backward induction

Process of reasoning backwards in time to determine an optimal sequence of actions. The backward induction algorithm starts from the last period at which a decision is to be made and identifies the optimal action at that point in time. With this information, the process continues backwards until determining the optimal action at every point in time. In dynamic programming, backwards induction is one of the most frequently used methods for solving the Bellman Equation.

blue-collar occupation

Occupation related to manual work that might involved skilled or unskilled labor. Blue-collar occupations typically involve manufacturing, agriculture, construction, mining, among others.


A covariate always has a corresponding parameter and can be part of the rewards or other parts defined in params. It has to be differentiated from a state because a covariate is defined by some function \(g\) on a state \(s\).

decision rule

Function that maps an observation to an appropriate action.

discounted utility

The utility associated with a future point in time \(t+1\) but perceived at time \(t\). Future utility is discounted back to the present using a discount factor which captures the notion of impatience in individual preferences.

discrete choice

A term used in economics and control theory to refer to settings in which two or more discrete alternatives are available.

dynamic programming

A mathematical optimization and a computer programming method which allows to break up a complex problem into smaller sub-problems in a recursive manner.


A property of a problem or model where time usually lasts from 0 to some $T$.

finite mixture model

Model-based approach that accounts for the fact that regression models or distributions might differ across groups or subgroups of the population. A finite mixture approach then models the probability of belonging to each unobserved group and estimates the parameters of a regression for each group.


The assumption that economic agents form expectations of the future based on the structure of the economy today. Under this assumption, the announcement of a policy can alter agent’s expectations and the development of the economy.

maximum likelihood estimation

Method for estimating the parameters of a statistical model given certain observed data, by maximizing the likelihood function of the probability distribution of the data.

measurement error

Statistical concept defined as the difference between the measured value of a parameter and its true value.

non-pecuniary utility

Utility that is associated with non-monetary payoffs. In respy, we usually use the term to refer to components of the reward functions that are not related to wages.

observable characteristic

An observable characteristic is a trait of individuals which is exogenously determined. It can either be treated as constant or malleable by exogenous processes.

parameter space

Space of possible parameter values that define a particular mathematical or statistical model.

principle of optimality

Principle related to the dynamic programming method and prescribes that no matter which is the initial state and decision of the process, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision.

sheepskin effect

Concept that describes the phenomenon that people who posses a complete academic degree earn a higher income than people who do not hold a degree but posses the same amount of knowledge and skills.

state space

The state space is the entirety of states in a structural model. Each state in the state space is unique and can also be thought of as a position on a playing field.

The dimensions of the state space comprise the necessary information for the model which can either be endogenously determined like experiences or exogenously like observable characteristics.

stochastic shock

Unexpected or unpredictable event that affects the economy, either positively or negatively. Technically, it is an unpredictable change in exogenous factors.

unobserved heterogeneity

Term that describes the existence of unmeasured differences among individuals within a sample that are correlated with observed variables of interest. Unobserved variables in a model might lead to biased estimates.

rational expectations

Assumption that agents in a model have the ability to use all the information they have about how the economy operates to make their decisions.

white-collar occupation

Occupation related to a person who performs usually high skilled labor in an office or an administrative setting.