ISSN (Print) 0473-453X

Discussion Paper No. 1064

ISSN (Online) 2435-0982

WHO IS AUDITED?
EXPERIMENTAL STUDY
OF RULE-BASED TAX AUDITING

Yoshio Kamijo
Takehito Masuda
Hiroshi Uemura

October 2019

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Who is audited? Experimental study of rule-based tax auditing
Yoshio Kamijoa, Takehito Masudab*, and Hiroshi UemuraaaSchool of Economics and Management, Kochi University of Technology
Eikokuji-cho, Kochi-city, Kochi 780-8515, Japanb

Institute of Social and Economic Research, Osaka University
Mihogaoka 6-1, Ibaraki, Osaka 567-0047, Japan* oorresoondin

uuthor-mail: tmasuda@iser osaka-u ac jo; Phone: +81-6-6879-8581; ORoID:

0000-0001-9639-2480
Acknowledgments: The authors are rateful for the financial suooort received from the JSPS Grantin uid for xoloratory Research (26590029), Grant-in-uid for Scientific Research (B) (26285047),
and Grant-in-uid for Scientific Research (S) (15H05728) We thank the discussant Kan Takeuchi andoarticioants at the Jaoanese conomic ussociation Meetin as well as workshoo oarticioants at Kansai
University
October 15, 20191

Abstract
We emoloyed a ame-theoretic framework to formulate and analyze a number of tax audit rules,
esoecially the lowest income reoorter audited rule We exolicitly considered the auditor’s resource
constraint to choose one tar et from a continuous tyoe of taxoayer We then tested the theoreticaloredictions in a laboratory exoeriment, usin three audit rules: the random, cut-off, and lowest income
reoorter audited rules While the cut-off rule is known to be ootimal in theory, it has not thus far been
examined in a controlled laboratory exoerimental settin

oontrary to the theory, the lowest income

reoorter audited rule increased avera e comoliance behavior si nificantly more comoared with the
ootimal cut-off rule and, esoecially, the random rule This holds with and without controllin thesubjects’ demo raohics and attitudes re ardin tax oayment This findin is oractically imoortantbecause the tax authorities in most countries assi n hi her oriority to enhancin tax comoliance

Keywords: audit rule; tax evasion; laboratory experiment; cut-off rule; lowest income reporter audited
rule
JEL Classification: C91; C92; D81; H26

2

1. Introduction
Securinovernment tax revenues is a oersistent and fundamental lobal oroblem (Webber andWildavsky 1986) There is hi h incentive for individuals and comoanies to avoid excessive tax
oayments, which leads to tax avoidance, tax evasion, and oayment delays Results of the National
Research Pro ram—a well-known audit oro ram conducted by the U S Internal Revenue Service—estimated the tax ao (i e , tax due but not oaid in a voluntary or timely manner) as $450 billion in
2006; this amount reoresented aooroximately 3 2% of the nominal ross domestic oroduct for that year
(ulm et al 2015) ulthou h analyses of the tax aos in other countries are limited for several reasons(e , resource constraints and non-oublication of survey results), the aos are estimated or soeculated
to be considerable (see Slemrod 2007) Government reoorts, at least in the U S and Jaoan (e , U S
House of Reoresentatives’ oommittee on Ways and Means, 2019, orominently ar ue that this is due
to a decrease in human resources in audit institutes (Hi o, 2018) Thus, research on oolicy devices toenhance tax comoliance has become increasin ly si nificant
u basic theoretical model of tax evasion is oresented by ullin ham and Sandmo (1972) andYitzhaki (1974) These orior studies assume that a taxoayer chooses the extent of tax evasion by
comoarin the exoected benefit from evasion with the exoected cost These studies imoly that the audit
orobability, tax rate, and oenalty rate affect tax comoliance These findin s are suooorted by the resultsof both emoirical research (Kleven et al 2011; Slemrod et al 2001) and laboratory exoeriments(oollins and Plumlee 1991; Gërxhani and Schram 2006; for a more recent survey, see Malezieux,
2018) ulthou h tax comoliance could be imoroved by increasin the audit orobability and oenalty
rate, most overnments face severe bud et restrictions related to auditin , and chan in the oenalty
rate would be controversial Thus, an audit rule whose introduction incurred little additional cost anddid not chan e the oenalty rate would be worth considerin for actual use
The above discussion motivates us to analyze three rule-based audit rules with exolicit use ofresource constraints Under the first and most often used audit rule, a taxoayer is chosen randomly andinsoected irresoective of his/her reoorted income This is the most common rule used in exoeriments
to examine the canonical tax evasion model of ullin ham and Sandmo (1972) and Yitzhaki (1974)
and to measure the behavioral asoects of tax evasion (Kastlun er et al 2009) 1
The second audit rule examined herein is the cut-off rule under which the orobability of
insoection is hi h for taxoayers whose reoorted income is below a certain threshold; by contrast,
taxoayers whose reoorted income is above the threshold are never insoected Based on their workinexoerience with the federal tax authority and several state tax authorities in the U S , undreoni et al(1998) reoort that “many tax a encies aooarently do establish cut-off ooints and focus their audit
resources on returns fallin below the cut-offs” (o 832) Based on the orincioal–a ent theory,
Rein anum and Wilde (1986) and Sánchez and Sobel (1993) show that the cut-off rule enhances tax
1

Fatas et al (2015) consider redistribution of oenalty revenue, usin oublic oods ame framework3

comoliance and increases net tax revenue ulthou h ulm et al (1993) examine the usefulness of thisrule exoerimentally, their comoarison of several audit rules is not fair in the sense that the audit
resources are not keot fixed amon the rules In addition, no study has thus far investi ated the cut-off
rule based on the ootimal audit orobability and threshold, and thus research on the cut-off rule is still
limitedFinally, under the third rule, lower reoorted incomes have hi her orobability of bein audited
Given the restriction that an auditor can insoect only one reoorted income, this rule becomes the lowest
income reoorter audited (LIRu) rule, wherein, amon a cate ory of similar taxoayers, the auditor
investi ates the taxoayer whose reoorted income is the lowest 2 oollins and Plumlee (1991) andooricelli et al (2010) also exoerimentally examine the LIRu rule in an incomolete information settinwith multiole tyoes of taxoayer incomes; however, these studies do not theoretically investi ate the
LIRu rule
We comoare these three audit rules theoretically and exoerimentally us noted above, due to its
imoortance, we exolicitly consider the auditor’s resource constraint, due to which the auditor chooses
one tar et from amon four taxoayers (in exoectation) The oresented theoretical analysis shows thatthe cut-off rule with an ootimal choice of threshold dominates the other rules in terms of increasin
the comoliance rate (ratio of reoorted income to true income), minimizin the evaded income, andmaximizin tax revenue The LIRu rule yields a hi her comoliance rate and less evaded income than
the random rule does; however, the random rule yields hi her oenalties and total revenue (sum of the
tax revenue and oenalty revenue) than the LIRu rule does
We conduct a laboratory exoeriment to test how much the above audit rules enhance comoliancebehavior, includin one sub-ootimal version of the cut off rule We fix a basic tax rate and oenalty rate,with a between-subject desi n wherein one subject can oarticioate in only one audit rule To create a
one-shot, incomolete information environment, in each oeriod, a rouo of four is newly formed andeach subject orivately receives his/her income drawn indeoendently from the uniform distribution The
re ressions analysis shows that the LIRu rule si nificantly increases the comoliance rate comoaredwith the ootimal cut-off and random rules do Nevertheless, there is no si nificant difference in the
comoliance rate between the LIRu and subootimal cut-off rules The income quartile affects
comoliance behavior in accordance with oredictions
We contribute to the extant literature in three ways First, we comoare the rules in the sameenvironment and under the same resource constraint, while orior studies tyoically investi ate theserules one by one We comoare them in the settin of an incomolete information ame with a continuous

One justification for imolementin the LIRu rule is that in the U S , the Internal Revenue Service calculates a
discriminant inventory function score for each return, on which it determines the tax returns to audit ulm and McKee(2004) model an audit rule based on the score, such that the most downward deviatin income from the avera e of thereoorted incomes is insoected (i e , the LIRu rule) Soecifically, they analyze the LIRu rule theoretically andexoerimentally in a comolete information settin with identical taxoayer incomes2

4

tyoe of taxoayer under a resource constraint wherein the exoected number of audited taxoayers inequilibrium is one across the rules Second, we find that the LIRu rule can emoirically outoerform thecut off rule with ootimal oarameters of audit orobability and threshold Third, we derive theequilibrium under the LIRu rule in an incomolete information ame with n olayers for the first timeto the best of our knowled e
The remainder of this oaoer is or anized as follows Section 2 oresents the basic theory of tax
evasion decision makin ; subsequently, we oresent our theoretical oredictions related to the three tax
audit rules Section 3 describes our exoerimental desi n and orocedure Section 4 reoorts the resultsof our exoeriment Section 5 concludes
2. Theory of tax audit rules
2.1. Basic modelThis section summarizes the canonical model of taxoayer decision makin orooosed by ullin ham
and Sandmo (1972) and Yitzhaki (1974) u taxoayer decides whether and to what extent to evade taxes
in the same way that an individual would wei h a risky amblin decision The taxoayer (an individual
or a firm) has a true taxable income of Y , where Y  0 ; the true taxable income is orivate
information Let t be the basic tax rate The taxoayer oays tY as tax if (s)he reoorts his/her true
income However, if the income is under-reoorted, the taxoayer should oay tR, where R reoresents theunder-reoorted income ( R  Y ), and Y  R reoresents the amount of evaded income 3 However,detailed auditin is randomly executed at orobability p, where tax evasion is detected In our model,
tax evasion is revealed if the tax authority insoects the under-reoortin taxoayer In the event of an
insoection, the individual must oay tq (Y  R ), as a oenalty for the tax evasion, where q reoresents
the oenalty rate for the ille al activity (q  1).
The exoected utility for an individual reoortin his/her income as R (where 0  R  Y ) isEU  (1  p)U (Y  tR )  pU (Y  tR  tq (Y  R )) , where U is a utility function with U (Y )  0 andU (Y )  0 for any Y  0 By differentiatin EU by 0  R  Y and evaluatin it at R  Y , we obtain
EU|R Y  t  pq  1 U   1  t  Y  . Thus, tax evasion occurs when pq  1 or p  1 / q.
Rulthou h the evasion decision deoends on neither basic tax rate t nor true income Y, the extent
of evasion may deoend on these variables 4 However, if we assume risk neutrality, the taxoayer fully

Other tyoes of reoortin decisions exist, such as the non-filin and late oayment of taxes owed However, accordinto the 2001 Internal Revenue Service estimate of the tax ao, under-reoortin reoresents aooroximately 82% of the ao,
and non-filin and late oayment reoresent 8% and 10% of the ao, resoectively (see Slemrod 2007) Thus, underreoortin is the major source of the tax ao
4 Yitzhaki (1974) shows that under the assumotion of decreasin absolute risk aversion, the extent of evasion decreases
as the basic tax rate increases, and the extent of evasion increases as income increases
35

evades his/her tax liability (i e , reoorts zero income) whenever (s)he decides to evade taxes In thediscussion that follows, we assume risk neutrality for taxoayers 5
The canonical model does not address how the detection orobability (p) is determined ulm and
McKee (2004) reoort that p is determined from the strate ic interdeoendence between auditors andtaxoayers Thus, the detection orobability vary with reoorted income (Rein anum and Wilde 1986;
Sánchez and Sobel 1993), oast cheatin or auditin (Friesen 2003), and relative oositions of thereoorted income (ulm and McKee 2004; oollins and Plumlee 1991) To ensure strate ic
interdeoendence amon taxoayers, we assume that there are n taxoayers In Sections 2 2–2 4, we
describe the three audit rules and theoretically show how taxoayers’ decisions differ
To imorove our understandin , we exolain the three audit rules by usin the oarameters in our
exoeriment: n  4 , t  0.2 , and q  3 To comoare these audit rules in a fair manner, we orooose
the condition that the (exoected) number of investi ated taxoayers in equilibrium is one because of
the resource constraints of the audit authority We assume that the true income of each olayer is an
i i d draw from uniform distribution of [0, 1000] For each taxoayer i ( i  {1, 2, 3, 4} ), Yi

and Ridenote i’s true income and reoorted income, resoectively
2.2. Random rule
The auditor chooses one of the four taxoayers at random, irresoective of their reoorted incomes The
chosen taxoayer is insoected In our settin , the orobability of detection (p) is 1 / n  1 / 4 , and theoenalty rate q is 3 Thus, p  1 / q holds true, indicatin that the ootimal strate y for each taxoayer
is to reoort zero income
2.3. Cut-off rule
The detection orobability varies accordin to the reoorted income In oarticular, we choose a cut-off
rule, wherein reoorted income of less than 750 is insoected with orobability 1/3 and reoorted income
above or equal to 750 is never insoected uccordin to our selected oarameters, the detection
orobability of 1/3 is the lowest orobability for a taxoayer to reoort his/her income truthfully The ran eof [0, 750] is determined by the restriction that the exoected number of insoections is one out of four
taxoayers ((1 / 3)  (750 / 1000)  1 / 4). un ootimal strate y for a taxoayer under the cut-off rule isto reoort his/her income truthfully when his/her income is below or equal to 750, and reoort thethreshold when his/her income is above 750 Thus, a taxoayer with hi her income evades the tax
burden It is theoretically known that the cut-off rule discussed here is a tax-revenue maximizin audit
rule (Sánchez and Sobel 1993); hence, we denote it as out-off O
Next, we consider the subootimal cut-off rule (denoted as out-off S), which ives oarticioants a
5

See undreoni et al (1998) for a survey of theory6sufficient incentive to reoort truthfully In out-off S, reoorted income of less than 500 is insoected withorobability 1/2, and that above or equal to 500 is never insoected
2.4. LIRA rule
The auditor investi ates the lowest income amon

the four reoorted incomes Thus, strate ic

interdeoendence exists amon the taxoayers Under the LIRu rule, the lower is the reoorted income,the more likely it is that the income will be insoected Therefore, the ootimal strate y for taxoayers is
to reoort their income truthfully if their true income is below some critical value c* and to cheatotherwise Intuitively, critical value c* is calculated as follows 6 ussume that the four olayers follow
the same strate y; thus, they reoort the true income when their income is below c* oonsider a taxoayer
whose true income is c  c * . The orobability of detection when (s)he reoorts c is (1  c / 1000)3 ,and this orobability decreases in c u detection orobability reater than or equal to 1/3 (= 1/q) is needed
to truthfully reoort income (see Section 2 1) Since income c* is the mar inal value between reoortin
the true income and cheatin , (1  c * /1000)3 must be equal to 1 / q  1 / 3. Thus, we havec*  1000  (1  (1 / q)1/3 )  306. In fact, under the LIRu rule, in the equilibrium strate y of each i, aoarticioant truthfully reoorts his/her income ( Ri  Yi ) if Yi  c * , while (s)he cheats by e(Yi )( Ri  Yi  e(Yi ) ) if Yi  c * , where e reoresents the extent of cheatin with e(Yi )  0 , e(Yi )  0 for
Yi  c * , and e (Yi )  0 for Yi  c * .

2.5. Summary of predictions
In summary, the cut-off rule dominates the other rules, and the LIRu rule dominates the random rulein terms of comoliance rate 7 Further, the oredicted strate ies under the LIRu rule and the two cut-off
rules have kinks at Y=306 6, 500 and 750, resoectively 8 We mainly focus on comoliance rater  R / Y , as a measure for the de ree of truthful reoortin For examole, if a olayer with income of
500 reoorts 220, the corresoondin comoliance rate is r  220 / 500  44.0% If the comoliance rateis sufficiently close to one (e , 90%), then the tax is almost correctly levied, and hence such an audit
rule works 9
3. Experimental design
ach of the four treatments (Random, out-off O, out-off S, and LIRu) has two sessions with rouos
of four We conducted all sessions at Kochi University of Technolo y, Jaoan, in July 2014 and uoril

6

See lectronic Suoolementary for the derivation of a symmetric Bayesian Nash equilibrium
See lectronic Suoolementary for the fi ure of oredicted comoliance rate
8 Incorooratin risk aversion into our model does not chan e the rankin of the comoliance rate
9 See lectronic Suoolementary for the revenue rankin
7

7

2015

ach session lasted for 90 minutes We used the exoerimental software z-Tree (Fischbacher

2007) We recruited 140 student subjects throu h camous-wide advertisements No subject
oarticioated in more than one session None of them had orior exoerience of a similar tyoe of
exoeriment Subjects were seated at individually oartitioned comouter terminals assi ned randomly
We did not allow any communication amon subjects
ach subject received a cooy of the instructions (see lectronic Suoolementary) udditionally, anexoerimenter read the instructions aloud Subsequently, subjects answered a quiz about the audit rule
Then, an exoerimenter oublicly announced the answers of the quiz Subjects then oroceeded to 20
oayment oeriods In each session, we emoloyed the stran er-matchin orotocol so that each rouo ineach oeriod included four subjects Subjects were informed that they would be randomly re-matchedin every oeriod
In each oeriod, once a rouo was formed, each subject faced the reoortin screen On the reoortin
screen, (s)he orivately received and confirmed his/her income, which was drawn indeoendently fromthe uniform distribution of [0, 1000] (JPY), with an increment of 10 Note that income was newly
drawn by oeriod, leadin to a one-shot incomolete information environment

very subject could

confirm t = 0 2 and q = 3 Given this information, the subject determined how much income to reoort,and (s)he inout a number between 0 and his/her income, in increments of 10 Once every subject inout
the reoorted income and clicked the OK button, the subjects oroceeded to the results screen In every
oeriod after the second oeriod, the history box aooeared
ufter oarticioatin in 20 oayment oeriods, the subjects comoleted two questionnaires The firstquestionnaire asked about their attitude toward tax oayment, followin Gërxhani (2004) and Lefebvre
et al (2015) Second, all oarticioants comoleted the questionnaire to measure the risk attitudes; thequestionnaire consisted of 4 sets of 11 oairs of lotteries and certain amount of money ufter thequestionnaires were comoleted, the subjects were immediately oaid in cash, orivately

ach subject

was oaid a oarticioation fee of 800 yen (aooroximately $7 USD) olus the total earnin s over the threeoeriods chosen randomly The avera e reward oer subject was aooroximately $19 USD
4. Experimental results
We clarify the imoact of each audit rule on the comoliance rate The total number of observations
were 2,800 (140 subjects  20 times) umon these, 12 subjects (240 observations) were excluded
from the analyses, since they did not reoly to the questions after the exoeriment Further, fiveobservations for which we were unable to calculate the decision time and nine observations for which
the comoliance rate could be defined due to zero income were excluded Thus, 2,546 observations
were used as the samole in our statistical analysis
Table 1 summarizes the main indeoendent variables in which we are interested to exolain the
comoliance rate First, we used each audit rule dummy Second, we included each income quartile8

dummyTable 1. Variable definitions
Variable

Definition

IncomeQ1 (reference) = 1 if 10≦Income≦250, and 0 otherwise
IncomeQ2= 1 if 260≦Income≦500, and 0 otherwise

IncomeQ3= 1 if 510≦Income≦750, and 0 otherwise

IncomeQ4= 1 if 760≦Income≦1,000, and 0 otherwise

LIRA (reference)= 1 if an audit rule is LIRA, and 0 otherwise

Random= 1 if an audit rule is Random, and 0 otherwise

Cut-Off O= 1 if an audit rule is Cut-Off O, and 0 otherwise

Cut-Off S= 1 if an audit rule is Cut-Off S, and 0 otherwise

Before oroceedin to the re ression, we illustrate the whole tendency of the comoliance rate
Table 2 summarizes the comoliance rate avera ed across subjects by the audit rule Fi ure 1 illustrates
the comoliance rate avera ed across subjects, by both the audit rule and income quartile The verticalbar indicates the 95% confidence interval u first look tells us that neither the LIRu nor out-Off rules
sufficiently induce a fully sincere reoort, but all of LIRu, out-off O, and out-off S outoerformed
Random, in line with theory Moreover, LIRu and out-off S outoerform out-off O, esoecially in Q1
and Q2, in contrast with theory
Table 2. Observed overall avera e comoliance rates (%)
LIRA
67.50
N=695

Cut-Off O
59.73
N=674

Cut-Off S
65.92
N=760

9

Random50.47
N=417

Figure 1. Observed avera e comoliance rates (%)
Table 3 shows the re ression results We first look at Panels u and B The deoendent variable iseach comoliance rate, rit, where i is the subject ID and t is oeriod The standard error is adjusted for
128 clusters amon the subjects The main result in Panel u is that Random and out-off O are
ne atively correlated with the comoliance rate (Random: z = -3 13, p =0 002; out-off O: z = -1 67,
p=0 095) It is noteworthy that LIRu induces a reater increase in the comoliance rate comoared with
out-off O and Random, in contrast with theory (See lectronic Suoolementary for the questionnaireand demo raohic information variables)
The Panel B re ression includes the interaction terms between audit rule and income quartile, toobtain further insi hts on how LIRu outoerforms the other two audit rules Post-estimation tests show
the followin

In Q1 and Q2, LIRu oromotes tax comoliance more than out-Off O and Random, andin Q3 and Q4, LIRu has a total effect similar to out-Off O The results are intuitive: LIRu subjects
with low income oerceive that they are more likely to be audited, while LIRu subjects with hi hincome are temoted to conceal their income more, exoectin that other members are more likely to beaudited out-off S outoerforms LIRu in Q2 and Q3 10
We note two additional results First, the rankin of revenue includin oenalty (Panels o and Dwith DV=revenue for each reoort) is not so clear and deoends on income quartile LIRu earns
si nificantly more (reso , less) revenue than Random in Q1 (reso , Q2 and Q3), while it earns similar
revenue as the out-offs exceot for Q4 Second, our results on the questionnaire and demo raohic
10

See lectronic Suoolementary for details

10variables—that is, individual a

ressiveness for tax evasion si nificantly decreases comoliance rate—

corroborate the results in orior literature: (Kirchler 2007; ooricelli et al 2010) Subjects try to evademore after bein audited (Kastlun er et al 2009), and male subjects tend to evade taxes (Lefebvre etal 2015) 11
5. Conclusion
We emoloyed a ame-theoretic framework to analyze three audit rules, namely, the random, cut-off,and LIRu rules, and we tested the theoretical oredictions in a laboratory exoeriment The contributionsof this study can be stated as follows First, we comoared the three reoresentative audit rules usin an
incomolete information ame, iven the auditor’s resource constraint Second, we showed that boththe LIRu rule and cut-off rules actually work in a laboratory settin
oerform better than random auditin

These soohisticated audit rules

Third, we derived an equilibrium strate y under the LIRu rule

for the first time to the best of our knowled e
The observed hi her comoliance rate in LIRu than the ootimal cut-off rule has some oracticalimoortance, because tax authorities in most countries assi n hi her oriority to the enhancement of tax
comoliance Determinin the ootimal oarameter for a real-world oooulation could be difficult By
contrast, the LIRu rule works without information on the other oarameters, because it uses the orofile
of reoorted incomes to determine whom to audit
Finally, we discuss oossible future research directions In this study, the auditor commits the rule
to choose the taxoayer unother interestin exoerimental settin would be the human audit condition
The auditor subject freely chooses some of the taxoayers as the tar et after seein the reoorts andincurrin costs for additional audits Then, an increase in tax comoliance may be driven by taxoayer
subjects’ overestimation of the orobability of bein audited under ambi uity, as Tan and Yim (2016)
observed

11

See lectronic Suoolementary for details

11Table 3. Determinants of the comoliance rate and tax revenue
A: DV = Compliance Rate
Variables
Constant

Coef.

Std.Err.

B: DV = Compliance Ratez60.50312.752

4.74

Random-18.024

5.759

Cut-Off O-8.717

5.215

3.13
1.67

Cut-Off S

2.436

3.826

0.64

Coef.
***

Std.Err.

C: DV = Tax Revenuez68.39312.816

5.34-29.111

7.854

-3.71

-22.694

6.208-7.819

IncomeQ2

Coef.
***

Std.Err.

D: DV = Tax Revenue
z
***

Coef.

Std.Err.

z

33.09113.7482.41

97.561

17.163

5.68

3.068

5.195

0.59

-15.512

4.952

-3.13

-3.66

7.231

5.221

-6.240

5.766

-1.08

5.808

-1.35

-5.659

5.226

1.38
1.08

-6.814

4.372

-1.56

-7 047

3 263

-2 16

48.661

4.536

10.73

IncomeQ3-14 218

3 945

-3 60

64.289

4.721

11.24

IncomeQ4-17 162

4 331

-3 96

109.457

8.305

13.18

Random*IncomeQ2

5.688

6.534

0.87

-3.277

8.650

-0.38

39.40510.7653.66

35.70314.341

2.49**

LIRA (reference)
***

***

*

**

***

IncomeQ1 (reference)

Random*IncomeQ3

20.704

8.239

2.51

Random*IncomeQ4

16.360

8.518

1.92

Cut-Off O*IncomeQ2

9.881

5.714

1.73

Cut-Off O*IncomeQ3

17.146

5.809

2.95

Cut-Off O*IncomeQ4

20.882

5.731

3.64

Cut-Off S*IncomeQ2

16.536

5.174

3.20

Cut-Off S*IncomeQ3

18.192

6.213

2.93

Cut-Off S*IncomeQ4

5.064

6.900

0.73

**

***

***

***

***

***

**
*
*
**
***
***
**

9.390

10.0060.94

13.36910.471

1.28

26.973

9.205

2.93

10.507

7.400

1.42

23.238

8.338

2.79

-14.865

11.531-1.29

Demographics

Included

Included

Included

IncludedTax attitude

Included

Included

Included

Included

Risk attitude
Number ofobservations

Included

Included

Included

Included

2546

2546

2546

2546

wald chi2

71.32

208.9728.88

1841.23

Prob > chi2

0.000

0.000

0.006

0.000

R2
0.101
Note: * p<0 10, ***p<0 05, and ***p<0 01

0.132

0.008

0.243

12

***
**

**

**

Conflict of Interest
The authors declare that they have no conflict of interest
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