Initial upload.

.gitignore

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+code/modeling_language
+*.pyc
+*.pdf
+*.xlsx
+*.svg
+*.png
+*ipynb_checkpoints*

README.md

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+This code replicates the graphs from the paper *Managing Capital Outflows: The Role of Foreign. Exchange Intervention.* by Suman S. Basu, Atish R. Ghosh, Jonathan D. Ostry and Pablo E. Winant.
+
+The code requires Python 3.6 and depends on two libraries:
+
+- [dolo](https://github.com/EconForge/dolo)
+- [backtothetrees](https://github.com/albop/backtothetrees)
+
+An up-to-date version of the code can be found on [github](https://github.com/albop/managing_capital_outflows_with_limited_reserves
+
+
+To generate the results run:
+
+- `python compute_simulations.py` : creates files with various simulation results
+    - `precomputed_decision_rules.pickle`
+    - `precomputed_moving_target.pickle`
+    - `precomputed_simulations.pickle`
+
+- `python compute_welfares.py`: create welfare comparison files:
+    - `simple_rules_welfare.xlsx` (p=1.0)
+    - `simple_rules_welfare_9.xlsx` (p=0.9)
+    - `simple_rules_welfare_8.xlsx` (p=0.8)
+
+
+The graphs are then created in the notebooke `gen_graphs.ipynb` which can be opened and run using Jupyter.

calibrations.py

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+
+import copy
+from collections import OrderedDict
+
+params = dict(
+    beta=0.8/(0.8+0.15),
+    a=0.8,
+    c=0.15,
+    estar=-0.0,
+    Rbar=0.5,
+    min_f=0,
+    kappa=1.0,
+    N=40,
+    zbar=0.1,
+    p=1,
+    model='optimal'
+)
+
+
+reserve_levels = [0.01, 0.5, 1.0, 1.5, 2.0, 3.0]
+policies = ['volume','peg','optimal','time-consistent']
+cases = {
+    'baseline': {},
+    'accumulation': {'min_f': -10000},
+    'low_beta': {'beta': 0.8},
+    'high_beta': {'beta': 0.9},
+    'super_low_a': {'a': 0.01},
+    'low_a': {'a': 0.4},
+    'high_a': {'a': 1.6},
+    'low_c': {'c': 0.075},
+    'high_c': {'c': 0.30},
+    'p_8': {'p': 0.8},
+    'p_85': {'p': 0.85},
+    'p_9': {'p': 0.9},
+    'p_95': {'p': 0.95},
+}
+
+list_of_calibrations = OrderedDict()
+for case in cases.keys():
+    for pol in policies:
+        for r in reserve_levels:
+            calib = copy.copy(params)
+            calib.update(cases[case])
+            calib['Rbar'] = r
+            calib['model'] = pol
+            list_of_calibrations[(case,pol,r)] = calib.copy()

compute_alpha.py

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+######## Solve
+import pandas
+import numpy
+from collections import OrderedDict
+# from solution import *
+from calibrations import *
+from time_consistent import solve as solve_time_consistent
+from time_consistent import simulate
+from bttt.trees import DeterministicTree, get_ts
+from matplotlib import pyplot as plt
+from bttt.trees import DeathTree
+from bttt.model import import_tree_model
+from matplotlib import pyplot as plt
+from numpy import *
+
+
+
+N = 25
+T = 25
+
+
+calib0 = calib.copy()
+beta = calib0['beta']
+a = calib0['a']
+p = calib0['p']
+zbar = calib0['zbar']
+max_R=5
+
+
+tree = DeterministicTree(N)
+for s in tree.nodes:
+    tree.values[s] = zbar
+    model = import_tree_model('models.yaml', key='stochastic', tree=tree)
+
+def solve_it(**cc):
+    tree = DeterministicTree(N)
+    for s in tree.nodes:
+        tree.values[s] = zbar
+    model = import_tree_model('models.yaml', key='optimal', tree=tree)
+    model.calibration.update(cc)
+    sol = model.solve(verbose=True)
+    df = numpy.concatenate( [get_ts(tree, sol, varname)[:,None] for varname in ['e','f', 'Gamma']], axis=1 )
+    df = pandas.DataFrame(df, columns=['e','f','Gamma'])
+    return df
+
+from collections import OrderedDict
+
+
+Rvec0 = linspace(0.01, 3.0, 20)
+
+
+
+pvec = [0.8, 0.85, 0.9, 0.95, 1.0]
+
+# Unconstrained solutions
+
+unconstrained_sols = OrderedDict()
+for p in pvec:
+    dfs = [solve_it(Rbar=i, min_f=0, p=p) for i in Rvec0]
+    unconstrained_sols[p] = dfs
+
+all_gammas = OrderedDict()
+for p in pvec:
+    dfs = unconstrained_sols[p]
+    max_gammas = numpy.array([dfs[i]['Gamma'].max() for i,r in enumerate(Rvec0)])
+    all_gammas[p] = max_gammas
+
+for p in pvec:
+    plt.plot(Rvec0, all_gammas[p])
+
+alpha = 0.5
+
+Rlimit = OrderedDict()
+
+for p in pvec:
+    dfs = unconstrained_sols[p]
+    max_gammas = numpy.array([dfs[i]['Gamma'].max() for i,r in enumerate(Rvec0)])
+    j = numpy.where(max_gammas<alpha)[0][0]
+    a0 = max_gammas[j-1]
+    a1 = max_gammas[j]
+    r0 = Rvec0[j-1]
+    r1 = Rvec0[j]
+    rmax = r0 + (r1-r0)*(alpha-a0)/(a1-a0)
+    Rlimit[p] = rmax
+
+# Constrained solutions
+
+R0 = 0.8
+
+constrained_solutions = OrderedDict()
+
+for p in pvec:
+    Rm = Rlimit[p]
+    R1 = min([R0, Rm])
+    if Rm>0:
+        df = solve_it(p=p, Rbar=R1)
+    elif Rm<=0:
+        df = solve_it(p=p, Rbar=0.001)
+    df['R'] = R0 - df['f'].cumsum().shift()
+    df['R'][0]  = R0
+    constrained_solutions[p] = df
+
+d = {'dfs':constrained_solutions}
+
+import pickle
+with open("precomputed_alpha_p.pickle",'wb') as f:
+    pickle.dump(d,f)
+
+###
+##
+###
+
+
+Rmax = 0.998
+nRvec0 = numpy.array([0.01, 0.5, 0.9, Rmax, 2.0, 3.0])
+ndfs = [solve_it(Rbar=i, min_f=0) for i in nRvec0]
+for i in [4,5]:
+    df = ndfs[3].copy()
+    ndfs[i] = df
+for i,df in enumerate(ndfs):
+    df['R'] = nRvec0[i] - df['f'].cumsum()
+#
+#
+# # In[43]:
+#
+#
+# def plot_dfs(dfs, labels):
+#     attributes = ['b', 'g', 'r']
+#     if not isinstance(dfs, list):
+#         dfs = [dfs]
+#     fig = plt.figure(figsize=(15,10))
+# #     plt.clear()
+#     plt.subplot(131)
+#     plt.plot(dfs[0].index,dfs[0].index*0+0.5,color='black', linestyle='--')
+#     for i,df in enumerate(dfs):
+#         plt.plot(df["Gamma"])
+#
+#     plt.grid()
+#     plt.title("Marginal Value of Intervention")
+# #     plt.figure()
+#     plt.subplot(132)
+#     for i,df in enumerate(dfs):
+#         plt.plot(df["e"], label=labels[i])
+#     plt.legend(loc='lower right')
+#     plt.grid()
+#     plt.title("Exchange Rate")
+#     plt.subplot(133)
+#     for i,df in enumerate(dfs):
+#         plt.plot(df["R"], label=labels[i])
+#     plt.grid()
+#     plt.title("Reserves")
+#     return fig
+#
+#
+# # In[44]:
+
+
+import pickle
+with open("precomputed_option_value.pickle","wb") as f:
+    pickle.dump({"commitment":ndfs},f)
+
+#
+# # In[82]:
+#
+#
+# f = plot_dfs(ndfs, labels=['$R_0={}$'.format(i) for i in Rvec0])
+# plt.savefig("optimal_choice_noconstraint.png", bbox_inches="tight")
+# plt.savefig("optimal_choice_noconstraint.pdf", bbox_inches="tight")
+# f
+#
+#
+# # In[11]:
+#
+#
+# Rvec0 = linspace(0.3, 3.0, 10)
+# dfs = [solve_it(Rbar=i) for i in Rvec0]
+#
+#
+# # In[12]:
+#
+#
+# f = plot_dfs(dfs, labels=['$R_0={}$'.format(i) for i in Rvec0])
+# plt.savefig("optimal_choice_constraint.png", bbox_inches="tight")
+# plt.savefig("optimal_choice_constraint.pdf", bbox_inches="tight")
+# f