from The Netherlands, it is plausible to conclude that subjects from Argentina were less likely to suffer from money illusion than subjects from The Netherlands. This conclusion is reasonable and the explanation is straightforward. Argentina is a country that is used to high inflation rates (IMF reports that annual inflation in Argentina in 2017 was 25.7%) while Dutch people are not used to high inflation processes (IMF reports that annual inflation in The Netherlands in 2017 was 1.3%). In Argentina, wages are usually updated twice a year and mortgage credits are inflation-indexed. Therefore, Argentinians are much more used to money illusion than Dutch people and are evidently more able to realize that larger nominal magni-tudes do not necessary imply a better option. This conclusion is also consistent with previous results of this research that state that experience and learning can lead to a reduction of money illusion.

abil-ities also suffered less from money illusion. Cognitive abilabil-ities were measured by a proxy created from responses in the first part of the experiment, which made subjects respond to ten questions that required logical thinking. This probit analysis shows that a marginal increase of an extra correct answer in the first part decreased the like-lihood of suffering from money illusion. To accurately measure the marginal effect of an extra correct answer, the derivative of the log-likelihood function can be computed and the outcome is that a marginal increase in correct answers during the first part implied an average reduction of 3.7% in the likelihood of suffering from money illusion, with p<.12. This conclusion is aligned with the previous literature conclusions, since Stephens and Tyran (2012) had also demonstrated that subjects´ cognitive abilities produce significant differences in the extent to which participants´ responses depend on winning or losing money. The rest of the results are not statistically significant, but some intuitions about their directions are insightful. Participants that study or work in fields related to economics, business or exact sciences (grouped under the Field

Bus-Econ-Exact variable) were less likely to experience money illusion than subjects

from other fields. Results about gender and age are neither strong nor conclusive.

Taking into consideration that subjects with money illusion were discriminated in an additional subgroup, it is possible to analyze their particular responses to the other questions, in order to investigate whether money illusion boosted or constrained the results of the other hypotheses. In hypothesis B, the difference of proportions for subjects with money illusion was much larger than for the whole sample. Particu-larly, while the full subject pool analysis had led to a 6% difference of proportions, significant with p<.10, the difference of proportions for subjects with money illusion was 20%, significant with p<.05. In hypothesis C, differences of proportions had been not significant in the full sample analysis and were still not significant in this case, although the difference was diminished in terms of percentage. Hypotheses D and

E also evidenced considerable increments in the choice of the stochastically domi-nated options. While the full sample analysis had led to 25% and 29% choices of the stochastically dominated options respectively, the analysis for subjects that suffer from money illusion exhibits that 44% of the subjects chose the suboptimal options in both hypotheses. Finally, in hypothesis F, the difference of proportions between Op-tion 17 and OpOp-tion 19 was much smaller and not significant. Moreover, both OpOp-tion 17 and Option 19 were considerably more preferred than their counterparts (Option 18 and Option 20 respectively) when just the Money Illusion TA subgroup is consid-ered. In summary, this last result is logical, since it means that in both problems the option with high inflation was considerably more chosen by the subjects with money illusion. In addition, this outcome also provides evidence to demonstrate that money illusion is not sufficient to explain the significant differences of proportions in hypoth-esis F when the full sample is taken into consideration. Tables with the difference of proportions tests for subjects with money illusion can be found in the Appendix 7.

4.3

Loss aversion

The third part of the experiment was designed to measure the standard loss aver-sion of this particular subject pool. Considering that preferences may be influenced by several effects, namely risk aversion, money illusion and loss aversion, it was cru-cial to control or measure all the potential explanations. Evidence shows existence of loss aversion within this particular experiment´s subject pool. As it was explained in the Methodology section, the third part consisted on three hypotheses, each of them divided into two problems. All the problems contained a risky and a safe option and related problems shared final outcomes but differed in their initial endowment. There-fore, risk aversion could not explain significant differences of proportions of choices

of risky options between related problems. In hypothesis G, a significant difference between choices of Option 21 of Problem 11 and Option 23 of Problem 12 could only be explained by loss aversion. Indeed, Option 21 was chosen 41% of the times and Option 23 just 18%. The difference is significant with p<.01.

Table 4.8: Difference of proportions in hypothesis G Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z)

Option 21 40.55% 2.57% 365 35.51% 45.58% Option 23 18.36% 2.03% 365 14.38% 22.33%

difference 22.19% 3.27% 15.78% 28.61% 6.58 0.0000 Notes: difference: prop(Option 21) - prop(Option 23)

H0: difference = 0 Ha: difference > 0

In hypothesis H, a significant difference between choices of Option 25 of Problem 13 and Option 27 of Problem 14 would be evidence of loss aversion. In fact, 30% of the subjects chose Option 25, while just 14% Option 27. The difference is also significant with p<.01.

Table 4.9: Difference of proportions in hypothesis H Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z)

Option 25 30.41% 2.41% 365 25.69% 35.13% Option 27 13.97% 1.81% 365 10.42% 17.53%

difference 16.44% 3.02% 10.53% 22.35% 5.34 0.0000 Notes: difference: prop(Option 25) - prop(Option 27)

H0: difference = 0 Ha: difference > 0

Finally, in hypothesis I, significant differences between choices of Option 29 of Problem 15 and Option 31 of Problem 16 could only be explained by loss aversion. 64% of the subjects chose Option 29 and 56% Option 31. In this case, the difference is significant with p<.05.

Table 4.10: Difference of proportions in hypothesis I Option Mean St.Dev. N [95% Conf. Interval] z Pr(Z>z)

Option 29 64.38% 2.51% 365 59.47% 69.30% Option 31 56.44% 2.60% 365 51.35% 61.53%

difference 7.95% 3.61% 0.87% 15.02% 2.19 0.0141 Notes: difference: prop(Option 29) - prop(Option 31)

H0: difference = 0 Ha: difference > 0

The above results provide strong evidence about existence of standard loss aver-sion within this subject pool. In order to understand the qualitative determinants of loss aversion, another probit regression can be run. To do so, subjects are categorized as Loss Averse if they shifted their preferences accordingly to loss aversion predictions at least two out of the three possible times. 73 out of 365 subjects were added to the

Loss Averse category. It is important to mention that in this part of the experiment

there was no treatment division, so it was not necessary to discard part of the sample from the analysis. The probit regression results, which can be found in the Appendix 6, suggest that neither the indicator variables nor the cognitive abilities produced significant modifications in the likelihood of suffering from loss aversion. The only qualitative attribute that had a relatively significant effect on loss aversion was gen-der, since the probit regression shows that women were more loss averse than men, with p<.17. This result is also coherent with previous literature findings (Brooks and Zank, 2005). Computing the difference in the cumulative distributive function of the normal distribution when the female indicator goes from zero to one, it is possible to conclude that females were 4.7% more likely to suffer from loss aversion than males.

As it was made with the subgroup of people that suffered from money illusion before, it is also insightful to evaluate the responses in the second part of the exper-iment of the subgroup of subjects that demonstrated strong levels of loss aversion in the third part. As it can be seen the Appendix 8, most of the hypotheses conclusions

are slightly stronger for subjects with loss aversion than for the complete subject pool. The only case in which the tendency is reversed is hypothesis A, but it is irrelevant in this section since it was the only hypothesis without nominal nor real losses. A particular result that must be noticed is that in hypothesis F, Option 19 (in which nominal gains did not completely hide the real losses) was considerably less chosen by loss averse subjects than by the full sample. In contrary, choices of Option 17 (in which real losses were fully hidden behind nominal gains), do not show substantial differences depending on which group is considered. This result provides further ev-idence in favor of the nominal loss aversion hypothesis, since it reflects that people that demonstrated to suffer from standard loss aversion, did not choose less an option with real losses if they were covered behind nominal gains. In contrast, loss averse subjects greatly disliked options with high inflation and nominal losses.

4.4

Rational behavior

Considering that the second part contained five situations in which subjects could make irrational decisions, it is interesting to analyze the composition of the Rational

Subjecs TA subgroup, which incorporates those participants from Treatment A that

consistently made rational and coherent decisions. In other words, this subgroup contains subjects that did not choose any stochastically dominated option and did not shift their preferences due to inflation. 41 out of 189 subjects met all the conditions and were added to the Rational Subjecs TA group. Again, in this case Treatment B is not considered, since the misleading framing could have guided participants to make an irrational decision that would not have happened in a transparent environment. The third model of Appendix 6 shows that rational behavior did not depend on most of the indicator variables. However, there are some exceptions. Counterintuitively,

relative to those with a high school education level, those with a bachelor and master education level were less likely to have rational behavior. The effect is significant for bachelor level but not significant for master level. This is an intriguing result, since it is opposed to what would have been expected. Unfortunately, this experiment had not anticipated this result and there were no other questions in the experiment to test this conclusion further. On the contrary, those subjects with a higher Score

Review were more likely to evidence rational behavior. Score Review is a variable

that measures how many review questions each subject answered correctly before the second part. As it was explained in the Methodology section, the review section was intended to measure subjects´ understanding of the instructions and the inflation mechanisms. There were three questions (that can be found in the Appendix 2), so every subject has a Score Review between zero and three. This probit regression and the margins analysis conclude that, with a confidence of 88%, participants with an extra correct answer in the review section were on average 6.5% more likely to have rational behavior.

Based on the previous conclusion, new differences of proportions tests were per-formed, but restricting the analysis to those subjects with a perfect score in the review section. If participants with better performance in the review section were more likely to choose rationally and consistently in the second part, it became interesting to dis-card the possibility that money illusion and nominal loss aversion were simply caused by a lack of instructions´ understanding. The complete set of tests can be found in the Appendix 9. In summary, there are no unidirectional modifications of results when only subjects with perfect Score Review are considered. Hypotheses A, B, C presented larger differences of proportions while hypotheses D, E and F had opposite results. Nevertheless, it is still appealing that subjects with a higher Score Review significantly chose less the stochastically dominated options in hypotheses D and E.

The following probit regressions and a margins analysis prove that a marginal increase in the Score Review made participants 6.5% and 6.7% less likely on average to choose the stochastically dominated option in hypotheses D and E respectively, both results significant with p<.10. Furthermore, the same analysis demonstrates that higher cognitive abilities did not have a significant impact in the choice of stochastically dominated options.

Table 4.11: Effect of cognitive abilities and review score on the choice of stochastically dominated options

Option 14 Option 15

Score Part1 0.05 0.03

(0.08) (0.08)

Score Review Part2 -0.21∗ -0.20∗

(0.11) (0.11)

_cons -0.68 -0.37

(0.65) (0.63)

N 189 189

Standard errors in parentheses

The above coefficients do not represent the marginal effects of the variables.

∗ _{p < 0.10,}∗∗ _{p < 0.05,}∗∗∗ _{p < 0.01}

4.5

Interaction between money illusion and loss

aversion

A detailed analysis of hypothesis F must be made, since this hypothesis is crucial to understand some of the mechanisms that determine people decision-making. As it was mentioned before, hypothesis F was the only situation in which the predicted results were not found in the evidence. This happened because in the experimental design it was not foreseen a dislike for inflation per se. Therefore, predictions expected a neutral effect of inflation, as long as real losses were not fully covered behind nominal

gains. Hypothesis F had been designed as the main test for nominal loss aversion, since it was the only situation in which money illusion could not have explained a significant difference of proportions between Option 17 and the random choice. Nevertheless, the unexpected dislike for inflation made it impossible to arrive to this conclusion at first sight, since the larger choice of Option 17 than Option 19 could also be fully explained by larger money illusion, in a situation in which Option 17 had 30% accumulated inflation and Option 19 just 15%.

Considering this problem, a deeper analysis of this hypothesis should be made, in order to find other evidence-based insights to prove or discard the existence of nominal loss aversion. Using the previously created subgroups, which include subjects with money illusion and standard loss aversion, two probit regressions are run, trying to understand the determinants of the choices of Option 17 and Option 19. As it can be seen in the Table 4.12, subjects with money illusion were significantly more likely to choose Option 17. Additionally, subjects with both money illusion and loss aversion were also significantly more likely to choose Option 17. The computation of the marginal effects leads to the outcome that they were respectively 21% and 38% more likely to choose Option 17. However, there were not significant effects regarding loss averse subjects. On the other hand, the other probit model reflects that subjects with money illusion were also significantly more likely to choose Option 19. In opposition, loss averse participants were significantly less likely to choose Option 19. The calculation of the marginal effects imply that subjects with money illusion were 27% more likely to choose Option 19 but loss averse participants were 14% less likely to choose that same option. These results are extremely insightful, since they are the strongest prove in favor of the existence of nominal loss aversion. Subjects with money illusion significantly preferred in both problems the option with larger inflation and nominal outcomes (Option 17 against Option 18 and Option 19