DEL TRABAJO Y DE LA PREVISION SOCIAL.

Table 3.4: Model specification without identification of protest answers

OLS TOBIT PROBIT SELECT TRUNC

(PARTIC) (2-STAGE)

(1) (2) (3) (4) (5)

Coeff. Coeff. Coeff. Coeff. Coeff.

(s.e.) (s.e.) (s.e.) (s.e.) (s.e.)

ONE -3444.33 -12286.5*** 1.64287*** -10204.4** -4723.4 (2826.68) (3425.36) (0.43343) (5422.03) (3573.58) SEX 456.13 1066.89 0.12942 938.298 748.2 (624.966) (918.762) (0.13932) (1017.33) (972.706) AGE -37.0655* -61.7619** -0.00267 -68.3139** -62.7125** (20.9916) (30.5878) (0.00448) (34.0104) (32.6861) EDUC 198.056 603.822 0.14947** 552.64 158.485 (329.09) (504.75) (0.07642) (619.61) (530.128) INCOME 0.09692** 0.13375*** 0.000007 0.17103*** 0.15636*** (0.04278) (0.03845) (0.000006) (0.04460) (0.04184) STATE_4 -568.369* -853.769* -0.06942 -964.712* -797.169 (343.545) (486.56) (0.07353) (550.295) (519.121) MON_3 587.457*** 611.685 — 1073.05** 1016.65** (238.217) (472.754) (494.669) (496.473) BEQUEST 965.415 49.4694 — 2109.59* 2242.66** (1026.47) (1023.85) (1128.24) (1130.51) NUMB_6 77.7745 114.255** — 82.946* 87.3008* (55.5932) (53.9191) (51.7561) (51.6684) RESP_9 551.365*** 1257.83*** 0.21836*** 886.978 351.934 (227.273) (407.15) (0.05773) (605.13) (450.966) INDEX_8 1768.48 3530.8* 0.59654** 3685.13* 2554.33 (1827.07) (1984.39) (0.31656) (2280.1) (2036.97) INDEX_13 -143.252 542.296 0.19956*** — — (285.065) (455.295) (0.06643) CHAR_8 333.488 1671.28* 0.61174*** — — (740.156) (976.725) (0.15907) BOR_14 -198.251 -777.337 0.13962 — — (880.157) (2404.26) (0.37766) lambda/sigma — 8209.59*** — 4188.25 7632.48 (371.143) (3043.85) (338.637) RHO — — — 0.52 — E(WTP) — 0.66 — — — P(+) — 0.34 — — — R2 0.12 — — 0.16 — C ffl2(df) — 79.35 (13) 81.60(10) — 42.96(10) LOG-L -4032.94 -2729.35 -224.5186 -2624.0663 -2631.21 N 396 396 405 254 254

Notes: Dependent variable: WTP; McDonald and Moffitt decomposition: E(WTP) is the effect on the payment decision and P(+) is the effect on participation; df = degrees of freedom.

Model (1) is the simple OLS regression on the full sample. The explanatory power of this model is low with an of only 0.12.^ Income and age are found to be significant determinants of WTP with the value o f conservation varying positively with income and inversely with age. Attitudes and perceptions also have a strong influence over WTP, with those who feel a sense of responsibility over heritage preservation and those who think monasteries conservation should have high priority in terms of cultural spending willing to pay more. As expected, the better the perceived state of conservation of monasteries, the lower the WTP for conservation.

In the Tobit model (2) a number o f other regressors become significant as well, with all the signs confirming prior expectations. Those who visited a larger number of monasteries attribute a higher value to preservation (which implies that use values are significant); people scoring more highly on the index of cultural activities also have a higher WTP; and having donated money to charity is also seen to have a positive impact on WTP (charitable giving can be interpreted as a proxy for ‘generosity’ traits). The results of the McDonald and Moffitt decomposition o f the marginal effect in the Tobit model, for an equi-marginal change in all dependent variables when initially set at their mean values, is shown in the last half of the table as E(WTP) and P(+). About 34% o f the effect is on the probability of submitting a positive bid (P(+)) with the remaining 66% being on the size o f the WTP amount, conditional on participation (E(WTP)). Hence, interpreting the Tobit marginal effect as simply reflecting the impact of an explanatory variable on the magnitude of WTP would lead to a non­ trivial over-estimation of the corresponding elasticity.

Models (3) and (4) correspond to the two-step selectivity model.^ This specification allows the participation and the payment decisions to be modelled separately.* The results are quite interesting. Column (3) shows that participation seems to be driven mainly by: education (the higher the level o f education the higher the probability of participating); interest in cultural activities (the more culturally active people are, the

^ Other specifications of the model were also examined. With the log-normal distribution the regression had a higher explanatory power of 21%. Those results are not presented here as the log-normal assumes that none of the limit observations correspond to an underlying negative WTP value, which is a conceivable possibility with this data set.

’ Full information maximum likelihood estimation was attempted but the model failed to converge. The two-step estimator used is consistent albeit not fully efficient.

more likely they are to participate in the programme); generosity attributes, as measured by charitable giving (those who donate to charitable causes are also more likely to pay for monasteries conservation); attitudes towards the proposed conservation programme (a higher level of agreement with various aspects of the programme implies a higher probability o f participating); and a sense of responsibility over heritage preservation (which impacts positively on participation). These results all conform to prior expectations.

In turn, the decision of how much to pay (column 4) is mainly driven by: income (which has a strong positive impact on WTP); age (which is negatively correlated with WTP); interest in cultural activities (which not only has a positive impact on the probability of participating but also influences positively the level of payment); number of monasteries visited (with a positive influence on WTP); perceived state of monasteries conservation (the better the perceived conservation state the lower the WTP); and two attitudinal variables (both those with bequest concerns and those who think monasteries should have high priority amongst heritage investments are willing to pay more).

In single index models such as the Tobit, the different motivations behind participation and payment choices do not become apparent. This constitutes a limitation to the applicability o f the results from these models as untangling the determinants of both decisions may have important implication in terms of policy. For example, the model estimates from columns (3) and (4) show that an increase in income may not lead to a significant increase in the number o f those willing to participate in a heritage conservation programme. In order to increase participation, education campaigns and efforts to raise cultural awareness may be more effective ways of promoting a more extensive participation.

The coefficient o f X (the inverse Mills ratio) indicates whether the sample selection specification used to model the data is statistically significant, i.e. whether selectivity on positive willingness to pay is significant. The results on column (5) show that the lambda coefficient is not significant at the 10% level, which implies that self-selection bias is not a serious problem in the data (the estimated correlation coefficient is 0.52).

The results from Cragg’s double-hurdle model are included in columns (3) and (5). As in the Heckman specification, this model assumes that both participation and payment choices may have different determinant factors. The results are qualitatively similar to those reported for the selectivity model.

3.5.2 Case 2: With Identification of ‘Protest’ Answers

Table 3.5 contains the results of estimating the models introduced in section 3.3.2, given availability of auxiliary information on protest answers. A probit model was used to analyse the determinants of protesting (assuming that this is an exogenous and independent decision). The results are given in column (1). As expected, those who object to various aspects of the conservation programme are more likely to protest (as measured by the negative coefficient on Index_13). Furthermore, finding the questionnaire to be boring strongly increases the probability of protesting. Thinking that monasteries are in a good state of conservation also increases the likelihood of a protest vote, and men are more likely to protest than women. It is interesting to note that the impact o f variables such as Bor_14 was concealed in the full sample regressions of Table 3.4.

Table 3.5: Model specification with identification of protest answers

PROBIT OLS TOBIT PROBIT SELECT TRUNC

(PROT) (PARTIC) (2-STAGE)

(1) (2) (3) (4) (5) (6)

Coeff. Coeff. Coeff. Coeff. Coeff. Coeff.

(s.e.) (s.e.) (s.e.) (s.e.) (s.e.) (s.e.)

ONE -1.73586*** -3918.42 -12187.6*** -1.67563*** -9794.3* -4723.4 (0.73602) (3090.73) (3444.34) (0.45232) (5305.24) (3573.58) SEX 0.54360** 598.42 1426.23 0.25640* 1137.26 748.2 (0.26018) (654.997) (923.477) (0.14655) (1046.32) (972.706) AGE -0.00312 -40.6281* -67.3017** -0.00418 -71.1934** -62.7125** (0.00819) (21.7728) (30.5648) (0.00463) (34.2309) (32.6861) EDUC -0.11396 209.429 569.033 0.13869* 493.427 158.485 (0.14813) (343.128) (501.621) (0.07829) (602.337) (530.128) INCOME 0.000002 0.10373** 0.14028*** 0.000008 0.17145*** 0.15636*** (0.00001) (0.04463) (0.03841) (0.000006) (0.04459) (0.04184) STATE_4 0.27827** -512.166 -658.357 -0.02339 -864.337* -797.169 (0.13638) (345.974) (487.841) (0.07676) (537.213) (519.121) MON_3 — 630.882*** 641.204 — 1070.72** 1016.65** (256.196) (473.61) (494.817) (496.473) BEQUEST — 1257.57 648.854 — 2121.2** 2242.66** (1155.6) (1035.25) (1127.78) (1130.51) NUMB_6 — 74.4665 106.083** — 83.6474* 87.3008* (54.6543) (53.3504) (51.7241) (51.6684) RESP_9 — 586.876*** 1237.69*** 0.23051*** 848.977 351.934 (242.696) (410.202) (0.06080) (595.735) (450.966) INDEX_8 -0.42982 1795.38 3351.94* 0.56678* 3503.06 2554.33 (0.55595) (1871.97) (1991.74) (0.33189) (2234.77) (2036.97) INDEX_13 -0.23152** -165.404 426.993 0.18687 — — (0.10966) (297.214) (459.852) (0.06967) CHAR_8 369.453 (787.134) 1728.8* (981.413) 0.68524*** (0.16954) BOR_14 1.13473*** (0.38637) — — — — — Lambda/sigma — — 8124.55 (366.26) — 3977.35 (3009.23) 7632.48 (338.637) RHO — — — — 0.49 — E(WTP) — — 0.64 — — — P(+) — — 0.36 — — — R2 — 0.13 — — 0.16 — CHI 2 (df) 29.03 (8) — 76.86 (12) 78.72 (9) 42.96(10) — LOG-L. -62.4492 -3846.42 -2717.991 -205.8675 -2624.15 -2631.21 N 411 377 377 386 254 254

Notes: Dependent variable: payment decision and P(+) is

WTP; McDonald and Moffitt decomposition: E(WTP) is the effect on the the effect on participation; df = degrees of freedom.

The remaining columns in Table 3.5 present the estimated coefficients of the models discussed previously that are now applied to the sub-sample of valid answers only. The main difference between the OLS (2) and the Tobit (3) models, 'with and without identification of protests, is the fact that the perceived state of monasteries conservation ceases to be significant once information on protests is incorporated. This suggests that the main influence of this variable is on the probability of protesting.

It is noteworthy that, in the presence of sample separation, the probit model on the protest decision (1) and the Tobit model (3) can be interpreted as a double-hurdle specification (Jones, 1989). The two hurdles now have the following interpretation: a positive WTP is only observed if a decision is made not to protest and there is a desire to participate in the contingent market. This specification assumes that participation and payment are determined by the same model.

Columns (4) and (5) contain the selectivity model. One important feature of introducing sample separation is that the Heckman specification together with the probit model of colunm (1) allow all the three consumer decisions presented in section 3.2 to be separately estimated (assuming independence o f (1)).^ In terms of the results, the main impact o f the identification of protests is that attitudes towards the proposed conservation programme are no longer significant determinants of the participation decision depicted in (4). This indicates that objecting to some aspect of the programme is likely to increase the probability of protesting rather than the probability of giving a genuine zero answer, which seems a reasonable assumption.

Gragg’s probit+truncated model is presented in columns (4) and (6). Together with the probit model of (1), this specification is an alternative way of estimating the trivariate model (3.1). The results are very similar to those o f the previous model.

^ The fact that the identification of protests allows the estimation to be conditioned on the sample of valid answers can help to avoid selectivity problems (Jones, 1989). However, selectivity bias was not an issue with these data.

The income elasticities implied in the estimated models vary from 1.2 to 2.1. This confirms the expectation that WTP for cultural heritage preservation behaves as a luxury item.^®

Overall, these results highlight the importance o f (i) separately modelling the participation and payment decisions and of (ii) collecting additional information on protest answers so that trivariate models can be estimated. Notwithstanding the relatively small sample size (483), the models successfully identified the major determinants o f the three choices of interest: the protest decision, the participation decision and the payment decision.

The models estimated in Tables 3.4 and 3.5 were also used to compute the predicted WTP mean, setting the independent variables to their sample means.

Following Bockstael et al. (1991), the formulas used for predicting WTP are given by equations (3.13) for the OLS regression, (3.14) for the Tobit model, (3.15) for the Heckman model and (3.16) for the Cragg two-step truncated specification:

E{WTPi) = p 'x i (3.13) E(WTPi) = ( ^ { p ' x i l a s W x i +(Tg (3.14) <P(/0 X i l G g ) y i ! a n ) E{WTPi) = < ^ { a ' y i l < T f , W x i + p o s ] (3. 15) E{WTPO = <!>(«>,• + (Tg / O f ) ] (3 .16)

where O and (j) denote the distribution and density functions o f the standard normal, respectively, and p is the correlation between errors in the selectivity model. Predictions are given in Table 3.6.

As noted in Chapter 1, this does not necessarily imply that monasteries conservation is a luxury good as the CV survey elicited the income elasticity of WTP for a fixed good rather than the income elasticity of demand (Flores and Carson, 1997).

Inspection o f Table 3.6 shows a wide disparity between predicted values. The OLS predictions (on the full sample and on the sample of positive answers) correspond to the sample means. The first Tobit predicted mean applies to the censored data, that is, to observations randomly drawn from the population which may or may not be censored (Greene, 1997). The second predicted mean from the Tobit model represents a prediction o f the latent WTP* variable that can take negative values (and is calculated as P ’x). Interestingly, the mean predicted true WTP is actually negative: according to this model, the part of the implied WTP distribution that is below zero is large enough to drive the mean WTP to a negative range. As mentioned above, it is conceivable that, at least for some respondents, the proposed monasteries preservation programme may be welfare reducing. Many people object to restoration o f cultural heritage assets that involve changes in original features or changes in its (ageing) appearance. There is also a lot of controversy surrounding repair techniques, as they vary in cost, duration and degree o f intrusiveness and damage to the original materials. In some cases, the originals may be so degraded that the repair may involve substituting original parts for replicas. However, the proposed monasteries conservation programme did not provide such level of detail and particular repair techniques were not mentioned. It is therefore difficult to interpret the mean negative predictions o f the Tobit model for this case.

Table 3.6: Predicted mean WTP (BGL per year) Statistical M odel W ithout identification o f

‘protest’ answers W ith identification o f protest’ answers OLS 2109.85 2216.18 OLS (WTP>0) 3289.37 3289.37 Tobit 3331.65 3501.89 Tobit E(WTP*) -743.19 -367.42 Selectivity model 822.81 1033.56 Cragg’s double-hurdle 2512.81 2867.33

WTP* is the true unobservable willingness to pay.

" Differences between these predictions and the sample means presented in Table 3.2 are due to the different sample sizes used to compute the predicted values, due to missing observations in the explanatory variables.

The predicted values from the selectivity and the double-hurdle models seem more reasonable in that they are both positive. They are however very different, with the prediction from the Cragg model approximating the sample mean and the Heckman predicted value being much lower. In general, caution is required when interpreting predictions from these models (as well as the Tobit). This is because these models also predict the WTP values o f non-participants but these are inferred solely from the positive WTP responses.

These results highlight the importance of further investigating the motivations behind non-participation, especially in the presence of a significant number o f non- participants. In particular, future contingent valuation surveys should include questions specifically designed to uncover the motives behind a zero WTP response: not only should protest answers be identified but also attempts should be made to distinguish instances where the change is welfare reducing rather than neutral. The results in Table 3.6 show that these assumptions can have a significant impact on predicted WTP.