def get_future_value(num_periods, num_draws_emax, period, k,
draws_emax_transformed, payoffs_systematic, edu_max,
edu_start, periods_emax, states_all, mapping_state_idx,
delta):
""" Simulate expected future value.
"""
# Calculate maximum value
emax_simulated = 0.0
for i in range(num_draws_emax):
# Select draws for this draw
draws = draws_emax_transformed[i, :]
# Get total value of admissible states
total_payoffs = get_total_value(period, num_periods, delta,
payoffs_systematic, draws, edu_max,
edu_start, mapping_state_idx,
periods_emax, k, states_all)
# Determine optimal choice
maximum = max(total_payoffs)
# Recording expected future value
emax_simulated += maximum
# Scaling
emax_simulated = emax_simulated / num_draws_emax
# Finishing
return emax_simulated
def get_exogenous_variables(period, num_periods, num_states, delta,
periods_payoffs_systematic, shifts, edu_max,
edu_start, mapping_state_idx, periods_emax,
states_all):
""" Get exogenous variables for interpolation scheme. The unused argument
is present to align the interface between the PYTHON and FORTRAN
implementations.
"""
# Construct auxiliary objects
exogenous = np.tile(np.nan, (num_states, 9))
maxe = np.tile(np.nan, num_states)
# Iterate over all states.
for k in range(num_states):
# Extract systematic payoff
payoffs_systematic = periods_payoffs_systematic[period, k, :]
# Get total value
total_payoffs = get_total_value(period, num_periods, delta,
payoffs_systematic, shifts, edu_max,
edu_start, mapping_state_idx,
periods_emax, k, states_all)
# Implement level shifts
maxe[k] = max(total_payoffs)
diff = maxe[k] - total_payoffs
exogenous[k, :8] = np.hstack((diff, np.sqrt(diff)))
# Add intercept to set of independent variables and replace
# infinite values.
exogenous[:, 8] = 1
# Finishing
return exogenous, maxe
def pyth_evaluate(coeffs_a, coeffs_b, coeffs_edu, coeffs_home, shocks_cholesky,
is_interpolated, num_draws_emax, num_periods,
num_points_interp, is_myopic, edu_start, is_debug, edu_max,
min_idx, delta, data_array, num_agents_est, num_draws_prob,
tau, periods_draws_emax, periods_draws_prob):
""" Evaluate criterion function. This code allows for a deterministic
model, where there is no random variation in the rewards. If that is the
case and all agents have corresponding experiences, then one is returned.
If a single agent violates the implications, then the zero is returned.
"""
# Construct auxiliary object
shocks_cov = np.matmul(shocks_cholesky, shocks_cholesky.T)
is_deterministic = (np.count_nonzero(shocks_cholesky) == 0)
# Solve requested model.
base_args = (coeffs_a, coeffs_b, coeffs_edu, coeffs_home, shocks_cholesky,
is_interpolated, num_draws_emax, num_periods,
num_points_interp, is_myopic, edu_start, is_debug, edu_max,
min_idx, delta)
periods_payoffs_systematic, _, mapping_state_idx, periods_emax, \
states_all = pyth_solve(*base_args + (periods_draws_emax, ))
# Initialize auxiliary objects
contribs = np.tile(-HUGE_FLOAT, (num_agents_est * num_periods))
j = 0
# Calculate the probability over agents and time.
for _ in range(num_agents_est):
for period in range(num_periods):
# Extract observable components of state space as well as agent
# decision.
exp_a, exp_b, edu, edu_lagged = data_array[j, 4:].astype(int)
choice = data_array[j, 2].astype(int)
is_working = choice in [1, 2]
# Transform total years of education to additional years of
# education and create an index from the choice.
edu, idx = edu - edu_start, choice - 1
# Get state indicator to obtain the systematic component of the
# agents payoffs. These feed into the simulation of choice
# probabilities.
k = mapping_state_idx[period, exp_a, exp_b, edu, edu_lagged]
payoffs_systematic = periods_payoffs_systematic[period, k, :]
# Extract relevant deviates from standard normal distribution.
# The same set of baseline draws are used for each agent and period.
draws_prob_raw = periods_draws_prob[period, :, :].copy()
# If an agent is observed working, then the the labor market shocks
# are observed and the conditional distribution is used to determine
# the choice probabilities.
if is_working:
# Calculate the disturbance which are implied by the model
# and the observed wages.
dist = np.clip(np.log(data_array[j, 3]), -HUGE_FLOAT, HUGE_FLOAT) - \
np.clip(np.log(payoffs_systematic[idx]), -HUGE_FLOAT,
HUGE_FLOAT)
# If there is no random variation in payoffs, then the
# observed wages need to be identical their systematic
# components. The discrepancy between the observed wages and
# their systematic components might be small due to the
# reading in of the dataset (FORTRAN only).
if is_deterministic and (dist > SMALL_FLOAT):
contribs[:] = 1
return contribs
# Simulate the conditional distribution of alternative-specific
# value functions and determine the choice probabilities.
counts, prob_obs = np.tile(0, 4), 0.0
for s in range(num_draws_prob):
# Extract the standard normal deviates sample for the iteration.
draws_stan = draws_prob_raw[s, :]
# Construct independent normal draws implied by the agents
# state experience. This is need to maintain the correlation
# structure of the disturbances. Special care is needed in case
# of a deterministic model, as otherwise a zero division error
# occurs.
if is_working:
if is_deterministic:
prob_wage = HUGE_FLOAT
else:
if choice == 1:
draws_stan[0] = dist / shocks_cholesky[idx, idx]
else:
draws_stan[1] = (
dist - shocks_cholesky[idx, 0] *
draws_stan[0]) / shocks_cholesky[idx, idx]
prob_wage = norm.pdf(draws_stan[idx], 0.0, 1.0) / \
np.sqrt(shocks_cov[idx, idx])
else:
prob_wage = 1.0
# As deviates are aligned with the state experiences, create
# the conditional draws. Note, that the realization of the
# random component of wages align withe their observed
# counterpart in the data.
draws_cond = np.dot(shocks_cholesky, draws_stan.T).T
# Extract deviates from (un-)conditional normal distributions
# and transform labor market shocks.
draws = draws_cond[:]
draws[:2] = np.clip(np.exp(draws[:2]), 0.0, HUGE_FLOAT)
# Calculate total payoff.
total_payoffs = get_total_value(period, num_periods, delta,
payoffs_systematic, draws,
edu_max, edu_start,
mapping_state_idx,
periods_emax, k, states_all)
# Record optimal choices
counts[np.argmax(total_payoffs)] += 1
# Get the smoothed choice probability.
prob_choice = get_smoothed_probability(total_payoffs, idx, tau)
prob_obs += prob_choice * prob_wage
# Determine relative shares
prob_obs = prob_obs / num_draws_prob
# If there is no random variation in payoffs, then this implies
# that the observed choice in the dataset is the only choice.
if is_deterministic and (not (counts[idx] == num_draws_prob)):
contribs[:] = 1
return contribs
# Adjust and record likelihood contribution
contribs[j] = prob_obs
j += 1
# If there is no random variation in payoffs and no agent violated the
# implications of observed wages and choices, then the evaluation return
# a value of one.
if is_deterministic:
contribs[:] = np.exp(1.0)
# Finishing
return contribs
def pyth_simulate(periods_payoffs_systematic, mapping_state_idx, periods_emax,
states_all, shocks_cholesky, num_periods, edu_start, edu_max,
delta, num_agents_sim, periods_draws_sims, seed_sim):
""" Wrapper for PYTHON and F2PY implementation of sample simulation.
"""
record_simulation_start(num_agents_sim, seed_sim)
# Standard deviates transformed to the distributions relevant for
# the agents actual decision making as traversing the tree.
periods_draws_sims_transformed = np.tile(np.nan,
(num_periods, num_agents_sim, 4))
for period in range(num_periods):
periods_draws_sims_transformed[period, :, :] = transform_disturbances(
periods_draws_sims[period, :, :], shocks_cholesky)
# Simulate agent experiences
count = 0
# Initialize data
dataset = np.tile(MISSING_FLOAT, (num_agents_sim * num_periods, 8))
for i in range(num_agents_sim):
current_state = states_all[0, 0, :].copy()
dataset[count, 0] = i
record_simulation_progress(i)
# Iterate over each period for the agent
for period in range(num_periods):
# Distribute state space
exp_a, exp_b, edu, edu_lagged = current_state
k = mapping_state_idx[period, exp_a, exp_b, edu, edu_lagged]
# Write agent identifier and current period to data frame
dataset[count, :2] = i, period
# Select relevant subset
payoffs_systematic = periods_payoffs_systematic[period, k, :]
draws = periods_draws_sims_transformed[period, i, :]
# Get total value of admissible states
total_payoffs = get_total_value(period, num_periods, delta,
payoffs_systematic, draws, edu_max,
edu_start, mapping_state_idx,
periods_emax, k, states_all)
# Determine optimal choice
max_idx = np.argmax(total_payoffs)
# Record agent decision
dataset[count, 2] = max_idx + 1
# Record earnings
dataset[count, 3] = MISSING_FLOAT
if max_idx in [0, 1]:
dataset[count,
3] = payoffs_systematic[max_idx] * draws[max_idx]
# Write relevant state space for period to data frame
dataset[count, 4:8] = current_state
# Special treatment for education
dataset[count, 6] += edu_start
# Update work experiences and education
if max_idx == 0:
current_state[0] += 1
elif max_idx == 1:
current_state[1] += 1
elif max_idx == 2:
current_state[2] += 1
# Update lagged education
current_state[3] = 0
if max_idx == 2:
current_state[3] = 1
# Update row indicator
count += 1
record_simulation_stop()
# Finishing
return dataset
def pyth_evaluate(coeffs_a, coeffs_b, coeffs_edu, coeffs_home, shocks_cholesky,
is_interpolated, num_draws_emax, num_periods, num_points_interp,
is_myopic, edu_start, is_debug, edu_max, min_idx, delta, data_array,
num_agents_est, num_draws_prob, tau, periods_draws_emax,
periods_draws_prob):
""" Evaluate criterion function. This code allows for a deterministic
model, where there is no random variation in the rewards. If that is the
case and all agents have corresponding experiences, then one is returned.
If a single agent violates the implications, then the zero is returned.
"""
# Construct auxiliary object
shocks_cov = np.matmul(shocks_cholesky, shocks_cholesky.T)
is_deterministic = (np.count_nonzero(shocks_cholesky) == 0)
# Solve requested model.
base_args = (coeffs_a, coeffs_b, coeffs_edu, coeffs_home, shocks_cholesky,
is_interpolated, num_draws_emax, num_periods, num_points_interp,
is_myopic, edu_start, is_debug, edu_max, min_idx, delta)
periods_payoffs_systematic, _, mapping_state_idx, periods_emax, \
states_all = pyth_solve(*base_args + (periods_draws_emax, ))
# Initialize auxiliary objects
contribs = np.tile(-HUGE_FLOAT, (num_agents_est * num_periods))
j = 0
# Calculate the probability over agents and time.
for _ in range(num_agents_est):
for period in range(num_periods):
# Extract observable components of state space as well as agent
# decision.
exp_a, exp_b, edu, edu_lagged = data_array[j, 4:].astype(int)
choice = data_array[j, 2].astype(int)
is_working = choice in [1, 2]
# Transform total years of education to additional years of
# education and create an index from the choice.
edu, idx = edu - edu_start, choice - 1
# Get state indicator to obtain the systematic component of the
# agents payoffs. These feed into the simulation of choice
# probabilities.
k = mapping_state_idx[period, exp_a, exp_b, edu, edu_lagged]
payoffs_systematic = periods_payoffs_systematic[period, k, :]
# Extract relevant deviates from standard normal distribution.
# The same set of baseline draws are used for each agent and period.
draws_prob_raw = periods_draws_prob[period, :, :].copy()
# If an agent is observed working, then the the labor market shocks
# are observed and the conditional distribution is used to determine
# the choice probabilities.
if is_working:
# Calculate the disturbance which are implied by the model
# and the observed wages.
dist = np.clip(np.log(data_array[j, 3]), -HUGE_FLOAT, HUGE_FLOAT) - \
np.clip(np.log(payoffs_systematic[idx]), -HUGE_FLOAT,
HUGE_FLOAT)
# If there is no random variation in payoffs, then the
# observed wages need to be identical their systematic
# components. The discrepancy between the observed wages and
# their systematic components might be small due to the
# reading in of the dataset (FORTRAN only).
if is_deterministic and (dist > SMALL_FLOAT):
contribs[:] = 1
return contribs
# Simulate the conditional distribution of alternative-specific
# value functions and determine the choice probabilities.
counts, prob_obs = np.tile(0, 4), 0.0
for s in range(num_draws_prob):
# Extract the standard normal deviates sample for the iteration.
draws_stan = draws_prob_raw[s, :]
# Construct independent normal draws implied by the agents
# state experience. This is need to maintain the correlation
# structure of the disturbances. Special care is needed in case
# of a deterministic model, as otherwise a zero division error
# occurs.
if is_working:
if is_deterministic:
prob_wage = HUGE_FLOAT
else:
if choice == 1:
draws_stan[0] = dist / shocks_cholesky[idx, idx]
mean = 0.0
sd = abs(shocks_cholesky[idx, idx])
else:
draws_stan[1] = (dist - shocks_cholesky[idx, 0] *
draws_stan[0]) / shocks_cholesky[idx, idx]
mean = shocks_cholesky[idx, 0] * draws_stan[0]
sd = abs(shocks_cholesky[idx, idx])
prob_wage = norm.pdf(dist, mean, sd)
else:
prob_wage = 1.0
# As deviates are aligned with the state experiences, create
# the conditional draws. Note, that the realization of the
# random component of wages align withe their observed
# counterpart in the data.
draws_cond = np.dot(shocks_cholesky, draws_stan.T).T
# Extract deviates from (un-)conditional normal distributions
# and transform labor market shocks.
draws = draws_cond[:]
draws[:2] = np.clip(np.exp(draws[:2]), 0.0, HUGE_FLOAT)
# Calculate total payoff.
total_payoffs = get_total_value(period, num_periods,
delta, payoffs_systematic, draws, edu_max, edu_start,
mapping_state_idx, periods_emax, k, states_all)
# Record optimal choices
counts[np.argmax(total_payoffs)] += 1
# Get the smoothed choice probability.
prob_choice = get_smoothed_probability(total_payoffs, idx, tau)
prob_obs += prob_choice * prob_wage
# Determine relative shares
prob_obs = prob_obs / num_draws_prob
# If there is no random variation in payoffs, then this implies
# that the observed choice in the dataset is the only choice.
if is_deterministic and (not (counts[idx] == num_draws_prob)):
contribs[:] = 1
return contribs
# Adjust and record likelihood contribution
contribs[j] = prob_obs
j += 1
# If there is no random variation in payoffs and no agent violated the
# implications of observed wages and choices, then the evaluation return
# a value of one.
if is_deterministic:
contribs[:] = np.exp(1.0)
# Finishing
return contribs