Expected consumer surplus

Computes the expected consumer surplus per choice situation (Train 2009, Ch. 3): $$E[CS_i] = \frac{logsum_i}{-\alpha},$$ where $logsum_i$ is the expected maximum utility (see logsum) and $\alpha$ is the (fixed) price coefficient, so that $-\alpha$ is the marginal utility of income. The formula assumes no income effects: utility is linear in price, and the marginal utility of income is constant across the price changes considered.

Usage

# S3 method for class 'choicer_hmnl'
consumer_surplus(
  object,
  price_var,
  newdata = NULL,
  level = 0.95,
  weights = NULL,
  n_draws = 200L,
  ...
)

# S3 method for class 'choicer_hmnp'
consumer_surplus(
  object,
  price_var,
  newdata = NULL,
  level = 0.95,
  weights = NULL,
  ...
)

consumer_surplus(
  object,
  price_var,
  newdata = NULL,
  level = 0.95,
  weights = NULL,
  ...
)

# S3 method for class 'choicer_mnl'
consumer_surplus(
  object,
  price_var,
  newdata = NULL,
  level = 0.95,
  weights = NULL,
  ...
)

# S3 method for class 'choicer_mxl'
consumer_surplus(
  object,
  price_var,
  newdata = NULL,
  level = 0.95,
  weights = NULL,
  ...
)

# S3 method for class 'choicer_nl'
consumer_surplus(
  object,
  price_var,
  newdata = NULL,
  level = 0.95,
  weights = NULL,
  ...
)

Arguments

object: A fitted model object (choicer_mnl, choicer_mxl, or choicer_nl).
price_var: Name of the price variable. Must be a fixed-coefficient variable (a column of the design matrix X).
newdata: Optional counterfactual data (data.frame or list), as in logsum and predict(). When NULL (default), the data stored at fit time is used (requires keep_data = TRUE).
level: Confidence level for the normal-approximation interval around the mean CS (MNL only). Default 0.95.
weights: Optional numeric vector with one weight per choice situation, used for the mean CS (and its SE), as in predict(): for a data.frame newdata, one weight per id in order of first appearance. Defaults to equal weights. Ignored when newdata is NULL (the stored fit weights apply).
n_draws: Number of posterior draws to integrate over (hierarchical Bayes methods).
...: Additional arguments passed to methods.

Value

A choicer_cs object: a list with cs (per-choice- situation surplus, length N), mean_cs (weighted mean), se_mean_cs (delta-method SE; NA for MXL/NL or when the variance-covariance matrix is unavailable), ci (confidence interval for the mean), price_var, level, and n.

Details

Consumer surplus levels inherit the additive utility normalization (in particular the ASC normalization), so the level is only defined up to a constant; differences in CS between scenarios — e.g. consumer_surplus(fit, "price", newdata = scenario) minus the baseline — are the economically meaningful quantity.

For MNL fits, a delta-method standard error of the weighted mean CS is reported (weights are the stored fit weights, or the resolved newdata weights). For MXL and NL fits only point estimates are returned (se_mean_cs = NA): the delta method for the simulated MXL logsum and the nested logsum is deferred; simulation-based intervals (Krinsky-Robb: resample coefficients from their asymptotic distribution and recompute the mean CS) are a practical alternative.

The price variable must have a fixed coefficient. For mixed logit a random price coefficient is rejected (as in wtp): with a random denominator $1/(-\alpha)$ generally has no finite moments.

Methods (by class)

consumer_surplus(choicer_hmnl): Posterior consumer surplus for the hierarchical logit: per-task logsum divided by the (positive) marginal utility of income $-\bar\gamma_{price}$, per posterior draw. With newdata, the return also carries the compensating variation against the estimation data (attr(, "cv")), i.e. the posterior of $(\mathrm{logsum}_{new} - \mathrm{logsum}_{base}) / (-\bar\gamma_{price})$ summed over tasks. Requires a fixed-sign price coefficient; the posterior-median ratio discipline of wtp.choicer_hb() applies. When newdata is supplied, weights is an optional non-negative length-n_tasks vector used in the aggregate CV; equal task weights are the default. The counterfactual must contain the same choice situations as the estimation data, identified by (person_col, id_col) (or id_col when person_col = NULL); rows and tasks may be reordered. Unnamed weights follow the baseline tasks' sorted (person_col, id_col) order used by the prepared data.
consumer_surplus(choicer_hmnp): Not available for the probit (see logsum.choicer_hmnp()); roadmapped via simulated Emax.

References

Train, K. (2009). Discrete Choice Methods with Simulation, 2nd ed., Ch. 3. Cambridge University Press.

Examples

# \donttest{
library(data.table)
sim <- simulate_mnl_data(N = 1000, J = 3, beta = c(0.8, -0.6), seed = 123,
                         outside_option = FALSE, vary_choice_set = FALSE)
fit <- run_mnlogit(sim$data, "id", "alt", "choice", c("x1", "x2"))
#> Optimization run time 0h:0m:0s

# treat x2 as the price variable
cs0 <- consumer_surplus(fit, price_var = "x2")
cs0
#> Consumer surplus, price variable: 'x2'
#>   Mean CS: 1.692 
#>   SE (delta method): 0.2281 
#>   95% CI: [1.245, 2.139]
#>   N: 1000 
#> Note: CS levels depend on the utility (ASC) normalization; differences between scenarios are the meaningful quantity.

# Change in consumer surplus from a price increase on alternative 2:
# levels depend on the ASC normalization, differences do not.
dt_cf <- copy(sim$data)[alt == 2, x2 := x2 + 0.5]
cs1 <- consumer_surplus(fit, price_var = "x2", newdata = dt_cf)
delta_cs <- cs1$mean_cs - cs0$mean_cs
delta_cs  # negative: the price increase lowers expected surplus
#> [1] -0.07643608
# }