API Documentation

The majority of the package consists of classes, which compartmentalize different aspects of the BLP model. There are some convenience functions as well.

Configuration Classes

Various components of the package require configurations for how to approximate integrals, solve fixed point problems, and solve optimimzation problems. Such configurations are specified with the following classes.

Formulation(formula[, absorb, …])

Configuration for designing matrices and absorbing fixed effects.

Integration(specification, size[, …])

Configuration for building integration nodes and weights.

Iteration(method[, method_options, …])

Configuration for solving fixed point problems.

Optimization(method[, method_options, …])

Configuration for solving optimization problems.

Data Construction Functions

There are also a number of convenience functions that can be used to construct common components of product and agent data.

build_matrix(formulation, data)

Construct a matrix according to a formulation.

build_blp_instruments(formulation, product_data)

Construct “sums of characteristics” excluded BLP instruments.

build_differentiation_instruments(…[, …])

Construct excluded differentiation instruments.

build_id_data(T, J, F)

Build a balanced panel of market and firm IDs.

build_ownership(product_data[, …])

Build ownership matrices, \(O\).

build_integration(integration, dimensions)

Build nodes and weights for integration over agent choice probabilities.

data_to_dict(data[, ignore_empty])

Convert a NumPy record array into a dictionary.

Problem Class

Given data and appropriate configurations, a BLP-type problem can be structured by initializing the following class.

Problem(product_formulations, product_data)

A BLP-type problem.

Once initialized, the following method solves the problem.

Problem.solve([sigma, pi, rho, beta, gamma, …])

Solve the problem.

Micro Moment Classes

Micro moment configurations can be passed to Problem.solve().

DemographicExpectationMoment(product_id, …)

Configuration for micro moments that match expectations of demographics for agents who choose certain products.

DemographicCovarianceMoment(X2_index, …[, …])

Configuration for micro moments that match covariances between product characteristics and demographics.

DiversionProbabilityMoment(product_id1, …)

Configuration for micro moments that match second choice probabilities of certain products for agents whose first choices are certain other products.

DiversionCovarianceMoment(X2_index1, …[, …])

Configuration for micro moments that match covariances between product characteristics of first and second choices.

Problem Results Class

Solved problems return the following results class.

ProblemResults

Results of a solved BLP problem.

The results can be converted into a dictionary.

ProblemResults.to_dict([attributes])

Convert these results into a dictionary that maps attribute names to values.

The following methods test the validity of overidentifying and model restrictions.

ProblemResults.run_hansen_test()

Test the validity of overidentifying restrictions with the Hansen \(J\) test.

ProblemResults.run_distance_test(unrestricted)

Test the validity of model restrictions with the distance test.

ProblemResults.run_lm_test()

Test the validity of model restrictions with the Lagrange multiplier test.

ProblemResults.run_wald_test(restrictions, …)

Test the validity of model restrictions with the Wald test.

In addition to class attributes, other post-estimation outputs can be estimated market-by-market with the following methods, which each return an array.

ProblemResults.compute_aggregate_elasticities([…])

Estimate aggregate elasticities of demand, \(\mathscr{E}\), with respect to a variable, \(x\).

ProblemResults.compute_elasticities([name, …])

Estimate matrices of elasticities of demand, \(\varepsilon\), with respect to a variable, \(x\).

ProblemResults.compute_diversion_ratios([…])

Estimate matrices of diversion ratios, \(\mathscr{D}\), with respect to a variable, \(x\).

ProblemResults.compute_long_run_diversion_ratios([…])

Estimate matrices of long-run diversion ratios, \(\bar{\mathscr{D}}\).

ProblemResults.compute_probabilities([market_id])

Estimate matrices of choice probabilities.

ProblemResults.extract_diagonals(matrices)

Extract diagonals from stacked \(J_t \times J_t\) matrices for each market \(t\).

ProblemResults.extract_diagonal_means(matrices)

Extract means of diagonals from stacked \(J_t \times J_t\) matrices for each market \(t\).

ProblemResults.compute_delta([agent_data, …])

Estimate mean utilities, \(\delta\).

ProblemResults.compute_costs([firm_ids, …])

Estimate marginal costs, \(c\).

ProblemResults.compute_approximate_prices([…])

Approximate equilibrium prices after firm or cost changes, \(p^*\), under the assumption that shares and their price derivatives are unaffected by such changes.

ProblemResults.compute_prices([firm_ids, …])

Estimate equilibrium prices after firm or cost changes, \(p^*\).

ProblemResults.compute_shares([prices, …])

Estimate shares.

ProblemResults.compute_hhi([firm_ids, …])

Estimate Herfindahl-Hirschman Indices, \(\text{HHI}\).

ProblemResults.compute_markups([prices, …])

Estimate markups, \(\mathscr{M}\).

ProblemResults.compute_profits([prices, …])

Estimate population-normalized gross expected profits, \(\pi\).

ProblemResults.compute_consumer_surpluses([…])

Estimate population-normalized consumer surpluses, \(\text{CS}\).

A parametric bootstrap can be used, for example, to compute standard errors for the above post-estimation outputs. The following method returns a results class with all of the above methods, which returns a distribution of post-estimation outputs corresponding to different bootstrapped samples.

ProblemResults.bootstrap([draws, seed, …])

Use a parametric bootstrap to create an empirical distribution of results.

Optimal instruments, which also return a results class instead of an array, can be estimated with the following method.

ProblemResults.compute_optimal_instruments([…])

Estimate feasible optimal or efficient instruments, \(Z_D^\text{opt}\) and \(Z_S^\text{opt}\).

Importance sampling can be used to create new integration nodes and weights. Its method also returns a results class.

ProblemResults.importance_sampling(draws[, …])

Use importance sampling to construct nodes and weights for integration.

Bootstrapped Problem Results Class

Parametric bootstrap computation returns the following class.

BootstrappedResults

Bootstrapped results of a solved problem.

This class has all of the same methods as ProblemResults, except for ProblemResults.bootstrap(), ProblemResults.compute_optimal_instruments(), and ProblemResults.importance_sampling(). It can also be converted into a dictionary.

BootstrappedResults.to_dict([attributes])

Convert these results into a dictionary that maps attribute names to values.

Optimal Instrument Results Class

Optimal instrument computation returns the following results class.

OptimalInstrumentResults

Results of optimal instrument computation.

The results can be converted into a dictionary.

OptimalInstrumentResults.to_dict([attributes])

Convert these results into a dictionary that maps attribute names to values.

They can also be converted into a Problem with the following method.

OptimalInstrumentResults.to_problem([…])

Re-create the problem with estimated feasible optimal instruments.

This method returns the following class, which behaves exactly like a Problem.

OptimalInstrumentProblem

A BLP problem updated with optimal excluded instruments.

Importance Sampling Results Class

Importance sampling returns the following results class:

ImportanceSamplingResults

Results of importance sampling.

The results can be converted into a dictionary.

ImportanceSamplingResults.to_dict([attributes])

Convert these results into a dictionary that maps attribute names to values.

They can also be converted into a Problem with the following method.

ImportanceSamplingResults.to_problem()

Re-create the problem with the agent data constructed from importance sampling.

This method returns the following class, which behaves exactly like a Problem.

ImportanceSamplingProblem

A BLP problem updated after importance sampling.

Simulation Class

The following class allows for evaluation of more complicated counterfactuals than is possible with ProblemResults methods, or for simulation of synthetic data from scratch.

Simulation(product_formulations, …[, …])

Simulation of data in BLP-type models.

Once initialized, the following method replaces prices and shares with equilibrium values that are consistent with true parameters.

Simulation.replace_endogenous([costs, …])

Replace simulated prices and market shares with equilibrium values that are consistent with true parameters.

A less common way to solve the simulation is to assume simulated prices and shares represent and equilibrium and to replace exogenous variables instead.

Simulation.replace_exogenous(X1_name[, …])

Replace exogenous product characteristics with values that are consistent with true parameters.

Simulation Results Class

Solved simulations return the following results class.

SimulationResults

Results of a solved simulation of synthetic BLP data.

The results can be converted into a dictionary.

SimulationResults.to_dict([attributes])

Convert these results into a dictionary that maps attribute names to values.

They can also be converted into a Problem with the following method.

SimulationResults.to_problem([…])

Convert the solved simulation into a problem.

Simulation results can also be used to compute micro moment values.

SimulationResults.compute_micro_values(…)

Compute simulated micro moment values \(v_{mt}\).

Structured Data Classes

Product and agent data that are passed or constructed by Problem and Simulation are structured internally into classes with field names that more closely resemble BLP notation. Although these structured data classes are not directly constructable, they can be accessed with Problem and Simulation class attributes. It can be helpful to compare these structured data classes with the data or configurations used to create them.

Products

Product data structured as a record array.

Agents

Agent data structured as a record array.

Multiprocessing

A context manager can be used to enable parallel processing for methods that perform market-by-market computation.

parallel(processes)

Context manager used for parallel processing in a with statement context.

Options and Example Data

In addition to classes and functions, there are also two modules that can be used to configure global package options and locate example data that comes with the package.

options

Global options.

data

Locations of example data that are included in the package for convenience.

Exceptions

When errors occur, they will either be displayed as warnings or raised as exceptions.

exceptions.MultipleErrors

Multiple errors that occurred around the same time.

exceptions.NonpositiveCostsError

Encountered nonpositive marginal costs in a log-linear specification.

exceptions.NonpositiveSyntheticCostsError

Encountered nonpositive synthetic marginal costs in a log-linear specification.

exceptions.InvalidParameterCovariancesError

Failed to compute standard errors because of invalid estimated covariances of GMM parameters.

exceptions.InvalidMomentCovariancesError

Failed to compute a weighting matrix because of invalid estimated covariances of GMM moments.

exceptions.DeltaNumericalError

Encountered a numerical error when computing \(\delta\).

exceptions.CostsNumericalError

Encountered a numerical error when computing marginal costs.

exceptions.MicroMomentsNumericalError

Encountered a numerical error when computing micro moments.

exceptions.XiByThetaJacobianNumericalError

Encountered a numerical error when computing the Jacobian of \(\xi\) (equivalently, of \(\delta\)) with respect to \(\theta\).

exceptions.OmegaByThetaJacobianNumericalError

Encountered a numerical error when computing the Jacobian of \(\omega\) (equivalently, of transformed marginal costs) with respect to \(\theta\).

exceptions.MicroMomentsByThetaJacobianNumericalError

Encountered a numerical error when computing the Jacobian of micro moments with respect to \(\theta\).

exceptions.MicroMomentCovariancesNumericalError

Encountered a numerical error when computing micro moment covariances.

exceptions.SyntheticPricesNumericalError

Encountered a numerical error when computing synthetic prices.

exceptions.SyntheticSharesNumericalError

Encountered a numerical error when computing synthetic shares.

exceptions.SyntheticDeltaNumericalError

Encountered a numerical error when computing the synthetic \(\delta\).

exceptions.SyntheticCostsNumericalError

Encountered a numerical error when computing synthetic marginal costs.

exceptions.SyntheticMicroMomentsNumericalError

Encountered a numerical error when computing synthetic micro moments.

exceptions.EquilibriumRealizationNumericalError

Encountered a numerical error when solving for a realization of equilibrium prices and shares.

exceptions.PostEstimationNumericalError

Encountered a numerical error when computing a post-estimation output.

exceptions.AbsorptionError

A fixed effect absorption procedure failed to properly absorb fixed effects.

exceptions.ClippedSharesError

Shares were clipped during the final iteration of the fixed point routine for computing \(\delta\).

exceptions.ThetaConvergenceError

The optimization routine failed to converge.

exceptions.DeltaConvergenceError

The fixed point computation of \(\delta\) failed to converge.

exceptions.SyntheticPricesConvergenceError

The fixed point computation of synthetic prices failed to converge.

exceptions.SyntheticDeltaConvergenceError

The fixed point computation of the synthetic \(\delta\) failed to converge.

exceptions.EquilibriumPricesConvergenceError

The fixed point computation of equilibrium prices failed to converge.

exceptions.ObjectiveReversionError

Reverted a problematic GMM objective value.

exceptions.GradientReversionError

Reverted problematic elements in the GMM objective gradient.

exceptions.DeltaReversionError

Reverted problematic elements in \(\delta\).

exceptions.CostsReversionError

Reverted problematic marginal costs.

exceptions.MicroMomentsReversionError

Reverted problematic micro moments.

exceptions.XiByThetaJacobianReversionError

Reverted problematic elements in the Jacobian of \(\xi\) (equivalently, of \(\delta\)) with respect to \(\theta\).

exceptions.OmegaByThetaJacobianReversionError

Reverted problematic elements in the Jacobian of \(\omega\) (equivalently, of transformed marginal costs) with respect to \(\theta\).

exceptions.MicroMomentsByThetaJacobianReversionError

Reverted problematic elements in the Jacobian of micro moments with respect to \(\theta\).

exceptions.HessianEigenvaluesError

Failed to compute eigenvalues for the GMM objective’s (reduced) Hessian matrix.

exceptions.FittedValuesInversionError

Failed to invert an estimated covariance when computing fitted values.

exceptions.SharesByXiJacobianInversionError

Failed to invert a Jacobian of shares with respect to \(\xi\) when computing the Jacobian of \(\xi\) (equivalently, of \(\delta\)) with respect to \(\theta\).

exceptions.IntraFirmJacobianInversionError

Failed to invert an intra-firm Jacobian of shares with respect to prices when computing \(\eta\).

exceptions.LinearParameterCovariancesInversionError

Failed to invert an estimated covariance matrix of linear parameters.

exceptions.GMMParameterCovariancesInversionError

Failed to invert an estimated covariance matrix of GMM parameters.

exceptions.GMMMomentCovariancesInversionError

Failed to invert an estimated covariance matrix of GMM moments.