Econometric model
Encyclopedia
Econometric models are statistical model
s used in econometrics
. An econometric model specifies the statistical
relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon under study. An econometric model can be derived from a deterministic
economic model by allowing for uncertainty, or from an economic model which itself is stochastic
. 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 on consumers' income in the previous month. Then the model will consist of the equation
where Ct is consumer spending in month t, Yt-1 is income during the previous month, and et is an error term measuring the extent to which the model cannot fully explain consumption. Then one objective of the econometrician is to obtain estimates of the parameter
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.
, as in statistics
in general, it is presupposed that the quantities being analyzed can be treated as random variable
s. An econometric model then is a set of joint probability distributions 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
ed by a finite number of real-valued parameters, the model is called a parametric model
; otherwise it is a nonparametric
or semiparametric model. A large part of econometrics is the study of methods for selecting
models, estimating
them, and carrying out inference
on them.
The most common econometric models are structural, in that they convey causal and counterfactual
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
) will end up actually occurring.
relationships are used by central bank
s and governments to evaluate and guide economic policy. Two famous econometric models of this nature are the Federal Reserve Bank
econometric model and the DRI-WEFA (now Global Insight
) model.
Statistical model
A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...
s used in econometrics
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
. An econometric model specifies the statistical
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon under study. An econometric model can be derived from a deterministic
Determinism
Determinism is the general philosophical thesis that states that for everything that happens there are conditions such that, given them, nothing else could happen. There are many versions of this thesis. Each of them rests upon various alleged connections, and interdependencies of things and...
economic model by allowing for uncertainty, or from an economic model which itself is stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
. 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
Consumption (economics)
Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally, consumption is defined in part by comparison to production. But the precise definition can vary because different schools of economists define production quite differently...
is linearly dependent on consumers' income in the previous month. Then the model will consist of the equation
where Ct is consumer spending in month t, Yt-1 is income during the previous month, and et is an error term measuring the extent to which the model cannot fully explain consumption. Then one objective of the econometrician is to obtain estimates of the parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....
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 econometricsEconometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
, as in statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
in general, it is presupposed that the quantities being analyzed can be treated as random variable
Random variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
s. An econometric model then is a set of joint probability distributions 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 set
In mathematics, the elements of a set A may be indexed or labeled by means of a set J that is on that account called an index set...
ed by a finite number of real-valued parameters, the model is called a parametric model
Parametric model
In statistics, a parametric model or parametric family or finite-dimensional model is a family of distributions that can be described using a finite number of parameters...
; otherwise it is a nonparametric
Non-parametric statistics
In statistics, the term non-parametric statistics has at least two different meanings:The first meaning of non-parametric covers techniques that do not rely on data belonging to any particular distribution. These include, among others:...
or semiparametric model. A large part of econometrics is the study of methods for selecting
Model selection
Model selection is the task of selecting a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered...
models, estimating
Estimation theory
Estimation theory is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured/empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the...
them, and carrying out inference
Statistical inference
In statistics, statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation...
on them.
The most common econometric models are structural, in that they convey causal and counterfactual
Counterfactual conditional
A counterfactual conditional, subjunctive conditional, or remote conditional, abbreviated , is a conditional statement indicating what would be the case if its antecedent were true...
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
Fiscal policy
In economics and political science, fiscal policy is the use of government expenditure and revenue collection to influence the economy....
) will end up actually occurring.
Basic models
Some of the common econometric models are:- Linear regressionLinear regressionIn statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
- Generalized linear modelGeneralized linear modelIn statistics, the generalized linear model 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 allowing the magnitude of the variance of each measurement to...
s - TobitTobit modelThe Tobit model is a statistical model proposed by James Tobin to describe the relationship between a non-negative dependent variable y_i and an independent variable x_i....
- ARIMAArimaThe Royal Borough of Arima is the fourth largest town in Trinidad and Tobago. Located east of the capital, Port of Spain, Arima supports the only organised indigenous community in the country, the Santa Rosa Carib Community and is the seat of the Carib Queen...
- Vector AutoregressionVector autoregressionVector autoregression is a statistical model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregression models. All the variables in a VAR are treated symmetrically; each variable has an equation explaining its evolution based on...
- CointegrationCointegrationCointegration is a statistical property of time series variables. Two or more time series are cointegrated if they share a common stochastic drift.-Introduction:...
Use in policy-making
Comprehensive models of macroeconomicMacroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...
relationships are used by central bank
Central bank
A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...
s and governments to evaluate and guide economic policy. Two famous econometric models of this nature are the Federal Reserve Bank
Federal Reserve Bank
The twelve Federal Reserve Banks form a major part of the Federal Reserve System, the central banking system of the United States. The twelve federal reserve banks together divide the nation into twelve Federal Reserve Districts, the twelve banking districts created by the Federal Reserve Act of...
econometric model and the DRI-WEFA (now Global Insight
Global Insight
Global Insight is the world's largest economics organization, serving over 3,800 clients in industry, finance and government worldwide, with revenues of over $95 million and employing more than 600 economists and other staff in 23 offices in 13 countries...
) model.