High order approximation of a multi-country trade model

Specific Domains Finance and Economics
, , ,
22

Thanks so much. This helps to improve the performance. But I have a related question. Why does the @btime result change in the following code?

#---------------------------------------

# housekeeping
#---------------------------------------

using FiniteDifferences, Profile, LinearAlgebra, BenchmarkTools

#---------------------------------------
# internal functions
#---------------------------------------

# function about equilibrium condition (excess labor demand)
@views function es_loop(wzet,y,x,kappa,sig,N,tau_mat,cma,cld)
    # define the matrix dimension
    broadcast!(.^, tau_mat, wzet[N+1], kappa)

    # armington condition
    # 1. compute the change in the market access (cma)
    cma_mat = x .* (tau_mat .* wzet[1:N]) .^ (1-sig)
    for i = 1:N
        cma .+= cma_mat[i:i,:]
    end
    # 2. sum over the change in labor demand across destination (cld)
    cld_mat = y .* (tau_mat .* wzet[1:N]) .^ (1-sig) .* wzet[1:N]' ./ cma
    for j = 1:N
        cld .+= cld_mat[:,j:j]
    end
    excess_loop = wzet[1:N] - cld
    return excess_loop
end

#---------------------------------------
# parameters and data
#---------------------------------------

N = 3;             # number of countries
sig = 4;            # elasticity of substitution

homebias = 0.9;     # the size of the domestic consumption tendency
X = homebias * Matrix{Float64}(I,N,N) + (1-homebias) * 1/N * ones(N,N);
y = X./sum(X,dims=2);
x = X./sum(X,dims=1);

# trade cost setting
kappa = vcat(zeros(N-1,N), [ones(N-1); 0]'); # the kernel of the trade cost change 
tau_mat = ones(N,N);    # pre-allocate the tau matrix

wzet = ones(N+1);   # initial point

# pre-allocate
cma = zeros(1,N);   # change in the market access
cld = zeros(N,1);   # change in labor demand
cma_mat = zeros(N,N);
cld_mat = zeros(N,N);

#---------------------------------------
# check performance
#---------------------------------------

es_loop(wzet,y,x,kappa,sig,N,tau_mat,cma,cld)

Specifically, the last line es_loop(wzet,y,x,kappa,sig,N,tau_mat,cma,cld) returns a correct answer as follows:

3×1 Matrix{Float64}:
 0.0
 0.0
 0.0

However, when I change the last line into @btime es_loop(wzet,y,x,kappa,sig,N,tau_mat,cma,cld), it returns a wrong answer as follows:

  240.423 ns (3 allocations: 336 bytes)
3×1 Matrix{Float64}:
 -12.700585535625594
 -12.700585535625592
 -12.700585535625592
23

@btime runs the same code several times, could it be because you expect some array (cma for instance) to be filled with zeros (or some other value) when the algorithm starts, and then you overwrite it so that it does not have the same initial value the next time @btime runs the expression?

24

Yes, of course. This makes perfect sense. Thanks so much, and I will work on a different approach for a while if I can compute the fourth order derivatives in a reasonable time :slight_smile: