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Econometrics is the application of statistical methods 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
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 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, also coined the term in the sense in which it is used today. A basic tool for econometrics is the multiple linear regression model. ''Econometric theory'' uses statistical theory 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 a ...
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,
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. ''Applied econometrics'' uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analysing economic history, and forecasting.


Basic models: linear regression

A basic tool for econometrics is the multiple linear regression 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 ever ...
, 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 A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous obser ...
. 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.


Theory

Econometric theory uses statistical theory 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 a ...
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,
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. 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 (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, generalized method of moments, or generalized least squares 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 for assessing economic theories, developing econometric models, analysing economic history, and forecasting. 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 data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, ...
s to study economic questions, but most often they are with observational 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 betwe ...
. 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 prima ...
may be useful for generating new hypotheses. Economics often analyses systems of equations and inequalities, such as supply and demand hypothesized to be in equilibrium. Consequently, the field of econometrics has developed methods for identification and estimation of simultaneous equations models. 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 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. 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 betwe ...
. Typically, the most readily available data is retrospective. However, retrospective analysis of observational data may be subject to omitted-variable bias, 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 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. 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 Insuran ...
(1999).


Journals

The main journals that publish work in econometrics are '' Econometrica'', 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 ...
'', ''
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 A ...
'', the '' Journal of Applied Econometrics'', ''
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 Palg ...
'', '' The Econometrics Journal'', and the '' Journal of Business & Economic Statistics''.


Limitations and criticisms

Like other forms of statistical analysis, badly specified econometric models may show a spurious relationship 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 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, 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 deman ...
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 In statistics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationar ...
*
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) i ...
*
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 19 ...
* Econometric software * Financial econometrics * Financial modeling *
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 caus ...
* Important publications in econometrics * Macroeconomic model *
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 avai ...
*
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 disciplin ...
*
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 ...


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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