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Econometrics
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## 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.BOOK, Greene, William, Econometric Analysis, 2012, Pearson Education, 9780273753568, 47â€“48, 7th, Chapter 1: Econometrics, 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., 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.(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 GDP growth 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_1text{Growth} + varepsilon.
The unknown parameters beta_0 and beta_1 can be estimated. Here beta_1 is estimated to be âˆ’1.77 and beta_0 is estimated to be 0.83. This means that if GDP growth increased by one percentage point, the unemployment rate would be predicted to drop by 1.77 points. The model could then be tested for statistical significance as to whether an increase in 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.

## Theory

{{see also|Estimation theory}}Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, 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 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.Clive Granger (2008). "forecasting,"The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. {{webarchive|url=https://web.archive.org/web/20120518001935weblink |date=18 May 2012 }}Econometrics may use standard statistical models to study economic questions, but most often they are with observational data, rather than in controlled experiments.BOOK, Wooldridge, Jeffrey, 2013, Introductory Econometrics, A modern approach, South-Western, Cengage learning, 978-1-111-53104-1, 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.Herman O. Wold (1969). "Econometrics as Pioneering in Nonexperimental Model Building," Econometrica, 37(3), pp. 369-381. 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-equation models. 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.One of the fundamental statistical methods used by econometricians is regression analysis.For an overview of a linear implementation of this framework, see linear regression. Regression methods are important in econometrics because economists typically cannot use controlled experiments. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. Observational data may be subject to omitted-variable bias and a list of other problems that must be addressed using causal analysis of simultaneous-equation models.Edward E. Leamer (2008). "specification problems in econometrics," The New Palgrave Dictionary of Economics. Abstract. {{webarchive|url=https://web.archive.org/web/20150923231333weblink |date=23 September 2015 }}In addition to natural experiments, quasi-experimental methods have been used increasingly commonly by econometricians since the 1980s, in order to credibly identify causal effects.JOURNAL, Angrist, Joshua D, Pischke, JÃ¶rn-Steffen, The Credibility Revolution in Empirical Economics: How Better Research Design is Taking the Con out of Econometrics, Journal of Economic Perspectives, May 2010, 24, 2, 3â€“30, 10.1257/jep.24.2.3, 0895-3309,

## Example

A simple example of a relationship in econometrics from the field of labour economics is:
ln(text{wage}) = beta_0 + beta_1 (text{years of education}) + 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{ 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 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.BOOK, Judea, Pearl, 2000, Causality: Model, Reasoning, and Inference, Cambridge University Press, 978-0521773621, An overview of econometric methods used to study this problem were provided by Card (1999).BOOK, David, Card, 1999, The Causal Effect of Education on Earning, Ashenfelter, O., Card, D., Handbook of Labor Economics, Amsterdam, Elsevier, 1801â€“1863, 978-0444822895,

## Journals

The main journals that publish work in econometrics are Econometrica, the Journal of Econometrics, the Review of Economics and Statistics, Econometric Theory, the Journal of Applied Econometrics, Econometric Reviews, the Econometrics Journal,WEB,weblink The Econometrics Journal â€“ Wiley Online Library, Wiley.com, 8 October 2013, Applied Econometrics and International Development, and the Journal of Business & Economic Statistics.

## 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, McCloskey concluded that some economists report p-values (following the Fisherian tradition of tests of significance of point null-hypotheses) and neglect concerns of type II errors; 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.JOURNAL, The Loss Function has been mislaid: the Rhetoric of Significance Tests, McCloskey, American Economic Review, May 1985, 75, 2, 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 {{webarchive|url=https://web.archive.org/web/20100625163446weblink |date=25 June 2010 }} (press +).In some cases, economic variables cannot be experimentally manipulated as treatments randomly assigned to subjects.JOURNAL, Leamer, Edward, Let's Take the Con out of Econometrics, American Economic Review, March 1983, 73, 1, 31â€“43, 1803924, In such cases, economists rely on observational studies, often using data sets with many strongly associated covariates, 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".

{{Commons category|Econometrics}}{{div col|colwidth=20em}} {{div col end}}

## Notes

{{reflist}}

• b:Econometric Theory|Econometric Theory book on Wikibooks]]
• Giovannini, Enrico Understanding Economic Statistics, OECD Publishing, 2008, {{ISBN|978-92-64-03312-2}}

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