542_PS1_Carril.jl

#%% Load libraries
using DataFrames, CSV
using Statistics
using Plots, LaTeXStrings

#%% Read and prepare data
cd("/home/alvaro/Dropbox/Princeton/2020-Spring/542-IO/PS1")
df = CSV.read("data/Pset1_2020Data.csv");

# Add dummy columns for number of active firms in each market
for j in levels(df.firms_in_market)
    var = Symbol(:Nfirms, Int(j))
    df[var] = Int.(df.firms_in_market .== j)
end

# Compute d_{-i} (total ATMs in market sans own)
d_total = by(df, :market_index, :d_i => sum)
df = join(d_total, df, on = :market_index)
df[:d_others] = (df.d_i_sum - df.d_i)./(df.firms_in_market .- 1)

#%% Define functions
# Define Moments() function
function Moments(β1, β2, df, instruments)
    ineq_minus = (df.r - df.r_minus) .- β1 .+ β2 .* (1 .- 2 .* df.d_i)
    ineq_plus  = (df.r - df.r_plus)  .+ β1 .+ β2 .* (1 .+ 2 .* df.d_i)
    Z = [DataFrame(Constant = ones(size(df)[1])) select(df, instruments)]
    M = hcat(ineq_minus .* Z, ineq_plus .* Z, makeunique = true)
    [mean(col) for col in eachcol(M)]
end

# Define searchB() function to search for parameters whose expected moment condition is non-negative
function searchB(β1_grid, β2_grid, data, instruments)
    B = zeros(size(β1_grid)[1]*size(β2_grid)[1], 2)
    k = 1
    for x = 1:size(β1_grid)[1]
        β1 = β1_grid[x]
        for y = 1:size(β2_grid)[1]
            β2 = β2_grid[y]
            M = Moments(β1, β2, df, instruments)
            if minimum(M) >= 0
                B[k, :] = [β1 β2]
                k = k + 1
            end
        end
    end
    # Truncate zeros from B matrix
    last_nonzero = findall(x->x==0, B)[1][1]-1
    B[1:last_nonzero, :]
end

#%% Define grids
# Note: values found after fine-tuning
β1_grid = collect(25000:100:45000)
β2_grid = collect(1500:10:4000)

#%% Question 6: Number-of-firms-in-market dummies as instruments
Z = [:Nfirms2, :Nfirms3, :Nfirms4]
B = searchB(β1_grid, β2_grid, df, Z)

# Plot B using [:Nfirms2, :Nfirms3, :Nfirms4] as instruments
plot(B[:,1], B[:,2], seriestype=:scatter,
    xlabel = L"\beta_1", ylabel = L"\beta_2",
    guidefontsize = 16,
    legend = false,
    marker = (:dot, 1, 0.2, :blue, stroke(1, 0.2, :blue))
    )
savefig("writeup/figs/params_Z_marketsize.pdf")


#%% Question 8
# Search for parameter values adding d_others as additional instrument
Z2 = [:d_others]
B2 = searchB(β1_grid, β2_grid, df, Z2)
B = Int.(B)
plot(B2[:,1], B2[:,2], seriestype=:scatter,
    formatter = Int,
    xlabel = L"\beta_1", ylabel = L"\beta_2",
    label = "Average number of ATMs of competitors",
    legendfont = 9,
    guidefontsize = 16,
    marker = (:dot, 1, 0.2, :red, stroke(1, 0.2, :red))
    )
plot!(B[:,1], B[:,2], seriestype=:scatter,
    marker = (:dot, 1, 0.2, :blue, stroke(1, 0.2, :blue)),
    legendfont = 9,
    label = "Number of firms in market (dummies)",
    legendtitle = "Instrument\n",
    legendtitlefont = 12,
    )
savefig("writeup/figs/params_Z_marketsize_plus.pdf")