Econometrics

For broader coverage of this topic, seeMathematical economics.

Econometricsis an application ofstatistical methodsto economic data in order to giveempiricalcontent to economic relationships.More precisely, it is "the quantitative analysis of actual economicphenomenabased 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 Tinbergenis 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 themultiple linear regressionmodel.Econometric theoryusesstatistical theoryandmathematical statisticsto evaluate and develop econometric methods.Econometricians try to findestimatorsthat have desirable statistical properties includingunbiasedness,efficiency,andconsistency.Applied econometricsuses theoretical econometrics and real-worlddatafor assessing economic theories, developingeconometric models,analysingeconomic history,andforecasting.

Basic models: linear regression

A basic tool for econometrics is themultiple linear regressionmodel.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.

Okun's law representing the relationship between GDP growth and the unemployment rate. The fitted line is found using regression analysis.

For example, considerOkun's law,which relatesGDPgrowth to the unemployment rate. This relationship is represented in a linear regression where the change in unemployment rate ($\Delta \ {\text{Unemployment}}$) 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,$\varepsilon$:

$\Delta \ {\text{Unemployment}}=\beta _{0}+\beta _{1}{\text{Growth}}+\varepsilon.$

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 forstatistical significanceas to whether an increase in GDP growth is associated with a decrease in the unemployment, ashypothesized.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 inpolynomial least squares.

Theory

See also:Estimation theory

Econometric theory usesstatistical theoryandmathematical statisticsto evaluate and develop econometric methods.Econometricians try to findestimatorsthat have desirable statistical properties includingunbiasedness,efficiency,andconsistency.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 theGauss-Markovassumptions. When these assumptions are violated or other statistical properties are desired, other estimation techniques such asmaximum likelihood estimation,generalized method of moments,orgeneralized least squaresare used.Estimators that incorporate prior beliefsare advocated by those who favourBayesian statisticsover traditional, classical or"frequentist" approaches.

Methods

Main article:Methodology of econometrics

Applied econometricsuses theoretical econometrics and real-worlddatafor assessing economic theories, developingeconometric models,analysingeconomic history,andforecasting.

Econometrics may use standardstatistical modelsto study economic questions, but most often they are withobservationaldata, rather than incontrolled experiments.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, althoughexploratory data analysismay be useful for generating new hypotheses.Economics often analyses systems of equations and inequalities, such assupply and demandhypothesized to be inequilibrium.Consequently, the field of econometrics has developed methods foridentificationandestimationofsimultaneous equations models.These methods are analogous to methods used in other areas of science, such as the field ofsystem identificationinsystems analysisandcontrol theory.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 isregression analysis.Regression methods are important in econometrics because economists typically cannot usecontrolled experiments.Typically, the most readily available data is retrospective. However, retrospective analysis of observational data may be subject toomitted-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 illuminatingnatural experimentsor applyquasi-experimental methodsto draw credible causal inference.The methods includeregression discontinuity design,instrumental variables,anddifference-in-differences.

Example

A simple example of a relationship in econometrics from the field oflabour economicsis:

$\ln({\text{wage}})=\beta _{0}+\beta _{1}({\text{years of education}})+\varepsilon.$

This example assumes that thenatural logarithmof 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,$\beta _{0}{\mbox{ and }}\beta _{1}$under specific assumptions about the random variable$\varepsilon$.For example, if$\varepsilon$is uncorrelated with years of education, then the equation can be estimated withordinary 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 byCard(1999).

Journals

The main journals that publish work in econometrics are:

• Econometrica,which is published byEconometric Society.
• The Review of Economics and Statistics,which is over 100 years old.
• The Econometrics Journal,which was established by theRoyal Economic Society.
• TheJournal of Econometrics,which also publishes the supplementAnnals of Econometrics.
• Econometric Theory,which is a theoretical journal.
• TheJournal of Applied Econometrics,which applies econometrics to a wide various problems.
• Econometric Reviews,which includes reviews on econometric books and software as well.
• TheJournal of Business & Economic Statistics,which is published by theAmerican Statistical Association.

Limitations and criticisms

See also:Criticisms of econometrics

Like other forms of statistical analysis, badly specified econometric models may show aspurious relationshipwhere two variables are correlated but causally unrelated. In a study of the use of econometrics in major economics journals,McCloskeyconcluded that some economists reportp-values(following theFisheriantradition oftests of significanceof pointnull-hypotheses) and neglect concerns oftype II errors;some economists fail to report estimates of the size of effects (apart fromstatistical significance) and to discuss their economic importance. She also argues that some economists also fail to use economic reasoning formodel selection,especially for deciding which variables to include in a regression.

In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects.In such cases, economists rely onobservational studies,often using data sets with many strongly associatedcovariates,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 Leamerurged 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
• Cowles Foundation
• Econometric software
• Financial econometrics
• Financial modeling
• Granger causality
• Important publications in econometrics
• Macroeconomic model
• Mathematical sociology
• Methodological individualism
• Predetermined variables
• Single-equation methods (econometrics)
• Spatial econometrics
• Unit root

Further reading

• Econometric Theory book on Wikibooks
• Giovannini, EnricoUnderstanding Economic Statistics,OECD Publishing, 2008,ISBN978-92-64-03312-2

External links

• Journal of Financial Econometrics
• Econometric Society
• The Econometrics Journal
• Econometric Links
• Teaching Econometrics(Index by theEconomics Network(UK))
• Applied Econometric Association
• The Society for Financial Econometrics
• The interview with Clive Granger – Nobel winner in 2003, about econometrics