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INTRODUCTIONIn behavioral economics, the endowment effect is the hypothesis that a person's willingness to accept (WTA) compensation for a good is greater than their willingness to pay (WTP) for it once their property right to it has been established.

I theoretically study dynamic general equilibrium economies populated with reference dependent agents. I show that under plausible axioms, these dynamic economies generate a countervailing force to the static endowment effect that I call the “momentum effect.”

Over the last three decades, dozens of experiments have demonstrated that human decision making can be powerfully shaped by reference points.

INTRO CONT’D If reference points track endowments, then these small trades will tend to make

agents open to additional rounds of trade. Over time this iterative process must eventually generate much greater trading volumes than would be observed in a static economy.

In my experiment I answer the question by using two microeconomic concepts. First, theoretically study dynamic general equilibrium economies populated with reference dependent agents. In these dynamic economies the static endowment effect seems to be countered which I call “momentum effect”. The momentum effect can reduce or even eliminate the trade-dampening effects of the initial endowment effect over time.

INTRO CONT’D Second, I work on an experiment to test the existence of dynamic effects predicted in

my theory. In the experiment, subjects completely rank 57 bundles containing various combinations of two goods. This helps subjects trade after the first round.

The process is then repeated in a second round where subjects get a chance to trade again. Unlike previous designs, the experimental setting is continuous and dynamic. This setting allowed me to test the hypothesis that subjects’ preference adjust in a trade-enhancing manner between periods.

HYPOTHESIS The momentum effect will have the

potential and evidence to disprove the endowment effect. This will be seen through the graphs of reference dependent curves. Subjects' willingness to trade their given amount of goods are expected to dramatically increase when they were allowed to trade as predicted by the theory (momentum effect).

MATERIALS AND METHODS I conducted 8 sessions using a total of 60 undergraduate subjects at Baruch College

between October, 2011 and May, 2012. In each session, subjects entered the laboratory and were given instructions that described the entire structure of the session in advance.

Undoubtedly subjects will suffer from boredom and fatigue so I put a great deal of effort into making it easy and quick to rank a large number of bundles, minimizing the costs of fine tuning rankings to accurately represent preferences. The software can be seen in Figure 4. The first number (in green – see figure 4) represents a number of lottery tickets, the second number (in blue) represents a number of chocolates. The combination of items they will be given at the beginning of the experiment will be represented by one of these slips, let's call it slip A. Each slip will be ordered by favorite to least favorite (1-57).

Once all 57 bundles had been ranked, a “Submit” button appeared at the bottom of the screen. Subjects could adjust the order of the bundles as much as they liked prior to submitting their final ranking.

MATERIALS AND METHODS CONT’D

Figure 4: Screenshot. Custom software allows users to drag and drop each bundle (left hand side of the screen) into a rank position (right hand side of the screen) to submit their preferences. This allows subjects to very quickly build up their rankings and to later fine tune them quickly and easily.

MATERIALS AND METHODS CONT’D After necessary swaps in the first period were completed, the

experiment was repeated for period 2 with the same procedure one more time. The subject was quietly informed which bundle had been randomly selected for her, and a trade was made if she had ranked the selected bundle lower (better) than her current endowment. After each subject had been informed of the result for the period, a new period proceeded identically to the first. The set of slips available will remain unchanged. If the randomly selected slip in this second round is ranked higher than the slip representing their current combination of items, the appropriate swap will occur. After all necessary swaps are complete; they will be free to leave the experiment.

MATERIALS AND METHODS CONT’D

Figure 5: Empirical Strategy. Each panel (one for each subject type) plots the set of rank-able bundles from the experiment as dots. Hypothetical GCES indifference curves are plotted through a second period endowment of (5, 10). In each case, one (solid line) is generated by a reference point at the first period endowment and the other (dotted line) by a reference point at the second period endowment. Hollow blue dots show bundles added to the preferred-to (the second period endowment) set in the second period; solid red dots show bundles removed from this set in the second period.

RESULT #1 Momentum Trading vs. Endowment Theory : Momentum trading predicts expansion in

willingness to trade and a freeze of it after one or several trades. While the Endowment theory predicts that trading will not start.

Result 1: Willingness to trade doubles. On average the anterior preferred-to set more than doubles between the first and second period,

evincing a large aggregate expansion in willingness to trade. Some subjects have little or no opportunity to reveal adjustment in the anterior quadrant at the second period endowment due to constraints provided by their location.

Most subjects show the adjustments during the posterior quadrants where momentum rotation predicts contraction of the preferred-to set. Figure 1 shows that the red bars dominate the posterior quadrant as the blue bars dominate the anterior quadrant The red indicates the contraction. The degree of adjustment is overall considerably more modest than in the anterior quadrant (as fewer subjects are observed uncensored in this region) and adjustments are somewhat smaller. Still, as Table 1 makes clear, over twice as many subjects contract as expand in the posterior quadrant.

RESULT #2 Result 2: Willingness to trade freezes after one or more trades as soon as

satisfaction is achieved. On average the posterior preferred-to set shrinks between the first and second period. This is consistent with momentum rotation.

I needed to adjust the anterior and posterior quadrant since it was a high powered test of patterns. After the data was collected each subject’s data was summed up of the changes to the preferred-to set consistent with momentum adjustment and those inconsistent with momentum adjustment. We exclude from our test subjects only capable of adjusting in momentum or anti-momentum consistent directions to avoid bias.

RESULTS #3 Result 3: 60% to 80% of the subjects demonstrate a behavior that supported the

momentum trading theory. The mean momentum adjustment is over 5 times larger than the mean anti-momentum adjustment. On net, 2/3 of subjects adjust in a manner consistent with momentum rotation. This proportion rises to nearly 80% in the subset of subjects who made strong systematic net adjustments in their preferences between the first and second period.

My experiment was designed to see changes in one subject and not multiple. Specifically, for most subjects we do not observe an incentive-compatible ranking of the first period endowment bundle of the opposite subject type, making it impossible to credibly compare how subjects of each type rank each other’s endowments. As seen through testing the reference dependence has a strong influence over first period preferences. When the subjects are allowed to rank the bundles, the endowed bundle, on average, is 30% lower (more strongly preferred) than the non-endowed bundles. This trend is highly significant.

RESULTS CONT’D Evidence From the Experimental Graphs: The left hand panel of Figure 1 is

dominated by blue, revealing a huge expansion in the average size of the anterior preferred-to set from the first to the second period. The expansion (supports my theory) for some subjects are visible in the graphs; by contrast only a small minority show evidence of net contraction (against my theory) and these contractions tend to be tiny in size relative to the typical expansion. Table 1 summarizes, revealing that the anterior set doubles in size from 7 to 14 between the first and second period. About 2/3 of subjects reveal net expansion while less than 1/4, on net, contract.

RESULTS CONT’D In Figure 1 (next slide) it can be seen that by plotting vertical bars it is broader in

viewing which visualizes the size preferred-to sets for each subject. The preferred to set is shown by the grey shaded area and the red bars in period 1 and the gray plus blue area represents the size in period 2. Thus, red represents net shrinkage in the preferred-to set and blue net expansion.

Figures for the anterior and the posterior quadrants are provided and in each case plot only subjects who were both capable of shrinking and expanding in the quadrant. This ensures that individual level censoring of the direction of adjustment in the plotted sample doesn’t generate bias for my results.

The left hand panel of Figure 1 is dominated by blue, revealing a huge expansion in the average size of the anterior preferred-to set from the first to the second period. The expansion for some subjects are visible in the graphs; by contrast only a small minority show evidence of net contraction and these contractions tend to be tiny in size relative to the typical expansion. Table 1 summarizes, revealing that the anterior set doubles in size from 7 to 14 between the first and second period. About 2/3 of subjects reveal net expansion while less than 1/4, on net, contract.

RESULTS

Figure 1: Preferred-to sets in the first and second period in the anterior and posterior quadrants. Gray plus red regions visualize the size of the first period preferred-to set (one bar is provided for each uncensored subject); gray plus blue regions visualize the size of the second period preferred-to set. Red shows net contraction between periods and blue net expansion.

Figure 2: Trade and Preference Rotation: A shift in reference point from A to B causes a counterclockwise rotation in the indifference curve (left panel). This rotation (by each trader) causes a new expansion in the individually rational set and outward shift in the Pareto set, generating new trade (right panel).

Table 1: The first groups of columns shows mean preferred-to set sizes. The second group shows the proportion of subjects who on-net expand versus contract in each quadrant. The final column calculates the mean (across subjects) ratio of the net change between periods to the size of the first period preferred-to set.

DISCUSSION My experiment joins others in literature and extends the findings in the

endowment effect, one of the most experimented topic in economics. In most texts they only went as far as to disagree with the mechanism and inexperience with trading environments play in generating the endowment effect.

My project is bases on a theoretical hypothesis rather than a methodological one. Theoretically my experiment shows that the same behavioral forces (reference dependence at current endowments) that generate the endowment effect at first will completely go against it in the long run. This is called the countervailing force the “momentum effect”.

DISCUSSION CONT’D It is fairly simple and can be easily understood: if the reference points change

with endowments, small amounts of trade will tend to push on for further rounds of trade in a dynamic setting. As a result, measurements of reference dependence made in static settings will tend to overstate the long-run impact of reference dependence on trade, often to a great degree.

In my experiment you can see that static elicitation actually understates the subject’s willingness to trade in the future. On average subjects tend to trade more from the first period to second period, as predicted by the model. The data also shows that the driver of the change was preference rotation, similar to what was assumed in the theory.

DISCUSSION CONT’D Even though my experiment supports my predictions strongly there are some

data that challenges my model. When subjects don’t trade in the second round, I still see a momentum rotation. This indicates that the changes in endowment are not necessary to generate trades predicted by my model. To interpret this finding, it is important to keep in mind that my theory was grown from the assumption that reference points are followed through by current endowments.

Classical experimental results in this literature depend on reference points being shaped primarily by current endowments. However, consistent present-orientated reference points should prevent non-traders’ reference points from changing and is therefore inconsistent with my results.

DISCUSSION CONT’D In summary, my predictions prove that dynamic economies long term trading

is greater than the ones in static economies. If I only tested “willingness” to trade in my first period, I would substantially underestimate eventual trade volumes implied by period 2 rankings.

My theory however does not anticipate an additional effect of market dynamics suggested in my data: markets create an opportunity for growth in sophistication and encourage agents to think about the future after any move is made.

The sophistication seen in my data suggests that market process may work better to limit the effect of reference dependence on trade than my theory predicts.

REFERENCES/ACKNOWLEDGEMENTS 1. Johannes Abeler, Armin Falk, Lorenz Goette, and David Huffman. Reference points and effort provision. The

American Economic Review, 101(2):470–492, 2011.

2. Amos Tversky and Daniel Kahneman. Loss aversion and riskless choice: A reference dependent model. Quarterly Journal of Economics, 106(4):1039–1061, 1991.

3. Jacob Sagi. Anchored preference relations. Journal of Economic Theory, 130(1):283–295, 2006. Jason F.

4. Crockett and Oprea 2012. In the Long Run We All Trade: Reference Dependence in Dynamic Economics, New York, Research Paper, Baruch College, 56 pg.

5. John A. List. Neoclassical theory versus prospect theory: Evidence from the marketplace. Econometrica, 72(2):615–625, 2004.

6. Yusufcan Masatligoglu and Neslihan Uler. Understanding the reference effect. 2012.

7. Alistair Munro and Robert Sugden. On the theory of reference-dependent preferences. Journal of Economic Behavior and Organization, 50(4):407–428, 2003.

8. Charles R. Plott and Kathryn Zeiler. The willingness to pay-willingness to accept gap, the ’endowment effect,’ subject misconceptions, and experimental procedures for eliciting valuations.The American Economic Review, 95(3):530–545, 2005.

9. Dirk Engelmann and Guillaume Hollard. Reconsidering the effect of market experience on the ’endowment effect. Econometrica, 78(6):2005–2019, 2010.

10. Specials thanks to my research teacher, Dr.Shapovalov, for guiding me through my research and professor, Sean Crockett, for allowing me to conduct the project at Baruch College with him.