Modelling Charitable Donations:
A Latent Class Panel Approach
Sarah Brown (Sheffield)
William Greene (New York)
Mark Harris (Monash)
Karl Taylor (Sheffield)
July 2011
I. INTRODUCTION AND BACKGROUND

In US during 2005 $260bn,  trend last three
decades (Chhacochharia and Ghosh, 2008).

Kolm (2006) notes that private giving (outside family)
is around 5% of GNP in US.

Academic focus on the supply side – role of tax
deductibility on donations, price and income
elasticity.

Methodological advances and better quality of data
over time.
I. INTRODUCTION AND BACKGROUND

Reece (1979) early methodological contribution
using tobit model.

Other examples Kingma (1989) and Auten and
Joulfaian (1996).

A problem with this approach decision to donate
and the decision on how much to donate can be
influenced by different characteristics.
I. INTRODUCTION AND BACKGROUND

Double Hurdle approach is an alternative – two
stage decision process:
1.
2.

Decision to donate (probability)
Level of donation conditional on donating
Can allow have different sets of explanatory
variables at (1) and (2) (or the same) and they can
have different effects.
I. INTRODUCTION AND BACKGROUND

Such two-part models make a sharp distinction
between those who donate and non donators.

Recent strand of econometrics uses latent class
approach to distinguish between different groups
of individuals.

Two part models – only two groups, in a latent
class approach potentially infinite number of
population sub groups.
II. MOTIVATION

Latent class modelling popular in health
economics e.g. Deb and Trivedi (2002), consumer
behaviour e.g. Reboussin et al. (2008), and mode
of transport e.g. Shen (2009).

Our approach – employ latent class model splitting
households into “low” and “high” donators.

The tobit part of the model then explores the
determinants of the level of each groups
donations.
II. MOTIVATION

At the extreme, similar to a hurdle approach there
would simply be participants and non participants.

Latent class split households into “low” and “high”
donators, or potentially further sub-groups.

Arguably class membership is not likely to vary
significantly over time (especially in a short panel)
– use (largely time invariant) characteristics to
parameterise such membership.
III. A LATENT CLASS TOBIT MODEL

Hypothesis that there are inherently two main types of
charitable donators in the population: “high” and “low”
givers.

Note not directly observed – all that is observed is the
level of the donation.

The level of the donation – corner solution model, i.e.
Censored or tobit regression – in the data 43%
III. A LATENT CLASS TOBIT MODEL

Approach:
1.
2.
Split sample into j classes (which prior to estimation
envisage to be “high” and “low” donators)
For each class separate tobit models apply.

The explanatory variables (x) in the tobit equation
(stage 2) can have differing effects across classes.

Stage (1) is based upon MNL function of z.
III. A LATENT CLASS TOBIT MODEL


Use panel data. Greene (2008) notes that this aids in
the identification of latent class models.
Largely time invariant variables z affect the probability
of being in class j, remaining variables x influence level
of donation for each j.
N
J


log L   log exp z i ' j  exp z i '  j  
i 1
j 1






 Ti

 f yit class  j , xit ,  j 
 t 1



IV. DATA

2001, 2003, 2005 and 2007 PSID – information
on charitable giving over past calendar year.
Unbalanced panel 30,779 head of households.

Median level of total donation over time and
percentage making no donation:
2001
$100.5
44%
2003
$103.5
45%
2005
$165.7
41%
2007
$175.9
42%
40
Percent
0
5
10
Log total donations
15
0
5
10
15
Log total donations - males
6
4
Percent
40
0
5
10
15
Log total donations - males
0
0
0
2
2
20
4
Percent
6
8
8
60
15
0
0
2
10
4
Percent
5
10
Log total donations
20
30
8
6
40
30
20
10
0
0
0
5
10
15
Log total donations - females
2
4
6
8
10 12
Log total donations - females
IV. DATA

Explanatory variables in latent class part of
model, (largely) time invariant: years of
completed schooling, gender, ethnicity, religious
denomination, and age dummies.

Explanatory variable in tobit part of the model:
no. of adults/kids in household, employment
status, marital status, log household income,
log household wealth, log household non labour
income, price of donating, and year dummies.
V. RESULTS

Firstly consider determinants of class membership.

Then focus upon latent class tobit model, i.e.
determinants of the level of donation in each class.

Finally comparison to alternative estimators.
Intercept
Years of Schooling
Male
White
Catholic
Protestant
Other Religion
Aged <30
Aged 30-40
Aged 40-50
Aged 50-60
Probability Class 1
Probability Class 2
OBSERVATIONS
COEF
STD. ERROR
-5.179
0.164
0.321
0.011
0.523
0.057
0.613
0.055
0.107
0.079
0.331
0.059
0.286
0.129
-1.415
0.070
-0.945
0.063
-0.394
3.980
-0.187
2.187
0.298
0.702
30,779
CLASS 1
CLASS 2
T.M.E COEF
M.E.
COEF
M.E.
Number of Adults
-0.03*
0.05*
-0.10*
-0.06*
Number of Kids
-0.13* -0.01* -0.01*
-0.31*
-0.18*
Employee
0.19* -0.14* -0.08*
0.51*
0.30*
Self Employed
0.06*
0.22*
0.13*
0.05*
0.03*
Married
0.91*
0.44*
0.25*
2.04*
1.19*
Log Lab. Income
0.03*
-0.01* -0.01*
0.07*
0.04*
Log Wealth
0.10*
0.05*
0.03*
0.23*
0.13*
Log Oth. Income
0.05*
0.01*
0.00*
0.12*
0.07*
E(V) Class j
OBSERVATIONS
0.08*
4.81 ($122.73)
30,779
0.88 ($2.41)
V. RESULTS
Price of donating
 US those who itemise in tax return reduce
taxable income.
 P=1-MTR
 Endogeneity – (1) decision to itemise
influence by donations; (2) P a function of Y.
 Inverse relationship between price and level
of donation. “High” donators less sensitive to
price.
V. RESULTS
AIC
BIC
Latent Class
3.132
3.139
Tobit (all covariates)
3.821
3.287
Tobit (subset of covariates)
3.873
3.877
Double Hurdle
3.337
3.347
VI. CONCLUSION



Household’s split into two groups “low” and
“high” donators.
Measurement error
Extensions:
(1) correlation between latent class and tobit
(2) panel aspect of data