Risk Management in Banking - University of Rome 3

Risk management in banking - University of Rome 3 Lecture #5: Binary model1

Binary responses (0 or 1) are modeled with logit and probit regressions.

Example, logit: webuse lbw describe summarize logit low smoke ereturn list

In order to see the meaning of the saved results see help logit at the very end

Example, probit: sysuse auto describe summarize probit foreign weight

Predicted probabilities

use http://dss.princeton.edu/training/Panel101.dta

If you want to perform the command, but suppress the final output, type in the Command window: quietly [:] command

Examples:

1) qui logit y_bin x1 x2 x3 i.opinion margins, atmeans post You have generated variables at mean values.

1 This lecture is based on “Predicted probabilities and marginal effects after (ordered) logit/probit using margins in Stata”, by Oscar Torres-Reyna, available at: http://www.princeton.edu/~otorres/Margins.pdf Risk management in banking - University of Rome 3

In fact: egen x1_mean=mean(x1) br x1_mean

The probability of y_bin = 1 is 85% given that all predictors are set to their mean values.

You can also choose to set a predictor to specific value: qui logit y_bin x1 x2 x3 i.opinion margins, at(x2=4) atmeans post

The probability of y_bin = 1 is 95% given that x2 = 4 and the other predictors are set to their mean values.

3) tab opinion qui logit y_bin x1 x2 x3 i.opinion margins, at(x2=4 x3=3 opinion=(3 4)) atmeans post

The probability of y_bin = 1 is 98% given that x2 = 4, x3 = 3, the opinion is “Disag” and the rest of predictors are set to their mean values.

The probability of y_bin = 1 is 99% given that x2 = 4, x3 = 3, the opinion is “Str disag” and the rest of predictors are set to their mean values.

4) qui logit y_bin x1 x2 x3 i.opinion margins opinion, atmeans post

The probability of y_bin= 1 is: 87% among those who “strongly agree” 51% among those who “agree” 90% among those who “disagree” 93% among those who “strongly disagree” marginsplot Risk management in banking - University of Rome 3

5) tab opinion tab country qui logit y_bin x1 x2 x3 i.opinion i.country margins opinion#country, post

The probability of y_bin= 1 is:

87% among those who “strongly agree” in country A 22% among those who “strongly agree”, in country B etc.

Marginal effects

Marginal effects gives you the change in probability when the predictor or independent variable increases by one unit. qui logit y_bin x1 x2 x3 i.opinion margins, dydx(*) atmeans post

The change in probability when opinion moves from ‘strongly agree’ to ‘agree’ decreases 36 percentage points or -0.36, and is significant.

The change in probability when opinion moves from ‘strongly agree’ to ‘disagree’ increases by 3 percentage points or 0.03.

The change in probability when opinion moves from ‘strongly agree’ to ‘strongly disagree’ increases by 5 percentage points or 0.05.

The change in probability for one instant change in x1 is: 13 percentage points, in x2 is 3 percentage points and in x3 is 4 percentage points.

EXERCISE #2

By using the dataset last_class.dta, write on your do file the commands to perform the following analysis:

1) Show the number of observations per value of the variable country, as well as the percentage shares and cumulative shares 2) Generate an individual member identifier (by country) 3) Generate the number of individuals by country 4) Generate a personal identifier 5) Browse only the three new variables that you have just created 6) Move the three new variables at the beginning of the dataset (before the Risk management in banking - University of Rome 3

variable country) 7) Check whether x1 and x2 are correlated 8) List all saved results 9) Generate the mean of x1 10)Test whether the mean of x1 is equal to 20 11)Perform a OLS regression (y is the dependent variable) 12)Change the confidence interval at 99 13)Perform a OLS regression (y is the dependent variable) by excluding year 1999 14)Perform a logit regression where y_bin is the dep var and x1, x2, x3, opinion are the independent variable. Then show the change in probability when opinion moves from ‘strongly agree’ to ‘agree’

References of Lectures 1-2-3-4-5

“ OLS Regression Using Stata – A Very Basic Introduction”, available at: https://www.nuffield.ox.ac.uk/teaching/economics/bond/OLS%20Regression%20Using %20Stata.pdf (last access: December 16, 2016)

“Predicted probabilities and marginal effects after (ordered) logit/probit using margins in Stata”, by Oscar Torres-Reyna, available at: http://www.princeton.edu/~otorres/Margins.pdf (last access: December 16, 2016)

“ Regression with Stata Chapter 1 - Simple and Multiple Regression”, available at: http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter1/statareg1.htm (last access: December 16, 2016)

“ Stata Annotated Output Descriptive statistics using the summarize command”, availabe at: http://www.ats.ucla.edu/stat/stata/output/stata_summ_output.htm (last access: December 16, 2016)

“Stata Tutorial”, by Germán Rodríguez, available at: http://data.princeton.edu/stata/ (last access: December 16, 2016)

“ Stata Web Books Regression with Stata Chapter 2 - Regression Diagnostics”, available at: http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter2/statareg2.htm (last access: December 16, 2016)

Stata’s help file and PDF documentation

“ Statistical Computing Workshop Introduction to Stata Programming”, available at: http://www.ats.ucla.edu/stat/stata/seminars/stata_programming/ (last access: December 16, 2016)

“ Using Stata 9 & Higher for OLS Regression”, by Richard Williams, available at: Risk management in banking - University of Rome 3 http://www3.nd.edu/~rwilliam/stats1/OLS-Stata9.pdf (last access: December 16, 2016)