Editing Econometrics

{{Short description|Empirical statistical testing of economic theories}}
{{broader|Mathematical economics}}
{{EngvarB|date=October 2017}}
{{Use dmy dates|date=October 2017}}
{{Economics sidebar}}

'''Econometrics''' is an application of [[Statistics|statistical methods]] to economic data in order to give [[Empirical evidence|empirical]] content to economic relationships.<ref name="Pesaran">[[M. Hashem Pesaran]] (1987). "Econometrics", ''[[The New Palgrave: A Dictionary of Economics]]'', v. 2, p. 8 [pp. 8–22]. Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave'', [https://books.google.com/books?id=gBsgr7BPJsoC&dq=econometrics&pg=PA1=false p. 1] {{Webarchive|url=https://web.archive.org/web/20230315074724/https://books.google.com/books?id=gBsgr7BPJsoC&dq=econometrics&pg=PA1=false |date=15 March 2023 }} [pp. 1–34].  [http://www.dictionaryofeconomics.com/article?id=pde2008_E000007&edition=current&q=Econometrics&topicid=&result_number=2 Abstract] {{webarchive|url=https://web.archive.org/web/20120518001558/http://www.dictionaryofeconomics.com/article?id=pde2008_E000007&edition=current&q=Econometrics&topicid=&result_number=2 |date=18 May 2012 }} ([[The New Palgrave Dictionary of Economics|2008]] revision by J. Geweke, J. Horowitz, and H. P. Pesaran).</ref> More precisely, it is "the quantitative analysis of actual economic [[Phenomenon|phenomena]] based on the concurrent development of theory and observation, related by appropriate methods of inference."<ref>[[Paul Samuelson|P. A. Samuelson]], [[Tjalling Koopmans|T. C. Koopmans]], and [[Richard Stone|J. R. N. Stone]] (1954). "Report of the Evaluative Committee for ''Econometrica''", ''Econometrica'' 22(2), p. 142. [p [https://www.jstor.org/pss/1907538 p. 141]-146], as described and cited in Pesaran (1987) above.</ref> An introductory [[economics]] textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships."<ref>Paul A. Samuelson and [[William D. Nordhaus]], 2004. ''[[Economics (textbook)|Economics]]''. 18th ed., McGraw-Hill, p. 5.</ref> [[Jan Tinbergen]] is one of the two founding fathers of econometrics.<ref>{{cite web|url=http://www.elsevierweekblad.nl/Economie/achtergrond/2015/10/1969---Jan-Tinbergen-Nobelprijs-economie-2700626W/?masterpageid=5573|title=1969 - Jan Tinbergen: Nobelprijs economie - Elsevierweekblad.nl|date=12 October 2015|website=elsevierweekblad.nl|access-date=1 May 2018|url-status=live|archive-url=https://web.archive.org/web/20180501212351/https://www.elsevierweekblad.nl/Economie/achtergrond/2015/10/1969---Jan-Tinbergen-Nobelprijs-economie-2700626W/?masterpageid=5573|archive-date=1 May 2018|df=dmy-all}}</ref><ref>Magnus, Jan & Mary S. Morgan (1987) ''The ET Interview: Professor J. Tinbergen'' in: 'Econometric Theory 3, 1987, 117–142.</ref><ref>Willlekens, Frans (2008) ''International Migration in Europe: Data, Models and Estimates.'' New Jersey. John Wiley & Sons: 117.</ref> The other, [[Ragnar Frisch]], also coined the term in the sense in which it is used today.<ref>• H. P. Pesaran (1990), "Econometrics", ''Econometrics: The New Palgrave'', [https://books.google.com/books?id=gBsgr7BPJsoC&dq=econometrics&pg=PA2=false p. 2] {{Webarchive|url=https://web.archive.org/web/20230315074724/https://books.google.com/books?id=gBsgr7BPJsoC&dq=econometrics&pg=PA2=false |date=15 March 2023 }}, citing Ragnar Frisch (1936), "A Note on the Term 'Econometrics'", ''Econometrica'', 4(1), p. 95.<br />&nbsp;&nbsp; {{*}} Aris Spanos (2008), "statistics and economics",  ''[[The New Palgrave Dictionary of Economics]]'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_S000502&edition=current&q=statistics&topicid=&result_number=1 Abstract.] {{webarchive|url=https://web.archive.org/web/20120518001702/http://www.dictionaryofeconomics.com/article?id=pde2008_S000502&edition=current&q=statistics&topicid=&result_number=1 |date=18 May 2012 }}</ref>

A basic tool for econometrics is the [[multiple linear regression]] model.<ref name="Greene Econometrics – multiple linear regression model" /> ''Econometric theory'' uses [[statistical theory]] and [[mathematical statistics]] to evaluate and develop econometric methods.<ref name="Greene Econometrics – mathematical statistics and statistical theory">{{cite book | author=Greene, William | title=Econometric Analysis | date=2012 | publisher=Pearson Education | isbn=9780273753568 | pages=34, 41–42 | edition=7th }}</ref><ref name="Wooldridge Econometrics – mathematical statistics">{{cite book | author=Wooldridge, Jeffrey | title=Introductory Econometrics: A Modern Approach | date=2012 | publisher=South-Western Cengage Learning | isbn=9781111531041 | page=2 | edition=5th | chapter=Chapter 1: The Nature of Econometrics and Economic Data }}</ref> Econometricians try to find [[estimator]]s that have desirable statistical properties including [[Bias of an estimator|unbiasedness]], [[Efficiency (statistics)|efficiency]], and [[Consistent estimator|consistency]]. ''Applied econometrics'' uses theoretical econometrics and real-world [[economic data|data]] for assessing economic theories, developing [[econometric model]]s, analysing [[economic history]], and [[Economic forecasting|forecasting]].

==Basic models: linear regression==
A basic tool for econometrics is the [[multiple linear regression]] model.<ref name="Greene Econometrics – 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.<ref name="Greene Econometrics – multiple linear regression model">{{cite book|author=Greene, William|title=Econometric Analysis|date=2012|publisher=Pearson Education|isbn=9780273753568|pages=47–48|edition=7th|chapter=Chapter 1: Econometrics | quote = Ultimately, all of these will require a common set of tools, including, for example, the multiple regression model, the use of moment conditions for estimation, instrumental variables (IV) and maximum likelihood estimation. With that in mind, the organization of this book is as follows: The first half of the text develops fundamental results that are common to all the applications. The concept of multiple regression and the linear regression model in particular constitutes the underlying platform of most modeling, even if the linear model itself is not ultimately used as the empirical specification.}}</ref> Estimating a linear regression on two variables can be visualized as fitting a line through data points representing paired values of the independent and dependent variables.

[[File:Okuns law differences 1948 to mid 2011.png|thumb|right|Okun's law representing the relationship between GDP growth and the unemployment rate. The fitted line is found using regression analysis.]]

For example, consider [[Okun's law]], which relates [[Gross domestic product|GDP]] growth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate (<math>\Delta\ \text{Unemployment}</math>) is a function of an intercept (<math> \beta_0 </math>), a given value of GDP growth multiplied by a slope coefficient <math> \beta_1 </math> and an error term, <math>\varepsilon</math>:

:<math> \Delta\ \text {Unemployment} = \beta_0 + \beta_1\text{Growth} + \varepsilon. </math>

The unknown parameters <math> \beta_0 </math> and <math> \beta_1 </math> can be estimated. Here <math> \beta_0 </math> is estimated to be 0.83 and <math> \beta_1 </math> 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, [[Ceteris paribus|other things held constant]]. The model could then be tested for [[statistical significance]] as to whether an increase in GDP growth is associated with a decrease in the unemployment, as [[Statistical hypothesis testing|hypothesized]]. If the estimate of <math> \beta_1 </math> 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==
{{see also|Estimation theory}}
Econometric theory uses [[statistical theory]] and [[mathematical statistics]] to evaluate and develop econometric methods.<ref name="Greene Econometrics – mathematical statistics and statistical theory" /><ref name="Wooldridge Econometrics – mathematical statistics" /> Econometricians try to find [[estimator]]s that have desirable statistical properties including [[Bias of an estimator|unbiasedness]], [[Efficiency (statistics)|efficiency]], and [[Consistent estimator|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 theorem|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. [[Bayes estimator|Estimators that incorporate prior beliefs]] are advocated by those who favour [[Bayesian statistics]] over traditional, classical or [[Frequentist probability|"frequentist" approaches]].

==Methods==
{{Main|Methodology of econometrics}}

''Applied econometrics'' uses theoretical econometrics and real-world [[economic data|data]] for assessing economic theories, developing [[econometric model]]s, analysing [[economic history]], and [[Economic forecasting|forecasting]].<ref>[[Clive Granger]] (2008). "forecasting",
''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_F000161&edition=current&q=forecast&topicid=&result_number=7 Abstract.] {{webarchive|url=https://web.archive.org/web/20120518001935/http://www.dictionaryofeconomics.com/article?id=pde2008_F000161&edition=current&q=forecast&topicid=&result_number=7 |date=18 May 2012 }}</ref>

Econometrics uses standard [[statistical model]]s to study economic questions, but most often these are based on [[observational study|observational]] data, rather than data from [[experiment|controlled experiments]].<ref name=Introductory_econometrics>{{cite book |last=Wooldridge |first=Jeffrey |date=2013 |title=Introductory Econometrics, A modern approach |publisher=South-Western, Cengage learning |isbn=978-1-111-53104-1}}</ref> 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]] may be useful for generating new hypotheses.<ref>[[Herman Wold|Herman O. Wold]] (1969). "Econometrics as Pioneering in Nonexperimental Model Building", ''Econometrica'', 37(3), pp. [https://www.jstor.org/pss/1912787 369] {{Webarchive|url=https://web.archive.org/web/20170824221048/http://www.dictionaryofeconomics.com/article?id=pde2008_E000186&q=Experimental |date=24 August 2017 }}-381.</ref> Economics often analyses systems of equations and inequalities, such as [[supply and demand]] hypothesized to be in [[Economic equilibrium|equilibrium]]. Consequently, the field of econometrics has developed methods for [[parameter identification problem|identification]] and [[estimation theory|estimation]] of [[simultaneous equations model]]s. These methods are analogous to methods used in other areas of science, such as the field of [[system identification]] in [[systems analysis]] and [[control theory]]. Such methods may allow researchers to estimate models and investigate their empirical consequences, without directly manipulating the system.

In the absence of evidence from controlled experiments, econometricians often seek illuminating [[natural experiment]]s or apply [[Quasi-experiment|quasi-experimental methods]] to draw credible causal inference.<ref>{{cite journal |last1=Angrist |first1=Joshua D. |author-link=Joshua Angrist|last2=Pischke |first2=Jörn-Steffen |title=The Credibility Revolution in Empirical Economics: How Better Research Design is Taking the Con out of Econometrics |journal=Journal of Economic Perspectives |date=May 2010 |volume=24 |issue=2 |pages=3–30 |doi=10.1257/jep.24.2.3 |issn=0895-3309|doi-access=free |hdl=1721.1/54195 |hdl-access=free }}</ref> The methods include [[regression discontinuity design]], [[Instrumental variables estimation|instrumental variables]], and [[Difference in differences|difference-in-differences]].

==Example==
A simple example of a relationship in econometrics from the field of [[labour economics]] is:

:<math> \ln(\text{wage}) = \beta_0 + \beta_1 (\text{years of education}) + \varepsilon. </math>

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 <math>\beta_1</math> measures the increase in the natural log of the wage attributable to one more year of education. The term <math>\varepsilon</math> is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, <math>\beta_0 \mbox{ and } \beta_1 </math> under specific assumptions about the random variable <math>\varepsilon</math>. For example, if <math>\varepsilon</math> is uncorrelated with years of education, then the equation can be estimated with [[linear regression|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 <math>\epsilon</math> 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 <math>\beta_1</math> identifiable.<ref name=pearl00>{{cite book |first=Judea |last=Pearl |year=2000 |title=Causality: Model, Reasoning, and Inference |publisher=Cambridge University Press |isbn=978-0521773621 |url-access=registration |url=https://archive.org/details/causalitymodelsr0000pear }}</ref> An overview of econometric methods used to study this problem were provided by [[David Card|Card]] (1999).<ref name=Card:00>{{cite book |first=David |last=Card |year=1999 |chapter=The Causal Effect of Education on Earning |editor-last=Ashenfelter |editor-first=O. |editor2-last=Card |editor2-first=D. |title=Handbook of Labor Economics |location=Amsterdam |publisher=Elsevier |pages=1801–1863 |isbn=978-0444822895 }}</ref>

==Journals==
The main journals that publish work in econometrics are:

* ''[[Econometrica]]'', which is published by [[Econometric Society]].<ref>{{Cite web |title=Home |url=http://www.econometricsociety.org/ |access-date=2024-02-14 |website=www.econometricsociety.org |language=en}}</ref>
* ''[[The Review of Economics and Statistics]]'', which is over 100 years old.<ref>{{Cite web |title=The Review of Economics and Statistics |url=https://direct.mit.edu/rest |access-date=2024-02-14 |website=direct.mit.edu}}</ref>
* ''[[The Econometrics Journal]]'', which was established by the [[Royal Economic Society]].<ref>{{cite web |url=http://www.wiley.com/bw/journal.asp?ref=1368-4221 |title=The Econometrics Journal |publisher=Wiley.com |access-date=8 October 2013 |archive-date=6 October 2011 |archive-url=https://web.archive.org/web/20111006043059/http://www.wiley.com/bw/journal.asp?ref=1368-4221 |url-status=live }}</ref>
* The ''[[Journal of Econometrics]]'', which also publishes the supplement ''Annals of Econometrics.''<ref>{{Cite web |title=Journal of Econometrics |url=https://www.scimagojr.com/journalsearch.php?q=28973&tip=sid&clean=0 |access-date=2024-02-14 |website=www.scimagojr.com}}</ref>
* ''[[Econometric Theory]]'', which is a theoretical journal.<ref>{{Cite web |title=Home |url=https://www.cambridge.org/core/journals/econometric-theory |access-date=2024-03-14|language=en}}</ref>
* The ''[[Journal of Applied Econometrics]]'', which applies econometrics to a wide various problems.<ref>{{Cite journal |title=Journal of Applied Econometrics |url=https://onlinelibrary.wiley.com/journal/10991255?journalRedirectCheck=true |journal=Journal of Applied Econometrics}}</ref>
* ''[[Econometric Reviews]]'', which includes reviews on econometric books and software as well.<ref>Econometric Reviews

Print ISSN: 0747-4938

Online ISSN: 1532-4168

https://www.tandfonline.com/action/journalInformation?journalCode=lecr20</ref>
* The ''[[Journal of Business & Economic Statistics]],'' which is published by the [[American Statistical Association]].<ref>{{Cite web |title=Journals |url=https://www.amstat.org/publications/journals |access-date=2024-02-14 |website=Default}}</ref>

==Limitations and criticisms==
{{see also|Criticisms of econometrics}}

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, [[Deidre McCloskey|McCloskey]] concluded that some economists report [[p-value|''p''-value]]s (following the [[Ronald Fisher|Fisherian]] tradition of [[tests of significance]] of point [[null hypothesis|null-hypotheses]]) and neglect concerns of [[type II error]]s; some economists fail to report estimates of the size of effects (apart from [[statistical significance]]) and to discuss their economic importance. She also argues that some economists also fail to use economic reasoning for [[model selection]], especially for deciding which variables to include in a regression.<ref>{{cite journal |title=The Loss Function has been mislaid: the Rhetoric of Significance Tests|last=McCloskey|journal=American Economic Review|date=May 1985|volume=75|issue=2}}</ref><ref>[[Stephen Ziliak|Stephen T. Ziliak]] and [[Deirdre McCloskey|Deirdre N. McCloskey]] (2004). "Size Matters: The Standard Error of Regressions in the ''American Economic Review''", ''Journal of Socio-Economics'', 33(5), pp. [http://faculty.roosevelt.edu/Ziliak/doc/Size%20Matters%20Journal%20of%20Socio-Economics%20Ziliak%20and%20McCloskey.pdf 527-46] {{webarchive|url=https://web.archive.org/web/20100625163446/http://faculty.roosevelt.edu/Ziliak/doc/Size%20Matters%20Journal%20of%20Socio-Economics%20Ziliak%20and%20McCloskey.pdf |date=25 June 2010 }} (press '''+''').</ref>

In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects.<ref name="Leamer 31–43">{{cite journal|last=Leamer|first=Edward|title=Let's Take the Con out of Econometrics|journal=American Economic Review|date=March 1983|volume=73|issue=1|pages=31–43|jstor=1803924}}</ref> In such cases, economists rely on [[observational studies]], often using data sets with many strongly associated [[covariate]]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".<ref name="Leamer 31–43"/>

==See also==
{{div col|colwidth=20em}}
* [[Choice modelling]]
* [[Cowles Foundation]]
* [[Econometric software]]
* [[Financial econometrics]]
* [[Financial modeling]]
* [[List of publications in economics#Econometrics|Important publications in econometrics]]
* [[Single-equation methods (econometrics)]]
{{div col end}}

==Further reading==
* [[b:Econometric Theory|Econometric Theory book on Wikibooks]]
* Giovannini, Enrico [http://www.oecd.org/sdd/41746710.pdf ''Understanding Economic Statistics''], OECD Publishing, 2008, {{ISBN|978-92-64-03312-2}}

==References==
{{reflist}}

==External links==
{{Commons category}}
{{Wiktionary}}
* [https://academic.oup.com/jfec Journal of Financial Econometrics]
* [https://www.econometricsociety.org/ Econometric Society]
* [https://www.res.org.uk/journals/the-econometrics-journal.html The Econometrics Journal]
* [https://sbe.vu.nl/en Econometric Links]
* [https://www.economicsnetwork.ac.uk/subjects/econometrics.htm Teaching Econometrics] (Index by the [[Economics Network]] (UK))
* [https://web.archive.org/web/20071014045229/http://aea-eu.com/ Applied Econometric Association]
* [http://sofie.stern.nyu.edu/ The Society for Financial Econometrics]
* [https://philpapers.org/rec/BRACAI-3 The interview with Clive Granger – Nobel winner in 2003, about econometrics]

{{Economics}}
{{Authority control}}

[[Category:Econometrics| ]]