Empirical Classification Analysis (CA) and Inference

Description

ca conducts CA estimation and inference on user-specified objects of interest: first (weighted) moment or (weighted) distribution. Users can use t to specify variables in interest. When object of interest is moment, use cl to specify whether want to see averages or difference of the two groups.

Usage

ca(
  fm,
  data,
  method = c("ols", "logit", "probit", "QR"),
  var_type = c("binary", "continuous", "categorical"),
  var,
  compare,
  subgroup = NULL,
  samp_weight = NULL,
  taus = c(5:95)/100,
  u = 0.1,
  interest = c("moment", "dist"),
  t = c(1, 1, rep(0, dim(data)[2] - 2)),
  cl = c("both", "diff"),
  cat = NULL,
  alpha = 0.1,
  b = 500,
  parallel = FALSE,
  ncores = detectCores(),
  seed = 1,
  bc = TRUE,
  range_cb = c(1:99)/100,
  boot_type = c("nonpar", "weighted")
)

Arguments

Details

All estimates are bias-corrected and all confidence bands are monotonized. The bootstrap procedures follow algorithm 2.2 as in Chernozhukov, Fernandez-Val and Luo (2018).

Value

If subgroup = NULL, all outputs are whole sample. Otherwise output are subgroup results. When interest = "moment", the output is a list showing

• est Estimates of variables in interest.

• bse Bootstrap standard errors.

• joint_p P-values that are adjusted for multiplicity to account for joint testing for all variables.

• pointwise_p P-values that doesn't adjust for join testing

If users have further specified cat (e.g., !is.null(cat)), the fourth component will be replaced with p_cat: P-values that are a djusted for multiplicity to account for joint testing for all variables within a category. Users can use summary.ca to tabulate the results.

When interest = "dist", the output is a list of two components:

• infresults A list that stores estimates, upper and lower confidence bounds for all variables in interest for least and most affected groups.

• sortvar A list that stores sorted and unique variables in interest.

We recommend using plot.ca command for result visualization.

Examples

data("mortgage")
### Regression Specification
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec +
ltv_med + ltv_high + denpmi + selfemp + single + hischl
### Specify characteristics of interest
t <- c("deny", "p_irat", "black", "hse_inc", "ccred", "mcred", "pubrec",
"denpmi", "selfemp", "single", "hischl", "ltv_med", "ltv_high")
### issue ca command
CA <- ca(fm = fm, data = mortgage, var = "black", method = "logit",
cl = "diff", t = t, b = 50, bc = TRUE)

Mortgage Denial

Description

Mortgage Denial

Usage

mortgage

Format

Contains the data on mortgage application in Boston from 1990, (Munnell et al., 1996.) We obtain the data from the companion website of Stock and Watson (2011). The file contains the following variables:

deny

indicator for mortgage application denied

p_irat

monthly debt to income ratio

black

indicator for black applicant

hse_inc

monthly housing expenses to income ratio

loan_val

loan to assessed property value ratio

ccred

consumer credit score with 6 categories. 1 if no "slow" payments or delinquencies, 2 if one or two "slow" payments or delinquencies, 3 if more than two "slow" payments or delinguencies, 4 if insufficient credit history for determination, 5 if delinquent credit history with payment 60 days overdue, and 6 if delinquent credit history with payments 90 days overdue.

mcred

mortgage credit score with 4 categories. 1 if no late mortgage payments, 2 if no mortgage payment history, 3 if one or two late mortage payments, and 4 if more than two late mortgages payments

pubrec

indicator for any public record of credit problems: bankruptcy , charge-offs, collection actions

denpmi

indicator for applicant applied for mortgage insurance and was denied

selfemp

indicator for self-employed applicant

single

indicator for single applicant

hischl

indicator for high school graduated applicant

probunmp

1989 Massachusetts unemployment rate in the applicant's history

condo

indicator for unit is a condominium

ltv_med

indicator for medium loan to property value ratio [.80, .95]

ltv_high

indicator for high loan to property value ratio >.95

Source

Munnell, Alicia, Geoffrey Tootell, Lynn Browne, and James McEneaney, "Mortgage Lending in Boston: Interpreting HMDA Data", The American Economic Review, 1996.

Distribution plotting

Description

Plots distributions and joint uniform confidence bands of variables in interest from ca command.

Usage

## S3 method for class 'ca'
plot(x, var, main = NULL, sub = NULL, xlab = NULL, ylab = NULL, ...)

Arguments

Examples

data("mortgage")
### Regression Specification
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec +
ltv_med + ltv_high + denpmi + selfemp + single + hischl
### Specify characteristics of interest for plotting
t2 <- "p_irat"
### issue ca command
CAdist <- ca(fm = fm, data = mortgage, var = "black", method = "logit",
t = "p_irat", b = 50, interest = "dist")
### plotting
plot(CAdist, var = "p_irat", ylab = "Prob",
xlab = "Monthly Debt-to-Income Ratio", sub = "logit model")

Plot output of spe command. The x-axis limits are set to the specified range of percentile index.

Description

Plot output of spe command. The x-axis limits are set to the specified range of percentile index.

Usage

## S3 method for class 'spe'
plot(
  x,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  xlab = "Percentile Index",
  ylab = "Sorted Effects",
  ...
)

Arguments

Examples

data("mortgage")
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec + ltv_med +
ltv_high + denpmi + selfemp + single + hischl
test <- spe(fm = fm, data = mortgage, var = "black", method = "logit",
us = c(2:98)/100, b = 50)

plot(x = test, main="APE and SPE of Being Black on the prob of
Mortgage Denial", sub="Logit Model", ylab="Change in Probability")

Plot 2-dimensional projections of variables in interest.

Description

Takes output from subpop command as inputs and plots 2-dimensional projection plots of two specified variables. If a variable in interest is of type factor, then the user must put it on the y-axis. If the variable on the y-coordinate is a factor, range of y-axis is set to be the factor level. Otherwise, users can use summary.subpop to know the ranges of variables in the two groups.

Usage

## S3 method for class 'subpop'
plot(
  x,
  varx,
  vary,
  xlim = NULL,
  ylim = NULL,
  main = NULL,
  sub = NULL,
  xlab = NULL,
  ylab = NULL,
  overlap = FALSE,
  ...
)

Arguments

Examples

data("mortgage")
### Regression Specification
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec +
   ltv_med + ltv_high + denpmi + selfemp + single + hischl
### Issue the subpop command
set_b <- subpop(fm, data = mortgage, method = "logit", var = "black",
u = 0.1, alpha = 0.1, b = 50)
### Plotting
plot(set_b, varx = mortgage$p_irat, vary = mortgage$hse_inc,
     xlim = c(0, 1.5), ylim = c(0, 1.5), xlab = "Debt/Income",
     ylab = "Housing expenses/Income", overlap = TRUE)

Empirical Sorted Partial Effects (SPE) and Inference

Description

spe conducts SPE estimation and inference at user-specifed quantile index. The bootstrap procedures follows algorithm 2.1 as in Chernozhukov, Fernandez-Val and Luo (2018). All estimates are bias-corrected and all confidence bands are monotonized. For graphical results, please use plot.spe.

Usage

spe(
  fm,
  data,
  method = c("ols", "logit", "probit", "QR"),
  var_type = c("binary", "continuous", "categorical"),
  var,
  compare,
  subgroup = NULL,
  samp_weight = NULL,
  us = c(1:9)/10,
  alpha = 0.1,
  taus = c(5:95)/100,
  b = 500,
  parallel = FALSE,
  ncores = detectCores(),
  seed = 1,
  bc = TRUE,
  boot_type = c("nonpar", "weighted")
)

Arguments

Value

The output is a list with 4 components: (1) spe stores spe estimates, the upper and lower confidence bounds, and standard errors; (2) ape stores ape estimates, the upper and lower confidence bounds, and the standard error; (3) us stores percentile index as in \ codespe command; (4) alpha stores significance level as in spe command.

Examples

data("mortgage")
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec + ltv_med +
ltv_high + denpmi + selfemp + single + hischl

test <- spe(fm = fm, data = mortgage, var = "black", method = "logit",
us = c(2:98)/100, b = 50)

Inference on Most and Least Affected Groups

Description

subpop conducts set inference on the groups of most and least affected. When subgroup = NULL, output is for whole sample. Otherwise the results are subgroup. The output of subpop is a list containing six components: cs_most, cs_least, u, subgroup, most and least. As the names indicate, cs_most and cs_least denote the confidence sets for the most and least affected units. u stores the u-th most and least affected index. subgroup stores the indicators for subpopulations. most and least store the data of the most and least affected groups. The confidence sets can be visualized using the plot.subpop command while the two groups can be tabulated via the summary.subpop command.

Usage

subpop(
  fm,
  data,
  method = c("ols", "logit", "probit", "QR"),
  var_type = c("binary", "continuous", "categorical"),
  var,
  compare,
  subgroup = NULL,
  samp_weight = NULL,
  taus = c(5:95)/100,
  u = 0.1,
  alpha = 0.1,
  b = 500,
  seed = 1,
  parallel = FALSE,
  ncores = detectCores(),
  boot_type = c("nonpar", "weighted")
)

Arguments

Examples

data("mortgage")
### Regression Specification
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec +
   ltv_med + ltv_high + denpmi + selfemp + single + hischl
### Issue the subpop command
set_b <- subpop(fm, data = mortgage, method = "logit", var = "black",
u = 0.1, alpha = 0.1, b = 50)

Return the output of ca function.

Description

Return the output of ca function.

Usage

## S3 method for class 'ca'
summary(object, ...)

Arguments

Examples

data("mortgage")
### Regression Specification
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec +
ltv_med + ltv_high + denpmi + selfemp + single + hischl
### Specify characteristics of interest
t <- c("deny", "p_irat", "black", "hse_inc", "ccred", "mcred", "pubrec",
"denpmi", "selfemp", "single", "hischl", "ltv_med", "ltv_high")
### Issue ca command
CA <- ca(fm = fm, data = mortgage, var = "black", method = "logit",
cl = "both", t = t, b = 50, bc = TRUE)
### Report summary table
summary(CA)

Tabulate the output of spe function.

Description

The option result allows user to tabulate either sorted estimates or average estimates. For sorted estimates, the table shows user-specified quantile indices, sorted estimates, standard errors, point-wise confidence intervals, and uniform confidence intervals. For average estimates, the table shows average estiamtes, standard errors, and confidence intervals.

Usage

## S3 method for class 'spe'
summary(object, result = c("sorted", "average"), ...)

Arguments

Examples

data("mortgage")
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec + ltv_med +
ltv_high + denpmi + selfemp + single + hischl
test <- spe(fm = fm, data = mortgage, var = "black", method = "logit",
us = c(2:98)/100, b = 50)
summary(test)

Return the output of subpop function.

Description

The subpop function stores the most and least affected groups. This command allows users to see these two groups and their corresponding characteristics. The command also allows users to check the summary statistics of variables in interest, which can be useful for plotting the projections plot via the plot.subpop method.

Usage

## S3 method for class 'subpop'
summary(object, vars = NULL, ...)

Arguments

Examples

data("mortgage")
### Regression Specification
fm <- deny ~ black + p_irat + hse_inc + ccred + mcred + pubrec +
   ltv_med + ltv_high + denpmi + selfemp + single + hischl
### Issue the subpop command
set_b <- subpop(fm, data = mortgage, method = "logit", var = "black",
u = 0.1, alpha = 0.1, b = 50)
### Produce summary of two variables
groups <- summary(set_b, vars = c("p_irat", "hse_inc"))

Wage Data

Description

Wage Data

Usage

wage2015

Format

Consists of white, non-hispanic individuals aging from 25 to 64 and working more than 35 hours per week during at least 50 weeks of the year. Excludes self-employed, individuals living in group quarters; individuals in the military, agricultural or private household sectors; individuals with inconsistent reports on earnings and employment status; individuals with allocated or missing information in any of the variables used in the analysis; individuals with hourly wage rate below $3. Contains 32,523 workers including 18,137 men and 14,382 women. The file contains the following variables:

lnw

log of hourly wages

weight

CPS sampling weight

female

gender indicator: 1 if female

exp1

max(age-years of educ-7, 0)

exp2

exp1^2/100

exp3

exp1^3/100

exp4

exp1^4/100

occ

Aggregated occupation with 5 categories: managers, service, sales, construction and production.

ind

Aggregated industry with 12 categories: minery, construction, manufacture, retail, transport, information, finance, professional, education, leisure, services, public.

educ

Education attainment with 5 categories: lhs (less than high school graduate, years of educ < 12), hsg (high school graduate: years of educ = 12), sc (some college: 13<=years of educ<=15), cg (college: 16<=years of educ<=17), ad (advanced degree: years of educ>=18).

ms

Marital Status with 5 categories: married, widowed, separated, divorced, and nevermarried.

region

Regions with 4 categories: mw (midwest), so (south), we (west), ne (northeast).

Source

U.S. March Supplement of the Current Population Survey (CPS) in 2015.