pyblp.OptimalInstrumentResults¶

class pyblp.OptimalInstrumentResults¶

Results of optimal instrument computation.

The OptimalInstrumentResults.to_problem() method can be used to update the original Problem with the computed optimal instruments.

problem_results¶

ProblemResults that was used to compute these optimal instrument results.

Type: ProblemResults

demand_instruments¶

Estimated optimal demand-side instruments for \(\theta\), denoted \(Z_D^\text{opt}\).

Type: ndarray

supply_instruments¶

Estimated optimal supply-side 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 demand-side instruments. This is only constructed if a supply side was estimated, and it can be changed in OptimalInstrumentResults.to_problem(). By default, this is the formulation for \(X_3^\text{ex}\) from Problem 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 supply-side instruments. This is only constructed if a supply side was estimated, and it can be changed in OptimalInstrumentResults.to_problem(). By default, this is the formulation for \(X_1^\text{ex}\) from Problem 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

expected_shares¶

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

Tutorial

Methods

`to_dict`([attributes])	Convert these results into a dictionary that maps attribute names to values.
`to_pickle`(path)	Save these results as a pickle file.
`to_problem`([supply_shifter_formulation, …])	Re-create the problem with estimated feasible optimal instruments.