Tools

Tauchen(rho,N,sigma,mue)

Generate a discrete approximation to an AR(1) process, following Tauchen (1987).

Uses importance sampling: each bin has probability 1/N to realize

Arguments

• rho: autocorrelation coefficient
• N: number of gridpoints
• sigma: long-run variance
• mue: mean of the AR(1) process

Returns

• grid_vec: state vector grid
• P: transition matrix
• bounds: bin bounds

distrSummaries(distr,c_a_star,c_n_star,n_par,inc,incgross,m_par)

Compute distributional summary statistics, e.g. Gini indexes, top-10% income and wealth shares, and 10%, 50%, and 90%-consumption quantiles.

Arguments

• distr: joint distribution over bonds, capital and income $(m \times k \times y)$
• c_a_star,c_n_star: optimal consumption policies with [a] or without [n] capital adjustment
• n_par::NumericalParameters, m_par::ModelParameters
• inc: vector of (on grid-)incomes, consisting of labor income (scaled by $\frac{\gamma-\tau^P}{1+\gamma}$, plus labor union-profits), rental income, liquid asset income, capital liquidation income, labor income (scaled by $\frac{1-\tau^P}{1+\gamma}$, without labor union-profits), and labor income (without scaling or labor union-profits)
• incgross: vector of (on grid-) pre-tax incomes, consisting of labor income (without scaling, plus labor union-profits), rental income, liquid asset income, capital liquidation income, labor income (without scaling or labor union-profits)

myinterpolate3(xgrd1, xgrd2, xgrd3, ygrd, xeval1, xeval2, xeval3)

Trilineary project ygrd on (xgrd1,xgrd2,xgrd3) and use it to interpolate value at (xeval1,xeval2,xeval3).

Example

julia> xgrd = [1.0,6.0];
julia> f((x,y,z)) = x+y+z;
julia> ygrd = f.(collect(Iterators.product(xgrid,xgrid,xgrid));
julia> xeval = [3.0,5.0];
julia> mylinearinterpolate3(xgrd,xgrd,xgrd,ygrd,xeval,xeval,xeval)
2x2x2 Array{Float64,3}:
[:,:,1] =
 9.0 11.0
11.0 13.0
[:,:,2] =
11.0 13.0
13.0 15.0