[R] System GMM yields identical results for any weighting matrix

[Bert Gunter]

Sorry, my advice is incorrect (and I should have known better!). Task
views are to search for relevant packages, not for posting questions.
R "special interest groups" (SIGs) are for the latter, which in your
case might be this one:
https://stat.ethz.ch/mailman/listinfo/r-sig-finance .

Cheers,
Bert


On Tue, Apr 23, 2024 at 11:45 AM Bert Gunter <bgunter.4567 using gmail.com> wrote:
>
> Generally speaking, this sort of detailed statistical question about a
> speccial package in R does not get a reply on this general R
> programming help list. Instead, I suggest you either email the
> maintainer (found by ?maintainer) or ask a question on a relevant R
> task view, such as
> https://cran.r-project.org/web/views/Econometrics.html . (or any other
> that you judge to be more appropriate).
>
> Cheers,
> Bert
>
> On Tue, Apr 23, 2024 at 9:41 AM Richard Hardy <brukalinis using gmail.com> wrote:
> >
> > A copy of this question can be found on Cross Validated:
> > https://stats.stackexchange.com/questions/645362
> >
> > I am estimating a system of seemingly unrelated regressions (SUR) in R.
> > Each of the equations has one unique regressor and one common regressor. I
> > am using `gmm::sysGmm` and am experimenting with different weighting
> > matrices. I get the same results (point estimates, standard errors and
> > anything else that I can see (**except** for the value of the $J$-test)
> > regardless of the weighting matrix. I do not think this is correct.
> > The phenomenon persists regardless of what type of covariance matrix
> > estimator I use: `MDS`, `CondHom` or `HAC`.
> > It also persists regardless of whether I use unrestricted estimation or
> > restrict the coefficients on one of the variables (the common regressor) to
> > be equal across equations.
> >
> > **Question:** Why does system GMM via `gmm::sysGmm` yield identical results
> > for any weighting matrix? How can I make it yield proper results that vary
> > with the weighting matrix (if that makes sense and I am not mistaken, of
> > course)?
> >
> > ------------------------------ R code for a reproducible example
> >
> > library(gmm)
> > library(systemfit)
> >
> > # Generate and prepare the data
> > n <- 1000 # sample size
> > m <- 100  # length of the "second part" of the sample
> > N <- 3    # number of equations
> > set.seed(321); x <- matrix(rnorm(n*N),ncol=N); colnames(x) <-
> > paste0("x",1:N) # generate regressors
> > dummy <- c( rep(0,n-m), rep(1,m) ) # generate a common regressor
> > x <- cbind(x,dummy)                # include the common regressor with the
> > rest of the regressors
> > set.seed(123); y <- matrix(rnorm(n*N),ncol=N); colnames(y) <-
> > paste0("y",1:N) # a placeholder for dependent variables
> > for(i in 1:N){
> >  y[,i] <- i + sqrt(i)*x[,i] - i*dummy + y[,i]*15*sqrt(i)
> >  # y[,i] is a linear function of x[,i] and dummy,
> >  # plus an error term with equation-specific variance
> > }
> > data1 <- as.data.frame(cbind(y,x)) # create a data frame of all data (y and
> > x)
> >
> > # Create the model equations and moment conditions
> > ES_g = ES_h <- list() # ES ~ equation system
> > for(i in 1:N){
> >  ES_g[[i]] <- as.formula(assign(paste0("eq",i), value=paste0("y",i," ~
> > x",i," + dummy"))) # define linear equations of SUR
> >  ES_h[[i]] <- as.formula(assign(paste0("eq",i), value=paste0(       "~
> > x",i," + dummy"))) # define the moment conditions for GMM
> > }
> >
> > # Estimate a WLS-type weighting matrix to use as a user-specified weighting
> > matrix in GMM
> > m0 <- systemfit(formula=ES_g, method="OLS", data=data1)
> > OLSmat <- diag(diag(m0$residCov)); Wmat <- solve(OLSmat)
> >
> > # Choose the type of covariance matrix in GMM
> > vc1 <- "MDS"
> > vc1 <- "CondHom"
> > vc1 <- "HAC"
> > #vc1 <- "TrueFixed"
> >
> > # Choose between restricted and unrestricted estimation
> > cec1=NULL # unrestricted
> > cec1=3    # restrict the coefficient on the dummy to be equal across
> > equations
> >
> > # Estimate the model with `sysGmm` using different weighting matrices:
> > identity, "optimal" and manually specified
> > m1a <- sysGmm(g=ES_g, h=ES_h, wmatrix="ident"  , weightsMatrix=NULL,
> > vcov=vc1, crossEquConst=cec1, data=data1); summary(m1a)
> > m1b <- sysGmm(g=ES_g, h=ES_h, wmatrix="optimal", weightsMatrix=NULL,
> > vcov=vc1, crossEquConst=cec1, data=data1); summary(m1b)
> > m1c <- sysGmm(g=ES_g, h=ES_h,                    weightsMatrix=Wmat,
> > vcov=vc1, crossEquConst=cec1, data=data1); summary(m1c)
> >
> > ------------------------------ R session info:
> >
> > R version 4.3.3 (2024-02-29 ucrt)
> > Platform: x86_64-w64-mingw32/x64 (64-bit)
> > Running under: Windows 10 x64 (build 19045)
> >
> > Matrix products: default
> >
> > locale:
> > [1] LC_COLLATE=English_United States.utf8  LC_CTYPE=English_United
> > States.utf8
> > [3] LC_MONETARY=English_United States.utf8 LC_NUMERIC=C
> >
> > [5] LC_TIME=English_United States.utf8
> >
> > time zone: Europe/Berlin
> > tzcode source: internal
> >
> > attached base packages:
> > [1] stats     graphics  grDevices utils     datasets  methods   base
> >
> > other attached packages:
> > [1] systemfit_1.1-30 lmtest_0.9-40    zoo_1.8-12       car_3.1-2
> >  carData_3.0-5    Matrix_1.6-1
> > [7] gmm_1.8          sandwich_3.0-2
> >
> > loaded via a namespace (and not attached):
> > [1] MASS_7.3-60.0.1   compiler_4.3.3    tools_4.3.3       abind_1.4-5
> > rstudioapi_0.15.0 grid_4.3.3
> > [7] lattice_0.22-5
> >
> > ------------------------------
> >
> > Kind regards,
> > Richard
> >
> >         [[alternative HTML version deleted]]
> >
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