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# 4. (30 marks) Consider the model with one exogenous covariate I:Br ify > 0 otherwisewhere y" is & latent (i.e: unobserved) variable and and â‚¬ are ...

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###### 4. (30 marks) Consider the model with one exogenous covariate I:Br ify > 0 otherwisewhere y" is & latent (i.e: unobserved) variable and and â‚¬ are independently distributed.Show that the above model is the probit model when follows the standard normal distribution (i.e. it yields the same distribution of ylz as the probit model). marks)Suppose now that we have an iid sample (y;, I,); 1 Conduct Monte- Carlo experiment to study:(a) The properties of the probit estimator of 3 when foll

4. (30 marks) Consider the model with one exogenous covariate I: Br ify > 0 otherwise where y" is & latent (i.e: unobserved) variable and and â‚¬ are independently distributed. Show that the above model is the probit model when follows the standard normal distribution (i.e. it yields the same distribution of ylz as the probit model). marks) Suppose now that we have an iid sample (y;, I,); 1 Conduct Monte- Carlo experiment to study: (a) The properties of the probit estimator of 3 when follows the standard normal distribution: Explain your results. (10 marks) The properties of the probit estimator o 8 When follows the standard uniform distribution_ Explain your results. (10 marks) Throughout your experiment use the parameter values N = 100, 8 = and suppose that I follows normal distribution with mean 0 and variance [ (iii) Repeat part (ii) with N results 5 marks _ 10, 000. Explain any change(s) in your

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