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Encyclopedia > Econometrics

Econometrics is concerned with the tasks of developing and applying quantitative or statistical methods to the study and elucidation of economic principles.[1] Econometrics combines economic theory with statistics to analyze and test economic relationships. Theoretical econometrics considers questions about the statistical properties of estimators and tests, while applied econometrics is concerned with the application of econometric methods to assess economic theories. A scale for measuring mass A quantitative property is one that exists in a range of magnitudes, and can therefore be measured. ... For Wikipedia statistics, see m:Statistics Statistics is the science and practice of developing human knowledge through the use of empirical data expressed in quantitative form. ... Face-to-face trading interactions on the New York Stock Exchange trading floor. ... A graph of a normal bell curve showing statistics used in educational assessment and comparing various grading methods. ...

The two main purposes of econometrics are to give empirical content to economic theory and to subject economic theory to potentially falsifying tests.[2] In philosophy generally, empiricism is a theory of knowledge emphasizing the role of experience in the formation of ideas, while discounting the notion of innate ideas. ...

For example, consider one of the basic relationships in economics, the relationship between the price of a commodity and the quantity of that commodity that people wish to purchase (the demand relationship). According to economic theory, an increase in the price should lead to a decrease in the quantity demanded. Using econometric tools, a researcher would write a mathematical equation that described the relationship between price and quantity (which may include other variables like income): The supply and demand model describes how prices vary as a result of a balance between product availability at each price (supply) and the desires of those with purchasing power at each price (demand). ...

$Q = beta_0 + beta_1 Price + beta_2 Income + varepsilon$

Econometric methods would be used to estimate the unknown parameters β0, β1, and β2 in the relationship, using data on price, income, and quantity demanded. The researcher would then statistically test that an increase in price leads to a decrease in the quantity demanded by testing the hypothesis that β1 < 0. One may be faced with the problem of making a definite decision with respect to an uncertain hypothesis which is known only through its observable consequences. ...

Even in this example, however, the complications of econometrics become apparent. In order to estimate the demand relationship, the observations in the data set must be price and quantity pairs that are collected along a demand equation that is stable or unshifting. Since we can't guarantee that this is true in any given data set, simultaneous equations methods must be employed to estimate a demand relationship.

## Methods

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. Observational data may be subject to omitted-variable bias and other problems which must be addressed statistically using regression models. Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). ... In statistics, linear regression is a regression method that models the relationship between a dependent variable Y, independent variables Xp, and a random term Îµ. The model can be written as where Î²1 is the intercept (constant term), the Î²is are the respective parameters of independent variables, and p is the... Omitted-variable bias is the bias that appears in an estimate of a parameter if a regression run does not have the appropriate form and data for other parameters. ... A natural experiment is a naturally occurring instance of observable phenomena which approach or duplicate a scientific experiment. ...

Data sets to which econometric analyses are applied can be classified as time-series data sets, cross-sectional data sets, panel data sets, and multidimensional panel data sets. 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).

Econometric analysis may also be classified on the basis of the number of relationships modelled. Single equation methods model a single variable (the dependent variable) as a function of one or more explanatory (or independent) variables. In many econometric contexts, such single equation methods may not recover the effect desired, or may produce estimates with poor statistical properties. Simultaneous equation methods have been developed as one means of addressing these problems. Many of these methods use variants of instrumental variable to make estimates. A variety of methods are used in econometrics to estimate models consisting of a single equation. ... In experimental design, a dependent variable (also known as response variable, responding variable or regressand) is a factor whose values in different treatment conditions are compared. ... Simultaneous equation methods have been used in econometrics to take account of the fact that economic variables such as prices and quantities are, in general, jointly determined in market equilibrium. ... In statistics, an instrumental variable (IV, or instrument) can be used in regression analysis to produce a consistent estimator when the explanatory variables (covariates) are correlated with the error terms. ...

Other important methods include Method of Moments, Generalized Method of Moments (GMM), Bayesian methods, Two Stage Least Squares (2SLS), and Three Stage Least Squares (3SLS). In statistics, the method of moments is a method of estimation of population parameters such as mean, variance, median, etc. ... The generalized method of moments is a very general statistical method for obtaining estimates of parameters of statistical models. ... Bayesian refers to probability and statistics -- either methods associated with the Reverend Thomas Bayes (ca. ... In statistics, an instrumental variable (IV, or instrument) can be used in regression analysis to produce a consistent estimator when the explanatory variables (covariates) are correlated with the error terms. ... 3SLS (three stage least squares) is a statistical technique to analyze multivariate data. ...

### Example

A simple example of a relationship in econometrics from the field of labor economics is Labour economics seeks to understand the functioning of the market for labour. ...

ln(wage) = β0 + β1(Years of education) + ε.

Economic theory says 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 β1 measures the increase in the natural log of the wage attributable to one more year of education. The term ε is a random variable. The econometric goal is to estimate the parameters, β0 and β1 under specific assumptions about the random variable ε. For example, if ε and Years of Education are uncorrelated, then the equation can be estimated with ordinary least squares, assuming that the model is correctly specified. Least squares is a mathematical optimization technique that attempts to find a best fit to a set of data by attempting to minimize the sum of the squares of the differences (called residuals) between the fitted function and the data. ...

If the researcher could randomly assign people to different levels of education, the data set thus generated would allow the econometrician to estimate the effect of changes in years of education on wages. In reality, those experiements 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 with more innate ability may have higher wages and higher levels of education. Unless the econometrician controls for innate ability in the above equation, the effect of innate ability on wages may be falsely attributed to the effect of education on wages.

The most obvious way to control for innate ability is to include a measure of ability in the equation above. Exclusion of innate ability produces a misspecified model. A second technique for dealing with omitted variables is instrumental variables estimation.

## Notable Econometricians

Nobel Memorial Prize in Economics recipients in the field of econometrics: The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel (in Swedish Sveriges Riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is a prize awarded each year for outstanding intellectual contributions in the field of economics. ...

## Journals

The main journals which publish work in econometrics are Econometrica, The Journal of Econometrics, the Review of Economics and Statistics, and The Journal of Applied Econometrics. Econometrica is a prestigious academic journal of economics, publishing articles in not only econometrics but in many areas of economics. ...

## Software

Software packages that are widely used by econometricians can be roughly categorized as follows:

### General packages

The R programming language, sometimes described as GNU S, is a programming language and software environment for statistical computing and graphics. ... MATLAB is a numerical computing environment and programming language. ... GAUSS is a matrix programming language for mathematics and statistics, developed and marketed by Aptech Systems. ... The SAS System, originally Statistical Analysis System, is an integrated system of software products provided by SAS Institute that enables the programmer to perform: data entry, retrieval, management, and mining report writing and graphics statistical and mathematical analysis business planning, forecasting, and decision support operations research and project management quality...

### Time series packages

These are packages that are mainly used for time series analysis, although many include commands for other types of analysis as well.

RATS, an abbrevation of Regression Analysis of Time Series is a statistical package for time series analysis and econometrics. ... EViews is a statistical package for Windows, used mainly for econometric analysis. ... GRETL is a program created with open source for compiling and interpreting data for statistics and econometrics. ...

### Cross-section packages

These are packages that are mainly used for cross-section data.

Stata, created in 1985 by Statacorp, is a statistical program used by many businesses and academic institutions around the world. ... The computer program SPSS (originally, Statistical Package for the Social Sciences) was released in its first version in 1968, and is among the most widely used programs for statistical analysis in social science. ...

• web:reg

This is an incomplete list of software that is designed for the explicit purpose of performing statistical analyses. ... The following tables compare general and technical information for a number of statistical analysis packages. ...

Correlation does not imply causation is a phrase used in the sciences and statistics to emphasize that correlation between two variables does not imply there is a cause-and-effect relationship between the two. ... Much effort has gone into the study of financial markets and how prices vary with time. ... This is a list of important publications in economics, organized by field. ... A variety of methods are used in econometrics to estimate models consisting of a single equation. ... Granger causality is a technique for determining whether one time series is useful in forecasting another. ... In statistics, an augmented Dickey-Fuller test is a test for a unit root in a time series sample. ... A unit root is a concept from autoregressive models in econometrics. ...

## References

1. ^ Ragnar Frisch (1933). "Editor's Note". Econometrica 1. 1-4.
2. ^ * M. Pesaren Hashem. "Econometrics,"The New Palgrave: A Dictionary of Economics, v. 1 (1987), pp. 8-22.
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