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DISCUSSION PAPER SERIES
IZA DP No. 16372
Luca Piccoli
Silvia Tiezzi
Eggs When Young, Chicken When Old.
Time Consistency and Addiction over the
Life Cycle
AUGUST 2023
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DISCUSSION PAPER SERIES
ISSN: 2365-9793
IZA DP No. 16372
Eggs When Young, Chicken When Old.
Time Consistency and Addiction over the
Life Cycle
AUGUST 2023
Luca Piccoli
University of Trento and IZA
Silvia Tiezzi
University of Siena
ABSTRACT
IZA DP No. 16372 AUGUST 2023
Eggs When Young, Chicken When Old.
Time Consistency and Addiction over the
Life Cycle
This paper tests whether young and adult smokers have different time preferences, in
particular with respect to time consistency. The recent introduction of Tobacco 21 law in
the US were in part motivated by allegedly inconsistent time preferences of the young
consumers. This research empirically tests this hypothesis using individual cigarettes
consumption longitudinal data from RLMS, estimating a quasi-hyperbolic discounting
rational addiction model for young and adult smokers separately. While our test rejects
time inconsistency in the form of present-bias for both population groups, young smokers
are found to discount future utilities much more than adults. From a life-cycle perspective,
this is still a form of time inconsistency, which provides partial empirical support to the
T21 law motivation, but also highlights how the quasi-hyperbolic discounting formulation
might not be able to properly capture long-run time preferences.
JEL Classification: C23, D03, D12
Keywords: rational addiction, smoking behavior, time inconsistency, young
vs adult smokers, GMM
Corresponding author:
Luca Piccoli
Department of Sociology and Social Research
University of Trento
Via Verdi, 26
38122 Trento
Italy
E-mail: luca.piccoli@unitn.it
1. Introduction
In the analysis of intertemporal consumption models, the assumption of exponential discounting
has been criticized as early as in the middle of the past century (Strotz, 1956). To overcome such
critics and maintain a parsimonious specification, the well known quasi-hyperbolic discounting has
been proposed, which is characterized by present-biased intertemporal preferences where all future
utilities are further discounted by a constant term (see, for instance, Pollak, 1968; Laibson,
1997). This model allows consumers to be time inconsistent, meaning that their present optimal
consumption plan will not be automatically respected in the future, because when the future
becomes the present, present-biased preferences will kick in and the previous choices will not be
optimal anymore. This happens to na¨ıve consumers that do not account for the fact that in the
future they will still be present-biased.1This is still a very relevant research topic today (see
Grossman, 2022), especially because until very recently, empirical tests of the quasi-hyperbolic
discounting have been limited to the experimental setting (see Blow et al., 2021, for an overview of
such attempts). Although the experimental method has some limits, the results generally confirm
that quasi-hyperbolic discounting tends to outperform the exponential discounting model.
An empirical test of quasi-hyperbolic discounting using commonly available survey data, such
as household expenditure surveys, has been recently introduced by Blow et al. (2021). The authors
propose a revealed preference characterization of the quasi-hyperbolic consumption model and easy
conditions for testing its validity against the standard exponential discounting assumption. They
also show that, with their data, the behavior of na¨ıve versus sophisticated consumers is empirically
indistinguishable.
The hypothesis of time consistent agents is even more critical when analyzing the consumption
of addictive goods, for which the Rational Addiction (RA henceforth) model (Becker and Mur-
phy, 1988; Becker et al., 1994) has been widely criticized. In fact, the model’s assumption of an
addicted consumer being able to stick to an optimal long run consumption plan strucks with real
life observations, such as people trying hard to stop smoking but not being able to, for instance.
Quasi-hyperbolic discounting has been first introduced in the RA framework by Gruber and K¨oszegi
(2001), where dynamic inconsistency can deliver radically di↵erent implications for government poli-
cies. In particular, while time consistency implies that the optimal tax on addictive goods should
1Sophisticated consumers that are fully aware of their present-biased preferences will face a di↵erent optimization
problem, in the form of a sequential game played against future selves.
2
depend only on the externalities imposed on the society, time inconsistency suggests a much higher
tax depending also on the “internalities” that addictive goods impose on consumers’ future selves
(Gruber and K¨oszegi, 2001; O’Donoghue and Rabin, 2006). Despite the notable relevance of such
a model, because its empirical specification was believed to be indistinguishable from that of the
general specification of the RA model,2no empirical tests for time inconsistency in consumption of
addictive goods have emerged until Piccoli and Tiezzi (2021). The authors show how the general
specification of the quasi-hyperbolic RA model allows to test for the parameter being di↵erent
from 1, and how to identify its upper bound. Using the Russian Longitudinal Monitoring Survey
for years 2006 to 2018, the study cannot reject the null of a = 1 for a sample of adult smokers,
and finds an upper bound for the present bias parameter of 0.99.
In the present paper, we address a related question that emerged with the recent approval of
the State Tobacco 21 laws in the US, which raised the minimum legal purchasing age of tobacco
products to 21 years (Hansen et al., 2022). In addition to the usual health concerns of smoking,
especially at young ages, one of the motivations that emerged in the debate was that young people
are more likely to display time inconsistent and present-biased preferences (Crettez and Deloche,
2021), and thus tend to be unable to correctly evaluate the future consequences of smoking and
more likely to develop addiction. Empirical evidence based on representative data, however, is
still lacking. This paper fills the gap by testing whether young smokers aged 21 or less display
evidence of quasi-hyperbolic discounting, and compare their time preferences to those of the adult
population (aged 30 to 65) using data from the Russian Longitudinal Monitoring Survey for years
1994 to 2020.
The results confirm that adult Russian smokers are not time inconsistent and that their discount
rate conforms with what is generally found in the empirical literature. Young smokers do not display
present-biased preferences either, with an upper-bound limit for equal to 0.99, identical to that
of the adults. However, their discount factor is much smaller, 0.54 vs 0.97, indicating that they
discount future utilities much more than the adults. This may suggest a more complex form of time
inconsistency that cannot be captured by the quasi-hyperbolic discounting, at least in a life-cycle
perspective.
2The general specification of the RA model, rarely estimated in the literature, embeds current, lead and lagged
prices of the good in the demand equation. This is in contrast with the simplified specification, more frequently
estimated, which only includes current prices but needs to impose that addiction is not persistent over time.
3
The remainder of the paper is structured as follows. Section 2 presents a short theoretical
description of the model used in the empirical analysis. Section 3 describes the data used, sample
selections and the empirical specification. Section 4 presents the results and Section 5 concludes.
2. Method and data
The model specification is as follows. Individuals are assumed to maximize the sum of lifetime
discounted utility
Max Ut+
1
X
i=1
iUt+i=Ut+Ut+1 +2Ut+2 +... (1)
where =1
(1+r)is the long-run discount factor, ris the discount rate (that coincides with the
interest rate in the budget constraints), and the extra discount parameter 2(0,1] is intended to
capture the essence of hyperbolic discounting, namely, that the discount factor between consecutive
future periods () is larger than that between the current period and the next (). If 6= 1, time
preferences in equation (1) are dynamically inconsistent, in the sense that the optimal consumption
plan established in tis inconsistent with the one that will be established in t+ 1. As shown by
O’Donoghue and Rabin (2002), the equilibrium of both na¨ıve and time consistent individuals solves
the same optimization problem. Therefore, the demand equation that solves (1) applies to both time
consistent and na¨ıve consumers. As in the general specification of the RA model, the interaction
between past and future consumption is modeled by the investment function At=(1)At1+Ct1,
with Atbeing interpreted as an “addiction stock” that depreciates over time at rate <1 and
increases with current consumption. The consumer solves the maximization problem such that
C0=C0and (Yt+PtCt)+P1
i=1 i(Yt+i+Pt+iCt+i)=W0,whereC0measures the previous level
of consumption.
Taking a quadratic utility function in the three arguments and solving the consumer problem
produces the following Euler equation:3
Ct=✓0+✓LCt1+✓FCt+1 ✓1⇥1+(1)2⇤Pt+✓1(1 )Pt1+✓1(1 )Pt+1 (2)
3For a detailed derivation of the Euler equation, see Piccoli and Tiezzi (2021).
4
where:4
⌦=↵CA(1 + )(1 )↵AA ↵CC ⇥1+(1 )2⇤>0
✓0=
⌦+↵C(1 )1↵A
✓L=1
⌦↵CA ↵CC(1 )>0 (3)
✓F=1
⌦↵CA ↵CC(1 )>0 (4)
✓1=
⌦>.0
The RA model with quasi-hyperbolic discounting encompasses the original formulation with
exponential discounting. In particular setting = 1 the model reduces to the standard Becker,
Grossman, Murphy (1994) RA model, which implies time consistency. Equation (2) can thus be
used to test whether consumers are time consistent or not by testing the equality ✓L=✓F, as the
only di↵erence between the two coefficients is the presence of in ✓F.
Rewriting equation (2) as a reduced form equation leads to
Cit =0+LCit1+FCit+1 +'TPit +'LPit1+'FPit+1,(5)
which, if no parameters restrictions are imposed, allows us to identify all needed structural parame-
ters to perform the standard battery of tests for rational addiction and to test for time consistency.
The time consistency test verifies the null5
L'FF'L=0.(6)
If the test rejects the null hypothesis, then 6= 1 and the data do not support time consis-
tent preferences, as implied by the RA model, in favor of quasi-hyperbolic discounting for na¨ıve
consumers.
Given the parametric specification of equation (2) and the corresponding reduced-form equation
(5), it is not possible to directly point-identify the value of the present bias parameter . Never-
theless, it is possible to find an upper bound for compatible with the estimated coefficients. The
4In what follows, ↵xare parameters of the quadratic utility function.
5Quick proof: since ='F
'L,✓L=L,and✓F=F
=F'L
'F, from equations (3) and (4) it is possible to note
that =1ifandonly if✓L=✓F, i.e., L'F=F'L,orL'FF'L=0
5
upper bound for the present-bias parameter is max =F'L
L'F(for a proof see Piccoli and Tiezzi,
2021).6
3. Empirical strategy
We estimate two empirical demand equations, for young and adult individuals, of the form:
Cit =0+LCit1+FCit+1 +'TPit +'LPit1+'FPit+1 +⌘XXit +vi+dt+uit (7)
where Cit is the number of smoked cigarettes by individual iin period t,Pit is cigarettes real
price, Xit is a vector of exogenous economic and socio-demographic variables that a↵ect cigarettes
consumption, viare individual fixed e↵ects capturing time invariant preferences that are correlated
with lead and lagged consumption and probably with other determinants of consumption, dtare
time fixed e↵ects, and uit =⇠1et+⇠2et+1 is the idiosyncratic error term.
There are two problems that will bias OLS estimates of equation (7). First, OLS estimates can
su↵er from an omitted variable bias due to unaccounted demand shifters that may also be serially
correlated (Becker et al., 1994). Second, there is measurement error when we use actual values of
Cit+1.Cit+1 in equation 7 should be interpreted as planned cigarette consumption at time t+1
using the information at time t. However, planned and actual consumption at time t+ 1 might
di↵er. Since we use actual cigarette consumption at time t+1 to proxy planned consumption, Cit+1
might be a↵ected by measurement error which will enter the idiosyncratic error term (Picone, 2005).
The disturbance term in equation 7 would be:
uit =⇠1eit +⇠2eit+1 +rit+1 (8)
where rit+1 =C⇤
it+1 Cit+1 is the di↵erence between planned and actual cigarette consumption.
There are two consequences of this measurement error. First, rit+1 is correlated with Pit+1 and
Pit, so both Pit+1 and Pit should be treated as endogenous. Second, E(Pit1uit) = 0, which is the
assumption that Pit1is a predetermined random variable.
The standard route to correct for the endogeneity bias is to follow Arellano and Bond (1991)
in using a GMM procedure to obtain the vector of parameters. The idea is to take first-di↵erences
to deal with the unobserved fixed e↵ects and then use the suitably lagged levels of the endogenous
6Extensive simulations of the structural model for a wide range of plausible values of the parameters suggest that
the true value of the parameter is always very close to its upper bound max .
6
and predetermined variables as instruments for the first-di↵erenced series, under the assumption
that the error term in levels is spherical and taking into account the serial correlation induced by
the first-di↵erence transformation. This idea extends to the case of lags and leads of the dependent
variable and to the case where serial correlation already exists in the error term of the original
model, as in equation (7).
We need a set of instruments Zit that are uncorrelated with the first-di↵erenced error term uit
and correlated with the regressors. By definition
uit =⇠1eit +⇠2eit+1 +rit+1 (9)
for i=1,...,N and t=3,...,T 1. Given (9), the following moment conditions are available:
E(Citsuit) = 0 for t=4,...,T 1 and s3. This allows the use of lagged levels of the observed
consumption series dated t3 and earlier as instruments for the first-di↵erenced equation (10):
Cit =1Cit1+2Cit+1 +3Pit +4Pit1+5Pit+1 +6Xit +7dt+uit (10)
The moment restrictions can be written in matrix form as E(Z0
iui) = 0 for t=4,...,T 1,
where uiis the (T4) vector (ui4,ui5, ..., uiT 1)0.ui=uit uit1and Ziis a (T4) ⇥g
block diagonal matrix, whose ith block is:
Zi=
0
B
B
B
B
B
B
@
Ci1,P
i1,P
i200... 0... 0W0
i4
0Ci1,P
i1,P
i2Ci2,P
i2,P
i3... 0... 0W0
i5
.
.
..
.
..
.
.... .
.
..
.
..
.
..
.
.
000... C
i1,P
i1,P
i2... C
iT 4,P
iT 4,P
iT 3W0
iT 1
1
C
C
C
C
C
C
A
.
where the block diagonal structure at each time period exploits all of the instruments available,
concatenated to one-column of first di↵erenced exogenous regressors W0
it =(Xit) that act as
instruments for themselves (Arellano and Bond, 1991).
The first-di↵erenced GMM estimator is known to be poorly behaved in terms of finite sam-
ple properties (bias and imprecision) when instruments are weak. This can occur here given
that the lagged levels of consumption are usually only weakly correlated with subsequent first-
di↵erences. Better finite sample properties can be obtained with system-GMM (Arellano and
Bover, 1995; Blundell and Bond, 1998). This estimator exploits additional moment conditions,
which are valid under the “constant correlated e↵ects”assumption (Bun and Sarafidis, 2013). This
yields (T4) further linear moment conditions, E(Cit2uit) = 0 for t=4,...,T 1, which allow
7
the use of equations in levels with suitably lagged first-di↵erences of the series as instruments.
The complete system of moment conditions available can be expressed as E(Z+0
iu+
i) = 0, where
u+
i=(ui4, ..., uiT 1,u
i4,...,u
iT 1)0.
The instrument matrix, Z+
i, for this system is
Z+
i=
0
B
B
B
B
B
B
B
B
B
@
Zi00... 0
0Ci2,Pi30... 0
00Ci3,Pi4... 0
.
.
..
.
..
.
.... .
.
.
00 0... CiT 3,PiT 2
1
C
C
C
C
C
C
C
C
C
A
where the first row is the set of valid instrument for the equation at time t= 4.
In finite samples, such a large instruments collection generates a bias/efficiency trade-o↵(Biørn
and Klette, 1998; Roodman, 2009b; Ziliak, 1997). For this reason, after experimenting with the
instruments, we use two parsimonious matrices of instruments, ZY
iand ZA
i, for the young and
adults equations, respectively, where we use only a subset of the available instruments, discarding
the use of some valid ones either by collapsing or curtailing the instrument matrix (Kiviet, 2020).
As to the choice of the transformation used to remove individual e↵ects in GMM estimators,
while first di↵erencing (FD) is one option, Arellano and Bover (1995) propose forward orthogonal
deviations (FOD) as an alternative transformation for models with predetermined instruments,
involving subtracting the mean of all future observations for each individual. The FOD transfor-
mation does not introduce a moving average process in the disturbance, i.e. orthogonality among
errors is maintained, and preserves the sample size in panels with gaps, as in our case, where FD
would reduce the number of observations (Roodman, 2009a). Valid moment conditions for the
FOD model in presence of endogenous regressors (Kripfganz, 2019) are: E(Citsuit ) = 0 for
t=4,...,T 1 and s2. This allows the use of lagged levels of the observed consumption series
dated t2 and earlier as instruments for the FOD equation.
3.1. Data
The estimation of the general specification of the RA model for cigarettes consumption requires
sufficiently long individual longitudinal data on the number of cigarettes smoked along with prices
at local level. This requirement is not easy to fulfill. For instance most US longitudinal data,
including PSID and NLSY97, only include repeated information on whether the individual smokes
8
or not, not the number of cigarettes, and this hampers the estimation of a RA model. In addition,
the longer individuals are followed, the more information is available for the estimation of the
dynamics of smoking habits, thus leaving out rotational panel from the pool of candidates. To
the best of our knowledge, the longest longitudinal survey that collects individual information
on the number of cigarettes smoked along with local level prices and that follows individuals for
as long as possible is the Russia Longitudinal Monitoring Survey (RLMS-HSE), which started in
1994 and is till ongoing. The survey is conducted by the Higher School of Economics and ZAO
Demoscop, together with the Carolina Population Center, and follows individuals and their families
from childhood to adulthood.7Households participating in the survey were selected through a
multistage probability sampling procedure to guarantee cross-sectional national representativeness.
Within each of the 38 primary sample units (PSUs), the population was stratified into urban and
rural substrata to guarantee the representativeness of the sample in both areas. The survey covers
approximately 5,000 hh, 12,000 adults and 2,000 children (aged up to 15 years) per wave.
The empirical analysis of cigarette addiction is thus based on waves 5 to 29 (corresponding to
years 1994 to 2020) of the RLMS-HSE. For each individual aged 13 years and above, the survey
asks whether she/he smokes and, if so, the number of cigarettes smoked per day. This is the
main consumption measure used in our study. The price variable is computed from the community
questionnaire, where interviewers go to local stores in the community and check minimum and max-
imum prices of a large sample of commodities, including domestic- and foreign-branded cigarettes.
Because several missing values are recorded at the community level (if, for instance, no store had
a particular item or if the store was closed), the price was averaged across communities within the
same primary sample units to reduce the impact of measurement errors. Because the prices are
at the current level, and the survey does not provide consumer price indices to deflate prices, we
compute a consumer price index at the PSU level following the T¨ornqvist procedure (T¨ornqvist,
1936). The reference price is that of the Moscow PSU in 1998, and the index is computed on a wide
set of food commodities, excluding tobacco and alcohol items. Cigarette prices are then deflated
using this consumer price index.
In order to be able to observe young smokers still living with their parents, but avoid complex
multi-family households, we selected smokers living in households with up to 4 components. the
Young’s equation is estimated for individuals no older than 21, for which about two thousand ob-
7More information can be found in the RLMS-HSE site: http://www.cpc.unc.edu/projects/rlms-hse.
9
servations and about one thousand individuals are available. The Adults’ equation is estimated for
individuals aged 30 to 65, corresponding to about 31 thousand observations and 6.4 thousand indi-
viduals. We use identical specifications for both equations with a minimal set of strictly exogenous
covariates, Xit, which includes: waves’ indicators, gender of the respondent (female = 1), age (in
years) of the respondent and its square. Time dummies have been specified in the level model only
to avoid redundancy (Kripfganz, 2019).8
4. Results
Table 1 reports estimates of model (7) for young and adult individuals. The table also reports
the instruments count and the p-value of the Hansen test for the joint validity of all instruments
(Hansen p-value), together with the Arellano-Bond test for second and third-order serial correlations
in the residuals.9
Estimates are consistent with the RA framework for both young and adult individuals. In both
equations past consumption has a significant positive e↵ect. Future consumption also has a signifi-
cant positive e↵ect, supporting the idea that smokers’ behavior is forward looking. The coefficient
of lagged price is greater than the coefficient of lead price, determining a positive discount rate.
We obtain a negative coefficient on the current price and a positive coefficient on both past and
future prices. So, the signs on the two consumption variables and on the three price variables
conform to theoretical predictions. The p-values of the Hansen J statistic for over-identifying re-
strictions for the full model are consistent with the null hypothesis of no-overidentification. Finally,
the Arellano-Bond test for third-order autocorrelation in the residuals does not detect third-order
serial correlation in the residuals of either of the two equations.
The conditions necessary for stability of the second-order di↵erence equation in current con-
sumption include that the sum of the coefficients on past and future consumption is less than unity
(Chaloupka, 1990). In both equations, the sum of coefficients on past and future consumption is
less than unity (0.523 for young individuals; 0.869 for Adults).
As to the covariates, being female has a negative and statistically significant impact on the
number of cigarettes smoked. Age and smoked cigarettes display a non linear relationship in both
8For estimations we used the xtabond2 command in STATA 17.
9Because in our model current consumption depends on both past and future consumption, this is an autoregressive
process of order 2 (AR2) and we have second-order serial correlation by construction. So, for the validity of our
instrument set, we need to detect no serial correlation of order 3 in the residuals.
10
Table 1: General Rational Addiction Model Estimates: Young & Adult smokers
Vari a b l es Young ( age 21) Adult (30 age 65)
Ct10.339*** 0.442***
(0.079) (0.076)
Ct+1 0.183*** 0.427***
(0.071) (0.088)
Pt-0.060** -0.033***
(0.029) (0.013)
Pt10.046* 0.017**
(0.026) (0.007)
Pt+1 0.025** 0.016*
(0.010) (0.009)
Gender -1.220** -0.780**
(0.472) (0.314)
Age 0.683** 0.059**
(0.311) (0.027)
Age2-0.012** -0.001**
(0.006) (0.000)
Time dummies Yes Yes
Hansen p-value full 0.100 0.537
p-value Arellano-Bond test for AR(2) 0.001 0.000
p-value Arellano-Bond test for AR(3) 0.146 0.358
# Obs 2,037 31,189
Instruments count 172 136
Notes: Robust SE in parentheses using Windmeijer correction. * p<0.10, ** p<0.05,
*** p<0.01.
equations: one additional year of age is associated with an increase in the number of cigarettes
smoked per day but at a decreasing rate. This non-linear relationship is stronger for young smokers
for whom we obtain larger coefficients (in absolute value) for both Age and Age squared signalling
that, compared to adult individuals, one additional year of age is associated with a larger increase
in the number of cigarettes smoked per day and with a larger decrease in marginal consumption.
Table 2 shows the results of the time consistency tests and time preferences parameters com-
puted from the estimated parameters. The test consists of testing the null hypothesis 1524=
0. For the non-linear test, under the null, the test statistics has a 2distribution with 1 degree of
11
Tabl e 2: T ime c o nsis tenc y test s
Young (age 21) Adult (30 age 65)
max 0.992 0.997
Time -consistency nl-test 2(1) (p-val) 0.00 (0.993) 0.00 (0.997)
Discount factor 0.543 0.969
Discount rate 0.842 0.032
freedom. We obtain a test statistics of 2(1) = 0.00 with a Prob > 2=0.992 for young individ-
uals, and a test statistics of 2(1) = 0.00 with a Prob > 2=0.996 for adult individuals. This
means that the null of time consistency cannot be rejected for either group. The estimated upper
bound for the present bias parameter is max =
b
✓+
b
✓=24
15=0.992 for young individuals and 0.997
for adult individuals. However, we cannot reject the null hypothesis max = 1 for either sample.
As to the estimated discount factor and discount rate, for young individuals we estimate a
discount factor =5/4=0.543 and a discount rate of 0.842, while for the adults we estimate a
discount factor of =0.969 and a discount rate of 0.032.
One possible issue in estimating the general version of the RA model when assuming = 1,
as supported by our results, is overparametrization. The problem is that the same structural
parameters would be derived by di↵erent empirical parameters. More specifically, the discount
factor would be obtained by the ratios F
Land 'F
'L, with no guarantee that the result is identical,
and generally will not. One possibility, would be to constrain one of the parameters, although
this is not easily achievable using the available statistical programs and commands. Most of the
empirical literature, instead, facing difficulties in properly estimating the general version of the
RA model, resorted to the restricted version. The restricted version excludes from the empirical
specification lead and forward prices. From a theoretical perspective, this corresponds to assume
complete depreciation of the addiction stock in each time period, i.e. = 1 in the addiction
motion equation and in equation (2). This may be reasonably considered implausible, knowing
how persistent addiction can be in the real word. However, this specification still allows to recover
the discount factor as F
L, avoids overparametrization, and, considering that our time period is
one year, it may not be completely out of logic to assume that in one time period addiction fully
12
Table 3: Restricted model estimation
Young (age 21) Adult (30 age 65)
Ct10.361*** 0.497***
(0.074) (0.057)
Ct+1 0.194*** 0.492***
(0.076) (0.063)
Pt-0.044* -0.010**
(0.023) (0.0048)
Discount factor 0.538 0.988
Discount rate 0.859 0.012
Notes: Robust SE in parentheses using Windmeijer correction. *
p<0.10, ** p<0.05, *** p<0.01.
depreciates.10
Thus, to check the robustness of our results we also estimate the restricted version of the
RA model on the samples of young and adult smokers with the same set of covariates. The
results, presented in Table 3 are indeed very close to those obtained for the general specification.
In particular, with the restricted specification, the discount factor for young smokers is just 1%
smaller than with the general specification, and for the adults is 2% larger, confirming our main
result.
Summarizing, the estimation results suggest that both young and adults Russian are rationally
addicted smokers with non-present-biased time preferences, but young individuals discount future
utilities much more than adults. Observing such a large di↵erence in time preferences at di↵erent
ages rises some doubts on the validity of the quasi-hyperbolic discounting model, which assumes
that both the and the are constant over the life cycle, as discussed later.
There are very few works to which we may compare our results, because estimates of quasi-
hyperbolic preferences using observational data have been achieved only very recently in the lit-
erature. In a previous article, Piccoli and Tiezzi (2021) found very similar results in terms of
present-bias and discount factor using the same data but with a di↵erent sample selection and
reference period. For a sample of adults aged 22-74 and years 2006-2018, with a slightly di↵erent
10This would mean that a smoker that stops smoking today and never smokes for one year could be considered
addiction free in the next period.
13
empirical specification and covariates set, they still reject present bias, with max =0.99, and find
a discount factor of 0.988, remarkably close to the 0.969 found in the present study. No estimates
were proposed for young smokers, though.
More interesting is the comparison with Blow et al. (2021). Although their setting does not
account for addiction in consumption, and the empirical test is very di↵erent, as they apply a
revealed preference approach, for a sample of Spanish households they find a remarkably close
discount factor (0.957). Where they di↵er substantially is about present bias. They find very poor
support for time consistent exponential discounting, with only 2% of households in their sample
passing the test, but much better support for quasi-hyperbolic discounting, with a 45% pass-rate.
Their average present bias parameter is 0.836, and a relevant proportion of the sample shows
even larger present bias: about 10% of families show a present-bias parameter of 0.729 or less.
While 45% might not seem a stellar number, for sure quasi-hyperbolic discounting performs much
better than exponential discounting in their sample.
One possible explanation may reside on the reference period. O’Donoghue and Rabin (2015)
pointed out how present bias (i.e. <1) is all about noticeable short-term discounting, such as
daily discounting, that is to say it is about, e.g., comparing utility now and in one day from now,
versus comparing utilities in two adjacent future days. Instead, here we estimate yearly discount
factors, i.e. how much individuals care today about utility in one year. In this long-run perspective,
finding no evidence of present bias seems plausible. As to Blow et al. (2021), they use quarterly
data, i.e. their data frequency is 4 times faster than ours, and this might be sufficient to let some
present-bias emerge.
5. Discussion
Time inconsistency of young individuals is one of the motivations behind the adoption of To-
bacco 21 Law in recent years in the US, which bans tobacco sales to individuals younger than 21. In
addition, as Gruber and K¨oszegi (2002, 2004) point out, when agents are time inconsistent, positive
taxation is optimal even in the absence of externalities, as time inconsistency will imply self-control
problems and the optimal future consumption path planned at time twill not be realized by the
agent, because not optimal anymore in t+ 1 and onward. Hence, in the case of time inconsistent
agents, taxes on addictive goods are substantially larger than those for time consistent consumers.
In the present paper we test whether young and adult smokers have di↵erent time preference,
in particular with respect to time consistency, using individual cigarettes consumption longitudinal
14
data. We reject present-bias for both groups and find that they display a rational addictive behavior,
in the sense that they are both addicted and forward looking, although young smokers discount
future utilities much more than the adults.
While we reject present-bias as a form of time inconsistency, the much larger discounting of
future utilities of the young suggests a more complex form of life-cycle time inconsistency –that
cannot be properly accounted for using quasi-hyperbolic discounting– where young individuals are
much more present-oriented than the adults. This has relevant implications both from a policy and
research perspective.
These results are consistent with Crettez and Deloche (2021) suggesting that young individuals
discount the future more heavily than the adult population. Adults display a much smaller discount
rate and a much larger discount factor, i.e. they give future actions and future utility a much larger
weight than young individuals. This gives empirical support to one of the motivations behind the
Tobacco 21 law even using large scale consumption survey data (in addition to the evidence based
on experimental methods). Clearly, this also supports larger taxes on addictive goods due to the
unforeseen consequence of addiction on future selves. This is despite the fact that the empirical
test of present-biased preferences is rejected, and more complex forms of time inconsistency could
not be formally tested.
Further extension would be needed to model time inconsistent preferences in the presence of
addiction in a life-cycle perspective. The economic literature has generally proposed to treat the
discount factor as endogenous and dependent on some choice or state variables determined by the
model. The first proposal dates back to Becker and Mulligan (1997) who consider an endogenous
discount factor that depends on some endogenous investment/e↵ort choice from the individual.
The idea is that the individual seeks to become more forward looking but to do so she must make
some e↵ort and invest some time or resources in that direction. While this hypothesis may well
be supported by the evidence produced in our analysis, it is empirically difficult to implement. In
fact, it is based on unobservable choice variables that would be quite difficult to proxy. To the
best of our knowledge no empirical results from these types of models using survey data have been
produced by the literature yet.
An interesting alternative is based on recent work by Strulik (2018), in which smoking acceler-
ates health deficit accumulation and reduces the survival probability, which in turns a↵ects time
preferences through the discount factor. While such proposal may work very well for explaining
the long term impact of addiction on time preferences, it seems less useful to explain why young
15
individuals display such a smaller discount factor compared to adults. Besides, it is also based on
unobserved state variables that may limits its empirical applicability. In fact, if survival probability
may well be proxied by health status and other socio-economic variables, the stock of addiction is
an artificial construct that is difficult to proxy using observational data.
An alternative specification recognizes that the addictive stock itself may impact individuals’
time preferences (Shi and Epstein, 1993). The idea is that people who are severely addicted could
discount future utilities much more, as they “need” to consume now. Hence, a larger stock of
addiction would reduce the discount factor. While high degree of addiction of young consumers
and oscillatory behavior of consumption are compatible with the model predictions (Perali and
Piccoli, 2022), the existence of a unique steady state suggests that these kind of models may be
unable to properly account for the much lower discount factors of young smokers. Interestingly,
however, empirical applications of such models start to emerge in the literature. In particular,
in a recent working paper, Hai and Heckman (2022) estimate a model where the discount factor
depends on the stock of addiction using a simulated GMM estimator. This way of estimating more
complex models with inconsistent time preferences might well be one way forward.
Finally, we foresee that a more pragmatic modeling of inconsistent time preference might be
possible. Given that age seems to be one of the most relevant factor in explaining the discount
rate,11 and it is readily available information in most surveys that also collect information on
consumption of addictive goods, the discount factor might be modeled directly as a function of age.
A na¨ıve consumer knows that she has a certain discount factor but she ignores that in the future it
will change with age. This would produce time inconsistent consumption plans similar to the na¨ıve
present-biased preferences, but would account for a possibly non-linear relationship of the discount
factor with age. The properties of such a model, the existence of a steady state, its stability and
its empirical tractability will be subject of future research.
11Other factors, closely related with age, might be important as well. For instance, getting married, having children,
or retire from work may be important life cycle events that may a↵ect time preference.
16
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