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Modelling Charitable Donations: A Latent Class Panel Approach

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.

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Modelling Charitable Donations: A Latent Class Panel Approach

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  1. Modelling Charitable Donations: A Latent Class Panel Approach Sarah Brown (Sheffield) William Greene (New York) Mark Harris (Monash) Karl Taylor (Sheffield) July 2011

  2. 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.

  3. 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.

  4. I. INTRODUCTION AND BACKGROUND • Double 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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%

  9. III. A LATENT CLASS TOBIT MODEL • Approach: • 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.

  10. 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.

  11. 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:

  12. 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.

  13. 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.

  14. 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.

  15. V. RESULTS

  16. 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

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