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Econometrics

Methods

 * See also Methodology of econometrics

Theoretical econometrics examines the statistical properties of econometric methods. Such properties include the power of hypothesis tests and efficiency of estimators and of survey-sampling methods. Applied econometrics uses theoretical econometrics and real-world data for assessing economic theories, developing econometric models, analyzing aspects of economic history, and forecasting.

One of the fundamental statistical methods used by econometricians is regression analysis, which commonly uses linear regression. Single-equation methods model one variable (the dependent variable) as a function of one or more explanatory (independent) variables. A regression equation with one explanatory variable is called a simple regression, distinguished from multiple regression with more than one explanatory variable. Ordinary least squares is the most common such method.

Out of necessity, most applied analysis uses observational data, say from official or business sources rather than from controlled experiments. Regression methods allow estimation of statistical relationships even in the absence of controlled experiments. Econometricians often seek illuminating natural or quasi-natural experiments in the absence of evidence from controlled experiments. Analysis using observational data may be subject to spurious correlation, including from omitted-variable bias, and a list of other problems that appropriate methods may be able to address.

Data sets to which econometric analyses are applied can be classified in different ways. Time-series data have observations for one or more series, such as GDP and government spending in successive periods for a given country. Time-series analysis comprises methods for analyzing time-series data in order to extract meaningful economic relationships from the data. Cross-section data are data collected from multiple subjects (such as households or countries), for example family size and income, possibly in the same period. Such data differences may call for different techniques or interpretations. For example, the ARMA model applies to time-series analysis. Cross-country analysis may estimate long-run relationships, unlike short-run relationships estimated from time-series analysis for a given country.

In many econometric contexts, ordinary least squares may not recover the approriate theoretical relation or may produce estimates with poor statistical properties, because the assumptions for valid use of the method are violated. One widely-used remedy is the method of instrumental variables (IV). For an economic model described by more than one equation, simultaneous-equation methods may be used to remedy similar problems, including two IV variants, Two-Stage Least Squares (2SLS), and Three-Stage Least Squares (3SLS).

Econometrics in its use of observational rather than experimental data has been described earlier as a pioneer in nonexperimental model building. Analysis of data from an observational studies is guided by the study protocol, although exploratory data analysis may by useful for generating new hypotheses. In these aspects, it is similar to methods of such other disciplines as astronomy, epidemiology, and political science. Economics often analyzes 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.

Other important unifying or distinguishing methods include the Method of Moments, Generalized Method of Moments (GMM), and Bayesian methods.

panel data,Gary Chamberlain, 1984. "Panel data," Handbook of Econometrics, v. 2, pp. 1247-1318. Outline. and multidimensional panel data. Time-series data sets contain observations over time; for example, inflation over the course of several years. Cross-sectional data sets contain observations at a single point in time; for example, many individuals' incomes in a given year. Panel data sets contain both time-series and cross-sectional observations. Multi-dimensional panel data sets contain observations across time, cross-sectionally, and across some third dimension. For example, the Survey of Professional Forecasters contains forecasts for many forecasters (cross-sectional observations), at many points in time (time series observations), and at multiple forecast horizons (a third dimension).

Computational concerns are important for evaluating econometric methods and for use in decision making. Such concerns include mathematical well-posedness: the existence, uniqueness, and stability of any solutions to econometric equations. Another concern is the numerical efficiency and accuracy of software. A third concern is also the usability of econometric software.

Still, in recent decades, econometricians have increasingly turned to development of experimental methods to evaluate the often-contradictory conclusions of observational studies. Here, controlled and randomized experiments provide statistical inferences that may yield better empirical performance than do purely observational studies.

Cheng Hsiao, 2008. "longitudinal data analysis," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.

field experimentJohn A. List and David Reiley, 2008. "field experiments," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.

treatment effect. Joshua D. Angrist, 2008. "treatment effect," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.

An example is the econometric evaluation of social programs,James J. Heckman et al., 2007. "Econometric Evaluation of Social Programs: ...," Handbook of Econometrics, Elsevier v. 6B, ch. 70, 71, and 72.

Divisia index

Keisuke Hirano, 2008. "decision theory in econometrics," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract. • James O. Berger, 2008. "statistical decision theory," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.

index numbers W. Erwin Diewert, 2008. "index numbers," The New Palgrave Dictionary of Economics, 2nd Edition. Abstract.

Zvi Griliches, 1986. "Economic Data Issues," ch. 25, in Handbook of Econometrics, v. 3, pp. 1465-1514. Outline.

dirty data and flawed modelsWilliam S. Krasker, Edwin Kuh, Roy E. Welsch, 1983. ch. 11, "Estimation for Dirty Data and Flawed models," in Handbook of Econometrics, v. 1,, pp. 651-698. Outline.