def simulated_problem(request: Any) -> SimulatedProblemFixture:
"""Configure and solve a simulated problem, either with or without supply-side data. Preclude overflow with rho
bounds that are more conservative than the default ones.
"""
name, supply = request.param
simulation, simulation_results, simulated_data_override, simulated_micro_moments = (
request.getfixturevalue(f'{name}_simulation')
)
# override the simulated data
product_data = None
if simulated_data_override:
product_data = update_matrices(
simulation_results.product_data,
{k: (v, v.dtype) for k, v in simulated_data_override.items()}
)
# compute micro moments
micro_moments: List[Any] = []
if simulated_micro_moments:
micro_values = simulation_results.compute_micro(simulated_micro_moments)
for moment, value in zip(simulated_micro_moments, micro_values):
if isinstance(moment, DemographicExpectationMoment):
micro_moments.append(DemographicExpectationMoment(
moment.product_id, moment.demographics_index, value, moment.market_ids
))
elif isinstance(moment, DemographicCovarianceMoment):
micro_moments.append(DemographicCovarianceMoment(
moment.X2_index, moment.demographics_index, value, moment.market_ids
))
elif isinstance(moment, DiversionProbabilityMoment):
micro_moments.append(DiversionProbabilityMoment(
moment.product_id1, moment.product_id2, value, moment.market_ids
))
else:
assert isinstance(moment, DiversionCovarianceMoment)
micro_moments.append(DiversionCovarianceMoment(
moment.X2_index1, moment.X2_index2, value, moment.market_ids
))
# initialize and solve the problem
problem = simulation_results.to_problem(simulation.product_formulations[:2 + int(supply)], product_data)
solve_options = {
'sigma': simulation.sigma,
'pi': simulation.pi,
'rho': simulation.rho,
'beta': np.where(simulation._parameters.alpha_index, simulation.beta if supply else np.nan, np.nan),
'rho_bounds': (np.zeros_like(simulation.rho), np.minimum(0.9, 1.5 * simulation.rho)),
'method': '1s',
'check_optimality': 'gradient',
'micro_moments': micro_moments
}
problem_results = problem.solve(**solve_options)
return simulation, simulation_results, problem, solve_options, problem_results
def large_nested_blp_simulation() -> SimulationFixture:
"""Solve a simulation with 20 markets, varying numbers of products per market, a linear constant, log-normal
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, three
nesting groups with the same nesting parameter, and a log-linear cost specification.
"""
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,
'nesting_ids': np.random.RandomState(2).choice(['f', 'g', 'h'], id_data.size),
'clustering_ids': np.random.RandomState(2).choice(range(30), id_data.size)
},
beta=[1, 1, 2, 3, 1],
sigma=[
[0.5, 0],
[0.0, 2]
],
pi=[
[2, 1, 0],
[0, 0, 2]
],
gamma=[0.1, 0.2, 0.3],
rho=0.1,
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_micro_moments = [DemographicExpectationMoment(
product_id=None, demographics_index=1, value=0, market_ids=simulation.unique_market_ids[3:5]
)]
return simulation, simulation_results, {}, 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,
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