TAILIEUCHUNG - Lecture Advanced Econometrics (Part II) - Chapter 6: Models for count data

Lecture "Advanced Econometrics (Part II) - Chapter 6: Models for count data" presentation of content: Poisson regression model, goodness of fit, overdispersion, negative binomial regression model, too many zeros data. | Advanced Econometrics - Part II Chapter 6 Models for count data Chapter 6 MODELS FOR COUNT DATA A count variable is a variable that takes on non-negative integer values There is no natural upper bound The outcome will be zero for at least some members of the population Y is count variable X is a vector of explanatory variables. It is better to model E Y X directly and to choose functional forms that ensure possibility for any value of X and any parameter value. When Y has no upper bound the most popular of these is the exponential function E Y X exp Xp I. POISSON REGRESSION MODEL The basic Poisson regression model assumes that Y given X X1 X2 . Xk has a Poisson distribution. The Poisson regression model specifies that each Y is drawn from a Poisson distribution with parameter which is related to the regressor X . e Prob Y Y X -p Y 1X 2 X .X Y and X are related as ln X ịp or eX p The expected number of events is given by E Yi Xi Var YX eXp Poisson distribution properties SE Y X _ So p dX With the parameter estimate in hand this vector can be computed using any data vector desired. In principle the Poisson model is simply a non-linear regression but it is easier to estimate the parameters with maximum likelihood techniques. The log-likelihood function is Nam T. Hoang UNE Business School 1 University of New England Advanced Econometrics - Part II Chapter 6 Models for count data n n L lnf -A Yt Xp - ln Y Yp-e 3 Y Xp - ln Y i 1 i 1 The likelihood equations are d ln L dp n Y Y - A X 0 i 1 n Y Y - ep Xi 0 i 1 The Hessian is d2 ln L dpdp n -YA XX i i i i 1 The Hessian is negative definite for all X and p. Newton-Raphson method is a simple algorithm for this model and will converge rapidly. At convergence n YAXXi i i i . i 1 is an . . . n z estimator of the asymptotic covariance matrix for p. A exp XịP . A is the prediction for observation i A exp Xp estimated variance of A will be AXiVXị where V is the estimated asymptotic covariance matrix for p V n . Yaxx III . i 1 -1 .

• Kinh tế học
• Lecture Advanced Econometrics
• Models for count data
• Poisson regression model
• Goodness of fit
• Negative binomial regression model
• Too many zeros data
• Advanced Econometrics
• Lecture Heteroskedasticity
• Proterties of ols in rpesence
• Teesting for heteroskedasticity
• Treatment for heteroskedasticity
• Simultaneous equations models
• Order conditions for identification
• Estimation of a simultaneous equation system
• Lecture Simultaneous equations models
• Review of least squares
• Likelihood methods
• Least quares methods
• Maximum likelihood estimation
• Limited dependent variable models
• Some issues in specification
• Sample selection model
• Regression analysis of treatment effects
• Greneralized linear regression model
• Properties of ols estimators
• Whites heteroscedascity consistent estimator
• Greneralized least squares estimation
• Properties of ols estimator under autocorrelation
• Disturnabce rprocess
• Estimation under autocorrelation
• Estimator under autocorrelation
• General framework for panel data
• Pooled regression
• Fixed effects
• Random effects model
• Choosing between fixed
• Seemingly unrelated regressions
• Generalized least squares estimation
• Kronecker product
• Two case when sur provides
• Eficiency gain over
• Hypothesis testing
• Lecture Hypothesis testing
• Maximum likelihood estimators
• Likelihood ratio test
• Lagrange multiplier test
• Hausman specification test
• Discrete choice analysis
• Binary outcome models
• Discrete choice model
• Basic types of discrete values
• The probability models
• Multinomial models
• The multinomial logit model
• Conditional logit model
• Mixed logit mode
• Dummy varialable
• Intercept dummies with interactions
• Seasonal efects
• Test for structure break
• Differences in differences
• Generalized method of moments
• Orthogonality condition
• Method of moments
• The advantages of GMM estimator