Boudreau-style discounted utility

Computes discounted multi-period utility with optional value, tax, and cost adjustments. The expected standardized criterion gain can be supplied directly as delta_z_y, or computed from validity and selection-ratio parameters.

Usage

boudreau_utility(
  delta_z_y = NULL,
  validity = NULL,
  selection_ratio = NULL,
  baseline_validity = 0,
  baseline_selection_ratio = NULL,
  sdy,
  n_by_period = NULL,
  variable_value = 0,
  contribution_margin = NULL,
  variable_value_convention = c("paper_plus", "cost_rate"),
  tax_rate = 0,
  discount_rate = 0,
  cost_by_period = NULL,
  discount_costs = TRUE,
  n_t = NULL,
  cost_t = NULL
)

Arguments

delta_z_y

Expected incremental standardized criterion gain. If NULL, it is computed from validity, selection_ratio, baseline_validity, and baseline_selection_ratio.

validity

Focal validity, used when delta_z_y is NULL.

selection_ratio

Focal selection ratio, used when delta_z_y is NULL.

baseline_validity

Baseline validity. Defaults to zero.

baseline_selection_ratio

Baseline selection ratio. Defaults to selection_ratio.

sdy

Standard deviation of job performance in monetary units.

n_by_period

Vector of selected/retained employees in each period. This is the preferred v0.4.0 name for the literature's N_t.

variable_value

Boudreau-style multiplier V. By default the multiplier is (1 + variable_value), matching the printed Boudreau-style notation. Set variable_value_convention = "cost_rate" to use (1 - variable_value), or pass contribution_margin directly when the margin is known.

contribution_margin

Optional contribution-margin multiplier. Overrides variable_value when supplied.

variable_value_convention

Either "paper_plus" for (1 + V) or "cost_rate" for (1 - V).

tax_rate

Tax rate.

discount_rate

Discount rate.

cost_by_period

Cost in each period. Scalar or vector matching n_by_period.

discount_costs

Should costs be discounted by period? Defaults to TRUE.

n_t

Legacy alias for n_by_period. Use n_by_period in new code.

cost_t

Legacy alias for cost_by_period. Use cost_by_period in new code.

Value

A psu_boudreau object.

References

Boudreau, J. W. (1983). Economic considerations in estimating the utility of human resource productivity improvement programs. Personnel Psychology, 36, 551-576.

Boudreau, J. W. (1991). Utility analysis for decisions in human resource management. In M. D. Dunnette & L. M. Hough (Eds.), Handbook of industrial and organizational psychology (Vol. 2, pp. 621-745). Consulting Psychologists Press.

Sturman, M. C. (2001). Utility analysis for multiple selection devices and multiple outcomes. Journal of Human Resource Costing and Accounting, 6(2), 9-28.

Holling, H. (1998). Utility analysis of personnel selection: An overview and empirical study based on objective performance measures. Methods of Psychological Research Online, 3(1), 5-24.

Examples

# Literature: Boudreau (1983, 1991); Sturman (2001); Holling (1998).
# Use the first call as a minimal example; the longer block illustrates
# how to interpret the function in the substantive setting discussed in the literature.
# Minimal example (Boudreau (1983, 1991); Sturman (2001); Holling (1998)).
boudreau_utility(validity = .35, selection_ratio = .20, sdy = 50000,
                 n_by_period = c(100, 90, 80), discount_rate = .08,
                 cost_by_period = c(75000, 10000, 10000))
#> <psu_boudreau>
#>   delta_z_y: 0.489933
#>   sdy: 50000
#>   variable_value: 0
#>   effective_margin: 1
#>   tax_rate: 0
#>   discount_rate: 0.08
#>   net_present_value: 5628130

# Substantive example (Boudreau, 1983, 1991;
# Sturman, 2001; Holling, 1998).
# Use an explicit contribution margin and operating baseline.
boudreau_utility(
  validity = .35,
  baseline_validity = .20,
  selection_ratio = .20,
  sdy = 50000,
  n_by_period = c(100, 90, 80, 70),
  contribution_margin = .30,
  tax_rate = .25,
  discount_rate = .08,
  cost_by_period = c(75000, 10000, 10000, 10000)
)
#> <psu_boudreau>
#>   delta_z_y: 0.209971
#>   sdy: 50000
#>   variable_value: 0
#>   contribution_margin: 0.3
#>   effective_margin: 0.3
#>   tax_rate: 0.25
#>   discount_rate: 0.08
#>   net_present_value: 579234