def monte_carlo(file, which, grid_points=10):
"""This function estimates various effect parameters for
increasing presence of essential heterogeneity, which is reflected
by increasing correlation between U_1 and V.
"""
# simulate a new data set with essential heterogeneity present
model_dict = read(file)
original_correlation = model_dict["DIST"]["params"][2]
model_dict["DIST"]["params"][2] = -0.191
print_dict(model_dict, file.replace(".grmpy.yml", ""))
grmpy.simulate(file)
effects = []
# Loop over different correlations between V and U_1
for rho in np.linspace(0.00, -0.99, grid_points):
# effects["rho"] += [rho]
# Readjust the initialization file values to add correlation
model_spec = read(file)
X = model_spec["TREATED"]["order"]
update_correlation_structure(file, model_spec, rho)
sim_spec = read(file)
# Simulate a Data set and specify exogeneous and endogeneous variables
df_mc = create_data(file)
treated = df_mc["D"] == 1
Xvar = df_mc[X]
instr = sim_spec["CHOICE"]["order"]
instr = [i for i in instr if i != "const"]
# We calculate our parameter of interest
label = which.lower()
if label == "conventional_average_effects":
ATE = np.mean(df_mc["Y1"] - df_mc["Y0"])
TT = np.mean(df_mc["Y1"].loc[treated] - df_mc["Y0"].loc[treated])
stat = (ATE, TT)
elif label in ["random", "randomization"]:
random = np.mean(df_mc[df_mc.D == 1]["Y"]) - np.mean(
df_mc[df_mc.D == 0]["Y"])
stat = random
elif label in ["ordinary_least_squares", "ols"]:
results = sm.OLS(df_mc["Y"], df_mc[["const", "D"]]).fit()
stat = results.params[1]
elif label in ["instrumental_variables", "iv"]:
iv = IV2SLS(df_mc["Y"], Xvar, df_mc["D"], df_mc[instr]).fit()
stat = iv.params["D"]
elif label in ["grmpy", "grmpy-par"]:
rslt = grmpy.fit(file)
beta_diff = rslt["TREATED"]["params"] - rslt["UNTREATED"]["params"]
stat = np.dot(np.mean(Xvar), beta_diff)
elif label in ["grmpy-semipar", "grmpy-liv"]:
rslt = grmpy.fit(file, semipar=True)
y0_fitted = np.dot(rslt["X"], rslt["b0"])
y1_fitted = np.dot(rslt["X"], rslt["b1"])
mte_x_ = y1_fitted - y0_fitted
mte_u = rslt["mte_u"]
us = np.linspace(0.005, 0.995, len(rslt["quantiles"]))
mte_mat = np.zeros((len(mte_x_), len(mte_u)))
for i in range(len(mte_x_)):
for j in range(len(mte_u)):
mte_mat[i, j] = mte_x_[i] + mte_u[j]
ate_tilde_p = np.mean(mte_mat, axis=1)
stat = ate_tilde_p.mean()
else:
raise NotImplementedError
effects += [stat]
# Restore original init file
model_dict = read(file)
model_dict["DIST"]["params"][2] = original_correlation
print_dict(model_dict, file.replace(".grmpy.yml", ""))
grmpy.simulate(file)
return effects
def monte_carlo(file, which, grid_points=10):
"""
This function conducts a Monte Carlo simulation to compare
the true and estimated treatment parameters for increasing
(absolute) correlation between U_1 and V (i.e essential
heterogeneity).
In the example here, the correlation between U_1 and V becomes
increasingly more negative. As we consider the absolute value
of the correlation coefficient, values closer to -1
(or in the analogous case closer to +1)
denote a higher degree of essential heterogeneity.
The results of the Monte Carlo simulation can be used
to evaluate the performance of different estimation strategies
in the presence of essential heterogeneity.
Depending on the specification of *which*, either the true ATE
and TT, or an estimate of the ATE are returned.
Options for *which*:
Comparison of ATE and TT
- "conventional_average_effects"
Different estimation strategies for ATE
- "randomization" ("random")
- "ordinary_least_squares" ("ols")
- "instrumental_variables" ("iv")
- "grmpy_par" ("grmpy")
- "grmpy_semipar"("grmpy-liv")
Post-estimation: To plot the comparison between the true ATE
and the respective parameter, use the function
- plot_effects() for *which* = "conventional_average_effects", and
- plot_estimates() else.
Parameters
----------
file: yaml
grmpy initialization file, provides information for the simulation process.
which: string
String denoting whether conventional average effects shall be computed
or, alternatively, which estimation approach shall be implemented for the ATE.
grid_points: int, default 10
Number of different values for rho, the correlation coefficient
between U_1 and V, on the interval [0, -1), along which the parameters
shall be evaluated.
Returns
-------
effects: list
If *which* = "conventional_average_effects",
list of lenght *grid_points* x 2 containing the true ATE and TT.
Else, list of length *grid_points* x 1 containing an estimate
of the ATE.
"""
# simulate a new data set with essential heterogeneity present
model_dict = read(file)
original_correlation = model_dict["DIST"]["params"][2]
model_dict["DIST"]["params"][2] = -0.191
print_dict(model_dict, file.replace(".grmpy.yml", ""))
grmpy.simulate(file)
effects = []
# Loop over different correlations between U_1 and V
for rho in np.linspace(0.00, -0.99, grid_points):
# effects["rho"] += [rho]
# Readjust the initialization file values to add correlation
model_spec = read(file)
X = model_spec["TREATED"]["order"]
_update_correlation_structure(file, model_spec, rho)
sim_spec = read(file)
# Simulate a Data set and specify exogeneous and endogeneous variables
df_mc = _create_data(file)
treated = df_mc["D"] == 1
Xvar = df_mc[X]
instr = sim_spec["CHOICE"]["order"]
instr = [i for i in instr if i != "const"]
# We calculate our parameter of interest
label = which.lower()
if label == "conventional_average_effects":
ATE = np.mean(df_mc["Y1"] - df_mc["Y0"])
TT = np.mean(df_mc["Y1"].loc[treated] - df_mc["Y0"].loc[treated])
stat = (ATE, TT)
elif label in ["randomization", "random"]:
random = np.mean(df_mc[df_mc.D == 1]["Y"]) - np.mean(
df_mc[df_mc.D == 0]["Y"]
)
stat = random
elif label in ["ordinary_least_squares", "ols"]:
results = sm.OLS(df_mc["Y"], df_mc[["const", "D"]]).fit()
stat = results.params[1]
elif label in ["instrumental_variables", "iv"]:
iv = IV2SLS(df_mc["Y"], Xvar, df_mc["D"], df_mc[instr]).fit()
stat = iv.params["D"]
elif label in ["grmpy", "grmpy-par"]:
rslt = grmpy.fit(file)
beta_diff = rslt["TREATED"]["params"] - rslt["UNTREATED"]["params"]
stat = np.dot(np.mean(Xvar), beta_diff)
elif label in ["grmpy-semipar", "grmpy-liv"]:
rslt = grmpy.fit(file, semipar=True)
y0_fitted = np.dot(rslt["X"], rslt["b0"])
y1_fitted = np.dot(rslt["X"], rslt["b1"])
mte_x_ = y1_fitted - y0_fitted
mte_u = rslt["mte_u"]
us = np.linspace(0.005, 0.995, len(rslt["quantiles"]))
mte_mat = np.zeros((len(mte_x_), len(mte_u)))
for i in range(len(mte_x_)):
for j in range(len(mte_u)):
mte_mat[i, j] = mte_x_[i] + mte_u[j]
ate_tilde_p = np.mean(mte_mat, axis=1)
stat = ate_tilde_p.mean()
else:
raise NotImplementedError
effects += [stat]
# Restore original init file
model_dict = read(file)
model_dict["DIST"]["params"][2] = original_correlation
print_dict(model_dict, file.replace(".grmpy.yml", ""))
grmpy.simulate(file)
return effects