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Multivariate Regression Models: Advantages and Assumptions

This chapter discusses the advantages and assumptions of multivariate regression models (MRMs) in econometrics. It explains the benefits of joint estimation, such as a better understanding of the topic, different levels of Type I error, and accounting for correlation in error terms. It also introduces SURE models and compares individual vs. joint estimation methods.

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Multivariate Regression Models: Advantages and Assumptions

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  1. CHAPTER 21 MULTIVARIATE REGRESSION MODELS Damodar Gujarati Econometrics by Example, second edition

  2. MULTIVARIATE REGRESSION MODELS (MRMs) • MRM may be the appropriate method of estimation in situations where dependent variables are correlated. Damodar Gujarati Econometrics by Example, second edition

  3. ADVANTAGES OF JOINT ESTIMATION • 1. A better understanding of the topic under study. • 2. Nominal and true levels of Type I error (probability of falsely rejecting the null hypothesis) may be different. • 3. Separate estimation of each regression will neglect the correlation in error terms. • MRM methodology considers this correlation in estimating the between-equation covariances. • 4. OLS regressions will neither produce multivariate results nor will they allow us to test coefficients across equations. • 5. Taking into account intercorrelations across equations, we may be able to obtain more efficient estimates of the parameters. Damodar Gujarati Econometrics by Example, second edition

  4. MRM ASSUMPTIONS • 1. Each regression in the system is linear in the parameters. • 2. The error variance in each regression is homoscedastic. • 3. The error terms in each regression are uncorrelated. • 4. However, the error terms in the two (or more) regressions may be correlated. This is called contemporaneous correlation: • 5. The dependent variables in the system follow a multivariate normal distribution – that is, they are jointly normally distributed. Damodar Gujarati Econometrics by Example, second edition

  5. SURE MODELS • Seemingly Unrelated Regression Equations (SURE): • In MRMs, the regressands are different, but the regressors are the same. • In SURE, the regressands are the same, but the regressors may be different. • If the regressors are the same, then there is no difference between the coefficients in OLS and SURE (only the standard errors). Damodar Gujarati Econometrics by Example, second edition

  6. INDIVIDUAL VS. JOINT ESTIMATION • The SURE method may not be appropriate in all situations. • First, the number of equations in the system must be smaller than the number of observations per equation. • Second, if the error terms in the system of equations are uncorrelated, OLS may be more efficient than SURE. • Third, OLS and SURE will give identical estimates if the same regressors appear in each equation. Damodar Gujarati Econometrics by Example, second edition

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