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.

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: $100.5$103.5$165.7$ %45%41%42%

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.

COEFSTD. ERROR Intercept Years of Schooling Male White Catholic Protestant Other Religion Aged < Aged Aged Aged Probability Class Probability Class OBSERVATIONS30,779

CLASS 1CLASS 2 T.M.ECOEFM.E.COEFM.E. Number of Adults-0.03*0.08*0.05*-0.10*-0.06* Number of Kids-0.13*-0.01* -0.31*-0.18* Employee0.19*-0.14*-0.08*0.51*0.30* Self Employed0.06*0.22*0.13*0.05*0.03* Married0.91*0.44*0.25*2.04*1.19* Log Lab. Income0.03*-0.01* 0.07*0.04* Log Wealth0.10*0.05*0.03*0.23*0.13* Log Oth. Income0.05*0.01*0.00*0.12*0.07* E(V) Class j4.81 ($122.73)0.88($2.41) OBSERVATIONS30,779

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 AICBIC Latent Class Tobit (all covariates) Tobit (subset of covariates) Double Hurdle

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