Add slides

254 views
218 views

Published on

Published in: Technology, Economy & Finance
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
254
On SlideShare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Add slides

  1. 1. LU p230 onwards… Multilevel modeling: A brief Introduction Many kinds of data have a hierarchical or clustered structure. Multilevel models recognise the existence of such data hierarchies by allowing for residual components at each level in the hierarchy. For example, a two-level model which allows for grouping of child outcomes within schools would include residuals at the child and school level. Thus the residual variance is partitioned into a between-school component (the variance of the school-level residuals) and a within-school component (the variance of the child-level residuals). The school residuals, often called ‘school effects’, represent unobserved school characteristics that affect child outcomes. It is these unobserved variables which lead to correlation between outcomes for children from the same school. Traditional multiple regression techniques treat the units of analysis as independent observations. One consequence of failing to recognise hierarchical structures is that standard errors of regression coefficients will be underestimated, leading to an overstatement of statistical significance. Statistical Analysis of our data Our statistical analysis of the survey data was carried out in several steps: (A) Conventional Analysis of SBDC Responses using the Logit Model Before analyzing the DBDC data using MLM we have first carried out conventional analysis of the Single Bound Dichotomous Choice data first using logistic regression.
  2. 2. Those who gave a negative response to the payment principle question (Q39) were recognised as protest bids and excluded from the analysis. The dependent variable in this model is the ‘yes’ and ‘no’ response (binary data) to whether a respondent will pay the initial bid as a monthly WWTF. In the logistic regression of the SBDC responses we found that apart from pcy and bid none of the other explanatory variables were significant. The equation we get is: Li = ln (Yi / 1- Yi) = 2.007 + -.039 bid + .001 pcY (B) Using MLM to estimate WTP from DBDC data The random effects at Level 2 may contain up to six terms. We have a variance term associated with the intercepts, one with the slope of BID, one with the slope of PCY, one for the variance between slope of BID and the intercept, one for the variance between slope of PCY and the intercept and one for the variance between slope of BID and the slope of PCY. The MLM analysis was carried out on LISREL 8.30. On running the software program we found that there is no significant estimated variance between the response variable and BID and the insignificant terms were omitted. The best model is given as equation (7.38) (7.38) Li = ln (Yi / 1- Yi) = 1.20881 + (0.38446) (0.00154) -0.01946BID (0.00021) + 0.00013PCY The final model includes PCY and BID as explanatory variables and significant first order interactions. We get the median WTP as equal to Rs 93.74. Note that the variance in the model has been divided
  3. 3. between individual effects and effects due to different mean responses to each bid amount offered. The multilevel model is therefore a correct representation of the information gathered in the CV study, as it models the natural hierarchy present in the data. This also shows that the multi-level approach requires more thoughtful interpretation than OLS equivalents (Bateman and Langford 1999) Our Use of MLM method MLM is the appropriate approach for analyzing DBDC data since it provides the opportunity to study variation at different levels of the hierarchy. The DBDB data generated by the CV survey is essentially hierarchical in character. It is a three level model with responses at level 1, individuals at level 2, and initial bid level presented at level 3. However in carrying out the MLM exercise we are principally concerned with estimating the E(WTP) using DBDC data and separating out effects due to the design of the response structure from those due to individuals. Consequently in this study we have only considered a two-stage hierarchy with responses nested within individuals by defining the former as level-1 variation and the latter as level-2. Moreover for modeling the 3 level hierarchical data the number of initial bids should be large which we did not have. Since we found pcY and bid as the only significant variables in the analysis of the SBDC data these were included in the estimation of WTP. The multilevel model we have estimated is: LOGIT ki= a + bBIDki+cPCYki + viBIDki + wiPCYki + ui + eki, PCY = per capita income of the household of the respondent wi = allows random slopes, vi ~ N (0, σ2v)
  4. 4. The random effects at Level 2 may contain up to six terms. We have a variance term associated with the intercepts, one with the slope of BID, one with the slope of PCY, one for the variance between slope of BID and the intercept, one for the variance between slope of PCY and the intercept and one for the variance between slope of BID and the slope of PCY. The MLM analysis was carried out on LISREL 8.30. On running the software program we found that there is no significant estimated variance between the response variable and BID and the insignificant terms were omitted. The best model is given as equation: Li = ln (Yi / 1- Yi) = 1.20881 + -0.01946BID+ 0.00013PCY (0.38446) (0.00154) (0.00021) (C) Estimating the incidence of the benefits from WQIYD For this we used the linear regression model where the dependent variable is SWTP i.e. the maximum WTP figure stated by the respondents in response to the open-ended question at the end of the DBDC valuation questions. The figures are considered to be continuous in nature. After the protest bids outliers were excluded the final count of observations stood at 440 and the OLS regression was run on these using the software package SPSS. The variable bid was included to examine the presence of any anchoring effect or starting point bias. Taking bid C as default, bid B did not turn out to be significant but bid A was positive and significant indicating that those who were offered a bid of Rs 100 did state a higher WTP. Effects of the bid variable were removed by setting bid_a = 0. The mean WTP for WQIYD comes down from Rs 79.46 to Rs 63.23 after correcting for the starting point bias. The median WTP is Rs. 60.41. We see that the WTP estimates obtained from the OLS regression are the most conservative figures. DBDC data have yielded much higher WTP estimates.
  5. 5. Moreover the OLS regression method yields the mean WTP whereas the other two give us estimates of median WTP. Since median cannot be aggregated over the population (Duffield and Patterson 1991) the OLS estimates have been used for determining the incidence of these benefits between different income groups. In this study we have used the income groups fixed by the Market Information Survey of Households (MISH) 2001-02 conducted by NCAER. The NCAER survey fixes income groups and the population is divided into 5 income groups: lower income group (an annual household income of upto Rs 45000), lower-middle income group (Rs 45001 to Rs 90000), middle income group (Rs 90001 to Rs 135000), upper-middle income group (Rs 135000 to Rs 180,000) and higher income group (more than Rs 180,000 of annual household income). Using the SWTP data collected in the survey we were able to estimate the average WTP of households belonging to different income groups a monthly WWTF tabulated below. Average WTP for Different Income Classes The average WTP per month per household (for the user and non user values associated with WQIYD) has been estimated by taking the average of the SWTP of the individuals belonging to each income class. In our study we have taken this WTP figure as the measure of the benefits derived by different income groups (Ebert 2003).
  6. 6. The above figure clearly shows that water quality improvement is a normal good and, as expected, overall the demand for water quality improvement increases with income. The WTP a higher monthly WWTF by the higher income groups is of course a very positive result since they are the ones who have the ability to fund environmental protection programs. Some reconsideration of the meaning of ‘regression’ and ‘progression’ is needed here since the incidence of benefits as well as costs is estimated. Using the terms in parallel fashion this study assumes that a benefit schedule is regressive when the gain as a percentage of income declines as the level of income rise, and that it is progressive when the opposite occurs. It follows, however, that the implications for equality differ depending on whether the regressive schedule is applied to benefits or to costs. Whereas a regressive tax/costs schedule is “against the poor” and “pro-rich”, a regressive benefits/ expenditure schedule is “pro- poor” and “against the rich”. A crucial issue in this method is the choice of the bids offered to respondents since it can affect the estimation of the mean WTP. Three questionnaires were designed with varying double dichotomous bids to measure the respondents’ willingness to pay. These were Questionnaire A: 80-100-120, Questionnaire B: 35-50-65 and Questionnaire C: 10-20-30. These were based on the WTP figures obtained in a pilot study where an open ended format was used. This is, in fact, supported by literature. Most examinations of elicitation effects have compared WTP measures between open-ended (OE) and dichotomous choice (DC) studies, with the majority reporting DC mean WTP exceeding those from OE experiments (Bateman et. al. 1999).

×