pyblp.OptimalInstrumentResults¶

class
pyblp.
OptimalInstrumentResults
¶ Results of optimal instrument computation.
The
OptimalInstrumentResults.to_problem()
method can be used to update the originalProblem
with the computed optimal instruments.
problem_results
¶ ProblemResults
that was used to compute these optimal instrument results. Type
ProblemResults

demand_instruments
¶ Estimated optimal demandside instruments for \(\theta\), denoted \(Z_D^\text{opt}\).
 Type
ndarray

supply_instruments
¶ Estimated optimal supplyside instruments for \(\theta\), denoted \(Z_S^\text{opt}\).
 Type
ndarray

supply_shifter_formulation
¶ Formulation
configuration for supply shifters that will by default be included in the full set of optimal demandside instruments. This is only constructed if a supply side was estimated, and it can be changed inOptimalInstrumentResults.to_problem()
. By default, this is the formulation for \(X_3^\text{ex}\) fromProblem
excluding any variables in the formulation for \(X_1^\text{ex}\). Type
Formulation or None

demand_shifter_formulation
¶ Formulation
configuration for demand shifters that will by default be included in the full set of optimal supplyside instruments. This is only constructed if a supply side was estimated, and it can be changed inOptimalInstrumentResults.to_problem()
. By default, this is the formulation for \(X_1^\text{ex}\) fromProblem
excluding any variables in the formulation for \(X_3^\text{ex}\). Type
Formulation or None

inverse_covariance_matrix
¶ Inverse of the sample covariance matrix of the estimated \(\xi\) and \(\omega\), which is used to normalize the expected Jacobians. If a supply side was not estimated, this is simply the sample estimate of \(1 / \sigma_{\xi}^2\).
 Type
ndarray

expected_xi_by_theta_jacobian
¶ Estimated \(E[\frac{\partial\xi}{\partial\theta} \mid Z]\).
 Type
ndarray

expected_omega_by_theta_jacobian
¶ Estimated \(E[\frac{\partial\omega}{\partial\theta} \mid Z]\).
 Type
ndarray

expected_prices
¶ Vector of expected prices conditional on all exogenous variables, \(E[p \mid Z]\), which may have been specified in
ProblemResults.compute_optimal_instruments()
. Type
ndarray
Vector of expected market shares conditional on all exogenous variables, \(E[s \mid Z]\).
 Type
ndarray

computation_time
¶ Number of seconds it took to compute optimal excluded instruments.
 Type
float

draws
¶ Number of draws used to approximate the integral over the error term density.
 Type
int

fp_converged
¶ Flags for convergence of the iteration routine used to compute equilibrium prices in each market. Rows are in the same order as
Problem.unique_market_ids
and column indices correspond to draws. Type
ndarray

fp_iterations
¶ Number of major iterations completed by the iteration routine used to compute equilibrium prices in each market for each error term draw. Rows are in the same order as
Problem.unique_market_ids
and column indices correspond to draws. Type
ndarray

contraction_evaluations
¶ Number of times the contraction used to compute equilibrium prices was evaluated in each market for each error term draw. Rows are in the same order as
Problem.unique_market_ids
and column indices correspond to draws. Type
ndarray
Examples
Methods
to_dict
([attributes])Convert these results into a dictionary that maps attribute names to values.
to_problem
([supply_shifter_formulation, …])Recreate the problem with estimated feasible optimal instruments.
