The Effect of Learning and Fatigue on Preferences and WTP in a ...

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Table 3: Likelihood ratio tests for equality <strong>of</strong> model parameters. Model Likelihood Sum <strong>of</strong> sample 2 x (sum <strong>of</strong> sample A Critical values for chisquare statistics at 5% value A <strong>and</strong> B <strong>and</strong> B - pooled) First 8 CS -2533.9 Last 8 CS -2414.6 -4948.6 Pooled -4303.5 -1290.13 18.31 Pooled with scaling -4299.7 -1297.81 16.92 This test also shows that the hypothesis <strong>of</strong> equal parameters in the two models can be rejected at the 5% level (with a test value at 1298), suggesting that the preference structure is clearly different in the last 8 CS, even after an adjustment for differences in the error variance. Recall that the scale parameter is the inverse <strong>of</strong> the st<strong>and</strong>ard deviation <strong>of</strong> the error term (Swait & Louviere 1993). <strong>The</strong> scale factor <strong>of</strong> 1.14 identified in table 2 implies that the variance <strong>of</strong> the error term or “noise” in the model based on the last 8 CS is 23% smaller than in model based on the first 8 CS 3 . <strong>The</strong> appearance <strong>of</strong> smaller error variance in the model based on the last 8 CS indicates that respondents’ preferences have settled <strong>and</strong> that a learning effect has taken place during the first 8 CS. This corresponds to the comparison <strong>of</strong> model fit between the two models (i) <strong>and</strong> (ii), where the model based on the last 8 CS clearly provides a better fit to the data. This is equivalent to the findings by Holmes & Boyle (2005). <strong>The</strong> above tests are joint tests that demonstrate a change in the overall preference structure. In a more detailed analysis <strong>of</strong> how the preferences change, we compare the relative size <strong>of</strong> the attribute coefficients across sub-samples. In order to avoid the confounding <strong>of</strong> scale <strong>of</strong> the Gumbel error <strong>and</strong> structure <strong>of</strong> utility across the two sub-samples used in Models (i) <strong>and</strong> (ii) (Hausman & Ruud 1987, 3 (1/1.14 2 ) = 0.7695, hence there is a 23% difference in the variance between the two models. 14
Scarpa et al. 2008, Swait & Louviere 1993), we focus on the marginal rate <strong>of</strong> substitution between price <strong>and</strong> attributes, which is equivalent to the WTP for each attribute. Table 4: WTP estimates, variance <strong>of</strong> WTP <strong>and</strong> t-values based on Models (i) <strong>and</strong> (ii). Model (i): First 8 CS Model (ii): Last 8 CS WTP Var(WTP) 1 WTP Var(WTP) 1 |t-value| Campylobacter-free label 21.60 1.96 20.77 1.98 0.418 Salmonella-free label 16.53 2.01 21.54 2.65 2.318 Domestic produce 31.79 3.37 30.34 4.98 0.500 Organic production 12.11 4.11 17.32 5.28 1.703 ASC (Status quo) 3.79 12.57 7.26 11.12 0.713 Price St<strong>and</strong>ard Deviation Campylobacter-free label 1.99 15.97 4.99 20.75 0.495 Salmonella-free label 14.40 8.71 19.05 14.51 0.964 Domestic produce 18.03 10.10 23.54 13.04 1.146 Outdoor production 27.89 12.86 28.03 20.39 0.023 ASC (Status quo) 51.47 21.66 47.85 20.97 0.555 Note: <strong>The</strong> WTP estimates are calculated as marginal rates <strong>of</strong> substitution between the given non-price variable <strong>and</strong> the price variable. <strong>The</strong> estimates are presented in DKK (DKK 10 ~ EUR 1.34). 1) <strong>The</strong> variation <strong>of</strong> the WTP is estimated with the Delta method (Greene 2003). <strong>The</strong> WTP estimates reported in table 4 reveals that the learning effect found when looking at the error variance between the first 8 <strong>and</strong> the last 8 CS as well as the LR test for identical preferences translates into some significant differences in the WTP estimates. However, only for the Salmonella-free attribute do we see a significant change in terms <strong>of</strong> an increase in WTP going from the first 8 CS to the last 8 CS. Relaxing the cut-<strong>of</strong>f level for statistical significance to a 0.10 level, 15
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