Discussion Papers In Economics
And Business

Tax-Price Elasticities of Charitable Giving and
Selection of Declaration: Panel Study of South Korea

Hiroki Kato, Tsuyoshi Goto, and Youngrok Kim

Discussion Paper 23-05

March 2023

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANTax-Price Elasticities of Charitable Giving and
Selection of Declaration: Panel Study of South Korea*
Hiroki Kato † a , Tsuyoshi Goto ‡ b , and Youngrok Kim caGraduate School of Economics, Osaka University, Osaka, Japan
Graduate School of Social Sciences, Chiba University, Chiba, Japanc
Research Institute for Socionetwork Strategies, Kansai University, Osaka,JapanbMarch 20, 2023

Abstract
This study estimates the tax-price elasticity of donations, considering the bias causedby the fact that the claim of tax incentives for charitable giving depends on the taxpayer’s
decision. We first present a way to eliminate this bias by supporting the intention-to-treat
analysis. We then estimate the price elasticity by our method, using exogenous variationin tax incentives due to the 2014 tax reform in South Korea. We find that a 1% increase indonation prices reduces donor contributions by 1.6% and the donor ratio by 2.6%. Next, we
use the control function approach, one of the instrumental variable methods, to examine how
endogeneity from the decision to use tax incentives biases the estimation of price elasticity.
We find that those with large amounts of charitable giving without tax incentives do notdeclare their giving, leading to an underestimation (in absolute value) of the price elasticity
of donors’ contribution amount.
Keywords: Charitable giving, Tax incentives, Price elasticities, Selection, Declaration.
JEL: D64, H24, H31.

* We would like to thank Fumio Ohtake, Sasaki Masaru, Makoto Hasegawa, Takeshi Miyazaki, participants ofthe 25th Annual Conference of The Japan Public Choice Society, participants of the 77th Annual Congress of theInternational Institute of Public Finance, and participants of the OSIPP Lunch Time Seminar at Osaka University
for their helpful comments.
†
Corresponding author. E-mail addresses: h-kato@econ.osaka-u.ac.jp‡
E-mail addresses: t.goto@chiba-u.jp1

1

Introduction

In many countries, governments provide tax relief for charitable giving, and many papers attempt
to estimate the price elasticity of giving as a key variable to understand the impact of the tax
relief for giving (e.g., Almunia et al., 2020). However, taxpayers may not declare all of theirgiving to tax agencies. In the U.S., 35 % of total individual giving is estimated to be nondeclared
giving (Giving USA, 2022, p.337). Such a large nondeclared giving share implies that donors
may not use tax relief as policymakers intended, and the estimation of the impact of the giving
price on charitable giving may be biased if the existence of taxpayers who do not declare theirgiving (nondeclarers) is not considered (Rehavi and Shack, 2013). Therefore, understanding theimpact of tax relief on charitable giving while accounting for nondeclarers is important for theevaluation of tax expenditure policy.
In this paper, we estimate the price elasticity of giving while recognizing that declaring
giving is optional by exploiting the Korean government’s change in the tax relief for charitablegiving from an income deduction to a tax credit in 2014. Although the giving price determinedby the amount of giving and income results in reverse causality, the distinctive quasi-experimentin Korea where income deduction for giving turned to a tax credit equal to 15% of total giving
exogenously creates variation in the change of the giving price.
In addition, we also offer the estimation that mitigate the selection bias that only donors who
gain will declare their giving. Depending on whether or not the declaration is taken into account,
there are two giving prices: that is applicable for all taxpayers if declared (the applicable pricehereafter) and that is effective only for declarers (the effective price hereafter). Since the 2014
tax reform brings the exogenous variations in applicable prices, the estimation of the applicable
price elasticity should not suffer from self-selection bias and is equivalent to the estimand called
intention-to-treat (ITT).1 However, this might differ from a key parameter to evaluate welfare
shown by Saez (2004). Moreover, the simple fixed-effect (FE) estimation of the effective priceelasticity generates bias since declaration is self-selected.2 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
1

As policymakers cannot compel taxpayers to declare all of their giving but only can offer tax relief, the resultof the applicable price elasticity may be valuable to understand the effect of offering tax relief for giving.
2
Although Saez (2004) does not consider the existence of declaration, we argue that the effective price elasticity
in this paper corresponds to the price elasticity of giving in his model in the sense that both elasticities identify theextent to which taxpayers increase their giving when they face a 1% reduction in the giving price, not a reductionin the offered giving price. See also Fack and Landais (2016) for related theoretical discussion.

2

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 declaredsuch giving. From this data, we obtain both applicable and effective giving prices and show thatthe effective and applicable price elasticities for the intensive margin are − 1.422 and −0.979,
respectively. The former value is more elastic than −1, which is the standard result in the empirical literature on the giving price elasticity, and the latter is close to −1. Following Almunia
et al. (2020), we also find that the estimated applicable and effective price elasticities for the extensive margin are − 0.712 and − 2.308, respectively. The results are in line with the predictionthat the applicable price elasticity will be less elastic than the effective price elasticity. Moreover, we find that the simple FE estimation of the effective price elasticity generates upwardbias for the intensive margin and downward bias for the extensive margin.
Although the proposed method is very attractive because of its feasibility, it does not directly
address the fact that the optional declaration of giving causes self-selection. Therefore, we examine the self-selection bias in declaration by using the control function approach and check
whether the proposed method corrects the bias in the right direction. Since the endogeneityof the giving price comes from the correlation between the declaration and the error term, we
can address the endogeneity by controlling the correlation. The control function approach utilizes this idea by adopting an instrumental variable (Wooldridge, 2015) and enables us to checkthe direction of bias and the correlation between the error term and the endogenous variable.
We use a wage earner dummy as an instrumental variable because wage earners may have theopportunity to give through a program offered by their company, and the declaration process
of offered giving is considerably simpler than others such as the self-employed in Korea. As
giving behavior would be irrelevant to whether the donor is a wage earner after controlling foroccupation and income level, we exploit the wage earner dummy as an instrument.
The result of the control function approach shows that the estimated price elasticity is −1.23
for the intensive margin. Considering that the result of the simple FE estimation is −0.840, thecontrol function approach confirms that the simple FE estimation generates upward bias andthe proposed method corrects the bias in the right direction. Moreover, the correlation between
the giving price and the error terms is negative, which implies that taxpayers with a higher
preference for giving tend to hesitate to declare their giving. As behavioral economics suggeststhat one motivation for donation is image, this result may indicate that image-motivated donors

3

who give substantially may be hesitant to claim the donation deduction since the declaration
will harm their altruistic image (e.g., Ariely et al., 2009; Eckel and Grossman, 2008).
This paper contributes to the empirical literature examining the price elasticity of giving inaugurated Feldstein and Taylor (1976) by filling the gap between two strands of studies: studies
using exogenous policy change and studies using panel survey data. In the first strand, Almunia
et al. (2020) and Fack and Landais (2010) utilize the change in income tax rates in the U.K. andthe tax credit rate in France, respectively, as an identification strategy.3 However, extant studies
in this strand use tax record data, which do not include data on nondeclared giving, and estimate
the price elasticity of tax-relieved giving.4
The studies in the second strand, which utilize panel survey data, have addressed the issue
of nondeclared giving utilizing the fact that the data contain nondeclared giving data. Most of
extant studies in this strand use U.S. panel survey data and capture nondeclared giving (Backus
and Grant, 2019; Rehavi and Shack, 2013; Zampelli and Yen, 2017).5 However, these studies
do not exploit exogenous policy change but utilize tax rate changes using the change in income
level as identifying variation, which may entail several endogeneity issues, such as endogenous
income determination.6
This study attempts to fill this gap between the two strands of literature and utilizes a policychange and panel survey data focusing on the Korean context. Due to the policy change, we canexogenously estimate the elasticity. In this sense, this paper closely relates to Duquette (2016),
who exploits changes in state income tax rates in the U.S. and charities’ data. Our novelty inthe literature on the giving price elasticity is, while addressing the issue of declaring giving, tosuggest the existence of two different giving price elasticities and to estimate them.7
Another novelty of this paper is that we consider the self-selection bias generated the factthat the declaration of giving is optional. Recent studies address this issue by modeling taxpayer
3

In addition, Fack and Landais (2016) and Gillitzer and Skov (2018) exploit policy changes that change the costof the declaration of giving.
4
Because of the lack of the data on nondeclaration, the applicable price and effective price cannot be obtainedin tax record data.
5
Using the same data, Brown et al. (2012) and Brown et al. (2015) examine the determinant of donations for the2004 Indian Ocean tsunami and the giving behavior of poor and wealthy taxpayers, respectively, by constructing
structural models.
6
By using tax record data, Randolph (1995), Auten et al. (2002) and Bakija and Heim (2011) also utilize tax
rate changes by the change in income level as a variation for identification.
7
Although Almunia et al. (2020) and Fack and Landais (2016) are aware that the giving price elasticity estimatedfrom tax record data using reduced-form regressions should differ from the price elasticity of total giving (including
nondeclared giving), they do not derive it directly from the data. Duquette (2016) does not address the issue of
declaring giving.

4

behavior.8 In this paper, we address the self-selection issue by proposing a simple method
and checking its validity with the control function approach. Moreover, by accounting for thedifference in the costs of declaring giving using an instrumental variable and the issue of selfselection, we also contribute to the growing literature addressing the declaration cost of tax relief(Benzarti, 2020; Fack and Landais, 2016; Gillitzer and Skov, 2018; Zwick, 2021).
This paper consists of six sections. Sections 2 and 3 explain the institutional backgroundand data, respectively. Section 4 examines the difference between the applicable and effective
price elasticities based on ITT. Section 5 addresses self-selection problem when estimating theeffective price elasticity using the control function approach. Section 6 concludes the paper.

2

Institutional BackgroundWe describe the 2014 tax reform in Korea used as an identification strategy for estimating priceelasticities. We also state that the application for tax incentives differs depending on whether ataxpayer is a wage earner, demonstrating that a dummy variable to indicate a wage earner is anappropriate instrument.

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 giving price, 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 constraintthat 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 progressive in
Korea, we assume that T (·, ·) satisfy Ty (·, ·) > 0 and Tyy (·, ·) > 0, where the subscript means
partial differentiation.
Before 2014, the income deduction was a tax relief system for charitable giving in Korea.
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 by xi and gi is dxi + (1 − T 0 (yi − gi ))dgi = 0. This leads to8

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.

5

Table 1: Marginal Income Tax Rate
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%

(G) 50000 -

38%
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.

the giving price (relative to private consumption), 1 − T 0 (yi − gi ). Since the marginal income
tax rate is progressively determined as shown in Table 1, taxpayers facing a higher marginalincome tax rate can enjoy a lower giving price for each 1 KRW donation. In other words, thegiving price was regressive before 2014.
In 2014, to relax the regressivity of giving prices, the Korean government reformed the tax
system, where a tax credit was introduced instead of the 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% of the total amount of declaredcharitable giving as a tax credit (m = 0.15), which means that the giving price fromin 2014 was
0.85 KRW for each 1 KRW of donation regardless of income level9 .
In short, the applicable giving price, which is the giving price that declaring taxpayers face,is 1 − q, where q represents tax incentives. The tax incentives were q = T 0 (yi − gi ) before 2014
and q = m = 0.15 after 2014.10 Therefore, high-income households, whose income tax rate wasmore than 15% before 2014 (income brackets (C)–(G) of Table 1 in 2013), face a higher giving
prices due to the 2014 tax reform. On the other hand, low-income households, whose (average)
income tax rate was less than 15% (income bracket (A) in Table 1 in 2013), have faced lower
giving prices due to the 2014 tax reform. Finally, among middle-income households, whose9

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.
10
We here review the deductibility limits for donations. During the income deduction period, the upper limit
was 15% of income during the years 2008-2010, 20% of income in 2011, and 30% of income during the years
2012-2013. Note that the deduction limit for religious-related donations was always 10% of income. For the tax
credit period, the limit is KRW 30 million, regardless of the purpose of the donation. Note that the tax credit rate
for donations exceeding KRW 30 million is 25%.

6

income tax rate was equal to 15% (income bracket (B) in Table 1 in 2013), the 2014 tax reform
does not affect the giving prices. We exploit the variation in the giving price generated by the2014 tax reform as our main identification source to estimate the giving price elasticity.

2.2

Claiming Tax Relief for Donations

An important aspect, which is perhaps often ignored, is that receiving a tax incentive depends
on the taxpayer’s choice. If taxpayers donate but do not declare it, they cannot obtain the tax
incentive. To construct a simple decision-making model for this application, let R be the indicator of a claim. Let VR (·) be the indirect utility of each claiming status. Thus, R = 1 if
V1 (y, q) − V0 (y) ≥ Ki , where Ki is the fixed compliance cost.11 That is, the taxpayer claims
tax relief only if the benefit exceeds the fixed compliance cost. Then, given the optimal claiming status, the effective giving price, which is the actual donation price the taxpayer faces, is
p = 1 − Rq.
We provide an overview of the application process for tax relief for charitable 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 thefollowing year. Unlike the U.S., Korea has introduced year-end settlements, so wage earners do
not need to file an income tax return. Instead, in January or February of the following year, wage
earners collect receipts and certificates, prepare income and tax credit documents, and submit
them to their employer. Note that wage earners can file unclaimed tax relief in the year-end
settlement when filing their income tax return in May.
Although taxpayers have to claim tax relief for charitable giving through the year-end settlement or income tax return, some wage earners can receive tax incentives for donations fromtheir employers without having to prepare receipts and documentation. In such a donation opportunity, the employer, instead of the wage earner, deducts a portion of the worker’s salary to
donate and submits receipts and documents to the tax agency.
Since this system is not available for others, such as the self-employed, we expect that the
fixed compliance cost, Ki , for wage earners is lower than that for others. Thus, we use a dummy
variable indicating wage earners to capture the different declaration costs for taxpayers. In
Section 5, we address the selection issue in claiming using the control function method with the11

If the donor does not apply (R = 0), no tax incentive q is received, so indirect utility V0 is a function of income
y. Additionally, the benefit of applying V1 (y, q) − V0 (y) includes tax savings.

7

wage-earner dummy as an instrument.

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 5,634 household heads and economically active household members aged 15 or older. The survey asks about income, charitable giving, demographics
such as years of education, and attitudes toward the tax system.
To focus on an exogenous change in the giving price 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 changes in the giving price depend only on income (before2014) and the 2014 tax reform. Thus, once we control for annual income, variation in the giving
comes from the 2014 tax reform. Since we determine income brackets based on an individual’s
pretax gross income, we exclude samples with pretax income of KRW 1 million (equivalent toapproximately USD 1,000) around the threshold for each bracket to remove price changes due
to income manipulation such as bracket shifting through income deduction without charitablegiving.
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.12
We present descriptive statistics for the final sample in Table 2. The analysis sample consists
primarily of older men. Approximately 70% of the analysis sample is male, and the averageage 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.
The solid stepwise line and the dashed horizontal line in Figure 1 are the giving prices when
the tax incentive is applied (applicable giving prices). The solid stepwise line shows the applicable giving prices for the income deduction period (2010–2013), and the dashed horizontal line
shows the applicable prices for the tax credit period (2014–2017). As stated in Section 2, the12
We also establish exclusion requirements related to donations. First, we exclude observations for which donations exceed total income (N = 226). Second, we exclude observations that claim tax incentives and whose total
contributions exceed the deduction limit for religious-related contributions (N = 210).

8

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 a tax relief

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

0.375

0.75

0.250

0.50

0.125

0.25

0.000

0.00

Giving Price

Relative frequency

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

1200

4600

8800

30000

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

Relative frequency

Figure 1: Income Distribution in 2013 and Relative Giving Price. Notes: The left and right axes
measure the relative frequency of respondents (grey bars) and the relative giving price (solid
step line and dashed line), respectively. The solid stepwise line represents the relative giving
price in 2010–2013. The dashed horizontal line represents the giving price in 2014–2017.
9Panel A. Amount of Giving

Panel B. Proportion of Donors
2.5

Normalized proportion of donors

Normalized average giving

2.5

2.0

1.5

1.0

0.5

0.0

2.0

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 by 2013 Income bracket.
Notes: The group averages are normalized to one in 2013.
changes in tax incentives due to the 2014 tax reform differ for three income groups. The firstincome group is below KRW 12 million (bracket (A) in Table 1), for which the tax reform expanded tax incentives and decreased the applicable giving prices. The second group is between
KRW 12 million and KRW 46 million (Bracket (B) in Table 1), for which the tax reform did notaffect tax incentives and the applicable giving prices. The last group is above KRW 46 million(Brackets (C), (D), and (E) in Table 1), for which the tax reform reduced tax incentives andincreased the applicable giving prices. Exploiting this variation, we identify the price elasticity
of donations based on DID analysis.
The two outcome variables that capture donation behavior are the amount of giving and adummy variable indicating donors. Table 2 shows that the average donation amount is KRW
360,000 (equivalent to USD 300), approximately 1.1% of pretax gross income. In comparison,
the amount the United Kingdom is 0.5% (Almunia et al., 2020), and that in the United States is
1.5% (Backus and Grant, 2019). In addition, the proportion of donors is 23%.
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 income bracket (A) in Table
1, where the applicable giving price decreased after the tax reform, was more significant than10Panel B. Grouped by Wage Earner or Not

Proportion of application for tax relief

Proportion of application for tax relief

Panel A. Grouped by Income Bracket
0.4

0.3

0.2

0.1

0.0

0.4

0.3

0.2

0.1

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(C) 4600−−8800(B) 1200−−4600(D) & (E) 8800−−30000

Wage earners

OthersFigure 3: The proportion Having Applied for Tax Incentives by 2013 Income Bracket (PanelA) and Wage Earner Status (Panel B).
that in income bracket (B) in Table 1, where the applicable giving prices remained unchanged
after the tax reform. On the other hand, the increase in average donations and donor ratios inincome brackets (C)–(E) in Table 1, where the applicable giving prices increased following the
tax reform, was smaller than that in income bracket (B) in Table 1. Thus, we expect a standard
price effect on donation behavior.
In addition to income, the giving price, and giving behavior, another important variable isclaiming status. Since NaSTaB examines whether a taxpayer filed a charitable contribution ineach year-end adjustment and tax return system, we create a dummy variable that takes value one
if the taxpayer filed in either system. We use this variable to identify the price that individuals
actually face (effective giving price). If taxpayers claim, the effective price will be equivalent
to the applicable price shown in Figure 1; otherwise, the effective price is 1. Table 2 shows thatthe proportion applying for tax incentives is 11%, indicating that only approximately half of all
donors declare their giving. Panel A of Figure 3 shows the percentage of tax benefits claimedin each income bracket. The income brackets with lower applicable prices for the tax deduction
period have a higher proportion of applications and a significant decrease in application rates
due to the introduction of the tax credit system.
Panel B of Figure 3 shows the transition in the proportion applying for the tax benefit, clas11

sified by whether the respondent is a wage earner. We find that the percentage applying fortax incentives among wage earners is higher throughout all periods than among the remaining
observations. This finding may reflect the differences in application costs described in Section 2. However, the difference in application ratios shown in Panel B of Figure 3 may also
be influenced by income and other factors. Therefore, while controlling for income and othereffects, we use the wage earner dummy as a proxy variable for a fixed compliance cost and as
an instrumental variable for application for tax benefits (see Section 5).

4

Estimating Price Elasticities

4.1

Estimation Model and Parameter of Interest

In this section, we provide a simple method to obtain unbiased effective price elasticities andestimate them. To begin, we clarify the parameters of interest. As introduced in Section 2, theeffective price of individual i in year t is pit = 1 − Rit qit , where Rit is a dummy variable indicating application for tax incentives and qit represents the tax incentives.13 Outcome variables,
Yit , are determined by the following two-way fixed effects model:
Yit = µi + θt + βe ln pit + δXit + it ,(1)

where µi , θt , and Xit are individual fixed effects, year fixed effects, and a vector of covariates(including pretax income, yit ), respectively. The term it is an idiosyncratic error.
Our parameter of interest is a coefficient βe . Using this estimate, we obtain the effective
price elasticities. As in previous studies (e.g. Backus and Grant, 2019; Almunia et al., 2020),
we estimate two types of elasticities. The first is the intensive-margin price elasticity, whichindicates by what percentage a 1% price increase leads to an increase in the amount donors
give. In this estimation, we restrict our sample to donors and use the log value of donations,
In the pre-2014 tax deduction period, the tax incentive is the marginal income tax rate T 0 (yit − git ). Since thattax rate depends on the amount of giving, the endogeneity of the effective price is due not only to Rit but also to
the marginal income tax rate. To avoid this, we calculate the relative giving price (first price) using the marginalincome tax rate T 0 (yit ) when the donation amount is set to zero. We estimate the price elasticities using the firstprice. As a robustness check, we also calculate the giving price based on the marginal income tax rate T 0 (yit − git )under the actual donation amount (last price) and estimate the price elasticities by a fixed effects two-stage model(FE-2SLS) with the first price as an instrumental variable. The results are quantitatively similar to the first priceelasticities. See Section 4.4 for details. If income Yit is determined simultaneously with giving behavior, we cannot
completely rule out the endogeneity problem of marginal income tax rates. However, since we add pretax income
as an explanatory variable, we believe that this endogeneity can be eliminated to some extent.
13

12

ln git , as the outcome variable. Then, the coefficient βe indicates the price elasticity.
The second is the extensive-margin price elasticity, which indicates by what percent thedonor ratio increases with a 1% price increase. For estimation, we include donors and nondonors in our analysis sample and use a dummy variable Dit = 1[git > 0] indicating donors
as the outcome variable. Because we have a binary outcome variable, we cannot interpret thecoefficient βe in this estimation as an elasticity. Therefore, using the estimate βe , we obtain theimplied extensive-margin price elasticity as β̂e /D̄, where D̄ is the sample mean of Dit .
Since claiming, Rit , depends on the taxpayer’s decision, the effective price can be endogenous due to the selection of claiming. Thus, standard fixed effects models (1) may estimate abiased βe . In this section, 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 individuals assigned to a treatment do not actually receive thattreatment and examines the effect of providing the opportunity for treatment. We can estimate
this effect using an estimation model assuming that all persons assigned to treatment receive thetreatment. In the context of tax incentives, we acknowledge that some people who are eligible
for tax incentives do not actually receive them. We then estimate the following model:
Yit = µi + θt + 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. This elasticity is a valuable measure for the policy evaluation of tax reform because policymakers cannot
directly manipulate individuals’ application for tax incentives. When policymakers implement a
reduction in tax incentives equivalent to a 1% increase in donation prices, the amount of donors’
giving changes by β̂a % (intensive margin), and the donor ratio changes by (β̂a /D̄)% (extensive
margin).
For estimation of the applicable price elasticities, our identification strategy is a DID model
exploiting the exogenous change in tax incentives qit due to the 2014 tax reform. Thus, thestandard fixed-effects model (2) obtains unbiased applicable price elasticities.
However, since the ITT analysis assumes that nonapplicants for tax incentives receive tax

13incentives, the applicable price elasticity is different from our parameter of interest, βe , theeffective price elasticity. To illustrate this point, we derive the estimator of βa . By the regression
anatomy theorem (Angrist and Pischke, 2009), the estimator of βa is
Cov(Yit , r̂it )βˆa =,Var(r̂it )(3)

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

(4)

Since the residual is a linear combination of all explanatory variables and fixed effects in Equation (4), the residual r̂it 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 r̂it is uncorrelated with the error term it in Equation (1).
The ITT analysis estimates Equation (2), but the outcome variable Yit is determined by Equation (1). Thus, substituting Equation (1) into Equation (3) yieldsβ̂a =Cov(Yit , r̂it )Cov(βe ln pit , r̂it )Cov(ln pit , r̂it )== βe ·.
Var(r̂it )Var(r̂it )Var(r̂it )(5)

Furthermore, since r̂it is a residual of auxiliary regression (4), the regression anatomy theorem
implies that the parameter Cov(ln pit , r̂it )/Var(r̂it ) is a coefficient γ1 in the following model:
ln pit = µi + θt + 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 r̂it and application for tax incentives are mean independent, then the parameterγ1 will always be in the range from 0 to 1 (See Appendix B for the proof). In this case, theapplicable price elasticity is more inelastic than the effective price elasticity. Furthermore, thefewer nonclaimants of the tax incentive there are, the stronger the correlation between effective
and applicable prices, and the closer the values of the two elasticities. As an extreme example,
when all taxpayers donate and apply for tax incentives, γ1 = 1 because the effective price is14

equal to the applicable price. Therefore, Equation (5) implies that β̂a = βe . Conversely, when
no taxpayers apply for tax incentives, the logarithm of the effective price must be 0, and Equation(5) implies that β̂a = 0.
Some donors do not apply for tax incentives (Table 2), and nondonors cannot claim thededuction. Therefore, in our estimation of price elasticities, βa is not equal to βe . We can also
estimate Equation (6), which allows us to accurately measure the extent to which applicable
price elasticities differ from effective price elasticities. Table A.1 in Appendix A shows theestimation results of Equation (6) for the intensive-margin price elasticity and the extensivemargin price elasticity. By the estimated value of γ1 , the applicable price elasticity is 0.688
times the effective price elasticity for the intensive-margin price elasticity. For the extensivemargin price elasticity, the applied price elasticity is 0.297 times the effective price elasticity.
Equation (5) presents a way to recover the effective price elasticity from the applicable priceelasticity. Since we can estimate Equation (2), we obtain an estimate of the parameter βa . We
also already have an estimate of the parameter γ1 from the estimation results presented in Table
A.1 in Appendix A. Thus, by computing βa /γ1 , we can recover the coefficient βe used to estimate
the effective price elasticity. The parameter βa /γ1 is also a Wald estimator of βe in the following
two-stage model with fixed effects (FE-2SLS):Yit = µi + θt + βe ln pit + δXit + it ,(7)

ln pit = µi + θt + γ1 ln(1 − qit ) + λXit + uit ,Here, the logarithm of the applicable price ln(1 − qit ) is the instrumental variable for the endogenous variable, the logarithm of the effective price ln pit . Again, once we control for income,ln(1−qit ) is independent of it . Thus, ln(1−qit ) is a valid instrument for ln pit . We use Equation(7) as the main model to estimate the parameter βe and obtain the effective price elasticity.

4.3

Estimation Results

Table 3 presents the estimation results for price elasticities. Columns (1)–(3) report the estimation 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. Column (1)estimates the applicable price elasticities. The estimated elasticity is −1.072, which is statistically significant.

15

Table 3: Estimation Results of Price Elasticities
Log donation
FE(1)
Applicable price (βa )FE-2SLS(2)(3)−1.072***(0.330)Effective price (βeF E )FE(4)−0.640**(0.254)1.624(1.333)

FE-2SLS(5)(6)−0.182***(0.058)−2.728***(0.073)

Effective price (βeIV )Log income

Dummy of donor−1.559***(0.487)1.274(1.333)1.846(1.321)

Implied price elasticity
Estimates
1st stage information (Excluded instrument: Applicable price)
F-statistics of instruments
Wu-Hausman test, p-value
Num.Obs.
7786
7786
RMSE
0.66
0.66

1379.445
0.004
7786
0.66

1.454***(0.208)0.674***(0.189)−0.615***(0.182)
1.411***(0.201)−0.783***(0.248)−11.707***(0.314)−2.639***(0.783)30 2800.23

1796.440< 0.00130 2800.25

30 2800.26

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

We then turn to the effective price elasticity. The elasticity estimated in Column (1) differsfrom the effective price elasticity because only approximately half of the donors apply for tax
incentives. Thus, we estimate the FE-2SLS model (7) to obtain an unbiased estimate of theeffective price elasticity. In Column (3), the results show that the effective price elasticity is−1.559, which is statistically significant. Thus, a 1% increase in the price of giving decreases
the donor’s contribution by 1.6%. This value is consistent with the ratio of the applicable priceelasticity estimated in Column (1) to the estimated value of the parameter γ1 in Equation (6)presented in Column (1) of Table A.1 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 of the
instrument is sufficiently high. Therefore, the effective price elasticity estimated in Column (3)is reliable.
Column (2) estimates the effective price elasticity using the standard FE model (1). By
comparing this result with that in Column (3), we can discuss the direction of the estimation
bias in the effective price elasticity estimated by the standard FE model. The estimate obtainedin Column (2) is more inelastic than the unbiased effective price elasticity (Column (3)). Thissuggests that the logarithm of the effective price is positively correlated with unobservable do-

16

nation behavior (the error term it in model (1)). The logarithm of the effective price varies andnegatively correlates with the claiming decision. Since the source of endogeneity in effective
prices is the claiming decision, Columns (2) and (3) suggest that unobservable donation behavior negatively correlates with the claiming decision. Section 5 explicitly tests this suggestion
using the control function method and discusses it in detail.
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 nondonors
as the sample. Column (4) estimates the applicable price elasticities. The estimated value ofthe coefficient on the applicable price is −0.182, which is statistically significant. Since theoutcome variable is binary, we cannot directly interpret this coefficient estimate as an elasticity.
Therefore, we calculate the implied 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.
We turn to the effective price elasticity. Since nondonors cannot claim the donation deduction, the elasticity estimated in Column (4) differs from the effective price elasticity. This motivates us to estimate the FE-2SLS model (7). Column (6) indicates that the estimated coefficienton the effective price is −0.615, which is statistically significant. Dividing this value by the sample proportion of donors yields −2.639(= −0.615/0.23). Thus, a 1% increase in the donation
price decreases the donor ratio by approximately 2%. 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 A.1 of Appendix A (−0.783/0.297 = −2.636). In
addition, there is no weak instrumental variable problem in this estimation because the F-valueof the instrument is sufficiently high. Thus, the effective price elasticity estimated in Column(6) is reliable.
Column (5) estimates the effective price elasticity with bias using the standard FE model (1)and finds that it is more elastic than the unbiased effective price elasticity obtained in Column (6).
This suggests that the logarithm of the effective price is negatively correlated with unobservabledecisions about whether to donate. In other words, the claiming decision is positively correlatedwith the unobservable decision of whether to donate, which stems from the institutional factor
that only donors can file for tax benefits.

17

4.4

Robustness Check

Excluding Announcement Effect. Since the Korean government announced the 2014 tax reformin 2013, intertemporal substitution may have occurred. Individuals who anticipated that the2014 tax reform would result in higher donation prices may have reduced their donations in2014 and beyond 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 by assumingthat intertemporal substitution occurs only in that period and estimate elasticities (Table A.2 inAppendix A). As expected, the estimated elasticities are somewhat elastic when we exclude theannouncement effect.
Last-Price Elasticities. The tax incentive in the income deduction period is the marginal income
tax rate. The marginal income tax rate 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 to
calculate the relative price (first-unit price). However, the actual effective and applicable prices
are the relative prices used in actual donation amounts, referred to as the last-unit price. Thus,
we estimate elasticities using the last-unit price. Since the last-unit price depends on the amountof giving, we estimate an FE-2SLS model with the applicable first price as the instrumental
variable (see Table A.3 in Appendix A for the intensive-margin price elasticities; see Table A.4
in Appendix A for the extensive-margin price elasticities). The results are quantitatively similar
to the elasticities estimated in Table 3.

5

Control Function Approach

In the previous section, we noted that the effective price elasticity estimated by the simple FE
model is biased because the effective price can be endogenous and proposed FE-2SLS for theestimation of the effective price elasticity. Although this method assumes that the effective priceis determined as (6), considering that the effective price is written as ln pit = Rit ln(1 − qit ), theroot of the endogeneity is in the self-selection into declaration, Rit .14 Therefore, in this section,
we examine the size and direction of the bias in declaration, Rit , by using the control function
approach and check whether the method proposed in the previous section corrects the bias in
14
If Rit = 1, then ln pit = ln(1 − Rit qit ) = ln(1 − qit ). If Rit = 0, then ln pit = ln(1 − Rit qit ) = 0. Thus,ln pit = ln(1 − Rit qit ) = Rit ln(1 − qit ).

18

the right direction.

5.1

Framework

Our aim in this section to examine the bias in the estimation of the giving price elasticity byusing the control function approach (Wooldridge, 2015). This approach considers the dummy
variable Rit indicating the application for tax incentives as an endogenous variable and explicitly
models the endogeneity of Rit .
To demonstrate this point precisely, let us consider (1), which is shown as
Yit = µi + θt + βe Rit ln(1 − qit ) + δXit + it .

(1’)

If Rit is endogenous, the simple FE estimation of this model yields β̂ = β + Cov(Rit ln(1 −qit ), it )/Var(Rit ln(1−qit )), and this corresponds to the results in Columns (2) (for the intensive
margin) and (5) (for the extensive margin) in Table 3. This estimation is clearly incorrect because
the endogeneity issue comes from the correlation between the error term and the explanatory
variables. In particular, considering ln(1 − qit ) ≤ 0, we can expect that the positive (negative)correlation between Rit and it generates negative (positive) bias for β̂.
The control function approach fixes the estimation bias by controlling for the correlation
between the endogenous variable and the error term. Recall that taxpayers should declare theirgiving Rit = 1 if V1 (y, q) − V0 (y) ≥ Ki , where V1 (y, q) and V0 (y) are the indirect utility if
giving is declared and not declared, respectively, and Ki is the compliance cost for declaration.
This means that the structure of Rit can be written as Rit = 1(V1 (y, q) − V0 (y) − Ki ≥ 0). In
this paper, we define a reduced-form model to determine Rit as follows:R
Rit = E(Ri |1 − qit , Xit , Zit , µt , θt ) + uR
it = µi + θt + π1 ln(1 − qit ) + π2 Zit + π3 Xit + uit ,(8)
where Zit is an instrumental variable only affecting the application for tax incentives but notaffecting Yit . As this equation approximates the structure of Rit , the increase of each termon the right-hand side can be regarded as observed components of net utility. The last term ofEquation (8), uR
it , is an error term and can be considered the preference for declaration that cannot
be explained by the covariates. uR
it is not correlated with the covariates but a part of Yit , whichRR
is not explained by the covariates. Then, it = ψ1 uR
it + eit , where ψ1 = Cov(it , uit )/Var(uit )19and Cov(Rit ln(1 − qit ), eit ) = 0 hold since uR
it captures all of Rit that is not explained by thecovariates. Based on this idea, plugging it = ψ1 uR
it + eit into (1’) yields
Yit = µi + θt + βe Rit ln(1 − qit ) + δXit + ψ1 uR
it + eit .

(9)

The inclusion of uR
it in the estimation works to control the endogeneity of Rit . Since Cov(Rit , it ) =R
RR
Cov(uRit + E(Rit |1 − qit , Xit , Zit , µt , θt ), it ) = Cov(uit , it ) and ψ1 = Cov(it , uit )/Var(uit )hold, we can find that ψ1 shows the opposite direction of the estimation bias, β̂−β = Cov(Rit ln(1−qit ), it )/Var(Rit ln(1 − qit )), where ln(1 − qit ) ≤ 0.
R 15
To estimate Equation (9), we use the residual of (8), ûR
In addition, we use
it , instead of uit .

a dummy variable indicating wage earners as the instrument Zit . As discussed in Section 2, theapplication process for the donation deduction differs depending on whether a taxpayer is a wage
earner or self-employed. Wage earners are offered the chance of giving from their company,
and the declaration process for such giving is considerably simpler than declaration through the
tax return, although such a system is absent for the self-employed. We assume that, once wecontrol for income, residence, and industry, the amount of giving does not directly correlatewith whether one is a wage earner. Thus, since wage earners have lower declaration costs, Kit ,than the self-employed, we use a dummy variable indicating wage earners as the instrument.
However, the dummy for wage earners may violate the exclusion restriction in the estimationof the extensive margin since the company’s donation offer not only reduces the cost of giving
but also increases the opportunity for donation. Although this issue is not a problem in theestimation of the intensive margin since the sample is limited to donors in the estimation of
the intensive margin, it is problematic in the estimation of the extensive margin. Therefore, weconcentrate on the estimation of the intensive margin in this part.16
Our aim in this part is to examine the self-selection bias coming from the fact that declaring
giving is optional for taxpayers by using the control function approach. The sign of ψ is notknown a priori since each positive and negative ψ can be the result of different self-selection
biases. Recall that it is the amount of giving conditional on the covariates including the price
15

When applying the control function approach to panel data, Wooldridge (2015) suggests replacing individual
fixed effects with the Chamberlain-Mundlak device. This device assumes that individual fixed effects, µi , follow
a normal distribution with mean α0 + α1 X̄it + α2 Z̄it and variance σµ2 and models the individual fixed effects withPT
µi = α0 + α1 X̄i + α2 Z̄i + ηi , where X̄i and Z̄i are time averages (for example, X̄i = T −1 t=1 Xit ) and ηi iserror term (Papke and Wooldridge, 2008). Then, we can replace the individual fixed effects in Equation (9) with
α1 X̄it + α2 Z̄it . We use this device in our estimation.
16
The results of the analysis for the extensive margin are included in the Appendix for reference. See Table A.6
in Appendix A.

20

of giving. Therefore, the preference for giving will be captured by it in the regression. If
ψ > 0 is observed, this implies that, conditional on the covariates, the donors with preferences
to donate more (it > 0) will select into declaration (Rit > 0). In this story, conditional on thecovariates, donors with giving preferences are likely to enjoy tax relief. If ψ < 0 is observed, this
implies that taxpayers with a greater preference for donation (it > 0) do not declare their giving(Rit < 0). In this case, taxpayers with giving preferences hesitate to declare their donations.

5.2

Estimation Results

To begin, we review the results of estimating Equation (8) with a linear probability model using asample that includes nondonors (Table A.5 in Appendix A). The wage earner dummy positively
correlates with application. As expected, this correlation reflects that wage earners apply fortax incentives more easily than others. In addition, the higher the applicable giving price (thatis, the lower the possible tax incentive), the less likely they are to declare their giving.17 This
result implies that the decrease in tax incentives lowers the benefit of tax savings and that thosewith higher tax benefits are more likely to apply. There are two notable findings for individual
attributes. First, the older a taxpayer is, the more likely the taxpayer is to declare his or her
giving. Second, the fewer household members and the more dependents a taxpayer has, themore likely the taxpayer is to claim his or her giving. This may be because older taxpayers may
have more experience with tax payments and taxpayers with more dependents attempt to save
tax payments and make money for dependents.
We estimate Equation (9), using the residuals obtained from the estimated model shown in
Table A.5 in Appendix A for an explanatory variable. Table 4 presents the estimation results of
the intensive-margin price elasticity by restricting the sample to donors only.
The coefficient on the effective price represents the effective price elasticity. It shows thatthe effective price elasticity to donor contributions is −1.646. This result is reasonable in thesense that it is similar to the result from the FE-2SLS in the previous section, −1.559. Moreover,since the simple FE estimation of (1) yields the results of Column (2) (for the intensive margin)
in Table 3, -0.840, we find that the result of the control function approach corrects for the upward/positive bias, as in FE-2SLS. The results of ψ̂ also support this view since the negative ψ̂indicates that the simple FE estimators have positive bias. Thus, we confirm that the method17

The coefficient on the applicable price is −0.233. Since the application ratio is 11%, the price elasticity ofclaiming is −2.29 (= −0.252/0.11). Almunia et al. (2020) estimates the price elasticity of claiming using tax
return data and finds it to be −0.9.

21Table 4: Estimation Results of Control Function Model (Intensive-margin Sample)
Log donation(1)−1.646***(0.355)
3.216***(1.180)−0.425***(0.084)

Effective price (βe )Log income
Residuals of Application (ψ1 )Num.Obs.
R2 Adj.

7786
0.095

Notes: * p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at household level are in parentheses.
An outcome variable is logged value of amount of charitable giving. For estimation, we use only donors(intensive-margin sample). We control squared age (divided by 100), number of household members, adummy that indicates having dependents, a set of dummies of industry, a set of dummies of residentialarea, and time fixed effects. We use an wage earner dummy as an instrument to obtain residuals of
application. Instead individual fixed effects, we control a vector of individual-level sample mean of all
exogenous variables including instruments (Chamberlain-Mundlak device).

proposed in the previous section corrects the bias in the right direction. The estimated effective
price elasticity in this analysis is approximately 46 percentage points larger than the effective
price elasticity obtained by simple FE estimation, suggesting that the size of the correct bias isquite large.
Regarding the direction of self-selection bias, ψ̂ was negative when estimating the intensive
margin. In other words, the result reveals the existence of the self-selection issue in the sensethat ψ̂ < 0 suggests that the donors with a preference to donate (it > 0) are not more likely todeclare their giving (uRit < 0), when controlling for covariates including the giving price. Thismay be because, conditional on the covariates, declarers donate less than nondeclarers. This
does not support the view that declarers are more likely to donate based on financial motivation
than nondeclarers.
We can explain this result by the motives for donation. Behavioral economics (e.g. Ariely
et al., 2009) argues that there are three driving forces behind prosocial behaviors such as donation: (i) intrinsic motives (utility from the prosocial action itself); (ii) extrinsic motives (utility
from the exogenous material rewards that accompany prosocial behavior); and (iii) image motives (utility from social reputation and praise). These motives are considered to not only affectprosocial behavior in isolation but also interact with each other. Our results suggest that donors
who give more without declaring their giving have a strong intrinsic motivation and seem indifferent to extrinsic rewards such as tax incentives. In other words, our results imply that thedonors’ intrinsic and extrinsic motives are substitutes.
Alternatively, substitution between extrinsic and image motives can explain the result. Image22

motivated donors want to send an altruistic signal to others. Here, financial incentives, such as
tax incentives, will add noise to the altruistic signals they send (Bénabou and Tirole, 2006).
In other words, others cannot distinguish whether donors who apply for tax incentives are altruistic or selfish. When this is the case, extrinsic rewards weaken the image motive. Thus,
image-motivated donors who donate large sums without tax incentives may be hesitant to claim
the donation deduction. This hypothesis was also highlighted by Eckel and Grossman (2008),
who presented a field experiment on financial incentives for donations.

6

Discussions and Conclusions

Since tax relief application depends on taxpayer decisions, even if we exploit exogenous variation in the applicable price of giving, standard fixed effects 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 showed that a 1%
increase in the giving price reduces donors’ contributions by 1.4–1.5% and the donor proportion by 2.1–2.3%.
This result is more elastic than previous studies. For example, a meta-analysis of studies
using U.S. panel surveys finds an average elasticity of −1.29 (Peloza and Steel, 2005). Backus
and Grant (2019) also estimate the price elasticity of donations using a U.S. panel survey, explicitly accounting for the bias that tax incentives cause due to taxpayer choice. As a result, theyfind that the elasticity is approximately −1. Testing whether our results are Korea-specific is a
topic for future research.
We then discussed the selection issue of claiming and checked whether our proposed method
corrects the selection bias in the right direction using a control function approach, an instrumental variable method. We found that donors who give more without tax incentives do not receive
tax incentives. This finding is consistent with the direction of bias that arises in the usual fixed
effects model. Using an argument from behavioral economics, we proposed one possible mechanism: substitution between intrinsic or image motives and an extrinsic motive. In other words,
altruistic donors or donors who value reputation-building may not be willing to apply for tax
incentives. Testing this mechanism in the context of tax incentives is a topic for future research.
There are two limitations of this study. First, we could not empirically demonstrate thevalidity of the instrument used in the control function approach. We exploited the fact that23

the application process for tax incentives in Korea differs significantly depending on whether ataxpayer is a wage earner and used a wage earner dummy as an instrument. We assumed that if
we controlled for individual income and area of residence, donation behavior would not change
depending on whether the individual is a wage earner. Second, we could not accurately measuretaxable income. We determined income tax rates based on pretax gross income. If the income
bracket in which pretax income falls differs from the bracket in which taxable income falls due
to deductions and other factors, then there will be measurement error in the income tax rate,
which will also cause bias in the giving price. We dropped observations whose pretax income
falls around the bracket thresholds to eliminate the bracket shifting effect as much as possible.
Finally, we summarize some policy implications. If the estimated effective price elasticities
are correct, this study has implications for the welfare of tax incentives in Korea. According toSaez (2004), the government should expand tax incentives if the absolute value of the elasticity
exceeds 1. Furthermore, according to Almunia et al. (2020), if the sum of the intensive- andextensive-margin price elasticities is greater than 1 (in absolute value), then the expansion oftax incentives can induce donations that exceed their costs. Combining these theoretical resultswith our estimates, we conclude that Korea should expand tax incentives for charitable giving.

References
Almunia, M., Guceri, I., Lockwood, B., Scharf, K., 2020. More giving or more givers? The
effects of tax incentives on charitable donations in the UK. Journal of Public Economics 183,
104114. doi:10.1016/j.jpubeco.2019.104114.
Angrist, J.D., Pischke, J.S., 2009. Mostly Harmless Econometrics: An Empiricist’s Companion.
Princeton University Press, Princeton.
Ariely, D., Bracha, A., Meier, S., 2009. Doing Good or Doing Well? Image Motivation andMonetary Incentives in Behaving Prosocially. American Economic Review 99, 544–555.
doi:10.1257/aer.99.1.544.
Auten, G.E., Sieg, H., Clotfelter, C.T., 2002.

Charitable Giving, Income, and Taxes:

An Analysis of Panel Data. American Economic Review 92, 371–382. doi:10.1257/
000282802760015793.
Backus, P.G., Grant, N.L., 2019. How sensitive is the average taxpayer to changes in the24

tax-price of giving?

International Tax and Public Finance 26, 317–356. doi:10.1007/

s10797-018-9500-9.
Bakija, J., Heim, B.T., 2011. How Does Charitable Giving Respond to Incentives and Income?
New Estimates From Panel Data. National Tax Journal 64, 615–650. doi:10.17310/ntj.
2011.2S.08.
Bénabou, R., Tirole, J., 2006. Incentives and Prosocial Behavior. American Economic Review
96, 1652–1678. doi:10.1257/aer.96.5.1652.
Benzarti, Y., 2020. How Taxing Is Tax Filing? Using Revealed Preferences to Estimate Compliance Costs. American Economic Journal: Economic Policy 12, 38–57. doi:10.1257/pol.
20180664.
Brown, S., Greene, W.H., Harris, M.N., Taylor, K., 2015. An inverse hyperbolic sine heteroskedastic latent class panel tobitmodel: An application to modelling charitable donations.
Economic Modelling 50, 228–236. doi:10.1016/j.econmod.2015.06.018.
Brown, S., Harris, M.N., Taylor, K., 2012. Modelling charitable donations to an unexpectednatural disaster: Evidence from the u.s. panel study of income dynamics. Journal of Economic
Behavior & Organization 84, 97–110. doi:10.1016/j.jebo.2012.08.005.
Duquette, N.J., 2016. Do tax incentives affect charitable contributions? evidence from publiccharities’ reported revenues. Journal of Public Economics 137, 51–69. doi:https://doi.
org/10.1016/j.jpubeco.2016.02.002.
Eckel, C.C., Grossman, P.J., 2008. Subsidizing charitable contributions: A natural field experiment comparing matching and rebate subsidies. Experimental Economics 11, 234–252.
doi:10.1007/s10683-008-9198-0.
Fack, G., Landais, C., 2010. Are Tax Incentives for Charitable Giving Efficient? Evidence from
France. American Economic Journal: Economic Policy 2, 117–141. doi:10.1257/pol.2.
2.117.
Fack, G., Landais, C., 2016. The effect of tax enforcement on tax elasticities: Evidence fromcharitable contributions in France. Journal of Public Economics 133, 23–40. doi:10.1016/
j.jpubeco.2015.10.004.

25

Feldstein, M., Taylor, A., 1976. The Income Tax and Charitable Contributions. Econometrica
44, 1201. doi:10.2307/1914255.
Gillitzer, C., Skov, P.E., 2018. The use of third-party information reporting for tax deductions:
Evidence and implications from charitable deductions in Denmark. Oxford Economic Papers
70, 892–916. doi:10.1093/oep/gpx055.
Giving USA, 2022. The annual report on philanthropy for the year 2021.
Papke, L.E., Wooldridge, J.M., 2008. Panel data methods for fractional response variables with
an application to test pass rates. Journal of Econometrics 145, 121–133. doi:10.1016/j.
jeconom.2008.05.009.
Peloza, J., Steel, P., 2005. The Price Elasticities of Charitable Contributions: A Meta-Analysis.
Journal of Public Policy & Marketing 24, 260–272. doi:10.1509/jppm.2005.24.2.260.
Randolph, W.C., 1995. Dynamic Income, Progressive Taxes, and the Timing of Charitable
Contributions. Journal of Political Economy 103, 709–738. doi:10.1086/262000.
Rehavi, M.M., Shack, D., 2013. Partial Reporting: An Example from Charitable Giving. Technical Report. The University of British Columbia.
Saez, E., 2004. The optimal treatment of tax expenditures. Journal of Public Economics 88,
2657–2684. doi:10.1016/j.jpubeco.2003.09.004.
Wooldridge, J.M., 2015. Control Function Methods in Applied Econometrics. Journal of Human
Resources 50, 420–445. doi:10.3368/jhr.50.2.420.
Zampelli, E.M., Yen, S.T., 2017. The Impact of Tax Price Changes on Charitable Contributions
to the Needy: Charitable Contributions to the Needy. Contemporary Economic Policy 35,
113–124. doi:10.1111/coep.12177.
Zwick, E., 2021. The Costs of Corporate Tax Complexity. American Economic Journal: Economic Policy 13, 467–500. doi:10.1257/pol.20180406.

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Appendix A

Additional Tables
Table A.1: First-Stage Models
Effective priceDonors (Intensive-margin)

Donors and Non-donors (Extensive-margin)

(1)

(2)

0.688***(0.038)0.297***(0.019)−0.030***(0.009)−0.225(0.146)−0.010***(0.002)−0.069(0.047)7786
0.05

30 2800.04

Excluded instruments
Applicable priceCovariates
Wage earner
Log income
Num.Obs.
RMSE

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

Table A.2: Estimation of Price Elasticities Excluding Announcement EffectLog donation
FE(1)
Applicable price (βa )FE-2SLS(2)(3)−1.286***(0.471)

Effective price (βeF E )FE(4)−0.616*(0.343)1.657(1.854)

FE-2SLS(5)(6)−0.218***(0.077)−2.807***(0.088)

Effective price (βeIV )Log income

Dummy of donor−1.829***(0.682)
1.175(1.893)1.931(1.858)Implied price elasticity
Estimates
1st stage information (Excluded instrument: Applicable price)
F-statistics of instruments
Wu-Hausman test, p-value
Num.Obs.
5944
5944
RMSE
0.62
0.62

918.108
0.003
5944
0.63

1.576***(0.253)0.816***(0.235)−0.764***(0.248)1.510***(0.245)−0.936***(0.330)−12.047***(0.378)−3.278***(1.062)22 7070.23

1127.703< 0.001
22 7070.24

22 7070.25

Notes: * p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at household level are in parentheses. An outcome
variable is logged value of amount of charitable giving for models (1)–(3) and a dummy of donor for models (4)–(6). For
estimation, models (1)–(3) use donors only (intensive-margin sample), and models (4)–(6) use not only donors but also nondonors (extensive-margin sample). To exclude announcement effect, we exclude samples from 2013 and 2014. For outcome
equation, we control squared age (divided by 100), number of household members, a dummy that indicates having dependents,
employee dummy, a set of dummies of industry a set of dummies of residential area, and individual and time fixed effects. For
FE-2SLS, we use a logged applicable price as an instrument. To obtain the extensive-margin price elasticities in models (4)–(6),we calculate implied price elasticities by divding estimated coeffcient on price by sample proportion of donors.

27

Table A.3: Estimation Results of Intensive-Margin Last-Price Elasticities
Log donationFE

FE-2SLS(1)
Applicable last-price(2)−0.803**(0.345)(4)−1.110***(0.343)−0.594**(0.259)1.867(1.323)

Effective last-priceLog income

(3)

1.768
(1.334)

1st stage information (Excluded instrument: Applicable price)
F-statistics of instruments
Wu-Hausman test, p-value
Num.Obs.
7786
7786
RMSE
0.66
0.66

1.585
(1.335)−1.623***(0.510)1.215(1.338)85 032.657< 0.001
7786
0.66

1275.410
0.002
7786
0.66

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

Table A.4: Estimation Results of Extensive-Margin Last-Price Elasticities
A dummy of donor
FE

FE-2SLS(1)
Applicable last-price−0.146**(0.058)Implied price elasticity
Estimates

(3)

(4)

−0.185***(0.059)1.488***(0.209)−2.758***(0.074)0.656***(0.189)1.452***(0.208)−0.634***(0.188)1.403***(0.201)−0.625**(0.251)−11.835***(0.317)−0.793***(0.251)−2.720***(0.806)

1 491 942.086< 0.00130 2800.26

1709.919< 0.00130 2800.25

Effective last-priceLog income(2)

1st stage information (Excluded instrument: Applicable price)
F-statistics of instruments
Wu-Hausman test, p-value
Num.Obs.
30 28030 280
RMSE
0.26
0.23

Notes: * p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at household level are in parentheses.
An outcome variable is a dummy indicating that donor. For estimation, we use not only donors but also
non-donors (extensive-margin sample). For outcome equation, we control squared age (divided by 100),number of household members, a dummy that indicates having dependents, a employee dummy, a set ofdummies of industry, a set of dummies of residential area, and individual and time fixed effects. For FE2SLS, we use a logged applicable price as an instrument. We calculate implied price elasticities by dividing
estimated coeffcient on price by sample proportion of donors.

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Table A.5: Estimation Results of Tax Relief Application Model (Linear Probability Model)
Dummy of application(1)
Excluded instrument
Wage earner

0.098***(0.008)

Covariates
Applicable price−0.252***(0.045)2.662***(0.203)0.001**(0.001)−0.009**(0.004)0.014**(0.007)

Log income
Squared age (divided by 100)
Number of household members
Having dependents
Num.Obs.
R2 Adj.

30 2800.225

Notes: * p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at household level are in parentheses.
An outcome variable is a dummy of application of tax relief. For estimation, we use both donors andnon-donors (extensive-margin sample). Additionally, we control a set of dummies of industry, a set ofdummies of residential area, and time fixed effects. We use a wage earner dummy as an instrument.
Instead individual fixed effects, we control a vector of individual-level sample mean of all exogenous
variables including instrument (Chamberlain-Mundlak device).

Table A.6: Estimation Results of Control Function Model (Extensive-margin Sample)
Dummy of donors(1)−0.268***(0.042)2.676***(0.151)0.785***(0.009)Effective price (βe )Log income
Residuals of Application (ψ1 )Implied price elasticity
Estimate−1.152***(0.179)30 2800.483

Num.Obs.
R2 Adj.

Notes: * p < 0.1, ** p < 0.05, *** p < 0.01. Standard errors clustered at household level are in parentheses. An outcome variable is a dummy of donor. For estimation, we use both donors and non-donors(extensive-margin sample). We control squared age (divided by 100), number of household members,
a dummy that indicates having dependents, a set of dummies of industry, a set of dummies of residential area, and time fixed effects. We use an wage earner dummy as an instrument to obtain residuals of
application. Instead individual fixed effects, we control a vector of individual-level sample mean of all
exogenous variables including instruments (Chamberlain-Mundlak device).

29

Appendix B

Proof

We show that the parameter Cov(ln pit , r̂it )/Var(r̂it ) is in the range 0 to 1 if residuals r̂it is mean
independent to a dummy indicating application of tax incentives Rit . We obtain the residualsr̂it from the following model:ln(1 − qit ) = µi + θt + λXit + rit ,(B.1)

By E(r̂it ) = 0, Var(r̂it ) = E(r̂it2 ). Also, E(r̂it ) = 0 implies Cov(ln pit , r̂it ) = E(ln pit r̂it ). By
the law of iterated expectation,
Cov(ln pit , r̂it ),Var(r̂it )E(ln pit r̂it )=,E(r̂it2 )E(ln(1 − qit )r̂it |Rit = 1)Pr(Rit = 1)=.
2
E(r̂it |Rit = 1)Pr(Rit = 1) + E(r̂it2 |Rit = 0)Pr(Rit = 0)

(B.2)

Note that pit = 1 − Rit qit .
By the auxiliary regression model (B.1), the variable ln(1 − qit ) is a sum of predicted valueE[ln(1 − qit )|µi , θt , Xit ] and residual r̂it . Thus, we can reformulate the numerator of equation(B.2) as follows:E{ln(1 − qit )r̂it |Rit = 1}Pr(Rit = 1),=E{(E[ln(1 − qit )|µi , θt , Xit ] + r̂it )r̂it |Rit = 1}Pr(Rit = 1),=E{E[ln(1 − qit )|µi , θt , Xit ]r̂it |Rit = 1}Pr(Rit = 1) + E(r̂it2 |Rit = 1)Pr(Rit = 1),=E[ln(1 − qit )|µi , θt , Xit ]E(r̂it |Rit = 1)Pr(Rit = 1) + E(r̂it2 |Rit = 1)Pr(Rit = 1).

(B.3)

Thus, if the residual r̂it and the dummy variable Rit are mean independent, that is E(r̂it |Rit =1) = E(r̂it ) = 0, then equation (B.3) reduces to E(r̂it2 |Rit = 1)Pr(Rit = 1) and the parameterCov(ln pit , r̂it )/Var(r̂it ) becomes
Cov(Rit ln(1 − qit ), r̂it )E(r̂it2 |Rit = 1)Pr(Rit = 1)=
, (B.4)Var(r̂it )E(r̂it2 |Rit = 1)Pr(Rit = 1) + E(r̂it2 |Rit = 0)Pr(Rit = 0)
which is in the range 0 to 1.

30