Transition Equations

Contains transition functions and corresponding helper functions.

Below the signature and purpose of a transition function and its helper functions is explained with a transition function called example_func:

example_func( sigma_points, params*)**:

The actual transition function.

Args:

• sigma_points: 4d numpy array of sigma_points or states being transformed.

  The shape is n_obs, n_mixtures, n_sigma, n_fac.

• params: 1d numpy array with coefficients specific to this transition function

Returns

• np.ndarray: Shape is n_obs, n_mixtures, n_sigma

index_tuples_example_func( factor, factors, period ):

Generate a list of index tuples for the params of the transition function.

Each index tuple contains four entries

• ‘transition’ (fix)

• period

• factor

• ‘some-name’

The transition functions have to be JAX jittable and differentiable. However, they should not be jitted yet.

linear(sigma_points, params)

Linear production function where the constant is the last parameter.

index_tuples_linear(factor, factors, period)

Index tuples for linear transition function.

translog(sigma_points, params)

Translog transition function.

The name is a convention in the skill formation literature even though the function is better described as a linear in parameters transition function with squares and interaction terms of the states.

index_tuples_translog(factor, factors, period)

Index tuples for the translog production function.

log_ces(sigma_points, params)

Log CES production function (KLS version).

index_tuples_log_ces(factor, factors, period)

Index tuples for the log_ces production function.

constant(sigma_points, params)

Constant production function should never be called.

index_tuples_constant(factor, factors, period)

Index tuples for the constant production function.

Modules Related to Simulation A note on endogeneity correction methods: