HIAS-E-134

Tax-Price Elasticities of Charitable Giving and
Selection of Declaration: Panel Study of South Korea
Hiroki Kato(a), Tsuyoshi Goto(b), Youngrok Kim(c)(a)

Hitotsubashi University(b) Chiba University(c) University of Hyogo

Sep 2023

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
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Tax-Price Elasticities of Charitable Giving and
Selection of Declaration: Panel Study of South Korea ∗Hiroki Kato †Tsuyoshi Goto ‡Youngrok Kim §September 28, 2023

Abstract
In this study, we estimate the tax-price elasticity of charitable giving and address thebias caused by the existence of unreported donations and self-selection to the declaration ofgiving. To eliminate this bias, we propose a simple estimation method based on intentionto-treat analysis. Using our proposed method and the exogenous variation in tax incentives
in the 2014 South Korean tax reform, we estimate the price elasticity of donations to be −1.6
for the intensive margin and −2.6 for the extensive margin, which are more elastic than thestandard results that do not account for unreported donations and self-selection. The result
implies that the 2014 tax reform reduced the total amount of giving and that tax incentives
should be expanded.

Keywords: Charitable giving, Tax incentives, Price elasticity, Selection, Declaration
JEL Codes: D64, H24, H31∗ We would like to thank Nobuo Akai, Masayoshi Hayashi, Makoto Hasegawa, Sasaki Masaru, Takeshi Miyazaki,

Hikaru Ogawa, Fumio Ohtake, Yasuhiro Sato, participants in the 25th Annual Conference of The Japan Public
Choice Society, participants in the 77th Annual Congress of the International Institute of Public Finance, andparticipants in the OSIPP Lunch Time Seminar at Osaka University for their helpful comments. This paper reflects
the views of the authors and not necessarily the position of the organizations to which the authors belong. The
authors have no financial arrangements that might give rise to conflicts of interest with respect to the research
reported in this paper.
† Corresponding author. Hitostubashi Institute for Advanced Study, Hitotsubashi University, Tokyo, Japan(hkato.econ@r.hit-u.ac.jp)‡ Graduate School of Social Sciences, Chiba University, Chiba, Japan (t.goto@chiba-u.jp)§ School of Economics and Management, University of Hyogo, Kobe, Japan (econ.maple@gmail.com)

1

Introduction

In many countries, governments provide tax relief for charitable giving to encourage the private
provision of goods considered beneficial for society. To evaluate this policy, many papers
attempt to estimate the price elasticity of giving using tax record data (e.g. Almunia et al., 2020).
However, not all donations are recorded and reported to the tax authorities. In the U.S., 35
percent of total individual giving is estimated to be undeclared giving (Giving USA Foundation,
2022, p.337). Therefore, the price elasticity of giving estimated using tax record data is actually
the price elasticity of reported giving and differs from the price elasticity of total giving, whichis considered a key measure for assessing the optimality of tax expenditure on giving (Saez,
2004; Fack and Landais, 2016).
Unfortunately, this problem cannot be solved by a simple regression using panel survey datawith undeclared giving data because the decision to declare giving is self-selected by taxpayers
and a simple regression will be affected by selection bias. Moreover, even if the self-selection
problem is solved, changes in the price of giving may be endogenous without the exogenous
policy change regarding the price of giving. Therefore, the price elasticity estimates will bebiased in a simple regression.
In this paper, we estimate the price elasticity of total giving while recognizing that declaring
giving is self-selected and exploiting an exogenous policy change in Korea. In Korea, the tax
relief for charitable giving was changed from an income deduction to a tax credit in 2014, andthis policy change exogenously creates variation in the price of giving.
To address the self-selection issue, we offer an estimation that mitigates selection bias bydefining two prices of giving, depending on whether the giving declaration is considered: One isapplicable for all taxpayers if declared, which we call “the applicable price”; the other is effective
only for declarers, which we call “the effective price”. They differ in that the effective pricedepends on taxpayers’ self-selection, whereas the applicable price does not since the applicable
price is calculated as if all taxpayers declared their giving.1
Because the 2014 tax reform generates exogenous variation in the applicable prices, theestimation of the applicable price elasticity of total giving should not suffer from self-selection
bias and is equivalent to the estimand called intention-to-treat (ITT). However, it differs fromthe price elasticity of total giving because the applicable price is the price of giving that assumes
1 For example, when reporting their giving allows taxpayers to reduce their giving price from 1 to 1 − 𝑞, theapplicable price is always 1 − 𝑞 (because 1 − 𝑞 is applicable if the giving is declared), and the effective price is 1 − 𝑞
if the giving is declared and 1 if it is not declared (because the effective price depends on the reporting status).

1that all taxpayers report their giving. Instead of the applicable price, the estimation basedon the effective price will return the price elasticity of total giving, but the simple regression
will fail since the effective price depends on the self-selection. Corresponding to this issue, we
propose the two-stage least squares (2SLS) estimation where the effective price is the endogenous
variable and the applicable price is an instrument. We theoretically predict that the effective
price elasticity will be more elastic than the applicable price elasticity.
We use household survey panel data from Korea called the National Survey of Tax and
Benefit (NaSTaB), which include the total amount of giving and whether a taxpayer declared thegiving.2 From this data, we obtain both applicable and effective prices of giving and estimatethat the price elasticity of total giving is −1.599 on the intensive margin. This value is moreelastic than −1, which is the standard result in the empirical literature on the elasticity of theprice of giving. In addition to the intensive margin, we also estimate the elasticity of the price of
total giving on the extensive margin following Almunia et al. (2020) and the estimate is −2.639,
which is also more elastic than the standard result.
These elastic estimates may arise because that the standard results using tax records estimate
the price elasticity of reported giving, which differs from the price elasticity of total giving. In
theory, Fack and Landais (2016) suggest that, if some taxpayers do not declare their giving, “theelasticity of reported contributions may appear too small, and lead to an inefficiently low levelof the subsidy.” (Fack and Landais, 2016, p.27) Along with this prediction, we find that theprice elasticities of reported giving estimated by our data are less elastic than the estimated priceelasticities of total giving.3 As existing theoretical studies recommend increasing the subsidy on
giving when the price elasticity of total giving is greater than −1 (Saez, 2004; Fack and Landais,
2016; Almunia et al., 2020), we conclude that tax expenditure on charitable giving should be
expanded in Korea. Moreover, our data imply that the effective price of giving increased andthe amount of giving decreased due to the 2014 tax reform in Korea.
In addition, we present several robustness checks in line with the various estimation issues
addressed in the literature, which include the change in the price of giving by manipulating theamount of giving and income and the announcement effect, while the baseline analyses alreadyaddress some of these issues.
2 ”National Survey of Tax and Benefit,” Korea Institute of Public Finance, https://www.kipf.re.kr/panel/(in Korean).
3 In our data, the estimated price elasticities of reported giving are −1.147 on the intensive margin and −1.982
on the extensive margin. Note that, although Fack and Landais (2016) suggest a difference in the price elasticityof reported and total giving, their focus is not on the existence of unreported giving but on falsely overreported
giving. Hence, they use tax record data rather than panel survey data.

2

Our paper relates to the literature on the price elasticity of giving, in particular some recent
papers that use policy change as a source of identification using tax record data.4 Almunia et al.
(2020) utilize the change in income tax rates in the U.K..5 Fack and Landais (2010) and Fack
and Landais (2016) use the change in the tax credit rate and the cost of reporting in France,
respectively.6 We contribute to this strand by using panel survey data and capturing total giving,
including undeclared giving without structural settings.7
In addition to studies using tax records, there is also a large body of work using panel survey
data. Most extant studies in this strand use U.S. panel survey data and capture undeclared giving(Rehavi and Shack, 2013; Zampelli and Yen, 2017; Backus and Grant, 2019).8 In particular,
Rehavi and Shack (2013) and Backus and Grant (2019) are similar to this paper in that theyeach address the issue of declaration, although they do not utilize an exogenous price shock suchas policy changes for identification.9 Our paper contributes to this strand by considering theself-selection issue and a policy change as the identification strategy.
Our paper also closely relates to Duquette (2016), who exploits policy changes in state
income tax rates in the U.S. and circumvents the issue of giving declarations by using charities’
data. Our result is consistent with Duquette (2016) in that the estimated elasticity of the priceof giving is more elastic than the standard result, -1.
Our novelty in the literature on the elasticity of the price of giving is that we consider the
self-selection bias generated by the fact that the declaring giving is optional. Although somerecent studies address this issue by modeling taxpayer behavior10 , we address the self-selection
issue by proposing a simple 2SLS method. This method also contributes to the growing literature
4 Note that our focus is on the price elasticity of giving.

In the literature on giving behavior, Hong and Kang
(2022) examine the effect of the 2014 Korean tax reform on giving behavior using NaSTaB data as we do, but they
do not derive price elasticities of giving or address the self-selection problem.
5 Note that Almunia et al. (2020) are aware that unreported giving is not captured in the tax record data andaddress this by using structural estimation, which is not required in our approach.
6 In addition, Gillitzer and Skov (2018) focus on the policy changes in Denmark that change the cost of declaring
giving. However, they do not estimate the price elasticity of giving.
7 Related to this, many papers use the tax record data (e.g. Auten, Sieg and Clotfelter, 2002; Bakija and Heim,
2011; Randolph, 1995). Many of them use the change in the price of giving by income fluctuation as a source ofidentification.
8 Using data from the U.S., Brown, Harris and Taylor (2012) and Brown et al. (2015) examine the determinant of
donations for the 2004 Indian Ocean tsunami and the giving behavior of poor and wealthy taxpayers, respectively,by constructing structural models.
9 Moreover, Rehavi and Shack (2013) uses a simple regression in which the effective price is a regressor on
giving, which may introduce a self-selection problem. Backus and Grant (2019) focus on the problem in the US
context that taxpayers cannot combine the standard deduction with other deductions.
10 Almunia et al. (2020) construct a structural model with a self-selection process and estimate a fixed cost for
declaring giving. Backus and Grant (2019) addresses the endogeneity issue generated by the fact that the giving
declaration is selected depending on the amount of other tax relief measures in the U.S. tax system.

3

addressing the declaration costs of tax expenditures (Fack and Landais, 2016; Gillitzer and Skov,2018; Tazhitdinova, 2018; Benzarti, 2020) and the choice to claim tax incentives (Zwick, 2021;
Orihara and Suzuki, 2023), such as tax breaks for R&D investment, in that this method allows us
to accurately estimate the price elasticity of tax expenditures given the presence of undeclared
items.
This paper consists of six sections. Sections 2 and 3 explain the institutional background anddata, respectively. Section 4 proposes a simple 2SLS model based on the ITT analysis. Section
5 examines the applicable and effective price elasticities based on 2SLS estimation, presents
several robustness checks and discusses our results. Section 6 concludes the paper.

2

Institutional BackgroundIn this section, we first describe the 2014 tax reform in Korea used as an identification strategy
for estimating price elasticities. Next, we state that the application for tax incentives.

2.1

2014 Tax Reform

The Korean tax system offers tax incentives for charitable giving in the income tax. To explain
how tax incentives determine the price of giving, we introduce a simple budget constraint.
Assume that a taxpayer with pretax income, 𝑦𝑖 , has a choice between private consumption,
𝑥𝑖 , and charitable giving, 𝑔𝑖 . When a taxpayer decides to declare charitable giving, the budget
constraint that the taxpayer faces is 𝑥𝑖 +𝑔𝑖 = 𝑦𝑖 −𝑇 (𝑦𝑖 , 𝑔𝑖 ), where 𝑇 is the tax amount that depends
on the pretax income and charitable giving. Since the marginal income tax rate is progressivein Korea, we assume that 𝑇 (·, ·) satisfy 𝑇𝑦 (·, ·) > 0 and 𝑇𝑦𝑦 (·, ·) > 0, where the subscript means
partial differentiation.
[Table 1 about here.]
Before 2014, the tax relief system for charitable giving in Korea was an income deduction.
This system reduced the amount of taxable income before determining the marginal income
tax rate. Thus, the amount of tax is 𝑇 (𝑦𝑖 , 𝑔𝑖 ) = 𝑇 (𝑦𝑖 − 𝑔𝑖 ) when taxpayers claim. The total
differential of the budget constraint with respect to 𝑥𝑖 and 𝑔𝑖 is 𝑑𝑥𝑖 + (1 − 𝑇 ′ (𝑦𝑖 − 𝑔𝑖 ))𝑑𝑔𝑖 = 0.
This leads to the price of giving (relative to private consumption), 1 − 𝑇 ′ (𝑦𝑖 − 𝑔𝑖 ). Since themarginal income tax rate is progressively determined as shown in Table 1, taxpayers facing a4higher marginal income tax rate can enjoy a lower giving price for each 1 KRW donation. In
other words, the price of giving was regressive before 2014.11
In 2014, to relax the regressivity of the prices of giving, the Korean government reformed thetax system, where a tax credit was introduced instead of an income deduction. The new tax relief
system directly reduces the amount of tax. That is, the amount of tax is 𝑇 (𝑦𝑖 , 𝑔𝑖 ) = 𝑇 (𝑦𝑖 ) − 𝑚𝑔𝑖 ,where 𝑚 is the tax credit rate. Thus, the total differential of the budget constraint leads to therelative giving price, 1 − 𝑚. The Korean government allows 15 percent of the total amount of
declared charitable giving as a tax credit (𝑚 = 0.15), which means that the price of giving from2014 was 0.85 KRW for each 1 KRW of donation regardless of income level.1213
In short, the applicable price of giving, which is the price of giving that can be applied after
the declaration, is 1−𝑞, where 𝑞 represents tax incentives. The tax incentives were 𝑞 = 𝑇 ′ (𝑦𝑖 −𝑔𝑖 )before 2014 and 𝑞 = 𝑚 = 0.15 after 2014. Therefore, high-income households, whose income
tax rate was more than 15 percent before 2014 (income brackets (C)–(G) in Table 1 in 2013), facea higher price of giving due to the 2014 tax reform. On the other hand, low-income households,
whose (average) income tax rate was less than 15 percent (income bracket (A) in Table 1 in2013), faced lower prices of giving due to the 2014 tax reform. Finally, among middle-income
households, whose income tax rate was equal to 15 percent (income bracket (B) in Table 1 in2013), the 2014 tax reform does not affect the price of giving. We exploit the variation in theprice of giving generated by the 2014 tax reform as our main identification source to estimate
the elasticity of the price of giving.

2.2

Process of Declaration

In estimating the price elasticity of total giving, including unreported giving, an importantbut often ignored aspect is that receiving a tax incentive depends on the taxpayer’s choice. If
taxpayers donate but do not declare it, their tax amount is 𝑇 (𝑦𝑖 ); thus, they cannot obtain the
tax incentive. Then, given the optimal claiming status, the effective giving price, which is the
11 In the income deduction regime, there was a limitation that no deduction was allowed for donations exceeding acertain percentage of income: it was 15% in 2008-2010; 20% in 2011; and 30% in 2012-2013. Similarly, tax relief
for religious-related donations was allowed if it was within 10 % of income. To exclude the effect of the limitation,
we omit claimants donating more than 10% of their income from the sample, which consists of approximately 3%of all taxpayers in the data.
12 During the transition period, taxpayers were able to declare donations made prior to 2014 after 2014. In thiscase, the taxpayer would still be eligible for the income deduction system.
13 Note that, with the introduction of the tax credit in 2014, the tax credit rate for donations exceeding KRW 30
million was set at 25 percent. We omit these data from the analysis sample, although such large donations are rarely
observed in our sample (approximately 0.03%).

5

actual donation price the taxpayer faces, is 𝑝 = 1 − 𝑅𝑞, where 𝑅 is a dummy variable that takes
one if taxpayers report their donations and zero otherwise.
We provide an overview of the process for declaring giving in Korea. In Korea, personal
income tax is assessed for one year, from 1 January to 31 December. In principle, taxpayers
submit their income tax returns and pay income taxes in May of the following year. Moreover,unlike the U.S., wage earners have additional chance to report their giving through the year-end
settlements in January or February of the following year.
This complex process would impose significant costs on taxpayers. Indeed, Table 2 showsthat only approximately half of all donors receive tax incentives. This means that reported giving
may be a part of total giving. Thus, we would expect the price elasticity of total giving, which isconsidered an important parameter for assessing the optimality of the tax system, to differ fromthe price elasticity of reported giving.
In estimating the price elasticity of total giving, even if the 2014 tax reform creates anexogenous variation in tax incentives 𝑞, the effective price of giving 𝑝 is endogenous due tothe self-selection of declaration, 𝑅. Section 4 presents a way to solve this endogenous problem
using only exogenous variation in 𝑞.

3

Data

This study uses the NaSTaB, conducted by the Korea Institute of Taxation and Finance since2008, which is annual panel data on household tax burden and public assistance. The survey
targets 5,634 households nationwide, with household heads and economically active household
members aged 15 or older. The survey asks about income, charitable giving, demographics suchas years of education, and attitudes toward the tax system.

3.1

Study Sample

To focus on an exogenous change in the price of giving due to the 2014 tax reform, we use
2010–2017 NaSTaB data, excluding observations in income brackets (F) and (G) shown in Table
1. This sample exclusion ensures that within-individual changes in the price of giving depend
only on intertemporal income changes (before 2014) and the 2014 tax reform.
[Table 2 about here.]6[Figure 1 about here.]
In addition, to focus on taxable respondents who have sufficient income and assets, we use
respondents aged 24 or older who are not unpaid family workers, housewives, or students.14
We present descriptive statistics for the study sample in Table 2. The analysis sample consists
primarily of older men. Approximately 70 percent of the analysis sample is male, and theaverage age is 51. The average pretax gross income is KRW 30 million, similar to the average
income shown in the National Tax Statistical Yearbook 2012-2018 published by the Korean
National Tax Service (KRW 32.77 million). Figure 1 shows the pretax gross income distribution
for 2013.

3.2

Key Variables: Price of Giving, Giving Behavior, and Claiming Status

The solid stepwise line and the dashed horizontal line in Figure 1 are the prices of giving when
taxpayers declare their giving (applicable prices of giving). The solid stepwise line shows
the applicable prices of giving for the income deduction period (2010–2013), and the dashedhorizontal line shows the applicable prices for the tax credit period (2014–2017). As statedin Section 2, the changes in tax incentives due to the 2014 tax reform differ for three income
groups. The first income group is below KRW 12 million (Bracket (A)), for which the tax reform
expanded tax incentives and decreased the applicable prices of giving. The second group is
between KRW 12 million and KRW 46 million (Bracket (B)), for which the tax reform did notaffect tax incentives and the applicable prices of giving. The last group is above KRW 46 million(Brackets (C), (D), and (E)), for which the tax reform reduced tax incentives and increased theapplicable prices of giving. Exploiting this variation, we identify the price elasticity of donations
based on DID analysis.
[Figure 2 about here.]
The two outcome variables that capture donation behavior are the amount of giving anda dummy variable indicating donors. Table 2 shows that the average donation amount is
KRW 360,000 (equivalent to USD 300), approximately 1.1 percent of pretax gross income. In
comparison, the amount in the United Kingdom is 0.5 percent (Almunia et al., 2020), and that in
14 We also impose exclusion conditions on donations.

First, we exclude observations where donations exceed
total income. Second, we exclude claimants whose total donations exceed the limit for religious donations (10%of their income), recognizing that the price of giving for religious donations exceeding the limits differs from thestandard price of giving explained in Section 2.1. See also footnote 11.

7the United States is 1.5 percent (Backus and Grant, 2019). In addition, the proportion of donors
is 23 percent.
Figure 2 divides the sample by income bracket based on gross income in 2013 and showschanges in average donation amounts (Panel A) and donor ratios (Panel B) in each group.
The increase in average donation amounts and proportion of donors in Bracket (A), where theapplicable price of giving decreased after the tax reform, was more significant than that inBracket (B), where the applicable prices of giving remained unchanged after the tax reform. On
the other hand, the increase in average donations and donor ratios in Brackets (C)–(E), where theapplicable prices of giving increased following the tax reform, was smaller than that in Bracket(B). Thus, we expect a standard price effect on donation behavior.
[Figure 3 about here.]
In addition to income, the price of giving, and giving behavior, another important variable isdeclaration status. Since NaSTaB examines whether a taxpayer declared a charitable contribution
in each year-end adjustment and tax return system, we create a dummy variable that takes value
one if the taxpayer declared their giving in either system. We use this variable to identify the pricethat individuals actually face (effective price of giving). If taxpayers declare, the effective pricewill be equivalent to the applicable price shown in Figure 1; otherwise, the effective price is 1.
Table 2 shows that the proportion of declaration is 11 percent, indicating that only approximately
half of all donors declare their giving. Figure 3 shows the percentage of declaration in each
income bracket. After the introduction of the tax credit system, the percentage of claims in
Bracket (A) remained almost unchanged, while declaration in other brackets decreased. Notethat this trend cannot be explained by changes in the donor ratio, as this trend is also observedin the declaration rates among donors (see Figure A1 in Appendix A).

4

Estimating Price Elasticities

4.1

Estimation Model and Parameter of Interest

Our aim is to obtain unbiased price elasticities of total giving. In this section, we provide a
simple method to estimate them. To begin, we clarify the parameters of interest. As introducedin Section 2, the effective price of individual 𝑖 in year 𝑡 is 𝑝𝑖𝑡 = 1 − 𝑅𝑖𝑡 𝑞𝑖𝑡 , where 𝑅𝑖𝑡 is adummy variable indicating declaration of giving and 𝑞𝑖𝑡 represents the tax incentives. Outcome
8variables, 𝑌𝑖𝑡 , are determined by the following two-way fixed effects model:
𝑌𝑖𝑡 = 𝜇𝑖 + 𝜃 𝑡 + 𝛽𝑒 ln 𝑝𝑖𝑡 + 𝛿𝑋𝑖𝑡 + 𝜖𝑖𝑡 ,(1)

where 𝜇𝑖 , 𝜃 𝑡 , and 𝑋𝑖𝑡 are individual fixed effects, year fixed effects, and a vector of covariates(including pretax income, 𝑦𝑖𝑡 ), respectively. The term 𝜖𝑖𝑡 is an idiosyncratic error.
Our parameter of interest is a coefficient 𝛽𝑒 . Using this estimate, we obtain the effective priceelasticities (price elasticities of total giving). As in previous studies (e.g. Backus and Grant,
2019; Almunia et al., 2020), we estimate two types of elasticities. The first is the intensivemargin price elasticity, which indicates the percentage by which a 1 percent price increase leads
to an increase in the amount donors give. In this estimation, we restrict our sample to donors anduse the log value of donations, ln 𝑔𝑖𝑡 , as the outcome variable. Then, the coefficient 𝛽𝑒 indicatesthe price elasticity.
The second is the extensive-margin price elasticity, which indicates the percent by which
the donor ratio increases with a 1 percent price increase. For estimation, we include donors andnon-donors in our analysis sample and use a dummy variable 𝐷 𝑖𝑡 = 1[𝑔𝑖𝑡 > 0] indicating donors
as the outcome variable following Almunia et al. (2020). Because we have a binary outcome
variable, we cannot interpret the coefficient 𝛽𝑒 in this estimation as an elasticity. Therefore,¯ whereusing the estimate 𝛽𝑒 , we obtain the implied extensive-margin price elasticity as 𝛽ˆ𝑒 / 𝐷,𝐷¯ is the sample mean of 𝐷 𝑖𝑡 .
Since declaration, 𝑅𝑖𝑡 , depends on the taxpayer’s decision, the effective price can be endogenous due to selection into declaration. Thus, standard fixed effects models (1) may estimate abiased 𝛽𝑒 . In the next subsection, we propose a simple method to obtain an unbiased 𝛽𝑒 , aided
by ITT analysis.

4.2

Recovering Effective Price Elasticities

ITT analysis recognizes that some people assigned to treatment will not actually receive treatment
and examines the effect of providing the opportunity to receive treatment. We can estimate thiseffect using an estimation model that assumes that all people assigned to treatment receive
treatment. In our context, we recognize that some taxpayers who are eligible for tax benefits do
not actually receive them. Then, assuming that all taxpayers receive tax incentives (𝑅𝑖𝑡 = 1 for

9

all 𝑖, 𝑡), we estimate the following model:
𝑌𝑖𝑡 = 𝜇𝑖 + 𝜃 𝑡 + 𝛽𝑎 ln(1 − 𝑞𝑖𝑡 ) + 𝛿𝑎 𝑋𝑖𝑡 + 𝜂𝑖𝑡 .

(2)

The variable ln(1 − 𝑞𝑖𝑡 ) is the log value of applicable prices. We refer to the price elasticity
using the coefficient 𝛽𝑎 estimated in Equation (2) as an applicable price elasticity. For estimationof the applicable price elasticities, our identification strategy is a DID model exploiting theexogenous change in tax incentives 𝑞𝑖𝑡 due to the 2014 tax reform. Thus, the standard fixed
effects model (2) obtains unbiased applicable price elasticities.
The applicable price elasticity may be a valuable measure for the policy evaluation of tax
reform because policymakers cannot directly manipulate individual declaration choices. When
policymakers implement a reduction in tax incentives equivalent to a 1 percent increase indonation prices, the amount of donors’ giving changes by 𝛽ˆ𝑎 percent (intensive margin), and the¯ percent (extensive margin).
donor ratio changes by ( 𝛽ˆ𝑎 / 𝐷)
However, the applicable price elasticity differs from our parameter of interest, 𝛽𝑒 , the effective
price elasticity, since the ITT analysis assumes that even non-applicants for tax incentives receive
tax incentives. To illustrate this point, we derive the estimator of 𝛽𝑎 . By the regression anatomy
theorem (Angrist and Pischke, 2008), the estimator of 𝛽𝑎 is
Cov(𝑌𝑖𝑡 , 𝑟ˆ𝑖𝑡 )𝛽ˆ𝑎 =,Var(𝑟ˆ𝑖𝑡 )(3)

where 𝑟ˆ𝑖𝑡 is a residual of the following auxiliary regression model:ln(1 − 𝑞𝑖𝑡 ) = 𝜇𝑖 + 𝜃 𝑡 + 𝜆𝑋𝑖𝑡 + 𝑟𝑖𝑡 .

(4)

Since the residual is a linear combination of all explanatory variables and fixed effects inEquation (4), the residual 𝑟ˆ𝑖𝑡 should be uncorrelated with the explanatory variables and fixed
effects in Equation (4). In addition, since the covariate vector includes gross income, which
determines the income tax rate, the change in the residual should depend only on the 2014 tax
reform. Therefore, we assume that the residual 𝑟ˆ𝑖𝑡 is uncorrelated with the error term 𝜖𝑖𝑡 in
Equation (1).
The ITT analysis estimates Equation (2), but the outcome variable 𝑌𝑖𝑡 is determined by10

Equation (1). Thus, substituting Equation (1) into Equation (3) yields
Cov(𝑌𝑖𝑡 , 𝑟ˆ𝑖𝑡 ) Cov(𝛽𝑒 ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 )Cov(ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 )𝛽ˆ𝑎 === 𝛽𝑒 ·.
Var(𝑟ˆ𝑖𝑡 )Var(𝑟ˆ𝑖𝑡 )Var(𝑟ˆ𝑖𝑡 )(5)

Furthermore, since 𝑟ˆ𝑖𝑡 is a residual of auxiliary regression (4), the regression anatomy theorem
implies that the parameter Cov(ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 )/Var(𝑟ˆ𝑖𝑡 ) is a coefficient 𝛾1 in the following model:
ln 𝑝𝑖𝑡 = 𝜇𝑖 + 𝜃 𝑡 + 𝛾1 ln(1 − 𝑞𝑖𝑡 ) + 𝛾2 𝑋𝑖𝑡 + 𝑢𝑖𝑡 .

(6)

Thus, the applicable price elasticity is the product of two effects: (i) an effective price elasticity(parameter 𝛽𝑒 ) and (ii) the partial correlation between effective and applicable prices (parameter𝛾1 ).
If the residual 𝑟ˆ𝑖𝑡 and declaration of giving, 𝑅𝑖𝑡 , are mean independent, then the parameter 𝛾1will always be in the range from 0 to 1 (see Appendix B for the proof). In this case, the applicable
price elasticity is more inelastic than the effective price elasticity. Furthermore, the fewer nonclaimants there are, the stronger the correlation between effective and applicable prices, and thecloser the values of the two elasticities. As an extreme example, when all taxpayers donate anddeclare, 𝛾1 = 1 because the effective price is equal to the applicable price. Therefore, Equation(5) implies that 𝛽ˆ𝑎 = 𝛽𝑒 . Conversely, when no taxpayers declare, the logarithm of the effective
price must be 0, and Equation (5) implies that 𝛽ˆ𝑎 = 0. In our data, half of the donors declaregiving (Table 2), and non-donors cannot claim the deduction. Therefore, in our estimation ofprice elasticities, 𝛽𝑎 should not be equal to 𝛽𝑒 .
Equation (5) presents a way to recover the effective price elasticity from the applicable
price elasticity. Since we can estimate Equations (2) and (6), we can obtain an estimate of theparameter 𝛽𝑎 and 𝛾1 . Thus, by computing 𝛽𝑎 /𝛾1 , we can recover the coefficient 𝛽𝑒 used toestimate the effective price elasticity. The parameter 𝛽𝑎 /𝛾1 is also a Wald estimator of 𝛽𝑒 in thefollowing two-stage model with fixed effects (FE-2SLS):𝑌𝑖𝑡 = 𝜇𝑖 + 𝜃 𝑡 + 𝛽𝑒 ln 𝑝𝑖𝑡 + 𝛿𝑋𝑖𝑡 + 𝜖𝑖𝑡 ,(7)
ln 𝑝𝑖𝑡 = 𝜇𝑖 + 𝜃 𝑡 + 𝛾1 ln(1 − 𝑞𝑖𝑡 ) + 𝜆𝑋𝑖𝑡 + 𝑢𝑖𝑡 ,Here, the logarithm of the applicable price, ln(1 − 𝑞𝑖𝑡 ), is the instrumental variable for theendogenous variable, the logarithm of the effective price, ln 𝑝𝑖𝑡 . Again, once we control forincome, ln(1 − 𝑞𝑖𝑡 ) is independent of 𝜖𝑖𝑡 . Thus, ln(1 − 𝑞𝑖𝑡 ) is a valid instrument for ln 𝑝𝑖𝑡 . We
11

use Equation (7) as the main model to estimate the parameter 𝛽𝑒 and obtain the effective priceelasticity.

4.3

Other Issues

In addition to the issue of self-selection bias that has been discussed thus far, the estimationbiases that have been highlighted in existing studies should be addressed. First, extant studies
indicate that taxpayers may manipulate their marginal income tax rate, 𝑇 ′ (𝑦𝑖𝑡 − 𝑔𝑖𝑡 ), by changing
the amount of giving, 𝑔𝑖𝑡 , and moving the tax bracket and the price of giving called the “last-won”
price of giving (last price, hereafter) may be endogenous in the income deduction regime (e.g.
Almunia et al., 2020). To avoid this, we calculate the “first-won” price of giving (first price,
hereafter) using the marginal income tax rate 𝑇 ′ (𝑦𝑖𝑡 ) where the donation amount is set to zeroand estimate the price elasticities using the first price in the baseline analysis. We also estimate
the price elasticities using the last price by a FE-2SLS with the first price as an instrumental
variable.
Second, we address the issue of tax bracket change by the manipulation of the pretax income.
We exclude samples with a pretax income of KRW 1 million (equivalent to approximately USD
1,000) around the threshold for each bracket. This enables us to remove price changes due toincome manipulation around the threshold of each tax bracket.
Third, although our primary focus is on the price effect of charitable giving, the (indirect)
income effect may confound the estimate even when controlling for pretax income. This isbecause the change in the price of giving is driven by the change in the income level in theincome deduction period, considering that the observed income is the synthesis of transitoryand permanent incomes, and their effects on the price of giving may be different (Randolph,
1995; Auten, Sieg and Clotfelter, 2002; Bakija and Heim, 2011). Since the change in pricesof giving in our estimate is driven by the 2014 tax reform, our identification strategy allows us
to largely isolate the change in the price of giving from the change in income level. However,given that the price of giving might be changed by the income level under the income deduction
system in 2010-2013, we perform two additional estimations as robustness checks. First, we
exclude samples whose applicable prices of giving changed during the income deduction period.
Second, we use only two periods, before and after the policy change. By construction, the priceelasticity estimates in these analyses should not be affected by income fluctuations.
We summarize the results of the analyses addressing these issues in Section 5.2.
12

5Results

5.1

Estimation Results[Table 3 about here.]

Table 3 presents the estimation results for first-price elasticities. Columns (1)–(3) report theestimation results for the intensive-margin price elasticities. In this case, we estimate models
using only donors as the sample, with the log value of donations as the outcome variable.
Columns (4)–(6) present the estimation results for the extensive-margin price elasticities. We
estimate models with donor dummies as the outcome variable, using donors and non-donors as
the sample.
Columns (1) and (4) estimate the applicable price elasticities on the intensive and extensive
margin, respectively. In Column (1), the estimated intensive-margin price elasticity is −1.082,
which is statistically significant. In Column (4), the estimated value of the coefficient on theapplicable price is −0.182, which is statistically significant. Since the outcome variable is binary,
we cannot directly interpret this coefficient estimate as an extensive-margin price elasticity.
Therefore, we calculate the implied price elasticity by dividing the coefficient value by the sample
proportion of donors. As a result, the applicable price elasticity is −0.783(= −0.182/0.23),
which is also statistically significant. This implies that a reduction in tax incentives equivalent
to a 1 percent increase in donation prices, the amount of donors’ giving decreases by 1 percent
and the donor ratio decreases by 0.8 percent.
Actually, only donors can declare, and only half of all donors declare, but in estimating theapplicable price elasticity, we assume that everyone declares their giving, regardless of whether
they donate. Thus, while the applicable price elasticity may be useful in discussing policy
effects, it should be distinguished from the price elasticity of total giving, which is an importantparameter in the welfare evaluation of tax policies.
Table A1 in Appendix A shows the estimation results of Equation (6) (equivalent to thefirst-stage equation of the FE-2SLS model (7)) for the intensive-margin price elasticity andthe extensive-margin price elasticity. The results suggest that the applicable price elasticity
is 0.7 times the effective price elasticity for the intensive-margin price elasticity. For theextensive-margin price elasticity, the applicable price elasticity is 0.3 times the effective priceelasticity. Thus, we expect that effective price elasticities are more elastic than the applicable
price elasticities. This motivates us to estimate the unbiased effective price elasticities by the13FE-2SLS model (7).
Columns (3) and (6) of Table 3 estimate the effective price elasticities for the intensive andextensive margin, respectively. In Column (3), the estimated intensive-margin price elasticity
is −1.559, which is statistically significant. Thus, a 1 percent increase in the price of giving
decreases the donor’s contribution by 1.6 percent. This value is consistent with the ratio of theapplicable price elasticity estimated in Column (1) to the estimated value of the parameter 𝛾1 inEquation (6) presented in Column (1) of Table A1 of Appendix A (−1.072/0.688 = −1.558). In
addition, there is no weak instrumental variable problem in this estimation because the F-value ofthe instrument is sufficiently high. Therefore, the effective price elasticity estimated in Column(3) is reliable.
Column (6) indicates that the estimated coefficient on the effective price is −0.615, which isstatistically significant. Dividing this value by the sample proportion of donors yields −2.639(=−0.615/0.23). Thus, a 1 percent increase in the donation price decreases the donor ratio by 2.6
percent. This elasticity is quantitatively consistent with the ratio of the applicable price elasticity
to the estimated value of the parameter 𝛾1 in Equation (6) presented in Column (2) of Table A1of Appendix A (−0.783/0.297 = −2.636). In addition, there is no weak instrumental variableproblem in this estimation because the F-value of the instrument is sufficiently high. Thus, theeffective price elasticity estimated in Column (6) is reliable.
Columns (2) and (5) of Table 3 estimate the effective price elasticities using the standard FE
model (1). The significant Wu-Hausman test results shown in Table 3 imply that these estimation
results are affected by endogeneity. Given that the standard FE model does not consider selection
bias in the declaration of giving, by comparing these FE results with that of the FE-2SLS model(7), we can discuss the direction of the selection bias in the effective price elasticity on theintensive and extensive margin, respectively. The estimate obtained in Column (2) is moreinelastic than the unbiased effective price elasticity on the intensive margin in Column (3). This
upward bias for the results in Column (2) suggests that the logarithm of the effective price,ln(1 − 𝑅𝑖𝑡 𝑞𝑖𝑡 ), is positively correlated with the error term, 𝜖𝑖𝑡 , in Equation (1). Since the error
term captures unobservable factors in giving behavior given Equation (1), Columns (2) and (3)suggest that self-selection into declaring giving and the unobservable factors of giving behavior
are negatively correlated.15
The estimated price elasticity in Column (5) is more elastic than the unbiased effective price
15 Note that, since the endogenous variable in ln(1 − 𝑅

𝑖𝑡 𝑞 𝑖𝑡 ) is 𝑅𝑖𝑡 , the positive correlation between ln(1 − 𝑅𝑖𝑡 𝑞 𝑖𝑡 )and the error term means the negative correlation between 𝑅𝑖𝑡 and the error term here.

14

elasticity for the extensive margin in Column (6). Given the similar discussion for the intensive
margin, this suggests that the decision to declare is positively correlated with the unobservablefactors of whether to donate. In fact, the positive correlation in the extensive margins may benatural, since only those who make the decision to donate can report their donations, and sucha decision is partly driven by the unobservables. However, since further discussion is needed
for the estimation bias of effective price elasticities and its implications for the intensive margin,
we discuss them in Section 6.

5.2

Robustness

Last-Price Elasticities. As discussed in Section 4.3, the tax incentive in the income deduction
period is the marginal income tax rate, which varies with the amount of the donation. The
analysis thus far has used the marginal income tax rate in the case when the amount of giving
is zero, 𝑇 ′ (𝑦𝑖𝑡 ), to calculate the price of giving (first prices). However, the actual effective andapplicable prices (last prices) are calculated from the marginal income tax rate considering theactual amount of giving, 𝑇 ′ (𝑦𝑖𝑡 − 𝑔𝑖𝑡 ). Thus, we estimate applicable and effective last-priceelasticities. Since the last price depends on the amount of giving, we estimate an FE-2SLS
model with the applicable first price as the instrumental variable. The results are quantitatively
similar to the elasticities estimated in Table 3 (see Appendix C.1 for the results).
Excluding Announcement Effect. Since the Korean government announced the 2014 tax
reform in 2013, intertemporal substitution may have occurred. Individuals who anticipated thatthe 2014 tax reform would result in higher donation prices may have reduced their donations
after 2014 and increased their giving in 2013. Since this would introduce positive bias in
the elasticity, the results in Table 3 show the lower bound of the elasticity in absolute value.
To rule out these announcement effects, we exclude observations from 2013 and 2014 byassuming that intertemporal substitution occurs only in that period and estimate elasticities.
While the estimated elasticities are somewhat elastic when we exclude the announcement effect,
as expected, the results are in line with the baseline result when the standard error is taken into
account (see Appendix C.2 for the results).
Remove price variation in income deduction period. The baseline analysis exploits withinindividual price variation due to income changes in the income deduction period as well as the2014 tax reform. Since the transitory or permanent nature of income changes can have different
effects on price, the former price variation cannot isolate the effect on price from the (indirect)
15

income effect. Since the latter price variation does not depend on income changes, this problem
does not arise. To exploit only the price variation due to the 2014 tax reform, we conduct two
subsample analyses. First, we exclude those whose prices changed during the income deduction
period. Second, we use only data from 2012 and 2015. These methods yield similar baseline
results (see Appendix C.3 for the results). However, the second method is marginally statisticallysignificant due to the small sample.

5.3

Comparison with Price Elasticities of Reported Giving

Given that our panel data include undeclared contributions, our estimation of the effective priceelasticities of total giving should differ from the price elasticities of declared giving, which isestimated in the previous papers using tax record data. To confirm this point, we estimatedintensive-margin price elasticities for those who declared their giving (see Appendix C.4 forthe results). This is equivalent to the price elasticity of declared giving, which previous papers
have estimated.16 We find that this elasticity is approximately -1, which is less elastic thanour baseline estimation of the effective price elasticity of total giving. Moreover, this result is
consistent with the fact that the previous papers using tax record data report that their estimatesof the price elasticity are approximately -1 (e.g., Bakija and Heim, 2011; Fack and Landais,
2016; Almunia et al., 2020).
Our estimation of extensive-margin effective price elasticity, estimated by using the panel
data, shows the price effect on the decision to donate. In contrast, the extensive-margin priceelasticity estimated using tax record data shows the price effect on the decision to declaregiving since the tax record data do not record undeclared giving. Thus, these elasticities should
differ. To test this point, we estimate the price elasticity of the declaration (see Appendix C.5
for the results). We find that this elasticity is approximately -2, which is less elastic than theextensive-margin effective price elasticity of giving.
These results are consistent with the prediction of Fack and Landais (2016) that if contributions are underreported due to costs of declaration and other factors, the price elasticity of total
giving will be more elastic than the price elasticity of declared giving.

5.4

Policy Implications[Table 4 about here.]

16 We implicitly assume that claimants report all contributions on their tax returns (no partial reporting).

16

We discuss policy implications, particularly the policy effects of the 2014 tax reform. Ourestimates show that the amount of donations in South Korea decreased due to the 2014 tax
reform, which is consistent with Hong and Kang (2022). Columns (2)–(6) of Table 4 show
declaration rates and effective prices by income groups calculated from our data. In Bracket(A), the 2014 tax reform reduced the applicable price from 0.94 to 0.85 (−9.57% change).
However, the effective price only decreased by 0.1% because the rate of declaration increasedslightly from 2013 to 2014 but was too low (approximately 1%). In contrast, in Brackets (C)and (D)–(E), the 2014 tax reform increased the applicable price from 0.76 and 0.65 to 0.85
(11.84% and 30.77% change, respectively). Since claiming rates remain low in these brackets,the change in the effective price is smaller than the change in the applicable price. Overall, theeffective price increased as a result of the 2014 tax reform.
The overall average increase in effective price suggests that the 2014 tax reform reduced
giving behavior. We quantify the decline in charitable giving. By multiplying the effective
price change by the effective price elasticities, we can estimate the percentage changes in giving
among donors and donor ratio by income bracket. Columns (8) and (10) of Table 4 show thatthe high-income groups (Brackets (B), (C), and (D)–(E)) decreased their giving in terms of bothintensive and extensive margins, while the lowest income group (Bracket (A)) increased theirgiving in terms of both the intensive and extensive margins. As a result, Table 4 shows that the
total giving was reduced 3.53% on the intensive margin and 5.99% on the extensive margin due
to the 2014 tax reform.
Related to the policy evaluation, Saez (2004) and Fack and Landais (2016) show that the
government should expand tax incentives if the elasticity of the price of giving is more than -1,
and Almunia et al. (2020) use the sum of the elasticities of the intensive and extensive margins
as an estimate of the price elasticity.17 Following them, we can conclude that the Korean
government should expand tax incentives for charitable donation, as our estimation shows thatthe sum of the elasticity of the price of giving in terms of the intensive margin and the elasticityof the price of giving in terms of the extensive margin is greater than -1.
In terms of future policy, given that our estimates suggest that the expansion of tax incentives
for charitable giving is desirable, the Korean government should set the tax credit rate fordonations higher than 15%, or policies equal to or better than this should be adopted. Reducing
17 In Equation (15) in Almunia et al. (2020), they write 𝜀 = |𝜀𝐼 𝑁 𝑇 | + |𝜀 𝐸𝑋𝑇 |, where 𝜀 is the elasticity of the priceof giving, 𝜀 𝐼 𝑁 𝑇 is the estimated price elasticity in terms of intensive margins, and 𝜀 𝐸𝑋𝑇 is the estimated priceelasticity in terms of intensive margins.

17the declaration costs of giving would also be important in reducing the effective price of giving
as a way to expand the substantial tax incentives for giving.18

6

Discussion and Conclusions

Considering unreported donations, panel data, rather than tax records, are more appropriate
for estimating the price elasticity of total giving needed to assess the optimality of tax policy.
However, since the declaration of giving depends on taxpayer decisions, even if we exploit
exogenous variation in the applicable price of donations, standard fixed effect models would
estimate effective price elasticities with bias. Therefore, we proposed a simple FE-2SLS using
exogenous variation in tax incentives as the instrumental variable. The estimation results showthat a 1 percent increase in the donation price reduces donor contributions by 1.5 percent andthe donor share by 2.6 percent. Using these estimates, we derive the policy implication that tax
incentives should be expanded.
One limitation of this study is that we could not accurately measure taxable income. In thisstudy, we determined income tax rates based on gross pretax income. Therefore, if the income
bracket into which pretax income falls differs from the bracket into which taxable income falls
due to deductions and other factors, then there will be measurement error in the income tax rate,
which will also bias the donation price. We dropped observations whose pretax income falls
around the bracket thresholds to eliminate as much of the bracket-shifting effect as possible.
Our estimation can also shed light on understanding the unobservable factors of giving andselection to declare giving by considering the direction of estimation bias. As discussed at theend of Section 5.1, given Equation (1) and that the error term captures unobservable factors ofgiving behavior, we can consider that the direction of self-selection bias reflects the correlation
between the unobservable factors of giving behavior and the choice to declare giving.19
In particular, the self-selection bias observed in the estimation of the intensive-margin effective price elasticity suggests that the declaration of giving and the unobservable factors that
increase giving are negatively correlated. This implies that taxpayers with a preference for donation, which cannot be explained by the covariates, are unlikely to declare their giving.20 Given
18 In this context, Gillitzer and Skov (2018) show that reducing the reporting costs of giving led to an increase intotal tax expenditure on giving in Denmark.
19 This idea is important in papers interested in the characteristics of those who self-select. For example, Ma,
Abdulai and Ma (2018) discuss the characteristics of those who self-select into participating in off-farm work by
examining the direction of bias. For a related discussion, see Wooldridge (2015).
20 This cannot be explained solely by the financial incentive that large donations generate tax savings.

18

that prosocial behaviors such as giving are motivated in part by the utility of social reputationand praise, i.e., the image motive (e.g., Ariely, Bracha and Meier, 2009), this implication isquite natural since image-motivated donors gain utility by sending an altruistic signal to others
and receiving financial incentives, such as tax incentives, will be noise for them when sending
altruistic signals (Bénabou and Tirole, 2006).21
While our study focused on the self-selection behavior of tax incentives for charitable giving,the methodology used in this study may be valid for other tax expenditures, such as tax breaks
for R&D investment in the corporate tax. To understand self-selection in taxation in greater
detail, including issues such as the characteristics of taxpayers who self-select and the directionof the self-selection bias, more research is needed in the future.

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19

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21

Table 1. Marginal Income Tax Rates (%)
Income/Year

2008

2009

2010 - 20112012 - 20132014 - 2016

2017

2018

(A) - 1200

8

6

6

6

6

6

6

(B) 1200 - 4600

17

16

15

15

15

15

15

(C) 4600 - 8800

26

25

24

24

24

24

24

35

35

35

(D) 8800 - 15000
35(E) 15000 - 30000(F) 30000 - 50000

35

35

38
38

35

38

38

(G) 50000 -

40

40
42

Notes: Marginal income tax rates applied from 2008 to 2018 are summarized. The income levelis shown in terms of 10,000 KRW, which is approximately 10 United States dollars (USD) at an
exchange rate of 1,000 KRW to one USD.

Table 2. Descriptive StatisticsN

Mean

Std.Dev.

Income and giving price
Annual labor income (unit: 10,000KRW)
Annual total income (unit: 10,000KRW)
Appricale price

37901
37901
37901

1924.133088.100.85

2631.33
2808.140.05

Charitable giving
Annual chariatable giving (unit: 10,000KRW)
Dummary of donation > 0
Dummy of declaration of giving

37901
37901
37901

32.48
0.23
0.11

122.760.42
0.31

Demographics
Age
Wage earner dummy
Number of household members
Dummy of having dependents
Female dummy
Academic history: University
Academic history: High school

37901
37893
37901
37901
37901
37900
37900

51.33
0.48
3.20
0.68
0.35
0.46
0.32

15.95
0.50
1.26
0.47
0.48
0.50
0.47

Notes: Our data is unbalanced panel data consisting of 8,441 unique individuals and8 years period (2010–2017)22

Table 3. Estimation Results of First-Price Elasticities
Log donation

Dummy of donor

FE

FE-2SLS

(1)

(2)

(3)

−1.082***(0.332)

Applicable price (𝛽𝑎 )

FE
(4)

(5)

−2.729***(0.073)−1.560***(0.486)1.277(1.348)

Effective price (𝛽𝑒𝐼𝑉 )Log income(6)−0.184***(0.058)−0.641**(0.255)

Effective price (𝛽𝑒𝐹𝐸 )FE-2SLS

1.629(1.347)

1.862(1.334)

Implied price elasticity
Estimate
1st stage information (Excluded instrument: Applicable price)
F-statistics of instrument
Wu-Hausman test, p-value
Num.Obs.
7776
7776

1401.509
0.004
7776

1.464***(0.209)0.675***(0.190)−0.617***(0.182)1.420***(0.202)−0.791***(0.250)−11.717***(0.314)−2.647***(0.782)30 2521812.348< 0.00130 25230 252

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are in parentheses. An
outcome variable is the logged value of the effective price. For estimation, Models (1)–(3) use donors only (intensive-margin
sample), and Models (4)–(6) use not only donors but also non-donors (extensive-margin sample). In addition to logged income,covariates consist of squared age (divided by 100), number of household members, a dummy that indicates having dependents,
a dummy that indicates wage earner, a set of industry dummies, a set of residential area dummies, and individual and time fixed
effects. The excluded instrument is a logged applicable price. The excluded instrument is a logged applicable price in Models(3) and (6).

Table 4. Policy Effect of 2014 Tax Reform
Declaration (%)
2013 Income bracket(A) –1200(B) 1200–4600(C) 4600–8800(D) & (E) 8800–30000
Weighted average

Effective priceIntensive margin

Extensive margin

N

2013

2014

2013

2014

Change (%)

2013 average

Change (%)

2013 average

Change (%)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

1084
2222
823
174

0.738
11.11638.27536.782

1.015
5.986
28.31131.034

1.000
0.983
0.908
0.871

0.998
0.991
0.958
0.953

-0.1070.952
6.666
12.9692.264

8.074
18.32465.649146.2130.167-1.485-10.399-20.231-3.532

0.122
0.204
0.450
0.494

0.283
-2.520-17.645-34.328-5.993

Notes: We use those whose declaration status is observed for 2013 and 2014. Column (1) shows the sample size by income bracket for 2013. Columns (2) and (3)are the declaration rates for each year. Columns (4) and (5) are the average effective price for each year. Column (6) reports the percentage change in the effective
price. Column (8) shows the percentage change in donor contributions, which is the product of the value in Column (6) and the estimated intensive-margineffective price elasticity ( −1.56). Column (10) shows the percentage change in the donor rate, which is the product of the value in Column (6) and the estimatedextensive-margin effective price elasticities ( −2.647). Columns (7) and (9) show the average donor contribution and the donor ratio in 2013, respectively. Columns(2)–(10) divide the sample by income bracket, claiming status in 2013, and claiming status in 2014, calculate the corresponding indicator in each subset, and thencalculate the average of each indicator weighted by the subset sample size in each income bracket. The bottom row shows the average weighted by the bracket
sample size.

23

Relative frequency

0.75

0.250

0.50

0.125

0.25

0.000

0.00

Prices of Giving

0.375

1200

4600

8800

30000

Annual total income (10,000KRW)
Prices of Giving in 2010−2013

Relative frequency

Figure 1. Income Distribution in 2013 and Prices of Giving by Income Bracket
Notes: This figure plots income distribution in 2013 (grey bars) and the prices of giving (solid step line and dashedline) by income bracket. The left and right axes measure the relative frequency of respondents and the price ofgiving, respectively. The solid step line represents the giving price in 2010–2013. The dashed horizontal line
represents the price of giving in 2014–2017.

24

Panel A. Amount of Giving

Panel B. Proportion of Donors

Normalized proportion of donors

Normalized average giving

2.5

2.0

1.5

1.0

0.5

0.0

1.5

1.0

0.5

0.0
2010 2011 2012 2013 2014 2015 2016 20172010 2011 2012 2013 2014 2015 2016 2017

Year

Year
Income bracket (unit:10,000KRW)(A) −−1200(B) 1200−−4600(C) 4600−−8800(D) & (E) 8800−−30000

Figure 2. Average Giving Amount (Panel A) and Proportion of Givers (Panel B) by 2013
Income Bracket.
Notes: The trend of the average amount of giving and proportion of givers in each income bracket of 2013 arerespectively shown in Panel A and B. The values are normalized to one in 2013. For panel A, we limit the sample
to the donors to make the graph.

25

Proportion of claimants

0.4

0.3

0.2

0.1

0.0
2010

2011

2012

2013

2014

2015

2016

2017

Year
Income bracket (unit:10,000KRW)(A) −−1200(B) 1200−−4600(C) 4600−−8800(D) & (E) 8800−−30000

Figure 3. Declaration Rates by 2013 Income Bracket
Notes: This Figure shows the change in the proportion of claimants as a share of all taxpayers including non-donors
in each income bracket in 2013.

26

Appendix A

Additional Tables and Figures

Proportion of claimants

0.8

0.6

0.4

0.2

2010

2011

2012

2013

2014

2015

2016

2017

Year
Income bracket (unit:10,000KRW)(A) −−1200(B) 1200−−4600(C) 4600−−8800(D) & (E) 8800−−30000

Figure A1. Declaration Rates of Donors by 2013 Income Bracket
Notes: This figure shows the change in the proportion of claimants as a share of donors in each income bracket in2013.

Table A1. First-Stage Models
Effective priceExcluded instruments
Applicable priceCovariates
Log income
Num.Obs.
RMSE

Donors (Intensive margin)

Donors and Non-donors (Extensive margin)

(1)

(2)

0.694***(0.038)0.299***(0.019)−0.225(0.147)−0.071(0.047)7776
0.05

30 2520.04

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at household level are in parentheses. The
outcome variable is the logged value of the effective price. For estimation, Model (1) uses donors only (intensive-margin
sample), and Model (2) uses not only donors but also non-donors (extensive-margin sample). In addition to logged income
shown in table, covariates consist of squared age (divided by 100), number of household members, a dummy that indicateshaving dependents, a dummy that indicates a wage earner, a set of industry dummies, a set of residential area dummies,
and individual and time fixed effects. The excluded instrument is the logged applicable price.

27

Appendix B

Proof

We show that the parameter Cov(ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 )/Var(𝑟ˆ𝑖𝑡 ) is in the range 0 to 1 if residuals 𝑟ˆ𝑖𝑡 aremean independent of a dummy indicating declaration of giving, 𝑅𝑖𝑡 . We obtain the residuals 𝑟ˆ𝑖𝑡from the following model:ln(1 − 𝑞𝑖𝑡 ) = 𝜇𝑖 + 𝜃 𝑡 + 𝜆𝑋𝑖𝑡 + 𝑟𝑖𝑡 ,(B1)

By 𝐸 (𝑟ˆ𝑖𝑡 ) = 0, Var(𝑟ˆ𝑖𝑡 ) = 𝐸 (𝑟ˆ𝑖𝑡2 ). Additionally, 𝐸 (𝑟ˆ𝑖𝑡 ) = 0 implies Cov(ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 ) = 𝐸 (ln 𝑝𝑖𝑡 𝑟ˆ𝑖𝑡 ).
By the law of iterated expectations,
Cov(ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 ),Var(𝑟ˆ𝑖𝑡 )𝐸 (ln 𝑝𝑖𝑡 𝑟ˆ𝑖𝑡 )=,𝐸 (𝑟ˆ𝑖𝑡2 )𝐸 (ln(1 − 𝑞𝑖𝑡 ) 𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1).
=
2
𝐸 (𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1) + 𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 0)Pr(𝑅𝑖𝑡 = 0)

(B2)

Note that 𝑝𝑖𝑡 = 1 − 𝑅𝑖𝑡 𝑞𝑖𝑡 .
By the auxiliary regression model (B1), the variable ln(1 − 𝑞𝑖𝑡 ) is a sum of a predicted value
𝐸 [ln(1 − 𝑞𝑖𝑡 )|𝜇𝑖 , 𝜃 𝑡 , 𝑋𝑖𝑡 ] and a residual 𝑟ˆ𝑖𝑡 . Thus, we can reformulate the numerator of Equation(B2) as follows:
𝐸 {ln(1 − 𝑞𝑖𝑡 ) 𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 = 1}Pr(𝑅𝑖𝑡 = 1),=𝐸 {(𝐸 [ln(1 − 𝑞𝑖𝑡 )|𝜇𝑖 , 𝜃 𝑡 , 𝑋𝑖𝑡 ] + 𝑟ˆ𝑖𝑡 ) 𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 = 1}Pr(𝑅𝑖𝑡 = 1),=𝐸 {𝐸 [ln(1 − 𝑞𝑖𝑡 )|𝜇𝑖 , 𝜃 𝑡 , 𝑋𝑖𝑡 ] 𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 = 1}Pr(𝑅𝑖𝑡 = 1) + 𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1),=𝐸 [ln(1 − 𝑞𝑖𝑡 )|𝜇𝑖 , 𝜃 𝑡 , 𝑋𝑖𝑡 ]𝐸 (𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1) + 𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1).

(B3)

Thus, if the residual 𝑟ˆ𝑖𝑡 and the dummy variable 𝑅𝑖𝑡 are mean independent, that is 𝐸 (𝑟ˆ𝑖𝑡 |𝑅𝑖𝑡 =1) = 𝐸 (𝑟ˆ𝑖𝑡 ) = 0, then Equation (B3) reduces to 𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1), and the parameterCov(ln 𝑝𝑖𝑡 , 𝑟ˆ𝑖𝑡 )/Var(𝑟ˆ𝑖𝑡 ) becomes𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1)
Cov(𝑅𝑖𝑡 ln(1 − 𝑞𝑖𝑡 ), 𝑟ˆ𝑖𝑡 )=,Var(𝑟ˆ𝑖𝑡 )𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 1)Pr(𝑅𝑖𝑡 = 1) + 𝐸 (𝑟ˆ𝑖𝑡2 |𝑅𝑖𝑡 = 0)Pr(𝑅𝑖𝑡 = 0)
which is in the range 0 to 1.

28

(B4)

Appendix C

Additional Exercises

For the robustness of our main results, we perform three exercises.
1. Estimate effective last-price elasticities
2. Estimate effective price elasticities excluding the announcement effect
3. Estimate effective price elasticities removing price variation in the income deduction
periodTo show that our main results differ from the price elasticities of declared contributions estimatedusing tax record data, we perform the following two exercises.
4. Estimate the intensive-margin price elasticities for claimants
5. Estimate the price elasticities of the declaration
In this appendix, we discuss each exercise in detail.

C.1

Exercise 1

Motivation. In the income deduction period, the tax incentive depends on the giving amount,𝑇 ′ (𝑦–𝑔). Thus, the actual effective and applicable prices are the relative prices in the case of theactual donation amount (last prices). However, in our main analysis, we use the relative price inthe case of zero donation (first price), 𝑇 ′ (𝑦), which differs from the last price. Note that the firstprices are equal to the last price in the income credit period. Thus, we estimate the effective andapplicable last-price elasticities.
Method. Since the last price depends on the amount of giving, we estimate an FE-2SLS modelwith the applicable first prices as the instrumental variable. Let 𝑝𝑖𝑡 (𝑔𝑖𝑡 ) be the effective last
price. Let 1–𝑞𝑖𝑡 (𝑔𝑖𝑡 ) be the applicable last price. We estimate the following FE-2SLS:𝑌𝑖𝑡 = 𝜇𝑖 + 𝜃 𝑡 + 𝛽 ln 𝑝𝑖𝑡 (𝑔𝑖𝑡 ) + 𝛿𝑋𝑖𝑡 + 𝜖𝑖𝑡 ,(C1)
ln 𝑝𝑖𝑡 (𝑔𝑖𝑡 ) = 𝜇𝑖 + 𝜃 𝑡 + 𝛾 ln(1 − 𝑞𝑖𝑡 (0)) + 𝜆𝑋𝑖𝑡 + 𝑢𝑖𝑡 ,where 𝑝𝑖𝑡 (0) and 1 − 𝑞𝑖𝑡 (0) are the effective first price and the applicable first price, respectively.
Our parameter of interest is 𝛽, which represents the effective last-price elasticities. Note thatthe parameter 𝛽 is equal to 𝛽𝑒𝐼𝑉 , which is our main result of effective price elasticities when29

we use ln 𝑝𝑖𝑡 (0). For estimation of the applicable last-price elasticities, we replace 𝑝𝑖𝑡 (𝑔𝑖𝑡 )with 1–𝑞𝑖𝑡 (𝑔𝑖𝑡 ). Then, the parameter 𝛽 shows the applicable last-price elasticities. Note that
this model can solve the endogeneity problem due to the selection of declaration, which is ouroriginal research motivation.
Table C1. Last-Price Elasticities on the Intensive Margin
Log donationFE

FE-2SLS(1)
Applicable last-price(2)−0.812**(0.347)(4)−1.122***(0.345)−0.595**(0.259)1.884(1.336)

Effective last-priceLog income

(3)

1.777
(1.348)1.589(1.349)−1.625***(0.508)1.217(1.353)84 392.469< 0.0017776

1295.556
0.002
7776

1st stage information (Excluded instrument: Applicable price)
Estimate
F-statistics of instrument
Wu-Hausman test, p-value
Num.Obs.

7776

7776

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are inparenthesis. The outcome variable is the logged value of the amount of charitable giving. For estimation,
we use donors only (intensive-margin sample). For the outcome equation, we control for squared age(divided by 100), number of household members, a dummy that indicates having dependents, a dummythat indicates a wage earner, a set of industry dummies, a set of residential area dummies, and individual
and time fixed effects. For FE-2SLS, we use the logged applicable first price as an instrument.

Table C2. Last-Price Elasticities on the Extensive Margin
Donor dummyFE

FE-2SLS(1)
Applicable last-price−0.147**(0.059)Implied price elasticity
Estimate(3)(4)−0.187***(0.059)1.499***(0.210)−2.759***(0.074)0.657***(0.190)1.462***(0.209)−0.636***(0.187)1.412***(0.202)−0.632**(0.252)−11.845***(0.317)−0.801***(0.253)−2.729***(0.805)

1 481 835.010< 0.00130 2521725.090< 0.00130 252

Effective last-priceLog income(2)

1st stage information (Excluded instrument: Applicable price)
F-statistics of instrument
Wu-Hausman test, p-value
Num.Obs.
30 25230 252

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level arein parentheses. The outcome variable is a dummy indicating a donor. For estimation, we use not only
donors but also non-donors (extensive-margin sample). For the outcome equation, we control for squaredage (divided by 100), number of household members, a dummy that indicates having dependents, a dummythat indicates a wage earner, a set of industry dummies, a set of residential area dummies, and individual
and time fixed effects. For FE-2SLS, we use the logged applicable first price as an instrument. We calculate
implied price elasticities by dividing the estimated coefficient on price by the sample proportion of donors.

Results. See Table C1 for the intensive-margin price elasticities and Table C2 for the extensive30

margin price elasticities. The results are quantitatively similar to our main results.

C.2

Exercise 2

Motivation. Since the Korean government announced the 2014 tax reform in 2013, intertemporal
substitution may have occurred. For example, individuals who anticipated that the 2014 tax
reform would result in higher donation prices may have reduced their donations in 2014 andbeyond and increased their giving in 2013. Since this would introduce a positive bias in theelasticities, we estimate the price elasticities while excluding this announcement effect.
Method. Assuming that intertemporal substitution occurs in 2013 and 2014, we exclude observations in that period and estimate the FE-2SLS model (7) that we propose in Section 4.2.
Table C3. First-Price Elasticities Excluding Announcement Effects
Log donation
FE(1)
Applicable price (𝛽𝑎 )

(2)

(3)

−1.312***(0.474)

FE
(4)

(5)

(6)

−2.809***(0.088)−1.843***(0.679)1.150(1.920)Effective price (𝛽𝑒𝐼𝑉 )1.642(1.880)FE-2SLS−0.220***(0.077)−0.618*(0.344)

Effective price (𝛽𝑒𝐹𝐸 )Log income

Donor dummy
FE-2SLS

1.936(1.884)

Implied price elasticity
Estimate
1st stage information (Excluded instrument: Applicable price)
F-statistics of instrument
Wu-Hausman test, p-value
Num.Obs.
5936
5936

941.601
0.002
5936

1.591***(0.255)0.820***(0.236)−0.765***(0.247)1.523***(0.247)−0.928***(0.325)−11.824***(0.371)−3.219***(1.039)22 6841141.395< 0.001
22 68422 684

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are in parentheses. The
outcome variable is the logged value of the amount of charitable giving in Models (1)–(3) and a donor dummy in Models(4)–(6). For estimation, Models (1)–(3) use donors only (intensive-margin sample), and Models (4)–(6) use not only donors
but also non-donors (extensive-margin sample). To exclude the announcement effect, we exclude observations from 2013 and2014. For the outcome equation, we control for squared age (divided by 100), number of household members, a dummythat indicates having dependents, a dummy that indicates a wage earner, a set of industry dummies, a set of residential area
dummies, and individual and time fixed effects. For FE-2SLS, we use the logged applicable price as an instrument. To obtain theextensive-margin price elasticities in Models (4)–(6), we calculate implied price elasticities by dividing the estimated coefficienton price by the sample proportion of donors.

Results. See Table C3. As expected, the estimated elasticities are somewhat elastic when we
exclude the announcement effect.

31

C.3

Exercise 3

Motivation. The indirect income effect may confound the price effect since the change in theprice of giving is driven by the change in the income level in the income deduction period. Thisis because the observed income is the synthesis of transitory and permanent incomes, and theireffects on the price of giving may differ. This motivates us to perfectly isolate the change in theprice of giving from the change in income level.
Method. We use two subsets and estimate the FE-2SLS model (7) that we propose in Section
4.2. The first subset excludes those whose price of giving changed during the income deduction
period from our main study sample. The second subset uses 2012 data (before the 2014 tax
reform) and 2015 data (after the 2014 tax reform).
Table C4. First-Price Elasticities Removing Price Variation in Income Deduction Period
Log donation
FE(1)
Applicable price (𝛽𝑎 )FE-2SLS(2)(3)−1.172***(0.436)

FE
(4)

(5)

(6)

−2.878***(0.094)−1.563***(0.589)2.007(1.692)

Effective price (𝛽𝑒𝐼𝑉 )2.496(1.666)

FE-2SLS−0.276***(0.090)−0.670**(0.320)Effective price (𝛽𝑒𝐹𝐸 )Log income

Donor dummy

2.258(1.674)

Implied price elasticity
Estimate
1st stage information (Excluded instrument: Applicable price)
F-statistics of instrument
Wu-Hausman test, p-value
Num.Obs.
5825
5825

1068.639
0.021
5825

2.046***(0.300)1.090***(0.304)−0.673***(0.203)
1.859***(0.286)−1.176***(0.385)−12.270***(0.400)−2.869***(0.866)

21 9621770.695< 0.001
21 96221 962

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are in parentheses. The
outcome variable is the logged value of the amount of charitable giving in Models (1)–(3) and a donor dummy in Models (4)–(6).
For estimation, Models (1)–(3) use donors only (intensive-margin sample), and Models (4)–(6) use not only donors but also
non-donors (extensive-margin sample). We exclude those whose prices changed during the income deduction period. For theoutcome equation, we control for squared age (divided by 100), number of household members, a dummy that indicates having
dependents, a dummy that indicates a wage earner, a set of industry dummies, a set of residential area dummies, and individual
and time fixed effects. For FE-2SLS, we use the logged applicable price as an instrument. To obtain the extensive-margin priceelasticities in Models (4)–(6), we calculate implied price elasticities by dividing the estimated coefficient on price by the sample
proportion of donors.

32

Table C5. First-Price Elasticities Using 2012 and 2015 Data
Log donation
FE(1)
Applicable price (𝛽𝑎 )FE-2SLS
(2)

FE

(3)

−1.275(1.276)

(4)

(5)

(6)

−2.757***(0.225)−1.725(1.754)−3.951(10.299)

Effective price (𝛽𝑒𝐼𝑉 )−3.555(10.491)

FE-2SLS−0.326*(0.190)−1.129(1.601)

Effective price (𝛽𝑒𝐹𝐸 )Log income

Donor dummy−3.777(10.312)

Implied price elasticity
Estimate
1st stage information (Excluded instrument: Applicable price)
F-statistics of instrument
Wu-Hausman test, p-value
Num.Obs.
2004
2004

2.062**(0.838)1.550**(0.725)−1.084*(0.574)2.034***(0.761)−1.388*(0.808)−11.734***(0.958)−4.612*(2.443)288.8022004

282.264
7671

7671

7671

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are in parentheses. The
outcome variable is the logged value of the amount of charitable giving in Models (1)–(3) and a donor dummy in Models(4)–(6). For estimation, Models (1)–(3) use donors only (intensive-margin sample), and Models (4)–(6) use not only donors
but also non-donors (extensive-margin sample). We use only data from 2012 and 2015. For the outcome equation, we control
for squared age (divided by 100), number of household members, a dummy that indicates having dependents, a dummy thatindicates a wage earner, a set of industry dummies, a set of residential area dummies, and individual and time fixed effects.
For FE-2SLS, we use the logged applicable price as an instrument. To obtain the extensive-margin price elasticities in Models(4)–(6), we calculate implied price elasticities by dividing the estimated coefficient on price by the sample proportion of donors.

Results. Table C4 shows estimation results using the first subset. The results are similar to
our main results. Table C5 shows estimation results using the second subset. The estimatedintensive-margin price elasticities are quantitatively similar to our main results. The estimatedextensive-margin price elasticities are twice as elastic as our main results. However, the statisticalsignificance of these estimates is weak due to the small sample.

C.4

Exercise 4

Motivation. Effective price elasticities are price elasticities of total giving. This may be different
from the price elasticities of declared giving estimated using tax record data. To check this point,
we attempt to estimate the price elasticities of declared giving, using the Korean household panel
survey data, NASTAB (see Section 3 in the data description).
Method. We use only claimants (exclude non-claimants from the main study sample). Since
claimants are donors, we cannot estimate the extensive-margin price elasticities. Moreover, theeffective prices are equal to the applicable prices in these data. Thus, we are free from theendogeneity problem due to the selection into claiming. Then, we employ the FE model (2),which estimates the applicable price elasticities (see Section 4.2).

33

Table C7. First-Price Elasticity of Declaration
1 = DeclarationFE(1)−0.220***(0.050)1.380***(0.177)

Applicable priceLog income
Implied price elasticity
Estimate−1.982***(0.452)30 252

Num.Obs.

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are inparentheses. The outcome variable is a declaration dummy. We control for squared age (divided by 100),
the number of household members, a dummy that indicates having dependents, a dummy that indicates awage earner, a set of industry dummies, a set of residential area dummies, and individual and time fixed
effects. To obtain the price elasticity, we calculate implied price elasticities by dividing the estimatedcoefficient on price by the sample proportion of claimants.

Table C6. Intensive-Margin First-Price Elasticities for Claimants
Log donationFE(1)−1.147**(0.506)−1.221(2.213)

Applicable price (𝛽𝑎 )Log income
Num.Obs.

4171

Notes: * 𝑝 < 0.1, ** 𝑝 < 0.05, *** 𝑝 < 0.01. Standard errors clustered at the household level are inparentheses. The outcome variable is the logged value of the amount of charitable giving. For estimation,
we use claimants only. We control for squared age (divided by 100), the number of household members,
a dummy that indicates having dependents, a dummy that indicates a wage earner, a set of industry
dummies, a set of residential area dummies, and individual and time fixed effects.

Results. See Table C6. We assume that all claimants report all contributions on their tax returns(no partial reporting). Under this assumption, the estimated elasticities can be interpreted as theprice elasticity of reported contributions.

C.5

Exercise 5

Motivation. The extensive-margin price elasticities estimated using tax record data capture theprice effect on the decision to file a tax return for the donation. This may be different fromthe price effect on the decision to donate, which is captured by our extensive-margin priceelasticities. To show this, we estimate the price elasticities of claiming.
Method. We use the original study sample and estimate the standard FE model (2), replacing
the outcome variable with a claiming dummy, 𝑅𝑖𝑡 .
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Results. See Table C7. We find that the estimated price elasticity of claiming is approximately-2, which is less elastic than our main results.

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