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The fundraising efficiency in U.S. non-profit art organizations: an application of a Bayesian estimation approach using the stochastic frontier production model


This article examines how efficient art organizations are in raising funds from private giving. We measure fundraising efficiency using a Bayesian estimation approach using the stochastic frontier production model. We show that fundraising efficiencies are generally quite low for art organizations in the U.S. when private giving is only considered as a fundraising output; however, when the effect of fundraising on ticket sales is considered, fundraising efficiencies improve substantially. We also show that government grants have a negative impact on fundraising efficiency and therefore partially crowd out private giving.

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  1. 1.

    Private giving is labeled as direct public support in the IRS 990 Form. According to Hansmann (1980), non-profit organizations can raise funds through two specific means: (1) through fees for the services that they provide and (2) through private donations and public grants like government subsidies.

  2. 2.

    See Brooks (2003) and Andreoni and Payne (2003) for recent developments in this important issue.

  3. 3.

    Other researchers have measured efficiency of art organizations using a technique called Data Envelopment Analysis (DEA). See Luksetich and Hughes (1997) and Basso and Funari (2004).

  4. 4.

    See citeNknitte02 [electricity], Rezitis et al. (2002) [agriculture], (Kim and Han 2001) and Harris (2001) [manufacturing], Balcombe et al. (2006) [dairy], and Bishop and Brand (2003) [museums].

  5. 5.

    The choice of the exponential distribution assumption is discussed in the following subsection.

  6. 6.

    The deviance is defined as

    $$ D(\theta )=-2log(p(y|\theta))+C $$

    where y is the data, θ are the unknown parameters of the model and p(y|θ) is the likelihood function. C is a constant. DIC is calculated as

    $$ DIC=p_{D}+ED $$

    where p D  = ED − D(Eθ) measures the effective number of parameters of the model and Eθ = E(θ). The second term ED = E θ[D(θ)].

  7. 7.

    See Spiegelhalter et al. (2002) for a discussion.

  8. 8.

    Bishop and Brand (2003), in their study of overall production efficiency of museums, defines capital input as approximated value of the total running and maintenance costs of the museum.

  9. 9.

    These assumptions are consistent with the existing literature, e.g. Griffin and Steel (2007).

  10. 10.

    The initial parameter values assigned for prior distributions in our estimation are a 1 = a 2 = 0.01,  b 1 = b 2 = 0.01, and c 1 = c 2 = 0.01.

  11. 11.

    According to (Koop et al. 1995), MCMC estimation method is the most appropriate method in the presence of the complexity of numerical integrations involved with estimation of stochastic frontier models. Lately, MCMC estimation has been employed in the estimation of stochastic production frontiers and technical efficiency. See van den Broeck et al. (1994), Tsionas (2002), Huang (2004), and Kumbhakara and Tsionas (2005) for the MCMC approach in the study of stochastic frontier model.

  12. 12.

    See footnote 6.

  13. 13.

    56 organizations that reported negative or zero private donations and negative fundraising expenditures are eliminated from the original dataset.

  14. 14.

    Bishop and Brand (2003) also reports fairly low average levels of production efficiency among museums in U.K. estimated to be about 45%. In a study of efficiency of sympony orchestra fundraising efforts using DEA by Luksetich and Hughes (1997)s also reports significant inefficiencies in fundraising efforts.

  15. 15.

    This again points out the fact that simple ratio of fundraising expentitute over private donation may not be an appropriate way of measuring fundraising efficiency for art organizations.

  16. 16.

    Efficiency estimated using private giving as output is used to estimate the effects of grants and visibility.


  1. Aigner D, Lovell C, Schmidt P (1977) Formulation and estimation of stochastic frontier production function models. J Econom 6:21–37

    Article  Google Scholar 

  2. Andreoni J (1990) Impure altruism and donations to public goods: a theory of warm-glow giving. Econ J 100:464–477

    Article  Google Scholar 

  3. Andreoni J (1993) An experimental test of the public goods crowding-out hypothesis. Am Econ Rev 83:1317–1327

    Google Scholar 

  4. Andreoni J, Payne A (2003) Do government grants to private charities crowd out giving or fund-raising? Am Econ Rev 93:792–812

    Article  Google Scholar 

  5. Balcombe K, Fraser I, Kim J (2006) Estimating technical efficiency of australian dairy farms using alternative frontier methodologies. Appl Econ 38:2221–2236

    Article  Google Scholar 

  6. Basso A, Funari S (2004) A quantitative approach to evaluate the relative efficiency of museums. J Cult Econ 28:195–216

    Article  Google Scholar 

  7. Bergstrom T, Blume L, Varian H (1986) On the private provision of public goods. J Public Econ 29:25–49

    Article  Google Scholar 

  8. Bishop P, Brand S (2003) The efficiency of museums: A stochastic frontier production function approach. Appl Econ 35:1853–1858

    Article  Google Scholar 

  9. Brooks AC (2003) Do government subsidies to nonprofits crowd out donations or donor? Public Finance Rev 31:166–179

    Article  Google Scholar 

  10. Duncan B (1999) Modeling charitable contributions of time and money. J Public Econ 72:213–242

    Article  Google Scholar 

  11. Frumkin P, Kim MT (2001) Strategic positioning and the financing of nonprofit organizations: is efficiency rewarded in the contributions marketplace. Public Admin Rev 61:266–275

    Article  Google Scholar 

  12. Griffin J, Steel M (2007) Bayesian stochastic frontier analysis using winbugs. J Prod Anal 27:163–176

    Article  Google Scholar 

  13. Hansmann H (1980) The role of nonprofit enterprise. Yale Law J 89:835–901

    Article  Google Scholar 

  14. Harris R (2001) Comparing regional technical efficiency in uk manufacturing plants: the case of northern ireland 1974–1995. Reg Stud 35:519–539

    Article  Google Scholar 

  15. Huang H-C (2004) Estimation of technical inefficiencies with heterogeneous technologies. J Prod Anal 21:277–296

    Article  Google Scholar 

  16. Jondrow J, Lovell C, Materov I, Schmidt P (1982) On the estimation of technical inefficiency in the stochastic frontier production function model. J Econom 19:233–238

    Article  Google Scholar 

  17. Kim S, Han G (2001) A decomposition of total factor productivity growth in korean manufacturing industries: a stochastic frontier approach. J Prod Anal 16:269–281

    Article  Google Scholar 

  18. Koop G, Steel M, Osiewalski J (1995) Posterior analysis of stochastic frontier models using gibbs sampling. Comput Stat 10:353–373

    Google Scholar 

  19. Kumbhakara SC, Tsionas EG (2005) Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach. J Econom 126:355–384

    Article  Google Scholar 

  20. Lee L-F, Tyler WG (1978) The stochastic frontier production function and average efficiency: an empirical analysis. J Econom 7:385–389

    Article  Google Scholar 

  21. Luksetich W, Hughes P (1997) Efficiency of fund-raising activities: An application of data envelopment analysis. Nonprofit Volunt Sect Q 26:73–84

    Article  Google Scholar 

  22. Meeusen W, van den Broeck J (1977) Efficiency estimation from cobb–douglas production functions with composed error. International Economic Review 8:435–444

    Article  Google Scholar 

  23. Rezitis A, Tsiboukas K, Tsoukalas S (2002) Technical efficiency in the greek agricultural sector. Appl Econ 34:1345–1357

    Article  Google Scholar 

  24. Spiegelhalter D, Best N, Carlin B, der Linde AV (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc 64:583–616

    Article  Google Scholar 

  25. Tsionas E (2002) Stochastic frontier models with random coefficients. J Appl Econ 17:127–147

    Article  Google Scholar 

  26. van den Broeck J, Koop G, Osiewalski J, Steel M (1994) Stochastic frontier model: a Bayesian perspective. J Econom 61:273–303

    Article  Google Scholar 

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Correspondence to David T. Yi.

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Song, S., Yi, D.T. The fundraising efficiency in U.S. non-profit art organizations: an application of a Bayesian estimation approach using the stochastic frontier production model. J Prod Anal 35, 171–180 (2011).

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  • Fundraising efficiency
  • Stochastic frontier models
  • Bayesian estimation
  • Non-profit art organizations
  • Crowding out

JEL Classification

  • C11
  • H32
  • H5
  • L31