Econometric models are
statistical model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model repre ...
s used in
econometrics
Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
. An econometric model specifies the
statistical
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon. An econometric model can be derived from a
deterministic
Determinism is the metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping mo ...
economic model
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed ...
by allowing for uncertainty, or from an economic model which itself is
stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
. However, it is also possible to use econometric models that are not tied to any specific economic theory.
A simple example of an econometric model is one that assumes that monthly
spending by consumers is linearly
dependent
A dependant (US spelling: dependent) is a person who relies on another as a primary source of income and usually assistance with activities of daily living
Activities of daily living (ADLs) is a term used in healthcare to refer to an individ ...
on consumers' income in the previous month. Then the model will consist of the equation
:
where ''C''
''t'' is
consumer spending
Consumer spending is the total money spent on final goods and services by individuals and households.
There are two components of consumer spending: induced consumption (which is affected by the level of income) and autonomous consumption (which ...
in month ''t'', ''Y''
''t''-1 is income during the previous month, and ''e
t'' is an
error term In mathematics and statistics, an error term is an additive type of error.
In writing, an error term is an instance of faulty language or grammar.
Common examples include:
* errors and residuals in statistics, e.g. in linear regression
* the error ...
measuring the extent to which the model cannot fully explain consumption. Then one objective of the
econometrician
Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8� ...
is to obtain estimates of the
parameter
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
s ''a'' and ''b''; these estimated parameter values, when used in the model's equation, enable predictions for future values of consumption to be made contingent on the prior month's income.
Formal definition
In
econometrics
Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics", '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8 ...
, as in
statistics
Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
in general, it is presupposed that the quantities being analyzed can be treated as
random variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...
s. An econometric model then is a
set
Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics Mathematics
*Set (mathematics), a collection of elements
*Category of sets, the category whose objects and morphisms are sets and total functions, respectively
Electro ...
of
joint probability distribution
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw- ...
s to which the true joint probability distribution of the variables under study is supposed to belong. In the case in which the elements of this set can be
index
Index (: indexes or indices) may refer to:
Arts, entertainment, and media Fictional entities
* Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index''
* The Index, an item on the Halo Array in the ...
ed by a finite number of real-valued ''parameters'', the model is called a
parametric model
In statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters.
Defi ...
; otherwise it is a
nonparametric
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric sta ...
or
semiparametric model In statistics, a semiparametric model is a statistical model that has parametric and nonparametric components.
A statistical model is a parameterized family of distributions: \ indexed by a parameter \theta.
* A parametric model is a model i ...
. A large part of econometrics is the study of methods for
selecting models,
estimating
Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is de ...
them, and carrying out
inference
Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinct ...
on them.
The most common econometric models are
structural
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
, in that they convey causal and
counterfactual
Counterfactual conditionals (also ''contrafactual'', ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be he ...
information,
and are used for policy evaluation. For example, an equation modeling consumption spending based on income could be used to see what consumption would be contingent on any of various hypothetical levels of income, only one of which (depending on the choice of a
fiscal policy
In economics and political science, fiscal policy is the use of government revenue collection ( taxes or tax cuts) and expenditure to influence a country's economy. The use of government revenue expenditures to influence macroeconomic variab ...
) will end up actually occurring.
Basic models
Some of the common econometric models are:
*
Linear regression
In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ...
*
Generalized linear model
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by ...
s
*
Probit
In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and ...
*
Logit
In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in Data transformation (statistics), data transformations.
Ma ...
*
Tobit
*
ARIMA
Arima, officially The Royal Chartered Borough of Arima is the easternmost and second largest in area of the three boroughs of Trinidad and Tobago. It is geographically adjacent to Sangre Grande and Arouca at the south central foothills of the ...
*
Vector Autoregression
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregres ...
*
Cointegration
In econometrics, cointegration is a statistical property describing a long-term, stable relationship between two or more time series variables, even if those variables themselves are individually non-stationary (i.e., they have trends). This means ...
*Hazard
Use in policy-making
Comprehensive models of
macroeconomic
Macroeconomics is a branch of economics that deals with the performance, structure, behavior, and decision-making of an economy as a whole. This includes regional, national, and global economies. Macroeconomists study topics such as output/ GDP ...
relationships are used by
central bank
A central bank, reserve bank, national bank, or monetary authority is an institution that manages the monetary policy of a country or monetary union. In contrast to a commercial bank, a central bank possesses a monopoly on increasing the mo ...
s and governments to evaluate and guide economic policy. One famous econometric model of this nature is the
Federal Reserve Bank
A Federal Reserve Bank is a regional bank of the Federal Reserve System, the central banking system of the United States. There are twelve in total, one for each of the twelve Federal Reserve Districts that were created by the Federal Reserve A ...
econometric model.
See also
*
Benefit financing model
{{Use dmy dates, date=October 2023
The Benefit Financing Model (BFM), also known as ''Unemployment Insurance Benefit Financing Model'' (UIBFM), is an actuarial forecasting model designed to help analysts project the condition of Unemployment Tru ...
References
Further reading
*
*
*
*
*
External links
Manuscript of Bruce Hansen's book on Econometrics* by
Mark Thoma
Mark Allen Thoma (born December 15, 1956) is a macroeconomist and econometrician and a professor of economics at the Department of Economics of the University of Oregon. Thoma is best known as a regular columnist for ''The Fiscal Times'' through ...
{{DEFAULTSORT:Econometric Model
*
Mathematical and quantitative methods (economics)
pl:Model ekonometryczny