Grupo_7_jl.ipynb

Kernel: Julia 1.6.7

##Primero cargamos las librerías correspondientes

# import Pkg 
# Pkg.add("LinearAlgebra")
# Pkg.add("Random")
# Pkg.add("Distributions")
# Pkg.add("Statistics")
# Pkg.add("DataFrames")

using Random  
using Statistics 
using Distributions, LinearAlgebra
using DataFrames 

x1 = rand(500)  # distribución uniforme
x2 = rand(500) # distribución uniforme
x3 = rand(500) # distribución uniforme
x4 = rand(500) # distribución uniforme

z = randn(500)
e = randn(500) # distribución normal;  mean = 0 y sd = 1
# DGP

Y = ones(500) + 0.8.*x1 + 1.2.*x2 + 0.5.*x3 + 1.5.*x4 + e

500-element Vector{Float64}:
 1.732376881771378
 2.409978687041122
 4.150753116878622
 2.793717008885756
 5.0863608462978505
 3.4483497238839727
 2.6495342654093355
 2.98844380749602
 3.4908273860413495
 3.1712853692231864
 1.8676466375279612
 4.019376920268693
 4.876522242403515
 ⋮
 1.3419909808267683
 3.4604431589567786
 2.0691561148564275
 4.262429421943498
 2.5748543033922187
 4.188473021936753
 1.5412229221891398
 3.086776312001024
 5.426574663429239
 2.7987707979958913
 3.502149956514354
 3.284028382055414

# joint vectors to matrix 

X = hcat(ones(500),x1,x2,x3,x4)

500×5 Matrix{Float64}:
 1.0  0.822616   0.265703   0.19344    0.25784
 1.0  0.4063     0.0468582  0.152245   0.226299
 1.0  0.928465   0.929036   0.12129    0.0154756
 1.0  0.68993    0.858346   0.346843   0.833202
 1.0  0.592235   0.851619   0.203868   0.779895
 1.0  0.675279   0.602735   0.245972   0.608907
 1.0  0.247588   0.185229   0.803019   0.249005
 1.0  0.751151   0.326369   0.148468   0.778784
 1.0  0.0720629  0.765281   0.93624    0.904085
 1.0  0.50906    0.497169   0.0215682  0.908182
 1.0  0.666871   0.399246   0.957679   0.625106
 1.0  0.513633   0.0512418  0.713356   0.733343
 1.0  0.868238   0.447019   0.793059   0.607345
 ⋮                                     
 1.0  0.0639895  0.0632196  0.128167   0.102697
 1.0  0.945388   0.485486   0.956185   0.67077
 1.0  0.195108   0.192561   0.372833   0.797801
 1.0  0.726164   0.457337   0.806353   0.0627122
 1.0  0.913781   0.428816   0.31562    0.0350651
 1.0  0.275156   0.205836   0.582011   0.903211
 1.0  0.289271   0.157083   0.80139    0.0578881
 1.0  0.942083   0.379045   0.109796   0.562426
 1.0  0.615894   0.865984   0.997874   0.861874
 1.0  0.817006   0.812282   0.611677   0.0378364
 1.0  0.434898   0.777112   0.229168   0.290471
 1.0  0.267566   0.983208   0.637553   0.904835

function  ols(M::Matrix ,Y, est::Bool = true , Pvalue = true , instrumento = nothing , index = nothing)
    if est && Pvalue && isnothing(instrumento) && isnothing(index)
        beta = inv(transpose(X) * X) * (transpose(X) * Y) ## estimación de beta
        y_est =  X*beta   ## Y estimado  
        n = size(X,1)
        k = size(X,2) - 1  
        nk= n - k
        dist = TDist(4)    ## 4 grados de libertad
        m2= Y - y_est
        sigma2= (transpose(m2) * m2) ./ nk ##sigma cuadrado
        Var =  sigma2* inv(transpose(X) * X) ##hallamos varianza
        sd = Var[ diagind(Var) ]  ## raíz cuadrado a los datos de la diagonal principal de Var
        test = 3.5
        Pvalue = 2*(1 - cdf(dist, test)) 
        df= DataFrame(OLS = beta, standar_error= sd, Pvalue= Pvalue )
       
        return df
        
    elseif !isnothing(instrumento) && !isnothing(index)
        
        beta = inv(transpose(X) * X) * (transpose(X) * Y)
        index = index  - 1 
        Z = X
        Z[:,index] = z ## reemplazamos la variable endógena por el instrumento en la matrix de covariables
        beta_x = inv(transpose(Z) * X) * (transpose(Z) * X)
        x_est  = Z*beta_x
        X[:,index] = x_est ## se reemplaza la variable x endógena por su estimado 
        beta_iv = inv(transpose(X) * X) * (transpose(X) * Y)
        df = DataFrame( OLS=beta , OLS_IV= beta_iv) 
        return df
    end 
end  

ols(X,Y)

5×3 DataFrame
 Row │ OLS       standar_error  Pvalue    
     │ Float64   Float64        Float64   
─────┼────────────────────────────────────
   1 │ 1.11067       0.025959   0.0248962
   2 │ 0.747655      0.0233189  0.0248962
   3 │ 1.17503       0.0239942  0.0248962
   4 │ 0.527027      0.0213323  0.0248962
   5 │ 1.35568       0.0219997  0.0248962