Feature parity with Wooldridge and other packages

[azev77]

Wooldridge tweeted that every econometrics package should come with the following options for standard errors for virtually every command:

• Robust to allow complete model misspecification of the modeled parts.
• HAC to allow for unmodeled time series correlation.
• Cluster to allow serial correlation in panels and cluster sampling/clustered assignment generally.
• Driscoll-Kraay to allow unmodeled serial correlation in large-T panels as well as cross-sectional correlation.
  @PaulSoderlind has https://github.com/PaulSoderlind/PaulSoderlindCode/tree/master/DriscollKraay
• Spatial HAC to allow unmodeled spatial correlation in the cross-sectional dimension (requires a cross-sectional ordering of the data).
• Spatial HAC with clustering to allow for any kind of serial correlation and cross-sectional spatial correlation (small T).

"In Stata, I'd like to type things like"
glm y x1 ... xK, fam(logit) vce(hac nw 4)
xtpoisson y x1 ... xK, fe vce(shac lat(Lx) long(Ly) dist(50))
qreg y x1 ... xK, q(.25) vce(dk 4)

[azev77]

I myself have written some (unoptimized) code too:

using LinearAlgebra, BenchmarkTools, DataFrames;
x =[ones(506) randn(506,3)]; n,p =size(x);
y = x*[1;2;3;4] + randn(506);

b_ls = x\y; y_ls = x*b_ls; e_ls = y-y_ls; s2_ls = ((e_ls'e_ls)/(n-p))[1];

# Sandwich: v(Ω; x=x) = (x'x)^-1 * (x'Ω*x) * (x'x)^-1
v(Ω; x=x) = (x'x) \ (x'Ω*x) / (x'x)

# Newey West Lags 
relu(x) = max(x,0)
NW(nlags,n) = [relu(1 - abs(j-i)/(nlags+1)) for i=1:n, j=1:n]

# SE: 12 methods
function SE(x, y, n, p, e_ls, s2_ls)
    H = x/(x'x) * x'     #H = x*inv(x'x)*x'     ŷ = Hy
    M = I - H            #                      ε̂ = My
    δ = min.(4,n/p .* diag(H) )
    δm = min.(1,n/p .* diag(H) ) + min.(1.5,n/p  .* diag(H) )
    mx = max(n*0.7*maximum(diag(H))/p, 4)
    α  = min.(mx, n/p .* diag(H))
    e_ti = e_ls ./ (diag(I-H))
    #
    HS   = v( Diagonal(fill(s2_ls,n)) )                      #Spherical
    HC0  = v( Diagonal(e_ls*e_ls') * 1.00 )
    HC1  = v( Diagonal(e_ls*e_ls') * (n/(n-p)) )
    HC2  = v( Diagonal(e_ls*e_ls') / (Diagonal(I-H)) )
    HC3  = v( Diagonal(e_ls*e_ls') / ((Diagonal(I-H))^2 ) )
    HC4  = v( Diagonal(e_ls*e_ls') / ((Diagonal(I-H)) .^ δ ) )
    HC4m = v( Diagonal(e_ls*e_ls') / ((Diagonal(I-H)) .^ δm ) )
    HC5  = v( Diagonal(e_ls*e_ls') / sqrt.((Diagonal(I-H)) .^ α ) )
    HCJ  = v( ((n-1)/n) * (Diagonal(e_ti*e_ti') - (1/n)*e_ti*e_ti') )
    # CRVE example w/ 3 clusters
    ix =[1:200 , 201:400 , 401:506]
    blocks = [e_ls[ix[1]]*e_ls[ix[1]]', e_ls[ix[2]]*e_ls[ix[2]]', e_ls[ix[3]]*e_ls[ix[3]]']
    #D      = Diagonal(blocks)
    G = size(ix,1);
    HLZ = v( cat(blocks...,dims=(1,2)) * ((G)/(G-1)) * ((n-1)/(n-p)) )
    #HBC = v( M^(-1/2) * cat(blocks...,dims=(1,2)) * M^(-1/2) )
    HBC = v( real(sqrt(Hermitian(M^-1))) * cat(blocks...,dims=(1,2)) * real(sqrt(Hermitian(M^-1))) )
    # Multi-way clustering
    # NW
    lags = Int(max(round(n^0.25),1.0))
    HNW = v( (e_ls*e_ls') .* NW(lags,n) )
    #
    # Spatially Correlated SE: Conley, Driscoll-Kraay
    # Bootstrap: Wildclustered Bootstrap
    #
    #return HS, HC0, HC1, HC2, HC3, HC4, HC4m, HC5, HCJ, HLZ, HNW
    cov = [HS, HC0, HC1, HC2, HC3, HC4, HC4m, HC5, HCJ, HLZ, HBC, HNW]
    se = [sqrt.(diag(x)) for x in cov]
    #
    se = reshape(vcat(se...), 4, 12)
    se = DataFrame(round.(se, sigdigits=3))
    rename!(se, [:HS, :HC0, :HC1, :HC2, :HC3, :HC4, :HC4m, :HC5, :HCJ, :HLZ, :HBC, :HNW])
    insertcols!(se, 1, :coef => ["β0","β1","β2","β3"])
    return se
end

se1 = SE(x, y, n, p, e_ls, s2_ls)

Here is a screenshot w/ part of the table:

[PaulSoderlind]

I have several of those, but in somewhat crude versions. In particular, the combination of autocorrelation and (some kind of) clustering tends to make things messy. I have the code, but it's not pretty.

Still, If anyone takes the lead to create a common approach, I am happy o contribute.

/Paul S

[PaulSoderlind]

Another thought/observation: things like
HC0 = v( Diagonal(e_ls*e_ls') * 1.00 )
work on balanced panels.

It becomes substantially messier with unbalanced panels. To keep the matrix notation, a set of interactive "data exists" dummies can be used (see Hayashi's text). Alternatively, create a loop.

[matthieugomez]

@azev77 Yes it'd be great to have more types of standard errors!
@PaulSoderlind Yes, being able to write these loops without being slower is definitely one of the advantages of Julia. This is already the case for clustered std, i.e. https://github.com/matthieugomez/Vcov.jl/blob/b324f45b788b06e46301963fadb9da8ceaceb150/src/covarianceestimators/vcovcluster.jl#L172

[azev77]

@matthieugomez have you defined the scope of Vcov.jl?

• is it intended to work w/ other packages? GLM.jl, QuantileRegressions.jl, etc
• are you open to including resampling methods? (wild clustered bootstrap?)

[matthieugomez]

The goal is for developers (like GLM etc) to depend on this package and use it to compute standard errors. This would simplify things for users (i.e. simply specify Vcov.robust() as an argument of the function fit) without requiring every package to implement standard errors computation.

[IljaK91]

Is there any movement in this direction? Working out these things would allow many people to move some workflows from R to Julia (regression -> custom standard errors -> latex regression table -> inclusion in paper). I am happy to join efforts if there is someone else who has a good idea of how to tackle this.

[azev77]

Btw, @droodman, has: https://github.com/droodman/WildBootTests.jl