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 Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. 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 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. Econometricians try to find estimators that have desirable statistical properties including unbiasedness, efficiency, and consistency. Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analyzing economic history, and forecasting. Basic models: linear regression A basic tool for econometrics is the multiple linear regression model. 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. 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 the unemployment rate is a function of an intercept, a given value of GDP growth multiplied by a slope coefficient \beta_1 and an error term, \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 as to whether an increase in GDP growth is associated with a decrease in 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 as a function of the independent variable is given in polynomial least squares. Theory Econometric theory uses statistical theory and mathematical statistics to evaluate and develop econometric methods. Econometrics may use standard statistical models to study economic questions, but most often they are with observational data, rather than in controlled 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, although exploratory data analysis 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 the 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. 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. 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. Example A simple example of a relationship in econometrics from the field of labor economics is: 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 a 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 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 a 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 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 an 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 was provided by Card. 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, 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-values and neglect concerns of type II errors; some economists fail to report estimates of the size of effects 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. 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 covariates, resulting in enormous numbers of models with similar explanatory abilities 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".