Notation#
The following table summarizes the notation in order of their appearance.
Symbol |
Explanation |
|---|---|
\(s_t\) |
state space at time \(t\) |
\(s_t\) |
state space at time \(t\) |
\(\mathcal{S}_t\) |
set of admissible states at time \(t\) |
\(a_t\) |
chosen alternative at time \(t\) |
\(\mathcal{A}\) |
set of feasible alternatives |
\(\pi\) |
particular policy |
\(\Pi\) |
set of implementable policies |
\(a_t^{\pi}(\cdot)\) |
state-dependent decision rule under \(\pi\) |
\(p_t(\cdot)\) |
transition probability distribution for state \(s_{t+1}\) |
\(\mathbb{E}_{p}[\cdot]\) |
expectation under probability measure p |
\(\mathcal{J}\) |
set of types |
\(e_{j,a}\) |
skill endowment of type j in alternative a |
\(h_t\) |
years of completed schooling at \(t\) |
\(\bf{k}_{t}\) |
vector of work-experience at \(t\) |
\(\bf{\epsilon}\) |
vector of productivity shocks |
\(r_a\) |
market equilibrium rental price in alternative a |
\(x_a(\cdot)\) |
occupation-specific skill level |
\(\Gamma_a(\cdot)\) |
deterministic component of occupation-specific skill level |
\(\bar{u}_a\) |
observable part per-period utility |
\(\bar{s}_t\) |
observable part state-space |
\(\mathcal{D}\) |
data structure |
\(M_D\) |
moments of observed data |
\(M_S(\theta)\) |
moments of simulated data under \(\theta\) |