Föreläsning 4 - Ordered probit, count data, multinomial and Tobit 1

Question 1

Give examples of different ordered outcome variables

Answer 1

Employment: unemployd, part time, full time.

Grades: A, B, C, D…..

Credit rankings: AAA, AA, A, BBB…….

Utfallsvariablen är alltså ordinaldata. ska vara 3 eller mer.

Question 2

Sett upp en ordered probit using the latent variable approach with 3 outcomes. use y*=X’B

Answer 2

Se koncept 4.

Question 3

What is the marginal effect in the ordered model?

Answer 3

Se concept 4.

Question 4

What is example of count data?

Answer 4

The number of times someone has been arrested over a year. Count variable = {0,1,2,……}. y ≥ 0. most often = 0. so we have a skweed distribution.

Question 5

How do you set up a count data regression?

Answer 5

Assign RHS to a exponential distribution so E(Y|X) = exp(X’B) which is offcoure bigger then zero.

Question 6

How do you estimate a count data regression?

Answer 6

Since it is non-linier we do use MLE instead of OLS. SInce the assumption regarding normal distribution only applies to continuous variables that can take on any value, we instead use the Poisson distribution.

Thus, we let exp(X’B) be lambda in the poisson dist and estimate the log likelihood. Here we have no closed form solution. Just as in the case with probit and logit, we can directly interpret the coefficients.

A assumption in the poisson dist is that mean = variance = lambda. If we find out the the variance is not equal to the mean, we have to inflate the SEs.

Question 7

What is overdispersion? Why is it a problem and how do we solv it?

Answer 7

See concept 4.

Question 8

What is a Multinomial Logit?

Answer 8

A model where the dependent variable is a categorical variable ≥ 3.

Question 9

Formulate the multinomial model

Answer 9

See concept 4.

Question 10

Show the tobit model when the dependent variable is censured from below.

Answer 10

See concept 4.

Question 11

Show the bias when we have censoring due to top coding and when we have a conrner solution in the case of reservation wages.

Answer 11

See concept 4.

Question 12

Why do we use tobit model?

Answer 12

Det finns två huvudsakliga användingar av dessa modeller.

1. Truly censord application. I USA är den mesta datan top-codad ovanför en viss inkomstnivå. Vi kan inte observera ett utfall ovanför t.ex $10000. Det är ju ett stort no no att bara studera de vi kan observera! Vi får ett biased estimat. Vi är censorerar mer troligt höga nivåer. Detta ger oss biaset. Dont do that! Istället ska vi använda metoder fölr detta!
2. Den andra anledningen är pga Corner solution outcomes. ….se engelkurvcan. x är inkomst. Vid något tillvälle kommer man sluta röka ekker dricka…. vi börjar se nollor på den beroende variablen. Det beytuder inte att man är okänslig för….. kommer man ovanför tröskeln börjar man se vad som häner…. ett annat exempel är labour supply. X = wage offer. Wj = houers of workl. Får vi wage offer under tröskeln är vi inte med i labour force, är vi ovanför så börjar vi erbjuda positiva nummer av timmar.

Question 13

Derive the tobit model.

Answer 13

See concept 4.

Question 14

What do the deriven tobit model look like?

Answer 14

See concept 4.

Question 15

What is the inverse mills ratio?

Answer 15

See concept 4.

Question 16

Show the definition of truncated vs censoring

Answer 16

See concept 4.