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Jacek Wallusch _________________________________ Introduction to Econometrics

Jacek Wallusch _________________________________ Introduction to Econometrics. Lecture 4 : Count Data Models. Count Data ____________________________________________________________________________________________. definitions. Count. 1 . to name numbers in regular order ;

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Jacek Wallusch _________________________________ Introduction to Econometrics

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  1. Jacek Wallusch_________________________________Introduction to Econometrics Lecture 4: Count Data Models

  2. Count Data____________________________________________________________________________________________ definitions Count 1.to name numbers in regular order; 2. to have a specified value [a touchdown counts for six points]*; Integer 1. anything complete in itself; entity; 2. any positice or negative whole number or zero; ItE: 4 Webster’s New World College Dictionary * That’s Webster as well!!!

  3. Count Data____________________________________________________________________________________________ Example Doctor Visits:number of doctor visits per one respondent within a specified period of time explanatory variables: socioeconomic – gender, age, squared age, income health insurance status indicators – insured, not insured recent health status measure – number of illnesses in past 2 weeks, number of days of reduced activity long-term health status measure – health questionnaire score ItE: 4 Example: Cameron and Trivedi 1998

  4. Count Data____________________________________________________________________________________________ Example Doctor Visits:see cont_docvisits.xls exlaining variable:avg. = 6.823 std.dev. = 7.395 skew = 4.176 kurt = 46.744 ItE: 4 Example: Katchova 2013

  5. Count Data____________________________________________________________________________________________ Examples Other Topics: research and development: patents granted, domestic patents, foreign patents etc. sales: number of items sold quality control: number of defective items produced Important note: time structure and/or cross-section ItE: 4

  6. Count Data____________________________________________________________________________________________ Background Poisson distribution and rare events Poisson density: expected value and variance: Warning: equidispersion property is often violated in practice, i.e. ItE: 4 m – intensity (rate) coefficient, t – exposure (length of time during which the events are recorded)

  7. Estimation____________________________________________________________________________________________Estimation____________________________________________________________________________________________ coefficients Poisson distribution and rare events The model: left-hand variable y: number of occurences of the event of interest (e.g. doctor visits) mean coefficient: ItE: 4 b – coefficient vector, x – vector of linearly independent regressors

  8. Probability____________________________________________________________________________________________Probability____________________________________________________________________________________________ Poisson model Poisson distribution and estimatedprobabilities Using the estimated mean to calculate probabilities: condition Conditional probability that the left hand variable = y ItE: 4 b – coefficient vector, x – vector of linearly independent regressors

  9. Other Distributions____________________________________________________________________________________________ negative binomial Important limitation: Overdispersion Solution: negative binomial model mean coefficient: variance: ItE: 4 r – number of trials at wich success occurs, p – probability of success

  10. Distributions____________________________________________________________________________________________Distributions____________________________________________________________________________________________ examples Randomly generated distributions descriptive statistics: ItE: 4

  11. Results____________________________________________________________________________________________Results____________________________________________________________________________________________ Interpretation Marginal Effects Exponential conditional mean: differentiation: Procedures: ItE: 4 (1) average response after aggregating over all individuals vs. (2) response for the individual with average characteristics

  12. Methods of Estimatios____________________________________________________________________________________________ Overdispersion GRETL Test for overdispersion: null hypothesis: no overdispersion interpretation: rejection of the null suggests the need for different distribution ItE: 4

  13. Methods of Estimatios____________________________________________________________________________________________ Overdispersion GRETL NEG BIN 2: a-coefficient: measure of heterogeneity between individuals NEG BIN 1: conditional variance: scalar multiple (g) of conditional mean ItE: 4

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