R.OLS {OptSig}

Restricted OLS estimation and F-test

Description

Function to calcuate the Restricted (under H0) OLS Estimators and F-test statistic

Usage

R.OLS(y, x, Rmat, rvec)

Arguments

y

a matrix of dependent variable, T by 1

x

a matrix of K independent variable, T by K

Rmat

a matrix for J restrictions, J by (K+1)

rvec

a vector for restrictions, J by 1

Details

Rmat and rvec are the matrices for the linear restrictions, which a user should supply.

Refer to an econometrics textbook for details.

Value

coef

matrix of estimated coefficients, (K+1) by 2, under H1 and H0

RSq

R-square values under H1 and H0, 2 by 1

resid

residual vector under H1 and H0, T by 2

F.stat

F-statistic and p-value

ncp

non-centrality parameter, estimated by replaicing unknowns using OLS estimates

Note

The function automatically adds an intercept, so the user need not include a vector of ones in x matrix.

Author(s)

Jae H. Kim

References

Kim and Choi, 2020, Choosing the Level of Significance: A Decision-theoretic Approach, Abacus, Wiley. <https://doi.org/10.1111/abac.12172>

See Also

Leamer, E. 1978, Specification Searches: Ad Hoc Inference with Nonexperimental Data, Wiley, New York.

Kim, JH and Ji, P. 2015, Significance Testing in Empirical Finance: A Critical Review and Assessment, Journal of Empirical Finance 34, 1-14. <DOI:http://dx.doi.org/10.1016/j.jempfin.2015.08.006>

Kim, Jae H., 2020, Decision-theoretic hypothesis testing: A primer with R package OptSig, The American Statistician. <https://doi.org/10.1080/00031305.2020.1750484.>

Examples

data(data1)
# Define Y and X
y=data1$lnoutput; x=cbind(data1$lncapital,data1$lnlabor)
# Restriction matrices to test for constant returns to scale
Rmat=matrix(c(0,1,1),nrow=1); rvec=matrix(1,nrow=1)
# Model Estimation and F-test
M=R.OLS(y,x,Rmat,rvec)