dcegm.egm.solve_euler_equation

Auxiliary functions for the EGM algorithm.

Functions

calculate_candidate_solutions_from_euler_equation(...)

Calculate candidates for the optimal policy and value function.

compute_optimal_policy_and_value(...)

Compute EGM candidates for one state-choice and one continuous-state point.

solve_euler_equation(→ Tuple[jax.numpy.ndarray, ...)

Solve the Euler equation for given discrete choice and child states.

Module Contents

dcegm.egm.solve_euler_equation.calculate_candidate_solutions_from_euler_equation(continuous_grids_info: Dict[str, Any], continuous_state_space: Dict[str, jax.numpy.ndarray], marg_util_next: jax.numpy.ndarray, emax_next: jax.numpy.ndarray, state_choice_mat: Dict[str, jax.numpy.ndarray], idx_post_decision_child_states: jax.numpy.ndarray, model_funcs: Dict[str, Any], params: Dict[str, float]) → Tuple[jax.numpy.ndarray, jax.numpy.ndarray, jax.numpy.ndarray, jax.numpy.ndarray]

Calculate candidates for the optimal policy and value function.

dcegm.egm.solve_euler_equation.compute_optimal_policy_and_value(marg_util_next: jax.numpy.ndarray, emax_next: jax.numpy.ndarray, continuous_state_vec: Any, assets_grid_end_of_period: jax.numpy.ndarray, state_choice_vec: Any, model_funcs: Dict[str, Any], params: Dict[str, float]) → Tuple[jax.numpy.ndarray, jax.numpy.ndarray, jax.numpy.ndarray, jax.numpy.ndarray]

Compute EGM candidates for one state-choice and one continuous-state point.

Parameters:

  • marg_util_next – Marginal utilities in child states for one assets grid point.

  • emax_next – Expected maximum values in child states for one assets grid point.

  • continuous_state_vec – Continuous-state values for one continuous-state point.

  • assets_grid_end_of_period – Exogenous end-of-period asset grid.

  • state_choice_vec – Dictionary of discrete states and choice.

  • model_funcs – Processed model functions used by the EGM step.

  • params – Model parameter dictionary.

Returns:

A tuple (endog_grid, policy, value, expected_value) where each array is state-choice specific on the assets grid.

dcegm.egm.solve_euler_equation.solve_euler_equation(state_choice_vec: dict, marg_util_next: jax.numpy.ndarray, emax_next: jax.numpy.ndarray, compute_inverse_marginal_utility: Callable, compute_stochastic_transition_vec: Callable, params: Dict[str, float], discount_factor: float, interest_rate: float) → Tuple[jax.numpy.ndarray, jax.numpy.ndarray]

Solve the Euler equation for given discrete choice and child states.

We integrate over the exogenous process and income uncertainty and then apply the inverese marginal utility function.

Parameters:

  • marg_utils (np.ndarray) – 1d array of shape (n_stochastic_states,) containing the state-choice specific marginal utilities for a given point on the savings grid.

  • emax (np.ndarray) – 1d array of shape (n_stochastic_states,) containing the state-choice specific expected maximum value for a given point on the savings grid.

  • trans_vec_state (np.ndarray) – 1d array of shape (n_stochastic_states,) containing for each exogenous process state the corresponding transition probability.

  • compute_inverse_marginal_utility (callable) – Function for calculating the inverse marginal utility, which takes the marginal utility as only input. (n_stochastic_states, n_grid_wealth) with the maximum values.

  • params (dict) – Dictionary of model parameters.

Returns:

  • policy (np.ndarray): 1d array of the agent’s current state- and

    choice-specific consumption policy. Has shape (n_grid_wealth,).

  • expected_value (np.ndarray): 1d array of the agent’s current state- and

    choice-specific expected value. Has shape (n_grid_wealth,).

Return type:

tuple