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. Decision to donate (probability)

2. 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. Split sample into j classes (which prior to estimation envisage to be “high” and “low” donators)

2. 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.

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log log exp ' exp '

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i j i ji j

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it it jt

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f y class j

z z

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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 2003 2005 2007

$100.5 $103.5 $165.7 $175.9

44% 45% 41% 42%

010

2030

40P

erce

nt

0 5 10 15Log total donations

02

46

8P

erce

nt

0 5 10 15Log total donations

010

2030

40P

erce

nt

0 5 10 15Log total donations - males

02

46

8P

erce

nt

0 5 10 15Log total donations - males

020

4060

Per

cent

0 5 10 15Log total donations - females

02

46

8P

erce

nt2 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.

COEF STD. ERRORIntercept -5.179 0.164Years of Schooling 0.321 0.011Male 0.523 0.057White 0.613 0.055Catholic 0.107 0.079Protestant 0.331 0.059Other Religion 0.286 0.129Aged <30 -1.415 0.070Aged 30-40 -0.945 0.063Aged 40-50 -0.394 3.980Aged 50-60 -0.187 2.187

Probability Class 1 0.298Probability Class 2 0.702OBSERVATIONS 30,779

CLASS 1 CLASS 2

T.M.E COEF M.E. COEF M.E.

Number of Adults -0.03* 0.08* 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 4.81 ($122.73) 0.88 ($2.41)

OBSERVATIONS 30,779

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