Check weights

Description

Helper function to check a weights vector. Makes sure the weights are positive numeric values (not all zeros) and of the same length as the dependent variable dep_var. Replaces all NAs with 0 and sets all weights to 1 if weights is set to NULL.

Usage

check_weights(dep_var, weights)

Arguments

Value

positive numeric vector of length(dep_var) containing the checked weights. If weights = NULL, all weights are set to 1.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
check_weights(dep_var, weights)

Generalized Lorenz ordinates

Description

Compute the generalized Lorenz ordinates of dep_var (i.e. the share of total income observations up to each value in dep_var amass scaled by the mean income).

Usage

compute_generalized_lorenz_ordinates(dep_var, weights)

Arguments

Value

thes generalized Lorenz ordinates for a vector dep_var.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
generalized_lorenz_ordinates <-
  compute_generalized_lorenz_ordinates(
    dep_var = dep_var,
    weights = weights
  )

Compute Gini coefficient

Description

Compute a weighted Gini coefficient by integrating the generalized Lorenz curve.

Usage

compute_gini(dep_var, weights)

Arguments

Value

The numeric value indicating the weighted Gini coefficient of the the dependent variable.

References

Firpo, Sergio P., Nicole M. Fortin, and Thomas Lemieux. 2018. “Decomposing Wage Distributions Using Recentered Influence Function Regressions.” Econometrics 6(2), 28.

Examples

set.seed(123)
dep_var <- rlnorm(100)
weights <- rep(1, 100)
compute_gini(dep_var, weights)

Weighted ECDF value

Description

Compute values of the ECDF for a vector dep_var (i.e. the empirical probability for each observation in dep_var that a value in dep_var is smaller or equal).

Usage

compute_weighted_ecdf(dep_var, weights)

Arguments

Value

the values of ECDF for a vector dep_var.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
value_of_ecdf <-
  compute_weighted_ecdf(
    dep_var = dep_var,
    weights = weights
  )

Estimate Recentered Influence Functions

Description

This function estimates the recentered influence function (RIF) of a chosen distributional statistic (e.g. quantiles, variance or gini).

Usage

get_rif(
  dep_var,
  weights = NULL,
  statistic,
  probs = NULL,
  custom_rif_function = NULL,
  ...
)

Arguments

Value

a data frame with the RIF value for each observation and in the case of several quantiles a column for each quantile.

References

Firpo, Sergio P., Nicole M. Fortin, and Thomas Lemieux. 2009. “Unconditional Quantile Regressions.” Econometrica 77(3): 953–73.

Cowell, Frank A., and Emmanuel Flachaire. 2015. “Statistical Methods for Distributional Analysis.” In Anthony B. Atkinson and François Bourguignon (eds.), Handbook of Income Distribution. Amsterdam: Elsevier.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
probs <- seq(1:9) / 10
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
rif <- get_rif(
  dep_var = dep_var,
  weights = weights,
  statistic = "quantiles",
  probs = probs
)

# custom function
custom_variance_function <- function(dep_var, weights, probs = NULL) {
  weighted_mean <- weighted.mean(x = dep_var, w = weights)
  rif <- (dep_var - weighted_mean)^2
  rif <- data.frame(rif, weights)
  names(rif) <- c("rif_variance", "weights")
  return(rif)
}

set.seed(123)
dep_var <- rlnorm(100)
weights <- rep(1, 100)

# custom function top 10% percent income share
# (see Essam-Nassah & Lambert, 2012, and Rios-Avila, 2020)
custom_top_income_share_function <- function(dep_var, weights, probs = 0.1) {
  probs <- 1 - probs
  weighted_mean <- weighted.mean(x = dep_var, w = weights)
  weighted_quantile <- Hmisc::wtd.quantile(x = dep_var, weights = weights, probs = probs)
  lorenz_ordinate <-
    sum(dep_var[which(dep_var <= weighted_quantile)] *
      weights[which(dep_var <= weighted_quantile)]) / sum(dep_var * weights)
  if_lorenz_ordinate <- -(dep_var / weighted_mean) * lorenz_ordinate +
    ifelse(dep_var < weighted_quantile,
      dep_var - (1 - probs) * weighted_quantile,
      probs * weighted_quantile
    ) / weighted_mean
  rif_top_income_share <- (1 - lorenz_ordinate) - if_lorenz_ordinate
  rif <- data.frame(rif_top_income_share, weights)
  names(rif) <- c("rif_top_income_share", "weights")
  return(rif_top_income_share)
}

rif_custom <- get_rif(
  dep_var = dep_var,
  weights = weights,
  statistic = "custom",
  custom_rif_function = custom_variance_function
)

Estimate RIF of Gini coefficient

Description

Compute the recentered influence function (RIF) of a weighted Gini coefficient.

Usage

get_rif_gini(dep_var, weights)

Arguments

Value

A data frame with one column containing the RIF of the Gini coefficient for each observation.

References

Cowell, Frank A., and Emmanuel Flachaire. 2007. "Income distribution and inequality measurement: The problem of extreme values." Journal of Econometrics, 141(2), 1044-1072.

Firpo, Sergio P., Nicole M. Fortin, and Thomas Lemieux. 2018. “Decomposing Wage Distributions Using Recentered Influence Function Regressions.” Econometrics 6(2), 28.

Monti, Anna Clara. 1991. "The study of the Gini concentration ratio by means of the influence function." Statistica 51(4), 561–577.

Examples

set.seed(123)
dep_var <- rlnorm(100)
weights <- rep(1, 100)
rif_gini <- get_rif_gini(dep_var = dep_var, weights = weights)
rif_gini

gini <- compute_gini(dep_var = dep_var, weights = weights)
all.equal(gini, mean(rif_gini$rif_gini))

Estimate RIF of interquantile range

Description

Compute the recentered influence function (RIF) of a weighted interquantile range.

Usage

get_rif_interquantile_range(dep_var, weights, probs, ...)

Arguments

Value

A data frame with one column containing the RIF of the interquantile range for each observation and one column containing the weights.

References

Firpo, Sergio P., Nicole M. Fortin, and Thomas Lemieux. 2018. “Decomposing Wage Distributions Using Recentered Influence Function Regressions.” Econometrics 6(2), 28.

Examples

set.seed(123)
dep_var <- rlnorm(100)
weights <- rep(1, 100)
get_rif_interquantile_range(dep_var, probs = c(0.1, 0.9), weights = weights)

Estimate RIF of interquantile ratio

Description

Compute the recentered influence function (RIF) of a weighted interquantile ratio.

Usage

get_rif_interquantile_ratio(dep_var, weights, probs, ...)

Arguments

Value

A data frame with one column containing the RIF of the interquantile ratio for each observation.

References

Chung, Choe, and Philippe Van Kerm. 2018. "Foreign workers and the wage distribution: What does the infuence function reveal?", Econometrics 6(3), 41.

Examples

set.seed(123)
dep_var <- rlnorm(100)
weights <- rep(1, 100)
get_rif_interquantile_ratio(dep_var, probs = c(0.1, 0.9), weights = weights)

Estimate RIF at the Mean

Description

Function to estimate the recentered influence function (RIF) at the mean of a weighted distribution of a dependent variable.

Usage

get_rif_mean(dep_var)

Arguments

Value

A data frame with one column of length(dep_var) containing the RIF at the mean.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
get_rif_mean(dep_var)

Estimate RIF at Quantiles

Description

Function to estimate the recentered influence function (RIF) at one or several specified quantiles of a weighted distribution of a dependent variable.

Usage

get_rif_quantiles(dep_var, weights, probs, ...)

get_rif_quantile(dep_var, weights, probs, ...)

Arguments

Value

A data frame with the number of columns equaling the length of vector probs and an additional column containing the weights. Each column contains the RIF values at the quantile's probabilities.

Functions

• get_rif_quantile(): Helper function to estimate the RIF values at a specific quantile.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
probs <- seq(1:9) / 10
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
get_rif_quantiles(dep_var, probs, weights = weights)

Estimate RIF of variance

Description

Function to estimate the recentered influence function (RIF) of the variance of a weighted distribution of a dependent variable.

Usage

get_rif_variance(dep_var, weights)

Arguments

Value

A data frame with one column containing the RIF of the variance for each observation and one column containing the weights.

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
get_rif_variance(dep_var, weights = weights)

Integrate generalized Lorenz curve

Description

Computes the area under the lorenz curve.

Usage

integrate_generalized_lorenz_curve(dep_var, weights)

Arguments

Value

the size of the area under the lorenz curve (the integrated lorenz curve).

Examples

dep_var <- c(1, 3, 9, 16, 3, 7, 4, 9)
weights <- c(2, 1, 3, 4, 4, 1, 6, 3)
integrated_lorenz_curve <-
  integrate_generalized_lorenz_curve(
    dep_var = dep_var,
    weights = weights
  )

Sample of male wage data from the CPS 1983-1985

Description

A sample of the the Merged Outgoing Rotation Group of the Current Population Survey of 1983, 1984 and 1985 used by Firpo, Fortin & Lemieux (2009). The data contains a selection of 10 variables and a sample of 26,695 observations of male workers – corresponding to a tenth of the original 266,956 observations. See Lemieux (2006) for details on data selection and recoding.

Usage

men8385

Format

A data frame with 26,695 rows and 10 variables.

wage

Hourly wage in US dollars at constant prices

union

Union status indicator

nonwhite

Non-white indicator

married

Married indicator

education

Factor variable with 6 education levels: high-school graduates (reference), elementary, high-school dropouts , some college, college graduates, post college graduates

experience

Factor variable with 9 potential experience levels, each of five years gap, 20 to 24 years as reference level)

weights

CPS sample weights

age

Age in years

education_in_years

Education in years

experience_in_years

Experience in years

Source

Sergio Firpo, Nicole M. Fortin, and Thomas Lemieux, "Unconditional Quantile Regressions", Econometrica, Vol. 77, No. 3 (May, 2009), pp. 953-973.

Replication files: <https://www.econometricsociety.org/publications/econometrica/2009/05/01/unconditional-quantile-regressions>

Thoms Lemieux, "Increasing Residual Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill?", American Economic Review, Vol. 96, No. 3 (June, 2006), pp. 461-498.

Plot the coefficients of a rifreg object

Description

Coefficients are plotted for each quantile and each covariate. Specific covariates can be selected and standard errors displayed if desired.

Usage

## S3 method for class 'rifreg'
plot(
  x,
  varselect = NULL,
  confidence_level = 0.05,
  vcov = sandwich::sandwich,
  ...
)

Arguments

Value

a "ggplot" containing the coefficients for each (selected) covariate

Examples

rifreg <- rifreg(
  formula = log(wage) ~ union +
    nonwhite +
    married +
    education +
    experience,
  data = men8385,
  statistic = "quantiles",
  probs = seq(0.1, 0.9, 0.1),
  weights = weights
)

plot(rifreg)

plot(rifreg, varselect = c("age", "unionyes"), confidence_level = 0.1)

Print method for class "rifreg"

Description

Print method for class "rifreg"

Usage

## S3 method for class 'rifreg'
print(x, ...)

Arguments

Value

the function print.rifreg() returns the the covariates' coefficients of the RIF regressions derived from the fitted linear model given in object x.

Examples

rifreg <- rifreg(
  formula = log(wage) ~ union +
    nonwhite +
    married +
    education +
    experience,
  data = men8385,
  statistic = "quantiles",
  probs = seq(0.1, 0.9, 0.1),
  weights = weights
)

print(rifreg)

RIF regression

Description

Estimate a recentered influence function (RIF) regression for a distributional statistic of interest.

Usage

rifreg(
  formula,
  data,
  statistic = "quantiles",
  weights = NULL,
  probs = c(1:9)/10,
  custom_rif_function = NULL,
  na.action = na.omit,
  bootstrap = FALSE,
  bootstrap_iterations = 100,
  cores = 1,
  ...
)

Arguments

Value

rifreg returns an object of class "rifreg".

A "rifreg" object is a list containing the following components:

References

Firpo, Sergio P., Nicole M. Fortin, and Thomas Lemieux. 2009. “Unconditional Quantile Regressions.” Econometrica 77(3): 953–73.

Cowell, Frank A., and Emmanuel Flachaire. 2015. “Statistical Methods for Distributional Analysis.” In Anthony B. Atkinson and François Bourguignon (eds.), Handbook of Income Distribution. Amsterdam: Elsevier.

Examples

rifreg <- rifreg(
  formula = log(wage) ~ union +
    nonwhite +
    married +
    education +
    experience,
  data = men8385,
  statistic = "quantiles",
  weights = weights,
  probs = seq(0.1, 0.9, 0.1),
  bootstrap = FALSE
)


# custom function
custom_variance_function <- function(dep_var, weights, probs = NULL) {
  weighted_mean <- weighted.mean(x = dep_var, w = weights)
  rif <- (dep_var - weighted_mean)^2
  rif <- data.frame(rif, weights)
  names(rif) <- c("rif_variance", "weights")
  return(rif)
}

rifreg <- rifreg(
  formula = log(wage) ~ union + nonwhite + married + education + experience,
  data = men8385,
  statistic = "custom",
  weights = weights,
  probs = NULL,
  custom_rif_function = custom_variance_function,
  bootstrap = FALSE
)

summary method for class "rifreg"

Description

summary method for class "rifreg"

Usage

## S3 method for class 'rifreg'
summary(object, vcov = sandwich::sandwich, ...)

Arguments

Value

the function summary.rifreg() returns a list of summary statistics derived from the rifreg object given in object. For further details see summary.lm.

Examples

rifreg <- rifreg(
  formula = log(wage) ~ union +
    nonwhite +
    married +
    education +
    experience,
  data = men8385,
  statistic = "quantiles",
  probs = seq(0.1, 0.9, 0.1),
  weights = weights
)
summary(rifreg)