Econometrics :
The two main purposes of econometrics are to give empirical content to economic theory and to subject economic theory to potentially falsifying tests.
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). 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:
Regression analysis could be used to estimate the unknown parameters β0, β1, and β2 in the relationship, using data on price, income, and quantity. 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: β1 < 0.
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 relation 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.
] 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. 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.
Data sets to which econometric analyses are applied can be classified as time-series data, cross-sectional data, panel data, 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).
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.
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).
Example
A simple example of a relationship in econometrics from the field of labor economics is
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. 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, 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.
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.
Notable Econometricians
John Denis Sargan
Nobel Prize in Economics recipients in the field of econometrics:
Jan Tinbergen and Ragnar Frisch were awarded (in 1969) the first Nobel Prize for Economic Sciences for having developed and applied dynamic models for the analysis of economic processes.
Lawrence Klein, Professor of Economics at the University of Pennsylvania, was awarded in 1980 for his computer modeling work in the field.
Trygve Haavelmo was awarded in 1989. His main contribution to econometrics was his 1944 article (published in Econometrica) "The Probability Approach to Econometrics."
Daniel McFadden and James Heckman shared the award in 2000 for their work in microeconometrics. McFadden founded the econometrics lab at the University of California, Berkeley.
Robert Engle and Clive Granger were awarded in 2003 for work on analysing economic time series. Engle pioneered the method of autoregressive conditional heteroskedasticity (ARCH) and Granger the method of cointegration.
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, and the Journal of Applied Econometrics.
Online Text and Notes in Econometrics
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[Applied econometrics lecture notes] (UK)
Roger Perman, Strathclyde University
Lecture notes and references notes in Word format are listed on this course home page.
Introduction to econometrics: course materials (UK)
Christopher Dougherty, LSE
From this page you can access lecture notes, handouts and past exam papers from this LSE course, all in PDF format.
[Time series and forecasting: lectures and brief notes] (UK)
D. S. G. Pollock, Queen Mary College, University of London
This archive has eight chapters of detailed PDF-format lecture notes for a course given at the Institute for Advanced Studies in Vienna. The topics covered are: Trends in Economic Time Series, Seasons and Cycles in Time Series, Models and Methods of Time-Series Analysis, Time-Series Analysis in the Frequency Domain, Linear Stochastic Models, Forecasting with ARIMA Models, Identification and Estimation of ARIMA Models, and Seasonality and Linear Filtering. There are also thirty brief explanatory notes in Time Series Analysis. This site supports the author's courses titled "Methods of Time-Series Analysis" and "Economic Forecasting".
Mathematical theory for social scientists: [lecture notes] (UK)
D. S. G. Pollock, Queen Mary College, University of London
Thirteen PDF files on this page each contain detailed lecture notes on: Sets and Subsets, Numbers, Limits, Derivatives, Maxima and Minima, Geometric Growth, Taylor's Theorem, The Binomial Theorem, Exponential and Logistic Growth, Bivariate Optimisation, Constrained Optimisation, Matrix Algebra 1, and Matrix Algebra 2.
Lectures in mathematical statistics (UK)
D. S. G. Pollock, Queen Mary College, University of London
Fifteen detailed lecture handouts in PDF format are archived here along with 11 exercise sheets with answers. The lecture topics are: Sets and Boolean Algebra, The Binomial Distribution, The Multinomial Distribution, The Poisson Distribution, The Binomial Moment Generating Function, The Normal Moment Generating Function, Characteristic Functions and the Uncertainty Principle, The Bivariate Normal Distribution, The Multivariate Normal Distribution, Conditional Expectations and Linear Regression, Sampling Distributions, Maximum Likelihood Estimation, Regression estimation via Maximum Likelihood, Cochrane's Theorem, and Stochastic Convergence.
Topics in econometrics: course webpage (UK)
Alan Duncan, University of Nottingham, Peter Wright, University of Nottingham
The Topics in econometrics: course webpage, reflects the topic as taught by Alan Duncan and Peter Wright at the University of Nottingham. The page includes lecture overheads and notes, support materials such as result sets and data, computer based practical exercises and past exam papers.
[Econometric theory: texts and exercises] (UK)
D. S. G. Pollock, Queen Mary College, University of London
This is the home page for an intermediate econometrics course, containing two complete course texts, downloadable as a series of PDF chapters. One of these is "A Course of Econometrics", consisting of seventeen chapters from "Elementary Regression Analysis" to "Multivariate Autoregressive Moving-Average Models". The other is "Topics in Econometric Theory," a set of 27 brief lecture handouts. There is also a set of detailed worksheets.
Econometrics/statistics: [lecture notes]
Daniel L. McFadden, University of California, Berkeley
Available are notes from seven lectures, six problem sets, and a sample exam. Lecture topics are: Discrete Response Models, Sampling and Selection, Generalized Method of Moments, Instrumental Variables, Systems of Regression Equations, Simultaneous Equations, and Robust Methods in Econometrics.
Introduction to econometrics/statistics: [lecture notes and problem sets]
Daniel McFadden, James Powell, University of California, Berkeley
This 1998 course page has seven sets of extensive lecture notes totalling more than 160 pages of explanatory material. There are also seven quizzes, also in PDF and PostScript formats.
Economics, statistics and econometrics: [lecture notes]
Andrew K. G. Hildreth, University of California, Berkeley
This Spring 2000 course page has brief notes from a series of 23 lectures.
Deterministic modeling: linear optimization with applications
Hossein Arsham, University of Baltimore
This page has a great deal of illustrated text on optimization and linear programming with many related external links.
Econometrics I: [lecture handouts and exams]
Chris Sims, Princeton University
This course page includes lecture notes and some practice questions and exam papers. Answers are in separate files.
Time series econometrics: [notes and exercises]
Chris Sims, Princeton University
This course site from 2001 has lecture notes and exercises. By following the links, you can see archived materials from the course from 2000, 1999 and 1997.
Discrete choice methods with simulation
Kenneth Train, University of California, Berkeley
Discrete choice methods with simulation is an online text written by Kenneth Train of University of California, Berkeley in 2003. It covers topics such as numerical maximization, simulation assisted estimation and Bayesian procedures. Each chapter is available as a PDF file to download, and the site also provides an index, bibliography and errata discovered since publication. Users can also download the whole text as a single zip file.
Lecture notes on optimization
Pravin Varaiya, University of California, Berkeley
This 140-page book, originally published in 1971 but now out of print, is available online in its entirety as a single PDF file.
[Time series analysis: forecasting product demand and revenue: lecture notes]
James L. Powell, University of California, Berkeley
Lecture notes totally 163 pages from a 1997 short course are available here in PDF format. Most of the text refers to exercises using the accompanying TSP 4 and Excel files.
[Statistical decision tree]
Frank M. Andrews et al., Van Eck Computer Consulting
Subtitled "A guide for selecting statistical techniques for analysing survey data", this presents you with a tree of choices about your data and the hypotheses being tested, resulting in a recommended statistical test. It was created by the authors of the MicrOsiris statistical software. It is freeware that is downloaded with MicrOsiris.
How to do a painless econometrics project
Mike Moffat, University of Rochester
This is a short, very introductory article, spread over four pages, which takes the reader through a simple regression test in Excel. The given example involves testing whether Okun's Law applies to US data, and there is a downloadable Excel file used in the exercise.
Vector Autoregression: Uses and Abuses of VARS
Prof. James D Hamilton, University of California, San Diego
Theory and application of VAR, using example of US GDP forecasting. Supplied on Powerpoint slides - may be problem reading symbols into some versions of Powerpoint.
Prize Lectures from Economics Nobel Laureates
The Nobel Foundation
The Nobel Foundation makes available a great deal of material on each of the Economics prize winners, including video of each Prize Lecture since Robert Mundell in 1999. As well as a lay introduction to each prize winner's research, there are "Advanced information" links giving a more technical explanation. This link is to the Economics Network's quick index of lecture videos and related materials on the site. Each video is a full lecture (usually between 40 and 60 minutes) with good audio and video quality, and pitched at a non-technical audience. Transcripts of each lecture are available in PDF form.
Using gretl for Principles of Econometrics
Prof. Lee Adkins, Oklahoma State University
Freely downloadable as a 374-page PDF, this manual shows students how to use Gretl software to reproduce all the examples from Hill, Griffiths, and Lim's Principles of Econometrics, 3rd edition (Wiley). The data sets and script files used in the book are also freely downloadable. The current version dates from November 2007.
What's New in Econometrics
Guido Ibens, National Bureau for Economic Research, Inc., Jeffrey Wooldridge, National Bureau for Economic Research, Inc.
From a Summer Institute mini-course run by the National Bureau of Economic Research in 2007, this is a set of resources from each of 15 lectures, including video (usually 1hr long and hosted on Google Video) as well as handouts and slides in PDF format. This link goes to Economics Network's index of these materials.
2007-12-05 22:24:34
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