Package 'npiv' reference manual

Title:	Nonparametric Instrumental Variables Estimation and Inference
Description:	Implements methods introduced in Chen, Christensen, and Kankanala (2024) <doi:10.1093/restud/rdae025> for estimating and constructing uniform confidence bands for nonparametric structural functions using instrumental variables, including data-driven choice of tuning parameters. All methods in this package apply to nonparametric regression as a special case.
Authors:	Jeffrey S. Racine [aut], Timothy Christensen [aut, cre], Patrick Alken [ctb], Rhys Ulerich [ctb], Simon N. Wood [ctb]
Maintainer:	Timothy Christensen <[email protected]>
License:	GPL (>= 3)
Version:	0.1.3
Built:	2025-01-08 17:14:16 UTC
Source:	CRAN

Nonparametric Instrumental Variables Estimation and Inference

Description

This package implements the nonparametric instrumental variables estimation and inference methods described in Chen, Christensen, and Kankanala (2024) and Chen and Christensen (2018). The function npiv estimates the nonparametric structural function h0 using B-splines and constructs uniform confidence bands for h0. The function npiv_choose_J performs data-driven choice of sieve dimension. All methods in this package apply to estimation and inference for nonparametric regression as a special case.

Details

This package provides a function npiv(...) with a simple interface for performing nonparametric instrumental variable estimation and inference.

Given a dependent variable vector Y, matrix of endogenous regressors X, and matrix of instruments W, npiv nonparametrically estimates the structural function h0 and its derivative using B-splines. npiv can also be used for estimting the conditional mean h0 of Y given X, as as well as the derivative of the conditional mean function, by nonparametric regression.

The function npiv also constructs uniform confidence bands for h0 and its derivative.

Sieve dimensions are determined in a data-dependent way if not provided by the user via the function npiv_choose_J, which implements the methods described in Chen, Christensen, and Kankanala (2024). This data-driven choice of sieve dimension ensures estimators of h0 and its derivatives converge at the optimal sup-norm rate. The resulting uniform confidence bands for h0 and its derivative contract within a logarithmic factor of the optimal rate. In this way, npiv facilitates fully data-driven estimation and uniform inference on h0 and its derivative.

If sieve dimensions are provided by the user, npiv implements the bootstrap-based procedure of Chen and Christensen (2018) to construct uniform confidence bands for h0 and its derivative.

Author(s)

Jeffrey S. Racine <[email protected]>, Timothy Christensen <[email protected]>

Maintainer: Timothy Christensen <[email protected]>

References

Chen, X. and T. Christensen (2018). “Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression.” Quantitative Economics, 9(1), 39-85. doi:10.3982/QE722

Chen, X., T. Christensen and S. Kankanala (2024). “Adaptive Estimation and Uniform Confidence Bands for Nonparametric Structural Functions and Elasticities.” Review of Economic Studies, forthcoming. doi:10.1093/restud/rdae025

1995 British Family Expenditure Survey

Description

This dataset is based on a sample taken from the British Family Expenditure Survey for 1995. It includes households consisting of married or cohabiting couples with an employed head of household, aged between 25 and 55 years, and with at most two children. There are 1655 household-level observations in total.

Usage

data("Engel95")data("Engel95")

Format

A data frame with 10 columns, and 1655 rows.

food: expenditure share on food, of type numeric
catering: expenditure share on catering, of type numeric
alcohol: expenditure share on alcohol, of type numeric
fuel: expenditure share on fuel, of type numeric
motor: expenditure share on motor, of type numeric
fares: expenditure share on fares, of type numeric
leisure: expenditure share on leisure, of type numeric
logexp: logarithm of total expenditure, of type numeric
logwages: logarithm of total earnings, of type numeric
nkids: '0' indicates no children, '1' indicates 1-2 children, of type numeric

Source

Richard Blundell and Dennis Kristensen

References

Blundell, R., X. Chen and D. Kristensen (2007). “Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves.” Econometrica, 75(6), 1613-1669. doi:10.1111/j.1468-0262.2007.00808.x

Examples

## Load data
data("Engel95", package = "npiv")

## Sort on logexp (the regressor) for plotting purposes
Engel95 <- Engel95[order(Engel95$logexp),] 
attach(Engel95)
logexp.eval <- seq(4.5,6.5,length=100)

## Estimate the Engel curve for food using logwages as an instrument
food_engel <- npiv(food, logexp, logwages, X.eval = logexp.eval)

## Plot the estimated function and uniform confidence bands
plot(food_engel, showdata = TRUE)
## Load data
data("Engel95", package = "npiv")

## Sort on logexp (the regressor) for plotting purposes
Engel95 <- Engel95[order(Engel95$logexp),] 
attach(Engel95)
logexp.eval <- seq(4.5,6.5,length=100)

## Estimate the Engel curve for food using logwages as an instrument
food_engel <- npiv(food, logexp, logwages, X.eval = logexp.eval)

## Plot the estimated function and uniform confidence bands
plot(food_engel, showdata = TRUE)

GSL (GNU Scientific Library) B-spline/B-spline Derivatives

Description

gsl.bs generates the B-spline basis matrix for a polynomial spline and (optionally) the B-spline basis matrix derivative of a specified order with respect to each predictor

Usage

gsl.bs(...)
## Default S3 method:
gsl.bs(x,
       degree = 3,
       nbreak = 2,
       deriv = 0,
       x.min = NULL,
       x.max = NULL,
       intercept = FALSE,
       knots = NULL,
       ...)
gsl.bs(...)
## Default S3 method:
gsl.bs(x,
       degree = 3,
       nbreak = 2,
       deriv = 0,
       x.min = NULL,
       x.max = NULL,
       intercept = FALSE,
       knots = NULL,
       ...)

Arguments

`x`	the predictor variable. Missing values are not allowed
`degree`	degree of the piecewise polynomial - default is ‘3’ (cubic spline)
`nbreak`	number of breaks in each interval - default is ‘2’
`deriv`	the order of the derivative to be computed-default if `0`
`x.min`	the lower bound on which to construct the spline - defaults to `min(x)`
`x.max`	the upper bound on which to construct the spline - defaults to `max(x)`
`intercept`	if ‘TRUE’, an intercept is included in the basis; default is ‘FALSE’
`knots`	a vector (default `knots="NULL"`) specifying knots for the spline basis (default enables uniform knots, otherwise those provided are used)
`...`	optional arguments

Details

Typical usages are (see below for a list of options and also the examples at the end of this help file)

    B <- gsl.bs(x,degree=10)
    B.predict <- predict(gsl.bs(x,degree=10),newx=xeval)

Value

gsl.bs returns a gsl.bs object. A matrix of dimension ‘c(length(x), degree+nbreak-1)’. The generic function predict extracts (or generates) predictions from the returned object.

A primary use is in modelling formulas to directly specify a piecewise polynomial term in a model. See https://www.gnu.org/software/gsl/ for further details.

Author(s)

Jeffrey S. Racine [email protected]

References

Examples

## Plot the spline bases and their first order derivatives
x <- seq(0,1,length=100)
matplot(x,gsl.bs(x,degree=5),type="l")
matplot(x,gsl.bs(x,degree=5,deriv=1),type="l")

## Regression example
n <- 1000
x <- sort(runif(n))
y <- cos(2*pi*x) + rnorm(n,sd=.25)
B <- gsl.bs(x,degree=5,intercept=FALSE)
plot(x,y,cex=.5,col="grey")
lines(x,fitted(lm(y~B)))
## Plot the spline bases and their first order derivatives
x <- seq(0,1,length=100)
matplot(x,gsl.bs(x,degree=5),type="l")
matplot(x,gsl.bs(x,degree=5,deriv=1),type="l")

## Regression example
n <- 1000
x <- sort(runif(n))
y <- cos(2*pi*x) + rnorm(n,sd=.25)
B <- gsl.bs(x,degree=5,intercept=FALSE)
plot(x,y,cex=.5,col="grey")
lines(x,fitted(lm(y~B)))

Nonparametric Instrumental Variable Estimation and Inference

Description

npiv performs nonparametric a structural function h0 and its derivatives using a B-spline sieve. It also constructs uniform confidence bands for h0 and its derivative.

Sieve dimensions are determined in a data-dependent way if not provided by the user, via the methods described in Chen, Christensen, and Kankanala (2024). This data-driven choice of sieve dimension ensures estimators of h0 and its derivatives converge at the optimal sup-norm rate. The resulting uniform confidence bands for h0 and its derivatives also converge at the minimax rate up to log factors; see Chen, Christensen, and Kankanala (2024).

If sieve dimensions are provided by the user, npiv implements the bootstrap-based procedure of Chen and Christensen (2018) to construct uniform confidence bands based on undersmoothing for h0 and its derivatives.

The methods in npiv apply to estimation and inference on a nonparametric regression function as a special case.

Usage

npiv(...)

## S3 method for class 'formula'
npiv(formula,
     data=NULL,
     newdata=NULL,
     subset=NULL,
     na.action="na.omit",
     call,
     ...)

## Default S3 method:
npiv(Y,
     X,
     W,
     X.eval=NULL,
     X.grid=NULL,
     alpha=0.05,
     basis=c("tensor","additive","glp"),
     boot.num=99,
     check.is.fullrank=FALSE,
     deriv.index=1,
     deriv.order=1,
     grid.num=50,
     J.x.degree=3,
     J.x.segments=NULL,
     K.w.degree=4,
     K.w.segments=NULL,
     K.w.smooth=2,
     knots=c("uniform","quantiles"),
     progress=TRUE,
     ucb.h=TRUE,
     ucb.deriv=TRUE,
     W.max=NULL,
     W.min=NULL,
     X.min=NULL,
     X.max=NULL,
     ...)

npiv(...)

## S3 method for class 'formula'
npiv(formula,
     data=NULL,
     newdata=NULL,
     subset=NULL,
     na.action="na.omit",
     call,
     ...)

## Default S3 method:
npiv(Y,
     X,
     W,
     X.eval=NULL,
     X.grid=NULL,
     alpha=0.05,
     basis=c("tensor","additive","glp"),
     boot.num=99,
     check.is.fullrank=FALSE,
     deriv.index=1,
     deriv.order=1,
     grid.num=50,
     J.x.degree=3,
     J.x.segments=NULL,
     K.w.degree=4,
     K.w.segments=NULL,
     K.w.smooth=2,
     knots=c("uniform","quantiles"),
     progress=TRUE,
     ucb.h=TRUE,
     ucb.deriv=TRUE,
     W.max=NULL,
     W.min=NULL,
     X.min=NULL,
     X.max=NULL,
     ...)

Arguments

`formula`	a symbolic description of the model to be fit.
`data`	an optional data frame containing the variables in the model.
`newdata`	an optional data frame in which to look for variables with which to predict (i.e., predictors in `X` passed in `X.eval` which must contain identically named variables).
`subset`	an optional vector specifying a subset of observations to be used in the fitting process (see additional details about how this argument interacts with data-dependent bases in the ‘Details’ section of the `model.frame` documentation).
`na.action`	a function which indicates what should happen when the data contain NAs. The default is set by the `na.action` setting of `options`, and is `na.fail` if that is unset. The ‘factory-fresh’ default is `na.omit`. Another possible value is `NULL`, no action. Value `na.exclude` can be useful.
`call`	the original function call (this is passed internally by `npiv`). It is not recommended that the user set this.
`Y`	dependent variable vector.
`X`	matrix of endogenous regressors.
`W`	matrix of instrumental variables. Set `W=X` for nonparametric regression.
`X.eval`	optional matrix of evaluation data for the endogenous regressors.
`X.grid`	optional vector of grid points for `X` when determining model complexity. Default (`X.grid=NULL`) uses 50 equally spaced points (can be changed in `grid.num`) over the support of each `X` variable.
`alpha`	nominal size of the uniform confidence bands. Default is `0.05` for 95% uniform confidence bands.
`basis`	basis type (if `X` or `W` are multivariate), a character string. Options are: `tensor` tensor product basis. Default option. `additive` additive basis for additively separable models. `glp` generalized B-spline polynomial basis.
`boot.num`	number of bootstrap replications.
`check.is.fullrank`	check that `X` and `W` have full rank. Default is `FALSE`.
`deriv.index`	integer indicating the column of `X` for which to compute the derivative.
`deriv.order`	integer indicating the order of derivative to be computed.
`grid.num`	number of grid points for each `X` variable if `X.grid` is not provided.
`J.x.degree`	B-spline degree (integer or vector of integers of length `ncol(X)`) for approximating the structural function. Default is `degree=3` (cubic B-spline).
`J.x.segments`	B-spline number of segments (integer or vector of integers of length `ncol(X)`) for approximating the structural function. Default is `NULL`. If either `J.x.segments=NULL` or `K.w.segments=NULL`, these are both chosen automatically using `npiv_choose_J`.
`K.w.degree`	B-spline degree (integer or vector of integers of lenth `ncol(W)`) for estimating the nonparametric first-stage. Default is `degree=4` (quartic B-spline).
`K.w.segments`	B-spline number of segments (integer or vector of integers of length `ncol(W)`) estimating the nonparametric first stage. Defulat is `NULL`. If either `J.x.segments=NULL` or `K.w.segments=NULL`, these are both chosen automatically using `npiv_choose_J`.
`K.w.smooth`	non-negative integer. Basis for the nonparametric first-stage uses $2^{K.w.smooth}$ more B-spline segments for each instrument than the basis approximating the structural function. Default is `2`. Setting `K.w.smooth=0` uses the same number of segments for `X` and `W`.
`knots`	knots type, a character string. Options are: `quantiles` interior knots are placed at equally spaced quantiles (equal number of observations lie in each segment). `uniform` interior knots are placed at equally spoaced intervals over the support of the variable. Default option.
`progress`	whether to display progress bar or not. Default is `TRUE`.
`ucb.h`	whether to compute a uniform confidence band for the structural function. Default is `TRUE`.
`ucb.deriv`	whether to compute a uniform confidence band for the derivative of the structural function. Default is `TRUE`.
`W.min`	lower bound on the support of each `W` variable. Default is `min(W)`.
`W.max`	upper bound on the support of each `W` variable. Default is `max(W)`.
`X.min`	lower bound on the support of each `X` variable. Default is `min(X)`.
`X.max`	upper bound on the support of each `X` variable. Default is `max(X)`.
`...`	optional arguments

Details

npiv estimates and constructs uniform confidence bands for a nonparametric structural function $h_0$ and its derivatives in the model $Y=h_0(X)+U,\quad E[U|W]=0\quad{(\rm almost\, surely).}$ Estimation is performed using nonparametric two-stage least-squares with a B-spline sieve. The key tuning parameter is the dimension $J$ of the sieve used to approximate $h_0$ . The dimension is tuned via modifying the number and placement of interior knots in the B-spline basis (equivalently, the number of segments of the basis). Sieve dimensions can be user-provided or data-determined using the procedure of Chen, Christensen, and Kankanala (2024).

Typical usages mirror ivreg (see above and below for a list of options and the example at the bottom of this document)

    foo <- npiv(y~x|w)
    foo <- npiv(y~x1+x2|w1+w2)
    foo <- npiv(Y=y,X=x,W=w)

npiv can be used in two ways:

1. Data-driven sieve dimension is invoked if either K.w.segments or J.x.segments are unspecified or NULL (the default). Sieve dimensions are chosen automatically using npiv_choose_J. Uniform confidence bands for $h_0$ and its derivatives are constructed using the data-driven method of Chen, Christensen, and Kankanala (2024).

2. The user may specify the sieve dimensions of both bases by specifying values for K.w.segments and J.x.segments. Uniform confidence bands for $h_0$ and its derivatives are constructed using the method of Chen and Christensen (2018).

npiv can also be used for estimation and inference on a nonparametric regression function by setting W=X.

Value

npiv returns a npiv object. The generic function fitted extracts the estimated values for the sample (or evaluation data, if provided), while the generic function residuals extracts the sample residuals. The generic function summary provides a simple model summary. The generic function plot also plots the estimated function and derivative, together with uniform confidence bands.

The function npiv returns a list with the following components:

`h`	estimated structural function evaluated at the sample data (or evaluation data, if provided).
`residuals`	residuals for the sample data.
`deriv`	estimated derivative of the structural function evaluated at the sample data (or evaluation data, if provided).
`asy.se`	pre-asymptotic standard errors for the estimator of the structural function evaluated at the sample data (or evaluation data, if provided)
`deriv.asy.se`	pre-asymptotic standard errors for the estimator of the derivative of the structural function evaluated at the sample data (or evaluation data, if provided).
`deriv.index`	index for the estimated derivative.
`deriv.order`	order of the estimated derivative.
`K.w.degree`	value of `K.w.degree` used.
`K.w.segments`	value of `K.w.segments` used (will be data-determined if not provided).
`J.x.degree`	value of `J.x.degree` used.
`J.x.segments`	value of `J.x.segments` used (will be data-determined if not provided).
`beta`	vector of estimated spline coefficients.

Author(s)

Jeffrey S. Racine <[email protected]>, Timothy Christensen <[email protected]>

References

Examples

## load data
data("Engel95", package = "npiv")

## sort on logexp (the regressor) for plotting purposes
Engel95 <- Engel95[order(Engel95$logexp),] 
attach(Engel95)

## Estimate the Engel curve for food using logwages as an instrument
fm1 <- npiv(food ~ logexp | logwages)

## Plot the estimated Engel curve and data-driven uniform confidence bands
plot(logexp,food,
     ylab="Food Budget Share",
     xlab="log(Total Household Expenditure)",
     xlim=c(4.75, 6.25),
     ylim=c(0, 0.4),
     main="",
     type="p",
     cex=.5,
     col="lightgrey")
lines(logexp,fm1$h,col="blue",lwd=2,lty=1)
lines(logexp,fm1$h.upper,col="blue",lwd=2,lty=2)
lines(logexp,fm1$h.lower,col="blue",lwd=2,lty=2)

## Estimate the Engel curve using pre-specified sieve dimension 
## (dimension 5 for logexp, dimension 9 for logwages)
fm2 <- npiv(food ~ logexp | logwages,
            J.x.segments = 2,
            K.w.segments = 5)

## Plot uniform confidence bands based on undersmoothing
lines(logexp,fm2$h.upper,col="red",lwd=2,lty=2)
lines(logexp,fm2$h.lower,col="red",lwd=2,lty=2)

## Plot pointwise confidence bands based on pre-asymptotic standard errors
lines(logexp,fm2$h+1.96*fm2$asy.se,col="red",lwd=2,lty=3)
lines(logexp,fm2$h-1.96*fm2$asy.se,col="red",lwd=2,lty=3)

legend("topright",
       legend=c("Data-driven Estimate",
                "Data-driven UCBs",
                "Undersmoothed UCBs",
                "Pointwise CBs"),
       col=c("blue","blue","red","red"),
       lty=c(1,2,2,3),
       lwd=c(2,2,2,2))

## Plot the data-driven estimate of the derivative of the Engel curve
plot(logexp,fm1$deriv,col="blue",lwd=2,lty=1,type="l",
     ylab="Derivative of Food Budget Share",
     xlab="log(Total Household Expenditure)",
     xlim=c(4.75, 6.25),
     ylim=c(-1,1))

## Plot data-driven uniform confidence bands for the derivative
lines(logexp,fm1$h.upper.deriv,col="blue",lwd=2,lty=2)
lines(logexp,fm1$h.lower.deriv,col="blue",lwd=2,lty=2)

## Plot uniform confidence bands based on undersmoothing
lines(logexp,fm2$h.upper.deriv,col="red",lwd=2,lty=2)
lines(logexp,fm2$h.lower.deriv,col="red",lwd=2,lty=2)

## Plot pointwise confidence bands based on pre-asymptotic standard errors
lines(logexp,fm2$deriv+1.96*fm2$deriv.asy.se,col="red",lwd=2,lty=3)
lines(logexp,fm2$deriv-1.96*fm2$deriv.asy.se,col="red",lwd=2,lty=3)

legend("topright",
       legend=c("Data-driven Estimate",
                "Data-driven UCBs",
                "Undersmoothed UCBs",
                "Pointwise CBs"),
       col=c("blue","blue","red","red"),
       lty=c(1,2,2,3),
       lwd=c(2,2,2,2))
## load data
data("Engel95", package = "npiv")

## sort on logexp (the regressor) for plotting purposes
Engel95 <- Engel95[order(Engel95$logexp),] 
attach(Engel95)

## Estimate the Engel curve for food using logwages as an instrument
fm1 <- npiv(food ~ logexp | logwages)

## Plot the estimated Engel curve and data-driven uniform confidence bands
plot(logexp,food,
     ylab="Food Budget Share",
     xlab="log(Total Household Expenditure)",
     xlim=c(4.75, 6.25),
     ylim=c(0, 0.4),
     main="",
     type="p",
     cex=.5,
     col="lightgrey")
lines(logexp,fm1$h,col="blue",lwd=2,lty=1)
lines(logexp,fm1$h.upper,col="blue",lwd=2,lty=2)
lines(logexp,fm1$h.lower,col="blue",lwd=2,lty=2)

## Estimate the Engel curve using pre-specified sieve dimension 
## (dimension 5 for logexp, dimension 9 for logwages)
fm2 <- npiv(food ~ logexp | logwages,
            J.x.segments = 2,
            K.w.segments = 5)

## Plot uniform confidence bands based on undersmoothing
lines(logexp,fm2$h.upper,col="red",lwd=2,lty=2)
lines(logexp,fm2$h.lower,col="red",lwd=2,lty=2)

## Plot pointwise confidence bands based on pre-asymptotic standard errors
lines(logexp,fm2$h+1.96*fm2$asy.se,col="red",lwd=2,lty=3)
lines(logexp,fm2$h-1.96*fm2$asy.se,col="red",lwd=2,lty=3)

legend("topright",
       legend=c("Data-driven Estimate",
                "Data-driven UCBs",
                "Undersmoothed UCBs",
                "Pointwise CBs"),
       col=c("blue","blue","red","red"),
       lty=c(1,2,2,3),
       lwd=c(2,2,2,2))

## Plot the data-driven estimate of the derivative of the Engel curve
plot(logexp,fm1$deriv,col="blue",lwd=2,lty=1,type="l",
     ylab="Derivative of Food Budget Share",
     xlab="log(Total Household Expenditure)",
     xlim=c(4.75, 6.25),
     ylim=c(-1,1))

## Plot data-driven uniform confidence bands for the derivative
lines(logexp,fm1$h.upper.deriv,col="blue",lwd=2,lty=2)
lines(logexp,fm1$h.lower.deriv,col="blue",lwd=2,lty=2)

## Plot uniform confidence bands based on undersmoothing
lines(logexp,fm2$h.upper.deriv,col="red",lwd=2,lty=2)
lines(logexp,fm2$h.lower.deriv,col="red",lwd=2,lty=2)

## Plot pointwise confidence bands based on pre-asymptotic standard errors
lines(logexp,fm2$deriv+1.96*fm2$deriv.asy.se,col="red",lwd=2,lty=3)
lines(logexp,fm2$deriv-1.96*fm2$deriv.asy.se,col="red",lwd=2,lty=3)

legend("topright",
       legend=c("Data-driven Estimate",
                "Data-driven UCBs",
                "Undersmoothed UCBs",
                "Pointwise CBs"),
       col=c("blue","blue","red","red"),
       lty=c(1,2,2,3),
       lwd=c(2,2,2,2))

Data-driven Choice of Sieve Dimension for Nonparametric Instrumental Variables Estimation and Inference

Description

npiv_choose_J implements the data-driven choice of sieve dimension developed in Chen, Christensen, and Kankanala (2024) for nonparametric instrumental variables estimation using a B-spline sieve. It applies to nonparametric regression as a special case.

Usage

npiv_choose_J(Y, 
              X,
              W,
              X.grid = NULL,
              J.x.degree = 3,
              K.w.degree = 4,
              K.w.smooth = 2,
              knots = c("uniform", "quantiles"),
              basis = c("tensor", "additive", "glp"),
              X.min = NULL,
              X.max = NULL,
              W.min = NULL,
              W.max = NULL,
              grid.num = 50,
              boot.num = 99,
              check.is.fullrank = FALSE,
              progress = TRUE)
npiv_choose_J(Y, 
              X,
              W,
              X.grid = NULL,
              J.x.degree = 3,
              K.w.degree = 4,
              K.w.smooth = 2,
              knots = c("uniform", "quantiles"),
              basis = c("tensor", "additive", "glp"),
              X.min = NULL,
              X.max = NULL,
              W.min = NULL,
              W.max = NULL,
              grid.num = 50,
              boot.num = 99,
              check.is.fullrank = FALSE,
              progress = TRUE)

Arguments

`Y`	dependent variable vector.
`X`	matrix of endogenous regressors.
`W`	matrix of instrumental variables. Set `W=X` for nonparametric regression.
`X.grid`	vector of grid point(s). Default uses 50 equally spaced points over the support of each `X` variable.
`J.x.degree`	B-spline degree (integer or vector of integers of length `ncol(X)`) for approximating the structural function. Default is `degree=3` (cubic B-spline).
`K.w.degree`	B-spline degree (integer or vector of integers of lenth `ncol(W)`) for estimating the nonparametric first-stage. Default is `degree=4` (quartic B-spline).
`K.w.smooth`	non-negative integer. Basis for the nonparametric first-stage uses $2^{K.w.smooth}$ more B-spline segments for each instrument than the basis approximating the structural function. Default is `2`. Setting `K.w.smooth=0` uses the same number of segments for `X` and `W`.
`knots`	knots type, a character string. Options are: `quantiles` interior knots are placed at equally spaced quantiles (equal number of observations lie in each segment). `uniform` interior knots are placed at equally spoaced intervals over the support of the variable. Default option.
`basis`	basis type (if `X` or `W` are multivariate), a character string. Options are: `tensor` tensor product basis. Default option. `additive` additive basis for additively separable models. `glp` generalized B-spline polynomial basis.
`X.min`	lower bound on the support of each `X` variable. Default is `min(X)`.
`X.max`	upper bound on the support of each `X` variable. Default is `max(X)`.
`W.min`	lower bound on the support of each `W` variable. Default is `min(W)`.
`W.max`	upper bound on the support of each `W` variable. Default is `max(W)`.
`grid.num`	number of grid points for each `X` variable if `X.grid` is not provided.
`boot.num`	number of bootstrap replications.
`check.is.fullrank`	check that `X` and `W` have full rank. Default is `FALSE`.
`progress`	whether to display progress bar or not. Default is `TRUE`.

Value

`J.hat.max`	largest element of candidate set of sieve dimensions searched over.
`J.hat.n`	second largest element of candidate set of sieve dimensions searched over.
`J.hat`	bootstrap-based Lepski choice of sieve dimension.
`J.tilde`	data-driven choice of sieve dimension using the method of Chen, Christensen, and Kankanala (2024). Minimum of `J.hat` and `J.hat.n`.
`J.x.seg`	data-driven number of segments for `X` using the method of Chen, Christensen, and Kankanala (2024).
`K.w.seg`	data-driven number of segments for `W` using the method of Chen, Christensen, and Kankanala (2024).
`theta.star`	Lepski critical value used in determination of `J.hat`.

Author(s)

Jeffrey S. Racine <[email protected]>, Timothy Christensen <[email protected]>

References

Examples

library(MASS)

## Simulate the data
n <- 10000
cov.ux <- 0.5
var.u <- 0.1
mu <- c(1,1,0)
Sigma <- matrix(c(1.0,0.85,cov.ux,
                  0.85,1.0,0.0,
                  cov.ux,0.0,1.0),
                3,3,
                byrow=TRUE)
foo <- mvrnorm(n = n,
               mu,
               Sigma)
X <- 2*pnorm(foo[,1],mean=mu[1],sd=sqrt(Sigma[1,1])) -1
W <- 2*pnorm(foo[,2],mean=mu[2],sd=sqrt(Sigma[2,2])) -1
U <- foo[,3]
## Cosine structural function
h0 <- sin(pi*X)
Y <- h0 + sqrt(var.u)*U

npiv_choose_J(Y,X,W)
library(MASS)

## Simulate the data
n <- 10000
cov.ux <- 0.5
var.u <- 0.1
mu <- c(1,1,0)
Sigma <- matrix(c(1.0,0.85,cov.ux,
                  0.85,1.0,0.0,
                  cov.ux,0.0,1.0),
                3,3,
                byrow=TRUE)
foo <- mvrnorm(n = n,
               mu,
               Sigma)
X <- 2*pnorm(foo[,1],mean=mu[1],sd=sqrt(Sigma[1,1])) -1
W <- 2*pnorm(foo[,2],mean=mu[2],sd=sqrt(Sigma[2,2])) -1
U <- foo[,3]
## Cosine structural function
h0 <- sin(pi*X)
Y <- h0 + sqrt(var.u)*U

npiv_choose_J(Y,X,W)

Package 'npiv'

Help Index

Nonparametric Instrumental Variables Estimation and Inference

Description

Details

Author(s)

References

1995 British Family Expenditure Survey

Description

Usage

Format

Source

References

Examples

GSL (GNU Scientific Library) B-spline/B-spline Derivatives

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Nonparametric Instrumental Variable Estimation and Inference

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Data-driven Choice of Sieve Dimension for Nonparametric Instrumental Variables Estimation and Inference

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples