Presented by Gulzat

1. Implementation of a double-hurdle modelBruno GarciaThe Stata Journal (2013), 13, Number 4, pp. 776-794 Presented by Gulzat

2. The paper is about • A double hurdle model (DHM) (Cragg, 1971 Econometrica 39: 829-844) • What is new: Stata command dblhurdle (and predict after dblhurdle )

3. Censored dependent variable models • E.g. Consumer or not if a consumer the value of the expenditure is known • Tobit: assumes that the factors explaining of becoming a consumer and how much to spend have the same effect on these two decisions • DHM: allows these effects to differ

4. Tobit Model • and Two variables and one model to explain these two variables

5. Double Hurdle Model 1. Potential consumer or not, D is not observed 2. • >0 • (or or () ) • ,)= unobserved elements effecting consumers/nonconsumers may affect amount of expenditure • Individuals make decisions in two steps

6. Double Hurdle Model (following the paper.....) • Decision 1: participation • Decision 2: quantity (maybe zero) • =the observed consumption of an individual, dependent variable continous over positive values, but

7. Double Hurdle Model • The log liklihood function for the DHM ():

8. Double Hurdle Model • models the quantity equation • models the participation equation • The command estimates where • Restriction:

9. Double Hurdle Model: Stata

11. Double Hurdle Model

13. Example: The use of the dblhurdle command using smoke.dta from Wooldridge (2010).

16. Marginal effects • The number of years of schooling (educ) on: 1. The probability of smoking 2. The expected number of cigarettes smoked given that you smoke 3. The expected number of cigarettes smoked

17. Prediction • ppar - the probability of being away from the corner conditional on the covariates: • ycond - expectation: • yexpected - expected value of y conditional on x and z:

18. Marginal effects

19. Marginal effects

20. Marginal effects

21. Monte Carlo simulation: Finite sample properties of the estimator • Three measures of performance: • The mean of the estimated parameters should be close to their true values. • The mean standard error of the estimated parameters over the repetitions should be close to the standard deviation of the point estimates. • The rejection rate of hypothesis tests should be close to the nominal size of the test.

22. Monte Carlo simulation The data-generating process can be summarized as follows:

23. Monte Carlo simulation • A dataset of 2,000 observations was created. • The x’s were drawn from a standard normal distribution, and the d’s were drawn from a Bernoulli with p = 1/2. • Refer to this dataset as “base”. • Iteration of the simulation: 1. Use “base”. 2. For each observation, draw (gen) from a standard normal. 3. For each observation, draw (gen) u from a standard normal. 4. For each observation, compute y according to the data-generating process presented above. 5. Fit the model, and save the values of interest with post.

24. Monte Carlo simulation

25. Monte Carlo simulation • A less intuitive issue: The set of regressors in the participation equation=the set of regressors of the quantity equation. • The model is weakly identified. • The data-generating process:

26. Monte Carlo simulation

27. Conclusion • Researchers may consider dblhurdle when using tobit model • Its flexibility allows the researcher to break down the modeled quantity along two useful dimensions, the “quantity” dimension and the “participation” dimension • The command presented in this article only allows for a single corner in the data • One desirable feature to add is the capability to handle dependent variables with two corners