Unofficial Development Assistance: A Model of Development Charities’ Donation Income

The empirical literature on the determinants of charities’ donation income, distinguishing the charitable cause, is small. We consider the case of development charities specifically. Using a panel covering a quarter of a century, we observe a strong fundraising effect and a unitary household income elasticity. We find evidence that the conventionally identified ‘price’ effect may simply be the product of omitted variable bias. Our results further suggest that public spending on development crowds in private donations for development. We find a positive spillover effect of fundraising, suggesting the efforts of one development charity may increase contributions to other development charities.


I. Introduction
Discussion of development finance often focuses on Official Development Assistance (ODA), given by governments in the form of bilateral or multilateral aid. However, contributions from private individuals are also prominent. These include both remittances from migrants (e.g. Solimano, 2005) and the donations made to charities working abroad for overseas aid and humanitarian assistance, which have received much less attention from *This research was supported by ESRC grant RES-155-25-0061 ('Giving to Development'), which formed part of the Non-Governmental Public Action programme. The project was conducted in conjunction with Tony Atkinson, Cathy Pharoah and Sylke Schnepf and we thank them for very helpful discussion and suggestions; we draw on our joint work developing the panel database reported on Atkinson et al. (2012), but errors in the current article are ours alone. We are grateful to the Charities Aid Foundation for access to their data; data from Charity Trends from 2001 onwards are used also with permission of Waterlow Ltd who retain the copyright in them. We thank Ian Mocroft for help in documenting government funding of development charities and Robin Naylor, David Clifford and the editor and referees for comments and suggestions. JEL Classification numbers: D1, D6, F3, L3.
researchers. The large theoretical and empirical literatures on charitable giving tend not to distinguish giving by cause (Andreoni, 2006). In this article, we model donations received by overseas development charities in the UK, the total of which, in 2004-5, equalled about a quarter of the UK's ODA. We use a newly constructed panel on individual charity finances that spans over 25 years. Our focus on giving for overseas development rather than total giving allows us to pay more attention to the particular characteristics of giving to this cause. We draw in part on the theoretical model in Atkinson (2009), which explicitly considers the giving to overseas development charities by private individuals. We extend the existing empirical literature on charities' donation incomes that has focused on charity level factors, such as fundraising and government grants received by charities, by introducing aggregate donor characteristics, ODA and humanitarian crises within a single framework, allowing also for possible dynamics. Section II outlines this approach. Sections III and IV describe our data and econometric approach. Section V presents results and section VI concludes.

II. Modelling charitable giving for development
Charities receive income from sources such as the sale of goods and services, grants and voluntary contributions in the form of money donations which have generally been modelled as a function of either donor characteristics or charity characteristics. On the donor side, theory describes behaviour based on public goods and 'warm-glow' motives and the empirical literature focuses on modelling donations as a function of personal characteristics such as income using household or individual level data (see Peloza and Steel, 2005). On the charities' side, a smaller body of theory describes their activities (e.g. Steinberg, 1986;Steinberg and Weisbrod, 2005), much of it focused on their objective function.The related empirical work (e.g. Weisbrod and Dominguez, 1986;Khanna, Posnett and Sandler, 1995;Khanna and Sandler, 2000;Tinkelman, 2004) has sought to model donation receipts as a function of charity characteristics such as fundraising expenditure, often testing hypotheses about charity objectives.
In both approaches, the cause (e.g. health, education, development) supported by donations or served by the charity is typically ignored. But, in general, people give deliberately to a specific cause and charities are established to serve a particular purpose. Atkinson (2009) argues that the public goods and warm-glow models each fail to capture key aspects of giving for international development and proposes a new 'identification' model that incorporates elements of both. 1 Empirical studies may estimate a model for different charitable causes, though there are generally no cause-specific variables in the models. Moreover, models of donor behaviour that ignore the activities of charities, or vice versa, may be mis-specified as the donation expenditure of households and receipts of charities are two sides of the same coin and are a function of both donor and charity characteristics. Andreoni (2006) emphasizes that 'the interaction between supply and demand for philanthropy has been largely neglected in both theoretical and empirical analysis'. Our empirical model contains elements suggested from work on both sides of the market, integrating both 1 Atkinson's model is similar in spirit to the 'impact giving' model of Duncan (2004), although Duncan had no specific charitable cause in mind. aggregate donor and individual charity characteristics into a single framework, as well as considering development-specific macro determinants of donations to development charities, namely, ODA and large humanitarian crises affecting the developing world.
From the donor side, we focus on household income, emphasized in the warm-glow approach and the identification model.The quarter-century covered by our panel of charities saw a 1.6-fold increase in real after-tax household incomes in the UK. Income growth was far from steady across the period which covers the recessions of the early 1980s and early 1990s. Besides total income, we also allow for changes in its distribution. Over the period as a whole, inequality of incomes rose substantially. Glazer and Konrad (1996) present a signalling model of charitable giving that predicts an increase in giving arising from an increase in inequality. But in the case of international development charities, an increase in domestic inequality may cause donors to shift their giving towards domestic services and away from international ones. We include a dummy variable from 2001 to control for a policy change that led to a more substantial tax incentive for giving. 'Gift Aid' allows the recipient charity to reclaim the basic rate (22% in 2000) income tax paid on the gift effectively increasing the value of the donation. Prior to 2000, the incentive was limited to cash donations in excess of £600. In 2000, this lower limit was removed.
From the charity side, we follow the existing practice by considering the impact of fundraising, a constructed 'price', government grants, and other autonomous or non-voluntary, income. Within Atkinson's identification model, fundraising campaigns help increase the awareness of recipients' need, increasing donations made to the charity undertaking the expenditure. However, that expenditure may also affect donations made to other charities via a spillover effect, not previously allowed for in the charity literature. The fundraising of one charity may raise awareness of development issues and so increase donations made to all charities in the sector. Or, it may increase the relative appeal to donors of that particular charity, diverting contributions away from other development charities. Evidence of a positive spillover effect has been found for private, for-profit firms. For example, Sahni (2013) finds evidence that one restaurant's advertising increases sales made by its competitors serving similar food. We test for the presence of an analogous spillover effect from fundraising.
Following Rose-Ackerman (1982) and Weisbrod and Dominguez (1986), fundraising has also been assumed to affect negatively the 'price' of donations -a measure of the cost to a donor of increasing charitable output of a charity by £1. The identification of the price effect has been central to this literature and appears in nearly every empirical model of donations. Tinkelman (2004) defines the price as p t = 1/ (1 − f t−1 ) where f = F/D is the proportion of total donations, D, spent by the charity on fundraising, F, in the previous period. 2 Donor utility can be modelled as a function of the welfare of the recipients of the charities' 'output' or charitable expenditure. The price of increasing 'output' by one unit accounts for the proportion of the donation that goes to any expense other than the end-recipients (ignoring any indirect benefit to them). We use Tinkelman's definition and follow him and others (e.g. Okten and Weisbrod, 2000) in excluding administrative expenditure from the construction of our price variable, and our model, as we agree that 'there is no clear way of reliably computing the relevant portion of the organization's total administrative costs' (Tinkelman, 2004(Tinkelman, : 2183. The lag is used because donors cannot observe price in the period in which they donate as the information necessary for its construction is not available until a charity's annual report is submitted at year-end (Okten and Weisbrod, 2000;Tinkelman, 2004). Use of the lag also addresses possible endogeneity but raises concerns about neglected dynamics. A negative price effect, found by several authors may simply result from omitting an autoregressive process when modelling donations, something our econometric specification deals with.
We include a control of non-voluntary income, as is often done in the literature (e.g. Khanna et al., 1995;Khanna and Sandler, 2000). Charities with higher levels of nonvoluntary income coming from, say, high street shops, may find it easier to raise donations given this added exposure. Conversely, donors may see such charities as less in need of donations.
The issue of how the grant income of a charity affects its donations has received much attention (e.g. Kingma, 1989;Khanna and Sandler, 2000;Andreoni and Payne, 2011). Government grants may crowd out donation income -donors seeing the charity as less needy. 3 Or, they may 'crowd in' giving, being viewed by donors as a signal that a charity is worth supporting. There are also arguments for no impact: Horne et al. (2005) find that US donors have little knowledge of the government grants received by the charities to which they give. In the case of the UK overseas development charities, these grants represented about £250m in 2004-5, compared to donations of about £1bn (Atkinson et al., 2012). Over the period we consider, they grew enormously, by a factor of 10 between the late 1970s and the mid-1990s when there was a levelling off.
Government ODA features prominently in Atkinson's identification model: it influences the living standards of the recipients with whom the donor identifies, reducing the marginal impact of a donation on the welfare of the recipient. This provides another possible source of crowding-out, leading to lower donations. 4 Alternatively, 'crowding in' can be expected if increases in ODA raise donors' perceptions of need by drawing attention to problems of developing countries. The UK government's prominent commitment in the late 1990s to increase ODA and its continued pledge to sustain development assistance might be seen in this light. Finally, some donors may of course be unaware of ODA levels or changes. The scale of official assistance in relation to private donations demands that we include ODA as an explanatory variable in our empirical model.
An empirical model that focuses on international development charities needs to recognise emergency relief as an important influence on giving. A major humanitarian crisis can have an immediate and large impact on the donor perceptions of need that are at the heart of the identification model. The period we consider includes two such crises: the Ethiopian famine in 1984-85 and the Asian Tsunami of Christmas 2004. Both saw huge responses from private donors which we seek to measure. 3 Andreoni and Payne (2011) present evidence that the observed crowding out in studies using US data operates largely via changes in the fundraising behaviour of charities which receive grants. 4 However, Atkinson (2009)  Finally, in a major departure from previous practice, we initially allow for a general dynamic model. Whereas previous studies used lagged regressors to avoid endogeneity (Khanna et al., 1995;Okten and Weisbrod, 2000), we begin with a general dynamic model including contemporaneous and lagged regressors, including lagged donations. There are good institutional reasons for such a dynamic specification. Many individuals make donations through bank standing orders, which they fail to adjust each year as their circumstances change. Consider a charity that hires fundraisers to find new donors among high street shoppers. Donors typically sign up to give indefinitely and the charity's fundraising expenditure in that year produces a continued stream of income. The specification we use allows us to separate out the persistence found in the donations data that is due to an unobserved charity-specific effect from that due to the effect coming via lagged donations. The dynamics also allow us to separate the long-run from the short-run effects of the explanatory variables.
Taken together, our approach allows us to control simultaneously for the characteristics of donors, the characteristics of charities, the environment in which donations are made and potential dynamics determining donations.

III. Data
Our data come from the Charity Trends reports published by the Charities Aid Foundation (CAF) from 1978 to 2006, covering donations to 2004. 5 The reports document the annual revenues and expenditures of the leading UK fundraising charities. We obtain our donations variable by subtracting the figure for legacies from the total reported 'voluntary income', the variable on which the CAF rankings are based. CAF first included the top 200 fundraising charities, increasing coverage to the top 300 in 1985, the top 400 in 1986 and the top 500 from 1991. There was no report in 1995 and we did not have access to the report from 1981. We assign observations to a calendar year by applying the rule that where the charity's reporting year finishes before June 30th, the observation is assigned to the previous calendar year.
The resulting panel is unbalanced and has gaps. The gaps appear for various reasons including changing accounting years, duplicate data used by CAF from one year to the next, the unavailable CAF reports or because a charity drops out of the rankings for a year. 6 Where a gap of a single year appears, we linearly interpolate the missing values by using the observations for the preceding and following years. 7 We test the sensitivity of results to the exclusion of these filled-in observations.
Although the charities for which we have data represent only a small fraction of the roughly 160,000 registered UK charities, they form a large share of the economic activity 5 The last report in this series was published in 2007 but the information for donations is not consistent with that in earlier reports. Khanna et al. (1995) and Khanna and Sandler (2000) also used CAF data but just for eight years. 6 Charities sometimes neglected to respond to CAF's requests for their financial reports. Rather than exclude them charities from the rankings, CAF would use the data from the previous year. We have identified and removed these duplicate observations. Full details of our assembly and cleaning of the panel are given in Atkinson et al. (2008). 7 In two cases (ActionAid and UNICEF), we know the charity existed and was large enough to enter the rankings in the first years they were compiled but these charities were excluded for some reason. In these two cases, we apply the average growth rate over the three subsequent years  to fill in the missing data for 1978-81. of the charitable sector. The largest 500 charities by donated income account for about half of all such income (Charities Aid Foundation, 2004: ix, 21 and 40). The great bulk of donations come from individuals; a small part comes from the corporate sector and grant-making charitable trusts but these donations cannot be separated in the data.
Our focus is on the development charities. We include both the charities under this heading in the CAF reports and the 'religious international' charities that are separately identified. The development charities include a number that serve domestic as well as overseas causes, for example, the Red Cross and Save the Children. The data set contains 70 development charities that appear in Charity Trends at least once during the period, of which we drop two -see below -leaving 68. We lose a further 12 (only 35 charity-years in total) as there must be at least three consecutive observations for our estimation method (see section IV).
In terms of aggregate giving for development, there was a striking rise in the real value of donations across the period we consider, with an average annual growth rate for overseas charities among the top 200 fundraisers of nearly 7.5%, a little above that for charities as a whole. This growth far outstripped the 2% average annual growth in real after-tax household income. It was also far larger than the rise in the UK government's ODA, which grew unevenly in real terms by a factor of just 1.5. 1984-85 saw a spike in overseas donations due to the response to the Ethiopian famine. This was in part stimulated by Bob Geldof, who organized the Band Aid Christmas single in 1984 and the Live Aid concerts in 1985. Geldof's Band Aid Trust was the charity with the most donations in the UK in 1985 -among all causes -with £122m (2007 prices). We exclude this charity from our analysis as it was not founded to engage in annual fundraising. Its removal still leaves a spike in the two years. For example, Oxfam had a record year in 1984, with its £109m of donations (2007 prices) nearly double the level of the year before. We also exclude Comic Relief which raises funds with a telethon and associated events every two years, so it does not raise funds each year like other charities. 8 Table 1 gives summary statistics for the continuous variables entered in our model. The unit of analysis in panel (a) is the charity-year. Mean annual donations received by development charities is £11.7m (2007 prices). Fundraising statistics are conditional on fundraising being recorded as positive -information is missing or is recorded as zero for 11% of development charities. The percentage of zeroes or missing data are substantially higher for government grants, 39%, for which the statistics are also based on positive values. The absence of positive values for fundraising is not easy to understand -these are all charities that are among the top 500 in terms of donated income and it does not seem likely that this status can be attained without spending money on raising funds. Following Tinkelman (2004), we exclude observations with zero recorded or missing fundraising expenditure information and we test the sensitivity of our results to their inclusion. Zeroes or missing values for government grants are easier to understand -many charities do not get such grants. Only seven observations have zero non-voluntary income. 9 We include all 8 We exclude the Priory of St John (St John Ambulance), which was included among development charities by CAF and missionary charities. 9 The manner in which shop income is reported in charity accounts changed in 1995. Prior to 1995, charities tended to reported the net profit of their shops. A change in the Charity Commissions 'Statement of Recommended Practice (SORP)' lead charities to switch to reporting the gross value of these goods. A number of charities asked the CAF to observations, with a dummy variable to capture the impact of zero grant income relative to positive grant income. Panel (b) summarizes the macroeconomic variables common to all charities in a given year: total household income, the Gini coefficient for household income and a dummy capturing the change to Gift Aid in 2000. In panel (c), we summarize the development-specific variables: ODA and humanitarian crises. ODA figures include grants paid to charities, so we use the values net of these grants (they constitute only a small part of the total -about 5% in 2004). We also use dummies for 1984 and 1985 to capture the impact of the Ethiopian famine and for 2004 given the Boxing Day Tsunami. The dummy for the Boxing Day Tsunami takes the value one for charities whose financial year ended in the first half of 2005. These charities are assigned to 2004 according to our rule outlined above. However, their financial reports will capture at least some of any increase in donations that arose from the Boxing Day Tsunami at the end of 2004. This applies to seven charities.
Following Tinkelman (2004) and Okten and Weisbrod (2000), we use the natural logarithm of all the continuous variables in our model, except the Gini. The model also includes dummy variables for zero grant income (noted above).
continue reporting the net profits to avoid affecting. In the case of Oxfam, by far the largest earner of shop income on our data, we have adjusted the figures from 1995-2004 by the ratio of the net profit to the gross value in 1995-98. These figures were obtained from Oxfam's annual reports.

IV. Model specification and estimation
We start with a general dynamic specification allowing current and lagged variables, including lagged donations, to affect donations such that: where i and t index charities and years respectively, y it is the charity's (log) donations and e it = i + it is a composite error term where i is a charity-specific fixed effect (possibly correlated with the included regressors) and it is a well-behaved error term. The vector z it contains the charity-specific variables: log fundraising expenditure, log government grants, log non-voluntary income and the log of the 'price' variable. 10 The vector x t includes the macroeconomic variables and the development specific variables affecting the environment in which donations to overseas development are made: the log of total household income, the Gini coefficient for household income and the log of ODA (net of grants paid). The vector D includes dummy variables to capture the very large disasters that occurred during the observation period, the Ethiopian famine in 1984-5 and the 2004 Boxing Day Tsunami. These dummies are not lagged. We consider the possible spillover effects apart from the main analysis below.
There are several econometric issues that need to be addressed in the estimation of equation (1). The current values of fundraising, non-voluntary income and grants may be correlated with the contemporaneous error term e it . A positive shock to donations means that a charity can afford to spend more on fundraising. Such a shock could have positive or negative effects on the government grants it receives, depending on how these grants are allocated. If the correlation between e it and the regressors can be captured by the unobserved heterogeneity i and we did not include the lag of donations among an explanatory variables, the within-group (WG) estimator would be consistent. However, in a dynamic model containing a lag of the dependent variable, such as ours, the WG estimator is biased in small samples although the bias goes to zero as T increases (Nickell, 1981).
A standard approach to the estimation of dynamic panel data models with endogenous regressors is the Generalized Method of Moments (GMM) applied to the first differenced equation (GMM-diff) in order to eliminate the unobserved heterogeneity i that might be correlated with the regressors. However, as our panel has gaps, we use the forward orthogonal deviation (FOD) transformation (Arellano and Bover, 1995). 11 This transformation eliminates i while preserving sample sizes in panel data with gaps as it is computable for all but the final observation. 12 GMM estimates are obtained using xtabond2 in Stata (Roodman, 2009a). 13 10 We do not include the age of each charity as is done in Tinkelman (1999Tinkelman ( , 2004 and in Khanna and Sandler (2000) because in the within-group approach we use the age would reduce to an individual time trend. 11 Instead of subtracting the previous observation from the current, the FOD transformation subtracts the average of all future available observations. Formally, forward orthogonal transformation will transform y it to (T it / (T it + 1)) y it − (1/ T it ) s>t y is . The weighting equalizes the variances in the above transformation. 12 With first-differencing if a particular y it is missing, then both y it = y it − y it−1 and y it+1 will be missing. 13 A more detailed discussion of GMM can be found in Appendix S1.
We use tests for over-identification and the tests for first and second order serial correlations to choose our preferred specification and the set of instruments. The first is the Sargan test for over-identification (Sargan, 1958), which requires non-rejection of the null hypothesis that the instruments are valid. The Sargan test is robust to instrument proliferation (see Roodman, 2009b) but not to heteroscedasticity. We therefore also use the Hansen test (Hansen, 1982) that, like the Sargan test, requires non-rejection of the null hypothesis that the instruments are valid. The Hansen test, however, is robust to heteroscedasticity, but not to instrument proliferation. A large number of instruments can severely weaken the Hansen test producing questionably high P-values. We also use serial correlation tests (Arellano and Bond, 1991). White noise errors " it would imply a MA(1) process for the it , thus the specification test is passed by rejecting the null of no first order [AR(1)] serial correlation but not rejecting the null of no second order [AR(2)] serial correlation.
Our main regression results are presented in Table 2 with results of specification tests reported at the bottom of the table. Note that, all the models in Table 2 were estimated using only those observations with positive values for fundraising. The grants effect is estimated using the positive values of grants as we include a dummy (not reported) to capture the zero reported grants income. Cluster robust standard errors are reported in parentheses (the charities are the clusters).
Column (1) is a fully dynamic specification, with all charity-specific and macroeconomic variables characteristics, as well as ODA, entered contemporaneously and lagged one period estimated via GMM treating all contemporaneous charity-specific regressors and the lagged donations as endogenous. This specification fails the Sargan test (affected by heteroscedasticity) but passes the Hansen test (affected by instrument proliferation). Neither the lagged nor the contemporaneous effects are individually significant at the 5% level and they are also jointly insignificant (P-value = 0.929) indicating that the model may be over-parameterised and thus suffers from a high degree of multicollinearity. To address this, we drop the lagged macroeconomic variables characteristics and re-estimate the model using GMM [column (2)], treating all the charity-specific regressors, including lagged donations, as endogenous. This model also fails the Sargan test, but again passes the Hansen test. Of the lagged effects, only the lagged donations is significant. The other lags are not individually nor jointly significant (P-value = 0.765). As multicollinearity still affects the identification of the charity-specific effects, we further simplify the specification in column (3), where we estimate a partial adjustment model (only a lagged dependent variable) using GMM, again treating all the charity-specific regressors, including lagged donations, as endogenous. This model performs well on all the specification tests. In column (4), we re-estimate the partial adjustment model using GMM, though here we treat only the lagged donations and the price (a function of lagged donations) as endogenous. In column (5), we estimate the partial adjustment model via WG using the sample used for the GMM. 14 In column (6), we re-estimate the partial adjustment model via WG using all the observations with positive fundraising.
The results obtained via WG are extremely similar to those obtained via GMM suggesting that: (i) the Nickell bias is mitigated by our large T and (ii) the potential endogeneity of the charity-specific variables does not adversely affect the consistency of the WG esti-   (1)-(4) were obtained via GMM. In columns (1)-(3), we treat all contemporaneous charityspecific variables and lagged donations as endogenous. In column (4), we treat only lagged donations and the price as endogenous. The remaining results were obtained using the WG estimator. Results from specification tests are presented at the bottom of the table. For GMM to be consistent, we must reject the AR(1) test, fail to reject the AR(2) test as well as the Sargan and Hansen tests. Asterisks indicate statistical significance according to the following schedule: *10%, **5% and ***1%. mates. Given that the relative complexity of the GMM approach provides no value added in terms of consistency or unbiasedness and imposes a cost in terms of efficiency, we opt to proceed with the simpler WG estimation and take the results in column (6) as our baseline.
As a robustness check, we test the hypothesis that the coefficients obtained in our baseline model are statistically equivalent to those coefficients obtained in a number of alternative specifications: (i) adding observations with zero reported or missing fundraising data (P-value = 0.706); 15 (ii) the exclusion of Oxfam, far and away the largest development charity making up between a sixth and a third of total donations to development charities in a given year (p-value > 0.999); (iii) the use of year fixed effects in place of the macroeconomic variables and development-specific variables (P-value = 0.289); (iv) the exclusion of the filled in observations, discussed above (P-value = 0.122) and (v) to sample selection due to the changing number of charities in the rankings (for the top 400: P-value = 0.122 and for the top 500: P-value = 0.100). The full results for these robustness checks are presented in Table A1 of Appendix S1. We also check the robustness of the GMM results to different instrument sets, the results of which are in Table A2 of Appendix S1. In general, the estimated coefficients vary little in terms of magnitude and significance over these different specifications demonstrating the robustness of the results in the baseline model [column (6), Table 2], on which the following discussion is based.

V. Discussion
Given the partial adjustment specification, the reported coefficients are interpreted as shortrun effects and the corresponding long-run effects are given by / (1 − ), where = , . 15 To do this, we add a dummy variable to pick up observations with non-positive fundraising expenditure (we have noted the prevalence of zeroes above.) In both this case and in our baseline case, the effect of fundraising on donations is estimated from the positive values only.
The coefficient on lagged donations is 0.50 and is well-defined indicating that the short-run effects are about half the size of the long-run effects.
We estimate a short-run fundraising elasticity of 0.19 with a long-run effect equal to 0.37. The long-run effects are similar in magnitude to the partial fundraising elasticities from earlier work (Khanna and Sandler, 2000;Okten and Weisbrod, 2000;Tinkelman, 2004) which were necessarily interpreted as long-run effects. We discuss the estimated fundraising effect in greater detail below. Neither non-voluntary income nor grants have an effect for either development.
The coefficient on the price of giving is close to zero and statistically insignificant, as is the long-run price effect ( = −0.07, P-value = 0.348). However, when we estimate a static version of our model (not presented), the coefficient on the price effect is negative ( = −0.80) and significant (SE = 0.19, P-value < 0.001), consistent with the general results in earlier work (e.g. Khanna et al., 1995;Khanna and Sandler, 2000;Tinkelman, 2004). That the price effect falls toward zero and becomes statistically insignificant in a partial adjustment specification suggests that the significant price effect estimated elsewhere may be driven by omitted variable bias from an otherwise unaccounted for autoregressive process in donations rather than a genuine responsiveness to changes in the severity of 'leakages' perceived by donors, that is, the price. The direction of the omitted variable bias is consistent with > 0 and @p t / @D t−1 < 0, where is the coefficient on lagged donations.
The significance of the price effect generally found in the literature may lead charities to spend too little on fundraising as the total estimated fundraising effect will be diminished by the price effect. For example, Okten and Weisbrod (2000) conclude that the total fundraising effect, which takes into consideration the impact of the price, is not statistically different from zero. Such results may also lead charities to systematically under-report the amount they do spend on fundraising (Froehlich and Knoepfle, 1996) as they try to mitigate the perceived negative price effect.
The estimated short-run household income elasticity of donations in column (6), Table  2 is 0.75 and we cannot reject the null hypothesis of a short-run unitary income elasticity (P-value = 0.508). We also fail to reject unitary elasticity for the long-run effect, equal to 1.50 (P-value = 0.550).
Evidence for the impact of the income distribution is mixed. The coefficient on the Gini coefficient is statistically significant and of an economically important magnitude in columns (2), (3) and (5) of Table 2. While the point estimate remains negative and of an economically important magnitude in column (6), it is no longer statistically significant at conventional levels. The significant effect in column (5) suggests that a one standard deviation increase in the Gini coefficient leads to a 12% decrease in donations to development, on average and ceteris paribus. This result conflicts with the prediction of Glazer and Konrad (1996), though their model has no development-specific component. It is difficult, however, to draw conclusions from such a inconsistently identified effect (it tends to be insignificant in our robustness checks) and more work is needed in this area. The change in Gift Aid in 2000 did not affect contributions to development charities.
The coefficient on ODA is not significant. We also estimated the model using alternative specifications of ODA (levels, share of GDP) but results were consistently insignificant when the effect was assumed constant over time. The relationship between ODA and donations may not, however, be adequately described by such a restrictive specification. We find evidence of a change in the relationship between ODA and donations to development following the Ethiopian famine of the mid-1980s (the effect of which we discuss below). We plot the total donations made to development charities among the largest 200 fundraising charities in each year against the annual level of ODA, using log scales on both axes (see Figure 1). The triangular markers and dashed line show the scatter plot and linear fit, respectively, for 1978-83. The circular markers and solid line are the scatter plot and linear fit, respectively, for 1984. From 1978to 1983, there is evidence that ODA 'crowded out' donations; as ODA fell (by 25% from 1978 to 1983) total donations to development charities in the top 200 increased by 50%. However, from the onset of the Ethiopian famine in 1984, there is a marked change in the relationship and the graphical evidence suggests 'crowding in'. To test this econometrically, we re-estimate our base line model adding a dummy for those years 1984-2004 and an interaction term between this dummy and the log of ODA, allowing the effect of ODA to differ between the two periods. The coefficient on the interaction term is significant, indicating that the effect of ODA does change between the two periods. The estimated effect of log ODA before 1984 is −0.40 (P-value = 0.02). From 1984 onwards, the estimated effect (the linear combination of the coefficient on log ODA and that on the interaction term) is 0.38 (P-value = 0.06), consistent with what we observe graphically. 16 The severity of the crisis and the effect Live Aid had on popular culture (Street, 1997) seems to have affected a lasting change in the relationship between the state provision and the private provision of development assistance. The social psychology underpinning such a shift is, however, beyond the scope of this article. Note the other coefficients were not qualitatively changed from our baseline model.
Both the Ethiopian famine and the Boxing Day Tsunami had a powerful, positive impact on giving for development. The Ethiopian famine saw donations to the development charities included in our panel increase, on average, by around a third in 1984. The insignificance of the 1985 dummy suggests that the continuation of the famine did not have an analogous impact in 1985. In fact, several large overseas charities, for example, Oxfam, saw donations fall from 1984 to 1985, presumably as donations were diverted to the Band Aid Trust, which we exclude from our panel for a reason given earlier. Total giving for development, including to Band Aid, actually increased by around a fifth from 1984 to 1985. The Boxing Day Tsunami had a similar impact on donations to development charities, seeing them increase by about 30%.
We next turn our attention to two additional issues. First, we consider the distribution of the marginal fundraising effects. Second, we test for possible fundraising externalities.

The distributions of marginal effects
It has long been recognized by researchers that the objective function of charity managers might be inferred from the marginal effectiveness of fundraising expenditure (Steinberg, 1986;Weisbrod and Dominguez, 1986). Managers maximizing the gross revenue of the charity will fundraise until the marginal pound spent on fundraising brings in no additional funding. Managers maximizing net revenues (net of fundraising expenditure) will fundraise until the marginal pound spent on fundraising brings in one pound of additional funds. This is sometimes called programme service maximization.
Conclusions about the objective functions of charity managers based on the estimated marginal effect of fundraising may depend on whether it is the marginal effect calculated at the mean characteristics or the mean marginal effect that is being interpreted (Tinkelman, 2004). The short-run marginal fundraising effect, calculated at the mean characteristics, for development charities is 0.97, obtained by multiplying the coefficient on log fundraising [taken from Table 2, column (6)] by the ratio of the mean of donations to the mean of fundraising expenditure for the sample used in estimation. Alternatively, we can assume that the estimated elasticities are constant over charities and time and so calculate a charityyear specific marginal effect. Table 3 shows the distribution of the short-and long-run marginal effects of fundraising in columns (1) and (2), respectively.
Consistent with Tinkelman (2004), the mean effect is larger than the marginal effect calculated at the mean characteristics. This supports Tinkelman's claim that the mean effect can inadequately describe the behaviour of the 'average' charity as the distribution of the effects can be skewed by extreme (low) values of fundraising expenditure. The extreme values also inflate the standard deviation of the distribution of marginal effects and so conclusions about the behaviour of charity managers can be sensitive to whether the analysis is of marginal effect calculated at the mean characteristics or of the mean marginal effect. In our case, the short-run marginal effect calculated at the mean values of fundraising and donations is about a quarter of the size of the the mean marginal effect. The median effect, being less sensitive to outliers, is similar in magnitude to the effect calculated at the mean characteristics in each column. We therefore consider the marginal effect calculated at the mean characteristics as it is more representative of the activities of the 'average' charity. The results suggest that the 'average' development charity maximizes net revenue in the short run as the short-run marginal effect (calculated at the mean characteristics) is not statistically different from one (P-value = 0.941). In the long run, the results suggest that the 'average' charity fundraises short of net revenue maximization as the long-run marginal effect (calculated at the mean characteristics) is different from one (P-value = 0.020). This means that charities fundraise at an 'inefficiently' low level; charities could increase both fundraising expenditure and programme services. The reasons for this inefficiency are not immediately clear but may be a function of the perception that higher levels of fundraising reduce donations via the supposed price effect. We have shown here that, in the case of development charities, a reasonable observation rule for the price and controlling for serial correlation in donations, result in the estimated price effect being close to zero and statistically insignificant. Charity managers operating under the assumption that fundraising expenditure will have a negative impact on donations via the price will underestimate the revenue (net or gross) maximizing level of fundraising and so spend too little on fundraising. Notes: WG, within-group. The spillover effect is captured by including a variable equal to the log of the total fundraising expenditure of the five largest development fundraisers in each year. In columns (1) and (2), we use the same specification as our baseline model, though the five largest fundraisers are excluded in column (2). In columns (3) and (4), we use year fixed effects instead of the macro-level variables in our baseline specification. We exclude the five largest fundraisers in column (4). Standard errors are presented in parentheses. Asterisks indicate statistical significance according to the following schedule: *10%, **5% and ***1%.

Spillover effects of fundraising
To test for a fundraising spillover effect (see section II) among development charities, we construct a new variable that is equal to the total annual fundraising expenditure of the five charities with the most fundraising expenditure in each year. 17 This construction preferable to using the total fundraising of all other (−i) development charities as the number of development charities in the sample changes from year to year thus causing artificial changes in such a total.
We re-estimate our partial adjustment model including the log of this new 'spillover' variable. We present the estimated spillover effect in Table 4.
In columns (1) and (2), we estimate the model using the aggregate household characteristics, charity-specific and development-specific variables. The point estimate on the spillover variable is positive but statistically insignificant. In column (2), where we exclude those charities among the five largest fundraisers (from which the spillover variable was constructed), the coefficient on household income (not reported) becomes insignificant, though the magnitude of the coefficient is not materially changed from our baseline model. 18 There is, however, a large ( = 0.616) and significant (P-value < 0.001) correlation between the spillover variable and household income. This collinearity may make identification difficult.
To address this possibility, we replace the aggregate household and developmentspecific variables with year fixed effects and re-estimate the model for all development charities in column (3) and excluding the five largest fundraisers in column (4).The spillover effect remains positive, though is now well identified. This suggests that an increase in the fundraising expenditure of the largest fundraisers leads to an increase in donations to other development charities, on average and ceteris paribus. The point estimate on the spillover effect is similar in size to that on fundraising in our baseline model, 0.19. However, the magnitude of the effect is much smaller. Using the results in column (3), a one standard deviation increase in the fundraising expenditure of the very largest development charities increases average donations to other development charities by about 9%. Whereas a one standard deviation increase in a charity's own fundraising will see donations increase by about a third.

VI. Conclusions
In this article, we have modelled the determinants of donations received by overseas development charities in the UK, contributing to the relatively small literature on charitable giving that considers particular causes. We have used panel data that span over 25 years and we have drawn on recent theory on giving for overseas causes. Given the length of the panel we use, we are able to include controls for donor (macroeconomic) characteristics, macro-level events that affect donations to development charities as well as a possible autoregressive process in donations. Our results may be summarized as follows: • A partial adjustment specification is a useful advance on the static models previously used in the literature. The partial adjustment specification we use allows us to identify both short-run and long-run impacts of regressors. • Fundraising has a powerful effect on donations received by development charities with a short-run elasticity of 0.19 and a long-run elasticity which is approximately twice the size of the short-run elasticity. • We find that the impact of the price faced by donors, as conventionally defined in the literature, is not a significant determinant of donations when we control for the autoregressive process driving donations. • We find some evidence that the relationship between the public provision of the public good in the form of ODA and donations fundamentally changed following the Ethiopian famine of the mid-1980s. Prior to the famine, our results are consistent with ODA crowding out donations. After the famine, the evidence suggests the effect reversed. • We cannot reject the hypothesis that giving to overseas development has a unitary income elasticity in both the short and long run. We find no robust significant impact from changes in the inequality of household incomes, holding constant total income though there is some weak evidence suggesting that increased inequality decreases giving for development. • Conclusions about the marginal effect of fundraising and the objective functions of charity managers depends on whether the analysis considers the mean marginal effect or the marginal effect calculated at the mean characteristics. • There is some evidence of a positive fundraising externality. The fundraising expenditure of the largest development charities increases the revenue not only of the fundraising charity itself but that of other development charities as well.