In [1]:
# This line configures matplotlib to show figures embedded in the notebook,
# instead of opening a new window for each figure. More about that later.
# If you are using an old version of IPython, try using '%pylab inline' instead.
%matplotlib inline
from pysolve.model import Model
from pysolve.utils import is_close,round_solution
import matplotlib.pyplot as plt
In [2]:
def create_openm_model():
model = Model()
model.set_var_default(0)
model.var('BcbN', desc='Bills held by the Central Bank in Country N')
model.var('BcbS', desc='Bills held by the Central Bank in Country S')
model.var('BhN', desc='Bills held by households, Country N')
model.var('BhS', desc='Bills held by households, Country S')
model.var('BsN', desc='Supply of government bills in Country N')
model.var('BsS', desc='Supply of government bills in Country S')
model.var('CN', desc='Consumption, Country N')
model.var('CS', desc='Consumption, Country S')
model.var('HhN', desc='Cash held by households, Country N')
model.var('HhS', desc='Cash held by households, Country S')
model.var('HsN', desc='Supply of cash in Country N')
model.var('HsS', desc='Supply of cash in Country S')
model.var('IMN', desc='Imports, Region N')
model.var('IMS', desc='Imports, Region S')
model.var('ORN', desc='Gold holding by Central bank in Country N')
model.var('ORS', desc='Gold holding by Central bank in Country S')
model.var('PgN', desc='Price of gold in Country N')
model.var('PgS', desc='Price of gold in Country S')
model.var('RN', desc='Interest rate on bills in Country N')
model.var('RS', desc='Interest rate on bills in Country S')
model.var('TN', desc='Tax payments, Country N')
model.var('TS', desc='Tax payments, Country S')
model.var('VN', desc='Household wealth, Country N')
model.var('VS', desc='Household wealth, Country S')
model.var('XN', desc='Exports, Country N')
model.var('XS', desc='Exports, Country S')
model.var('XR', desc='Exchange rate (units of currency S for one unit of currency N)')
model.var('YN', desc='National income, Country N')
model.var('YS', desc='National income, Country S')
model.var('YDN', desc='National disposable income, Country N')
model.var('YDS', desc='National disposable income, Country S')
model.set_param_default(0)
model.param('alpha1N', desc='Propensity to consume out of income, Country N')
model.param('alpha1S', desc='Propensity to consume out of income, Country S')
model.param('alpha2N', desc='Propensity to consume out of wealth, Country N')
model.param('alpha2S', desc='Propensity to consume out of wealth, Country S')
model.param('lambda0N', desc='Parameter in asset demand function, Country N')
model.param('lambda0S', desc='Parameter in asset demand function, Country S')
model.param('lambda1N', desc='Parameter in asset demand function, Country N')
model.param('lambda1S', desc='Parameter in asset demand function, Country S')
model.param('lambda2N', desc='Parameter in asset demand function, Country N')
model.param('lambda2S', desc='Parameter in asset demand function, Country S')
model.param('muN', desc='Import propensity, Country N')
model.param('muS', desc='Import propensity, Country S')
model.param('phiN', desc='Parameter in fiscal policy reaction function, Country N')
model.param('phiS', desc='Parameter in fiscal policy reaction function, Country S')
model.param('thetaN', desc='Tax rate in Country N')
model.param('thetaS', desc='Tax rate in Country S')
model.param('GN', desc='Government expenditure, Region N')
model.param('GS', desc='Government expenditure, Region S')
model.param('Pgbar', desc='Price of gold, set exogenously')
#model.param('RbarN', desc='Interest rate on bills set exogenously in Country N')
#model.param('RbarS', desc='Interest rate on bills set exogenously in Country S')
model.param('XRbar', desc='Exchange rate, set exogenously')
model.add('YN = CN + GN + XN - IMN')
model.add('YS = CS + GS + XS - IMS')
model.add('IMN = muN * YN')
model.add('IMS = muS * YS')
model.add('XN = IMS/XR')
model.add('XS = IMN*XR')
model.add('YDN = YN - TN + RN(-1)*BhN(-1)')
model.add('YDS = YS - TS + RS(-1)*BhS(-1)')
model.add('TN = thetaN * (YN + RN(-1)*BhN(-1))')
model.add('TS = thetaS * (YS + RS(-1)*BhS(-1))')
model.add('VN - VN(-1) = YDN - CN')
model.add('VS - VS(-1) = YDS - CS')
model.add('CN = alpha1N*YDN + alpha2N*VN(-1)')
model.add('CS = alpha1S*YDS + alpha2S*VS(-1)')
model.add('HhN = VN - BhN')
model.add('HhS = VS - BhS')
model.add('BhN = VN*(lambda0N + lambda1N*RN - lambda2N*(YDN/VN))')
model.add('BhS = VS*(lambda0S + lambda1S*RS - lambda2S*(YDS/VS))')
model.add('BsN - BsN(-1) = (GN + RN(-1)*BsN(-1)) - (TN + RN(-1)*BcbN(-1))')
model.add('BsS - BsS(-1) = (GS + RS(-1)*BsS(-1)) - (TS + RS(-1)*BcbS(-1))')
model.add('BcbN = BsN - BhN')
model.add('BcbS = BsS - BhS')
model.add('ORN - ORN(-1)= (HsN - HsN(-1) - (BcbN - BcbN(-1)))/PgN')
model.add('ORS - ORS(-1)= (HsS - HsS(-1) - (BcbS - BcbS(-1)))/PgS')
model.add('HsN = HhN')
model.add('HsS = HhS')
model.add('PgN = Pgbar')
model.add('PgS = PgN*XR')
model.add('XR = XRbar')
model.add('RN = RN(-1) - phiN*((ORN(-1) - ORN(-2))*PgN(-1))/ORN(-1)')
model.add('RS = RS(-1) - phiS*((ORS(-1) - ORS(-2))*PgS(-1))/ORS(-1)')
#model.add('GN = GN(-1) + phiN*(ORN - ORN(-1))*PgN(-1)')
#model.add('GS = GS(-1) + phiS*(ORS - ORS(-1))*PgS(-1)')
return model
openm_parameters = {'alpha1N': 0.6,
'alpha1S': 0.7,
'alpha2N': 0.4,
'alpha2S': 0.3,
'lambda0N': 0.635,
'lambda0S': 0.67,
'lambda1N': 5,
'lambda1S': 6,
'lambda2N': 0.01,
'lambda2S': 0.07,
'muN': 0.18781,
'muS': 0.18781,
'phiN': 0.02,
'phiS': 0.06,
'thetaN': 0.2,
'thetaS': 0.2}
openm_exogenous = {'Pgbar': 1,
'GN': 20,
'GS': 20,
'XRbar': 1}
openm_variables = {'BcbN': 11.622,
'BcbS': 11.622,
'BhN': 64.865,
'BhS': 64.865,
'BsN': 76.486,
'BsS': 76.486,
'ORN': 10,
'ORS': 10,
'PgN': 1,
'PgS': 1,
'RN': 0.025,
'RS': 0.025,
'VN': 86.487,
'VS': 86.487,
'HhN': 86.487 - 64.865,
'HhS': 86.487 - 64.865,
'HsN': 86.487 - 64.865,
'HsS': 86.487 - 64.865,
'XR': 1}
In [3]:
muS = create_openm_model()
muS.set_values(openm_parameters)
muS.set_values(openm_exogenous)
muS.set_values(openm_variables)
# run to convergence
# Give the system more time to reach a steady state
for _ in xrange(15):
muS.solve(iterations=100, threshold=1e-6)
# shock the system
muS.set_values({'muS': 0.20781})
for _ in xrange(10):
muS.solve(iterations=100, threshold=1e-6)
In [4]:
caption = '''
Figure 6.14 Evolution of interest rates, following an increase in the South
propensity to import, with monetary rules based on changes in gold reserves'''
rndata = [s['RN'] for s in muS.solutions[14:24]]
rsdata = [s['RS'] for s in muS.solutions[14:24]]
fig = plt.figure()
axes = fig.add_axes([0.1, 0.1, 0.9, 1.1])
axes.tick_params(top='off', right='off')
axes.spines['top'].set_visible(False)
axes.spines['right'].set_visible(False)
axes.set_ylim(0, 0.15)
axes.plot(rndata, linestyle='-', color='r')
axes.plot(rsdata, linestyle='--', color='b')
# add labels
plt.text(4, .09, 'South interest rate')
plt.text(4, .084, '(deficit country)')
plt.text(4, .032, 'North interest rate')
plt.text(4, .028, '(surplus country)')
#plt.text(25, 114, 'North country GDP')
#plt.text(25, 106, 'South country GDP')
fig.text(0.1, -.1, caption);
In [5]:
caption = '''
Figure 6.15 Evolution of trade accounts and government balances of both
countries, following an increase in the South propensity to import, with
moneary rules based on changes in gold reserves'''
tradeNdata = list()
tradeSdata = list()
govtNdata = list()
govtSdata = list()
for i in xrange(14, 20):
s = muS.solutions[i]
s_1 = muS.solutions[i-1]
tradeNdata.append(s['XN'] - s['IMN'])
tradeSdata.append(s['XS'] - s['IMS'])
govtNdata.append(s['TN'] - (s['GN'] + s['RN']*s_1['BsN']))
govtSdata.append(s['TS'] - (s['GS'] + s['RS']*s_1['BsS']))
fig = plt.figure()
axes = fig.add_axes([0.1, 0.1, 0.9, 1.1])
axes.tick_params(top='off', right='off')
axes.spines['top'].set_visible(False)
axes.spines['right'].set_visible(False)
axes.set_ylim(-4, 3)
axes.plot(tradeNdata, linestyle='-', color='k')
axes.plot(govtNdata, linestyle=':', color='r', linewidth=3)
axes.plot(tradeSdata, linestyle='--', color='g')
axes.plot(govtSdata, linestyle='-.', color='b', linewidth=2)
# add labels
plt.text(3, 1.7, 'North trade balance')
plt.text(3.5, 0.1, 'North government balance')
plt.text(4, -1, 'South trade balance')
plt.text(2.5, -2.1, 'South government')
plt.text(2.5, -2.4, 'balance')
fig.text(0.1, -.1, caption);
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