1 / 10

Introduction to Econometrics

Introduction to Econometrics. Lecture 6 Testing restrictions. Lecture plan. Testing restrictions about individual parameters groups of parameters. t-tests for individual parameters zero value under H 0 Some other value under H 0. F-tests for groups of parameters

chapa
Download Presentation

Introduction to Econometrics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Econometrics Lecture 6 Testing restrictions

  2. Lecture plan • Testing restrictions about • individual parameters • groups of parameters • t-tests for individual parameters • zero value under H0 • Some other value under H0 • F-tests for groups of parameters • the overall significance of a regression • group exclusion tests • other linear restrictions

  3. Testing restrictions: example cases Consider a simple log-linear demand function with 3 seasonal dummies lnQi = b0 + b1 lnPi + b2 lnYi +1D1i + 2D2i+ 3D3i+ui As well as the overall F test: b1 =b2=1=2=3=0 and standard individual t tests of zero values for individual parameters you might want to test (i) 1=2=3=0 (the seasonal effects can be excluded) or (ii) b1 = -1 (the price elasticity of demand is -1) These tests can be conducted using an F test or a t test respectively

  4. Testing restrictions: example cases Now consider a simple log-linear (Cobb-Douglas) production function lnQi = b0 + b1 lnLi + b2 lnKi + ui As well as the overall F test: b1 =b2=0 and standard individual t tests of zero values for individual parameters you might want to test b1 + b2= 1 (constant returns to scale) Here you can use an F test to test this restriction.

  5. t-tests of non-zero parameter values

  6. F tests of zero restrictions(group exclusion tests)

  7. F tests of other linear restrictions

  8. The F value and decision rule • F cal = [RSSR- RSSU]/m • RSSU/(n-k-1) • where m is the number of restrictions • RSSRis the Residual Sum of Squares in the restricted model • RSSuis the Residual Sum of Squares in the unrestricted model • H0: restrictions are valid • Decision rule: • reject H0 if Fcal > F(m,n-k-1) or if Pvalue < 0.05 • accept H0 if Fcal < F(m,n-k-1) or if Pvalue > 0.05

  9. Imposing restrictions by • reparameterising the model (incorporating the restriction by substitution and then rearranging the equation) • using Restricted Least Squares

  10. Other issues concerning testing restrictions • testing for parameter constancy - the Chow test • testing non-linear restrictions • tests to choose between non-nestedmodels

More Related