Econometrics

Econometrics is concerned with the tasks of developing and applying quantitative or statistical methods to the study and elucidation of economic principles. A quantitative attribute is one that exists in a range of magnitudes and can therefore be measured. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. ^[1] Econometrics combines economic theory with statistics to analyze and test economic relationships. Economics is the social science that studies the production distribution, and consumption of goods and services. Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. 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. Although the first known use of the term "econometrics" was by Pawel Ciompa in 1910, Ragnar Frisch is given credit for coining the term in the sense that it is used today. Ragnar Anton Kittil Frisch ( March 3, 1895 January 31, 1973) was a Norwegian Economist. ^[2]

Although many econometric methods represent applications of standard statistical models, there are some special features of economic data that distinguish econometrics from other branches of statistics. Statistical models are used in Applied statistics. Three notions are sufficient to describe all statistical models Economic data are usually numerical Time-series, ie sets of data (covering periods of time for part or all of a single economy or the international Economic data are generally observational, rather than being derived from controlled experiments. In Statistics, an observational study draws inferences about the effect of a treatment on subjects where the assignment of subjects into a treated group versus a Control In scientific inquiry an experiment ( Latin: Ex- periri, "to try out" is a method of investigating particular types of research questions or Because the individual units in an economy interact with each other, the observed data tend to reflect complex economic equilibrium conditions rather than simple behavioral relationships based on preferences or technology. In Economics, economic equilibrium is simply a state of the world where economic forces are balanced and in the absence of external influences the (equilibrium values of economic Preference (also called " taste " or "penchant" is a concept used in the Social sciences particularly Economics. In Economics, a production function is a function that specifies the output of a firm an industry or an entire economy for all combinations of inputs Consequently, the field of econometrics has developed methods for identification and estimation of simultaneous equation models. The parameter identification problem is a problem which can occur in the estimation of multiple-equation Econometric models where the equations have variables in common Estimation theory is a branch of Statistics and Signal processing that deals with estimating the values of parameters based on measured/empirical data 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 Early work in econometrics focused on time-series data, but now econometrics also fully covers cross-sectional and panel data. In Statistics, Signal processing, and many other fields a time series is a sequence of Data points measured typically at successive times spaced at (often Cross-sectional data in Statistics and Econometrics is a type of one-dimensional Data set. In Statistics and Econometrics, the term panel data refers to two-dimensional data

1 Purpose
2 A Simple Overview
3 Methods
- 3.1 Example
4 Notable econometricians
5 Journals
6 Notes
7 References
8 See also
9 Study Resources
10 External links

Purpose

The two main purposes of econometrics are to give empirical content to economic theory and to subject economic theory to potentially falsifying tests. In Philosophy, empiricism is a theory of Knowledge which asserts that knowledge arises from Experience. ^[2]

For example, consider one of the basic relationships in economics, the relationship between the price of a commodity and the quantities of that commodity that people wish to purchase at each price (the demand relationship). Supply and demand is an Economic model describing effects on price and quantity in a Market. According to economic theory, an increase in the price would lead to a decrease in the quantity demanded, holding other relevant variables constant to isolate the relationship of interest. A mathematical equation can be written that describes the relationship between quantity, price, other demand variables like income, and a random term ε to reflect simplification and imprecision of the theoretical model:

$Q = \beta_0 + \beta_1\text{Price} + \beta_2\text{Income} + \varepsilon.$

Regression analysis could be used to estimate the unknown parameters $β 0$ , $β 1$ , and $β 2$ in the relationship, using data on price, income, and quantity. In statistics regression analysis is a collective name for techniques for the modeling and analysis of numerical data consisting of values of a Dependent variable (response The model could then be tested for statistical significance as to whether an increase in price is associated with a decrease in the quantity, as hypothesized: $β 1 < 0$ . In Statistics, a result is called statistically significant if it is unlikely to have occurred by Chance. A statistical hypothesis test is a method of making statistical decisions using experimental data

There are complications even in this simple example. In order to estimate the theoretical demand relationship, the observations in the data set must be price and quantity pairs that are collected along a demand schedule that is stable. If those assumptions are not satisfied, a more sophisticated model or econometric method may be necessary to derive reliable estimates and tests.

A Simple Overview

Studying Economics can be abstract, we talk about imaginary concepts such as "rationality". Econometrics tries to put some numerical flesh on those ideas, for example in reality are income and expenditure related? Generally we apply statistical techniqes, which are from two distinct areas - cross section methods or time series methods. Imagine you only live for a minute and for that minute you have every statistic available to you, at that point you might ask "Is the American economy stonger than that of the British" and this is a problem for cross section econometrics. On the other hand you might want to see how economies develop over time, can we predict business cycles per say? The later is Time Series analysis.

In terms of methodolody, time series is the easier to grasp, in economics there tends to exist a relationship between last years GDP and next years GDP so the question is what is that relationsip, so we might want to say "I think this years GDP will be similar to last years, but with some error, as we can't be precise!". Where as the cross section people might want to look at two countries, they might say, France and Germany's GDP are connected (they're both in the EU afterall) so perhaps I can estimate some relationship between them, so your belief (or hypothesis) might be that France's GDP this year will be much like Germany's but with some small error.

Methods

One of the fundamental statistical methods used by econometricians is regression analysis. In statistics regression analysis is a collective name for techniques for the modeling and analysis of numerical data consisting of values of a Dependent variable (response For an overview of a linear implementation of this framework, see linear regression. In statistics linear regression is a form of Regression analysis in which the relationship between one or more Independent variables and another variable called Regression methods are important in econometrics because economists typically cannot use controlled experiments. In scientific inquiry an experiment ( Latin: Ex- periri, "to try out" is a method of investigating particular types of research questions or Econometricians often seek illuminating natural experiments in the absence of evidence from controlled experiments. A natural or Quasi-experiment is a naturally occurring instance of observable phenomena which approximate or duplicate the properties of a controlled Experiment. 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. Omitted-variable bias (OVB is the bias that appears in estimates of Parameters in a Regression analysis when the assumed specification is incorrect ^[3]

Data sets to which econometric analyses are applied can be classified as time-series data, cross-sectional data, panel data, and multidimensional panel data. A data set (or dataset) is a collection of Data, usually presented in tabular form In Statistics, Signal processing, and many other fields a time series is a sequence of Data points measured typically at successive times spaced at (often Cross-sectional data in Statistics and Econometrics is a type of one-dimensional Data set. In Statistics and Econometrics, the term panel data refers to two-dimensional 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).

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. A variety of methods are used in Econometrics to estimate models consisting of a single Equation. Dependent variables and independent variables refer to values that change in relationship to each other 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. 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 Many of these methods use variants of instrumental variable to make estimates. In Statistics, Econometrics, and related disciplines the method of instrumental variables ( IV) is used to estimate causal relationships when controlled

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). GMM may also mean Gaussian Mixture model. For the Thai entertainment company see GMM Grammy. In Statistics, Econometrics, and related disciplines the method of instrumental variables ( IV) is used to estimate causal relationships when controlled 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:

$\ln(\text{wage}) = \beta_0 + \beta_1 (\text{Years of education}) + \varepsilon.$

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. Labour economics seeks to understand the functioning of the Market and dynamics for labour. The parameter $β 1$ measures the increase in the natural log of the wage attributable to one more year of education. It should be noted that by using the natural log we have moved away from a simple linear regression model and are now using a non linear model, in this case, a semi-log y model. The term $ε$ is a random variable representing all other factors that may have direct influence on wage. The econometric goal is to estimate the parameters, $β 0 and β 1$ 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. The method of least squares is used to solve Overdetermined systems Least squares is often applied in statistical contexts particularly Regression analysis.

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 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 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, together with the assumption that $ε$ is uncorrelated with education produces a misspecified model. A second technique for dealing with omitted variables is instrumental variables estimation. In Statistics, Econometrics, and related disciplines the method of instrumental variables ( IV) is used to estimate causal relationships when controlled

Notable econometricians

The following are the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel recipients in the field of econometrics:

Jan Tinbergen and Ragnar Frisch were awarded the first Nobel Prize for Economic Sciences in 1969 for having developed and applied dynamic models for the analysis of economic processes. The Nobel Memorial Prize in Economic Sciences, officially named The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel (Sveriges riksbanks pris i ekonomisk Jan Tinbergen ( The Hague, April 12, 1903 June 9, 1994 The Hague) Dutch Economist, was awarded Ragnar Anton Kittil Frisch ( March 3, 1895 January 31, 1973) was a Norwegian Economist. Year 1969 ( MCMLXIX) was a Common year starting on Wednesday (link will display full calendar of the Gregorian calendar.
Lawrence Klein, Professor of Economics at the University of Pennsylvania, was awarded in 1980 for his computer modeling work in the field. Lawrence Robert Klein (born September 14, 1920) is an American economist. The University of Pennsylvania (also known as Penn) is a private University located in Philadelphia, Pennsylvania, USA. Year 1980 ( MCMLXXX) was a Leap year starting on Tuesday (link displays the 1980 Gregorian calendar)
Trygve Haavelmo was awarded in 1989. Trygve Magnus Haavelmo ( 13 December 1911 – 26 July 1999) was an Economist with main research interests centered on the fields Year 1989 ( MCMLXXXIX) was a Common year starting on Sunday (link displays 1989 Gregorian calendar) His main contribution to econometrics was his 1944 article (published in Econometrica) "The Probability Approach to Econometrics. Econometrica is an Academic journal of Economics, publishing articles not only in Econometrics but in many areas of Economics "
Daniel McFadden and James Heckman shared the award in 2000 for their work in microeconometrics. Daniel Little McFadden (born July 29, 1937) is an econometrician who won (jointly with James Heckman) the 2000 Nobel Memorial Prize James Joseph Heckman (born April 19, 1944) is a leading Economist at The University of Chicago, Distinguished Chair of Microeconometric 2000 ( MM) was a Leap year that started on Saturday of the Common Era, in accordance with the Gregorian calendar. McFadden founded the econometrics lab at the University of California, Berkeley. The University of California Berkeley (also referred to as Cal, Berkeley and UC Berkeley) is a major research university located in Berkeley
Robert Engle and Clive Granger at the University of California, San Diego, were awarded in 2003 for work on analyzing economic time series. Robert Fry Engle III (born November 10, 1942) is an American Economist and the winner of the 2003 Nobel Memorial Prize in Economic Sir Clive William John Granger (born September 4, 1934) is a Welsh Economist, and Professor Emeritus at the University of California The University of California San Diego (popularly known as UC San Diego or UCSD) is a public Research university in San Diego, California Year 2003 ( MMIII) was a Common year starting on Wednesday of the Gregorian calendar. Engle pioneered the method of autoregressive conditional heteroskedasticity (ARCH) and Granger the method of cointegration. "ARCH" redirects here For the children's rights organization see Action on Rights for Children. Cointegration is an Econometric property of Time series variables

The Econometric Author Links of the Econometrics Journal provides personal links to recent articles and working papers of econometric authors via the RePEc system in EconPapers.

Journals

The main journals which publish work in econometrics are Econometrica, the Journal of Econometrics, the Review of Economics and Statistics, the Econometric Theory, the Journal of Applied Econometrics, the Econometric Reviews, and the Journal of Business and Economic Statistics . Econometrica is an Academic journal of Economics, publishing articles not only in Econometrics but in many areas of Economics The Journal of Econometrics is a leading scholarly journal in Econometrics. The Review of Economics and Statistics is a scholarly journal specializing in applied (especially quantitative economics now called Econometrics. Econometric Theory is an Economic Journal specialising in Econometrics. The Journal of Applied Econometrics (JAE is a leading bi-monthly international scholarly journal in Econometrics. The Journal of Business and Economic Statistics (JBES is an Academic journal, published quarterly by the American Statistical Association.

Notes

^ Ragnar Frisch (1933). "Editor's Note". Econometrica 1. 1-4.
^ ^a ^b Pesaran, M. Hashem, “Econometrics”, in Eatwell, John; Milgate, Murray & Newman, Peter, The New Palgrave: A Dictionary of Economics, vol. Professor Mohammad Hashem Pesaran (born March 30, 1946 in Shiraz, Iran) is a British - Iranian economist John Leonard Eatwell Baron Eatwell ( 2 February, 1945 &ndash) is an influential British economist and the current President of Queens' College Cambridge The New Palgrave A Dictionary of Economics (1987 is a 4-volume reference edited by John Eatwell, Murray Milgate and Peter Newman 2, pp. 8–22
^ Edward E. Leamer, "specification problems in econometrics," The New Palgrave: A Dictionary of Economics, v. The New Palgrave A Dictionary of Economics (1987 is a 4-volume reference edited by John Eatwell, Murray Milgate and Peter Newman 4 (1987), pp. 472-75.

References

Handbook of Econometrics Elsevier, links to:

v. 1, pp. 3-771 (1983)

v. 2, pp. 775-1461 (1984)

v. 3, pp. 1465-2107 (1986)

v. 4, pp. 2111-3155 (1994)

v. 5, pp. 3159-3843 (2001)

v. 6, Part 1, pp. 3845-4776 (2007)

v. 6, Part 2, pp. 4777-5752 (2007)

Harry H. Kelejian and Wallace E. Oates (1989, 3rd ed. ) Introduction to Econometrics.
Peter Kennedy (2003). A Guide to Econometrics, 5th ed. Preview.
Robert S. Pindyck and Daniel L. Rubinfeld (1998, 4th ed. ).
A. H. Studenmund (2000, 4th ed. ) Using Econometrics: A Practical Guide.

Study Resources

MERLOT Learning materials in Econometrics (US-based catalogue of materials)
Teaching Econometrics (Index by the Economics Network (UK))
Econometric Theory book on Wikibooks

External links

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 and Econometrics, an augmented Dickey-Fuller test (ADF is a test for a Unit root in a Time series sample. In Time series models in Econometrics, a linear Stochastic process has a unit root if 1 is a root of the process's Characteristic equation

Dictionary

-noun

(finance) The branch of economics that applies statistical methods to the empirical study of economic theories and relationships.

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