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_dis_model():
model = Model()
model.set_var_default(0)
model.var('Ck', desc='REal consumption')
model.var('C', desc='Consumption at current prices')
model.var('F', desc='Realized firm profits')
model.var('Fb', desc='Realized bank profits')
model.var('IN', desc='Stock of inventories at current costs')
model.var('INk', desc='Real inventories')
model.var('INke', desc='Expected real inventories')
model.var('INkt', desc='Target level of real inventories')
model.var('Ld', desc='Demand for loans')
model.var('Ls', desc='Supply of loans')
model.var('Mh', desc='Deposits held by households')
model.var('Mhk', desc='Real alue of deposits held by households')
model.var('Ms', desc='Supply of deposits')
model.var('N', desc='Employment level')
model.var('NHUC', desc='Normal historic unit costs')
model.var('P', desc='Price level')
model.var('Rl', desc='Interest rate on loans')
model.var('Rm', desc='Interest rate on deposits')
model.var('S', desc='Sales at current prices')
model.var('Sk', desc='Real sales')
model.var('Ske', desc='Expected real sales')
model.var('UC', desc='Unit costs')
model.var('WB', desc='The wage bill')
model.var('Yk', desc='Real output')
model.var('YD', desc='Disposable income')
model.var('YDkhs', desc='Haig-Simons measure of real disposable income')
model.var('YDkhse', desc='Expected HS real disposable income')
model.set_param_default(0)
model.param('alpha0', desc='Autonomous consumption')
model.param('alpha1', desc='Propensity to consume out of income')
model.param('alpha2', desc='Propensity to consume out of wealth')
model.param('beta', desc='Parameter in expectation formations on real sales')
model.param('eps', desc='Parameter in expectation formations on real disposable income')
model.param('gamma', desc='Speed of adjustment of inventories to the target level')
model.param('phi', desc='Mark-up on unit costs')
model.param('sigmat', desc='Target inventories to sales ratio')
model.param('ADD', desc='Spread of loans rate over the deposit rate')
model.param('PR', desc='Labor productivity')
model.param('Rlbar', desc='Rate of interest on bank loans, set exogenously')
model.param('W', desc='Wage rate')
# The production decision
model.add('Yk = Ske + INke - INk(-1)')
model.add('INkt = sigmat*Ske')
model.add('INke = INk(-1) + gamma*(INkt - INk(-1))')
model.add('INk - INk(-1) = Yk - Sk')
model.add('Ske = beta*Sk(-1) + (1-beta)*Ske(-1)')
model.add('Sk = Ck')
model.add('N = Yk / PR')
model.add('WB = N*W')
model.add('UC = WB/Yk')
model.add('IN = INk*UC')
# The pricing decision
model.add('S = P*Sk')
model.add('P = (1 + phi)*NHUC')
model.add('NHUC = (1 - sigmat)*UC + sigmat*(1 + Rl(-1))*UC(-1)')
model.add('F = S - WB + IN - IN(-1) - Rl(-1)*IN(-1)')
# The banking system
model.add('Ld = IN')
model.add('Ls = Ld')
model.add('Ms = Ls')
model.add('Rl = Rlbar')
model.add('Rm = Rl - ADD')
model.add('Fb = Rl(-1)*Ld(-1) - Rm(-1)*Mh(-1)')
# The consumption decision
model.add('YD = WB + F + Fb + Rm(-1)*Mh(-1)')
model.add('Mh - Mh(-1) = YD - C')
model.add('YDkhs = Ck + (Mhk - Mhk(-1))')
model.add('C = Ck*P')
model.add('Mhk = Mh/P')
model.add('Ck = alpha0 + alpha1*YDkhse + alpha2*Mhk(-1)')
model.add('YDkhse = eps*YDkhs(-1) + (1 - eps)*YDkhse(-1)')
return model
dis_parameters = {'alpha0': 15,
'alpha1': 0.8,
'alpha2': 0.1,
'beta': 0.75,
'eps': 0.75,
'gamma': 0.25,
'phi': 0.25,
'sigmat': 0.15}
dis_exogenous = {'ADD': 0.02,
'PR': 1,
'Rlbar': 0.04,
'W': 0.86}
# Warning! If you wish to initialize the variables using equations.
# the order in which they appear is important. Ordinary Python
# dictionaries are not ordered, so the values will be incorrect,
# use a list of (name, equation) tuples or an OrderedDict()
#
dis_variables = [('UC', 'W/PR'),
('NHUC', '(1 + sigmat*Rlbar)*UC'),
('P', '(1+phi)*NHUC'),
('YDkhs', 'alpha0/(1-alpha1-alpha2*sigmat*UC/P)'),
('Ck', 'YDkhs'),
('Sk', 'Ck'),
('INk', 'sigmat*Sk'),
('IN', 'INk*UC'),
('Ld', 'IN'),
('Mh', 'Ld'),
('Mhk', 'Mh/P'),
('Ms', 'Mh'),
('Ls', 'Ld'),
('Ske', 'Sk'),
('YDkhse', 'YDkhs'),
('Rl', 'Rlbar'),
('Rm', 'Rl - ADD')]
In [3]:
phi = create_dis_model()
phi.set_values(dis_parameters)
phi.set_values(dis_exogenous)
phi.set_values(dis_variables)
# run to convergence
# Give the system more time to reach a steady state
for _ in xrange(15):
phi.solve(iterations=200, threshold=1e-6)
# shock the system
phi.set_values({'phi': 0.3})
for _ in xrange(40):
phi.solve(iterations=100, threshold=1e-6)
In [4]:
caption = '''
Figure 9.1 Evolution of (Haig-Simons) real disposable income and of real
consumption following a one-shot increase in the costing margin'''
ydkhsdata = [s['YDkhs'] for s in phi.solutions[5:]]
ckdata = [s['Ck'] for s in phi.solutions[5:]]
fig = plt.figure()
axes = fig.add_axes([0.1, 0.1, 1.1, 1.1])
axes.tick_params(top='off', right='off')
axes.spines['top'].set_visible(False)
axes.spines['right'].set_visible(False)
axes.set_ylim(79.3, 79.8)
axes.plot(ydkhsdata, linestyle='-', color='r')
axes.plot(ckdata, linestyle='--', color='b')
# add labels
plt.text(13, 79.74, 'Real consumption')
plt.text(12, 79.4, 'Haig-Simons real disposable income')
fig.text(0.1, -.05, caption);
In [5]:
sigmat = create_dis_model()
sigmat.set_values(dis_parameters)
sigmat.set_values(dis_exogenous)
sigmat.set_values(dis_variables)
# run to convergence
# Give the system more time to reach a steady state
for _ in xrange(15):
sigmat.solve(iterations=200, threshold=1e-6)
# shock the system
sigmat.set_values({'sigmat': 0.25})
for _ in xrange(40):
sigmat.solve(iterations=100, threshold=1e-6)
In [6]:
caption = '''
Figure 9.2 Evolution of (Haig-Simons) real disposable income and of real
consumption following an increase in the target inventories to sales ratio'''
ydkhsdata = [s['YDkhs'] for s in sigmat.solutions[5:]]
ckdata = [s['Ck'] for s in sigmat.solutions[5:]]
fig = plt.figure()
axes = fig.add_axes([0.1, 0.1, 1.1, 1.1])
axes.tick_params(top='off', right='off')
axes.spines['top'].set_visible(False)
axes.spines['right'].set_visible(False)
axes.set_ylim(79.3, 84.8)
axes.plot(ydkhsdata, linestyle='-', color='r')
axes.plot(ckdata, linestyle='--', color='b')
# add labels
plt.text(15, 81.5, 'Real consumption')
plt.text(8, 83, 'Haig-Simons')
plt.text(8, 82.8, 'real disposable')
plt.text(8, 82.6, 'income')
fig.text(0.1, -.05, caption);
In [7]:
caption = '''
Figure 9.3 Evolution of the desired increase in physical inventories and of
the change in realized inventories, following an increase in the target
inventories to sales ratio'''
inkdata = list()
inkedata = list()
for i in xrange(5, len(sigmat.solutions)):
s = sigmat.solutions[i]
s_1 = sigmat.solutions[i-1]
# to get the shape of the graph in the book,
# use INkt - INk
inkdata.append(s['INk'] - s_1['INk'])
inkedata.append(s['INke'] - s_1['INke'])
fig = plt.figure()
axes = fig.add_axes([0.1, 0.1, 1.1, 1.1])
axes.tick_params(top='off', right='off')
axes.spines['top'].set_visible(False)
axes.spines['right'].set_visible(False)
axes.set_ylim(-0.5, 2.1)
axes.plot(inkdata, linestyle='-', color='r')
axes.plot(inkedata, linestyle='--', color='b')
# add labels
plt.text(13, 0.2, 'Change in')
plt.text(13, 0.1, 'realized inventories')
plt.text(14, 1.0, 'Desired increase')
plt.text(14, 0.9, 'in physical inventories')
fig.text(0.1, -.1, caption);
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