Differences in Commitment

We analyze the difference of commitment status by comparing the choices of those sub-jects that have been observed under both conditions, i.e., we utilize the same subsub-jects as in the NPC analyses in Section 3.4.3. For each subject, we generate the difference

3.4. EMPIRICAL ANALYSIS 65

Notes: Reported is the mean difference of choice variables between non-pre-commitment (NPC) and pre-non-pre-commitment (PC) in percentage points. For the consumption share: N = 52 in period one and N = 51 in periods two and three, respectively. For the investment share: N = 51. Consumption Share is the fraction of current wealth transformed into internet time. Investment share is the fraction of remaining wealth after consumption that is invested in the risky asset. Differences are computed by subtracting PC values from NPC values for each subject. Paths that are compared to each other have the same color. The dashed line corresponds to the reference level of zero (no difference).

Figure 3.4: Commitment Differences of Choice Variables.

in consumption shares, ∆ρ_t := ρ^NPC_t − ρ^PC_t , and the difference in investment shares,

∆α_t := α^NPC_t − α_t^PC. We then perform the same analyses as before where we analyzed the choices under PC and NPC separately.

Figure 3.4 displays, for each realized path, the mean differences for the two choice variables.³⁰ We first analyze whether the difference between commitment status is sta-tistically different from zero. We account for the small sample size, specifically in period three, by using the SR test and the FPP test.

30Table 3.C.8 presents the according standard deviations. In contrast to the separate analyses of PC and NPC choices, investment shares do not always vary more strongly than consumption shares.

66 3. CONSUMPTION AND PORTFOLIO CHOICE

Consumption. We observe a general pattern of underconsumption relative to the plan made in the PC stage. Collapsing the data by subjects yields 52 independent observations and an average difference of -3.55 which is significantly different from zero (SR test, p = 0.0004, FPP test, p = 0.2303). In period one, subjects consume around two percentage points less under NPC (SR test, p = 0.0200, FPP test, p = 0.4529). In period two, underconsumption is not significant on the up path (SR test, p = 0.4004, FPP test, p = 0.5824) but on the down path (SR test, p = 0.0593, FPP test, p = 0.0433). The slight positive deviation on path UU is not significant (SR test, p = 0.3109, FPP test, p = 0.9001). On path UD, average underconsumption is large and amounts to an average of around 18 percentage points (SR test, p = 0.1094, FPP test, p = 0.0359). Similarly, subjects underconsume by around eleven percentage points on path DU (SR test, p = 0.1361, FPP test, p = 0.0981). We find no statistical difference on path DD (SR test, p = 0.3078, FPP test, p = 0.7646). These results indicate that subjects underconsume if they are not committed to their PC choices.

We analyze whether the commitment difference depends on the investment out-come by pathwise comparisons between subjects as in Section 3.4.3. Generally, com-mitment differences in consumption shares do not vary with the investment outcome.

Underconsumption is not significantly different in period two. In period three, only the seven percentage point difference between UD and DU is significant under the FPP test (p = 0.0572) but not under the U-test (p = 0.4969).³¹ Overall, we cannot reject that differences between PC and NPC consumption behavior is independent of the investment outcome. The difference in commitment does further not significantly change over time (Spearman’s rank correlation = -0.0590, p = 0.4675).

Investment. We find no general pattern in the commitment difference regarding invest-ment behavior. Collapsing over all paths by subjects, the average investinvest-ment difference is -0.869 and we cannot reject that investment shares are the same under PC and un-der NPC (SR test, p = 0.8539, FPP test, p = 0.5609). In period one and two, we find no statistical difference in commitment.³² In period three, the only difference that shows an effect that can be statistically distinguished from zero is the approximately ten percentage-point overinvestment in DD (SR test, p = 0.1293, FPP test, p = 0.0938).³³

31U vs D: U-test, p = 0.2821, FPP test, p = 0.3523. DU vs DD: U-test, p = 0.5637, FPP test, p = 0.1772.

32Period one: SR test, p = 0.3885, FPP test, p = 0.5098. Path U: SR test, p = 0.2658, FPP test, p = 0.4824. Path D: SR test, p = 0.5815, FPP test, p = 0.9158.

33UU: SR test, p = 0.8885, FP test, p = 1.000. UD: SR test, p = 0.1965, FPP test p = 0.1303. DU:

SR test, p = 0.6658, FPP test, p = 0.8759.

3.5. DISCUSSION 67

As with consumption behavior, we also find no indication that commitment dif-ferences in investment depend systematically on the investment outcome.³⁴ Further, the difference in investment behavior between NPC and PC does not systematically vary over time (Spearman’s rank correlation = 0.0484, p = 0.5523).

Tables 3.C.9 and 3.C.10 report the results of the parametric regressions. For the consumption share, we see that the commitment difference (given by the constant) is significant when we only control for the investment outcome (p < 0.01). However, if we include the other control variables, the underconsumption vanishes. This effect does not differ across estimation techniques. For the investment share, we find no significant impact of any of the independent variables.

Result 3 [Difference in Commitment] Overall, subjects underconsume under NPC rela-tive to their PC choices but this effect is not robust against parametric estimation under the inclusion of control variables. Investment behavior is not distinguishable between PC and NPC. Commitment differences for both consumption and investment behavior do neither systematically vary in the investment outcome nor over time.

3.5 Discussion

Standard preferences generally predict behavior well in the experiment. However, the significantly negative correlation between consumption shares and investment outcomes under PC and the significant underconsumption relative to the PC path are inconsistent with the model of Samuelson (1969). Hence, we present two alternative preference spec-ifications to explain these results. We further discuss the internal validity of our design and our implementation of real consumption.