Please cite the following paper if you use this package.

The R package **bndovb** implements a Hwang(2021) estimator to bound omitted variable bias using auxiliary data. The basic assumption is that the main data includes a dependent variable and every regressor but one omitted variable. So there is an omitted variable bias in the OLS result from the main data. However, if there is auxiliary data that includes every right-hand side regressor (or its noisy proxies), it can bound the omitted variable bias. Hwang(2021) provides a more general estimator for when there is more than one omitted variable and when the auxiliary data does not contain every right-hand side regressor (or its noisy proxies).

This package implements a simple estimator when the number of omitted variables is just one, and the auxiliary data contains every right-hand side regressor but the only omitted variable. This package provides two different functions.

The function ‘bndovb’ can be used when the auxiliary data contain every right-hand side variable without measurement errors. The function ‘bndovbme’ can be used when noisy proxies for the omitted variable exist in the auxiliary data. Other regressors in the auxiliary data are assumed measurement error-free. The function requires another R package, ‘factormodel,’ written by the same author.

When using ‘bndovb,’ a user should specify a method for density estimation as part of an estimation procedure, either 1 (parametric normal density assumption) or 2 (nonparametric kernel density estimation). In general, it is strongly recommended to use method 1 (parametric normal density assumption), particularly when data is large or the regression model is large. Method 2 calls an R package “np” (Li and Racine, 2008; Li, Lin and Racine, 2013) but this method is very slow, as emphasized in their vignette file. I recommend using their method only when (i) data is small and (ii) there is only one common variable, which makes the conditional CDF and quantile function univariate. The default method is 1, using parametric normal density assumption.

When using ‘bndovbme’, the auxiliary data must contain noisy proxy variables for the omitted variable. A user should set the type of the proxy variables, ptype, to either 1 (continuous) or 2 (discrete). When proxy variables are continuous, the auxiliary data must contain at least 2 proxy variables. When proxy variables are discrete, the auxiliary data must contain at least 3 proxy variables.

You can install a package **bndovb** using either CRAN or github.

or

The below example shows how to use a function ‘bndovb’ when the auxiliary data contain the omitted variable from main data without any measurement error. The code first simulates fake data using the same DGP in both main data and auxiliary data. Next, the main data omits one variable. The function ‘bndovb’ provides a bound on regression coefficients by using both main data and auxiliary data.

```
library(bndovb)
library(MASS)
# sample size
Nm <- 5000 # main data
Na <- 5000 # auxiliary data
# use same DGP in maindat and auxdat
maindat <- mvrnorm(Nm,mu=c(2,3,1),Sigma=rbind(c(2,1,1),c(1,2,1),c(1,1,2)))
auxdat <- mvrnorm(Na,mu=c(2,3,1),Sigma=rbind(c(2,1,1),c(1,2,1),c(1,1,2)))
maindat <- as.data.frame(maindat)
auxdat <- as.data.frame(auxdat)
colnames(maindat) <- c("x1","x2","x3")
colnames(auxdat) <- c("x1","x2","x3")
# this is a true parameter which we try to get bounds on
truebeta <- matrix(c(2,1,3,2),ncol=1)
# generate a dependent variable
maindat$y <- as.matrix(cbind(rep(1,Nm),maindat[,c("x1","x2","x3")]))%*%truebeta
# main data misses one omitted variable "x1"
maindat <- maindat[,c("x2","x3","y")]
# use "bndovb" function assuming parametric "normal" distribution for the CDF and quantile function (set method=1)
# see Hwang(2021) for further details
oout <- bndovb(maindat=maindat,auxdat=auxdat,depvar="y",ovar="x1",comvar=c("x2","x3"),method=1)
print(oout)
#> $hat_beta_l
#> con x1 x2 x3
#> 1.545978 -0.897721 3.165398 1.807142
#>
#> $hat_beta_u
#> con x1 x2 x3
#> 3.002594 1.087069 3.777266 2.512049
#>
#> $mu_l
#> [1] 34.83043
#>
#> $mu_u
#> [1] 37.47501
# use "bndovb" function using nonparametric estimation of the CDF and quantile function (set method=2)
# for nonparametric density estimator, the R package "np" was used. See Hayfield and Racine (2008), Li and Racine (2008), Li, Lin and Racine (2013)
#### The next line takes very long because of large sample size. You can try using a smaller sample and run the next line.
#oout <- bndovb(maindat=maindat,auxdat=auxdat,depvar="y",ovar="x1",comvar=c("x2","x3"),method=2)
#print(oout)
```