U enda, Julio; Koshele a, Olga
A icle
Randomized ax deadlines can help economy
Asian Jou nal o Economics and Banking (AJEB)
P o ided in Coope a ion wi h:
Ho Chi Minh Uni e si y o Banking (HUB), Ho Chi Minh Ci y
Sugges ed Ci a ion: U enda, Julio; Koshele a, Olga (2024) : Randomized ax deadlines can help
economy, Asian Jou nal o Economics and Banking (AJEB), ISSN 2633-7991, Eme ald, Leeds, Vol. 8,
Iss. 1, pp. 19-25,
h ps://doi.o g/10.1108/AJEB-05-2021-0055
This Ve sion is a ailable a :
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Randomized ax deadlines can
help economy
Julio U enda
The Uni e si y o Texas a El Paso, El Paso, Texas, USA, and
Olga Koshele a
Depa men o Teache Educa ion, The Uni e si y o Texas a El Paso,
El Paso, Texas, USA
Abs ac
Pu pose –While he main pu pose o epo ing –e.g. epo ing o axes –is o gauge he economic s a e o a
company, he ac ha epo ing is done a p e-de e mined da es dis o s he epo ing esul s. Fo example, o
c ea e a la ge imp ession o hei p oduc i i y, companies i e empo a y wo ke s be o e he epo ing da e
and e-hi e hen igh away. The pu pose o his s udy is o decide how o a oid such dis o ion.
Design/me hodology/app oach –This s udy aims o come up wi h a solu ion which is applicable o all
possible easonable op imali y c i e ia. Thus, a gene al o malism o desc ibing and analyzing all such c i e ia
is used.
Findings –This s udy shows ha mos dis o ion p oblems will disappea i he ixed p e-de e mined
epo ing da es a e eplaced wi h indi idualized andom epo ing da es. This s udy also shows ha o all
easonable op imali y c i e ia, he op imal way o assign epo ing da es is o do i uni o mly.
Resea ch limi a ions/implica ions –This s udy shows ha o all easonable op imali y c i e ia, he
op imal way o assign epo ing da es is o do i uni o mly.
P ac ical implica ions –I is ound ha he indi idualized andom ax epo ing da es would be bene icial
o economy.
Social implica ions –I is ound ha he indi idualized andom ax epo ing da es would be bene icial o
socie y as a whole.
O iginali y/ alue –This s udy p oposes a new idea o eplacing he ixed p e-de e mining epo ing da es
wi h andomized ones. On he in o mal le el, his idea may ha e been p oposed ea lie , bu wha is comple ely
new is ou analysis o which andomiza ion o epo ing da es is he bes o economy: i u ns ou ha unde all
easonable op imali y c i e ia, uni o m andomiza ion wo ks he bes .
Keywo ds Tax epo ing, Dis up ion caused by ixed epo ing da es, Randomized epo ing da es, Op imal
dis ibu ion o epo ing da es
Pape ype Resea ch pape
1. Fo mula ion o he p oblem
1.1 Need o some go e nmen egula ions and go e nmen con ol
Un il he 20 h cen u y, he e was no much go e nmen in e en ion in he economy, he
belie was ha he “in isible hand”o he ma ke s –using he amous exp ession by Adam
Smi h –would magically b ing economic g ow h and economic p ospe i y. F om his
iewpoin , he smalle he go e nmen ole, he be e : medicine, educa ion, e c., a e be e in
p i a e hands. Possibly only he a my needs o be con olled by he s a e –bu he supply o
he a my should be in p i a e hands. The esul ing elaxa ion o go e nmen in e en ion led
o economic g ow h –bu also deep c ises.
Randomized
ax deadlines
19
© Julio U enda and Olga Koshele a. Published in Asian Jou nal o Economics and Banking. Published by
Eme ald Publishing Limi ed. This a icle is published unde he C ea i e Commons A ibu ion (CC BY
4.0) licence. Anyone may ep oduce, dis ibu e, ansla e and c ea e de i a i e wo ks o his a icle ( o
bo h comme cial and non-comme cial pu poses), subjec o ull a ibu ion o he o iginal publica ion
and au ho s. The ull e ms o his licence may be seen a h p://c ea i ecommons.o g/licences/by/4.0/
legalcode
The au ho s a e hank ul o Nguyen Ngoc Thach and Hung T. Nguyen o hei encou agemen and
ad ice and o he anonymous e e ees o aluable sugges ions.
The cu en issue and ull ex a chi e o his jou nal is a ailable on Eme ald Insigh a :
h ps://www.eme ald.com/insigh /2615-9821.h m
Recei ed 5 May 2021
Re ised 8 June 2021
7 Ap il 2022
Accep ed 12 May 2022
Asian Jou nal o Economics and
Banking
Vol. 8 No. 1, 2024
pp. 19-25
Eme ald Publishing Limi ed
e-ISSN: 2633-7991
p-ISSN: 2615-9821
DOI 10.1108/AJEB-05-2021-0055
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The las such ca as ophic c isis occu ed in he la e 1920–1930s. This c isis was he las
s aw ha con inced scep ics all o e he wo ld ha some go e nmen in e en ion in he
economy is necessa y. O cou se, many coun ies o e did i and in oduced oo much
go e nmen con ol –which also had a nega i e e ec on economy, bu he ac ha
nowadays, pandemic no wi hs anding, he economy is imp o ing all o e he wo ld ha e
shown ha a co ec comp omise be ween oo li le and oo much go e nmen in e en ion
has been ound.
This in e en ion occu s on di e en le els: on he le el o he s a e banks ha egula e
in e es a es and hus egula e he economy and on he le el o go e nmen spending. The
go e nmen collec s axes and spends hem on educa ion, esea ch and de elopmen –wi h
he ul ima e goal o help he economy –and on social wel a e.
1.2 How axes and go e nmen egula ions a e de e mined now
In mos coun ies, axes a e collec ed on a yea ly o qua e ly basis: he amoun o axes
depends on he inancial si ua ion by a ce ain da e. Simila ly, he go e nmen egula ions
depend on he s a e o he economy by a ce ain da e –e.g. on he le el o economic g ow h,
unemploymen , in la ion, e c. a he end o each qua e .
1.3 Why his is a p oblem
One o he main pu poses o inancial epo ing is o p o ide a clea pic u e o he s a e o each
company (and o he economy as a whole). In pa icula , one o he main pu poses o ax-
ela ed epo ing is o make su e ha he company pays i s ai sha e o axes. Howe e , he
e y ac ha his is gauged by he s a e o he company a a ce ain da e dis o s he pic u e.
Fo example, he company’s p oduc i i y –one o he impo an cha ac e is ics
de e mining he company’s s ock p ice –is ob ained, c udely speaking, by di iding he
p o i by he numbe o wo ke s. A i s glance, his is exac ly wha p oduc i i y is, bu
he p oblem is ha , based on he way epo ing is se , he p o i is he whole p o i du ing he
whole epo ing pe iod, while he numbe o wo ke s is he numbe o wo ke s a
he epo ing da e. So, o c ea e a be e imp ession o p oduc i i y, a company may (and
some do) i e empo a y wo ke s jus be o e he epo ing da e and e-hi e hem once he da e
has passed.
The e a e many o he simila well-known dis o ions. I e en a ec s p i a e li e. Fo
example, in he USA, in many cases, i is be e ax-wise o ge ma ied in ea ly Janua y han
in Decembe , e c.
The go e nmen s a e e y amilia wi h hese p oblems, hey a e always upda ing he ax
ules –bu s ill, some new loopholes a e ound again and again; see, e.g. (G i i hs, 1992;
Oli e as and Ama , 2003;Ama and Gow ho pe, 2004;Mu o d and Comiskey, 2005;de la
To e, 2008;Jones, 2011).
1.4 Wha we do in his pape
In his pape , we use he gene al ideas o decision heo y –see (e.g. Fishbu n, 1969,1988;Luce
and Rai a, 1989;Rai a, 1997;Nguyen e al., 2009,2012;K eino ich, 2014)– o show ha o
a oid he abo e p oblems, he e is a s aigh o wa d –bu somewha adical –solu ion: o
eplace he ixed epo ing da es wi h andomized da es. We also show ha he op imal way
o a ange hese andomized epo ing da es is o use he uni o m andomiza ion.
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2. Main idea
2.1 Doping es ing o a hle es: si ua ion wi h simila possible p oblems
In p o essional spo s, doping is a big p oblem, when p ohibi ed chemical subs ances a e
used o boos he a hle es’pe o mance. To p e en his om happening, a hle es a e
pe iodically es ed o he p esence o di e en possible p ohibi ed subs ances.
I is well known ha in such a si ua ion, es s pe o med a known da es do no make much
sense: he a hle e in ending o chea will simply s op using he illegal d ug sho ly be o e he
es and hen esume using i immedia ely a e .
The known solu ion o his p oblem is o ha e es s a andom imes.
2.2 Tes ing a andom imes is exac ly wha we p opose o economic epo ing
Tes ing a andom imes is exac ly wha we p opose o sol e he abo e economic p oblems. I
he company does no know a wha day i will be equi ed o epo i s numbe o wo ke s, i
makes no sense o dis o he p oduc i i y s a is ics by i ing people only o immedia ely e-
hi e hem. I he ax deadline is andomly de e mined a an unp edic able ime, he e is no ax
ad an age in delaying ma iage.
Wi h his change, he epo ing will mo e adequa ely e lec he cu en s a e o he
economy.
2.3 Addi ional ad an age o he p oposed scheme
A p esen , when e e yone has he same deadline o epo ing axes, accoun an s who help
wi h his epo ing a e o e wo ked igh be o e he due da e –and unde -wo ked a all o he
imes. Simila ly, he ax se ices a e o e whelmed immedia ely a e he ax deadline –which
c ea es delays o axpaye s who o e -paid o ge hei money back.
I we make ax da es indi idually andom, hen bo h he accoun an s who help he
axpaye s and he go e nmen agency ha p ocesses ax e u ns will ha e hei wo k sp ead
mo e equally, hus d as ically dec easing delays.
3. Wha is he bes way o implemen ing his idea
3.1 Towa d a p ecise o mula ion o he p oblem
The ac ha he epo ing imes a e andom means ha we canno p e-de e mine hese imes,
all we can do is de e mine he p obabili y ha he andomized epo ing ime will happen a
di e en ime in e als. One way o desc ibe his is o desc ibe he densi y ( ) desc ibing
epo ing imes, i.e. he expec ed numbe o epo ing imes pe gi en ime in e al –so ha
o each ime in e al ½ ; , he mean alue E½N ð½ ; Þ o he numbe N ð½ ; Þ o
epo ing imes wi hin his ime in e al is equal o
EN ; ¼Z
ð Þd :
F om his iewpoin , he p oblem is –wha is he op imal densi y unc ion ( )?
3.2 Cla i ica ion
Please no e ha ( )isdi e en om he p obabili y densi y unc ion; e.g.:
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(1) while o a one-yea pe iod, he expec ed numbe o epo ing imes is 1:
EN ; ¼Z
ð Þd ¼1;
(2) o he wo-yea pe iod, he o e all expec ed numbe o epo ing imes is 2:
EN ; ¼Z
ð Þd ¼2;e c:
3.3 Wha do we mean by op imal? P oblems wi h he adi ional app oach o desc ibing
op imali y
In gene al, ou o se e al al e na i es, we need o selec he op imal one. In ou case,
al e na i es a e densi y unc ions, so ou goal is o selec he op imal densi y unc ion ( ).
The usual way o desc ibe wha is op imal is o selec an objec i e unc ion and o pick up
an al e na i e o which he alue o his objec i e unc ion is he la ges (o , i we a e
minimizing, he smalles ). The e a e wo p oblems wi h his usual app oach.
The i s p oblem is ha o en, i is no su icien o desc ibe a single objec i e unc ion. Le
us gi e an economy- ela ed example. Fo a company, a na u al objec i e unc ion is he
o e all expec ed p o i – aking in o accoun u u e p o i s (wi h app op ia e discoun s).
Howe e , o en, he e a e se e al di e en al e na i es wi h he same expec ed p o i . In his
case, a easonable idea is o use his non-uniqueness o selec , among he bes -p o i
al e na i es, he one o which, e.g. he isk is he smalles . I he e a e s ill se e al al e na i es
wi h he same alues o expec ed p o i and he same alue o expec ed isk, we can use he
emaining non-uniqueness o selec he al e na i e o which he e ec on he en i onmen
will be he smalles –o he one ha enables he company o p ese e mos o i s wo k o ce. In
all hese cases, he c i e ion by which he company selec s an al e na i e is mo e complica ed
han using a single objec i e unc ion.
The second p oblem wi h he usual app oach is ha o di e en objec i e unc ions, we
ge , in gene al, di e en op imal solu ions. So, ins ead o ying o pick a single objec i e
unc ion, i is desi able o come up wi h a way o ind an al e na i e ha is op imal wi h
espec o all easonable objec i e unc ions.
Le us see how we can o e come bo h p oblems.
3.4 Commen : wi hou losing gene ali y, we can conside only maximizing objec i e
unc ions
In some cases, we a e looking o objec i e unc ions ha maximize. In o he cases, we a e
looking o al e na i es ha minimize he gi en objec i e unc ion F(x)–e.g. we wan o
minimize he isk. This can be educed o maximiza ion i ins ead o he o iginal objec i e
unc ion F(x), we conside a new objec i e unc ion FnewðxÞ¼
de −FðxÞ. Clea ly, maximizing
F
new
(x)5F(x) is equi alen o minimizing F(x).
So, e e y minimiza ion p oblem can be easily e o mula ed as a maximiza ion p oblem. Thus,
wi hou losing gene ali y, we can es ic ou sel es o he case o maximizing objec i e unc ions.
3.5 Towa d a gene al desc ip ion o op imali y
In he usual desc ip ion o op imali y, o maximizing objec i e unc ions, we selec an
objec i e unc ion F(x), and we say ha an al e na i e ais be e han an al e na i e bi
F(a)>F(b). I F(a)5F(b), we say ha al e na i es aand ba e o he same alue wi h espec o
he gi en c i e ion. We say ha an al e na i e ais op imal i F(a)≥F(b) o all al e na i es b.
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As we ha e men ioned ea lie , i he e a e se e al op imal al e na i es, hen we can use
his non-uniqueness o op imize some o he objec i e unc ion G(x). In his case, we ha e a
mo e complica ed c i e ion o compa ing wo al e na i es:
(1) we say ha an al e na i e ais be e han an al e na i e b, i ei he F(a)>F(b), o we
ha e F(a)5F(b) and G(a)>G(b);
(2) we say ha an al e na i e ais o he same quali y as an al e na i e bwi h espec o
ou op imali y c i e ion i we ha e F(a)5F(b) and G(a)5G(b).
We say ha an al e na i e ais op imal i i is ei he be e o o he same quali y as all o he
al e na i es.
As we ha e men ioned, e en a e his e inemen , we can s ill ha e se e al op imal
al e na i es. In his case, we can use his non-uniqueness o op imize some o he objec i e
unc ion H(x). Then, we ge e en mo e complica ed ideas o which al e na i e is be e and
wha i means o an al e na i e o be op imal. How can we come up wi h a gene al de ini ion
ha co e s all such se ings?
F om he iewpoin o he decision-make , wha we eally need is a way o compa e he
al e na i es.
(1) Fo some pai s (a,b) o al e na i es, we wan o conclude ha ais be e han b; we will
deno e his by a≻b.
(2) Fo some o he pai s (a,b), we wan o conclude ha he al e na i es aand ba e o
he same quali y wi h espec o he gi en op imali y c i e ion. We will deno e his by
a∼b.
O cou se, hese conclusions mus be consis en : e.g. i ais be e han b, and bis be e han c,
hen we should be able o conclude ha ais be e han c.
Thus, i makes sense o de ine a gene al op imali y c i e ion as a pai o ela ions (≻,∼).
Once such ela ions a e gi en, we say ha an al e na i e ais op imal i o e e y o he
al e na i e b, we ha e ei he a≻bo a∼b.
I he e a e se e al op imal al e na i es, his means ha he gi en op imali y c i e ion is
no inal: we can use his non-uniqueness o op imize some o he c i e ion and hus, in e ec ,
o change he op imali y c i e ion. So, when he c i e ion is inal, he e is only one op imal
al e na i e. (O cou se, he e should be a leas one op imal al e na i e –o he wise, he
op imali y c i e ion is useless.)
So, we a i e a he ollowing de ini ion.
3.6 De ini ion 1
Le Abe a se . Elemen s o his se will be called al e na i es.Byanop imali y c i e ion,we
mean a pai (≻,∼) o bina y ela ions on he se A o which he ollowing condi ions hold o
e e y h ee al e na i es a,b, and c:
(1) i a≻band b≻c, hen a≻c;
(2) i a≻band b∼c, hen a≻c;
(3) i a∼band b≻c, hen a≻c;
(4) i a∼band b∼c, hen a∼c;
(5) a∼aand a a.
We say ha an al e na i e ais op imal i o e e y o he al e na i e b, we ha e ei he a≻bo
a∼b. We say ha he op imali y c i e ion is inal i he e exis s exac ly one op imal
al e na i e.
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3.7 F om gene al de ini ion o op imali y o ou p oblem
In ou case, al e na i es a e di e en densi y unc ions ( ). The main p oblems wi h he
adi ional de e minis ic se ing o epo ing da es a e caused by he ac ha hese da es a e
ixed o some momen s o ime, while he easonable objec i e unc ions –p ospe i y o he
coun y, p ospe i y o he company, e c. –should no depend on an a bi a ily chosen da e.
Le us desc ibe his no -depending in p ecise e ms.
Suppose ha we change he US ax epo da e om he cu en Ap il 15 o some o he
da e, e.g. o Ap il 13. This means, in e ec , ha wha co esponded o day now co esponds
o day þ
0
, whe e, in his case,
0
52 days. So, wha was p e iously he densi y unc ion ( )
becomes ( þ
0
).
This simple shi should no change he ela i e quali y o wo densi y unc ions: i we had
≻g, hen we should ha e he same ela ion o he shi ed densi y unc ions. Thus, we a i e
a he ollowing de ini ion.
3.8 De ini ion 2
Le (≻,∼) be an op imali y c i e ion on he se all non-nega i e unc ions ( ); we will call such
unc ions densi y unc ions. Fo each unc ion ( ) and o each alue
0
, we can de ine a shi ed
unc ion S 0ð Þ o which ðS 0ð ÞÞð Þ¼ ð þ 0Þ. We say ha he op imali y c i e ion is shi -
in a ian i ≻gimplies ha S 0ð Þ≻S 0ðgÞ, and ∼gimplies ha S 0ð Þ∼S 0ðgÞ.
3.9 Cla i ica ion
In his de ini ion, ≻gmeans ha he densi y unc ion is be e han he densi y unc ion g
acco ding o some op imali y c i e ion. In ou analysis, we do no speci y in wha sense i is
be e : i could e e o sho - e m bene i s o he coun y’s economy; i could e e o long-
e m bene i s; and i could e e o some o he desi able economic objec i e.
Ou main esul –desc ibed in he ollowing pa ag aph –is gene al: no ma e wha
op imali y c i e ion we use, as long as his c i e ion is shi -in a ian , he op imal densi y
unc ion is ( )5cons .
3.10 Main esul
Fo e e y shi -in a ian inal op imali y c i e ion, he op imal densi y unc ion is a cons an .
3.11 Discussion
Cons an densi y unc ion means ha he p obabili y o a epo ing da e o be wi hin any
ime pe iod is p opo ional o his ime pe iod. Fo example, o each mon h, he p obabili y
ha he epo ing da e will all in his mon h is 1/12. Fo each day o he yea , he p obabili y
ha he epo ing da e will all on his pa icula day is equal o 1/365. In his sense, he
cons an densi y unc ion means ha he epo ing da e should be selec ed andomly,
acco ding o he uni o m dis ibu ion.
Thus, o all easonable op imali y c i e ia, he uni o m dis ibu ion o eco ding da es
wo ks he bes .
In pa icula , wi h espec o ax epo ing, wha we p opose is ha each day, o each
indi idual and o each company, wi h p obabili y o 1/365, we send his pe son o company a
eques o ax epo ing. The nex day, he same p ocedu e epea s again, so o he
indi iduals and companies ge such eques s, e c.
3.12 P oo
F om he ma hema ical iewpoin , his esul is simila o se e al esul s p o en by Nguyen
and K eino ich (1997).
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Le
op
be he op imal unc ion. This means ha o e e y o he unc ion g, we ha e ei he
op
≻go
op
∼g. In pa icula , o e e y g, we ha e op ≻S− 0ðgÞo op ∼S− 0ðgÞ. Due o shi -
in a iance, his implies ha ei he S 0ð op Þ≻S 0ðS− 0ðgÞÞ ¼ go S 0ð op Þ∼g.
Since his is ue o all al e na i es g, his means ha he al e na i e S 0ð op Þis also
op imal. Howe e , since he op imali y c i e ion is inal, he e is only one op imal al e na i e.
So, we mus ha e S 0ð op Þ¼ op o all
0
. This means ha
op
( þ
0
)5
op
( ) o all and
0
.
Fo e e y wo alues and 0, by aking
0
5 0 , we conclude ha
op
( )5
op
( 0). Thus, he
unc ion
op
( ) is indeed cons an .
The p oposi ion is p o en.
Re e ences
Ama , O. and Gow ho pe, C. (2004), “C ea i e Accoun ing: na u e, incidence and e hical issues”,
Economics Wo king Pape 749, Uni e si a Pompeu Fab a, Ba celona, Depa men o
Economics and Business.
de la To e, I. (2008), C ea i e Accoun ing Exposed, Palg a e Macmillan, London.
Fishbu n, P.C. (1969), U ili y Theo y o Decision Making, John Wiley & Sons, New Yo k.
Fishbu n, P.C. (1988), Nonlinea P e e ence and U ili y Theo y, The John Hopkins P ess, Bal imo e,
Ma yland.
G i i hs, I. (1992), C ea i e Accoun ing: How o Make You P o i s wha You Wan Them o Be,
Rou ledge, London.
Jones, M.J. (Ed.), (2011), C ea i e Accoun ing, F aud and In e na ional Accoun ing Scandals, John Wiley
& Sons, Chishes e , UK.
K eino ich, V. (2014), “Decision making unde in e al unce ain y (and beyond)”, in Guo, P. and
Ped ycz, W. (Eds), Human-Cen ic Decision-Making Models o Social Sciences, Sp inge -Ve lag,
pp. 163-193.
Luce, R.D. and Rai a, R. (1989), Games and Decisions: In oduc ion and C i ical Su ey, Do e ,
New Yo k.
Mul o d, C.W. and Comiskey, E.E. (2005), The Financial Numbe s Game: De ec ing C ea i e
Accoun ing P ac ices, Wiley, New Yo k.
Nguyen, H.T. and K eino ich, V. (1997), Applica ions o Con inuous Ma hema ics o Compu e Science,
Kluwe , Do d ech .
Nguyen, H.T., Koshele a, O. and K eino ich, V. (2009), “Decision making beyond A ow’s
‘impossibili y heo em’, wi h he analysis o e ec s o collusion and mu ual a ac ion”,
In e na ional Jou nal o In elligen Sys ems, Vol. 24 No. 1, pp. 27-47.
Nguyen, H.T., K eino ich, V., Wu, B. and Xiang, G. (2012), Compu ing S a is ics unde In e al and
Fuzzy Unce ain y, Sp inge -Ve lag, Be lin, Heidelbe g.
Oli e as, E. and Ama , O. (2004), “E hics and c ea i e accoun ing: some empi ical e idence on
accoun ing o in angibles in Spain”, Economics Wo king Pape 732, Uni e si a Pompeu
Fab a, Ba celona, Depa men o Economics and Business.
Rai a, H. (1997), Decision Analysis, McG aw-Hill, Columbus, Ohio.
Co esponding au ho
Olga Koshele a can be con ac ed a : [email p o ec ed]
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