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  • Modelling Charitable Donations: A Latent Class Panel ApproachSarah Brown (Sheffield)William Greene (New York)Mark Harris (Monash)Karl Taylor (Sheffield)July 2011


    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 BACKGROUNDReece (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 BACKGROUNDDouble Hurdle approach is an alternative two stage decision process:

    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 BACKGROUNDSuch 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. MOTIVATIONLatent 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. MOTIVATIONAt 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 MODELHypothesis 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%


    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 MODELUse 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. DATA2001, 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:


  • IV. DATAExplanatory 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. RESULTSFirstly 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. ERRORIntercept-5.1790.164Years of Schooling0.3210.011Male0.5230.057White0.6130.055Catholic0.1070.079Protestant0.3310.059Other Religion0.2860.129Aged

  • CLASS 1CLASS 2T.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*-0.01*-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*Married 0.91*0.44*0.25*2.04*1.19*Log Lab. Income0.03*-0.01*-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. RESULTSPrice of donatingUS those who itemise in tax return reduce taxable income.P=1-MTREndogeneity (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.


    AICBICLatent Class3.1323.139Tobit (all covariates)3.8213.287Tobit (subset of covariates)3.8733.877Double Hurdle3.3373.347

  • VI. CONCLUSIONHouseholds split into two groups low and high donators.Measurement errorExtensions: (1) correlation between latent class and tobit(2) panel aspect of data



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