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offset function for known intercept and instrumental variables [ Reply ]
By: Jorge Zea on 2020-05-08 20:56

[forum:47765]

Hi,

I am new to Systemfit and I have two questions

1) How to use the offset function within a system of equations to predetermine a known intercept?. I have the following equation system structure where Y2 has no estimated intercept, but it does have a known intercept:
Eq. 1 <- Y1 ~ alpha0 + alpha1*X1 + alpha2*X2 + Y2
Eq. 2 <- Y2 ~ -1 (without intercept) + offset (Z) + beta1*X3 + beta*X4
Where Z is the known intercept: (Z = w1, W1 is any other variable), and alpha and beta are the parameters of each equation.

A reproducible (hypothetical) example follows:
##########################
library(systemfit)
data( "Kmenta" )
attach( Kmenta )

# fitting by systemfit
eqSupply <- consump ~ price + income + trend
eqTrend <- trend ~ 0 + offset(farmPrice) + price + income
eqSystem <- list( demand = eqTrend, supply = eqSupply )
inst <- ~ income + farmPrice + trend
fit3sls <- systemfit( eqSystem, method = "3SLS", inst = inst)
summary(fit3sls)
#Adjusted R-Squared (eqSupply): 0.763226
#Adjusted R-Squared (eqTrend): 0.090928

# fitting by OLS
eqSupply2 <- lm(consump ~ price + income + trend)
summary(eqSupply2) # Adjusted R-squared: 0.7739
eqTrend2 <- lm(trend ~ 0 + offset(farmPrice) + price + income)
summary(eqTrend2) #Adjusted R-squared: 0.4648
#################################
Note that the parameters and adjusted R squared for eqTrend (0.090928) by Systemfit is very different from eqTrend2 (0.4648) for OLS. Please help me identify the problem or tell me please, What other function or structure can be used in Y2 to include a known intercept in the model fit?

2) In simple terms, what is the concept of instrumental variables and how to identify them for each equation?
I have already read the package documentation, the "paper" related to the article (http://www.jstatsoft.org/v23/i04/paper) and a forum post (https: //r-forge.r-project. org / forum / forum.php? thread_id = 33628 & forum_id = 788 & group_id = 242) but it's not clear to me yet. If you can explain to me in a simple way, I appreciate it.

Thanks!

Jorge Zea
Forest engineer