def run_regressions_3(data=[], endog=[], exog=[], options=0, clusterfirm=0):
results = []
print(endog)
for index, elem in enumerate(data):
# name = 'endog' + '_' + str(index)
if options == 0:
mod = PanelOLS(elem[endog],
elem[exog],
entity_effects=True,
time_effects=True)
if options == 1:
mod = PanelOLS(elem[endog],
elem[exog],
entity_effects=False,
time_effects=True)
if options == 2:
print(type(elem))
mod = PooledOLS(elem[endog], elem[exog])
if clusterfirm == 0:
results.append(mod.fit(cov_type='clustered', clusters=elem.gvkey))
if clusterfirm == 1:
results.append(mod.fit(cov_type='clustered', cluster_entity=True))
if clusterfirm == 2:
results.append(mod.fit())
return results
def run_regressions(dataa, datab, endog1, endog2, exog1, exog2, options=0):
results = []
print(endog1)
for index, elem in enumerate(endog1):
name = 'endog1' + '_' + str(index)
if options == 0:
mod = PanelOLS(dataa[elem],
dataa[exog1],
entity_effects=True,
time_effects=True)
if options == 1:
mod = PanelOLS(dataa[elem],
dataa[exog1],
entity_effects=False,
time_effects=True)
results.append(mod.fit(cov_type='clustered', clusters=dataa.gvkey))
for index, elem in enumerate(endog2):
name = 'endog2' + '_' + str(index)
if options == 0:
mod = PanelOLS(datab[elem],
datab[exog2],
entity_effects=True,
time_effects=True)
if options == 1:
mod = PanelOLS(datab[elem],
datab[exog2],
entity_effects=False,
time_effects=True)
results.append(mod.fit(cov_type='clustered', clusters=datab.gvkey))
return results
def regressions(data, endog, exog, options, clusterfirm, constant):
#results = []
if constant == 1:
exog = sm.add_constant(data[exog])
if constant == 0:
exog = data[exog]
if options == 0:
mod = PanelOLS(data[endog],
exog,
entity_effects=True,
time_effects=True)
if options == 1:
mod = PanelOLS(data[endog],
exog,
entity_effects=False,
time_effects=True)
if options == 2:
#print(data[[endog]], exog)
mod = PooledOLS(data[endog], exog)
if clusterfirm == 0:
results = mod.fit(cov_type='clustered', clusters=data.gvkey)
if clusterfirm == 1:
results = mod.fit(cov_type='clustered', cluster_entity=True)
if clusterfirm == 2:
results = mod.fit()
return results
def run_regressions_2(data, endog=[], exog=[], options=0):
results = []
print(endog)
for index, elem in enumerate(endog):
name = 'endog' + '_' + str(index)
if options == 0:
for i, e in enumerate(endog):
mod = PanelOLS(data[elem],
data[e],
entity_effects=True,
time_effects=True)
if options == 1:
mod = PanelOLS(data[elem],
data[e],
entity_effects=False,
time_effects=True)
results.append(mod.fit(cov_type='clustered', clusters=data.gvkey))
return results
def get_fe(
regression_variables: List[Tuple],
data: Dict[str, pd.DataFrame],
datasets: Dict[pd.DataFrame, Any],
entity_effects: bool = False,
time_effects: bool = False,
) -> Tuple[DataFrame, Any, List[Any], Any]:
"""When effects are correlated with the regressors the RE and BE estimators are not consistent.
The usual solution is to use Fixed Effects which are called entity_effects when applied to
entities and time_effects when applied to the time dimension. [Source: LinearModels]
Parameters
----------
regression_variables : list
The regressions variables entered where the first variable is
the dependent variable.
data : dict
A dictionary containing the datasets.
datasets: dict
A dictionary containing the column and dataset names of
each column/dataset combination.
entity_effects : bool
Whether to include entity effects
time_effects : bool
Whether to include time effects
Returns
-------
The dataset used, the dependent variable, the independent variable and
the OLS model.
"""
regression_df, dependent_variable, independent_variables = get_regression_data(
regression_variables, data, datasets, "FE")
if regression_df.empty:
model = None
else:
with warnings.catch_warnings(record=True) as warning_messages:
exogenous = add_constant(regression_df[independent_variables])
model = PanelOLS(
regression_df[dependent_variable],
exogenous,
entity_effects=entity_effects,
time_effects=time_effects,
).fit()
console.print(model)
if len(warning_messages) > 0:
console.print("Warnings:")
for warning in warning_messages:
console.print(f"[red]{warning.message}[/red]".replace(
"\n", ""))
return regression_df, dependent_variable, independent_variables, model
def balancing_tests_cohort_results(df, exog):
post_exposure1 = PanelOLS(df.adult,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton1 = post_exposure1.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
post_exposure2 = PanelOLS(df.below_median_age_restr,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton2 = post_exposure2.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
post_exposure3 = PanelOLS(df.sex_ratio,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton3 = post_exposure3.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
post_exposure4 = PanelOLS(df.have_adults_patch,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton4 = post_exposure4.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
return (compare(
{
'Size of cohort': result_balancing_canton1,
'Below median age': result_balancing_canton2,
'Sex ratio': result_balancing_canton3,
'Have families': result_balancing_canton4
},
stars=True))
def balancing_tests_cantonal_results(df, exog):
##These are the conditional results
##between countries as= asylum seekers
mod_balancing = PanelOLS(df.share_AS_between * 100,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton = mod_balancing.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
mod_balancing2 = PanelOLS(df.share_AS_within * 100,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton2 = mod_balancing2.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
mod_balancing3 = PanelOLS(df.sex_ratio_AS_ntc * 100,
exog,
entity_effects=True,
time_effects=True,
singletons=False)
result_balancing_canton3 = mod_balancing3.fit(cov_type='clustered',
clusters=df.id_e,
singletons=False)
return (compare(
{
'Between countries': result_balancing_canton,
'Within countries': result_balancing_canton2,
'Sex ratio': result_balancing_canton3
},
stars=True))
def preprocessing_regression(self): #Filling missing values with mean values. imputer = SimpleImputer(missing_values=np.nan, strategy='mean') self.df.iloc[:, :9] = imputer.fit_transform(self.df.iloc[:, :9]) data = self.df.iloc[:, :10] #Taking natural log of variable that have outliers data.mezun = np.log(self.df.iloc[:, 2]) data.yogunluk = np.log(self.df.iloc[:, 3]) data.dogum = np.log(self.df.iloc[:, 4]) #Setting indexes in order to shape to data into panel form. data = data.set_index(['iller', 'yil']) #Regressing variables to find out time effect on the relation between regressand and regressors. mod = PanelOLS(data.mezun, data.iloc[:, 1:9], time_effects=True) res = mod.fit(cov_type='clustered', cluster_entity=True) return res
def panel_regression(y,
xs,
years,
country,
list_x,
prev=0,
show=False,
save=True,
path="",
diff=False,
constant=False,
entity_effects=False):
data = bdf.filter_origin_country_dataset(y, country, years,
xs.index.levels[0].tolist(), xs,
prev)
if constant == False:
exog = data[list_x]
else:
exog = sm.add_constant(data[list_x])
#
if diff == False:
mod = PanelOLS(data.y, exog, entity_effects=entity_effects)
else:
mod = FirstDifferenceOLS(data.y, exog)
res = mod.fit()
#print("The R-squared of the regression model is %f." %res.rsquared)
#print("Estimated parameters:")
#print(pd.DataFrame(res.params))
evaluation(data, res.fitted_values, constant, len(xs.columns.tolist()))
if show == True:
pmf.plot_real_VS_prediction(y, res.fitted_values, xs, years, country,
45, "Regression model", save, path)
else:
pass
return (res.params, res.fitted_values)
# CLO has much more positive holding period return than corporate bonds
# In[41]:
#Part B
# 1. OLS without fixed effect
hpr_OLS = smf.ols(formula='lnhpr ~ clo+tmkt_rf+tsmb+thml+tterm+tdef+hp',
data=ps5)
# I use panel data to regression holding period return on common risk factors (tmkt_rf,tsmb,thml,tterm,and tdef) and
# holding period. CLO is an indicator which is 1 if bond is CLO. If CLO is significant and positive, CLO has higher
# return than corporate bond.
res = hpr_OLS.fit()
print(res.summary())
# The significant positive coefficient for CLO shows that CLO has higher excess return than corporate bond
# In[59]:
# 2. OLS with firm fixed effect
startyear = pd.Categorical(ps5.startyear)
ps5 = ps5.set_index(['entity_name', 'startyear'])
# In[67]:
exog_vars = ['clo', 'tmkt_rf', 'tsmb', 'thml', 'tterm', 'tdef', 'hp']
exog = sm.add_constant(ps5[exog_vars])
mod = PanelOLS(ps5.lnhpr, exog, entity_effects=True)
res = mod.fit()
print(res)
# After adding firm fixed effect, the coefficient of CLO is still significant positive and at similiar magnititude.
# The argument that CLO has higher excess return than corporate return is valid.
need_sde,
tolerance,
r,
interactive_start_value_effect,
within_effect,
):
# gerate simulation data
X, Y, panel_df = dgp_func(T_N_sim.loc[case, "T"], T_N_sim.loc[case, "N"])
p = X.shape[0]
# within model require no collinear variable combinations
no_collinear_x_var = ["x" + str(i + 1) for i in range(min(p, 3))]
# run estimator for starting value for interactive estimator
if interactive_start_value_effect == "twoways":
start_value_estimator = PanelOLS(
panel_df.y,
panel_df[no_collinear_x_var],
entity_effects=True,
time_effects=True,
)
else:
start_value_estimator = PooledOLS(
panel_df.y, panel_df[["x" + str(i) for i in range(1, p + 1)]]
)
start_value_result = start_value_estimator.fit()
interactive_start_value = [
*start_value_result.params.tolist(),
*np.zeros(p - len(start_value_result.params)),
]
# run interactive fixed effect estimator
interactive_estimator = InteractiveFixedEffect(Y, X)
(
beta_hat_interactive,
print("1% :", orePriceRes_BDI_ADF[2])
print("5% :", orePriceRes_BDI_ADF[3])
print("10% :", orePriceRes_BDI_ADF[4])
# Setting up the DataFrame for PanelOLS and cluster effect by port
freightCost_panel = freightCost_df.set_index(["port", "date"])
# Defining the Explanatory Variables
freightCost_vars = [
"growth", "logd", "logf", "ore_price", "port_dummy1", "port_dummy2"
]
freightCost_reg = sm.add_constant(freightCost_panel[freightCost_vars])
# Running a panel regression
freightCost_results = PanelOLS(freightCost_panel["avefreight"],
freightCost_reg,
entity_effects=False).fit(cov_type="clustered",
cluster_entity=True)
# Setting up the DataFrame for PanelOLS and cluster effect by port
freightCost_BDI_panel = freightCost_df.set_index(["port", "date"])
# Defining the Explanatory Variables
freightCost_BDI_vars = [
"growth", "logd", "logf", "ore_price", "BDI", "port_dummy1", "port_dummy2"
]
freightCost_BDI_reg = sm.add_constant(
freightCost_BDI_panel[freightCost_BDI_vars])
# Running a panel regression
freightCost_BDI_results = PanelOLS(freightCost_BDI_panel["avefreight"],
freightCost_BDI_reg,
VIF[y] = 1 / (1 - res.rsquared)
with open('../result/VIF.txt', 'w') as f:
print(VIF, file=f)
# pooled 回归
x = data[["MV", "RM", "BM", "ROE", "Inv"]]
y = data["Ret"]
results = sm.OLS(y, x).fit()
with open('../result/pooled_reg.txt', 'w') as f:
print(results.summary(), file=f)
# 固定效应回归
data['Time'] = pd.to_datetime(data['Time'])
data = data.set_index(['Stkcd', 'Time'])
dependent = data.Ret
exog = sm.add_constant(data[['MV', 'BM', 'RM', 'ROE', 'Inv']])
mod = PanelOLS(dependent, exog, entity_effects=True)
res = mod.fit(cov_type='clustered')
with open('../result/fixed_effects.txt', 'w') as f:
print(res, file=f)
# 控制行业回归
data = pd.read_csv("../data/data_all.csv")
data['Time'] = pd.to_datetime(data['Time'])
data = data.set_index(['Industry', 'Time'])
dependent = data.Ret
exog = sm.add_constant(data[['MV', 'BM', 'RM', 'ROE', 'Inv']])
mod = PanelOLS(dependent, exog, entity_effects=True)
res = mod.fit(cov_type='clustered')
with open('../result/industry_control.txt', 'w') as f:
print(res, file=f)
def crime_by_type(df):
mi_data = df.set_index(["id_e_t", "id_a"])
exog_vars = [
"kid012_all", "all_exp_13", "all_exp_14", "all_exp_15", "all_exp_16",
"all_exp_17", "all_exp_18", "all_exp_19", "all_exp_20", "all_exp_21",
"all_exp_22", "all_exp_23", "all_exp_24", "all_exp_25", "all_exp_26",
"all_exp_27", "all_exp_28", "all_exp_29", "all_exp_30", "all_exp_31",
"all_exp_32", "all_exp_33", "all_exp_34", "all_exp_35", "all_exp_36",
"all_exp_37", "all_exp_38", "all_exp_39", "all_exp_40", "all_exp_41",
"all_exp_42", "all_exp_43", "all_exp_44", "all_exp_45", "all_exp_46",
"all_exp_47", "all_exp_48", "all_exp_49", "all_exp_50", "all_exp_51",
"all_exp_52", "all_exp_53", "all_exp_54", "all_exp_55", "all_exp_56",
"all_exp_57", "all_exp_58", "all_exp_59", "all_exp_60", "all_exp_61",
"all_exp_62", "all_exp_63", "all_exp_64", "all_exp_65", "all_exp_66",
"all_exp_67", "all_exp_68", "all_exp_69", "all_exp_70", "all_exp_71",
"all_exp_72", "all_exp_73", "all_exp_74", "all_exp_75", "all_exp_76",
"all_exp_77", "all_exp_78", "all_exp_79", "all_exp_80", "all_exp_81",
"all_exp_82", "all_exp_83", "all_exp_84", "all_exp_85", "all_exp_86"
]
exog_baseline_type = sm.add_constant(mi_data[exog_vars])
result_6_1 = PanelOLS(mi_data.crime_rate_violent_p30,
exog_baseline_type,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=True)
res_6_violent = result_6_1.fit(cov_type='clustered',
cluster=mi_data["id_e"])
result_6_2 = PanelOLS(mi_data.crime_rate_freedom_p30,
exog_baseline_type,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=True)
res_6_freedom = result_6_2.fit(cov_type='clustered',
cluster=mi_data["id_e"])
result_6_3 = PanelOLS(mi_data.crime_rate_sexual_p30,
exog_baseline_type,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=True)
res_6_sexual = result_6_3.fit(cov_type='clustered',
cluster=mi_data["id_e"])
result_6_4 = PanelOLS(mi_data.crime_rate_property_p30,
exog_baseline_type,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=True)
res_6_property = result_6_4.fit(cov_type='clustered',
cluster=mi_data["id_e"])
return (compare(
{
'violent': res_6_violent,
'freedom': res_6_freedom,
'sexual': res_6_sexual,
'property': res_6_property
},
stars=True))
from linearmodels.panel import PanelOLS
import statsmodels.api as sm
from linearmodels.panel import PooledOLS
import sys
import os
DATA_FILE = sys.argv[1]
OUTPUT_FILE = sys.argv[2]
change_df = pd.read_csv(DATA_FILE)
base = os.path.basename(OUTPUT_FILE)
incomegroup = base.split(".")[0].split("_")[-1]
select_df = change_df[change_df.IncomeGroup == incomegroup]
#filter out unbalanced data points
num_period = len(select_df.period.unique())
select_df['size'] = select_df.groupby('Code')['Code'].transform('size')
select_df = select_df[select_df['size'] == num_period]
select_df['Income_t0_log'] = np.log10(select_df['Income_t0'])
select_df = select_df.set_index(['Code', 'date'])
exog_vars = [
'Income_t0_log', 'nm_change', 'shm_change', 'ne_change', 'sum_adv_t0'
]
exog = sm.add_constant(select_df[exog_vars])
mod = PanelOLS(select_df.growth_rate, exog, entity_effects=True)
fe_res = mod.fit()
with open(OUTPUT_FILE, 'w') as f:
f.write(fe_res.summary.as_text())
# In[118]:
from linearmodels.panel import PanelOLS
# fixed effects
# documentation: https://bashtage.github.io/linearmodels/panel/models.html#linearmodels.panel.model.PanelOLS
independent_vars = [
'Gross fixed capital formation (% of GDP)',
'Gross domestic savings (% of GDP)', 'Population growth (annual %)',
'FDI, net inflows (% of GDP)', 'Aid/Gdp_sqr', 'Aid/Gdp', 'ln_ODA', 'wopen',
'Trade'
]
mod = PanelOLS(df['ln_gdp_pc'],
df[independent_vars],
entity_effects=True,
time_effects=True
) # you can turn on or off both entity_effects and time_effects
res = mod.fit(
cov_type='clustered',
cluster_entity=True) # here cov_type means covariance estimators type.
# cov_type can be ‘unadjusted’, ‘homoskedastic’ or ‘robust’, ‘heteroskedastic’ or ‘clustered` - One or two way clustering.
print(res)
# <h4> ODA - Official development assistance
# Three significant Independent Varibles: Aid/GDP, Aid/GDP^2, ln_ODA </h4>
# <h2><center>DIAGNOSTIC ANALYSIS</center></h2>
#mod = PanelOLS(temp.UE12M, temp[['activeWeight12M']], entity_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight3MSquared', 'activeWeight6MSquared', 'activeWeight12MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight3MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight6MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight12MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight3MSquared', 'activeWeight6MSquared', 'activeWeight12MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight3MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight6MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight12MSquared']], entity_effects = True) mod = PanelOLS(temp.UE12M, temp[['activeWeight3MSquared', 'activeWeight6MSquared', 'activeWeight12MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE12M, temp[['activeWeight3MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE12M, temp[['activeWeight6MSquared']], entity_effects = True) #mod = PanelOLS(temp.UE12M, temp[['activeWeight12MSquared']], entity_effects = True) #Both entity and time effect #mod = PanelOLS(temp.UE3M, temp[['activeWeight3M', 'activeWeight6M', 'activeWeight12M']], entity_effects = True, time_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight3M']], entity_effects = True, time_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight6M']], entity_effects = True, time_effects = True) #mod = PanelOLS(temp.UE3M, temp[['activeWeight12M']], entity_effects = True, time_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight3M', 'activeWeight6M', 'activeWeight12M']], entity_effects = True, time_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight3M']], entity_effects = True, time_effects = True) #mod = PanelOLS(temp.UE6M, temp[['activeWeight6M']], entity_effects = True, time_effects = True)
def panel_regression_training_test(y,
xs,
years_training,
years_test,
country,
list_x,
prev=0,
show=False,
save=True,
path="",
diff=False,
constant=False,
entity_effects=False):
years = years_training + years_test
data = bdf.filter_origin_country_dataset(y, country, years,
xs.index.levels[0].tolist(), xs,
prev)
data_tr = data.loc[(slice(None), years_training), :]
data_te = data.loc[(slice(None), years_test), :]
if constant == False:
exog_tr = data_tr[list_x]
exog_te = data_te[list_x]
else:
exog_tr = sm.add_constant(data_tr[list_x])
exog_te = sm.add_constant(data_te[list_x])
#
if diff == False:
mod = PanelOLS(data_tr.y, exog_tr, entity_effects=entity_effects)
else:
mod = FirstDifferenceOLS(data_tr.y, exog_tr)
res_tr = mod.fit()
#print("---------------- Training Results ----------------")
#evaluation(data_tr, res_tr.fitted_values, constant)
fitted_values_te = res_tr.params.values * exog_te
fitted_values_te["fitted_values"] = fitted_values_te.sum(axis=1)
fitted_values_ = fitted_values_te.append(res_tr.fitted_values)
fitted_values_ = fitted_values_.sort_index()
if show == True:
pmf.plot_real_VS_prediction(y,
fitted_values_,
xs,
years,
country,
45,
"Regression model",
save=save,
path="")
else:
pass
print("-------------- Trainin-Test Results --------------")
#print(data.head())
#print(fitted_values_.head())
#print(fitted_values_te.head())
evaluation(data.loc[(slice(None), years_test), ], fitted_values_te,
constant, len(xs.columns.tolist()))
#evaluation(data.loc[(slice(None), years_test), ], fitted_values_.loc[(slice(None), years_test), ], constant, len(xs.columns.tolist()))
return (res_tr.params, fitted_values_)
# Variable Constructions df['lognprints'] = np.log(df['NPRINTs']) w = (df['YENVOL'] / 100) * (df['volatility']) df['logwdbw'] = np.log(w / (601000 * 0.016)) # drop -inf when volatility equals to 0 df = df[~df.isin([np.nan, np.inf, -np.inf]).any(1)] # Pooled OLS exog = sm.add_constant(df['logwdbw']) mod = PooledOLS(df.lognprints, exog) pooled_res = mod.fit() print(pooled_res) """ # fixed effects with time dummy exog = sm.add_constant(df[['logwdbw','Date1']]) mod = PanelOLS(df.lognprints, exog, entity_effects=True) fe_res1 = mod.fit() print(fe_res1) """ # fixed effects with ticker dummy exog = sm.add_constant(df[['logwdbw', "Ticker1"]]) mod = PanelOLS(df.lognprints, exog, time_effects=True) fe_res3 = mod.fit() print(fe_res3) # two-way fixed effects """ exog = sm.add_constant(df['logwdbw']) mod = PanelOLS(df.lognprints, exog, entity_effects=True, time_effects=True) fe_res2 = mod.fit() print(fe_res2) """
#temp = PanelDataTrade3M.copy(deep = True) # (3) 6-month trade-based AFP #temp = PanelDataTrade6M.copy(deep = True) # (4) 12-month trade-based AFP #temp = PanelDataTrade12M.copy(deep = True) #Preparing the variables temp = temp.set_index(['crsp_portno', 'slided_caldt']) temp = temp[temp.AFP != -np.inf] temp = temp[temp.AFP != np.inf] # Please comment / uncomment the following if you want to choose for the dependent variable # (1) Carhart Alpha #mod = PanelOLS(temp.CarhartAlpha, temp.AFP, time_effects = True) # (2) Fama-French Alpha mod = PanelOLS(temp.FFAlpha, temp.AFP, time_effects=True) # Please comment / uncomment the following if you want to choose for the standard errors # (1) to be clustered by fund #res = mod.fit(cov_type = 'clustered', cluster_entity = True) # (2) to be clustered by time res = mod.fit(cov_type='clustered', cluster_time=True) #Print regression result print(res) del temp #%% # ============================================================================= # Part 2: Panel Data Regression with multiple independent variables: # - AFP
# print(data1)
d = pd.Categorical(data1['Date'])
data1 = data1.set_index(['ID', 'Date'])
data1['Date'] = d
# print(data1)
exog_vars = [
'Kilo', 'Brakes', 'Range', 'Speed', 'RPM', 'Engine fuel rate', 'Date'
]
a = ['Kilo', 'Brakes', 'Range', 'Speed', 'RPM', 'Engine fuel rate']
print(data1[a])
exog = sm.add_constant(data1[exog_vars])
exog1 = sm.add_constant(data1[a])
mod = PanelOLS(data1['Accelerator pedal position'],
exog,
entity_effects=True,
time_effects=False)
mod1 = PooledOLS(data1['Accelerator pedal position'], exog1)
mod2 = RandomEffects(data1['Accelerator pedal position'], exog1)
mod3 = BetweenOLS(data1['Accelerator pedal position'], exog1)
res = mod.fit()
pooled_res = mod1.fit()
re_res = mod2.fit()
be_res = mod3.fit()
print(res)
print(compare({'Pooled': pooled_res, 'RE': re_res, 'BE': be_res}))
if __name__ == '__main__':
pass
def baseline_results_women(df):
CPRT_baseline_female = df.groupby(by=['sex'])
CPRT_baseline_women = CPRT_baseline_female.get_group("F")
CPRT_baseline_womenage = CPRT_baseline_women[~(
CPRT_baseline_women['age'] <= 18)]
mi_data_women = CPRT_baseline_womenage.set_index(["id_e_t", "id_a"])
exog_vars = [
"kid012_all", "all_exp_13", "all_exp_14", "all_exp_15", "all_exp_16",
"all_exp_17", "all_exp_18", "all_exp_19", "all_exp_20", "all_exp_21",
"all_exp_22", "all_exp_23", "all_exp_24", "all_exp_25", "all_exp_26",
"all_exp_27", "all_exp_28", "all_exp_29", "all_exp_30", "all_exp_31",
"all_exp_32", "all_exp_33", "all_exp_34", "all_exp_35", "all_exp_36",
"all_exp_37", "all_exp_38", "all_exp_39", "all_exp_40", "all_exp_41",
"all_exp_42", "all_exp_43", "all_exp_44", "all_exp_45", "all_exp_46",
"all_exp_47", "all_exp_48", "all_exp_49", "all_exp_50", "all_exp_51",
"all_exp_52", "all_exp_53", "all_exp_54", "all_exp_55", "all_exp_56",
"all_exp_57", "all_exp_58", "all_exp_59", "all_exp_60", "all_exp_61",
"all_exp_62", "all_exp_63", "all_exp_64", "all_exp_65", "all_exp_66",
"all_exp_67", "all_exp_68", "all_exp_69", "all_exp_70"
]
exog_women = sm.add_constant(mi_data_women[exog_vars])
CPRT_baseline_womenage.head()
mod_women = PanelOLS(mi_data_women.crime_rate_all_violent_p30,
exog_women,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=False)
res_women = mod_women.fit(cov_type='clustered',
cluster=mi_data_women.id_e,
singletons=False)
CPRT_baseline_womenage_sub = CPRT_baseline_womenage[(
CPRT_baseline_womenage['allmk_periode'] == 1)]
mi_data2_women = CPRT_baseline_womenage_sub.set_index(["id_a", "id_e_t"])
exog_vars2 = [
"kid012_all", "all_exp_13", "all_exp_14", "all_exp_15", "all_exp_16",
"all_exp_17", "all_exp_18", "all_exp_19", "all_exp_20", "all_exp_21",
"all_exp_22", "all_exp_23", "all_exp_24", "all_exp_25", "all_exp_26",
"all_exp_27", "all_exp_28", "all_exp_29", "all_exp_30", "all_exp_31",
"all_exp_32", "all_exp_33", "all_exp_34", "all_exp_35", "all_exp_36",
"all_exp_37", "all_exp_38", "all_exp_39", "all_exp_40", "all_exp_41",
"all_exp_42", "all_exp_43", "all_exp_44", "all_exp_45", "all_exp_46",
"all_exp_47", "all_exp_48", "all_exp_49", "all_exp_50", "all_exp_51",
"all_exp_52", "all_exp_53", "all_exp_54", "all_exp_55", "all_exp_56",
"all_exp_57", "all_exp_58", "all_exp_59", "all_exp_60", "all_exp_61",
"all_exp_62", "all_exp_63", "all_exp_64", "all_exp_65", "all_exp_66",
"all_exp_67", "all_exp_68", "all_exp_69", "all_exp_70", "all_exp_71"
]
exog2_women = sm.add_constant(mi_data2_women[exog_vars2])
mod2_women = PanelOLS(mi_data2_women.crime_rate_all_violent_p30,
exog2_women,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=False)
res2_women = mod2_women.fit(cov_type='clustered',
cluster=mi_data2_women["id_e"],
singletons=False)
CPRT_baseline_womenage_sub_sub = CPRT_baseline_womenage[(
CPRT_baseline_womenage['all_periode'] == 1)]
mi_data3_women = CPRT_baseline_womenage_sub_sub.set_index(
["id_a", "id_e_t"])
exog_vars3 = [
"kid012", "exp_all_13", "exp_all_14", "exp_all_15", "exp_all_16",
"exp_all_17", "exp_all_18", "exp_all_19", "exp_all_20", "exp_all_21",
"exp_all_22", "exp_all_23", "exp_all_24", "exp_all_25", "exp_all_26",
"exp_all_27", "exp_all_28", "exp_all_29", "exp_all_30", "exp_all_31",
"exp_all_32", "exp_all_33", "exp_all_34", "exp_all_35", "exp_all_36",
"exp_all_37", "exp_all_38", "exp_all_39", "exp_all_40", "exp_all_41",
"exp_all_42", "exp_all_43", "exp_all_44", "exp_all_45", "exp_all_46",
"exp_all_47", "exp_all_48", "exp_all_49", "exp_all_50", "exp_all_51",
"exp_all_52", "exp_all_53", "exp_all_54", "exp_all_55", "exp_all_56",
"exp_all_57", "exp_all_58", "exp_all_59", "exp_all_60", "exp_all_61",
"exp_all_62", "exp_all_63", "exp_all_64", "exp_all_65", "exp_all_66",
"exp_all_67", "exp_all_68", "exp_all_69", "exp_all_70", "exp_all_71"
]
exog3_women = sm.add_constant(mi_data3_women[exog_vars3])
mod3_women = PanelOLS(mi_data3_women.crime_rate_all_violent_p30,
exog3_women,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=False)
res3_women = mod3_women.fit(cov_type='clustered',
cluster=mi_data3_women["id_e"],
singletons=False)
##Table 5 column 4 women
CPRT_baseline_womenage_sub4 = CPRT_baseline_womenage[(
CPRT_baseline_womenage['mk_periode'] == 1)]
mi_data4_women = CPRT_baseline_womenage_sub4.set_index(["id_a", "id_e_t"])
##had to delete nr. 71-86
exog_vars4 = [
"MK_kid012", "exp_mk_13", "exp_mk_14", "exp_mk_15", "exp_mk_16",
"exp_mk_17", "exp_mk_18", "exp_mk_19", "exp_mk_20", "exp_mk_21",
"exp_mk_22", "exp_mk_23", "exp_mk_24", "exp_mk_25", "exp_mk_26",
"exp_mk_27", "exp_mk_28", "exp_mk_29", "exp_mk_30", "exp_mk_31",
"exp_mk_32", "exp_mk_33", "exp_mk_34", "exp_mk_35", "exp_mk_36",
"exp_mk_37", "exp_mk_38", "exp_mk_39", "exp_mk_40", "exp_mk_41",
"exp_mk_42", "exp_mk_43", "exp_mk_44", "exp_mk_45", "exp_mk_46",
"exp_mk_47", "exp_mk_48", "exp_mk_49", "exp_mk_50", "exp_mk_51",
"exp_mk_52", "exp_mk_53", "exp_mk_54", "exp_mk_55", "exp_mk_56",
"exp_mk_57", "exp_mk_58", "exp_mk_59", "exp_mk_60", "exp_mk_61",
"exp_mk_62", "exp_mk_63", "exp_mk_64", "exp_mk_65", "exp_mk_66",
"exp_mk_67", "exp_mk_68", "exp_mk_69", "exp_mk_70"
]
exog4_women = sm.add_constant(mi_data4_women[exog_vars4])
mod4_women = PanelOLS(mi_data4_women.crime_rate_all_violent_p30,
exog4_women,
entity_effects=True,
time_effects=True,
drop_absorbed=True,
singletons=False)
res4_women = mod4_women.fit(cov_type='clustered',
cluster=CPRT_baseline_womenage_sub["id_e"],
singletons=False)
return (compare(
{
'Full': res_women,
'CC and MK': res2_women,
'CC': res3_women,
'MK': res4_women
},
stars=True))
x = np.stack([calc_mat[:, 1], calc_mat[:, 2], calc_mat[:, 3], calc_mat[:, 4]])
ones = np.ones(len(x[0]))
X = sm.add_constant(np.column_stack((x[0], ones)))
for elem in x[1:]:
X = sm.add_constant(np.column_stack((elem, X)))
res = sm.OLS(y,X).fit()
print(res.summary())
FE模型回归
company_codes = []
for each_file in file_list:
company_code = each_file.split('.')[0]
company_code = int(company_code)
company_codes.append(company_code)
time = [2019] * 50
df = pd.DataFrame({
'TDA': x[0],
'CR5': x[1],
'SIZE': x[2],
'ROE': x[3],
'REWARD': y,
'YEAR': time,
'CODE': company_codes
})
df.to_stata('Stock/res.dta')
df = df.set_index(['CODE', 'YEAR'])
exog_vars = ['TDA', 'LDA', 'SIZE', 'ROE']
exog = sm.add_constant(df[exog_vars])
model = PanelOLS(df['REWARD'], exog, entity_effects=True)
fe = model.fit()
print(fe)
import numpy as np import linearmodels as lm lm.WARN_ON_MISSING = False from linearmodels import utility utility.missing_warning(np.array([True, True, False])) from linearmodels.panel import PanelOLS, RandomEffects, PooledOLS from linearmodels.datasets import wage_panel import statsmodels.api as sm data = wage_panel.load() data = data.set_index(['nr','year']) dependent = data.lwage exog = sm.add_constant(data[['expersq','married','union']]) mod = PanelOLS(dependent, exog, entity_effects=True, time_effects=True) res = mod.fit(cov_type='unadjusted') res2 = mod.fit(cov_type='robust') exog = sm.add_constant(data[['exper', 'expersq','married','union']]) mod = PanelOLS(dependent, exog, entity_effects=True) res3 = mod.fit(cov_type='clustered',cluster_entity=True) mod = RandomEffects(dependent, exog) res4 = mod.fit(cov_type='robust') from linearmodels.panel.results import compare exog = sm.add_constant(data[['exper', 'expersq','married','union']].copy()) import pandas as pd exog['year'] = pd.Categorical(data.reset_index()['year']) mod = PooledOLS(dependent, exog) res5 = mod.fit(cov_type='robust') print(compare([res,res2, res3, res4, res5])) print(data.columns)
jtrain2 = jtrain
jtrain2[:5]
## Define the ID and Time column for Panel Regression
jtrain2 = jtrain2.set_index(['fcode', 'year'])
print(jtrain2.head(5))
exog_vars = ['d88', 'd89', 'grant', 'grant_1']
grant_vars = ['grant']
exog = sm.add_constant(jtrain2[exog_vars])
grant0 = sm.add_constant(jtrain2[grant_vars])
## Model Pooled OLS
model_pool = PooledOLS(jtrain2.lscrap, exog)
pooled_res = model_pool.fit()
print(pooled_res)
## Model Fixed Effects -- Entity Effects - True
model_fe = PanelOLS(jtrain2.lscrap, exog, entity_effects=True)
fe_res = model_fe.fit()
print(fe_res)
## Model Fixed Effects -- Entity and Time Effects - True
model_fe = PanelOLS(jtrain2.lscrap,
exog,
entity_effects=True,
time_effects=True)
fe_res = model_fe.fit()
print(fe_res)
## Random Effects Model
model_re = RandomEffects(jtrain2.lscrap, exog)
re_res = model_re.fit()
print(fe_res)
#################################################
## Regress scrap~grant
import numpy as np
import pandas as pd
from linearmodels.panel import PanelOLS
import statsmodels.api as sm
from linearmodels.panel import PooledOLS
import sys
DATA_FILE = sys.argv[1]
OUTPUT_FILE = sys.argv[2]
change_df=pd.read_csv(DATA_FILE)
num_period=len(change_df.period.unique())
change_df['size']=change_df.groupby('Code')['Code'].transform('size')
change_df=change_df[change_df['size']==num_period]
change_df['Income_t0_log']=np.log10(change_df['Income_t0'])
change_df=change_df.set_index(['Code','date'])
exog_vars = ['Income_t0_log','nm_change','shm_change','ne_change','sum_adv_t0']
exog = sm.add_constant(change_df[exog_vars])
mod = PanelOLS(change_df.growth_rate, exog,entity_effects=True)
fe_res = mod.fit()
with open(OUTPUT_FILE,'w') as f:
f.write(fe_res.summary.as_text())
import sys
import pandas as pd
import statsmodels.api as sm
from linearmodels.panel import PanelOLS
DATA_FILE = sys.argv[1]
OUTPUT_FILE = sys.argv[2]
change_df = pd.read_csv(DATA_FILE)
change_df = change_df.set_index(["Code", "date"])
exog_vars = ["Income_t0_log", "nm_change", "shm_change", "ne_change", "sum_adv_t0"]
exog = sm.add_constant(change_df[exog_vars])
mod = PanelOLS(change_df.growth_rate, exog)
fe_res = mod.fit()
with open(OUTPUT_FILE, "w") as f:
f.write(fe_res.summary.as_text())
def baseline_results(df):
##first column of baseline
mi_data = df.set_index(["id_e_t", "id_a"])
exog_vars = [
"kid012_all", "all_exp_13", "all_exp_14", "all_exp_15", "all_exp_16",
"all_exp_17", "all_exp_18", "all_exp_19", "all_exp_20", "all_exp_21",
"all_exp_22", "all_exp_23", "all_exp_24", "all_exp_25", "all_exp_26",
"all_exp_27", "all_exp_28", "all_exp_29", "all_exp_30", "all_exp_31",
"all_exp_32", "all_exp_33", "all_exp_34", "all_exp_35", "all_exp_36",
"all_exp_37", "all_exp_38", "all_exp_39", "all_exp_40", "all_exp_41",
"all_exp_42", "all_exp_43", "all_exp_44", "all_exp_45", "all_exp_46",
"all_exp_47", "all_exp_48", "all_exp_49", "all_exp_50", "all_exp_51",
"all_exp_52", "all_exp_53", "all_exp_54", "all_exp_55", "all_exp_56",
"all_exp_57", "all_exp_58", "all_exp_59", "all_exp_60", "all_exp_61",
"all_exp_62", "all_exp_63", "all_exp_64", "all_exp_65", "all_exp_66",
"all_exp_67", "all_exp_68", "all_exp_69", "all_exp_70", "all_exp_71",
"all_exp_72", "all_exp_73", "all_exp_74", "all_exp_75", "all_exp_76",
"all_exp_77", "all_exp_78", "all_exp_79", "all_exp_80", "all_exp_81",
"all_exp_82", "all_exp_83", "all_exp_84", "all_exp_85", "all_exp_86"
]
exog_baseline = sm.add_constant(mi_data[exog_vars])
mod = PanelOLS(mi_data.crime_rate_all_violent_p30,
exog_baseline,
entity_effects=True,
time_effects=True,
singletons=False)
res = mod.fit(cov_type='clustered',
clusters=mi_data.id_e,
singletons=False)
##second column of baseline results
CPRT_baseline_maleage_sub = df[(df['allmk_periode'] == 1)]
mi_data2 = CPRT_baseline_maleage_sub.set_index(["id_a", "id_e_t"])
exog_vars2 = [
"kid012_all", "all_exp_13", "all_exp_14", "all_exp_15", "all_exp_16",
"all_exp_17", "all_exp_18", "all_exp_19", "all_exp_20", "all_exp_21",
"all_exp_22", "all_exp_23", "all_exp_24", "all_exp_25", "all_exp_26",
"all_exp_27", "all_exp_28", "all_exp_29", "all_exp_30", "all_exp_31",
"all_exp_32", "all_exp_33", "all_exp_34", "all_exp_35", "all_exp_36",
"all_exp_37", "all_exp_38", "all_exp_39", "all_exp_40", "all_exp_41",
"all_exp_42", "all_exp_43", "all_exp_44", "all_exp_45", "all_exp_46",
"all_exp_47", "all_exp_48", "all_exp_49", "all_exp_50", "all_exp_51",
"all_exp_52", "all_exp_53", "all_exp_54", "all_exp_55", "all_exp_56",
"all_exp_57", "all_exp_58", "all_exp_59", "all_exp_60", "all_exp_61",
"all_exp_62", "all_exp_63", "all_exp_64", "all_exp_65", "all_exp_66",
"all_exp_67", "all_exp_68", "all_exp_69", "all_exp_70", "all_exp_71",
"all_exp_72", "all_exp_73", "all_exp_74", "all_exp_75", "all_exp_76",
"all_exp_77", "all_exp_78", "all_exp_79", "all_exp_80", "all_exp_81",
"all_exp_82", "all_exp_83", "all_exp_84", "all_exp_85", "all_exp_86"
]
exog2 = sm.add_constant(mi_data2[exog_vars2])
mod2 = PanelOLS(mi_data2.crime_rate_all_violent_p30,
exog2,
entity_effects=True,
time_effects=True,
singletons=False)
res2 = mod2.fit(cov_type='clustered',
clusters=mi_data2.id_e,
singletons=False)
##third column of baseline results
CPRT_baseline_maleage_sub_sub = df[(df['all_periode'] == 1)]
CPRT_baseline_maleage_sub_sub = CPRT_baseline_maleage_sub_sub.drop(
['kid012_all'], axis=1)
CPRT_baseline_maleage_sub_sub = CPRT_baseline_maleage_sub_sub.rename(
columns={"kid012": "kid012_all"})
mi_data3 = CPRT_baseline_maleage_sub_sub.set_index(["id_a", "id_e_t"])
exog_vars3 = [
"kid012_all", "exp_all_13", "exp_all_14", "exp_all_15", "exp_all_16",
"exp_all_17", "exp_all_18", "exp_all_19", "exp_all_20", "exp_all_21",
"exp_all_22", "exp_all_23", "exp_all_24", "exp_all_25", "exp_all_26",
"exp_all_27", "exp_all_28", "exp_all_29", "exp_all_30", "exp_all_31",
"exp_all_32", "exp_all_33", "exp_all_34", "exp_all_35", "exp_all_36",
"exp_all_37", "exp_all_38", "exp_all_39", "exp_all_40", "exp_all_41",
"exp_all_42", "exp_all_43", "exp_all_44", "exp_all_45", "exp_all_46",
"exp_all_47", "exp_all_48", "exp_all_49", "exp_all_50", "exp_all_51",
"exp_all_52", "exp_all_53", "exp_all_54", "exp_all_55", "exp_all_56",
"exp_all_57", "exp_all_58", "exp_all_59", "exp_all_60", "exp_all_61",
"exp_all_62", "exp_all_63", "exp_all_64", "exp_all_65", "exp_all_66",
"exp_all_67", "exp_all_68", "exp_all_69", "exp_all_70", "exp_all_71",
"exp_all_72", "exp_all_73", "exp_all_74", "exp_all_75", "exp_all_76",
"exp_all_77", "exp_all_78", "exp_all_79", "exp_all_80", "exp_all_81",
"exp_all_82", "exp_all_83", "exp_all_84", "exp_all_85", "exp_all_86"
]
exog3 = sm.add_constant(mi_data3[exog_vars3])
mod3 = PanelOLS(mi_data3.crime_rate_all_violent_p30,
exog3,
entity_effects=True,
time_effects=True,
singletons=False)
res3 = mod3.fit(cov_type='clustered',
clusters=mi_data3.id_e,
singletons=False)
##4th column
CPRT_baseline_maleage_sub4 = df[(df['mk_periode'] == 1)]
mi_data4 = CPRT_baseline_maleage_sub4.set_index(["id_a", "id_e_t"])
exog_vars4 = [
"MK_kid012", "exp_mk_13", "exp_mk_14", "exp_mk_15", "exp_mk_16",
"exp_mk_17", "exp_mk_18", "exp_mk_19", "exp_mk_20", "exp_mk_21",
"exp_mk_22", "exp_mk_23", "exp_mk_24", "exp_mk_25", "exp_mk_26",
"exp_mk_27", "exp_mk_28", "exp_mk_29", "exp_mk_30", "exp_mk_31",
"exp_mk_32", "exp_mk_33", "exp_mk_34", "exp_mk_35", "exp_mk_36",
"exp_mk_37", "exp_mk_38", "exp_mk_39", "exp_mk_40", "exp_mk_41",
"exp_mk_42", "exp_mk_43", "exp_mk_44", "exp_mk_45", "exp_mk_46",
"exp_mk_47", "exp_mk_48", "exp_mk_49", "exp_mk_50", "exp_mk_51",
"exp_mk_52", "exp_mk_53", "exp_mk_54", "exp_mk_55", "exp_mk_56",
"exp_mk_57", "exp_mk_58", "exp_mk_59", "exp_mk_60", "exp_mk_61",
"exp_mk_62", "exp_mk_63", "exp_mk_64", "exp_mk_65", "exp_mk_66",
"exp_mk_67", "exp_mk_68", "exp_mk_69", "exp_mk_70", "exp_mk_71",
"exp_mk_72", "exp_mk_73", "exp_mk_74", "exp_mk_75", "exp_mk_76",
"exp_mk_77", "exp_mk_78", "exp_mk_79", "exp_mk_80", "exp_mk_81",
"exp_mk_82", "exp_mk_83"
]
exp_mk4 = [
"exp_mk_13", "exp_mk_14", "exp_mk_15", "exp_mk_16", "exp_mk_17",
"exp_mk_18", "exp_mk_19", "exp_mk_20", "exp_mk_21", "exp_mk_22",
"exp_mk_23", "exp_mk_24", "exp_mk_25", "exp_mk_26", "exp_mk_27",
"exp_mk_28", "exp_mk_29", "exp_mk_30", "exp_mk_31", "exp_mk_32",
"exp_mk_33", "exp_mk_34", "exp_mk_35", "exp_mk_36", "exp_mk_37",
"exp_mk_38", "exp_mk_39", "exp_mk_40", "exp_mk_41", "exp_mk_42",
"exp_mk_43", "exp_mk_44", "exp_mk_45", "exp_mk_46", "exp_mk_47",
"exp_mk_48", "exp_mk_49", "exp_mk_50", "exp_mk_51", "exp_mk_52",
"exp_mk_53", "exp_mk_54", "exp_mk_55", "exp_mk_56", "exp_mk_57",
"exp_mk_58", "exp_mk_59", "exp_mk_60", "exp_mk_61", "exp_mk_62",
"exp_mk_63", "exp_mk_64", "exp_mk_65", "exp_mk_66", "exp_mk_67",
"exp_mk_68", "exp_mk_69", "exp_mk_70", "exp_mk_71", "exp_mk_72",
"exp_mk_73", "exp_mk_74", "exp_mk_75", "exp_mk_76", "exp_mk_77",
"exp_mk_78", "exp_mk_79", "exp_mk_80", "exp_mk_81", "exp_mk_82",
"exp_mk_83", "exp_mk_84", "exp_mk_85", "exp_mk_86", "exp_mk_87",
"exp_mk_88", "exp_mk_89", "exp_mk_90", "exp_mk_91", "exp_mk_92",
"exp_mk_93", "exp_mk_94", "exp_mk_95", "exp_mk_96", "exp_mk_97",
"exp_mk_98", "exp_mk_99"
]
exog4 = sm.add_constant(mi_data4[exog_vars4])
mod4 = PanelOLS(mi_data4.crime_rate_all_violent_p30,
exog4,
entity_effects=True,
time_effects=True,
singletons=False)
res4 = mod4.fit(cov_type='clustered',
clusters=mi_data4.id_e,
singletons=False)
##presentation
return (compare({
'Full': res,
'CC and MK': res2,
'CC': res3,
'MK': res4
},
stars=True))
