DOC PREVIEW
UCSB ECON 240 - Lecture Ten

This preview shows page 1-2-3-21-22-23-43-44-45 out of 45 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 45 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Lecture TenLectureOutline: RegressionAssumptions18.4 Error Variable: Required ConditionsThe Normality of ePathologiesPathologies ( Cont. )Pathologies (Cont.)18.9 Regression Diagnostics - IResidual AnalysisDiagnostics ( Cont. )DiagnosticsDiagnostics (Cont.)HeteroscedasticityHomoscedasticityDiagnostics ( Cont.)Non Independence of Error VariablesSlide 19Fix-UpsFix-ups (Cont.)Data Errors: May lead to outliersOutliersSlide 24Procedure for Regression DiagnosticsPart II: Experimental MethodOutlineCritique of RegressionExperimental Method: # ExamplesDeterrence and the Death PenaltyIsaac Ehrlich Study of the Death Penalty: 1933-1969Slide 32Ehrlich Results: Elasticities of Homicide with respect to ControlsCritique of Ehrlich by Death Penalty OpponentsSlide 35Experimental MethodSlide 37Slide 38Police Intervention with Experimental ControlsWhy is Treatment Assigned Randomly?Slide 41Experimental Method: Clinical TrialsConclusions from the Clinical TrialsSlide 44Slide 451Lecture Ten2Lecture•Part I: Regression•Part II: Experimental Method3Outline: Regression•The Assumptions of Least Squares•The Pathologies of Least Squares•Diagnostics for Least SquaresAssumptions•Expected value of the error is zero, E[e)t)]= 0•The error is independent of the explanatory variable, E{e(t) [x(t)-Ex(t)]}=0•The errors are independent of one another, E[e(i)e(j)] = 0 , i not equal to j.•The variance is homoskedatic, E[e(i)]2=E[e(j)]2 •The error is normal with mean zero and variance 2518.4 Error Variable: Required Conditions•The error is a critical part of the regression model.•Four requirements involving the distribution of  must be satisfied.–The probability distribution of  is normal.–The mean of  is zero: E() = 0.–The standard deviation of  is  for all values of x.–The set of errors associated with different values of y are all independent.The Normality of From the first three assumptions we have:y is normally distributed with meanE(y) = 0 + 1x, and a constant standard deviation From the first three assumptions we have:y is normally distributed with meanE(y) = 0 + 1x, and a constant standard deviation 0 + 1x10 + 1x20 + 1x3E(y|x2)E(y|x3)x1x2x3E(y|x1)The standard deviation remains constant,but the mean value changes with x7Pathologies•Cross section data: error variance is heteroskedatic. Example, could vary with firm size. Consequence, all the information available is not used efficiently, and better estimates of the standard error of regression parameters is possible.•Time series data: errors are serially correlated, i.e auto-correlated. Consequence, inefficiency.8Pathologies ( Cont. )•Explanatory variable is not independent of the error. Consequence, inconsistency, i.e. larger sample sizes do not lead to lower standard errors for the parameters, and the parameter estimates (slope etc.) are biased.•The error is not distributed normally. Example, there may be fat tails. Consequence, use of the normal may underestimate true 95 % confidence intervals.9Pathologies (Cont.)•Multicollinearity: The independent variables may be highly correlated. As a consequence, they do not truly represent separate causal factors, but instead a common causal factor.1018.9 Regression Diagnostics - I•The three conditions required for the validity of the regression analysis are:–the error variable is normally distributed.–the error variance is constant for all values of x.–The errors are independent of each other.•How can we diagnose violations of these conditions?11 Residual Analysis•Examining the residuals (or standardized residuals), help detect violations of the required conditions.•Example 18.2 – continued:–Nonnormality. •Use Excel to obtain the standardized residual histogram.•Examine the histogram and look for a bell shaped. diagram with a mean close to zero.12Diagnostics ( Cont. )•Multicollinearity may be suspected if the t-statistics for the coefficients of the explanatory variables are not significant but the coefficient of determination is high. The correlation between the explanatory variable can then be calculated. To see if it is high.13Diagnostics•Is the error normal? Using EViews, with the view menu in the regression window, a histogram of the distribution of the estimated error is available, along with the coefficients of skewness and kurtosis, and the Jarque-Bera statistic testing for normality.14Diagnostics (Cont.)•To detect heteroskedasticity: if there are sufficient observations, plot the estimated errors against the fitted dependent variableHeteroscedasticity•When the requirement of a constant variance is violated we have a condition of heteroscedasticity.•Diagnose heteroscedasticity by plotting the residual against the predicted y.++++++++++++++++++++++++The spread increases with y^y^Residual^y+++++++++++++++++++++++16 Homoscedasticity•When the requirement of a constant variance is not violated we have a condition of homoscedasticity.•Example 18.2 - continued-1000-5000500100013500 14000 14500 15000 15500 16000Predicted PriceResiduals17Diagnostics ( Cont.)•Autocorrelation: The Durbin-Watson statistic is a scalar index of autocorrelation, with values near 2 indicating no autocorrelation and values near zero indicating autocorrelation. Examine the plot of the residuals in the view menu of the regression window in EViews.18 Non Independence of Error Variables–A time series is constituted if data were collected over time.–Examining the residuals over time, no pattern should be observed if the errors are independent.–When a pattern is detected, the errors are said to be autocorrelated.–Autocorrelation can be detected by graphing the residuals against time.19Patterns in the appearance of the residuals over time indicates that autocorrelation exists.+++++++++++++++++++++++++TimeResidualResidualTime+++Note the runs of positive residuals,replaced by runs of negative residualsNote the oscillating behavior of the residuals around zero. 0 0 Non Independence of Error Variables20Fix-Ups•Error is not distributed normally. For example, regression of personal income on explanatory variables. Sometimes a transformation, such as regressing the natural logarithm of income on the explanatory variables may make the error closer to normal.21Fix-ups (Cont.)•If the explanatory variable is not independent of the error, look for a substitute that is


View Full Document

UCSB ECON 240 - Lecture Ten

Documents in this Course
Load more
Download Lecture Ten
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture Ten and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture Ten 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?