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ivregress.py
162 lines (114 loc) · 4.21 KB
/
ivregress.py
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import pandas as pd
import numpy as np
from copy import deepcopy
np.set_printoptions(suppress=True)
# Function for 2sls
def reg(X, y):
XTX_inv = np.linalg.inv(np.dot(X.T, X))
beta_hr = np.dot(XTX_inv, np.dot(X.T, y))
return beta_hr
def _ivregress(X, Z, y, verbose = False):
tmp1 = np.dot(Z, np.linalg.inv(np.dot(Z.T, Z)))
if verbose:
print(tmp1.shape)
X_hat = np.dot(tmp1, np.dot(Z.T, X))
beta_2sls = reg(X_hat, y)
if verbose:
print(beta_2sls)
Pz = np.dot(tmp1, Z.T)
if verbose:
print(Pz.shape)
eps = y - np.dot(X, beta_2sls)
sigma_2 = np.dot(eps.T, eps)/X.shape[0]
if verbose:
print(sigma_2)
Var_beta_2sls = sigma_2 * np.linalg.inv(np.dot(np.dot(X.T, Pz), X))
if verbose:
print(np.sqrt(np.diag(Var_beta_2sls)))
return beta_2sls, Var_beta_2sls
def ivregress_2sls(df, y_var, regs, ev, inst, verbose=False):
S = deepcopy(df)
S['_const'] = 1
# exogenous variables
ex_vars = list(set(regs) - set(ev))
z_vars = ['_const'] + inst + ex_vars
x_vars = ['_const'] + regs
if verbose:
print('Variables in Z matrix are')
print(z_vars)
print('Variables in X matrix are')
print(x_vars)
Z = S[z_vars].to_numpy()
X = S[x_vars].to_numpy()
y = S[y_var].to_numpy()
beta_2sls, Var_beta_2sls = _ivregress(X, Z, y)
std_err = np.sqrt(np.diag(Var_beta_2sls))
df_out = pd.DataFrame(data = np.concatenate([beta_2sls[:, None], std_err[:, None]], axis=1)
, columns = ['Coef.', 'Std. Err.']
, index = x_vars)
return df_out
# Functions for ts2sls
def _ts2sls(X2, X1, Z2, Z1, y1, y_z, ev_ind, verbose=False):
tmp_z2t2_inv = np.linalg.inv(np.dot(Z2.T, Z2))
tmp_z2tx2 = np.dot(Z2.T, X2)
X1_hat = np.dot(Z1, np.dot(tmp_z2t2_inv, tmp_z2tx2))
beta_ts2sls = np.dot(np.linalg.inv(np.dot(X1_hat.T, X1_hat)), np.dot(X1_hat.T, y1))
n1 = Z1.shape[0]
n2 = Z2.shape[0]
beta_1s = reg(Z2, y_z)
pred_y_z = np.dot(Z1, beta_1s)
pred_X1 = deepcopy(X1).astype('float64')
pred_X1[:, ev_ind] = pred_y_z[:,0]
k_p = pred_X1.shape[1]
eps = y1 - np.dot(pred_X1, beta_ts2sls)
sigma_2 = np.dot(eps.T, eps)/(n1 - k_p)
if verbose:
print(sigma_2)
Var_beta_2sls = sigma_2 * np.linalg.inv(np.dot(X1_hat.T, X1_hat))
if verbose:
print(Var_beta_2sls)
print(np.sqrt(np.diag(Var_beta_2sls)))
k_q = Z2.shape[1]
pred_X2 = deepcopy(X2).astype('float64')
pred_y_z2 = np.dot(Z2, beta_1s)
pred_X2[:, ev_ind] = pred_y_z2[:, 0]
eps_1s = X2 - pred_X2
sigma_nu = np.dot(eps_1s.T, eps_1s)/(n2-k_q)
if verbose:
print(sigma_nu)
sigma_f = sigma_2 + n1/n2 * np.dot(beta_ts2sls.T, np.dot(sigma_nu, beta_ts2sls))
if verbose:
print(sigma_f)
Var_beta_ts2sls = sigma_f * np.linalg.inv(np.dot(X1_hat.T, X1_hat))
if verbose:
print(Var_beta_ts2sls)
print(np.sqrt(np.diag(Var_beta_ts2sls)))
return beta_ts2sls, Var_beta_ts2sls
def ts2sls(df1, df2, y_var, regs, ev, inst, verbose=False):
S1 = deepcopy(df1)
S2 = deepcopy(df2)
S1['_const'] = 1
S2['_const'] = 1
# exogenous variables
ex_vars = list(set(regs) - set(ev))
z_vars = ['_const'] + inst + ex_vars
x_vars = ['_const'] + regs
if verbose:
print('Variables in Z matrix are')
print(z_vars)
print('Variables in X matrix are')
print(x_vars)
Z2 = S2[z_vars].to_numpy()
Z1 = S1[z_vars].to_numpy()
X2 = S2[x_vars].to_numpy()
X1 = S1[x_vars].to_numpy()
y1 = S1[y_var].to_numpy()
y_z = S2[ev].to_numpy()
# TODO: find a better way to communicate the positions of endogenous variables
ev_ind = x_vars.index(ev[0])
beta_ts2sls, Var_beta_ts2sls = _ts2sls(X2, X1, Z2, Z1, y1, y_z, ev_ind)
std_err = np.sqrt(np.diag(Var_beta_ts2sls))
df_out = pd.DataFrame(data = np.concatenate([beta_ts2sls[:, None], std_err[:, None]], axis=1)
, columns = ['Coef.', 'Std. Err.']
, index = x_vars)
return df_out