Merge pull request #31 from john-p-ryan/main

Add HSV tax estimation

Author: jdebacker

iot/inverse_optimal_tax.py

@@ -4,6 +4,7 @@
 import scipy
 from statsmodels.nonparametric.kernel_regression import KernelReg
 from scipy.interpolate import UnivariateSpline
+from scipy.linalg import lstsq
 
 
 class IOT:
@@ -127,33 +128,49 @@ def compute_mtr_dist(
                 * 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(),
                 var_type="c",
                 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
 
@@ -336,20 +353,22 @@ def sw_weights(self):
             + ((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