

IARA
increasing absolute risk aversion

IC constraint
IC stands for "incentive compatible". When solving a principalagent maximization problem for a contract that meets various criteria, the IC constraints are those that require agents to prefer to act in accordance with the solution. If the IC constraint were not imposed, the solution to the problem might be economically meaningless, insofar as it produced an outcome that met some criterion of optimality but which an agent would choose not to act in accord with. See also IR constraint.

ICAPM
Intertemporal CAPM. From Merton, 1973.

idempotent
A matrix M is idempotent if MM=M. (M times M equals M.) Example: the identity matrix, denoted I.

identification
A parameter in a model is identified if and only if complete knowledge of the joint distribution of the observed variables gives enough information to calculate the parameter exactly.
If the model has been written in such a way that its parameters can be consistently estimated from the observables, then the parameters are identified. There exist cases (mostly obscure) where parameters are identified but consistent estimators are not possible. (See, e.g. Gabrielsen, 1978) A model is identified if there is no observationally equivalent model. That is, potentially observable random variables in the model have different distributions for different values of the parameter.
Formally: Let h^{*} be a vector of unknown functions and distributions in an econometric model. Let H denote a set which h^{*} is known to belong. H is defined by the model's restrictions. Let P(h) denote the joint distribution of observable variables of the model for various elements of h in H. The distribution for the actual data will be assumed to be P(h^{*}). Now, vector h^{*} is identified within H if for all h in H such that h<>h^{*} it is true that P(h)<>P(h^{*}). Note: Linear models are either globally identified or there are an infinite number of observably equivalent ones. But for models that are nonlinear in parameters, "we can only talk about local properties." Thus the idea of locally identified models, which can be distinguished in data from any other 'close by' model.
"An identification problem occurs when a specifed set of assumptions combined with unlimited observations drawn by a specified sampling process does not reveal a distribution of interest."  Manski, Charles F. "Identification problems and decisions under ambiguity: empirical analysis of treatment response and normative analysis of treatment choice" Northwestern University Department of Economics and Institute for Policy Research, September 1998, p. 2

Identification
Charles Manski gave a brilliant example of what identification is all about:
Suppose that you observe the almost simultanous movement of a man his image in a mirror.
Does the mirror image cause the man's movements or reflect them? If you don't understand
something of optics and human behavior, you will not be able to tell.
(Manski, 1995, p. 1)
Methodological research in the social sciences uses statistical theory. The empirical
problem is to infer some feature of a population described by a probability distribution.
The data available to the researcher (be it field or experimental data) are observations
extracted from the population by some sampling process. In this framework, the statistical
and identification problems can be separated:
•Identification is about the conlusions that could be drawn if one could use the
sampling process to obtain an unlimited number of observations.
•Statistical inference is about the (generally weaker) conclusions that can be drawn
from a finite number of observations.
Identification problems cannot be solved by gathering more of the same kind of data. They
can be alleviated only by invoking stronger assumptions or by initiating new sampling
processes that yield different kinds of data.

identity matrix
An identity matrix is a square matrix of any dimension whose elements are ones on its northwesttosoutheast diagonal and zeroes everywhere else. Any square matrix multiplied by the identity matrix with those dimensions equals itself. One usually says 'the' identity matrix since in most contexts the dimension is unambiguous. It is standard to denote the identity matrix by I.

idle
Sometimes used to name the state of people who are not in school but also not working. Context is usually industrialized countries with established labor markets, and the idle are often poor.

IER
An abbreviation for the journal International Economic Review.

iff
abbreviation for "if and only if"

IGARCH
Integrated GARCH, a kind of econometric model of a stochastic process in which there is a unit root in a GARCH environment. The IGARCH(p,q) process was proposed in Engle and Bollerslev (1986).

IIA
stands for Irrelevance of Independent Alternatives, an assumption in a model. In a discrete choice setting, the multinomial logit model is appropriate only if the introduction or removal of a choice has no effect on the proportion of probability assigned to each of the other choices. This is a strong assumption; a standard example where IIA is not an appropriate assumption is if one compares a model of transportation choices between a car and a red bus, then introduces a blue bus. The blue bus is functionally like the red bus, so presumably its introduction draws ridership more heavily from the red bus than from the car.

iid
An abbreviation for "independently and identically distributed." One would say this about two or more random variables to describe their joint distribution. A common use is to describe ongoing disturbances to a stochastic process, indicating that they are not correlated to one another.

IJIO
An occasional abbreviation for the academic journal International Journal of Industrial Organization.

ILS
Indirect Least Squares, an approach to the estimation of simultaneous equations models. Steps: 1) Rearrange the structural form equations into reduced form 2) Estimate the reduced form parameters 3) Solve for the structural form parameters in terms of the reduced form parameters, and substitute in the estimates of the reduced form parameters to get estimates for the structural ones.

IMF
International Monetary Fund  an international organization with liquidity services to maintain financial stability.

implementable
A decision rule (a mapping from expressed preferences by each of a group of agents to a common decision) "is implementable (in Nash equilibrium) if there exists a game form whose Nash equilibrium outcome is the desired outcome for the true preferences."

implicit contract
A noncontractual agreement that corresponds to a Nash equilibrium to the repeated bilateral trading game other than the sequence of Nash equilibria to the oneshot trading game. In the labor market  an implicit contract is formally represented by a series of games in which the firm pays a salary and the employee works effectively because they expect to play the game again (continue the agreement) if it goes well, not because they have an explicit, enforceable contract. That is, "by implicit contracts is meant nonbinding commitments from employers to offer ... continuity of wages, employment, and working conditions, and from employees to forgo such temptations as shirking and quitting for better opportunities."  Granovetter, Ch 9

Imports
Goods and services that are produced abroad and purchased in oneā??s home country.

impossibility theorem
One of a class of theorems following Arrow (1951) showing that social welfare functions cannot have certain collections of desirable attributes in common.

impulse response function
Consider a shock to a system. A graph of the response of the system over time after the shock is an impulse response function graph. One use is in models of monetary systems. One graphs for example the percentage deviations in output or consumption over time after a onetime one percent increase in the money stock.

Inada conditions
A function f() satisfies the Inada conditions if: f(0) = 0, f'(0) = infinity, and f'(infinity) = 0. f() is usually a production function in this context.

inadmissible
A possible action by a player in a game may be said to be inadmissible if it is dominated by another feasible actions. The term comes the view of a game as a math problem. An action is or is not admissible as a candidate solution to the problem of choosing a utilitymaximizing strategy for the game player.
As used in Manski, Charles F. "Identification problems and decisions under ambiguity: empirical analysis of treatment response and normative analysis of treatment choice" Northwestern University Department of Economics and Institute for Policy Research, September 1998, p. 2

Incentive compatibility
In typical strategic interactions under incomplete information, different types
(of a player) can choose from among a menu of different actions (strategies) that comprises
the possibility that they mimic the behavior of other types (of the same, or of another player).
Incentive compatibility conditions ensure that different types (of each player) align themselves
such that they can be identified by their equilibrium choices.
Typically, they are used to prevent that some type profits from copying another type's action
(given the other types do not disguise themselves behind others' choices). More generally,
incentive compatibility conditions force a desired constellation of choices to form a
strategic equilibrium for a given array of types. In particular, they might as well ensure
that it be worthwhile for different types to choose the same action (the types pool on an action).
Yet in most economic problems, incentive compatibility conditions serve to induce a strategic
equilibrium which reveals the players' private information by having them choose different
'characteristic' equilibrium actions, i.e. they have the types 'sort themselves out'.
For a simple example, suppose several buyers that differ in their private (marginal) valuations of
some economic good (their types) select the quantity to buy from a seller. If the seller maximizes
his proceeds from sale, he will want the buyers with higher valuations to buy higher quantities, i.e. she
will want to separate her customers (or market segments) according to their marginal willingnesstopay.
To have such choices form a strategic equilibrium, the seller has to provide incentives to the high
valuations customers to buy higher quantities and to prevent market segments with lower
valuations from profitably micking the choices of highvaluation customers.
To meet both ends, it is often enough to simply offer a monotonic reward scheme that links
choices to rewards. In the example, it is enough that the seller rewards buying higher quantities by
offering a schedule of ever larger price discounts for larger quantities bought.
The basic idea that is with a monotonic reward scheme, lower types cannot find it worthwhile
to mimic the choices of higher types because higher types themselves find it worthwhile to choose
even more extreme actions which, in the end, are too costly to copy for lower types.
Thus, the price of having the types selfselect by giving monotonic rewards to them necessitates
that higher types are rewarded progressively higher rents for revealing their information,
relative to lower types. (For an illustration of this point, see the paragraph on information rents
in the entry rents.)
More generally, suppose the types are 'naturally ordered' in terms of increasing marginal profitability
(or costliness) of some economic action; e.g., the schedule of marginal willingnessestopay is
differently steep for different customers; different candidates have differently steep marginal
cost schedules in investing varying amounts in some activity, etc. Then, to put it in jargon,
any monotonic reward scheme "provides incentives to the types to separate themselves", i.e. it has
the players selfselect levels of actions which reveal the natural ordering of their types.
Incentive compatibility conditions occur throughout economics with incomplete information
because, as we have tried to argue, they are closely related to strategic equilibria with
certain features. Most often, incentive compatibility constraints are used to frame the ways of interaction
such as to create equilibria where the players' private information is revealed by their equilibrium choices.
Among important applications are the theory of optimal taxation of unobservable behavioral characteristics
in public finance, optimal selling schemes in nonlinear pricing and auctions, the optimal
regulation of firms under incomplete information, or incentive wage contracts eliciting effort inputs
from employees that can hide shirking under favorable conditions.

Income
The Concise Oxford Dictionary defines income as "receipts from one's lands, work,
investment etc." This definition has been adapted by economic theory, where, for
instance, a consumer may be said to maximize utility
subject to an income constraint. The meaning of income is somewhat modified in the
construction of income statistics, as generalized to national income.
Income in a microeconomic sense is the sum of earnings of all factors of production of an
individual. It includes all benefits to consumers as part of income, even benefits arising
from nonmarket activities ? such as the monetary value of the services of owneroccupied
housing or food grown and consumed on farms. This definition of income also includes
periodic and onetime transfers such as pensions, unemployment benefits, and bequests.

income elasticity
When used without another referent, appears to mean 'of consumption'. That is for income I and consumption C: income elasticity = (I/C)*(dC/dI) In one paper estimates were shown of .2 to .6 for a random sample of industrialized country middle class people. For more details see elasticity.

Increasing Returns to Scale
If a firm exhibits increasing returns to scale, when it increases the use of inputs then output increases by a greater proportion. For example, if the firm doubles the use of all inputs, then output will more than double. With increasing returns to scale, longrun average costs decrease as output increases.

indemnity
A kind of insurance, in which payment is made (often in previously determined amounts) for injuries suffered, not for the costs of recovery. The payment is designed not to be a dependent on anything the patient can control. From the point of view of the insurer, this mechanism avoids the moral hazard problem of victim spending too much in recovery.

independent
Two random variables X and Y are statistically independent if and only if their joint density (pdf) is the product of their marginal densities, that is if f(x,y)=f_{x}(x)f_{y}(y).
If two random variables are independent they are also uncorrelated.

independent private value
If a bidder has independent private values, it means that he is not influenced by the estimates of the other bidders, when determining how much an object is worth to him

indicator variable
In a regression, a variable that is one if a condition is true, and zero if it is false. Approximately synonymous with dummy variable, binary variable, or flag.

indifference curve
Represented for example on a graph whose horizontal and vertical axes are quantities of goods an individual might consume, an indifference curve represents a contour along which utility for that individual is constant. The curve represents a set of possible consumption bundles between which the individual is indifferent. Normally, with desirable goods on both axes (say, income today and income tomorrow) the curve has a certain shape, further from the origin when both quantities are positive than when one is zero.

indirect utility function
Denoted v(p, m) where p is a vector of prices for goods, and m is a budget in the same units as the prices. This function takes the value of the maximum utility that can be achieved by spending the budget m on the consumption goods with prices p.

individually rational
An allocation is individually rational if no agent is worse off in that allocation than with his endowment.

inductive
Characterizing a reasoning process of generalizing from facts, instances, or examples. Contrast deductive.

Industrial Revolution
A period commonly dated 17601830 in Britain (as in Mokyr, 1993, p 3 and Ashton, 1948). Characterized by: "a complex of technological advances: the substitution of machines for human skills and strength; the development of inanimate sources of power (fossil fuels and the steam engine); the invention, production, and use of new materials (iron for wood, vegetable for animal matter, mineral for vegetable matter); and the introduction and spread of a new mode of production, known by contemporaries as the factory system."  Landes (1993b) p 137.

industrialization
A historical phase and experience. The overall change in circumstances accompanying a society's movement population and resources from farm production to manufacturing production and associated services.

inf
Stands for 'infimum'. A value is an infimum with respect to a set if all elements of the set are at least as large as that value. An infimum exists in context where a minimum does not, because (say) the set is open; e.g. the set (0,1) has no minimum but 0 is an infimum.
inf is a mathematical operator that maps from a set to a value that is syntactically like the members of that set, although the value may not actually be a member of the set.

inflation
Reduction in value of a currency. Measured often by percentage increases in the general price level per year.

Information
A game
is of complete information if the payoffs of each player are common knowledge
among all the players, and it is of incomplete information if the utility
payoffs of each player, or certain parameters to it, remain private
information of each player. Games with incomplete information require the
players to form
beliefs
about their opponents' private information, and to evaluate uncertain streams of
payoff according to von NeumannMorgenstern
utility
function (or some other concept of expected utility).
A game with a perfect information is a game in which at each move in the game,
the player with the move knows the full history of the play of the game thus far.
Otherwise the game is called a game with imperfect information.
In a game of perfect recall, nobody ever forgets something they once knew.
An event A is common knowledge if all the players know that A occurred, and all
the players know that all the players know that A occurred, and all the players know that
all the players know that all the players know that A occurred, and so on, ad infinitum.

information
information

information matrix
In maximum likelihood estimation, the variance of the score vector. It's a k x k matrix, where k is the dimension of the vector of parameters being estimated. The vector of parameters is denoted q here: I(q) = var S(q) = E[(S(q)ES(q))^{2}] = E[S(q)^{2}] where the score is S(q) = dL(q)/d(q)
The information matrix can also be calculated by multiplying the Hessian of the loglikelihood function by (1).

information number
Synonym for Fisher information (which see).

Information processing
The information processing approach constitutes an important paradigm in psychology,
which evolved from computer science and communication science as an alternative to
behaviorism, which was the most influential paradigm from the early decades until
the mid of the 20th century. Compared to behaviorist theories, in which observable
responses are conceptualized as a function of observable stimuli, theories in the
information processing domain focus on mental operations intervening between stimulus
and response. Within social psychology this approach emphasizes the cognitive mediation
of social behavior, and, vice versa, the social impact on cognitive processes. Personal
involvement, affective states, or environmental factors can have a considerable influence
on logical thinking, stereotyping, social judgments and decisions. The sequence of
cognitive processes are typically decomposed into various stages, such as perception,
encoding, organization, inference making, retrieval, and judgment. These stages are
highly interdependent and characterized by various feedback loops. At all stages,
the individual's expectations or older knowledge structures come to interact with new
input information. It is quite typical for human information processing that datadriven
processes ("bottom up") and conceptually driven processes ("top down") mesh
(see Fiedler, 1996).

informational cascade
"An informational cascade occurs when it is optimal for an individual, having observed the actions of those ahead of him, to follow [that is, imitate] the behavior of the preceding individual without regard to his own information."  Bikhchandani, Hirshleifer, and Welch, 1992, p 992

INSEAD
An Americanstyle business school near Paris. Operates in English.

inside money
Any debt that is used as money. Is a liability to the issuer. Total amount of inside money in an economy is zero. Contrast outside money.

institution
There are several definitions. Here's one: 'An institution is a social mechanism through which men work together for common or like ends. It is a necessary arrangement wherever regulated group behavior over a broad field of activity is found. It is opposed in sociological thought to 'face to face' grouping and to local community forms of life ...' (Ware, p. 6)
For more see new institutionalism.

Institutionalism
(Neo)Institutionalism
is a theoretical school which is concerned with the question of which organizational
actions and routines become taken for granted. Within the school of NeoInstitutionalism
distinctions between the micro and the macro level of this theory are made.

instrumental variables
Either (1) an estimation technique, often abbreviated IV, or (2) the exogenous variables used in the estimation technique. Suppose one has a model: y = Xb + e Here y is a T x 1 vector of dependent variables, X is a T x k matrix of independent variables, b is a k x 1 vector of parameters to estimate, and e is a k x 1 vector of errors. OLS can be imagined, but suppose in the environment being modelled that the matrix of independent variables X may be correlated to the e's. Then using a T x k matrix of independent variables Z, correlated to the X's but uncorrelated to the e's one can construct an IV estimator that will be consistent: b_{IV} = (Z'X)^{1}Z'y The two stage least squares estimator is an important extension of this idea.
In that discussion above, the exogenous variables Z are called instrumental variables and the instruments (Z'Z)^{1}(Z'X) are estimates of the part of X that is not correlated to the e's.

instruments
When regressors are correlated to errors in a model, one may be able to replace the regressors by estimates for these regressors that are not correlated to the errors. This is the technique of instrumental variables, and the replacement regressors are called instruments.
The replacement regressors are constructed by running regressions of the original regressors on exogenous variables that are called the instrumental variables.

integrated
Said in reference to a random process. A random process is said to be 'integrated of order d' (sometimes denoted I(d)) for some natural number d if the series would be stationary after being firstdifferenced d times. Example: a random walk is I(1). Example: "Most macroeconomic flows and stocks that relate to population size, such as output or employment, are I(1)." They are growing. Example: "An I(2) series [might] be growing at an everincreasing rate."

intensive margin
Refers to the degree (intensity) to which a resource is utilized or applied. For example, the effort put in by a worker or the number of hours the worker works. Contrast extensive margin.

inter alia
"Among other things"

inter vivos
From Latin, 'between lives'. Used to describe gifts beetween people, usually from one generation to the next, which are like bequests except that both parties are alive. Quantities and timing of such gifts are studied empirically in the same way that quantities and purposes of bequests are subjects of empirical study.

interim efficient
Defined, apparently, in Holmstrom and Myerson (1983) with reference to Rothschild and Stiglitz (1976). In Imderst (2000) this term is used to characterize the set ('family') of RothschildSticlitz contracts in a particular model setting.

interior solution
A choice made by an agent that can be characterized as an optimum located at a tangency of two curves on a graph.
A classic example is the tangency between a consumer's budget line (characterizing the maximum amounts of good X and good Y that the consumer can afford) and the highest possible indifference curve. The slope of that tangency is where:
(marginal utility of X)/(price of X) = (marginal utility of Y)/(price of Y)
Contrast corner solution.

internal knowledge spillover
positive learning or knowledge externalities between programs or plants within a production organization.

Intertemporal decision making
Many economic decisions are intertemporal in the sense that current decisions
affect also the choices available in the future. Examples are saving and
retirement decisions of households, and investment decisions of firms. In the case
of saving, the saving decision made today affects not only the household's current
consumption but also his future consumption possibilities.
If someone saves more today, he can consume
less today and hence his current utility declines, but he can consume more in the future, and
his future utility increases.
As can be seen from the savings example, intertemporal decisions are characterized by some
kind of intertemporal tradeoff: If I give up something today, I want to be compensated for
the resulting utility loss in the future. The optimal intertemporal decision requires that current and
future changes of utility implied by current behavior correspond to the individual's
intertemporal preferences ? formally, that the rate of substitution be
equal to the rate of time preference.
An number of studies have shown that the standard theory of intertemporal choice is
frequently violated in experimental settings, just as standard (static)
expected utility (EU) theory of choice is systematically violated
(see Camerer, 1995). Intertemporal decisions are therefore
an important area of research in behavioral economics.

inverse demand function
A function p(q) that maps from a quantity of output to a price in the market; one might model the demand a firm faces by positing an inverse demand function and imagining that the firm chooses a quantity of output.

inverse Mills ratio
Usually denoted l(Z), and defined by l(Z)=phi(Z)/PHI(Z), where phi() is the standard normal pdf and PHI() is the standard normal cdf.

invertibility
In context of time series processes, represented for example by a lag polynomial, inverting means to solve for the e's (epsilons) in terms of the y's. One inverts moving average (MA) processes to get AR representations.

investment
Any use of resources intended to increase future production output or income.

IO
stands for 'Industrial Organization', the field of industry structure, conduct, and performance. By structure we usually mean the size of the firms in the industry  e.g. whether firms have monopoly power. IO

IPO
Stands for "initial public offering", the event of a firm's first sale of stock shares.

IPUMS
Integrated Public Use Microdata Series. These are collections of U.S. Census data, adapted for easy use by the University of Minnestota Social History Research Laboratory, at its Web site http://www.ipums.umn.edu.

IR constraint
IR stands for "individually rational". When solving a principalagent maximization problem for a contract that meets various criteria, the IR constraints are those that require agents to prefer to sign the contract than not to. If the IR constraint were not imposed, the solution to the problem might be economically meaningless, insofar as it was a contract that met some criterion of optimality but which an agent would refuse to sign. See also IC constraint.

IRS
The United States national tax collection agency, called the Internal Revenue Service.

is consistent for
means 'is a consistent estimator of'

isoquant
Given a production function, an isoquant is 'the locus of input combinations that yield the same output level.' (Chiang, p. 360) There is an isoquant set for each possible output level. Mathematically the isoquant is a level curve of the production function.
Examples and discussion is at Martin Osborne's web page: http://www.chass.utoronto.ca/~osborne/2x3/tutorial/ISOQUANT.HTM.

Ito process
A stochastic process: a generalized Wiener process with normally distributed jumps.

IV
abbrevation for Instrumental Variables, an estimation technique
