Hello:

I am working on a maximum simulated likelihood estimation on a multi-layer (group/firm/time) model. There are three random variables and I have to do simulation draws for two of them. The estimation is very slow because of the simulations; one small sample took about 8 minutes to estimate via MSLE. The speed becomes a hurdle for a Monte Carlo exercise where the model is to be estimated thousands of times.

I took out the time-consuming part of the log-likelihood function and made it into the following MWE. Any suggestion on how to further speed up the run time will be much appreciated.

```
using Random, Distributions, FLoops, StatsFuns
@fastmath NH_like(sigmau::Real, lambdau::Real, uit) =
(exp.(-0.5 * StatsFuns.abs2.( uit/sigmau )) * invsqrt2Ď€ ) .*
StatsFuns.erfc.(-(lambdau * uit / sigmau) * invsqrt2)/2
function test1(; S=200, G=100, F=3, T=2)
# S=Sw=Sc: simulation draws; G:groups; F:firms; T:times;
TF = T*F
ww = rand(S)
cc = rand(S)
wc = (repeat(ww, inner=S) + repeat(cc, outer=S))' # 1x(Sc*Sw)
wc_expand = repeat(wc, outer=(T,1)) # Tx(Sc*Sw)
epsi = rand(G*F*T, 1) # (G*F*T x 1)
lnLike = 0.0
@floop begin
@inbounds for g in 1:G
Like_g = ones(1, S)
@inbounds for i in 1:F
@views u_it = epsi[1 + (g-1)*TF + (i-1)*T : (g-1)*TF + i*T] .- wc_expand # Tx(Sw*Sc)
aa = NH_like(0.5, 1.1, u_it)
bb = prod(aa, dims=1) # 1 X (Sw*Sc)
cc = mean(reshape(bb, (S, S)), dims=1) # 1 X s_w
Like_g = Like_g .* cc # 1 X Sw matrix
end
lnLike += log(mean((Like_g)))
end # for_g
end # @floop
end
```