This is about 2SLS method in Econometrics. Hereโs the output for a dataset. This is just a test case
library(car)## Loading required package: carDatalibrary(carData)
library(car)
library(systemfit)## Loading required package: Matrix## Loading required package: lmtest## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## Please cite the 'systemfit' package as:
## Arne Henningsen and Jeff D. Hamann (2007). systemfit: A Package for Estimating Systems of Simultaneous Equations in R. Journal of Statistical Software 23(4), 1-40. http://www.jstatsoft.org/v23/i04/.
##
## If you have questions, suggestions, or comments regarding the 'systemfit' package, please use a forum or 'tracker' at systemfit's R-Forge site:
## https://r-forge.r-project.org/projects/systemfit/rm(list=ls()) #Removes all items in Environment!
library(systemfit)
library(broom) #for `glance(`) and `tidy()`
library(PoEdata) #for PoE4 dataset
library(knitr) #for kable()
data("truffles", package="PoEdata")
D <- q~p+ps+di
S <- q~p+pf
sys <- list(D,S)
instr <- ~ps+di+pf
truff.sys <- systemfit(sys, inst=instr,
method="2SLS", data=truffles)
summary(truff.sys)##
## systemfit results
## method: 2SLS
##
## N DF SSR detRCov OLS-R2 McElroy-R2
## system 60 53 692.472 49.8028 0.438964 0.807408
##
## N DF SSR MSE RMSE R2 Adj R2
## eq1 30 26 631.9171 24.30450 4.92996 -0.023950 -0.142098
## eq2 30 27 60.5546 2.24276 1.49758 0.901878 0.894610
##
## The covariance matrix of the residuals
## eq1 eq2
## eq1 24.30451 2.16943
## eq2 2.16943 2.24276
##
## The correlations of the residuals
## eq1 eq2
## eq1 1.00000 0.29384
## eq2 0.29384 1.00000
##
##
## 2SLS estimates for 'eq1' (equation 1)
## Model Formula: q ~ p + ps + di
## Instruments: ~ps + di + pf
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.279471 5.543884 -0.77193 0.4471180
## p -0.374459 0.164752 -2.27287 0.0315350 *
## ps 1.296033 0.355193 3.64881 0.0011601 **
## di 5.013977 2.283556 2.19569 0.0372352 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.92996 on 26 degrees of freedom
## Number of observations: 30 Degrees of Freedom: 26
## SSR: 631.917143 MSE: 24.304505 Root MSE: 4.92996
## Multiple R-Squared: -0.02395 Adjusted R-Squared: -0.142098
##
##
## 2SLS estimates for 'eq2' (equation 2)
## Model Formula: q ~ p + pf
## Instruments: ~ps + di + pf
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.0328022 1.2231148 16.3785 1.5543e-15 ***
## p 0.3379816 0.0249196 13.5629 1.4344e-13 ***
## pf -1.0009094 0.0825279 -12.1281 1.9456e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.497585 on 27 degrees of freedom
## Number of observations: 30 Degrees of Freedom: 27
## SSR: 60.554565 MSE: 2.242762 Root MSE: 1.497585
## Multiple R-Squared: 0.901878 Adjusted R-Squared: 0.89461