An inverse hyperbolic sine heteroskedastic latent class panel tobit model: An application to modelling charitable donations

Abstract

Abstract:We apply a latent class tobit framework to the analysis of panel data on charitable donations at the household level where the latent class aspect of the model splits households into two groups, which we subsequently interpret as "low" donators and "high" donators. The tobit part of the model explores the determinants of the amount donated by each household conditional on being in that class. We extend the standard latent class tobit panel approach to simultaneously include random effects, to allow for heteroskedasticity and to incorporate the inverse hyperbolic sine (IHS) transformation of the dependent variable. Our findings, which are based on U.S. panel data drawn from five waves of the Panel Study of Income Dynamics, suggest two distinct classes of donators. There is a clear disparity between the probabilities of zero donations across these classes, with one class dominated by the observed zero givers and associated with relatively low levels of predicted giving. We find clear evidence of both heteroskedasticity and random effects. In addition, all IHS parameters were significantly different from zero and different across classes. In combination, these findings endorse the importance of our three modelling extensions and suggest that treating the population as a single homogeneous group of donors, as is common in the existing literature, may lead to biased parameter estimates and erroneous policy inference. Although we use this model to explain charitable donations, we note that it has wide applicability.

How sensitive is the average taxpayer to changes in the tax-price of giving?

“…The estimated elasticity is − 1.24 (95% confidence interval − 1.59 to − 0.88). This result is closely in line with those surveyed in Peloza and Steel (2005) and Batina and Ihori (2010) and with more recent work also using PSID (Brown et al 2012;Yöruk 2010Yöruk , 2013Brown et al 2015;Zampelli 30 In general, non-donation itemizable expenditures (E) are not measured in survey data and even when information on E is available, as is the case with the PSID, it has not been, to our knowledge, included in models of donations in the literature to date. Such expenditures will be correlated with price via itemization status and likely correlated with donations since changes in, say, medical expenditures may affect one's donation amount.…”

“…By 26 Replacing P a it with P b it in our regression may lead to measurement error. Instead, some (e.g., (Yöruk 2010(Yöruk , 2013Brown et al 2012Brown et al , 2015 have used the price calculated using the first-dollar marginal tax rate as an instrument for P a it to address the endogeneity identified by Auten et al (2002). Given the very high correlation between P a it and first-dollar price in our data, we find that the use of the first-dollar price as an instrument or as a proxy provides qualitatively similar results.…”

“…In short, as itemizing is a function of donations for endogenous itemizers, so is not itemizing a function of donations for all non-itemizers. As a result, estimators of the price elasticity of giving based on data which includes non-itemizers (e.g., Brown and Lankford 1992;Andreoni et al 2003;Bradley et al 2005;Brown et al 2012;Yöruk 2010Yöruk , 2013Brown et al 2015;Zampelli and Yen 2017) will be downward biased. 7 To understand the intuition of the price endogeneity arising from the inclusion of non-itemizers in the sample, consider the case where a taxpayer switches from being an itemizer one year to a non-itemizer the next.…”

“…Footnote 4 continued a panel of tax-filer data and Yöruk (2010Yöruk ( , 2013, Reinstein (2011), Brown et al (2012) and Brown et al (2015) generally find price elasticities in excess, sometimes substantially so, of − 1 using the same survey panel data we use. In their working paper, Andreoni et al (1999) use a Gallop survey of household giving and find price elasticities ranging from − 1.73 to − 3.35, magnitudes that they note are 'consistent with the body of literature' (p. 11).…”

Improved density and distribution function estimation

“…here β = (δ, γ, θ) ⊤ and z = (y, x) ⊤ . The IHS transformation was proposed in Johnson (1949, p.158) as an alternative to the Box-Cox power transform, (y λ − 1)/λ, y ≥ 0, and developed in Burbidge et al (1988) and MacKinnon and Magee (1990); see also, e.g., Ramirez et al (1994), Brown et al (2015) and the references therein for recent applications in statistics and econometrics, and Tsai et al (2017) for comparisons with other transformations. When θ = 0, the IHS transform is defined as the limiting value, lim θ→0 arsinh(θy)/θ = y, which corresponds to the Box-Cox transform with λ = 1; when θ ̸ = 0, the shapes of the IHS transforms are similar to those of the Box-Cox with λ < 1.…”