ESTIMATING TEMPTATION AND COMMITMENT OVER THE LIFE CYCLE

• Author: Agnes Kovacs,Hamish Low,Patrick Moran
• Date: 01 February 2021
• Published date: 01 February 2021
• DOI: http://doi.org/10.1111/iere.12491

INTERNATIONALECONOMIC REVIEW

Vol. 62, No. 1, February 2021 DOI: 10.1111/iere.12491

ESTIMATING TEMPTATION AND COMMITMENT OVER THE LIFE CYCLE∗

By Agnes Kovacs, Hamish Low, and Patrick Moran1

Institute for Fiscal Studies, University of Manchester, UK; Institute for Fiscal Studies,

University of Oxford, UK; Center for Economic Behavior and Inequality, the Institute for

Fiscal Studies, University of Copenhagen, Denmark

This article estimates the importance of temptation for consumption smoothing and asset accumulation in a

life-cycle model. We use two complementary estimation strategies: f‌irst, we estimate the model-implied Euler

equation; second, we match liquid and illiquid wealth accumulation using the method of simulated moments.

In both cases, we f‌ind that the utility cost of temptation is one-quarter of the utility benef‌it of consumption.

Further, temptation is crucial for correctly estimating the elasticity of intertemporal substitution (EIS): EIS es-

timates are biased downward when ignoring temptation. Finally, the model only matches the share of illiquid

wealth if temptation is in the preference specif‌ication.

1. introduction

“Present bias” has recently received much attention from economists, psychologists, and

policymakers. The diff‌iculties individuals might have in planning for the future, to delay grat-

if‌ication to access higher returns on investments, or even to accumulate resources to f‌inance

consumption in the future, have extensively been discussed. In the context of life-cycle saving

decisions, immediate gratif‌ication might lead individuals to save much less than they planned

to save (see, e.g., Bernheim, 1995). However, individuals who understand this tendency might

have a demand for commitment devices—illiquid assets such as retirement plans or housing—

to implement their optimal savings plans (see Strotz, 1956; Laibson, 1997). These types of

behavior are inconsistent with the standard model of intertemporal choice where instanta-

neous utility depends only on chosen alternatives and where individuals discount the future

geometrically.

Two alternative preference structures that exhibit present bias have received considerable

attention. The “temptation model” proposed by Gul and Pesendorfer (2001) relaxes the stan-

dard model’s assumption about instantaneous utility so that instantaneous utility depends

partly on feasible alternatives that are not chosen, but which are tempting. By contrast, the

“β−δ” model, formally introduced by Phelps and Pollak (1968), relaxes the assumption of

the standard model on discounting and introduces “hyperbolic discounting,” where the dis-

count rate is different in the short and long run. The Gul–Pesendorfer framework has two

∗Manuscript received November 2019; revised August 2020.

1An early version of this article was circulated as Kovacs (2016) “Present bias, temptation and commitment over

the life-cycle: estimating and simulating Gul-Pesendorfer Preferences.” Wewant to thank Orazio Attanasio, Alessan-

dro Bucciol, Martin Browning, Peter Neary, Mario Padula, Morten Ravn, JoséVíctor Ríos Rull, Harald Uhlig, Akos

Valentinyi, Guglielmo Weber, and seminar and workshop participants at University College London, University of

Oxford, Arizona State University, the XIX Workshop on Dynamic Macroeconomics in Vigo, the 2015 Royal Eco-

nomic Society Meeting, and the NBER Summer Institute on the Aggregate Implications of Microeconomic Con-

sumption Behavior for helpful comments. The activities of CEBI are f‌inanced by the Danish National Research

Foundation, Grant DNRF134. Please address correspondence to: Agnes Kovacs,Department of Economics, The Uni-

versity of Machester, Oxford Road, Manchester, M13 9PL, United Kingdom. E-mail: agnes.kovacs@manchester.ac.uk.

101

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Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research

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102 kovacs, low, and moran

main advantages as a framework for testing present bias: f‌irst, temptation preferences in-

duce dynamically consistent choices; second, the importance of temptation preferences can be

tested directly in a simple linearized Euler equation framework.

The aim of this article is to provide a quantitative assessment of temptation preferences

in explaining consumption and wealth accumulation by introducing temptation into a life-

cycle model with liquid and illiquid wealth accumulation. Temptation, as introduced by Gul

and Pesendorfer (2001), is the idea that households may be tempted to consume their avail-

able liquid resources in each period, and that resisting this temptation is costly. This results in

higher current consumption. In a dynamic context, current consumption is raised further as

households reduce savings to avoid costly temptation tomorrow, thus distorting consumption

smoothing. To alleviate the cost of temptation while still accumulating wealth for both pre-

cautionary and life-cycle motives, households may lock away their wealth in housing, which is

partially illiquid and therefore may reduce temptation. We assess the importance of tempta-

tion preferences in two stages: f‌irst, we identify the strength of temptation by estimating the

underlying preference parameters using an Euler equation; second, we show the extent that

allowing for temptation is necessary for the model to match life-cycle wealth prof‌iles.

In the f‌irst part of the article, we develop a dynamic structural model of consumer de-

mand for housing and consumption with temptation preferences. The discrete housing choice

alongside the continuous liquid asset choice means that the Euler equation for consumption

on its own is not suff‌icient to characterize the optimal solution, as discussed in Fella (2014),

Iskhakov et al. (2017), Druedahl and Jørgensen (2017), and Clausen and Strub (2020). How-

ever, the model generates Euler equations for consumption that are conditional on whether

or not housing adjusts and these conditional Euler equations are necessary conditions for the

optimal solution. We use the Euler equation conditional on not adjusting housing to estimate

the main preference parameters of the model.

We derive the model-implied log-linearized consumption Euler equation when there is no

adjustment of housing. We estimate the model’s preference parameters and test for tempta-

tion using the Consumer Expenditure Survey (CEX) and synthetic panel techniques. We es-

timate the importance of temptation, as well as the curvature of the utility function that deter-

mines the elasticity of intertemporal substitution. We f‌ind a signif‌icant effect of temptation on

actual choices: The weight on temptation is about a quarter of the weight on consumption in

utility terms. This f‌inding implies that temptation introduces a motive to consume more now

because resisting temptation is costly. We also show that estimating the Euler equation with-

out temptation generates a serious omitted variable bias that leads to underestimation of the

consumption elasticity of intertemporal substitution (EIS) parameter. Allowing for tempta-

tion results in an estimate of the EIS of 1.2, but when we do not allow for temptation, we es-

timate the EIS to be only 0.6.1

In the second part of the article, we numerically solve and estimate the full structural

model, imposing different assumptions on whether temptation forms part of preferences. Us-

ing the method of simulated moments (MSMs), we estimate the discount factor, and for ro-

bustness reestimate the EIS and the temptation parameter, by matching moments of the life-

cycle prof‌iles describing liquid wealth, illiquid housing wealth, and consumption. We f‌ind that

the estimates of the EIS and the temptation parameter are very similar to those estimated in

the Euler equation despite the sources of variation being different. These results conf‌irm that

our parameter estimates do not vary with the estimation method used. We also estimate the

model without allowing for temptation. Using the estimated parameters in the two versions of

the model, we demonstrate that allowing for temptation is important for the model to simul-

taneously match low levels of liquid wealth and high levels of illiquid housing wealth observed

in the data. Without temptation, the best f‌it of the model leads to overaccumulation of liquid

wealth and underaccumulation of housing wealth compared to the data.

1This estimate is in line with others in the literature of traditional Euler equation estimation; see, for example, At-

tanasio and Weber (1993) and Blundell et al. (1994).

estimating temptation and commitment over the life-cycle 103

In the model without temptation, the split between illiquid and liquid wealth accumulation

is determined by relative returns. By contrast, in the model with temptation, there is an ad-

ditional motive to accumulate in illiquid housing because of the value of housing as a com-

mitment device. Realizing that temptation occurs in subsequent periods, households will lock

away their saving in the form of housing to reduce the cost of resisting temptation in the fu-

ture. In our model, accessing housing wealth requires selling the house and paying a transac-

tions cost. In other words, housing wealth is partially illiquid and we do not allow for home

equity withdrawal without moving house. We show how changes in transactions costs affect

demand for housing. Increasing the transactions cost has a direct effect reducing the consump-

tion smoothing value of housing, but an offsetting indirect effect of increasing the commit-

ment value of housing. We show that this indirect effect dominates and demand for housing

rises, especially among the young, when individuals face higher f‌ixed costs.

The main contribution of this article is to estimate the strength of temptation preferences in

a life-cycle context. In this regard, the closest papers to this one are Bucciol (2012) and Huang

et al. (2015). Bucciol (2012) estimates the importance of the temptation motive and f‌inds that

the utility weight on temptation is only 5% of the utility weight on consumption. This is in

contrast to Huang et al. (2015) who obtain an estimate of 19%. In this article, we estimate

the utility weight of temptation to be 22%. Relative to this literature, there are three substan-

tial differences in the contribution of our article. First, we use two different estimation meth-

ods and show that our estimates are consistent across methods. Second, we show how ignor-

ing temptation leads to biased EIS estimates. Third, we model explicitly how housing can be

used as a commitment device in the presence of temptation; and explore the empirical impli-

cations of this perspective. Our decision to study housing explicitly is important in explaining

the difference between our estimates and Bucciol (2012), as the latter paper estimates tempta-

tion using a def‌inition of illiquid wealth that includes only retirement accounts.

By estimating the importance of temptation, this article contributes to the growing litera-

ture that incorporates temptation preferences in a variety of applied contexts. For instance,

Amador et al. (2006) study minimum-saving policies in the presence of temptation. Krusell

et al. (2010) show that a savings subsidy would be welfare improving when households suf-

fer from temptation. Schlafmann (2016) uses temptation preferences to understand hous-

ing and mortgage choices and the welfare consequences of mortgage regulations. Her re-

sults show that households with higher temptation are less likely to become home owners,

but higher downpayment requirements could be benef‌icial to these households. Kovacs and

Moran (2019) and Kovacs and Moran (2020) apply the temptation framework of the current

article to two different applications. The f‌irst application (Kovacs and Moran, 2019) shows

that temptation and commitment can account for the large share of hand-to-mouth house-

holds and generate realistic heterogeneity in the marginal propensity to consume. The second

application (Kovacs and Moran, 2020) extends the current framework by adding in the possi-

bility of home equity withdrawal, using this framework to evaluate the costs and benef‌its of

f‌inancial liberalization that gives households greater access to home equity.

Finally, our f‌indings complement the growing literature that evaluates the importance of

commitment. Direct evidence of demand for commitment devices has been found in a vari-

ety of different contexts. Thaler and Benartzi (2004) report evidence of people committing in

advance to allocate a portion of their future salary increase toward retirement savings. Ashraf

et al. (2006) f‌ind a signif‌icant increase in saving by consumers who purchased a commitment

savings product. Beshears et al. (2020) report that people who have access to both liquid and

less liquid accounts allocate more savings to the less liquid commitment account. On the im-

portance of housing as a commitment device, Angelini et al. (2020) build a life-cycle model

with temptation preferences and conclude that housing is heavily used as a commitment de-

vice in later life. In contrast, Ghent (2015) develops a life-cycle model with β−δpreferences

and concludes that the commitment role of housing is not an important determinant of hous-

ing decisions. Our article contributes to this literature by directly estimating a model in which

housing may serve as a commitment device.