-------------------------------------------------------------------------------help for wtpcikr-------------------------------------------------------------------------------

Title

wtpcikr ---Estimate Krinsky and Robb Confidence Intervals for Mean and Median Willingness to Pay (WTP)+--------------------+ ----+ Table of Contents +-----------------------------------------------

Syntax General description of

wtpcikrDescription of the options Saved results Examples Author information Citation References Acknowledgments

wtpcikrvarlist[ifexp] [inrange] [,reps(#)seed(#)level(#)mymean(name)bmat(name)vmat(name)equation(name)exponentialmeanlistdotssaving(filename[,saving_options])]

optionsDescription ------------------------------------------------------------------------- Optionsreps(#)set the number of replicationsseed(#)specify the seed numberlevel(#)set the confidence levelmymean(name)supply a mean vectorbmat(name)specify a vector of parameter estimatesvmat(name)supply a variance covariance matrixequation(name)set the equation nameexponentialexponential functional formmeanlistreport the mean vector used in computationdotsdisplay replication dotssaving(filename, ...)save results tofilename

+-------------+ ----+ Description +------------------------------------------------------

wtpcikrcomputes mean and/or median willingness to pay (WTP), confidence intervals (CI) based on the Krinsky and Robb (1986) method, achieved significance levels (ASL) for testing the null hypothesis that WTP<=0, and relative efficiency measures (Loomis and Ekstrand, 1998). The command supports both linear and exponential contingent valuation models estimated with or without covariates using the Stata commandsprobit,logit, andbiprobit. It can also be used for user-written maximum likelihood programs as long as the formulas for WTP measures apply. The user bears the responsibility as to whether WTP formulas apply. Users are referred to Haab and McConnell (2002), pp. 52-57 and p. 104 for WTP models and mean/median WTP formulas, and pp. 110-112 for the Krinsky and Robb procedure. See also Park et al. (1991).It is crucial that the order of the variables in

varlistafterwtpcikrbe the same as invarlistafter the Stata estimation command. Equally important is the assumption that thebid variablefollows the dependent variable invarlistafter the estimation command and is the first variable specified invarlistafterwtpcikr(see examples below).

wtpcikruses Mata to take random draws from multivariate normal distribution using the variance-covariance matrixvmatand the vector of parameter estimatesbmator the defaults to these options.For exponential logit models, mean WTP is not defined if sigma>1. Stata will issue a warning and only median WTP will be calculated if sigma>1.

+---------------------+ ----+ Options for wtpcikr +----------------------------------------------

reps(#)specifies the number of replications to be performed for the simulations. The default isreps(5000).

seed(#)sets the random-number seed, which is defaulted toseed(032007). This option is useful to ensure replicability of the results.

level(#)sets the confidence level. The default islevel(95).

equation(name)causeswtpcikrto choose a specific equation for which WTP measures and confidence interval are requested, if there are multiple equations. This option is relevant for double bounded models estimated using thebiprobitcommand and user-written maximum likelihood programs which estimate ancillary parameters considered by Stata as equations. By default, computation is done using the first equation.

mymean(name)specifies a vector containing sample means of independent variables (dimension 1 x k-1, k is the number of independent variables specified invarlistafterwtpcikr) to be used in the calculations. For models with covariates, by default,wtpcikruses the sample means of the independent variables specified invarlistexcept the bid variable. Using this option, the user can supply a mean vector indicating the mean value to be used for each independent variable invarlistexcept the bid variable. This option may be of interest to adjust for the fact some socio-demographic characteristics of the sampled respondents sometimes differ from those of the general population in the study area. For example, secondary data from the Census Bureau on the socio-demographic characteristics of the study area population may be combined with socio-demographic characteristics of the sampled respondents in calculating WTP measures and confidence intervals (see example below).This option cannot be specified for constant-only models containing only a constant term and the bid variable as covariates.

bmat(name)specifies a vector of parameter estimates to be used. The default is the vector of estimated coefficients returned in e(b) by the estimation command.

vmat(name)specifies a variance-covariance matrix to be used. The default is the variance-covariance matrix returned in e(V) by the estimation command. Thebmat(name)andvmat(name)ormymean(name)options allow the user to trickwtpcikrto compute WTP measures and CI for models not even estimated in Stata or for models estimated in Stata but without using the above-mentioned Stata commands. In this case, the user is reminded that in the vector of the parameter estimatesbmat, the coefficients on the bid variable and the constant term must be listed in the first and last position respectively. The position of thevmatelements must match that of thebmatelements. The question as to which formulawtpcikrwill use in the calculations is an important one. By default, the formula corresponding to linear probit and logit models is used. If the user wants calculations to be done for an exponential logit model, a simple logit model must be first estimated before runningwtpcikrwith theexponentialoption.

exponentialspecifies that functional form of the underlying model is exponential. If this option is not specified, a linear functional form is assumed.

meanlistrequests that the vector containing the sample means of the explanatory variables used in the computation be displayed. Of course, this option cannot be used for constant-only models and when themymeanoption is specified.

dotscauses replication dots to be displayed. By default, replication dots are suppressed.

saving(filename[,saving_options])specifies that results be saved to a Stata data file,filename.saving_optionsare the options of the Statasavingcommand. The data file will contain the variablesmeanwtpand/ormedianwtp, depending on whether theexponentialoption was specified. The emprical distribution stored infilenamecan be useful in applying thecomplete combinatorialmethod, for example, to test whether differences in WTP measures are statistically significant (See Poe et al., 2005). Although not necessary (since a p-value is calculated), users can also use the stored dataset to calculate standard errors for WTP measures.If your

filename(including its path) contains embedded spaces, remember to enclose it in double quotes.

+---------------+ ----+ Saved results +----------------------------------------------------

wtpcikrreturns most of the calculated results in local macros. After runningwtpcikr, type in return list, to see the saved results.

+----------+ ----+ Examples +---------------------------------------------------------

Linear Probit and bivariate probit with covariates

. probit y1 bid1 income age sex household knowledge env_org. wtpcikr bid1 income age sex household knowledge env_org, reps(10000)meanl dots

. biprobit (y1 = bid1 income age sex household knowledge env_org) (y2 =bid2 income age sex household knowledge env_org). wtpcikr bid1 income age sex household knowledge env_org, reps(20000)equation(y1)

. biprobit (y1=bid1 income) (y2=bid2 income). matrix med_inc=(54)// Suppose this is median income (in $1000) from Census data for study area. wtpcikr bid1 income, reps(50000) eq(y1) mym(med_inc) dots. wtpcikr bid2 income, reps(50000) eq(y2) mym(med_inc) dots

Exponential probit model

. gen lbid=ln(bid). probit ypay lbid income educ age sex dummy1 dummy2. wtpcikr lbid income educ age sex dummy1 dummy2, reps(30000) expoTo use median income (in $1000) and average years of schooling from Census data combined with sample mean of the rest of the variables from survey data

. matrix matcens=[53, 12, 52, .61, .49, .72]// Here a value is not supplied for the bid variable and the constant term. wtpcikr lbid income educ age sex dummy1 dummy2, reps(30000)mym(matcens) expo

Linear constant-only model

. probit y1 bid. wtpcikr bid, reps(40000) dots

Exponential constant-only model

. gen lbid=ln(bid). probit y1 lbid. wtpcikr lbid, reps(40000) expo dots

To save in a Stata data file (myfile) mean and median WTP calculated in each re > plication

. logit y1 lbid. wtpcikr lbid, reps(20000) expo dots saving(C:\foldername\myfile)

P. Wilner Jeanty, Post-Doctoral Researcher, Dept. of Agricultural, Environmenta > l, and Development Economics, The Ohio State University (OSU). Send comments and suggestions to jeanty.1@osu.edu

Users should please cite the program in any published work as:

Jeanty, P. Wilner. 2007. "wtpcikr: Constructing Krinsky and Robb Confidence Int > erval for Mean and Median Willingness to Pay (WTP) Using Stata."North American Stata Users' Group Meetings 2007, 8.

Haab, T.C. and K.E. McConnell. 2002.Valuing Environmental Natural Resources:T> he Econometrics of Non-Market Valuation. Northampton, MA: Edward Elgar Publishing.

Krinsky, I. and A.L. Robb. 1986. "On Approximating the Statistical Properties o > f Elasticities."Review of Economic and Statistics68: 715-719.

Loomis, J. and E. Ekstrand. 1998. "Alternative Approach for Incorporating Uncer > tainty When Estimating Willingness to Pay: The Case of the Mexican Spotted Ow > l."Ecological Economics27: 29-41

Park, T, J.B. Loomis, and M. Creel. 1991. "Confidence Interval for Evaluating B > enefit Estimates from Dichotomous Choice Contingent Valuation Studies."Land Economics67: 64-73.

Poe, G.L., K.L. Giraud, and J.B. Loomis. 2005. "Computational Methods for Measu > ring the Difference of Empirical Distributions."American Journal of Agricultural Economics87:353-365.

The author thanks Arne Risa Hole for sharing a preprint version of his

wtpcomm > and. A grant from the US Dept. of Energy and support from the Office of Energy Efficiency, Ohio Dept. of Development and from the AE > D Economics Dept. are gratefully acknowledged.

See alsoManual:

[R] nlcomOnline: nlcom