Econometrics is an application of statistical methods to economic data in order to give empirical content to economic relationships.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, p. 1 [pp. 1–34]. Abstract (2008 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."P. A. Samuelson, T. C. Koopmans, and J. R. N. Stone (1954). "Report of the Evaluative Committee for Econometrica", Econometrica 22(2), p. 142. [p p. 141-146], as described and cited in Pesaran (1987) above. An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships."Paul A. Samuelson and William D. Nordhaus, 2004. Economics. 18th ed., McGraw-Hill, p. 5. Jan Tinbergen is one of the two founding fathers of econometrics.Magnus, Jan & Mary S. Morgan (1987) The ET Interview: Professor J. Tinbergen in: 'Econometric Theory 3, 1987, 117–142.Willlekens, Frans (2008) International Migration in Europe: Data, Models and Estimates. New Jersey. John Wiley & Sons: 117. The other, Ragnar Frisch, also coined the term in the sense in which it is used today.• H. P. Pesaran (1990), "Econometrics", Econometrics: The New Palgrave, p. 2 , citing Ragnar Frisch (1936), "A Note on the Term 'Econometrics'", Econometrica, 4(1), p. 95. Aris Spanos (2008), "statistics and economics", The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.
A basic tool for econometrics is the multiple linear regression model. 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. Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analysing economic history, and forecasting.
History The origins of econometrics can be traced to the development of the least squares method in the early nineteenth century. Initially applied in astronomy and geodesy to estimate celestial motions and other physical phenomena, least squares later became a foundational technique in regression analysis.Nievergelt, Yves. "A tutorial history of least squares with applications to astronomy and geodesy." Journal of Computational and Applied Mathematics 121, no. 1–2 (2000): 37–72.James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert; Taylor, Jonathan. An Introduction to Statistical Learning: With Applications in Python. Cham: Springer International Publishing, 2023, p. 5.
The development of statistical and econometric methods was influenced by earlier contributions to political arithmetic and quantitative social inquiry by figures such as Gregory King, Francis Ysidro Edgeworth, Vilfredo Pareto, and Sir William Petty. Early econometric research was exemplified by works such as Henry Ludwell Moore's Synthetic Economics.
As statistical applications expanded to classification problems, linear discriminant analysis (LDA) was introduced in 1936 to predict categorical outcomes.Cohen, Jacob; Cohen, Patricia; West, Stephen G.; Aiken, Leona S. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. 3rd ed. Mahwah, NJ: Lawrence Erlbaum Associates, 2003.James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert; Taylor, Jonathan. An Introduction to Statistical Learning: With Applications in Python. Cham: Springer International Publishing, 2023, p. 5. Logistic regression emerged during the 1940s as an alternative approach for modeling binary outcomes. In the early 1970s, the generalized linear model (GLM) framework was developed, unifying linear and logistic regression within a broader class of statistical models.Wedderburn, Robert W. M. "Quasi-likelihood functions, generalized linear models, and the Gauss–Newton method." Biometrika 61, no. 3 (1974): 439–447.James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert; Taylor, Jonathan. An Introduction to Statistical Learning: With Applications in Python. Cham: Springer International Publishing, 2023, p. 5.
Throughout much of the twentieth century, statistical learning methods were predominantly linear because non-linear techniques were computationally demanding. Improvements in computing power during the 1980s facilitated the development and adoption of non-linear approaches, including classification and regression trees (CART), generalized additive models (GAMs), and artificial neural networks. During the 1990s, support vector machines (SVMs) emerged as another important class of predictive models.James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert; Taylor, Jonathan. An Introduction to Statistical Learning: With Applications in Python. Cham: Springer International Publishing, 2023, p. 5.
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 visualized as fitting a line through data points representing paired values of the independent and dependent variables.
One of the earliest uses of linear regression was in 1889 by British statistician Udny Yule. Yule was seeking to causally identify a relationship between public assistance and the number of impoverished people in England. Using two time periods from the 1871 and 1881 census data at the county level, he estimated the effect of receiving social assistance on the rate of poverty. While it would likely not meet the threshold today, given concerns of two-way causality and bias in the error term, his regression specification was the following:
Another example, one that is rarely used today, can be found in macroeconomics. 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 () is a function of an intercept (), a given value of GDP growth multiplied by a slope coefficient and an error term, :
The unknown parameters and can be estimated. Here is estimated to be 0.83 and is estimated to be -1.77. This means that if GDP growth increased by 1 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 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 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 a 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.
Econometrics uses standard statistical models to study economic questions, but most often these are based on observational data, rather than data from 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. The study protocol guides analysis of data from an observational study, 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 equations models. These methods are analogous to those used in other areas of science, such as 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 experiments or apply quasi-experimental methods to draw credible causal inference. The methods include regression discontinuity design, instrumental variables, and difference-in-differences.
Example A simple example of a relationship in econometrics from the field of labour 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 measures the increase in the natural log of the wage attributable to one more year of education. The term is a random variable representing all other factors that may have a direct influence on wage. The econometric goal is to estimate the parameters, under specific assumptions about the random variable . For example, if 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 resulting data set 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 place of birth in the above equation, the effect of birthplace on wages may be falsely attributed to the effect of education on wages.