Upload
maille
View
31
Download
1
Embed Size (px)
DESCRIPTION
Demand for sex. Dependent variable. Ordered structure. Choice probability. Probability distribution, Logistic. Ordered Logit. Ordered logit. Likelihood. Marginal effects. Marginal effects. Utility function, use of condoms. Probability of using condoms. Log likelihood. - PowerPoint PPT Presentation
Citation preview
Demand for sex
*n n n ; n 1,2, , , N(1) y x
Dependent variable
nj
1 if client n belongs to category j; j 1,2,3,4(2) y
0 otherwise
Ordered structure
*nn1 1
*nn2 1 2*nn3 2 3*nn4 3
y 1 if y
y 1 if y(3)
y 1 if y
y 1 if y
Choice probability
*n n n nnj j 1 j j 1 j(4) P(y 1) P( y ) P( x x )
Probability distribution, Logistic
u1(5) F(u)
1 e
Ordered Logit
n nnj j j 1(6) P(y 1) F( x ) F( x )
Ordered logit
4
nj n4 3 nj 1
[P(y 1)] 1so that P(y 1) 1 F( x )
Likelihood
njyN 4
n nj j-1n=1 j=1
(7) L( , ) = F( - x ) -F( - x )
Marginal effects
n nnj j 1 j
n n n
P(y 1) F( x ) F( x );for j 1,2,3,4
x x x
Marginal effects
n11 n 1 n
n
n21 n 1 n 2 n 2 n
n
n32 n 2 n 3 n 3 n
n
n43 n 3 n
n
P(y 1)F( x )[1 F( x )]
x
P(y 1){F( x )[1 F( x )] F( x )[1 F( x )]}
x
P(y 1){F( x )[1 F( x )] F( x )[1 F( x )]}
x
P(y 1){F( x )[1 F( x )]}
x
Utility function, use of condoms
jnnj nj j 0,1; n 1, 2, , , N(10) U x ;
Probability of using condoms
K K
1k nk k nkk 0 k 0
n1 n0 K K K
0k nk 1k nk k nkk 0 k 0 k 0
n0k 1k 0k
exp( x ) exp( x )(11) P(U U )
exp( x ) exp( x ) 1 exp( x )
where
, and x 1.
Log likelihood
n1 n1N K K
y 1 yn nn1 n1k k
k 0 k 0n 1L( ) [ ( x )] [1 ( x )]
What money buys: clients of street sex workers in the US
• Maria Laura Di Tommaso, Marina della Guista, Isilda Shima and Steinar Strøm
Table A1. Dependent variable for the ordered logit
Frequency of sex with sex worker during last year . No of Obs 582Frequency per cent
=1 never 25.4
=2 once 27.0
=3 more than 1 but less than once per month 35.0
=4 1 to 3 times per month 12.5
VariablesOrdered Logit Logit: Probability of
being a “regular” client Logit: Probability of using condom
Education =1 college or more; =0 otherwise
0.160(0.194)
0.067(0.243)
0.067(0.474)
Work status =1 Full time; =0 otherwise 0.655**(0.281)
0.656*(0.347)
0.476(0.564)
Race =1 if non white; =0 white 0.491***(0.186)
0.201(0.226)
1.121**(0.576)
Job =1executives/business managers;=0 otherwise
-0.125(0.170)
-0.151(0.209)
-0.023(0.415)
Marriage =1 married; =0 otherwise -0.312*(0.173)
-0.118(0.213)
0.090(0.412)
Control dislike 0.276***(0.096)
0.220*(0.118)
-0.062(0.234)
Age 0.017*(0.009)
0.030***(0.011)
-0.031(0.020)
Factor1 'againstg ender violence' 0.181*(0.108)
0.274**(0.136)
0.464*(0.259)
Factor2 'against prostitution'
-0.159*(0.094)
-0.199*(0.112)
-0.400*(0.222)
Factor3 'sex workers not different and dislike their job'
0.198**(0.101)
0.200*(0.124)
-0.102(0.242)
Factor4 'like relationships' -0.536***(0.112)
-0.641***(0.137)
-0.351(0.266)
Factor5 'variety dislike' -0.968***(0.121)
-1.031***(0.151)
0.692***(0.281)
Factor6 'relationship troubles ' -0.026(0.109)
0.006(0.137)
0.482*(0.293)
Threshold 1 0.788(0.550)
Threshold 2 2.233***(0.559)
Threshold 3 4.452***(0.580)
Constant -2.501***(0.692)
3.643***(1.339)
# of observationsMcfaddens rho
5820.14
5820.18
5700.71
Table 7: Marginal effects in the ordered logit
VariablesNever with sex workers
Once with sex workers
More than 1 time but less then once per month
1 to 3 times per month
Education =1 college or more;=0 otherwise
-0.0269(0.033)
-0.012(0.014)
0.027(0.033)
0.012(0.014)
Work status =1 Full time; =0 otherwise
-0.123**(0.059)
-0.033***(0.008)
0.113**(0.048)
0.0429***(0.015)
Race =1 if non white;=0 white -0.077***(0.028)
-0.044**(0.018)
0.079***(0.029)
0.0425**(0.017)
Job =1executives/business managers=0 otherwise
0.02(0.028)
0.01(0.014)
-0.02(0.028)
-0.010(0.013)
Marriage =1 married; 0 otherwise 0.051*(0.0287)
0.026*(0.015)
-0.052*(0.029)
-0.025*(0.014)
Control Dislike -0.045***(0.016)
-0.023***(0.008)
0.046***(0.017)
0.022***(0.008)
Age -0.002**(0.002)
-0.001*(0.0008)
0.002*(0.0015)
0.001*(0.0007)
Factor1 'Against gender violence' -0.029*(0.018)
-0.015*(0.0094)
0.030*(0.018)
0.014*(0.0088)
Factor2 'Against prostitution' 0.026*(0.015)
0.013*(0.0083)
-0.026*(0.015)
-0.012*(0.0077)
Factor3 'Sex workers not different and dislike their job'
-0.032**(0.016)
-0.016*(0.009 )
0.033**(0.0172)
0.016*(0.0083)
Factor4 'Like Relationships' 0.088***(0.0186)
0.045***(0.011)
-0.09***(0.020)
-0.043***(0.009)
Factor5 'Variety dislike' 0.159***(0.02)
0.085***(0.015)
-0.162***(0.024)
-0.078***(0.012)
Factor6 'Relationship troubles' 0.004(0.017)
0.002(0.009)
-0.004(0.018)
-0.002(0.008)
Other examples
• Tax evasion and detection probabilities
• What is the chance for being detected when evading taxes?
4
*n n n
nj
*nn1 1
*nn2 1 2*nn3 2 3
*nn4 3
*nn5 4
; n 1,2, , , N
q
(1) q x
1 if individual n 'sanswer belongs to category j; j 1,2,3,4,5(2) q
0 otherwise
1 if q
q 1 if q
(3) q 1 if q
q 1 if q
q 1 if q
n nnj j j 1
5
nn5 4njj 1
(4) P(q 1) F( x ) F( x )
(5) [P(q 1)] 1so that P(q 1) 1 F( x )
The questions
What is the chance of being detected:
1. Will certainly be detected
2. Will almost certainly be detected
3. Will perhaps be detected
4. Will almost certainly not be detected
5. Will certainly not be detected