CODEWITHSUNDEEP
r
Kate
Kate

Reputation: 45

New lfe/felm syntax, variable-specific instrument

I want to estimate a regression with two exogenous variables, two endogenous variable and a pair of fixed effects. Each endogenous variable has its own instrument.

Y = b0 + b1*X1 + b2*X2 + b3*Q + b4*W + C1*factor(id) + C2*factor(firm)

W = d0 + d1*X3

Q = e0 + e1*X4

Here is the part where I use generated data for Y, X, Q, W

require(lfe)
oldopts <- options(lfe.threads=1)
x <- rnorm(1000)
x2 <- rnorm(length(x))
id <- factor(sample(20,length(x),replace=TRUE))
firm <- factor(sample(13,length(x),replace=TRUE))
id.eff <- rnorm(nlevels(id))
firm.eff <- rnorm(nlevels(firm))
u <- rnorm(length(x))
y <- x + 0.5*x2 + id.eff[id] + firm.eff[firm] + u
x3 <- rnorm(length(x))
x4 <- 5*rnorm(length(x))^2
Q <- 0.3*x3 - 0.3*rnorm(length(x),sd=0.3) - 0.7*id.eff[id]
W <- 0.3*log(x4)- 2*x + 0.1*x2  - 0.2*y+ rnorm(length(x),sd=0.6)
y <- y + Q + W

I can estimate the coefficients using the old lfe syntax

reg <- felm(y~x+x2+G(id)+G(firm),iv=list(Q~x3,W~x4))

But the package strongly discourages the use of old syntax and I do not know how to specify different first stage equations in the new syntax.

If I try this line, both x3 and x4 would be used for both Q and W first stage equations. 

reg_new <- felm(y ~ x + x2 | id+firm | (Q|W ~x3 + x4))

Upvotes: 1

Views: 1867

Answers (1)

Simen Gaure
Simen Gaure

Reputation: 291

I'm sorry for the late answer. As the author of the lfe package, I am not aware of any theory for using different sets of instruments for different endogenous variables. It should not have been allowed in the old syntax either. If one of the instruments is uncorrelated with one of the endogenous variables, its coefficient in the first stage will simply be estimated as zero. The theory for IV-estimation by means of two stage regression simply uses some matrix identities to split the IV-estimation into two stages of ordinary regression, for convenience and reduction to well-known methods. As far as I'm aware, there is no IV with separate sets of instruments for the endogenous variables.

See e.g. wikipedia's entry on this: https://en.wikipedia.org/wiki/Instrumental_variable#Estimation

Upvotes: 3

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