Parameterization and Laboratory Implementation

Study 1 entails 12 different treatments in a 2x2x3 mixed design, with one between-subject factor (OPERATIONS frame vs. NEUTRAL frame) and two within-subject factors (high vs. low profit, and three different number of states).

For each of the low profit scenarios (3, 5, or 7 states), we use a discrete uniform demand distribution with lower support A = 100 and upper support B = 160.

For each high profit scenario, A = 300 and B = 900. For the 3-states treatments, we prices and cost parameters such that ^p−w_p = 0.25 in low profit condition and

p−w

p = 0.75 in high profit condition (see Appendix for details on all choice ma-trices implemented in this study). For the 5- and 7-states treatments, we choose these parameters such that π(q₋₁^∗ ) = π(q^∗₊₁) for the two order options q^∗₋₁ and q^∗₊₁adjacent to q^∗, allowing us to assess risk preferences more easily. For the low profit condition these parameters entail losses for some combinations of order quantity and demand, but for the quantities of central interest for our study (q^∗₋₁, q^∗, and q^∗₊₁) all possible outcomes lie in the domain of gains.

The experiment was run at the experimental laboratory of the Collaborative Research Center 504 at the University of Mannheim. In total we recruited 52 subjects for Study 1, mostly undergraduate students, by means of a computer-ized recruitment system. 25 subjects participated in the OPERATIONS and 27 subjects in the NEUTRAL frame. Each subject made a decision for each com-bination of profit condition (HP , LP ) and number of states (3, 5, 7), resulting in six independent choice situations which were presented in random order to counterbalance possible order effects.

Each session began with participants reading manual instructions and re-maining questions were resolved. To ensure that the choice task was properly understood, subjects then had to answer a short series of practicing questions followed by the actual choice situations. In order to increase participants’ in-volvement in each of the choice situations, we omitted laboratory tokens and rather let the choice matrices contain real payoffs (in Euros), and chose the

random lottery procedure for determining the actual payments to the partici-pants (Benzion et al. 2005). After all choices had been made and all uncertainty had been resolved we randomly determined, for each subject independently, one choice situation the realized profit of which was payed out for real. Together with the limited number of choice situations faced by each participant, we ex-pected subjects to devote comparatively more time and cognitive effort on each decision than in previous experimental studies on newsvendor behavior. Also, participants were allowed (and, in fact, explicitly motivated) to revise earlier decisions.

The average duration of all experimental sessions was roughly 30 minutes and average earnings were e9.50 including a e2 participation fee.

3.3.2 Results

Figure 3.1 displays the average order quantities on the aggregate population level. We can reject the null hypothesis that the average orders match the

risk-(a) LP , 3 states (b) LP , 5 states (c) LP , 7 states

(d) HP , 3 states (e) HP , 5 states (f) HP , 7 states

Figure 3.1: Average choices (standard deviations in parantheses) neutral benchmark q^∗ for all high profit treatments (two-tailed sign-test, p = 0.01) but not for the low profit treatments (except in OPERATIONS frame with 5 states, where p = 0.06). Comparing orders under the two different frames, we find significant differences only for high profit with seven states where subjects in the OPERATIONS frame treatment order closer to mean demand than in the corresponding NEUTRAL frame treatment (two tailed Mann-Whitney-U-test, p = 0.012). On the aggregate level, we thus find no evidence for mean ordering behavior and only little differences between the two frames.

We now examine individual choice behavior, defining a subject’s choices as mean-ordering behavior if, given a HP /LP -pair for a number of states (3, 5, or 7), in both the LP and the HP condition the chosen quantity is closer to

mean demand than the profit-maximizing quantity q^∗. Likewise, we define risk aversion if none of the order quantities chosen in HP an LP is larger than q^∗ and at least one of them is lower than q^∗ (and vice versa in order to classify risk seeking behavior). Figure 3.2 displays the revealed choices.

(a) Operations (b) Neutral

Figure 3.2: Individual choice behavior

For the OPERATIONS frame, the data on individual choice patterns reveals that mean ordering behavior increases in the number of states involved in the choice task (Cochran-Q test, p = 0.01). This result speaks to Hypothesis 1 (complexity). As to Hypothesis 2 (framing), the data reveals a stronger ten-dency to anchor in the OPERATIONS frame than in the NEUTRAL frame.

This is intuitive because the latter simply does not provide the decision maker with the mean demand anchor. We conjecture that, given the absence of mean demand as a natural anchor, subjects in the NEUTRAL frame spent more effort on the decision, resulting in choices that potentially better reflect their under-lying preferences with respect to the monetary outcomes given in the decision matrices. This is supported by Table 3.2 which reports on average response times for each treatment. Testing a general linear model reveals a significant main effect of the number of states (within-subject, significant at the 1%-level) as well as of the framing (between-subject, significant at the 1%-level).

Table 3.2: Average response times (in seconds) States OPERATIONS (N=25) NEUTRAL (N=27)

3 30s 32s

5 35s 41s

7 38s 54s

3.3.3 Discussion

The results of Study 1 show the significant impact of task complexity and an-chorable information on mean ordering behavior. The majority of choices were in fact consistent with the predictions of expected utility theory, particularly

in the NEUTRAL frame. More than half of the subjects’ choices revealed risk-averse preferences. Nevertheless, results on the individual level indicate mean ordering even in simple decision situations. Since we controlled for learning opportunities, the chasing demand heuristic cannot account for this result. The question remains whether choices were pulled towards the mean by the mean anchor or due to the desire to minimize expected regret from an ex-post in-ventory error. We try to give a first lead to this by investigating the impact of regret on post-decision satisfaction, however noting that the mere experience of ex-post regret is, while apparently necessary, an insufficient condition for assuming ex-ante anticipation of decision regret. After the demand resolution and independently for each choice situation, in both treatments we provided participants with information on the realized as well as foregone profits and asked them how happy they were with their choice in hindsight. Satisfaction was elicited by means of a 12-point scale anchored by unhappy (1) and happy (12). Let Sit denote the satisfaction expressed by subject i for the resolved choice situation t. We estimate a least square dummy variable model with fixed effects for each decision maker,

Sit= β0+ β1π(qˇ it) + β2R^L/S_it , (3.9) where R^L/S_it = ˇπ(Dit) − ˇπ(qit). In this model, ex-post satisfaction is driven by the absolute payoff of the chosen option qit as well as its level relative to the counterfactual payoff had one chosen Ditinstead. Furthermore, we estimate the parameters of

Sit= β0+ β1π(qˇ it) + β2R^S/C_it (3.10) where R_it^S/C = |qit− Dit|. In this model, ex-post satisfaction is driven by the absolute payoff of the chosen option as well as the ex-post inventory error. The results in Table 3.3 indicate that post-decision utility is indeed driven by both the realized profit and counterfactual outcomes, regardless of how we capture the notion of decision regret.

Table 3.3: Ex-post regret evaluation

S/C L/S

NEUTRAL OPERATIONS NEUTRAL OPERATIONS

β0 5.346 5.561 5.290 5.415

β1 0.304 0.604 0.341 0.624

β2 -0.311 -0.245 -0.268 -0.282

adj. R² 0.494 0.652 0.474 0.671

F 6.609 11.730 6.173 12.703

Since factual experience of regret ex-post to the resolution of uncertainty is a quite natural prerequisite for this psychological sensation to have an ex-ante decision impact, we conjecture that regret plays a role in newsvendor decision making.⁷ In the next section, we try to shed further light on regret from ex-post inventory errors.

7In a separate estimation we included parameters of disappointment theory (Bell 1985)

3.4 Study 2: Regretting Ex-post Inventory