diff --git a/_modules/index.html b/_modules/index.html index 410d593..6c0f3c5 100644 --- a/_modules/index.html +++ b/_modules/index.html @@ -29,7 +29,7 @@ - + diff --git a/_modules/iot/inverse_optimal_tax.html b/_modules/iot/inverse_optimal_tax.html index a913e3d..be90c1a 100644 --- a/_modules/iot/inverse_optimal_tax.html +++ b/_modules/iot/inverse_optimal_tax.html @@ -29,7 +29,7 @@ - + @@ -330,17 +330,18 @@

Source code for iot.inverse_optimal_tax

-import numpy as np
-import pandas as pd
-import scipy.stats as st
-import scipy
-from statsmodels.nonparametric.kernel_regression import KernelReg
-from scipy.interpolate import UnivariateSpline
+import numpy as np
+import pandas as pd
+import scipy.stats as st
+import scipy
+from statsmodels.nonparametric.kernel_regression import KernelReg
+from scipy.interpolate import UnivariateSpline
+from scipy.linalg import lstsq
 
 
 

 [docs]
-class IOT:
+class IOT:
     """
     Constructor for the IOT class.
 
@@ -368,7 +369,7 @@ 
Source code for iot.inverse_optimal_tax
         class instance: IOT
     """
 
-    def __init__(
+    def __init__(
         self,
         data,
         income_measure="e00200",
@@ -417,7 +418,7 @@ 
Source code for iot.inverse_optimal_tax
 
 

 [docs]
-    def df(self):
+    def df(self):
         """
         Return all vector attributes in a DataFrame format
 
@@ -445,7 +446,7 @@ 
Source code for iot.inverse_optimal_tax
 
 

 [docs]
-    def compute_mtr_dist(
+    def compute_mtr_dist(
         self, data, weight_var, income_measure, mtr_smoother, mtr_smooth_param
     ):
         """
@@ -466,22 +467,23 @@ 
Source code for iot.inverse_optimal_tax
                 * mtr_prime (array_like): rate of change in marginal tax rates
                     for each income bin
         """
-        bins = 1000  # number of equal-width bins
-        data.loc[:, ["z_bin"]] = pd.cut(
-            data[income_measure], bins, include_lowest=True
-        )
-        binned_data = pd.DataFrame(
-            data[["mtr", income_measure, "z_bin", weight_var]]
-            .groupby(["z_bin"], observed=False)
-            .apply(lambda x: wm(x[["mtr", income_measure]], x[weight_var]))
-        )
-        # make column 0 into two columns
-        binned_data[["mtr", income_measure]] = pd.DataFrame(
-            binned_data[0].tolist(), index=binned_data.index
-        )
-        binned_data.drop(columns=0, inplace=True)
-        binned_data.reset_index(inplace=True)
+
         if mtr_smoother == "kreg":
+            bins = 1000  # number of equal-width bins
+            data.loc[:, ["z_bin"]] = pd.cut(
+                data[income_measure], bins, include_lowest=True
+            )
+            binned_data = pd.DataFrame(
+                data[["mtr", income_measure, "z_bin", weight_var]]
+                .groupby(["z_bin"], observed=False)
+                .apply(lambda x: wm(x[["mtr", income_measure]], x[weight_var]))
+            )
+            # make column 0 into two columns
+            binned_data[["mtr", income_measure]] = pd.DataFrame(
+                binned_data[0].tolist(), index=binned_data.index
+            )
+            binned_data.drop(columns=0, inplace=True)
+            binned_data.reset_index(inplace=True)
             mtr_function = KernelReg(
                 binned_data["mtr"].dropna(),
                 binned_data[income_measure].dropna(),
@@ -489,17 +491,32 @@ 
Source code for iot.inverse_optimal_tax
                 reg_type="ll",
             )
             mtr, _ = mtr_function.fit(self.z)
+            mtr_prime = np.gradient(mtr, edge_order=2)
+        elif mtr_smoother == "HSV":
+            # estimate the HSV function on mtrs via weighted least squares
+            X = np.log(data[income_measure].values)
+            X = np.column_stack((np.ones(len(X)), X))
+            w = np.array(data[weight_var].values)
+            w_sqrt = np.sqrt(w)
+            y = np.log(1-data["mtr"].values)
+            X_weighted = X * w_sqrt[:, np.newaxis]
+            y_weighted = y * w_sqrt
+            coef, _, _, _ = lstsq(X_weighted, y_weighted)
+            tau = -coef[1]
+            lambda_param = np.exp(coef[0]) / (1-tau)
+            mtr = 1 - lambda_param * (1-tau) * self.z ** (-tau)
+            mtr_prime = lambda_param * tau * (1-tau) * self.z ** (-tau - 1)
         else:
             print("Please enter a value mtr_smoother method")
             assert False
-        mtr_prime = np.gradient(mtr, edge_order=2)
+        
 
         return mtr, mtr_prime

 
 
 

 [docs]
-    def compute_income_dist(
+    def compute_income_dist(
         self, data, income_measure, weight_var, dist_type, kde_bw=None
     ):
         """
@@ -579,7 +596,7 @@ 
Source code for iot.inverse_optimal_tax
             f_prime = np.gradient(f, edge_order=2)
         elif dist_type == "Pln":
 
-            def pln_pdf(y, mu, sigma, alpha):
+            def pln_pdf(y, mu, sigma, alpha):
                 x1 = alpha * sigma - (np.log(y) - mu) / sigma
                 phi = st.norm.pdf((np.log(y) - mu) / sigma)
                 R = (1 - st.norm.cdf(x1)) / (st.norm.pdf(x1) + 1e-15)
@@ -587,7 +604,7 @@ 
Source code for iot.inverse_optimal_tax
                 pdf = alpha / y * phi * R
                 return pdf
 
-            def neg_weighted_log_likelihood(params, data, weights):
+            def neg_weighted_log_likelihood(params, data, weights):
                 mu, sigma, alpha = params
                 likelihood = np.sum(
                     weights * np.log(pln_pdf(data, mu, sigma, alpha) + 1e-15)
@@ -595,7 +612,7 @@ 
Source code for iot.inverse_optimal_tax
                 # 1e-15 to avoid log(0)
                 return -likelihood
 
-            def fit_pln(data, weights, initial_guess):
+            def fit_pln(data, weights, initial_guess):
                 bounds = [(None, None), (0.01, None), (0.01, None)]
                 result = scipy.optimize.minimize(
                     neg_weighted_log_likelihood,
@@ -623,7 +640,7 @@ 
Source code for iot.inverse_optimal_tax
                 data[income_measure], data[weight_var], initial_guess
             )
 
-            def pln_cdf(y, mu, sigma, alpha):
+            def pln_cdf(y, mu, sigma, alpha):
                 x1 = alpha * sigma - (np.log(y) - mu) / sigma
                 R = (1 - st.norm.cdf(x1)) / (st.norm.pdf(x1) + 1e-12)
                 CDF = (
@@ -632,7 +649,7 @@ 
Source code for iot.inverse_optimal_tax
                 )
                 return CDF
 
-            def pln_dpdf(y, mu, sigma, alpha):
+            def pln_dpdf(y, mu, sigma, alpha):
                 x = (np.log(y) - mu) / sigma
                 R = (1 - st.norm.cdf(alpha * sigma - x)) / (
                     st.norm.pdf(alpha * sigma - x) + 1e-15
@@ -658,7 +675,7 @@ 
Source code for iot.inverse_optimal_tax
 
 

 [docs]
-    def sw_weights(self):
+    def sw_weights(self):
         r"""
         Returns the social welfare weights for a given tax policy.
 
@@ -681,26 +698,28 @@ 
Source code for iot.inverse_optimal_tax
             + ((self.theta_z * self.eti * self.mtr) / (1 - self.mtr))
             + ((self.eti * self.z * self.mtr_prime) / (1 - self.mtr) ** 2)
         )
-        integral = np.trapz(g_z, self.z)
-        # g_z = g_z / integral
+        integral = np.trapz(g_z * self.f, self.z)
+        g_z = g_z / integral
+
         # use Lockwood and Weinzierl formula, which should be equivalent but using numerical differentiation
         bracket_term = (
             1
             - self.F
             - (self.mtr / (1 - self.mtr)) * self.eti * self.z * self.f
         )
-        # d_dz_bracket = np.gradient(bracket_term, edge_order=2)
-        d_dz_bracket = np.diff(bracket_term) / np.diff(self.z)
-        d_dz_bracket = np.append(d_dz_bracket, d_dz_bracket[-1])
+        d_dz_bracket = np.gradient(bracket_term, edge_order=2)
+        # d_dz_bracket = np.diff(bracket_term) / np.diff(self.z)
+        # d_dz_bracket = np.append(d_dz_bracket, d_dz_bracket[-1])
         g_z_numerical = -(1 / self.f) * d_dz_bracket
-        integral = np.trapz(g_z_numerical, self.z)
-        # g_z_numerical = g_z_numerical / integral
+        integral = np.trapz(g_z_numerical * self.f, self.z)
+        g_z_numerical = g_z_numerical / integral
+        
         return g_z, g_z_numerical

 

 
 
 
-def find_eti(iot1, iot2, g_z_type="g_z"):
+def find_eti(iot1, iot2, g_z_type="g_z"):
     """
     This function solves for the ETI that would result in the
     policy represented via MTRs in iot2 be consistent with the
@@ -737,7 +756,7 @@ 
Source code for iot.inverse_optimal_tax
     return eti_beliefs_lw, eti_beliefs_jjz
 
 
-def wm(value, weight):
+def wm(value, weight):
     """
     Weighted mean function that allows for zero division
 
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diff --git a/content/api/inverse_optimal_tax.html b/content/api/inverse_optimal_tax.html
index 358026d..0ff8625 100644
--- a/content/api/inverse_optimal_tax.html
+++ b/content/api/inverse_optimal_tax.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/content/api/public_api.html b/content/api/public_api.html
index 2e81dbc..e7e39c8 100644
--- a/content/api/public_api.html
+++ b/content/api/public_api.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/content/example/IOT_example.html b/content/example/IOT_example.html
index 874154d..a35374e 100644
--- a/content/example/IOT_example.html
+++ b/content/example/IOT_example.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
@@ -435,15 +435,15 @@ 
Step 1: Import the 
 

 
# imports
-from iot.iot_user import iot_comparison
-from IPython.core.display import display, HTML
-from plotly.offline import init_notebook_mode, plot
+from iot.iot_user import iot_comparison
+from IPython.core.display import display, HTML
+from plotly.offline import init_notebook_mode, plot
 init_notebook_mode(connected=True)
 

 

 

 

-
/tmp/ipykernel_2023/995651565.py:3: DeprecationWarning: Importing display from IPython.core.display is deprecated since IPython 7.14, please import from IPython.display
+
/tmp/ipykernel_1959/995651565.py:3: DeprecationWarning: Importing display from IPython.core.display is deprecated since IPython 7.14, please import from IPython.display
   from IPython.core.display import display, HTML
 

 

diff --git a/content/intro/contributing.html b/content/intro/contributing.html
index 44051dd..074aa01 100644
--- a/content/intro/contributing.html
+++ b/content/intro/contributing.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/content/intro/intro.html b/content/intro/intro.html
index 95d9987..90dc83c 100644
--- a/content/intro/intro.html
+++ b/content/intro/intro.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/content/intro/parameters.html b/content/intro/parameters.html
index 00450e8..6d337c5 100644
--- a/content/intro/parameters.html
+++ b/content/intro/parameters.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/content/references.html b/content/references.html
index 4b963ef..404f05d 100644
--- a/content/references.html
+++ b/content/references.html
@@ -30,7 +30,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/genindex.html b/genindex.html
index 07c13d4..3ef443e 100644
--- a/genindex.html
+++ b/genindex.html
@@ -29,7 +29,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/search.html b/search.html
index ab40871..218479f 100644
--- a/search.html
+++ b/search.html
@@ -28,7 +28,7 @@
   
 
 
-    
+    
     
     
     
diff --git a/searchindex.js b/searchindex.js
index 10b471a..4e557a6 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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