binstest {binsreg}

Data-Driven Nonparametric Shape Restriction and Parametric Model Specification Testing using Binscatter

Description

binstest implements binscatter-based hypothesis testing procedures for parametric functional forms of and nonparametric shape restrictions on the regression function of interest, following the results in Cattaneo, Crump, Farrell and Feng (2023a) and Cattaneo, Crump, Farrell and Feng (2023b). If the binning scheme is not set by the user, the companion function binsregselect is used to implement binscatter in a data-driven way and inference procedures are based on robust bias correction. Binned scatter plots based on different methods can be constructed using the companion functions binsreg, binsqreg or binsglm.

Usage

binstest(y, x, w = NULL, data = NULL, estmethod = "reg",
  family = gaussian(), quantile = NULL, deriv = 0, at = NULL,
  nolink = F, testmodel = NULL, testmodelparfit = NULL,
  testmodelpoly = NULL, testshape = NULL, testshapel = NULL,
  testshaper = NULL, testshape2 = NULL, lp = Inf, bins = NULL,
  nbins = NULL, pselect = NULL, sselect = NULL, binspos = "qs",
  binsmethod = "dpi", nbinsrot = NULL, randcut = NULL, nsims = 500,
  simsgrid = 20, simsseed = NULL, vce = NULL, cluster = NULL,
  asyvar = F, dfcheck = c(20, 30), masspoints = "on", weights = NULL,
  subset = NULL, numdist = NULL, numclust = NULL, estmethodopt = NULL,
  ...)

Arguments

y

outcome variable. A vector.

x

independent variable of interest. A vector.

w

control variables. A matrix, a vector or a formula.

data

an optional data frame containing variables used in the model.

estmethod

estimation method. The default is estmethod="reg" for tests based on binscatter least squares regression. Other options are "qreg" for quantile regression and "glm" for generalized linear regression. If estmethod="glm", the option family must be specified.

family

a description of the error distribution and link function to be used in the generalized linear model when estmethod="glm". (See family for details of family functions.)

quantile

the quantile to be estimated. A number strictly between 0 and 1.

deriv

derivative order of the regression function for estimation, testing and plotting. The default is deriv=0, which corresponds to the function itself.

at

value of w at which the estimated function is evaluated. The default is at="mean", which corresponds to the mean of w. Other options are: at="median" for the median of w, at="zero" for a vector of zeros. at can also be a vector of the same length as the number of columns of w (if w is a matrix) or a data frame containing the same variables as specified in w (when data is specified). Note that when at="mean" or at="median", all factor variables (if specified) are excluded from the evaluation (set as zero).

nolink

if true, the function within the inverse link function is reported instead of the conditional mean function for the outcome.

testmodel

a vector or a logical value. It sets the degree of polynomial and the number of smoothness constraints for parametric model specification testing. If testmodel=c(p,s) is specified, a piecewise polynomial of degree p with s smoothness constraints is used. If testmodel=T or testmodel=NULL (default) is specified, testmodel=c(1,1) is used unless the degree p or the smoothness s selection is requested via the option pselect or sselect (see more details in the explanation of pselect and sselect).

testmodelparfit

a data frame or matrix which contains the evaluation grid and fitted values of the model(s) to be tested against. The column contains a series of evaluation points at which the binscatter model and the parametric model of interest are compared with each other. Each parametric model is represented by other columns, which must contain the fitted values at the corresponding evaluation points.

testmodelpoly

degree of a global polynomial model to be tested against.

testshape

a vector or a logical value. It sets the degree of polynomial and the number of smoothness constraints for nonparametric shape restriction testing. If testshape=c(p,s) is specified, a piecewise polynomial of degree p with s smoothness constraints is used. If testshape=T or testshape=NULL (default) is specified, testshape=c(1,1) is used unless the degree p or smoothness s selection is requested via the option pselect or sselect (see more details in the explanation of pselect and sselect).

testshapel

a vector of null boundary values for hypothesis testing. Each number a in the vector corresponds to one boundary of a one-sided hypothesis test to the left of the form H0: sup_x mu(x)<=a.

testshaper

a vector of null boundary values for hypothesis testing. Each number a in the vector corresponds to one boundary of a one-sided hypothesis test to the right of the form H0: inf_x mu(x)>=a.

testshape2

a vector of null boundary values for hypothesis testing. Each number a in the vector corresponds to one boundary of a two-sided hypothesis test of the form H0: sup_x |mu(x)-a|=0.

lp

an Lp metric used for (two-sided) parametric model specification testing and/or shape restriction testing. The default is lp=Inf, which corresponds to the sup-norm of the t-statistic. Other options are lp=q for a positive integer q.

bins

a vector. If bins=c(p,s), it sets the piecewise polynomial of degree p with s smoothness constraints for data-driven (IMSE-optimal) selection of the partitioning/binning scheme. The default is bins=c(0,0), which corresponds to the piecewise constant.

nbins

number of bins for partitioning/binning of x. If nbins=T or nbins=NULL (default) is specified, the number of bins is selected via the companion command binsregselect in a data-driven, optimal way whenever possible. If a vector with more than one number is specified, the number of bins is selected within this vector via the companion command binsregselect.

pselect

vector of numbers within which the degree of polynomial p for point estimation is selected. If the selected optimal degree is p, then piecewise polynomials of degree p+1 are used to conduct testing for nonparametric shape restrictions or parametric model specifications. Note: To implement the degree or smoothness selection, in addition to pselect or sselect, nbins=# must be specified.

sselect

vector of numbers within which the number of smoothness constraints s for point estimation is selected. If the selected optimal smoothness is s, then piecewise polynomials of s+1 smoothness constraints are used to conduct testing for nonparametric shape restrictions or parametric model specifications. If not specified, for each value p supplied in the option pselect, only the piecewise polynomial with the maximum smoothness is considered, i.e., s=p.

binspos

position of binning knots. The default is binspos="qs", which corresponds to quantile-spaced binning (canonical binscatter). The other options are "es" for evenly-spaced binning, or a vector for manual specification of the positions of inner knots (which must be within the range of x).

binsmethod

method for data-driven selection of the number of bins. The default is binsmethod="dpi", which corresponds to the IMSE-optimal direct plug-in rule. The other option is: "rot" for rule of thumb implementation.

nbinsrot

initial number of bins value used to construct the DPI number of bins selector. If not specified, the data-driven ROT selector is used instead.

randcut

upper bound on a uniformly distributed variable used to draw a subsample for bins/degree/smoothness selection. Observations for which runif()<=# are used. # must be between 0 and 1. By default, max(5000, 0.01n) observations are used if the samples size n>5000.

nsims

number of random draws for hypothesis testing. The default is nsims=500, which corresponds to 500 draws from a standard Gaussian random vector of size [(p+1)*J - (J-1)*s]. Setting at least nsims=2000 is recommended to obtain the final results.

simsgrid

number of evaluation points of an evenly-spaced grid within each bin used for evaluation of the supremum (infimum or Lp metric) operation needed to construct hypothesis testing procedures. The default is simsgrid=20, which corresponds to 20 evenly-spaced evaluation points within each bin for approximating the supremum (infimum or Lp metric) operator. Setting at least simsgrid=50 is recommended to obtain the final results.

simsseed

seed for simulation.

vce

procedure to compute the variance-covariance matrix estimator. For least squares regression and generalized linear regression, the allowed options are the same as that for binsreg or binsqreg. For quantile regression, the allowed options are the same as that for binsqreg.

cluster

cluster ID. Used for compute cluster-robust standard errors.

asyvar

if true, the standard error of the nonparametric component is computed and the uncertainty related to control variables is omitted. Default is asyvar=FALSE, that is, the uncertainty related to control variables is taken into account.

dfcheck

adjustments for minimum effective sample size checks, which take into account number of unique values of x (i.e., number of mass points), number of clusters, and degrees of freedom of the different stat models considered. The default is dfcheck=c(20, 30). See Cattaneo, Crump, Farrell and Feng (2023c) for more details.

masspoints

how mass points in x are handled. Available options:

• "on" all mass point and degrees of freedom checks are implemented. Default.

• "noadjust" mass point checks and the corresponding effective sample size adjustments are omitted.

• "nolocalcheck" within-bin mass point and degrees of freedom checks are omitted.

• "off" "noadjust" and "nolocalcheck" are set simultaneously.

• "veryfew" forces the function to proceed as if x has only a few number of mass points (i.e., distinct values). In other words, forces the function to proceed as if the mass point and degrees of freedom checks were failed.

weights

an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. For more details, see lm.

subset

optional rule specifying a subset of observations to be used.

numdist

number of distinct for selection. Used to speed up computation.

numclust

number of clusters for selection. Used to speed up computation.

estmethodopt

a list of optional arguments used by rq (for quantile regression) or glm (for fitting generalized linear models).

...

optional arguments to control bootstrapping if estmethod="qreg" and vce="boot". See boot.rq.

Value

testshapeL

Results for testshapel, including: testvalL, null boundary values; stat.shapeL, test statistics; and pval.shapeL, p-value.

testshapeR

Results for testshaper, including: testvalR, null boundary values; stat.shapeR, test statistics; and pval.shapeR, p-value.

testshape2

Results for testshape2, including: testval2, null boundary values; stat.shape2, test statistics; and pval.shape2, p-value.

testpoly

Results for testmodelpoly, including: testpoly, the degree of global polynomial; stat.poly, test statistic; pval.poly, p-value.

testmodel

Results for testmodelparfit, including: stat.model, test statistics; pval.model, p-values.

imse.var.rot

Variance constant in IMSE, ROT selection.

imse.bsq.rot

Bias constant in IMSE, ROT selection.

imse.var.dpi

Variance constant in IMSE, DPI selection.

imse.bsq.dpi

Bias constant in IMSE, DPI selection.

opt

A list containing options passed to the function, as well as total sample size n, number of distinct values Ndist in x, number of clusters Nclust, and number of bins nbins.

Author(s)

Matias D. Cattaneo, Princeton University, Princeton, NJ. [e-mail].

Richard K. Crump, Federal Reserve Bank of New York, New York, NY. [e-mail].

Max H. Farrell, UC Santa Barbara, Santa Barbara, CA. [e-mail].

Yingjie Feng (maintainer), Tsinghua University, Beijing, China. [e-mail].

References

Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2023a: On Binscatter. Working Paper.

Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2023b: Nonlinear Binscatter Methods. Working Paper.

Cattaneo, M. D., R. K. Crump, M. H. Farrell, and Y. Feng. 2023c: Binscatter Regressions. Working Paper.

See Also

binsreg, binsqreg, binsglm, binsregselect.

Examples

 x <- runif(500); y <- sin(x)+rnorm(500)
 est <- binstest(y,x, testmodelpoly=1)
 summary(est)