

UL
Literature
Autorenkollektiv (1997),
Bogart (1985),
Funk & Stoer (1997),
Hausmeister (1952),
Lotterbottel (1983)

ultimatum game
An experiment. There are two players, an allocator A and a recipient R, who in the experiment do not know one another. They have received a windfall, e.g., of $1. The allocator, moving first, proposes to split the windfall by proposing to take share x, so that A receives x and R receives 1x. The recipient can accept this allocation, or reject it in which case both get nothing. The subgame perfect equilibrium outcome is that A would offer the smallest possible amount to R, e.g., the share $.99 for A and $.01 for R, and that the recipient should accept. The experimental evidence, however, is that A offers a relatively large share to R, often 5050, and that R would often reject smaller positive amounts. We may interpret R's behavior has willingness to pay a cost to punish "unfair" splits. With regard to A's behavior  does A care about fairness too? Or is A incomemaximizing given R's likely behavior? See also Dictator Game.

unbalanced data
In a panel data set, there are observations across crosssection units (e.g. individuals or firms), and across time periods. Often such a data set can be represented by a completely filled in matrix of N units and T periods. In the "unbalanced data" case, however, the number of observations per time period varies. (Equivalently one might say that the number of observations per unit is not always the same.) One might handle this by letting T be the total number of time periods and N_{t} be the number of observations in each period.

unbiased
An estimator b of a distribution's parameter B is unbiased if the mean of b's sampling distribution is B. Formally, if: E[b] = B.

uncertainty
If outcomes will occur with a probability that cannot even be estimated, the decisionmaker faces uncertainty. Contrast risk.
This meaning to uncertainty is attributed to Frank Knight, and is sometimes referred to as Knightian uncertainty.
The decisionmaker can apply game theory even in such a circumstance, e.g. the choice of a dominant strategy.
Kreps (1988), p 31, writes that three standard ways of modeling choices made under conditions of uncertainty are with von NeumannMorgenstern expected utility over objective uncertainty, the Savage axioms for modeling subjective uncertainty, and the AnscombeAumann theory which is a middle course between them.
A recent ad for a new book edited by Haim Levy (Stochastic Dominance: Investment Decision Making under Uncertainty) considers three ways of modeling investment choices under uncertainty: by tradeoffs between mean and variance, by choices made by stochastic dominance, and nonexpected utility approaches using prospect theory.

uncorrelated
Two random variables X and Y are uncorrelated if E(XY)=E(X)E(y). Note that this does not guarantee they are independent.

under the null
Means "assuming the hypothesis being tested is true."

unemployment
The state of an individual looking for a paying job but not having one. Does not include fulltime students, the retired, children, or those not actively looking for a paying job.

uniform distribution
A continuous distribution over a range which we will denote [a,b]. Pdf is (xa)/(ba). Mean is .5*(a+b). Variance is (1/12)(ba)^{2}.

uniform kernel
The uniform kernel function is 1/2, for 1<u<1 and zero outside that range. Here u=(xx_{i})/h, where h is the window width and x_{i} are the values of the independent variable in the data, and x is the value of the independent variable for which one seeks an estimate. Unlike most kernel functions this one is unbounded in the x direction; so every data point will be brought into every estimate in theory, although outside three standard deviations they make hardly any difference. For kernel estimation.

uniform weak law of large numbers
See Wooldridge chapter, p 2651. The UWLLN applies to a nonrandom criterion function q_{t}(w_{t},q), if the sample average of q_{t}() for a sample {w_{t}} from a random time series is a consistent estimator for E(q_{t}()).
A law like this is proved with Chebyshev's inequality.

union threat model
"Firms may find it profitable to pay wages above the market clearing level to try to prevent unionization." In a model this could lead to job rationing and unemployment, just as efficiency wage models can.

unit root
An attribute of a statistical model of a time series whose autoregressive parameter is one. In a data series y[t] modeled by: y[t+1] = y[t] + other terms the series y[] has a unit root.

unit root test
A statistical test for the proposition that in a autoregressive statistical model of a time series, the autoregressive parameter is one. In a data series y[t], where t a whole number, modeled by: y[t+1] = ay[t] + other terms where a is an unknown constant, a unit root test would be a test of the hypothesis that a=1, usually against the alternative that a<1.

unity
A synonym for the number 'one'.

univariate
A discrete choice model in which the choice is made from a onedimensional set is said to be a univariate discrete choice model.

univariate binary model
For dependent variable y_{i} that can be only one or zero, and a continuous indepdendent scalar variable x_{i}, that: Pr(y_{i}=1)=F(x_{i}'b) Here b is a parameter to be estimated, and F is a distribution function. See probit and logit models for examples.

unrestricted estimate
An estimate of parameters taken without constraining the parameters. See "restricted estimate."

upper hemicontinuous
no disappearing points.

urban ghetto
As commonly defined by U.S. researchers: areas where 40 percent or more of residents are poor.

utilitarianism
A moral philosophy, generally operating on the principle that the utility (happiness or satisfaction) of different people can not only be measured but also meaningfully summed over people and that utility comparisons between people are meaningful. That makes it possible to achieve a welldefined societal optimum in allocations, production, and other decisions, and achieve the goal utilitarian British philosopher Jeremy Bentham described as "the greatest good for the greatest number."
This form of utilitarianism is thought of as extreme, now, partly because it is widely believed that there exists no generally acceptable way of summing utilities across people and comparing between them. Utility functions that can be compared and summed arithmetically are cardinal utility functions; utility functions that only represent the choices that would be made by an individual are ordinal.

utility
utility is the internal satisfaction that a person acts to optimize

utility curve
synonym for indifference curve.

Utility expected utility
The concept of utility enters economic analysis typically via the concept
of a utility function which itself is just a mathematical representation
of an individualīs preferences over alternative bundels of
consumption goods (or, more generally, over goods, services, and leisure).
If the individualīs preferences are complete, reflexive,
transitive, and continuous, then they can be represented by a continuous
utility function. In this sense, utility itself is an almost empty concept:
It is just a number associated with some consumption bundle. A general
treatment of the existence of an utility function is due to
Debreu (1964).

UVAR
Unstructured VAR (Vector Autoregression)

UWLLN
Uniform weak law of large numbers
