WTP estimates

[rosmery.barroso]

Dear all, I am estimating a choice experiment on substitution across tobacco products (conventional cigarettes, disposable e-cigarettes, rechargeable e-cigarettes, and an opt-out alternative) using the Apollo package in R.
I estimate a panel mixed logit model (MMNL) in WTP space (following Apollo’s manual). The dataset groups respondents from three countries, totaling 22,056 observations (2,757 individuals). Alternative-specific constants are specified for the three product alternatives, while the opt-out is normalised to zero. The attributes included are:
The attributes included in the estimation are:
• Brand
• Price (in USD): $0.50, $1.00, $4.00, $7.00, $8.75, $17.5, $35.5, $56.0, $5, $15, $25, $50
• Flavour: Flavoured vs. unflavoured
• Harm to one's own health
• Harm to other persons’ health (passive smokers)
• Easiness to conceal its use in closed public spaces
The model converges well, parameter signs are behaviorally plausible, and the price coefficient (λ) is constrained negative. However, the implied WTP values are large relative to observed market prices, even after rescaling to comparable product units.
As a diagnostic, we also estimated a panel MMNL in preference space and derived WTP ex post; however, some specifications exhibited convergence difficulties, and even when the model converged properly the implied WTP values remained relatively large.
We would therefore appreciate guidance on potential modelling or identification issues that could explain the magnitude of the WTP estimates.
Many thanks in advance!
Rosmery

# ################################################################# #
#### DEFINE MODEL PARAMETERS ####
# ################################################################# #

### Vector of parameters, including any that are kept fixed in estimation
# for smokers, we use as starting value the estimates for "all smokers" in the
# three countries. In most of the cases it converges starting from zeros.
apollo_beta=c(wtp_asc_disp_mu = 0, wtp_asc_disp_sig = 0,
wtp_asc_rech_mu = 0, wtp_asc_rech_sig = 0,
wtp_asc_cig_mu = 0, wtp_asc_cig_sig = 0,
lambda_mu =-1, lambda_sig = 0,
wtp_ext1_mu = 0, wtp_ext1_sig = 0,
wtp_ext2_mu = 0, wtp_ext2_sig = 0,
wtp_ext3_mu = 0, wtp_ext3_sig = 0,
wtp_harm_mu = 0, wtp_harm_sig = 0,
wtp_hide_mu = 0, wtp_hide_sig = 0,
wtp_flavour1_mu = 0, wtp_flavour1_sig = 0,
wtp_flavour2_mu = 0, wtp_flavour2_sig = 0
)


##If we want to keep parameters fixed to their starting values during the estimation (eg. asc), we include their names in the character vector apollo_fixed.
## this vector is kept empty (apollo_fixed = c()) if all parameters are to be estimated. Parameters included in apollo_fixed are kept at the value used in apollo_beta, which may not be zero

apollo_fixed = c()


# ################################################################# #
#### DEFINE RANDOM COMPONENTS ####
# ################################################################# #

### Set parameters for generating draws. Now we have inter draws to account for heterogeneity intra-individual (across choices for the same individual).
apollo_draws = list(
interDrawsType = "mlhs",
interNDraws = 1000,
interNormDraws = c("draws_wtp_asc_disp","draws_wtp_asc_rech","draws_wtp_asc_cig",
"draws_lambda",
"draws_wtp_ext1","draws_wtp_ext2","draws_wtp_ext3",
"draws_wtp_harm","draws_wtp_hide",
"draws_wtp_flavour1","draws_wtp_flavour2")
)

### Create random parameters
apollo_randCoeff = function(apollo_beta, apollo_inputs){
randcoeff = list()

randcoeff[["wtp_asc_disp"]] = wtp_asc_disp_mu + wtp_asc_disp_sig * draws_wtp_asc_disp
randcoeff[["wtp_asc_rech"]] = wtp_asc_rech_mu + wtp_asc_rech_sig * draws_wtp_asc_rech
randcoeff[["wtp_asc_cig"]] = wtp_asc_cig_mu + wtp_asc_cig_sig * draws_wtp_asc_cig

randcoeff[["lambda"]] = -exp(lambda_mu + lambda_sig * draws_lambda)
randcoeff[["wtp_ext1"]] = wtp_ext1_mu + wtp_ext1_sig * draws_wtp_ext1
randcoeff[["wtp_ext2"]] = wtp_ext2_mu + wtp_ext2_sig * draws_wtp_ext2
randcoeff[["wtp_ext3"]] = wtp_ext3_mu + wtp_ext3_sig * draws_wtp_ext3
randcoeff[["wtp_harm"]] = wtp_harm_mu + wtp_harm_sig * draws_wtp_harm
randcoeff[["wtp_hide"]] = wtp_hide_mu + wtp_hide_sig * draws_wtp_hide
randcoeff[["wtp_flavour1"]] = wtp_flavour1_mu + wtp_flavour1_sig * draws_wtp_flavour1
randcoeff[["wtp_flavour2"]] = wtp_flavour2_mu + wtp_flavour2_sig * draws_wtp_flavour2

return(randcoeff)
}


# ################################################################# #
#### GROUP AND VALIDATE INPUTS ####
# ################################################################# #

apollo_inputs = apollo_validateInputs()

# ################################################################# #
#### DEFINE MODEL AND LIKELIHOOD FUNCTION ####
# ################################################################# #

apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){

### Function initialisation: do not change the following three commands
### Attach inputs and detach after function exit
apollo_attach(apollo_beta, apollo_inputs)
on.exit(apollo_detach(apollo_beta, apollo_inputs))

### Create list of probabilities P
P = list()

### List of utilities: these must use the same names as in mnl_settings, order is irrelevant
V = list()
V[["ecigdisp"]] = lambda * (price1 + wtp_asc_disp +
wtp_ext1*(ext1==1) + wtp_ext2*(ext1==2) + wtp_ext3*(ext1==3) +
wtp_harm*harm1 + wtp_hide*hide1 +
wtp_flavour1*(flavour1==1) + wtp_flavour2*(flavour1==2))

V[["ecigrech"]] = lambda * (price2 + wtp_asc_rech +
wtp_ext1*(ext2==1) + wtp_ext2*(ext2==2) + wtp_ext3*(ext2==3) +
wtp_harm*harm2 + wtp_hide*hide2 +
wtp_flavour1*(flavour2==1) + wtp_flavour2*(flavour2==2))

V[["cig"]] = lambda * (price3 + wtp_asc_cig +
wtp_ext2*ext3 + wtp_harm*harm3 + wtp_hide*hide3 +
wtp_flavour1*(flavour3==1) + wtp_flavour2*(flavour3==2))

V[["optout"]] = 0

### Compute probabilities for 'Colombia', 'Argentina, 'Chile' of the data using MNL model
mnl_settings = list(
alternatives = c(ecigdisp=1, ecigrech=2, cig=3, optout=4),
avail = list(ecigdisp=1, ecigrech=1, cig=1, optout=1),
choiceVar = chosen_option,
utilities = list(ecigdisp= V[["ecigdisp"]],
ecigrech= V[["ecigrech"]],
cig = V[["cig"]],
optout = V[["optout"]])
)

### Compute probabilities using MNL model
P[["model"]] = apollo_mnl(mnl_settings, functionality)

## Combined model - Joint estimation

### Take product across observation for same individual
P = apollo_panelProd(P, apollo_inputs, functionality)

### Average across inter-individual draws
P = apollo_avgInterDraws(P, apollo_inputs, functionality)

### Prepare and return outputs of function
P = apollo_prepareProb(P, apollo_inputs, functionality)
return(P)
}

# ################################################################# #
#### MODEL ESTIMATION ####
# ################################################################# #

model = apollo_estimate(apollo_beta, apollo_fixed, apollo_probabilities, apollo_inputs)

An example of the results of these estimations is the following:


Parameter Estimate Estimate per 20 cigarettes
wtp_asc_disp_mu -1,275975064 -25,51950128
wtp_asc_disp_sig -2,838701901 -56,77403803
wtp_asc_rech_mu -1,217917291 -24,35834582
wtp_asc_rech_sig 3,655677318 73,11354635
wtp_asc_cig_mu -1,357282697 -27,14565393
wtp_asc_cig_sig -3,414041939 -68,28083878
lambda_mu 0,61333938 12,2667876
lambda_sig -1,419790253 -28,39580506
wtp_ext1_mu 0,443163418 8,863268357
wtp_ext1_sig -0,04922976 -0,98459521
wtp_ext2_mu 0,927212082 18,54424164
wtp_ext2_sig 0,512091542 10,24183085
wtp_ext3_mu 0,478479233 9,569584665
wtp_ext3_sig -0,20573522 -4,11470439
wtp_harm_mu 0,445440496 8,908809928
wtp_harm_sig -0,409034468 -8,180689358
wtp_hide_mu 0,167625388 3,352507754
wtp_hide_sig 0,249399144 4,987982875
wtp_flavour1_mu -0,151822064 -3,036441286
wtp_flavour1_sig 0,165939484 3,318789687
wtp_flavour2_mu -0,228079256 -4,561585124
wtp_flavour2_sig -0,427339868 -8,546797358
Diff Conventional vs Disposable -0,081307633 -1,626152652
Diff Conventional vs Rechargable -0,139365406 -2,787308119
Diff Disposable vs Rechargable -0,058057773 -1,161155467

[stephanehess]

Hi

how about your MNL results? Were they also unexpectedly high?

Stephane