

DARA
decreasing absolute risk aversion

data
data

DataDesk
Data analysis software, discussed at http://www.datadesk.com.

Deadweight Loss
Deadweight loss is the loss of consumer and producer surplus that is caused by inefficiency in a market. It may be caused by taxes, monopoly pricing, or other factors that cause inefficiency.

Debiasing strategies
All kind of strategies to test the robustness of an observed bias by attempting to
eliminate it under controlled conditions (destructive testing).

decision rule
Either (1) a function that maps from the current state to the agent's decision or choice or (2) a mapping from the expressed preferences of each of a group of agents to a group decision. The first is more relevant to decision theory and dynamic optimization; the second is relevant to game theory.
The phrase allocation rule is sometimes used to mean the same thing as decision rule. The term strategyproof has been defined in both contexts.

Decision strategies
Decision strategies specify the type and order that information is processed to determine a
choice. Some examples for decision strategies are:

decomposition theorem
Synonym for FWL theorem or FrischWaughLovell theorem.

Decreasing Returns to Scale
If a firm exhibits decreasing returns to scale, when it increases the use of inputs then output increases by a smaller proportion. For example, if the firm doubles the use of all inputs, then output will increase by less than double. With decreasing returns to scale, longrun average costs increase as output increases.

deductive
Characterizing a reasoning process of logical reasoning from stated propositions. Contrast inductive.

deep
A capital market may be said to be deep if it has great depth (which see).
May less formally be used to describe a market with large total market capitalization.

delta
As used with respect to options: The rate of change of a financial derivative's price with respect to changes in the price of the underlying asset. Formally this is a partial derivative.
A derivative is perfectly deltahedged if it is in a portfolio with a delta of zero. Financial firms make some effort to construct deltahedged portfolios.

delta method
Gives the distribution of a function of random variables for which one has a distribution. In particular, for the function g(b,l), where b and l are estimators for true values b_{0} and l_{0}: g(b,l) ~ N(g(b_{0},l_{0}), g'(b,l)var(b,l)g'(b,l)')

demand
A relation between each possible price and the quantity demanded at that price.
[Aspects of the population doing the demanding are often left implicit. An actual supply is not necessary to conceive of demand because demand involves hypothetical quantities.]

demand curve
For a given good, the demand curve is a relation between each possible price of the good and the quantity that would be bought at market sale at that price.
Drawn in introductory classes with this arrangement of the axes, although price is thought of as the independent variable:
Price  \
 \
 \
 \ Demand
________________________
Quantity

demand deposits
The money stored in the form of checking accounts at banks.

demand set
In a model, the set of the mostpreferred bundles of goods an agent can afford. This set is a function of the preference relation for this agent, the prices of goods, and the agent's endowment.
Assuming the agent cannot have a negative quantity of any good, the demand set can be characterized this way: Define L as the number of goods the agent might receive an allocation of. An allocation to the agent is an element of the space R_{+}^{l}; that is, the space of nonnegative real vectors of dimension L. Define >^{p} as a weak preference relation over goods; that is, x>^{p}x' states that the allocation vector x is weakly preferred to x' . Let e be a vector representing the quantities of the agent's endowment of each possible good, and p be a vector of prices for those goods. Let D(>^{p},p,e) denote the demand set. Then: D(>^{p},p,e) = {x: px <= pe and x >^{p} x' for all affordable bundles x'}.

democracy
Literally "rule by the people". This is a dictionary definition and is not considered sharp enough for academic use. Schumpeter (1942) contrasts these two definitions below and regards only the second one as useful and plausible enough to work with: "The eighteenthcentury philosophy of democracy may be couched in the following definition: the democratic method is that institutional arrangement for arriving at political decisions which realizes the common good by making the people itself decide issues through the election of individuals who are to assemble in order to carry out its will." (p 250) This "classical" definition has the problem that the will of the people is not clearly defined here (e.g. consider voting paradoxes) or known (perhaps even to the people at the time), and this can lead to ambiguity about whether a given political system is democratic. The following definition is preferred for its clarity but has a modern feel that is at some distance from the original dictionary definition. Political representation is assumed to be necessary here. "[T]he democratic method is that institutional arrangement for arriving at political decisions in which individuals acquire the power to decide by means of a competitive struggle for the people's vote." (p 269) More clearly: the democratic method is one in which people campaign competitively for the people's votes to achieve the power to make public decisions. This definition is the sharpest.

demography
The study of the size, growth, and age and geographical distribution of human populations, and births, deaths, marriages, and migrations.

density function
A synonym for pdf.

depreciation
The decline in price of an asset over time attributable to deterioration, obsolescence, and impending retirement. Applies particularly to physical assets like equipment and structures.

depth
An attribute of a market.
In securities markets, depth is measured by "the size of an order flow innovation required to change prices a given amount." (Kyle, 1985, p 1316).

derivatives
securities whose value is derived from the some other timevarying quantity. Usually that other quantity is the price of some other asset such as bonds, stocks, currencies, or commodities. It could also be an index, or the temperature. Derivatives were created to support an insurance market against fluctuations.

deterioration
The process or occurrence of an asset's declining productivity as it ages. This is a component of depreciation.

determinant
An operator defined on square matrices or the value of that operator. For a matrix B the determinant is denoted B. Its value is a unique scalar. Calculation of the value of the determinant is discussed in linear algebra books.

deterministic
Not random. A deterministic function or variable often means one that is not random, in the context of other variables available.
That is, those other variables determine the variable in question unerringly, by a function that would give the same value every time those other variables were given to it as arguments, unlike a random one which with some probability would give different answers.

development
The study of industrialization. development

DickeyFuller test
A DickeyFuller test is an econometric test for whether a certain kind of time series data has an autoregressive unit root. In particular in the time series econometric model y[t] = by[t1] + e[t], where t is an integer greater than zero indexing time, and b=1, let b^{OLS} denote the OLS estimate of b from a particular sample. Let T be the sample size.
Then the test statistic T*(b^{OLS} 1) has a known, documented distribution. Its value in a particular sample can be compared to that distribution to determine a probability that the original sample came from a unit root autoregressive process; that is, one in which b=1.

dictator game
A formal game with two players: Allocator A and Recipient R. They have received a windfall of, say, $1. The allocator, moving first, proposes a split so that A would receive x and R would receive 1x. The recipient then accepts, no matter what A proposed. In a subgame perfect equilibrium, A would offer R nothing. In experiments with human subjects, however, in which A and R do not know one another, A offers relatively large shares to R (often 5050). See also Ultimatum Game.

diffuse prior
In Bayesian statistics the investigator has to specify a prior distribution for a parameter, before the experiment or regression that is to update that distribution. A diffuse prior is a distribution of the parameter with equal probability for each possible value, coming as close as possible to representing the notion that the analyst hasn't a clue about the value of the parameter being estimated.

discount factor
In a multiperiod model, agents may have different utility functions for consumption (or other experiences) in different time periods. Usually in such models they value future experiences, but to a lesser degree than present ones. For simplicity the factor by which they discount next period's utility may be a constant between zero and one, and if so it is called a discount factor. One might interpret the discount factor not as a reduction in the appreciation of future events but as a subjective probability that the agent will die before the next period, and so discounts the future experiences not because they aren't valued, but because they may not occur.
A presentoriented agents discounts the future heavily and so has a LOW discount factor. Contrast discount rate and futureoriented. In a discrete time model where agents discount the future by a factor of b, one usually lets b=1/(1+r) where r is the discount rate.

discount rate
At least two meanings:
(1) The interest rate at which an agent discounts future events in preferences in a multiperiod model. Often denoted r. A presentoriented agent discounts the future heavily and so has a HIGH discount rate. Contrast 'discount factor'. See also 'futureoriented'. In a discrete time model where agents discount the future by a factor of b, one finds r=(1b)/b, following from b=1/(1+r).
(2) The Discount Rate is the name of the rate at which U.S. banks can borrow from the U.S. Federal Reserve.

discrete choice linear model
An econometric model: Pr(y_{i}=1) = F(X_{i}'b) = X_{i}'b

discrete choice model
An econometric model in which the actors are presumed to have made a choice from a discrete set. Their decision is modeled as endogenous. Often the choice is denoted y_{i}.

discrete regression models
Econometrics models in which the dependent variables assumes discrete values.

Diseconomies of Scale
See decreasing returns to scale

diseconomies of scale
Like economies of scale but with the implication that they are negative, so larger scale would increase cost per unit.

disintermediation
prevention of banks from flowing money from savers to borrowers as an effect of regulations; e..g the U.S. home mortgage market is partly blocked from banks and left to savings and loan institutions.

dismal science
Refers to economics, which because it is so often about tradeoffs, is widely thought to be depressing to study.

distribution function
A synonym for cdf.

Divisia index
A continuoustime index number. "The Divisia index is a weighted sum of growth rates, where the weights are the components' shares in total value."  Hulten (1973, p. 1017)
See also http://www.geocities.com/jeab_cu/paper2/paper2.htm.

DOJ
Abbreviaton for the U.S. national Department of Justice, which does among other things investigations into violations of antitrust law. See also FTC.

Domar aggregation
This seems to be the principle that the growth rate of an aggregate is the weighted average of the growth rates of its components, where each component is weighted by the share of the aggregate it makes up. The idea comes up in the context of national accounts and national statistics.

dominant design
After a technological innovcation and a subsequent era of ferment in an industry, a basic architecture of product or process that becomes the accepted market standard. From Abernathy& Utterback 1978, cited by A&T 1991. Dominant designs may not be better than alternatives nor innovative. They have the benchmark features to which subsequent designs are compared. Examples include the IBM 360 computer series and Ford's Model T automobile, and the IBM PC.

Dominant strategy
In some games, a player can choose a
strategy that "dominates" all other
strategies in his strategy set: Regardless of what he expects his
opponents to do, this strategy always yields a better payoff than
any other of his strategies.
An example of a game where each player has a dominant strategy is a
secondprice auction
with independent valuations of the bidders: Here bidding one's true
valuation is always a best response, regardless of one's opponents' bids.

Donsker's theorem
Synonymous with Functional Central Limit Theorem (FCLT).

double coincidence of wants
phrasing from Jevons (1893). "[T]he first difficulty in barter is to find two persons whose disposable possessions mutually suit each other's wants. There may be many people wanting, and many possessing those things wanted; but to allow of an act of barter there must be a double coincidence, which will rarely happen." That is, paraphrasing Ostroy and Starr, 1990, p 26, the double coincidence is the situation where the supplier of good A wants good B and the supplier of good B wants good A. The point is that the institution of money gives us a more flexible approach to trade than barter, which has the double coincidence of wants problem.

dummy variable
In an econometric model, a variable that marks or encodes a particular attribute. A dummy variable has the value zero or one for each observation, e.g. 1 for male and 0 for female. Same as indicator variables or binary variables.

dumping
An informal name for the practice of selling a product in a foreign country for less than either (a) the price in the domestic country, or (b) the cost of making the product. It is illegal in some countries to dump certain products into them, because they want to protect their own industries from such competition.

Durbin's h test
An algorithm for detecting autocorrelation in the errors of a time series regression. The implicit citation is to Durbin (1970). The h statistic is asymptotically distributed normally if the hypothesis that there is no autocorrelation.

DurbinWatson statistic
A test for firstorder serial correlation in the residuals of a time series regression. A value of 2.0 for the statistic indicates that there is no serial correlation. For tables to interpret the statistic see Greene pgs 738743, and context discussing them is on pages 424425. This result is biased toward the finding that there is no serial correlation if lagged values of the regressors are in the regression. Formally, the statistic is: d=(sum from t=2 to t=T of: (e_{t}e_{t1})^{2}/(sum from t=1 to t=T of: e_{t}^{2}) where the series of e_{t} are the residuals from a regression.

Dutch auction
Sequential biding game where the standing price is gradually lowered, typically
by means of an exogenous counting device (a clock, or a pointer), until it is stopped
by a bidder. The first bidder to halt the clock wins the item and pays the price where
he stopped the wheel. Dutch auctions are strategically equivalent to first price
sealed bid auctions. The name derives from the fact that many agricultural products
worldwide, but in particular Dutch flowers, are sold in this way.

dyadic map
synonym for dyadic transformation.

dyadic transformation
For whole numbers t and initial value x_{0} in [0,1], consider the mapping:
x_{t+1} = (2x_{t}) mod 1
"This law of motion is a standard example of chaotic dynamics. It is commonly known as the dyadic transformation. It is mixing (and hence also ergodic)."  Domowitz and Muus, 1992, p 2849
All the x_{t}'s will be in [0,1]. Their distribution will depend on the initial value x_{0}. If x_{0} is rational, the mapping will eventually become periodic (for large enough values of t). If x_{0} is irrational, the mapping is never periodic.

dynamic
means 'changing over time'.

dynamic inconsistency
A possible attribute of a player's strategy in a dynamic decisionmaking environment (such as a game). When the best plan that a player can make for some future period will not be optimal when that future period arrives, the plan is dynamically inconsistent. In one stylized example, addicted smokers face this problem  each day, their best plan is to smoke today, and to quit (and suffer) tomorrow in order to get health benefits subesquently. But the next day, that is once again the best plan, so they do not quit then either. (In a model this can come about if the planner values the present much more than the near future,  that is, has a low shortrun discount factor  but has a higher discount factor between two future periods.) Monetary policy is sometimes said to suffer from a dynamic inconsistency problem. Government policymakers are best off to promise that there will be no inflation tomorrow. But once agents and firms in the economy have fixed nominal contracts, the government would get seigniorage revenues from raising the level of inflation.

dynamic multipliers
The impulse responses in a distributed lag model.

dynamic optimization
dynamic optimization

dynamic optimizations
maximization problems to which the solution is a function; equivalently, optimization problems in infinitedimensional spaces.

dynamic programming
The study of dynamic optimization problems through the analysis of functional equations like value equations.
This phrase is normally used, analogously to linear programming to describe the study of discrete problems; e.g. those for which a decision must be made at times t for t=1,2,3,...

dynamical systems
The branch of mathematics describing processes in motion. Some are predictable and others are not. Two reasons a process might be unpredictable are that it might be random, and it might be chaotic.
