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Econometrics is the application of
statistical methods Statistics (from German: ''Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industria ...
to economic data in order to give
empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
content to economic relationships.
M. Hashem Pesaran Mohammad Hashem Pesaran (born 30 March 1946) is a British-Iranian economist. He received his BSc in economics at the University of Salford (England) and his PhD in Economics at Cambridge University. Previously, Pesaran was professor at the Fa ...
(1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8–22 Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''
p. 1
p. 1–34 P. is an abbreviation or acronym that may refer to: * Page (paper), where the abbreviation comes from Latin ''pagina'' * Paris Herbarium, at the ''Muséum national d'histoire naturelle'' * ''Pani'' (Polish), translating as Mrs. * The ''Pacific Repo ...

Abstract
(
2008 File:2008 Events Collage.png, From left, clockwise: Lehman Brothers went bankrupt following the Subprime mortgage crisis; Cyclone Nargis killed more than 138,000 in Myanmar; A scene from the opening ceremony of the 2008 Summer Olympics in Beijing; ...
revision by J. Geweke, J. Horowitz, and H. P. Pesaran).
More precisely, it is "the quantitative analysis of actual economic
phenomena A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried W ...
based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships".
Jan Tinbergen Jan Tinbergen (; ; 12 April 19039 June 1994) was a Dutch economist who was awarded the first Nobel Memorial Prize in Economic Sciences in 1969, which he shared with Ragnar Frisch for having developed and applied dynamic models for the analysis of ...
is one of the two founding fathers of econometrics. The other,
Ragnar Frisch Ragnar Anton Kittil Frisch (3 March 1895 – 31 January 1973) was an influential Norwegian economist known for being one of the major contributors to establishing economics as a quantitative and statistically informed science in the early 20th ce ...
, also coined the term in the sense in which it is used today. A basic tool for econometrics is the
multiple linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is call ...
model. ''Econometric theory'' uses
statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical ...
and
mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...
to evaluate and develop econometric methods. Econometricians try to find
estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the ...
s that have desirable statistical properties including
unbiasedness In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called ''unbiased''. In stat ...
,
efficiency Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...
, and
consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
. ''Applied econometrics'' uses theoretical econometrics and real-world
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...
for assessing economic theories, developing
econometric model Econometric models are statistical models 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. An econome ...
s, analysing
economic history Economic history is the academic learning of economies or economic events of the past. Research is conducted using a combination of historical methods, statistical methods and the application of economic theory to historical situations and ins ...
, and
forecasting Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual ...
.


Basic models: linear regression

A basic tool for econometrics is the
multiple linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is call ...
model. In modern econometrics, other statistical tools are frequently used, but linear regression is still the most frequently used starting point for an analysis. Estimating a linear regression on two variables can be visualised as fitting a line through data points representing paired values of the independent and dependent variables. For example, consider
Okun's law In economics, Okun's law is an empirically observed relationship between unemployment and losses in a country's production. It is named after Arthur Melvin Okun, who first proposed the relationship in 1962. The "gap version" states that for every ...
, which relates
GDP Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced and sold (not resold) in a specific time period by countries. Due to its complex and subjective nature this measure is ofte ...
growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate (\Delta\ \text) is a function of an intercept ( \beta_0 ), a given value of GDP growth multiplied by a slope coefficient \beta_1 and an error term, \varepsilon: : \Delta\ \text = \beta_0 + \beta_1\text + \varepsilon. The unknown parameters \beta_0 and \beta_1 can be estimated. Here \beta_0 is estimated to be 0.83 and \beta_1 is estimated to be -1.77. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 1.77 * 1 points, other things held constant. The model could then be tested for
statistical significance In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis (simply by chance alone). More precisely, a study's defined significance level, denoted by \alpha, is the p ...
as to whether an increase in GDP growth is associated with a decrease in the unemployment, as hypothesized. If the estimate of \beta_1 were not significantly different from 0, the test would fail to find evidence that changes in the growth rate and unemployment rate were related. The variance in a prediction of the dependent variable (unemployment) as a function of the independent variable (GDP growth) is given in
polynomial least squares In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable ''x'' and the dependent variable ''y'' is modelled as an ''n''th degree polynomial in ''x''. Polynomial regression ...
.


Theory

Econometric theory uses
statistical theory The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. The theory covers approaches to statistical-decision problems and to statistical ...
and
mathematical statistics Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical an ...
to evaluate and develop econometric methods. Econometricians try to find
estimator In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the ...
s that have desirable statistical properties including
unbiasedness In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called ''unbiased''. In stat ...
,
efficiency Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...
, and
consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...
. An estimator is unbiased if its expected value is the true value of the parameter; it is consistent if it converges to the true value as the sample size gets larger, and it is efficient if the estimator has lower standard error than other unbiased estimators for a given sample size.
Ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the prin ...
(OLS) is often used for estimation since it provides the BLUE or "best linear unbiased estimator" (where "best" means most efficient, unbiased estimator) given the Gauss-Markov assumptions. When these assumptions are violated or other statistical properties are desired, other estimation techniques such as
maximum likelihood estimation In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statis ...
, generalized method of moments, or
generalized least squares In statistics, generalized least squares (GLS) is a technique for estimating the unknown parameters in a linear regression model when there is a certain degree of correlation between the residuals in a regression model. In these cases, ordinar ...
are used. Estimators that incorporate prior beliefs are advocated by those who favour
Bayesian statistics Bayesian statistics is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a ''degree of belief'' in an event. The degree of belief may be based on prior knowledge about the event, ...
over traditional, classical or "frequentist" approaches.


Methods

''Applied econometrics'' uses theoretical econometrics and real-world
data In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted ...
for assessing economic theories, developing
econometric model Econometric models are statistical models 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. An econome ...
s, analysing
economic history Economic history is the academic learning of economies or economic events of the past. Research is conducted using a combination of historical methods, statistical methods and the application of economic theory to historical situations and ins ...
, and
forecasting Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual ...
. Econometrics may use standard
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 repres ...
s to study economic questions, but most often they are with
observational Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data (information), data via the use of scienti ...
data, rather than in
controlled experiments A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable (i.e. confounding variables). This increases the reliability of the results, often through a comparison be ...
. In this, the design of observational studies in econometrics is similar to the design of studies in other observational disciplines, such as astronomy, epidemiology, sociology and political science. Analysis of data from an observational study is guided by the study protocol, although
exploratory data analysis In statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but pr ...
may be useful for generating new hypotheses. Economics often analyses systems of equations and inequalities, such as
supply and demand In microeconomics, supply and demand is an economic model of price determination in a Market (economics), market. It postulates that, Ceteris paribus, holding all else equal, in a perfect competition, competitive market, the unit price for a ...
hypothesized to be in equilibrium. Consequently, the field of econometrics has developed methods for
identification Identification or identify may refer to: *Identity document, any document used to verify a person's identity Arts, entertainment and media * ''Identify'' (album) by Got7, 2014 * "Identify" (song), by Natalie Imbruglia, 1999 * Identification ( ...
and
estimation 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 der ...
of
simultaneous equations model Simultaneous equations models are a type of statistical model in which the dependent variables are functions of other dependent variables, rather than just independent variables. This means some of the explanatory variables are jointly determined ...
s. These methods are analogous to methods used in other areas of science, such as the field of
system identification The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data f ...
in
systems analysis Systems analysis is "the process of studying a procedure or business to identify its goal and purposes and create systems and procedures that will efficiently achieve them". Another view sees system analysis as a problem-solving technique that b ...
and
control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...
. Such methods may allow researchers to estimate models and investigate their empirical consequences, without directly manipulating the system. One of the fundamental statistical methods used by econometricians is
regression analysis In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one ...
. Regression methods are important in econometrics because economists typically cannot use
controlled experiments A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable (i.e. confounding variables). This increases the reliability of the results, often through a comparison be ...
. Typically, the most readily available data is retrospective. However, retrospective analysis of observational data may be subject to
omitted-variable bias In statistics, omitted-variable bias (OVB) occurs when a statistical model leaves out one or more relevant variables. The bias results in the model attributing the effect of the missing variables to those that were included. More specifically, OV ...
, reverse causality, or other limitations that cast doubt on causal interpretation of the correlations. In the absence of evidence from controlled experiments, econometricians often seek illuminating
natural experiment A natural experiment is an empirical study in which individuals (or clusters of individuals) are exposed to the experimental and control conditions that are determined by nature or by other factors outside the control of the investigators. The pro ...
s or apply quasi-experimental methods to draw credible causal inference. Th
methods
include regression discontinuity designs, instrumental variables, and difference-in-differences.


Example

A simple example of a relationship in econometrics from the field of labour economics is: : \ln(\text) = \beta_0 + \beta_1 (\text) + \varepsilon. This example assumes that the
natural logarithm The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if ...
of a person's wage is a linear function of the number of years of education that person has acquired. The parameter \beta_1 measures the increase in the natural log of the wage attributable to one more year of education. The term \varepsilon is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, \beta_0 \mbox \beta_1 under specific assumptions about the random variable \varepsilon. For example, if \varepsilon is uncorrelated with years of education, then the equation can be estimated with
ordinary least squares In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the prin ...
. If the researcher could randomly assign people to different levels of education, the data set thus generated would allow estimation of the effect of changes in years of education on wages. In reality, those experiments cannot be conducted. Instead, the econometrician observes the years of education of and the wages paid to people who differ along many dimensions. Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education. For example, people born in certain places may have higher wages and higher levels of education. Unless the econometrician controls for place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages. The most obvious way to control for birthplace is to include a measure of the effect of birthplace in the equation above. Exclusion of birthplace, together with the assumption that \epsilon is uncorrelated with education produces a misspecified model. Another technique is to include in the equation additional set of measured covariates which are not instrumental variables, yet render \beta_1 identifiable. An overview of econometric methods used to study this problem were provided by
Card Card or The Card may refer to: * Various types of plastic cards: **By type ***Magnetic stripe card *** Chip card *** Digital card **By function ***Payment card ****Credit card **** Debit card ****EC-card ****Identity card ****European Health Insur ...
(1999).


Journals

The main journals that publish work in econometrics are ''
Econometrica ''Econometrica'' is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. The current editor-in-chief is Gui ...
'', the ''
Journal of Econometrics The ''Journal of Econometrics'' is a scholarly journal in econometrics. It was first published in 1973. Its current managing editors are Serena Ng and Elie Tamer, Torben Andersen and Xiaohong Chen serve as editors. The journal publishes work deal ...
'', ''
The Review of Economics and Statistics ''The'' ''Review of Economics and Statistics'' is a peer-reviewed 103-year-old general journal that focuses on applied economics, with specific relevance to the scope of quantitative economics. The ''Review'', edited at the Harvard University’s K ...
'', ''
Econometric Theory ''Econometric Theory'' is an economics journal specialising in econometrics, published by Cambridge Journals. Its current editor is Peter Phillips Peter Mark Andrew Phillips (born 15 November 1977) is a British businessman and the son of Ann ...
'', the ''
Journal of Applied Econometrics The ''Journal of Applied Econometrics'' is a peer-reviewed academic journal covering econometrics, published by John Wiley & Sons. It focuses on applications rather than theoretical issues. It was established in 1986 and is published seven times p ...
'', ''
Econometric Reviews ''Econometric Reviews'' is a scholarly econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New P ...
'', '' The Econometrics Journal'', and the ''
Journal of Business & Economic Statistics The ''Journal of Business & Economic Statistics'' is a quarterly peer-reviewed academic journal published by the American Statistical Association. The journal covers a broad range of applied problems in business and economic statistics, including ...
''.


Limitations and criticisms

Like other forms of statistical analysis, badly specified econometric models may show a
spurious relationship In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but '' not'' causally related, due to either coincidence or the presence of a certain third, uns ...
where two variables are correlated but causally unrelated. In a study of the use of econometrics in major economics journals, McCloskey concluded that some economists report
p-value In null-hypothesis significance testing, the ''p''-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small ''p''-value means ...
s (following the Fisherian tradition of
tests of significance A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...
of point null-hypotheses) and neglect concerns of
type II error In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...
s; some economists fail to report estimates of the size of effects (apart from
statistical significance In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis (simply by chance alone). More precisely, a study's defined significance level, denoted by \alpha, is the p ...
) and to discuss their economic importance. She also argues that some economists also fail to use economic reasoning for
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. However, the task can also involve the design of experiments such that the ...
, especially for deciding which variables to include in a regression. Stephen T. Ziliak and Deirdre N. McCloskey (2004). "Size Matters: The Standard Error of Regressions in the ''American Economic Review''," ''Journal of Socio-Economics'', 33(5), pp
527-46
(press +).
In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects. In such cases, economists rely on
observational studies In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample (statistics), sample to a statistical population, population where the dependent and independent variables, independ ...
, often using data sets with many strongly associated
covariate Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or demand ...
s, resulting in enormous numbers of models with similar explanatory ability but different covariates and regression estimates. Regarding the plurality of models compatible with observational data-sets, Edward Leamer urged that "professionals ... properly withhold belief until an inference can be shown to be adequately insensitive to the choice of assumptions".


See also

* Augmented Dickey–Fuller test *
Choice modelling Choice modelling attempts to model the decision process of an individual or segment via revealed preferences or stated preferences made in a particular context or contexts. Typically, it attempts to use discrete choices (A over B; B over A, B & C) ...
*
Cowles Foundation The Cowles Foundation for Research in Economics is an economic research institute at Yale University. It was created as the Cowles Commission for Research in Economics at Colorado Springs in 1932 by businessman and economist Alfred Cowles. In 1939 ...
*
Econometric software The following tables compare general and technical information for a number of statistical analysis packages. General information Operating system support ANOVA Support for various ANOVA methods Regression Support for various regression m ...
*
Financial econometrics Financial econometrics is the application of statistical methods to financial market data. Financial econometrics is a branch of financial economics, in the field of economics. Areas of study include capital markets, financial institutions, corpo ...
*
Financial modeling Financial modeling is the task of building an abstract representation (a model) of a real world financial situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio o ...
*
Granger causality The Granger causality test is a statistical hypothesis test for determining whether one time series is useful in forecasting another, first proposed in 1969. Ordinarily, regressions reflect "mere" correlations, but Clive Granger argued that cau ...
* Important publications in econometrics *
Macroeconomic model A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine the comparative statics and dynamics of aggregate quantities such as ...
*
Methodological individualism In the social sciences, methodological individualism is the principle that subjective individual motivation explains social phenomena, rather than class or group dynamics which are illusory or artificial and therefore cannot truly explain marke ...
*
Predetermined variables Predetermined variables are variables that were determined prior to the current period. In econometric models this implies that the current period error term is uncorrelated with current and lagged values of the predetermined variable but may be co ...
*
Single-equation methods (econometrics) A variety of methods are used in econometrics to estimate models consisting of a single equation. The oldest and still the most commonly used is the ordinary least squares method used to estimate linear regressions. A variety of methods are availab ...
*
Spatial econometrics Spatial econometrics is the field where spatial analysis and econometrics intersect. The term “spatial econometrics” was introduced for the first time by the Belgian economist Jean Paelinck (universally recognised as the father of the discipline ...
*
Unit root In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is ...


Further reading

* Econometric Theory book on Wikibooks * Giovannini, Enric
''Understanding Economic Statistics''
OECD Publishing, 2008,


References


External links


Journal of Financial Econometrics

Econometric Society



Econometric Links


(Index by the
Economics Network The Economics Network is one of the subject networks originally established by the Higher Education Academy (HEA). On its founding it was known as the ''Learning and Teaching Support Network (LTSN) for Economics'' later becoming independent of t ...
(UK))
Applied Econometric Association

The Society for Financial Econometrics

The interview with Clive Granger – Nobel winner in 2003, about econometrics
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