def large_blp_simulation() -> SimulationFixture:
"""Solve a simulation with 20 markets, varying numbers of products per market, a linear constant, log-linear
coefficients on prices, a linear/nonlinear/cost characteristic, another three linear characteristics, another two
cost characteristics, demographics interacted with prices and the linear/nonlinear/cost characteristic, dense
parameter matrices, a log-linear cost specification, and local differentiation instruments.
"""
id_data = build_id_data(T=20, J=20, F=9)
keep = np.arange(id_data.size)
np.random.RandomState(0).shuffle(keep)
id_data = id_data[keep[:int(0.5 * id_data.size)]]
simulation = Simulation(
product_formulations=(Formulation('1 + x + y + z + q'),
Formulation('0 + I(-prices) + x'),
Formulation('0 + log(x) + log(a) + log(b)')),
product_data={
'market_ids':
id_data.market_ids,
'firm_ids':
id_data.firm_ids,
'clustering_ids':
np.random.RandomState(2).choice(range(30), id_data.size)
},
beta=[1, 1, 2, 3, 1],
sigma=[[+0.5, 0], [-0.1, 2]],
pi=[[2, 1, 0], [0, 0, 2]],
gamma=[0.1, 0.2, 0.3],
agent_formulation=Formulation('1 + f + g'),
integration=Integration('product', 4),
xi_variance=0.00001,
omega_variance=0.00001,
correlation=0.9,
distributions=['lognormal', 'normal'],
costs_type='log',
seed=2)
simulation_results = simulation.replace_endogenous()
simulated_data_override = {
'demand_instruments':
np.c_[build_differentiation_instruments(
Formulation('0 + x + y + z + q'), simulation_results.product_data),
build_matrix(Formulation('0 + a + b'), simulation_results.
product_data)],
'supply_instruments':
np.c_[build_differentiation_instruments(
Formulation('0 + x + a + b'), simulation_results.product_data),
build_matrix(Formulation('0 + y + z + q'), simulation_results.
product_data)]
}
simulated_micro_moments = [
FirstChoiceCovarianceMoment(
X2_index=1,
demographics_index=1,
value=0,
market_ids=simulation.unique_market_ids[:5]),
FirstChoiceCovarianceMoment(
X2_index=0,
demographics_index=1,
value=0,
market_ids=simulation.unique_market_ids[-3:])
]
return simulation, simulation_results, simulated_data_override, simulated_micro_moments
def large_blp_simulation() -> SimulationFixture:
"""Solve a simulation with 20 markets, varying numbers of products per market, a linear constant, linear/nonlinear
prices, a linear/nonlinear/cost characteristic, another three linear characteristics, another two cost
characteristics, demographics interacted with prices and the linear/nonlinear/cost characteristic, dense parameter
matrices, a log-linear cost specification, and local differentiation instruments on the demand side.
"""
id_data = build_id_data(T=20, J=20, F=9)
keep = np.arange(id_data.size)
np.random.RandomState(0).shuffle(keep)
id_data = id_data[keep[:int(0.5 * id_data.size)]]
simulation = Simulation(
product_formulations=(Formulation('1 + prices + x + y + z + q'),
Formulation('0 + prices + x'),
Formulation('0 + log(x) + log(a) + log(b)')),
beta=[1, -10, 1, 2, 3, 1],
sigma=[[1, -0.1], [0, +2.0]],
gamma=[0.1, 0.2, 0.3],
product_data={
'market_ids':
id_data.market_ids,
'firm_ids':
id_data.firm_ids,
'clustering_ids':
np.random.RandomState(2).choice(range(30), id_data.size)
},
agent_formulation=Formulation('0 + f + g'),
pi=[[1, 0], [0, 2]],
integration=Integration('product', 4),
xi_variance=0.00001,
omega_variance=0.00001,
correlation=0.9,
costs_type='log',
seed=2)
simulation_results = simulation.solve()
differentiation_instruments = np.c_[
build_differentiation_instruments(Formulation('0 + x + y + z + q'),
simulation_results.product_data),
build_matrix(Formulation('0 + a + b'), simulation_results.product_data
)]
simulation_results.product_data = update_matrices(
simulation_results.product_data, {
'demand_instruments':
(differentiation_instruments,
simulation_results.product_data.demand_instruments.dtype)
})
return simulation, simulation_results
# pd.DataFrame(demand_instruments).describe()
#
# demand_instruments = demand_instruments[:,5]
# demand_instruments = demand_instruments.reshape((len(demand_instruments),1))
# product_data['demand_instruments0'] = demand_instruments[:,0]
#
# supply_instruments = pyblp.build_blp_instruments(pyblp.Formulation('obs_cost'), product_data)
# supply_instruments = supply_instruments[:,3]
# supply_instruments.reshape((len(supply_instruments),1))
# product_data['supply_instruments0'] = supply_instruments
# In[3]:
# quad diff instruments
demand_instruments = pyblp.build_differentiation_instruments(
pyblp.Formulation('0 + quality + obs_cost'),
product_data,
version='quadratic')
demand_instruments = demand_instruments[:, 2:4]
demand_instruments = demand_instruments.reshape((len(demand_instruments), 2))
product_data['demand_instruments0'] = demand_instruments[:, 0]
product_data['demand_instruments1'] = demand_instruments[:, 1]
supply_instruments = pyblp.build_differentiation_instruments(
pyblp.Formulation('0 + obs_cost'), product_data, version='quadratic')
supply_instruments = supply_instruments[:, 1]
supply_instruments.reshape((len(supply_instruments), 1))
product_data['supply_instruments0'] = supply_instruments
product_data_diff = product_data.copy()
# In[4]:
def large_blp_simulation() -> SimulationFixture:
"""Solve a simulation with 20 markets, varying numbers of products per market, a linear constant, log-linear
coefficients on prices, a linear/nonlinear/cost characteristic, another three linear characteristics, another two
cost characteristics, demographics interacted with prices and the linear/nonlinear/cost characteristic, dense
parameter matrices, a log-linear cost specification, and local differentiation instruments.
"""
id_data = build_id_data(T=20, J=20, F=9)
keep = np.arange(id_data.size)
np.random.RandomState(0).shuffle(keep)
id_data = id_data[keep[:int(0.5 * id_data.size)]]
product_ids = id_data.market_ids.copy()
for t in np.unique(id_data.market_ids):
product_ids[id_data.market_ids == t] = np.arange(
(id_data.market_ids == t).sum())
simulation = Simulation(
product_formulations=(Formulation('1 + x + y + z + q'),
Formulation('1 + I(-prices) + x'),
Formulation('0 + log(x) + log(a) + log(b)')),
product_data={
'market_ids':
id_data.market_ids,
'firm_ids':
id_data.firm_ids,
'product_ids':
product_ids,
'clustering_ids':
np.random.RandomState(2).choice(range(30), id_data.size)
},
beta=[1, 1, 2, 3, 1],
sigma=[[0, +0.0, 0], [0, +0.5, 0], [0, -0.2, 2]],
pi=[[0, 0, 0], [2, 1, 0], [0, 0, 2]],
gamma=[0.1, 0.2, 0.3],
agent_formulation=Formulation('1 + f + g'),
integration=Integration('product', 4),
xi_variance=0.00001,
omega_variance=0.00001,
correlation=0.9,
distributions=['normal', 'lognormal', 'normal'],
costs_type='log',
seed=2)
simulation_results = simulation.replace_endogenous()
simulated_data_override = {
'demand_instruments':
np.c_[build_differentiation_instruments(
Formulation('0 + x + y + z + q'), simulation_results.product_data),
build_matrix(Formulation('0 + a + b'), simulation_results.
product_data)],
'supply_instruments':
np.c_[build_differentiation_instruments(
Formulation('0 + x + a + b'), simulation_results.product_data),
build_matrix(Formulation('0 + y + z + q'), simulation_results.
product_data)]
}
simulated_micro_moments = [
DemographicExpectationMoment(product_ids=[0],
demographics_index=1,
value=0,
observations=simulation.N),
DemographicExpectationMoment(
product_ids=[None, 0],
demographics_index=1,
value=0,
observations=simulation.N,
market_ids=simulation.unique_market_ids[1:4],
market_weights=[0.2, 0.4, 0.4],
),
DemographicCovarianceMoment(
X2_index=0,
demographics_index=2,
value=0,
observations=simulation.N,
market_ids=simulation.unique_market_ids[3:5]),
DiversionProbabilityMoment(
product_id1=1,
product_id2=0,
value=0,
observations=simulation.N,
market_ids=simulation.unique_market_ids[6:10]),
DiversionProbabilityMoment(
product_id1=None,
product_id2=1,
value=0,
observations=simulation.N,
market_ids=[simulation.unique_market_ids[8]]),
DiversionProbabilityMoment(
product_id1=1,
product_id2=None,
value=0,
observations=simulation.N,
market_ids=[simulation.unique_market_ids[9]]),
DiversionCovarianceMoment(
X2_index1=1,
X2_index2=1,
value=0,
observations=simulation.N,
market_ids=[simulation.unique_market_ids[12]]),
]
return simulation, simulation_results, simulated_data_override, simulated_micro_moments
def large_blp_simulation() -> SimulationFixture:
"""Solve a simulation with 20 markets, varying numbers of products per market, a linear constant, log-linear
coefficients on prices, a linear/nonlinear/cost characteristic, another three linear characteristics, another two
cost characteristics, demographics interacted with prices and the linear/nonlinear/cost characteristic, dense
parameter matrices, a log-linear cost specification, and local differentiation instruments.
"""
id_data = build_id_data(T=20, J=20, F=9)
keep = np.arange(id_data.size)
np.random.RandomState(0).shuffle(keep)
id_data = id_data[keep[:int(0.5 * id_data.size)]]
product_ids = id_data.market_ids.copy()
for t in np.unique(id_data.market_ids):
product_ids[id_data.market_ids == t] = np.arange(
(id_data.market_ids == t).sum())
simulation = Simulation(
product_formulations=(Formulation('1 + x + y + z + q'),
Formulation('1 + I(-prices) + x'),
Formulation('0 + log(x) + log(a) + log(b)')),
product_data={
'market_ids':
id_data.market_ids,
'firm_ids':
id_data.firm_ids,
'product_ids':
product_ids,
'clustering_ids':
np.random.RandomState(2).choice(range(30), id_data.size)
},
beta=[1, 1, 2, 3, 1],
sigma=[[0, +0.0, 0], [0, +0.5, 0], [0, -0.2, 2]],
pi=[[0, 0, 0], [2, 1, 0], [0, 0, 2]],
gamma=[0.1, 0.2, 0.3],
agent_formulation=Formulation('1 + f + g'),
integration=Integration('product', 4),
xi_variance=0.00001,
omega_variance=0.00001,
correlation=0.9,
rc_types=['linear', 'log', 'linear'],
costs_type='log',
seed=2,
)
simulation_results = simulation.replace_endogenous()
simulated_data_override = {
'demand_instruments':
np.c_[build_differentiation_instruments(
Formulation('0 + x + y + z + q'), simulation_results.product_data),
build_matrix(Formulation('0 + a + b'), simulation_results.
product_data)],
'supply_instruments':
np.c_[build_differentiation_instruments(
Formulation('0 + x + a + b'), simulation_results.product_data),
build_matrix(Formulation('0 + y + z + q'), simulation_results.
product_data)]
}
inside_diversion_micro_dataset = MicroDataset(
name="diversion from 1",
observations=simulation.N,
compute_weights=lambda _, p, a: np.tile(p.product_ids == 1,
(a.size, 1, 1 + p.size)),
market_ids=simulation.unique_market_ids[6:10],
)
outside_diversion_micro_dataset = MicroDataset(
name="diversion from outside",
observations=simulation.N,
compute_weights=lambda _, p, a: np.concatenate([
np.ones((a.size, 1, 1 + p.size)),
np.zeros((a.size, p.size, 1 + p.size))
],
axis=1),
market_ids=[simulation.unique_market_ids[8]],
)
simulated_micro_moments = simulation_results.replace_micro_moment_values([
MicroMoment(
name="demographic 1 expectation for 0",
dataset=MicroDataset(
name="product 0",
observations=simulation.N,
compute_weights=lambda _, p, a: np.tile(
p.product_ids.flat == 0, (a.size, 1)),
),
value=0,
compute_values=lambda _, p, a: np.tile(a.demographics[:, [1]],
(1, p.size)),
),
MicroMoment(
name="demographic 1 expectation for 0 and outside",
dataset=MicroDataset(
name="product 0 and outside",
observations=simulation.N,
compute_weights=lambda _, p, a: np.c_[
np.ones((a.size, 1)),
np.tile(p.product_ids.flat == 0, (a.size, 1))],
market_ids=simulation.unique_market_ids[1:4],
),
value=0,
compute_values=lambda _, p, a: np.tile(a.demographics[:, [1]],
(1, 1 + p.size)),
),
MicroMoment(
name="1 to 0 diversion ratio",
dataset=inside_diversion_micro_dataset,
value=0,
compute_values=lambda _, p, a: np.concatenate([
np.zeros((a.size, p.size, 1)),
np.tile(p.product_ids.flat == 0, (a.size, p.size, 1))
],
axis=2),
),
MicroMoment(
name="outside to 1 diversion ratio",
dataset=outside_diversion_micro_dataset,
value=0,
compute_values=lambda _, p, a: np.concatenate([
np.zeros((a.size, 1 + p.size, 1)),
np.tile(p.product_ids.flat == 1, (a.size, 1 + p.size, 1))
],
axis=2),
),
MicroMoment(
name="1 to outside diversion ratio",
dataset=inside_diversion_micro_dataset,
value=0,
compute_values=lambda _, p, a: np.concatenate([
np.ones((a.size, p.size, 1)),
np.zeros((a.size, p.size, p.size))
],
axis=2),
),
MicroMoment(
name="diversion interaction",
dataset=MicroDataset(
name="inside first and second",
observations=simulation.N,
compute_weights=lambda _, p, a: np.ones(
(a.size, p.size, p.size)),
market_ids=[simulation.unique_market_ids[12]],
),
value=0,
compute_values=lambda _, p, a:
(np.tile(p.X2[:, [1]],
(a.size, 1, p.size)) * np.tile(p.X2[:, [1]].T,
(a.size, p.size, 1))),
),
])
return simulation, simulation_results, simulated_data_override, simulated_micro_moments