# Simultaneous equations econometrics lecture notes

Throughout this book, we have used regression analysis in a variety of ways. From the simplest bivariate regression to consideration of the effects of heteroskedasticity or autocorrelation, we have always worked with a single equation.

This chapter introduces you to simultaneous equations models SEM. As the name makes clear, the heart of this class of models lies in a data generation process that depends on more than one equation interacting together to produce the observed data. Unlike the single-equation model in which a dependent y variable is a function of independent x variables, other y variables are among the independent variables in each SEM equation. The y variables in the system are jointly or simultaneously determined by the equations in the system.

Notice that the first equation in the system has a conventional x variable, but it also has a dependent variable y 2 on the right-hand side. Likewise, the second equation has a dependent variable y 1 as a right-hand side variable. In a simultaneous equations system, variables that appear only on the right-hand side of the equals sign are called exogenous variables. They are truly independent variables because they remain fixed.

Variables that appear on the right-hand side and also have their own equations are referred to as endogenous variables. Unlike exogenous variables, endogenous variables change value as the simultaneous system of equations grinds out equilibrium solutions. They are endogenous variables because their values are determined within the system of equations. A natural question to ask is, What happens if we just ignore the simultaneity?

Suppose, for example, we are interested only in the effect of y 1 on y 2.

Could we simply toss out the first equation and treat the second one as a standalone, single equation, using our usual ordinary least squares regression to estimate the coefficients? In fact, this is what most single-equation regressions actually do — they simply ignore the fact that many x variables are not truly exogenous, independent variables.

Unfortunately, it turns out that closing your eyes to the other equations is not a good move: the single equation OLS estimator of? This important result, called simultaneity bias, occurs because y 1 is correlated with e 2as we will show in section Fortunately, there are ways to consistently estimate the coefficients in the system.

The most common approach is called the method of instrumental variables or IV. When several instrumental variables are available, they are combined via regression the first stage and then used in a second regression. We cannot hope to cover this wide and complex area of econometrics completely in this introductory text, but we can convey the essentials of SEMs. As we have done with other topics, we will focus on fundamental concepts, using concrete examples to illustrate key points.

The next section introduces a simple example used throughout the chapter.

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Section Chapter Simultaneous Equations Throughout this book, we have used regression analysis in a variety of ways.It discusses setting up your own python programming environment, relevant software libraries and techniques, then works through many examples in economics.

Each section of the material can be downloaded as a PDF using the buttons near the top of the text. Online, freely-reproducible textbook with examples in R. The online layout makes it possible to bookmark individual chapters and sections.

An archive of cheat sheets for different functions and packages of the R language, some of them contributed by the community of users.

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Materials from a course taught in Springincluding a syllabus, video lectures in quite a low resolution and an electronic version of the textbook Discrete Choice Methods with Simulation. Bayesian statistics and its application to econometrics - lecture slides and notes. The Powerpoint presentation comprises nearly slides. From a Summer Institute mini-course run by the National Bureau of Economic Research inthis 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.

This link goes to Economics Network's index of these materials. Freely downloadable as a 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.

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The data sets and script files used in the book are also freely downloadable. The current version dates from January 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 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. Fifteen detailed lecture handouts in PDF are archived here along with 11 exercise sheets with answers. It includes extensive course materials, lecture notes, statistical tables, datasets and assignments and a number of past exams, going back tosome with answers in separate files.

Lecture notes and references notes in Word format are listed on this course home page. It covers topics such as Dynamic Econometric Modelling, Model misspecification and misspecification testing, Stochastic regressors, instrumental variables and weak exogeneity and Panel data analysis. This is a short, very introductory article 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.

It was created by the authors of the MicrOsiris statistical software. It is freeware that is downloaded with MicrOsiris. This page book, originally published in but now out of print, is available online in its entirety as a single PDF file. Discrete choice methods with simulation is an online text written by Kenneth Train of University of California, Berkeley in 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.Calzolari, Giorgio : Econometric notes. Lecture notes for a course of Introductory Econometrics linear regression model and ordinary least squares, including concepts of Linear Algebra and Inferential Statisticsand for a second course of Econometrics simultaneous equations, instrumental variables, limited and full information estimation methods, maximum likelihood.

Amemiya, T. Griliches and M. I, Anderson, T. Basmann, R. Belsley, D. Berndt, E. Hall, R. Hall, and J. Bianchi, C. Calzolari, and P. Reprinted in Macroeconometric Modelling, ed. Wallis Cheltenham: Edward Elgar Publishing Ltd.

Bowden, R. Turkington : Instrumental Variables. Brundy, J. Calzolari, G. Panattoni, and C.General bill of burials by parish clerks of London, Cite This Course.

Don't show me this again. This is one of over 2, courses on OCW. Find materials for this course in the pages linked along the left. No enrollment or registration. Freely browse and use OCW materials at your own pace.

There's no signup, and no start or end dates. Knowledge is your reward. Use OCW to guide your own life-long learning, or to teach others. We don't offer credit or certification for using OCW. Made for sharing.

Download files for later. Send to friends and colleagues. Modify, remix, and reuse just remember to cite OCW as the source. Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement.

Some Description Instructor s Prof. Need help getting started? Don't show me this again Welcome! Course Description Course Features Assignments: problem sets no solutions Course Description Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression.Christopher DoughertyLSE For year 2 undergraduates, presumes some previous introductory study of statistics and calculus.

The course follows the author's textbook and is relatively unmathematical in its approach. Guy JudgePortsmouth 20 credit unit for year 2 undergraduates. Presumes some previous introductory study of statistics.

Stresses proper application of methods rather than formal derivations; aims to help students read applied econometrics and attempt their own. Contains material that maps well against undergraduate learning objectives.

Includes exercises.

Guy JudgePortsmouth Final year undergraduate elective course, presumes previous introductory unit. Extends coverage of single equation and simultaneous equation models; introduces e.

### Online Text and Notes in Econometrics

Contains material that maps well against learning objectives for undergraduates electing to study econometrics beyond the core requirements of their course. Logos remain the property of their respective institutions and organisations, all rights reserved. The Economics Network. Except where stated, resources on this page are available under a Creative Commons by-nc licence.

Home Top. Log in.Econometrics I. Class Notes. Professor W. Abstract: This is an intermediate level, Ph. Topics to be studied include specification, estimation, and inference in the context of models that include then extend beyond the standard linear multiple regression framework. After a review of the linear model, we will develop the asymptotic distribution theory necessary for analysis of generalized linear and nonlinear models.

We will then turn to instrumental variables, maximum likelihood, generalized method of moments GMMand two step estimation methods.

## Econometric notes

Inference techniques used in the linear regression framework such as t and F tests will be extended to include Wald, Lagrange multiplier and likelihood ratio and tests for nonnested hypotheses such as the Hausman specification test.

Specific modelling frameworks will include the linear regression model and extensions to models for panel data, multiple equation models, and models for discrete choice. Notes: The following list points to the class discussion notes for Econometrics I. These are Power Point. Introduction: Paradigm of Econometrics pptx pdf 2. Regression Fit, Restricted Least Squares pptx pdf 6.

Interval Estimation, Prediction, Quantile Regression pptx pdf Instrumental Variables and Treatment Effects pptx pdf The Generalized Regression Model pptx pdf Panel Data Modeling pptx pdf Linear Models for Panel Data, Applications pptx pdf Nonlinear Regression pptx pdf Maximum Likelihood Estimation, Binary Choice pptx pdf Time Series Data pptx pdf Monte Carlo Methods: Bayesian Analysis pptx pdf.It calls for the annual recruitment of some 10,000 science and maths teachers, proposing that science undergraduates be lured into the classroom with generous scholarships, with the lofty goal of improving science education at school for some 10 million people.

This proposal may appear to some US politicians to be central planning run amok and it doesn't really address the low pay and social standing of teachers in the United States.

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But it does have potential and precedent: an existing programme called Teach for America has succeeded in recruiting thousands of young college graduates to teach in the nation's most troubled neighbourhoods. Other recommendations of note include a call for the creation of a new energy-research agency that would conduct low-cost, high-risk, high-reward research projects.

This would be modelled on the Defense Advanced Research Projects Agency (DARPA), which has been highly successful in backing exciting, basic research that may spawn useful technology. Another new entity would be set up expressly to arrange for the construction of scientific facilities. It suggests a new category of generous grants that would allow young researchers early in their career to firmly establish their own lines of enquiry. Furthermore, it calls for changes in US immigration policy that would make it easier for foreign students and scientists to stay in the country to continue their careers.

Both these suggestions will require serious political commitment to implement but they would go a long way towards fostering fresh scientific talent. Senators Lamar Alexander (Republican, Tennessee) and Jeff Bingaman (Democrat, New Mexico), who commissioned the study, must now try to drum up support on Capitol Hill for the implementation of its recommendations.

They face an uphill battle, given the size of the US budget deficit and inevitable political resistance to such concepts as further federal involvement in school education.

The United States' competitors, in Europe and the Far East, also need to consider such measures, and might actually find some of them easier to implement. You are viewing the new design.

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