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Oaxaca-Blinder decomposition of an achievement gap

Source: R/oaxaca_gap.R
oaxaca_gap.Rd

Decomposes the mean achievement gap between two groups (for example native vs immigrant-background students) into a part explained by differences in characteristics (endowments/composition) and an unexplained part due to differences in returns (structure). This is the standard stratification tool for asking "how much of the gap is because the groups differ in their resources, and how much remains after accounting for them?".

Usage

oaxaca_gap(
  data,
  achievement,
  group,
  predictors,
  groups = NULL,
  weight = NULL,
  repweights = NULL,
  rep_method = c("BRR", "JK2", "JK1"),
  fay = 0.5,
  design = NULL,
  type = c("twofold", "threefold"),
  level = 0.95
)

Arguments

data

A data frame of student-level records.

achievement

Character vector of achievement plausible-value columns.

group

Name of the two-group column.

predictors

Character vector of explanatory variables.

groups

Optional length-2 character vector c(high, low); the gap is mean(high) - mean(low). Defaults to the two levels present (the more advantaged, by mean achievement, is taken as high).

weight

Name of the final student weight column. If NULL, equal weights are used (with a message).

repweights

Optional character vector of replicate-weight columns.

rep_method, fay

Replication design and Fay factor; see rep_factor().

design

Optional lsa_design() bundling weight, repweights, rep_method and fay; when supplied it overrides those arguments.

type

"twofold" (default) or "threefold".

level

Confidence level for the stored interval (default 0.95).

Value

An object of class "oaxaca_gap" / "lsastrat_estimate".

Details

The "twofold" form uses a pooled reference model (Neumark) and reports gap, explained and unexplained. The "threefold" form reports gap, endowments, coefficients and interaction. Estimates are pooled over plausible values with replicate-weight standard errors (see pool_pv()).

References

Oaxaca, R. (1973). Male-female wage differentials in urban labor markets. International Economic Review, 14(3), 693-709. Blinder, A. S. (1973). Wage discrimination: reduced form and structural estimates. Journal of Human Resources, 8(4), 436-455.

Examples

data(pisa_mini)
# native vs first-generation immigrant gap, explained by ESCS, books, parental ed
d <- pisa_mini[pisa_mini$IMMIG %in% c("native", "first_gen"), ]
d$IMMIG <- factor(d$IMMIG)
oaxaca_gap(d, paste0("PV", 1:10, "MATH"), group = "IMMIG",
           predictors = c("ESCS", "books", "parental_edu"),
           weight = "W_FSTUWT", repweights = paste0("W_FSTURWT", 1:64))
#> Oaxaca-Blinder gap decomposition (twofold)
#>   IMMIG: native - first_gen  |  10 plausible value(s)  |  n = 1421
#>   Variance: BRR, 64 replicate weights (+ PV imputation); t reference
#> 
#> 
#>             Estimate Std.Error    t       df       p
#> gap           32.004     9.690 3.30    627.4 1.0e-03
#> explained     29.250     5.364 5.45 134118.7 5.0e-08
#> unexplained    2.755     8.819 0.31    476.5 7.5e-01
#> 
#> gap = mean(native) - mean(first_gen); components sum to gap