Discussion Paper No. 1036

CURRENT ACCOUNT DYNAMICSUNDER INFORMATION RIGIDITY
AND IMPERFECT CAPITAL MOBILITY
Akihisa Shibata
Mototsugu Shintani
Takayuki Tsuruga

July 2018

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

Current Account Dynamics under Information Rigidity
and Imperfect Capital Mobility
Akihisa Shibatay, Mototsugu Shintaniz, and Takayuki Tsurugax
This draft: July 2018

Abstract
The current account in developed countries is highly persistent and volatile in comparison to output growth. The standard intertemporal current account model withrational expectations (RE) fails to account for the observed current account dynamics
together with persistent changes in consumption. The RE model extended with imperfect capital mobility by Shibata and Shintani (1998) can account for persistent changes
in consumption, but only at the cost of the explanatory power for the volatility of thecurrent account. This paper replaces RE in the intertemporal current account modelwith sticky information (SI) in which consumers are inattentive to shocks to their income and infrequently adjust their consumption. The SI model can better explaina persistent and volatile current account than the RE model but it overpredicts thepersistence of changes in consumption. The SI model extended with imperfect capital
mobility almost fully explains current account dynamics and the persistence of changes
in consumption, if high degrees of information rigidity and imperfect capital mobility
are taken into account.
JEL Classi…cations: E21, F21, F32, F41
Keywords: Capital mobility, Imperfect information, Inattentiveness, Permanent
income hypothesis
We thank Takashi Kano, Eiji Okano, Jun Nie, and seminar and conference participants at the CabinetO¢ ce (Government of Japan), Otaru University of Commerce, Shiga University, the University of Tokyo,
and the Asian Meeting of the Econometric Society, Annual Meeting of Japan Society of Monetary Economics,
and Econometric Society Australasian Meeting for helpful comments and discussions. The authors greatly
acknowledge the …nancial support of Grant-in-aid for Scienti…c Research (16H02026, 15H05729, 15H05728,
and 18K01684). Akihiko Ikeda provided excellent research assistance. All remaining errors are our own.
yKyoto University; e-mail: shibata@kier.kyoto-u.ac.jp.
zCorresponding author. The University of Tokyo; e-mail: shintani@econ.rcast.u-tokyo.ac.jp.
xOsaka University; e-mail: tsuruga@iser.osaka-u.ac.jp.

11Introduction

The persistent and volatile current account surplus and de…cit have attracted the attention ofresearchers and policymakers because they are associated with a large imbalance in international trade, or global capital in‡ows and out‡ows. Despite this considerable attention, thestandard intertemporal current account (ICA) model has only limited success in accounting
for the persistent and volatile current account.1 A reason for the limited success of the standard ICA model is that the model depends on the permanent income hypothesis. Under thepermanent income hypothesis, changes in consumption are unpredictable, but the changes
in consumption observed in developed countries are often predictable.2 Such predictablechanges in consumption have often been explained by hand-to-mouth consumers who have
only limited access to …nancial markets (e.g., Campbell and Mankiw 1989, 1990).3 In thecontext of the ICA model, limited access to …nancial markets means that international capital mobility is imperfect. Shibata and Shintani (1998) study the ICA model with imperfectinternational capital mobility. They estimate the degree of imperfect capital mobility, which
can be translated into the fraction of hand-to-mouth consumers in the economy.
The objective of this paper is to understand theoretically how the ICA model can better
explain current account dynamics. The data of OECD countries indicate that the current
account is much more persistent and volatile than net output growth.4 We show that the ICA
model with rational expectations (RE) underpredicts the persistence and volatility of thecurrent account. As in Shibata and Shintani (1998), we introduce imperfect capital mobility
by combining forward-looking consumers and hand-to-mouth consumers. We argue that thishybrid RE model can explain persistent consumption growth but achieve this prediction onlyat the cost of undermining the predicted volatility of the current account.
To better explain current account dynamics, we replace RE in the ICA model with sticky
information (SI) as developed by Mankiw and Reis (2002, 2007) and Reis (2006). In theliterature on the permanent income hypothesis, a number of previous studies have argued
for the role of inattentiveness to shocks (e.g., Pischke, 1995, Sims, 2003, Reis, 2006, Carroll
and Slacalek, 2007, Luo, 2008, Sims, 2010, Luo, Nie, and Young, 2015, and Gabaix, 2016,
among others). In these previous studies, agents are subject to information rigidities and
1

See Nason and Rogers (2006) and the reference therein.
Carroll, Slacalek, and Sommer (2011) provide robust evidence on the persistence of consumption growth.
3
For the international evidence on hand-to-mouth consumers, see Campbell and Mankiw (1991). The
theoretical implications for hand-to-mouth consumers have been explored well in the general equilibrium
models (e.g., Galí, López-Salido and Vallés 2004, 2007 and Bilbiie 2008).
4
Net output in the ICA model is obtained by subtracting investment and government spending from
output. For a more formal de…nition, see Section 2.
22

inattentive to income shocks. The resulting consumption does not follow a random walkand the changes in consumption are predictable, depending on the degree of information
rigidity. Overall, consumption dynamics with information rigidities are shown to …t the dataof aggregate consumption well, in comparison to the RE model.
Following this line of research, we explore current account dynamics under the SI model,
one of the simplest models of information rigidity. Under SI, consumers cannot update theirinformation with a constant probability. Consequently, some consumers are inattentive tonews and such inattentive consumers stick to the consumption level planned in the past period. We demonstrate that the SI model can explain a persistent and volatile current accountbut it tends to overpredict persistent changes in consumption. We show that the hybrid SI
model that combines forward-looking consumers with SI and hand-to-mouth consumers generates moderately persistent consumption growth without undermining predictions of thecurrent account. If we allow for a high degree of imperfect information and imperfect capital
mobility, the hybrid SI model can almost fully explain current account dynamics along withpersistent consumption growth.
At least two important recent studies on open macroeconomy are closely related to ourwork in terms of the importance of information rigidity.5 The …rst is Luo, Nie, and Young(2012) who extend the ICA model with rational inattention and robustness.6 While ourpaper is similar to theirs in that economic agents in our model imperfectly observe statevariables, the primary focus of Luo, Nie, and Young (2012) is on how robustness, that is, theuncertainty on the model economy, improves the ICA model’s prediction and its interaction
with rational inattention.7 The other important contribution is Ekinci (2017) who develops
the general equilibrium model under SI. His analysis of SI is motivated by explaining thewell-known puzzles in the two-country, open-economy models, such as the real exchange
5

We also note that, apart from information rigidity, a number of the previous studies have investigatedexplanations for current account dynamics and are thus closely related to our paper. Examples include
Glick and Rogo¤ (1995), Ghosh and Ostry (1997), Bergin and She¤rin (2000), Işcan (2002), Gruber (2004),
Kunieda and Shibata (2005), and Kano (2008, 2009).
6
See also a recent work by Li, Luo, and Nie (2017) who use the rational inattention and study international
consumption comovement puzzle.
7Luo, Nie, and Young (2012) argue that the current account detrended by the Hodrick-Prescott (HP)…lter tends to be less persistent than the standard RE model predicts. By contrast, we argue that thecurrent account scaled by net output tends to be more persistent than the standard RE model implies. On
top of the de…nition of variables, the di¤erence from Luo, Nie, and Young’s (2012) argument also stems
from di¤erence in the assumption on the stochastic process of net output. In particular, while Luo, Nie, andYoung (2012) focus on the case where the net output detrended by the HP …lter follows a stationary AR(1)process or a random walk, we consider the case where net output growth follows the AR(1) process so that astochastic trend is always present as in other previous works in the literature. For example, see She¤rin andWoo (1990), Otto (1992), Ghosh (1995), Ghosh and Ostry (1997), Bergin and She¤rin (2000), and Gruber(2004).

3

rate volatility puzzle and the Backus-Smith puzzle. In contrast, our analysis of SI aims
to understand the persistence and volatility of the current account in small open-economy
models.8This paper is organized as follows. In Section 2, we provide the evidence on current
account dynamics. Section 3 reviews the RE model. We discuss that the model is di¢ cultto reconcile with the data. In Section 4, we describe the SI model. Section 5 assesses theempirical performance of the SI and hybrid SI models. Section 6 concludes our analysis.

2

Evidence

The data source is the annual data from 16 OECD countries over 1980–2013 taken from theInternational Financial Statistics of the International Monetary Fund. The selected countries
are also included in the previous empirical studies such as She¤rin and Woo (1990), Ghosh(1995), and Shibata and Shintani (1998), among others. Our sample of developed countries
includes Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Iceland,
Italy, Japan, the Netherlands, Norway, Sweden, UK, and US.9 Here, current account data areconstructed from gross national income minus the sum of the household …nal consumption
expenditure, gross capital formation, and government …nal consumption expenditure.10 The
net output is de…ned by the gross domestic product (GDP) minus the sum of gross capitalformation and government …nal consumption expenditure. Consumption is the household…nal consumption expenditure, including non-pro…t institutions serving households. All theseries are converted to real series with the GDP de‡ator and measured in per capita terms.11
In our empirical analysis, the current account is normalized by the net output. This8

See also Crucini, Shintani, and Tsuruga (2010) who assume SI and sticky prices in …rms’price setting
and explain the persistence and volatility of good-level real exchange rates.
9
We select these countries based on the following criteria: First, the number of observations of the current
account exceeds 30. Second, the sample countries are classi…ed as rich countries based on Uribe and SchmittGrohé (2017). Third, the mean growth rate of net output over 1980 –2013 is less than 4 percent. The last
criterion is employed because the numerical exercise in Section 5 requires that the mean growth rate of net
output be low in comparison to the world interest rate.
10
The only exception is the Netherlands, where gross national income is not available in the International
Financial Statistics. For this country, we take current account data based on Balance of Payments Manual
Fifth edition (BPM5) from the OECD website. To be consistent with the data source, the data from theOECD website is also used for constructing the net output for the Netherlands.
11
If we use quarterly data, net output and the current account constructed from the seasonally-adjusted
series of the GDP, consumption, investment, and the government expenditure do not match the seasonallyadjusted series of net output and the current account. However, raw data (before the seasonal adjustment)
are not typically available so that seasonally adjusted series of net output and the current account cannot be
constructed for many countries. For this reason, we do not use the quarterly data but focus on the analysis
based on annual data.

4

normalization is useful in describing the current account dynamics, particularly when thegrowth rate of net output is stationary.12 A similar normalization was …rst employed byCampbell and Deaton (1989) in the context of the optimal saving rate under the permanent
income hypothesis when labor income growth is stationary. For the same reason, we also
express changes in consumption as a fraction of lagged net output. The same reformulationof consumption change has also been used by Shibata and Shintani (1998) in their analysis
of ICA model with imperfect capital mobility.
Table 1 assesses current account dynamics in the sample countries. In the table, wereport the cross-country average of persistence and volatility of the current account, alongwith the persistence of net output growth and changes in consumption. The persistence
13of the current account is measured by the …rst-order autocorrelation, denoted by dataca .
Volatility is measured by the standard deviation ratio of the current account to net output
growth. We denote the volatility measure by Vcadata . In this measure, when the current
account is more volatile than the net output growth, Vcadata exceeds one.
Table 1 indicates that the current account is much more persistent and volatile than
the net output growth. We see that the observed persistence of the current account ( data
ca )
data
is 0.82, which is much more persistent than that of the net output growth of 0.16 ().
While the table reports, for brevity, only the persistence averaged across countries, theseinequalities are preserved for all single-country data. When we examine the volatility, thecurrent account is about twice as volatile as the net output growth. In terms of the singlecountry data, the volatility of the current account in all countries except for Japan exceeds
unity. We note that the persistence of changes in consumption ( datac ) deviates from zero,and is 0.25 on average.

3

The RE models

In this section, we present RE models, focusing on the persistence and volatility of thecurrent account.

3.1

Setup

Consider a small open economy inhabited by a continuum of identical consumers located in aPjunit interval. A consumer’s lifetime expected utility is Et 1
u (Ct+j ) where Ct denotes
j=0
12

We remove the stochastic trend in the net output by the log di¤erence rather than Hodrick-Prescott…lter, in contrast to Luo, Nie, and Young (2012).
13
Here, we measure the …rst-order autocorrelation using the OLS estimator of the AR(1) model.

5consumption and is the discount factor satisfying 2 (0; 1). Also, Et [ ] represents the
expectations operator conditional on the information available in period t. Following Uribe
2and Schmitt-Grohé (2017), we specify u ( ) as u (Ct ) = 0:5 Ct C , where C is the bliss
point so that Ct < C for all t. The consumers’‡ow budget constraint is
At+j+1 = (1 + r)At+j + Xt+j

Ct+j ;(1)for all j > 0. Here, At denotes foreign asset holdings at the beginning of period t. In
this budget constraint, consumers have access to perfect international capital markets where
capital can be saved or borrowed at a constant world interest rate r. To facilitate the analysis,
we assume that the rate of time preference is equal to r: = 1= (1 + r). Finally, Xt is theexogenous stochastic endowment which we can also interpret as net output.
The …rst-order condition implies that Ct = Et Ct+j for j = 1; 2; :::. The optimal consumption is given by
Ct = rAt + Xtp ;(2)Pj
Et Xt+j .
where Xtp is the non-…nancial permanent income given by Xtp = [r= (1 + r)] 1
j=0 (1 + r)p
Changes in consumption are calculated as Ct+1 = Et+1 Xt+1 , where Et+1 denotes achange in the expectations operator de…ned by Et+1 = Et+1 Et . This equation meansthat consumption between periods t and t + 1 changes only if changes in the permanent
income are recognized by consumers.
By the fundamental balance-of-payments identity, the current account CAt equals changes
in the country’s net foreign assets (i.e., CAt At+1 At ). Therefore, using (1) and (2), we
have
1
X
p
CAt = Xt Xt =(1 + r) j Et Xt+j ;(3)
j=1

meaning that the current account is minus the present discounted value of future expectedchanges in the net output.
It is straightforward to extend this standard RE model with imperfect capital mobility.
Shibata and Shintani (1998) consider consumers with limited access to the international
capital market, as in Campbell and Mankiw (1989, 1990). A fraction 1of consumers
have perfect access to international capital markets and their consumption is determinedby (2). The remaining fraction 2 [0; 1) of consumers hold neither international …nancial
assets nor liabilities: They are hand-to-mouth consumers who consume all endowment within
a single period. When we introduce the hand-to-mouth consumer into the RE model, we callthis model the hybrid RE model. Denoting the aggregate consumption in the hybrid model6

be the current account) Ct + Xt . Likewise, let CAHY
by CtHY , we express CtHY = (1tin the hybrid model. Because hand-to-mouth consumers do not hold international …nancial
assets, CAHY
becomest
CAHY= (1) CAt :
(4)tThis implies that the magnitude of the current account changes is small compared to thecase of perfect capital mobility described by (3). We thus call the degree of imperfectcapital mobility.

3.2

Characterizing the RE models

We characterize the pure and hybrid RE models using (3) and (4). We look at theoreticalpredictions for the persistence and volatility of the current account under the assumption of
AR(1) process of the net output growth.
Let gt ln (Xt =Xt 1 ) be the net output growth. Assume that gt = (1
) + gt 1 + "t ,2where "ti:i:d: (0; ) and j j < 1. As discussed in Campbell and Deaton (1989), thisassumption of the stationary net output growth rate requires some reformulation of variables.
In particular, to ensure the stationarity of the current account, we divide both sides of (3)P1j
Et ( Xt+j =Xt ). While we will evaluate
by Xt . We obtain cat CAt =Xt =j=1 (1 + r)
the model with 6= 0 in Section 5, we temporarily set = 0 only for expositional purposes.
In this case, the …rst-order approximation of cat yields
cat '

1
X

(1 + r) j Et gt+j =

j=1

1+r

gt :

(5)

The left column of Table 2 summarizes the characterization of the RE model’s predictions.
The proportionality of cat to gt in (5) implies that the persistence of cat should be the sameas that of gt , namely, ca = . It also implies that the predicted volatility is given by Vca =sd (cat ) =sd (gt ) = = (1 + r). From Hall’s random walk hypothesis, it is evident thatchanges in consumption are serially uncorrelated in the RE model. In our case with reformulation of variables, we de…ne ct+1
Ct+1 =Xt . These newly de…ned (normalized) changesp=Xt ' [(1 + r) = (1 + r)] "t+1
in consumption can be expressed as ct+1 = Et+1 Xt+1
by the …rst-order approximation. Since "t is independent and identically distributed, thepredicted persistence of changes in consumption is zero, namely, c = 0.
These predictions of the pure RE model are inconsistent with the evidence in Section 2.
While the model predicts that ca = , the data suggests that data
> data , as indicated incaTable 1. It also fails to explain the volatility of the current account, if we recall Vcadata ' 2.
7

For the pure RE model to generate Vca ' 2, taking the world interest rate r as given, it
requires a su¢ ciently large value of . For example, if r = 0:04, needs to be as large as
0:69, as opposed to the data of data = 0:16.14 Note also that serially uncorrelated changes
in consumption, c = 0; is against the data, datac > 0.
The hybrid RE model can generate better predictions for the persistence of changes
HY
=Xt ,
Ct+1
in consumption (see the right column of Table 2). Again, denoting cHY
t+1
HY
we have ct+1 ' (1) ct+1 + gt+1 in the hybrid RE model. Since gt+1 is seriallycorrelated, the assumption of imperfect capital mobility leads to predictable changes in
consumption. The resulting HYc takes a form of HYc = 0 6= 0, where 0 is a function ofand the second moments of ct and gt (see the footnote of Table 2 for the
analytical expression). The improvement can be made at least without in‡uencing the= (1) CAt from (4),predicted persistence of the current account. Because CAHY
t
HY
HY
HY
cat = (1) cat = (1
) = (1 + r) gt , where cat
CAt =Xt . The proporHY
tionality of cat to cat means that the …rst-order autocorrelation of caHY
is unchanged int
HYcomparison to the pure RE model: ca = ca = .
However, the better prediction for the persistence of changes in consumption is achievedat the cost of undermining the predicted volatility of the current account. The above proportionality also implies that VcaHY = (1
) Vca , where VcaHY
sd caHY=sd (gt ). Sincetis dampened by . Therefore, for the hybrid RE model to2 [0; 1), the volatility of caHYtgenerate Vca ' 2, the hybrid model needs an even larger value of than the pure RE model.
For example, if r = 0:04 and = 0:50, the hybrid RE model requires that = 0:83, whichis larger than 0.69 required in the pure RE model.15

4

The SI models

To improve predictions of the ICA model, we replace RE in the ICA model with SI. In thissection, we leave the detailed maximization problem of the SI model to Appendix A.1 andfocus on how the current account dynamics are described in the SI model.

4.1

Setup

Let us assume that, in every period, only randomly selected 1 ! fraction of consumers
update their information set and that the remaining fraction ! 2 [0; 1) of consumers do not
14

Solving Vca ' 2 = = (1 + r) for yields ' 2 (1 + r) =3. When r = 0:04, turns to be 0.69.
HY
Solving Vca' 2 = (1) = (1 + r) foryields= 2 (1 + r) = (3). If we evaluate it atr = 0:04 and = 0:50, ' 0:83.
15

8

update their information set. We call ! the degree of information rigidity. Our assumption
simpli…es the SI model of consumption by Reis (2006), who considers endogenous infrequent information updating.16 Despite the simpli…cation, as we will later show, the model
predictions are very similar to Reis (2006).
Given infrequently updated information, consumers make decisions as rationally as theycan. Suppose that a consumer updated his information in period t and does not obtain new
information in t + 1. In this case, he does not change his consumption in period t + 1 since
he recognizes no changes in the permanent income. He sticks to a consumption plan thathe could make in period t. Therefore, if the information is not updated in period t + 1, any
shock in period t + 1 is unrecognized and absorbed by the consumer’s saving. Reis (2006)
refers to consumers who stick to their consumption plans as inattentive consumers.
More formally, an inattentive consumer who has period-t information chooses the exante optimal plan of consumption fCt+j;j g1
j=0 , where Ct+j;j is consumption chosen for periodt + j with j-period delay of information. Note that Ct;0 represents consumption that theconsumer enjoys in period t with full information. This Ct;0 must be the same as the
optimal consumption under the RE model. If the consumer does not receive new information
until period t + j, the consumer chooses Ct+j;j that was planned in period t. Note alsothat Ct+j;j = Ct;0 is satis…ed because the inattentive consumer perceives no changes in his
permanent income. Therefore, for j = 1; 2; :::, we haveCt+j;j = Ct;0 = rAt + Xtp :(6)

Let St+j;j be changes in the foreign asset holdings of the consumer in period t+j, conditionalthat his information was updated in period t but has not been updated until period t + j.
Then, St+j;j is given by
St+j;j = rAt+j + Xt+j Ct+j;j ;(7)where At+j follows (1) evaluated at Ct+j = Ct+j;j . That is, At+j+1 = (1 + r) At+j + Xt+j
Ct+j;j .
While St+j;j in (7) looks similar to the current account in the RE model, they need to be
distinguished in two aspects. First, St+j;j absorbs all changes in endowment between t andt + j, together with returns of the unintended change in the foreign asset holdings. Using
16

In Reis (2006), consumers face the cost of obtaining and processing information and decide whether
to update their information and recompute the optimal consumption plan. In our setting, the information
updating is exogenously given.

9

(6), we can rewrite St+j;j as
St+j;j = r (At+j

At ) + Xt+j

= r ( At+j + ::: +Xtp

At+1 ) +Xt+j + ::: +Xt+1 + St;0 , for j = 0; 1; 2; :::; (8)where St;0 = Xt Xtp which equals the current account under the RE model. Under SI, theinattentive consumer’s consumption (Ct+j;j ) does not respond to the unrecognized changes
in endowment between periods t and t + j. In (8), saving absorbs all unrecognized changes
in endowment Xt+1 , Xt+2 ,:::, Xt+j . Accordingly, changes in the inattentive consumer’s
foreign asset holdings also include returns from the unrecognized changes in endowment (i.e.,r ( At+j + ::: + At+1 )). We rewrite (8) recursively as17
St+j;j = (1 + r) St+j 1;j 1 +Xt+j for j = 1; 2; 3; ::::

(9)The second aspect that should be distinguished from the current account in the RE modelis that changes in foreign asset holdings di¤er across inattentive consumers, depending on
how they update their information. To obtain the current account in the SI model, we needto aggregate individual foreign asset holdings across all inattentive consumers. Based on theassumption of information updating, the current account in the SI model is
CAt = (1!)

1
X

! k St;k ;

(10)

k=0

where St;k is the period-t changes in the inattentive consumer’s foreign assets based on theinformation in period t k. Using (9), St;k can also be written as
St;k = (1 + r) St 1;k 1 +

Xt ;

(11)

where St k;0 = Xt k Xtp k .
It is again straightforward to extend the SI model with imperfect capital mobility. The
aggregate consumption is given by CtHY = (1) Ct + Xt and the current account is given
by
CAHY
= (1
) CAt
(12)
t
in the hybrid SI model so that (4) continues to hold.18
17

See Appendix A.2.
Reis (2006) also provides the microfoundation for (12). In particular, consumers may stick to saving plans
and let their consumption respond to unrecognized shocks to endowment, instead of sticking to consumption
18

10

4.2

Characterizing the SI models

We characterize the SI and the hybrid SI models using (10) –(12). We establish propositions
for the current account and changes in consumption under the pure SI model. We thendiscuss the hybrid SI model.
4.2.1

Persistence and volatility of the current account

The following proposition describes current account dynamics under the pure SI model:
Proposition 1 Suppose that inattentive consumers update their information with theprobability of 1 ! every period. Suppose also that the degree of information rigidity ! issu¢ ciently low such that ! (1 + r) < 1. Then, the current account is given by
CAt = ! CAt 1 + (1(13)!) St;0 + ! Xt ;where St;0 = Xt Xtp and ! = ! (1 + r).
Furthermore, suppose that the net output growth follows a covariance-stationary AR(1)process with mean zero: gt = gt 1 + "t , where "t i:i:d: (0; 2 ). Then, cat can be approximated by the AR(2) process:cat = (! + ) cat 1(!

) cat 2 +

!
1+r

"t :

(14)

Proof : See the Appendix A.3.
The …rst part of Proposition 1 tells us that the current account is written as the …rst-orderdi¤erence equation with the two driving forces. The …rst driving force is St;0 , changes in foreign asset holdings under full information. The impact of St;0 becomes weaker as ! becomes
higher. The second driving force is Xt . A fraction ! of inattentive consumers with oldinformation let their saving absorb unrecognized shocks to endowment. For this reason, Xt
appears in (13) with its coe¢ cient !. Also, recall that the e¤ect of unrecognized changes in endowment on CAt is carried over to the subsequent periods with interest earnings. Therefore,plans and letting their saving respond to shocks. He refers to such consumers as inattentive savers. Reis
(2006) shows that, if the costs of planning are not too small, it is optimal for inattentive savers not to re-plan
their savings at all. This result suggests that inattentive savers behave like consumers without any accessto the international capital market, since their consumption is perfectly correlated with endowment. If theinitial assets of inattentive savers are zero, the presence of inattentive savers reproduces the same equationas (12).

11

as ! = ! (1 + r) increases, the coe¢ cient on CAt 1 becomes larger, making CAt more persistent. Turning to the second part of the proposition, cat follows the AR(2) process, generalizing (5) in the RE model. Indeed, substituting ! = ! (1 + r) = 0 in (13) results in the AR(1)Pjprocess cat = cat 1= (1 + r) "t . Comparing cat == (1 + r) 1"t j with
j=0
P1 j
gt = j=0 "t j implies cat == (1 + r) gt , reproducing (5).
The persistence of cat is now increasing in ! so that the pure SI model can generate
a persistent current account even when net output growth is not persistent. In particular,
the …rst-order autocorrelation of cat is calculated as (! + ) = (1 + ! ) from (14) as longas ! 6= . The left panel of Figure 1 shows the …rst-order autocorrelation of the current
account against !.19 The blue line is the persistence under = 0:20, while the red line isthat under = 0:80. We recon…rm that persistence of the current account increases with!, regardless of the value of , except for the case of ! = . If ! happens to equal , thecoe¢ cient on "t is zero in (14) and the current account is constant for all t. Our result on
the persistence of the current account can be summarized in the next corollary:
Corollary 1 Under the pure SI model with = 0, the …rst-order autocorrelation of thecurrent account cat is given by
! +
;
(15)
ca =
1+!
and is always greater thanca =under the pure RE model, as long as ! 6= .

We move on to volatility of the current account in the SI model. Equation (14) implies
the following corollary:
Corollary 2 Under the pure SI model with
Vca = sd (cat ) =sd (gt ) is given by
Vca =

s

(1

1+!
! ) [1= 0, the volatility of the current account(! )2 ]s(!
(1 + r

)2
:
)2

(16)

The middle panel of Figure 1 plots the volatility against !. The volatility decreases with! if ! < and increases with ! if ! > . When = 0:20, the volatility increases with! over a wide range of !. Therefore, even when takes a low value as in the data, the SI
model can generate a volatile current account with a large value of !. By contrast, as shownin the red line, when = 0:80, the volatility increases with ! over a very narrow range of !.
19

Here, we set r = 0:04 to plot the curves. We also choose the range of ! 2 [0; 0:96], which ensures thestationarity of the current account.

124.2.2

Persistence of consumption growth

It is worthwhile discussing persistent changes in consumption in the SI model. Using themodel with endogenous infrequent information updating, Reis (2006) demonstrates that his
SI model of consumption can successfully generate predictable changes in consumption. We
con…rm persistent changes in consumption under exogenous infrequent information updating.
In the next proposition, we analytically derive the stochastic process of ct+1 :Proposition 2 Suppose that inattentive consumers update their information with the probability of 1 ! every period. Suppose also that the degree of information rigidity ! issu¢ ciently low such that ! (1 + r) < 1. Then, changes in the consumption are given by
Ct+1 = !

Ct + (1p!) Et+1 Xt+1:

(17)

Furthermore, suppose that net output growth follows a covariance-stationary AR(1) processwith mean zero: gt = gt 1 + "t , where "t i:i:d: (0; 2 ). Then, ct+1 can be approximatedby the AR(1) process:ct+1 = !

ct + (1

!)

1+r
1+r

"t+1 :(18)

Proof : See the Appendix A.4.
As is clear in (18), the persistence of changes in consumption critically depends on ! . In
the right panel of Figure 1, we plot the …rst-order autocorrelation of ct . It has a one-to-one
relationship with !. For example, when ! = 0:80 and r = 0:04, c = (1 + r) ! = 0:83. We
summarize this result in the following corollary:
Corollary 3 Under the pure SI model with = 0, the …rst-order autocorrelation of
given byc = ! , and is always greater thanc = 0 under the pure RE model.

ct is

We have two additional remarks on changes in consumption. First, not surprisingly, thedynamic properties of changes in consumption are very close to those in Reis (2006). His
proposition 2 states that, when the maximum length of time during which consumers areinattentive is q periods, changes in consumption follow the MA(q) process with monotonically decreasing MA coe¢ cients. In our SI model, the maximum length of time of being
inattentive is in…nity and the MA(1) representation of the AR(1) process (18) implies that
MA coe¢ cients are exponentially decaying.
13

Second, as Reis (2006) argues, the representative-agent habit formation model can be analternative explanation for persistent changes in consumption. It can be shown analyticallythat the current account in the habit formation model is the observational equivalent to thecurrent account in the SI model. In particular, if the period utility in the habit formation
model is given by u(CtCt 1 ) and the habit parameter is equal to ! , the current accountin the habit formation model follows the same stochastic process as that in our SI model.
Therefore, the two models are indistinguishable in the aggregate data.20 In the micro data,
however, there are mixed evidence for the presence of habit formation.21 In addition, while
the structure of SI models suggest disagreements about expectations, some empirical studies
based on the micro survey data support such disagreements about expectations on maineconomic variables. For example, Dovern, Fritsche, and Slacalek (2012) report disagreement
among professionals for main economic indicators including GDP growth in G7 countries.
Mankiw, Reis, and Wolfers (2003) and Coibion, Gorodnichenko, and Kumar (2018) …nd
much stronger disagreement among economic agents such as households and …rms thanamong professional forecasters. While Gruber (2004) …nds that the representative-agent
habit formation model performs better than the model without habits in predicting thecurrent account dynamics, the better performance of his model may also re‡ect the presenceof SI. An advantage of our SI model is that the explanation based on SI is broadly in linewith the above evidence from the micro data.
4.2.3

Impulse responses

To better understand the current account in the SI model, it is helpful to investigate theimpulse response functions. Figure 2 plots the impulse response functions of gt , cat , and ct
to one unit increase in "t . The leftmost panel points to the impulse response of gt . Here we
set at 0:20, so the response of gt decays quickly. In the middle and right panels, we compare
the response of cat and ct under the RE model (! = 0) and the SI model (! = 0:20 or0:80).
Let us …rst consider the impulse response functions of cat and ct under the RE model(! = 0). As shown in the blue line in the middle panel of Figure 2, the current accountdeclines in response to "t . Because the shock has a positive permanent e¤ect on endowment,
consumers’ permanent income increases more than the current endowment. In this case,increases in consumption at the impact period are larger than those in endowment at the20

See also Carroll, Slacalek, and Sommer (2011) for the similarity between the habit formation model andtheir “sticky expectations” model.
21
For example, see Dynan (2000) and Guariglia and Rossi (2002) among others.

14

same period. As a result, the economy runs current account de…cits.
How do the impulse responses di¤er in the SI model (! > 0)? When ! = 0:20, thecurrent account is nearly constant, as the coe¢ cient on "t in (14) is close to zero. To perceive
the intuition, recall that inattentive consumers let their saving absorb unrecognized shocks
between periods of planning. Even though a permanent e¤ect on endowment increases thepermanent income of all consumers, some consumers do not reduce their saving. Instead,they unintentionally increase their foreign asset holdings. The unintended increases in foreign
asset holdings o¤set reductions in foreign asset holdings resulting from a permanent shock
to endowment.
If the degree of information rigidity is su¢ ciently high (e.g., ! = 0:8), the current accountincreases. In response to a positive shock "t , unintended increases in foreign asset holdings
exceed decreases in foreign asset holdings. In this case, the increases in consumption aresmaller than those in endowment at the impact period. As a result, the economy runs thecurrent account surplus.
4.2.4

The hybrid SI model

Figure 3 plots the persistence and volatility of the current account and the persistence ofchanges in consumption against ! under the pure and hybrid SI models. In the …gure, we
set = 0:50 for the hybrid SI model. The value is borrowed from the simple average of
estimates in Shibata and Shintani (1998) who estimate of 11 developed countries.
to cat is fully preserved in the hybrid SI model. The relaThe proportionality of caHYt
HYtionship of ca = ca continues to hold in the hybrid SI model, and the curve for HY
ca traces
HY
out the upward-sloping curve for ca in the left panel of Figure 3. Therefore, ca can also
be high under information rigidity. This result is summarized in the following corollary:
Corollary 4 Under the hybrid SI model with = 0, the …rst-order autocorrelation of thecurrent account caHY
is given by HY) and is the same as that undertca = (! + ) = (1 + !
the pure SI model.
Turning to the volatility of the current account, the proportionality of caHY
to cat conttinues to imply that VcaHY = (1
) Vca . The dashed line corresponds to the hybrid SI modelwith = 0:50, while the solid line points to the pure SI model (i.e., = 0). The dashed linein the middle panel of Figure 3 indicates that the volatility of the current account in the
hybrid SI model is reduced in comparison to the solid line. However, Vca on the right-handside can increase with ! as long as ! 2 ( = (1 + r) ; 1), as in the case of the pure SI model.
15

When takes a low value and ! is su¢ ciently large, the current account can be volatilein the hybrid SI model. The analytical expression for VcaHY is provided by the following
corollary:
Corollary 5 Under the hybrid SI model with=sd (gt ) is given by
VcaHY = sd caHY
t
VcaHY

= (1

) Vca = (1

)

s

(1

= 0, the volatility of the current account1+!
! ) [1(! )2 ]s(!
(1 + r

)2
:
)2

(19)

How can we describe the persistence of changes in the aggregate consumption in the
hybrid SI model? Recall that changes in the aggregate consumption cHY
t+1 is a convex combination of ct+1 and gt+1 . We demonstrate that persistence of changes in the aggregate
consumption is a weighted average of persistence of ct and gt , that is, ! and . The
analytical expression for the persistence of changes in consumption in the hybrid SI model
is summarized by the following corollary:
Corollary 6 Under the hybrid SI model withis given by the weighted average of ! and :
HY
c

where

= (1

= 0, the …rst-order autocorrelation of

)! +

ct

(20)

;

2 [0; 1] is a weight given by=( ; ; !)
2=

(1

V ar (gt ) + (1) Cov (gt ; ct )) V ar ( ct ) + 2 (1) Cov (gt ; ct ) +22

V ar (gt )

:

(21)

Proof : See the Appendix A.5.
The persistence of changes in the aggregate consumption in the hybrid SI model nolonger has a one-to-one relationship with !. The extreme right panel of Figure 3 plots
the persistence of changes in the aggregate consumption in the pure and the hybrid SI
models. When ! is low, the dashed line is located above the solid line, increasing the overallpersistence of changes in the aggregate consumption by means of the persistence of net output
growth. When ! is large, the dashed line is located below the solid line, preventing the overallpersistence from increasing.22 In other words, imperfect capital mobility breaks the tight link
22

The dashed line in the right panel of Figure 3 also shows that the persistence of changes in the aggregate

16between the persistence of changes in consumption and the degree of information rigidity.

5

Assessment of the SI models

This section assesses the SI models in comparison to the RE models.

5.1

Methodology

We begin by slightly generalizing the pure SI model with the possibility of the non-zero mean
growth rate of gt , i.e., 6= 0. While this generalization does not a¤ect the steady state of
ct , the steady state value of cat is no longer zero.23 To address the non-zero steady state, itwould be convenient to de…ne c^
at and g^t by c^at cat E (cat ) and g^t gt, respectively.
The following proposition generalizes the second part of Propositions 1 and 2:
Proposition 3 Suppose that information rigidity is present as in Propositions 1 and 2.
Suppose also that net output growth follows a covariance-stationary AR(1) process with
nonzero mean: gt = (1
) + gt 1 + "t , where "ti:i:d: (0; 2 ). Assume thatand
! are both su¢ ciently low such that < r and !
! (1 + r) = (1 + ) < 1. The stochastic
process of c^at and ct+1 can be approximated byc^at = ! +

c^
at 1

!

c^
at 2 +

andct+1 = !

ct + (1

!)

r
r

r
r

!
(1 + r) = (1 + )(1 + r) (1 + )"t+1 ;
1+r(1 + )

"t ;

(22)

(23)

respectively.
Proof : See the Appendix A.6.
Here we impose a restriction that the net output grows at a slower rate
than theforeign asset holdings: < r. We require this assumption to ensure the stationarity of thenon-…nancial permanent income scaled by the net output.24 A positive slightly decreases
consumption decreases with !, even though an increase in ! generally raises the persistence of ct , whichis included in cHY. The decline occurs because the weight in (20) increases as ! ! 1.
t23
See (34) in Appendix A.3.2. If the net output has a positive deterministic trend, the economy issustainable under the current account de…cit in the steady state.
24
To understand the stationarity, consider P
the non-…nancial permanent income scaled1jby the net output, Xtp =Xt=
r= (1 + r) j=0 (1 + r) Et (Xt+j =Xt )=r= (1 + r) +
h
i
P1
Pj
j
r= (1 + r) j=1 (1 + r) Et exp. In the nonstochastic steady state, the non-…nancial
k=1 gt+k

17

the persistence of the current account and consumption growth, since a higher negativelyin‡uences ! . Obviously, these results are applicable to the RE models and can be extended
to the hybrid SI model.
Before we discuss the performance of the SI models, let us quickly recon…rm the poor
performance of the RE models under nonzero . Table 3 summarizes predictions of the pureand hybrid RE models for the theoretical moments. The left panel reports the predictionsof the pure RE model. They are inconsistent with the actual moments (shown in the mostright panel) even if nonzero is taken into account. The predicted persistence of the current account is 0.16 on the cross-country average, which is much lower than the observed
persistence of 0.82. The predicted volatility is 0.44 on average, again much lower than thedata of 2.29. Of course, changes in consumption have no persistence under = 0.
The poor performance can also be recon…rmed under = 0:5. As we discussed in Section
3, the hybrid RE model can generate serially correlated changes in consumption at the cost ofundermining the predicted volatility of the current account. While the persistence of changes
in consumption is slightly positive (0.05 on average) due to imperfect capital mobility, thepredicted volatility of the current account is reduced from 0.44 in the pure RE model to 0.22
in the hybrid RE model.
To assess the SI models, we estimate ! and using the data of 16 developed OECD
countries listed in Table 1, rather than using pre-speci…ed values of ! and . We obtain ! andto match the theoretical moments of the persistence and volatility of the current accountand the persistence of changes in consumption with the sample moments in each country. Let
f ( ) be a vector of distances between the theoretical and sample moments for the persistence
and volatility of the current account and the persistence of changes in consumption, where
denotes the vector of parameter consisting of ! and . In the case of the hybrid SI model, fordata 0
HY
data. Using the data of cat
Vcadata ; HYc ( )example, f ( ) = HY
ca ( )
ca ; Vca ( )c^ from the inverse of the bootstrap
and ct in each country, we obtain the weighting matrix W0data data
covariance matrix of data
.25 The objective function Q ( ) to be minimized isca ; Vca ;cde…ned by the quadratic form:^ f ( ):Q ( ) = f ( )0 W
When minimizing Q ( ), we impose the restriction that ! 2 [0; (1 + ) = (1 + r)) to ensure

P1jpermanent income scaled by the net output reduces to r= (1 + r) j=0 [(1 + ) = (1 + r)] . For thisexpression to be non-explosive, must be lower than r. See also Campbell and Deaton (1989).
25
A block bootstrap method with a block length of four is employed to compute the bootstrap covariancematrix .

18

that ! < 1 for both of the pure and hybrid SI models. We further impose the restrictionthat = 0 in the pure SI model and 2 [0; 1) in the hybrid SI model, respectively. The
minimizers of Q ( ) are denoted by ~ = (~! ; 0)0 for the former and ^ = (^! ; ^ )0 for the latter,
respectively.

5.2

Predictions of the SI models

The left panel of Table 4 shows the predictions of the pure SI model and the middle panelpresents those of the hybrid SI model. The two models’predictions are based on our estimatesof ! and , which we will discuss in the next section. For comparison, the right panel again
reports the actual moments from the OECD countries.
Let us …rst consider the pure SI model. Overall, it exhibits a great improvement incomparison to the RE models in Table 3. For example, the pure SI model can almost
fully account for the three targeted moments in the Netherlands. In particular, the predicted moments are ( ca ; Vca ; c ) = (0:83; 2:05; 0:76), as opposed to the actual moments:
data data
data= (0:85; 2:07; 0:74). The SI model also performs well in other countries,
ca ; Vca ;cthough all moments are not fully explained. For example, the predicted moments in Denmark are ( ca ; Vca ; c ) = (0:77; 1:75; 0:78), while the actual moments are (0:94; 3:73; 0:20).
This outcome is a remarkable improvement in predictions relative to the RE models, beHY
HY
cause the RE models predict ( ca ; Vca ; c ) = ( 0:01; 0:02; 0:00) and HY=
ca ; Vca ;c( 0:01; 0:01; 0:01).
While the pure SI model remarkably improves predictions of the current account, it
tends to overpredict the persistence of changes in consumption. In particular,
c is 0.65
in the cross-country average but the actual persistence is only 0.25, which is much lower
than in the model. The overprediction stems from the one-to-one relationship ofc =! = ! (1 + r) = (1 + ) in (23). That is, although a large ! helps the SI model explain
the persistence and volatility of the current account, the one-to-one relationship betweenc and ! also increases the persistence of changes in consumption far beyond the observed
persistence.
The hybrid SI model breaks the tight link. The middle panel of Table 4 presents thetheoretical moments generated by the hybrid SI model. The hybrid SI model continues topredict a persistent and volatile current account but now with a moderate degree of persistentconsumption growth. In the example of Denmark, the prediction of the hybrid SI model is
HY
HY
HY= (0:98; 3:83; 0:21) as opposed to the data of (0:94; 3:73; 0:20). In terms ofca ; Vca ;c
the cross-country average, the predicted persistence and volatility of the current account is
0.94 and 2.39, respectively. Unlike that in the pure SI model, the predicted persistence of19changes in consumption is now suppressed to 0.34, which is fairly close to the data of 0.25.
It may not be surprising that imperfect capital mobility leads to the good performanceof the SI model because the hybrid SI model has one additional free parameter . However,imperfect capital mobility alone does not necessarily improve the predictions, unless information rigidity is incorporated. When we estimate in the hybrid RE model with the same
objective function, the estimated turns out to be zero in 11 out of 16 countries.26 In our
exercise, the improvement of predictions are achieved only under the information rigidity.

5.3

Degrees of information rigidity and imperfect capital mobility

While the hybrid SI model achieves a fairly good model performance, we should note a caveat
in the estimated values of ! and . The hybrid SI model can achieve good performance underrelatively high degrees of information rigidity and imperfect capital mobility. Table 5 shows! and that are estimated for each country in the two SI models. On average, !
^ is 0.64
in the pure SI model and 0.89 in the hybrid SI model. These values imply that the average
duration of holding information until the next update is 2.8 years in the pure SI model andis 9.1 years in the hybrid SI model.27 The latter value seems extremely large compared tothe average duration estimate of 1.3 years obtained by Mankiw and Reis (2007).
We also note that an improvement with the hybrid SI model relies on a high degree ofimperfect capital mobility in some countries. While ^ is only 0.08 in the Netherlands, it isalmost one in Belgium and Germany under the parameter restriction of 2 [0; 1). Overall,however, the cross-country average of ^ is 0.58. This average is not extremely high in the
consumption literature though it may be considered to be high compared to the estimates ofsome previous studies.28 For single country’s estimates, they are statistically signi…cant inmany countries. In the right panel of Table 5, we report Q(~) Q(^), the di¤erence between
the objective functions evaluated at ~ and ^. The di¤erence is asymptotically distributed
as 2 (1) under the null hypothesis of = 0. In 11 out of 16 countries, is found to bestatistically signi…cant at the conventional signi…cance level.
An interpretation of the high degrees of information rigidity and imperfect capital mobility may be that the ICA model does not allow for other possible frictions and that the26

The countries in which the estimatedis zero are Australia, Austria, Belgium, Canada, Denmark,Finland, Iceland, Italy, Japan, Norway, and Sweden. We also …nd that the estimated turns out to be unity
in four countries of France, Germany, the Netherlands, and the UK.
27
Given the annual data, the average duration of holding information until the next update can be com1
1
puted from (1 0:64) = 2:8 and (1 0:89) = 9:1.
28
For example, Campbell and Mankiw (1990) use the US data and estimate to range between 0.30 and
0.64. Reis (2006) estimates , considering SI explicitly. His estimate of is quite low, a value between 0.05
and 0.15.

20

estimated parameters may re‡ect such frictions outside the model. Therefore, while the SI
model continues to be a promising approach to explaining the current account, introducing
other types of frictions and/or shocks into SI model may result in more reasonable estimates
for the degrees of information rigidity and imperfect capital mobility.

6

Conclusions

This paper extends the intertemporal current account (ICA) model with sticky information(SI). In our ICA model, consumers are inattentive to shock to net output and infrequently
update their information, as developed by Mankiw and Reis (2002, 2007) and Reis (2006).
Under the assumption that a permanent shock to net output drives the current account, therational expectations model fails to predict a persistent and volatile current account as wellas persistent changes in consumption. In our SI models, information rigidity improves thepredicted persistence and volatility of the current account. If the SI model is extended withimperfect capital mobility as in Shibata and Shintani (1998), our SI model exhibits a fairly
good performance in predicting changes in consumption as well as the current account. In
particular, the SI model almost perfectly explains the data of the 16 OECD countries if thedegrees of information rigidities and imperfect capital mobility are su¢ ciently high.
Our analysis also suggests that these frictions may need to be introduced into a richer
model of the current account to reduce too much reliance on imperfect information and imperfect capital mobility. Toward this end, it may be important to consider the production
economy and to include other frictions in the ICA model.29 Consideration of other shocks,
such as the world interest rate shock and the exchange rate shock, may also be helpful.30 Extending the ICA model in these directions under information rigidity would be an important
step for future research.

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One of the most important avenues of research may be the general equilibrium model with SI by Ekinci(2017), although he focuses on a two-country model rather than on small open economies.
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25

A

Appendix

A.1

The maximization problem and the optimality conditions

Our formal description of the consumer’s maximization problem follows Mankiw and Reis (2007).
Suppose that a consumer has the information set available in period t. We consider an inattentive
consumer who receives the newest information only with the probability 1! every period. Given

the infrequent information updating and the information set in period t, he chooses a consumption
plan to solve the following maximization problem:
V (At ; Xt ) =max1

fCt+j;j gi=0

+ (1

1
X

( !)j u (Ct+j;j )

(24)

j=0

!) Et

1
X

( !)j V (At+j+1 ; Xt+j+1 ) ;j=0

subject to At+j+1 = (1 + r) At+j + Xt+j

Ct+j;j ,for j = 0; 1; 2; :::;

(25)

where V (At ; Xt ) is the value function of the consumer in period t. Using the information available
in period t, he chooses the consumption plan fCt+j;j g1
j=0 , where Ct+j;j represents the amount ofgoods consumed in period t + j but predetermined j periods in advance. The value function issomewhat complicated since the plan is speci…ed as consumption from period t and revised once
he receives the new information. Other variables, parameters, and the function u (C) are de…nedin the main text.
The …rst-order condition and the envelope condition areu0 (Ct+j;j ) =

(1

!) Et

1
X

[ ! (1 + r)]k V 0 (At+j+k+1 ; Xt+j+k+1 ) ;

(26)

k=0

V 0 (At ; Xt ) =(1!) (1 + r) Et

1X[ ! (1 + r)]k V 0 (At+k+1 ; Xt+k+1 ) ;

(27)

k=0

for j = 0; 1; 2; :::, respectively. Here, u0 (C) = du (C) =dC and V 0 (At ; Xt ) is the partial derivativewith respect to the foreign asset. That is, V 0 (A; X) = @V (A; X) =@A.
P
k 0
Evaluating (26) at j = 0 yields u0 (Ct;0 ) = (1 !) Et 1
k=0 [ ! (1 + r)] V (At+k+1 ; Xt+k+1 ).
This result implies

V 0 (At ; Xt ) = (1 + r) u0 (Ct;0 ) :

26

(28)

Rewriting (27) recursively, we haveV 0 (At ; Xt ) =(1!) (1 + r) Et

1X[ ! (1 + r)]k V 0 (At+k+1 ; Xt+k+1 )

k=0=!) (1 + r) Et V 0 (At+1 ; Xt+1 )
(
)
1
X
k
(1 !) (1 + r)
+ ! (1 + r) Et[ ! (1 + r)] Et+1 V (At+k+2 ; Xt+k+2 )
(1

k=0

=
=

(1

!) (1 + r) Et V 0 (At+1 ; Xt+1 ) + ! (1 + r) Et V 0 (At+1 ; Xt+1 )(1 + r) Et V 0 (At+1 ; Xt+1 ) :(29)

Combining (28) and (29), we have the Euler equation that is standard in the RE model:
u0 (Ct;0 ) =(1 + r) Et u0 (Ct+1;0 ) :(30)

We next consider the expected marginal utility Et u0 (Ct+1;0 ). Update (26) by one period and set
P
k 0
j = 0. Then, we have u0 (Ct+1;0 ) = (1 !) Et+1 1
k=0 [ ! (1 + r)] V (At+k+2 ; Xt+k+2 ). By thelaw of iterated expectations,

Et u0 (Ct+1;0 ) =

(1

!) Et

1
X

[ ! (1 + r)]k V 0 (At+k+2 ; Xt+k+2 )k=0= u0 (Ct+1;1 ) :Therefore, along with the assumption of(1 + r) = 1, (30) implies

Ct+j;j = Ct;0 for j = 1; 2; :::.

(31)

We note that the optimal consumption in period t under the SI and RE models must be the same
because the information used to determine the optimal period-t consumption is identical. Therefore,(2) and (31) imply (6) in the main text: Ct+j;j = rAt + Xtp ; for j = 0; 1; 2; :::.

A.2

Inattentive consumer’s saving

Using (6), it is straightforward to derive (9) in the main text:
St+j;j= At+j+1

At+j = rAt+j + Xt+j

= r (At+j

At ) + Xt+j

Xtp

= r(At+j At+j 1 ) + Xt+j
|
{z
}
st+j

1;j

1

= (1 + r) St+j 1;j 1 +Ct+j;j

Xt+j 1 + r (At+j 1|

Xt+j for j = 1; 2; 3,....

27

At ) + Xt+j 1
{z

st+j

1;j

1

Xtp
}

(32)

A.3

Proof of Proposition 1

A.3.1

Derivation of (13)

To obtain the current account in the economy, we aggregate all individual savings over informationdi¤ering across households. Notice that St;k is the period-t saving of the inattentive consumers who
updated their information k periods ago. Using (32), we have an individual’s saving in period t:
St;k = (1 + r) St 1;k 1 +2= (1 + r) St 2;k 2 +Xt = (1 + r) [(1 + r) St 2;k 2 +Xt 1 ] +Xt

Xt + (1 + r) Xt 1

= :::= (1 + r)k St k;0 +Xt + (1 + r) Xt 1 + ::: + (1 + r)k 1

Xt k+1 ;Xtp k for k = 1; 2; 3; :::. The distribution of St;k follows (10) in the main

where St k:0 = Xt k

text so that the current account is aggregated by
CAt = (1!) St;0+ (1!) ! (1 + r) St 1;0 + (1!) ! Xt

2!) ! 2 (1 + r) St 2;0 + (1+ (1!) ! 2 Xt + (1!) ! 2 (1 + r) Xt 1+::::
Using the de…nition of ! = ! (1 + r), this equation can be rearranged as
CAt = (1!)

1
X(! )k St k;0

k=0

+! (1

!)

1
X

! k Xt + !! (1

!)

k=0

= (1

!)

1
X

(! )k St k;0 + !

1X! k Xt 1 + !(! )2 (1k=0

Xt + !

!)

1X! k Xt 2 + :::k=0

Xt 1 + (! )2 Xt 2 + :::

k=0

=

1
X

(! )k [(1!) St k;0 + ! Xt k ] :k=0Assume that ! = ! (1 + r) < 1. Then, using the lag operator L, CAt = (1

! L) 1 [(1!) St;0 + ! Xt ].

This equation is equivalent to (13) in Proposition 1.

A.3.2

Derivation of (14)In the proof, we derive the stochastic process of cat under the generalized case of non-zero . It isconvenient because the general case allows us to derive (22) and (23) in Proposition 3. To prove28

the second part of Proposition 1, we divide both sides of (13) by Xt 1 :exp (gt ) cat = ! cat 1 + (1where st;0!) exp (gt ) st;0 + ! [exp (gt )

1] ;

(33)

St;0 =Xt . We note that the steady state value of st;0 equals the steady state value ofcat because St;0 is identical to the current account under the RE model. Let ca be the steady statevalue of cat . In the steady state, (33) becomesexp ( ) ca = ! ca + (1!) exp ( ) ca + ! [exp ( )1] :Noting that exp ( ) = 1 + , ! = ! (1 + r), we can solve the above equation for ca as follows:ca =That is, ca is zero if and only if

:

r

(34)

= 0. In addressing the case of non-zero , it is convenient tointroduce the deviations of a variable from the mean:c^
at = catca, s^t;0 = st;0ca, and g^t = gt:

The …rst-order Taylor expansion of both sides of (33) around the steady state isexp ( ) c^
at + [exp ( ) ca] g^t = ! c^
at 1 + (1!) exp ( ) s^t;0 + (1!) [exp ( ) ca] g^t + ! exp ( ) g^t :Arranging terms yieldsc^at = ! c^
at 1 + (1!) s^t;0 + ! (1ca) g^t ;(35)

where ! = ! (1 + r) = exp ( ) = ! (1 + r) = (1 + ).
We would like to rewrite the last two terms of (35). As a preparation, note that st;0 = 1 Xtp =Xt
since St;0 = Xt

Xtp . Here, we have
1

Xtp
r X
=
Xt
1+r
j=0

1
1+r

j

Et

Xt+j
Xt

:

(36)

Focusing on each Xt+j =Xt inside the summation, we have the …rst-order Taylor expansions of
Xt+j =Xt :

29

Xt
Xt

= (1 + )0

1

Xt+1
Xt
Xt+2
Xt

' (1 + )1(1 + g^t+1 )' (1 + )2(1 + g^t+1 + g^t+2 )

:::
Xt+j
Xt

' (1 + )j(1 + g^t+1 + g^t+2 + ::: + g^t+j ) :Substituting these approximants into Xtp =Xt in (36), we have
Xtp
Xt

'
=
=
=

1

r X
1+r
j=0

r
r
r
r
r
r

+
+
+

1+
1+r
r

r
r
r

j

1

r X
+
1+r
j=1

1

r X
Et g^t+1 +
1+r

j

1+
1+r

j=2

1+
r
Et g^t+1 +
1+r
r
1
j
X 1+
Et g^t+j
1+r

1+
1+r

j

1+
1+r

Et g^t+2 + :::2

Et g^t+2 + :::

j=1

r
r

g^t ;

(1 + r) = (1 + )(37)

where the last line is due to AR(1) process of g^t .
Equation (37) provides the expression of the second term of (35). Since s^t;0 = 1

Xtp =Xtca,the second term of (35) is given by(1!) s^t;0 =

(1

!)

r
r

g^t :

(1 + r) = (1 + )(38)

Plugging in (34) and (38) into (35) yieldsc^at = ! c^
at 1= ! c^
at 1 += ! c^
at 1 +
Using g^t = g^t 1 + "t = (1c^at = ! +

(1

!)
r

r

r
!

r
r

r
(1 + r) = (1 + )(1!)

g^t + !

rr

(1 + r) = (1 + )!
(1 + r) = (1 + )

g^t

g^t

g^t :

L) 1 "t , we can further rewrite the above equation as
c^
at 1

!

which proves (22) in the main text. Imposingc^at 2 +rr!
(1 + r) = (1 + )"t ;= 0 also yields (14) in the main text.

30

(39)

A.4

Proof of Proposition 2

A.4.1

Derivation of (17)

To obtain changes in the aggregate consumption

Ct+1 , we aggregate all individual changes in

consumption between periods t and t + 1. Notice that consumers do not change their individual
consumption if they do not realize shocks between period t and t + 1 (i.e., Ct+1;k+1
for any k

Ct;k = 00). Therefore, for aggregation, it su¢ ces to consider only consumers who receive thenewest information in period t + 1. When aggregating changes in their consumption, however, weneed to take into account the history of information updating. For this reason, we …rst consider
a sequence of changes in consumption fCt+j+1;0

Ct+j;j g1
j=0 , given the foreign asset holdings At .

This sequence consists of changes in consumption for an individual consumer, conditional on thefact that he receives no additional information between t and t + j + 1. We derive the expression forthe changes in individual consumption as accumulated forecast errors. We then cross-sectionally
aggregate changes in individual consumption di¤ering across histories of individual information
updating. The aggregation is made based on the distribution of information updating.
Consider a sequence of changes in consumption fCt+j+1;0

of j = 0 (i.e., Ct+1;0

Ct+j;j g1
j=0 . The simplest is the case

Ct;0 ). If a consumer with information in period t updates the information inperiod t + 1, the changes in consumption are the same as that in the RE model:
Ct+1;0

Ct;0 = r (At+1p
At ) + Xt+1

Xtpp
= rSt;0 + Xt+1

Xtpp
= rXt + Xt+1

(1 + r) Xtp=

p;
Et+1 Xt+1(40)

where the …rst equality uses the optimal consumption given by Ct;0 = rAt +Xtp (See (6) in the maintext); the second equality arises from At+1

At = St;0 ; the third equality is from St;0 = Xt

Xtp ;and the …nal equality can be obtained from the de…nition of the non-…nancial permanent incomePj
Xtp = r= (1 + r) 1
Et Xt+j . Equation (40) indicates that changes in consumption in
j=0 (1 + r)

period t + 1 equal unrecognized changes in permanent income.

Next, consider the case of j = 1. Suppose that a consumer with information in period t does
not update his information set in period t + 1, but updates the information in period t + 2. Changes
in consumption between periods t + 1 and t + 2 can analogously be calculated as
Ct+2;0Ct+1;1 = Ct+2;0= r (At+2

Ct;0
At+1 + At+1p
At ) + Xt+2

p
p
Xt+1
+ Xt+1p= rSt+1;1 + Xt+2

p
p
Xt+1
+ rSt;0 + Xt+1

p
= rSt+1;1 + Xt+2

p
Xt+1
+

31

p
Et+1 Xt+1
:

Xtp

Xtp
(41)

Here, the third equality is based on the fact that At+2

At+1 = St+1;1 because the consumer does

not update information in period t + 1. The last equality can be derived from (40). Furthermore,
the …rst two terms of the right-hand side can be rewritten asp
rSt+1;1 + Xt+2

p
Xt+1

= r [(1 + r) St;0 +p
Xt+1 ] + Xt+2

p
Xt+1

p
= r rXt + Xt+1p
(1 + r) Xtp + rXt+1 + Xt+2p
= r Et+1 Xt+1+

p
Et+2 Xt+2;

p(1 + r) Xt+1

where the …rst equality is due to (32); the second equality is obtained from arranging terms with
St;0 = Xt

Xtp ; and the third equality is due to (40). Substituting the above equation into (41), we

obtain changes in consumption when the consumer with information in period t updates informationin period t + 2:
Ct+2;0Ct+1;1 =pp:+ (1 + r) Et+1 Xt+1
Et+2 Xt+2(42)

This equation indicates that, if he updates the information in period t + 2 but did not update it inperiod t + 1, the changes in consumption include the unrecognized changes in permanent income
in both periods t + 1 and t + 2.
For the general case of j > 1, we repeat the above calculation. The general expression ofchanges in individual consumption is
Ct+j;0 Ct+j 1;j 1 =pp
j 1
Et+j Xt+j+(1 + r) Et+j 1 Xt+j
1 +:::+(1 + r)p
Et+1 Xt+1, for j = 1; 2; ::::

(43)
We now aggregate the consumption change between t and t + 1 across all consumers, usingPkthe distribution of inattentive consumers: Ct = (1 !) 1
k=0 ! Ct;k . Recall that it is su¢ cient
to consider only consumers who receive the newest information in period t + 1. The fraction of
information-updating consumers is 1 !. Therefore, changes in the aggregate consumption become
Ct+1 = (1pEt+1 Xt+1

!)2
+!
+ !2
+ !3

h

h

(44)

p
Et+1 Xt+1+ (1 + r) Et Xtpip
Et+1 Xt+1+ (1 + r) Et Xtp + (1 + r)2

Et 1 Xtp 1

p
Et+1 Xt+1+ (1 + r) Et Xtp + (1 + r)2

Et 1 Xtp 1 + (1 + r)3io
Et 2 Xtp 2 + ::: :In the above equation, the …rst line in the curly brackets represents changes in consumption for
consumers whose period-t consumption was Ct;0 . The second line points to that for consumers whose
period-t consumption was Ct;1 (= Ct 1;0 ). We can understand the remaining lines analogously. This32

equation can further be simpli…ed to
Ct+1 = (1

"

!) (1

!)

1
X

p
! k Et+1 Xt+1

(45)

k=0

+ (1 + r) ! (1
+ (1 + r)2 ! 2 (1

!)

1
X

! k Et Xtp

k=0
1
X

!)

!k

k=0
p
Et+1 Xt+1 + !

= (1 !)
1 !
p
Et+1 Xt+1;=
1 ! L
where the second equality comes from (1!)#

Et 1 Xtp 1 + :::P1

Et Xtp + (! )2 Et 1 Xtp 1 + :::k=0 !

k = 1. By multiplying 1! L by both sides

and arranging terms, we obtain (17) in the main text:
Ct+1 = !

A.4.2

Ct + (1p:!) Et+1 Xt+1

Derivation of (18)Turning to the derivation of (18), divide both sides of (17) by Xt :ct+1 = ! exp ( gt ) ct + (1!) Et+1

p
Xt+1
Xt

:

(46)

We approximate each term in the right-hand side of (46). First, the …rst-order Taylor approximationof the …rst term is! exp ( gt ) ct ' ! exp (where) ( c) + ! exp () ( ctc)!
1+( c) g^t ;c is the steady state value of changes in consumption (divided by net output). In the steadystate, however,c = 0. Therefore, noting that exp () = (1 + ) 1 and !

! (1 + r) = (1 + ),we can simplify the above equation as! exp ( gt ) ct ' !

33

ct :

(47)

p
The second term of the right-hand side of (46) includes Et+1 Xt+1
=Xt , which can be approximated

by
Et+1

p
Xt+1
Xt

=

1

r X
(1 + r) j Et+1
1+r

Xt+j+1
Xt

j=0

= r

' r
= r

1
X

j=1
1
X

j=1
1
X
j=1

=

1
1+r

j

1+
1+r

j

1+
1+r

j

Et+1

Xt+j
Xt

Et+1 (1 + g^t+1 + g^t+2 + ::: + g^t+j )
+r

1
X

j=1
1
X

r (1 + ) r (1 + )
+
r
r

j

1+
1+r

Et+1 g^t+1 +

1+
1+r

j=0

1+
1+r

r

1
X
j=1

j

1+
1+r

j

Et+1 g^t+2 + :::Et+1 g^t+j+1 :Because g^t+1 follows AR(1) process, we can simplify the equation as
Et+1

p
Xt+1
Xt

'
=

1

r (1 + ) r (1 + ) X
+
r
r
j=0

1+
1+r

j

g^t+1

1+r
r (1 + ) r (1 + )+g^t+1 :rr
1 + r (1 + )Using the law of iterated expectations, we obtain the …rst-order approximation ofp
Et+1 Xt+1=Xtp
Et+1 Xt+1=Xt =p
Et Xt+1
=Xt :
p
Xt+1
Xt

Et

'

1+r
r (1 + ) r (1 + )+rr
1 + r (1 + )g^t :Therefore,
Et+1

p
Xt+1
Xt

=
=

r (1 + )
1+r
(^
gt+1
r
1 + r (1 + )
1+rr (1 + )"t+1 :r
1 + r (1 + )

g^t )
(48)

We now substitute (47) and (48) into (46):
ct+1 = !

ct + (1!)

which proves (23) in the main text. Imposingrr(1 + r) (1 + )"t+1 ;
1 + r (1 + )= 0 also leads to (18) in the main text.

34

(49)

A.5

Proof of Corollary 6

HY = Covc
HY
Changes in consumption under the hybrid model are expressed as Ct+1
Xt+1 , which we normalize by Xt to obtain cHY) ct+1 + gt .
t+1 = (1HYHY
HYFirst, Cov ct+1 ; ct
, the numerator of c , is given by

From the de…nition of the …rst-order autocorrelation, we calculate

HYcHY
t+1 ; ct

Cov

)2 Cov ( ct+1 ; ct ) + (1

= (1
+ (1

Because both

) Cov ( ct+1 ; gt ) +2

HY =V arcHY
t+1 ; ct

= (1) Ct+1 +) Cov (gt+1 ; ct )Cov (gt+1 ; gt ) :ct and gt follow the AR(1) process (see Proposition 2), Cov ( ct+1 ; ct ) = ! V ar ( ct ),Cov (gt+1 ; ct ) = ! Cov (gt ; ct ), Cov ( ct+1 ; gt ; ) = Cov (gt ; ct ), and Cov (gt+1 ; gt ) = V ar (gt ).
Substituting these expressions into the above equation yields
Cov

HY
cHY
t+1 ; ct=hNext, the variance V ar

)2 V ar ( ct ) + (1

(1

+

2

V ar (gt ) + (1cHY
, the denominator ofti) Cov (gt ; ct ) !

) Cov (gt ; ct )

:

(50)

HY , can similarly be calculated. The resultingcexpression is
V ar

cHY
t

= (1

)2 V ar ( ct ) + 2 (1) Cov (gt ; ct )+ 2 V ar (gt ) :(51)

Finally, taking the ratio of (50) to (51) yields
HY
c

=

(1

= (1

cHY
.
t

)2 V ar ( ct ) + (1V ar cHYt)! +;) Cov (gt ; ct )which is (20) in the main text. We note that2

! +V ar (^gt ) + (1) Cov (gt ; ct )HY
V ar ct

is a function not only of

but also of V ar ( ct ),Cov (gt ; ct ), and V ar (gt ):V ar ( ct ) =Cov (gt ; ct ) =V ar (gt ) =1(1 !) (1 + r) 2
1 (! )2
1+r
1(1 !) (1 + r) 2
;
1 !
1+r
1
2
;
2
1

2

;

where all of these moments are a function of , and !. In this proof, we used the assumption that
= 0. In the case of

6= 0, we can similarly calculate

35

HY , using the stochastic process ofc

ct+1

given by (23) in Proposition 3 and obtain the essentially same result.

A.6

Proof of Proposition 3

The derivations of (39) and (49) in the previous sections are applicable to the case of non-zero .
Therefore, we can derive (22) and (23) directly from (39) and (49), respectively.

36

37

0

0.5

SI (
SI (

= 0.20)= 0.80)

1

0

0.5

1

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.1
0

0.5

= 0.20)= 0.80)c against !: The SI model

0

SI (
SI (

1

Note: The persistence (the left panel), volatility (the middle panel) of cat , and the persistence of ct (the right panel) against the degree of
information rigidity !. In the left panel, each line has a disconnect at ! = = (1 + r), because the current account is independent of "t at! = = (1 + r). In the right panel, the predictions of the SI model are the same between = 0:20 and = 0:80, because
c is independent of .

ca , Vca , and

0

0.1

0.2

0.5

= 0.20)= 0.80)

0.2

SI (
SI (

0.3

1

1.5

2

2.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Vca

Figure 1: The current account and changes in consumption:

ca

1

c

38
0

5
PeriodCurrent account10

Figure 2: Impulse response function of gt , cat , and

-0.2

-0.2
10

0

0

5
Period

0.2

0.2

0

0.4

0.6

0.8

1

1.2

1.4

0.4

0.6

0.8

1

1.2

cat

ct

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0

5
Period10

RE ( = 0.00)
SI ( = 0.20)
SI ( = 0.80)

Changes in consumption

Note: Impulse response functions of the net output growth gt (left panel), the current account cat (middle panel) and changes in consumption ct(right panel) to a unit increase in "t . The stochastic process of net output growth is given by gt = (1
) + gt 1 + "t , where = 0:2 and = 0.

gt

1.4

Net output growth

ct

39

HY
ca

,

0

SI ( = 0.20,= 0)Hybrid SI (= 0.20,= 0.50)

1

0

0.5

1

0.4

0.5

0.6

0.7

0.8

0.9

0

0.1
0

Figure 3: Impact of imperfect capital mobility on

0.5

0ca , Vca , and

0

0.1

0.2

= 0.50)

1

0.2

0.5

SI ( = 0.20,= 0)Hybrid SI (= 0.20,

0.3

1

1.5

2

2.5

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

HY
Vca, Vcac

0.5

SI ( = 0.20,= 0)Hybrid SI (= 0.20,= 0.50)1

Note: The persistence (the left panel) and volatility (the middle panel) of cat and the persistence of changes in consumption ct (the right panel)against the degree of information rigidity !. The solid lines represent predictions of the SI model while the dashed lines point to predictions of
the hybrid SI model with = 0:50. In the left panel, predictions of the two models are the same, because HY
ca = ca .

ca

HY
c

,
c

Table 1: Sample moments of the current account in rich OECD countries (1980-2013)
OECD data
Persistence of current account (ρdata
ca )

0.82

data
Volatility of current account (Vca
)

2.29

data

Persistence of net output growth (φ)

Persistence of changes in consumption (ρdata
∆c )

0.16
0.25

Note: Numbers reported are the sample mean of actual moments across 16 OECD countries over 1980-2013.
The selected countries include Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany,
Iceland, Italy, Japan, the Netherlands, Norway, Sweden, UK, and US. In the table, the current account andchanges in consumption are scaled as a percent of net output.

Table 2: Theoretical predictions of the RE models
RE modelHybrid RE model

Persistence of current accountφφVolatility of current account

φ
1+r−φ

φ
(1 − λ) 1+r−φ

Persistence of changes in consumption

0

Λ0 φ

Note: The theoretical predictions are made under the assumption that gt follows AR(1) process with µ = 0.
In volatility of the current account, we assess φ = φdata = 0.16 and r = 0.04. In persistence of changes in
consumption, Λ0 is a function of r, φ, and λ, satisfying 0 ≤ Λ0 ≤ 1 and takes a value between 0 and 1. Morespeciﬁcally, Λ0 = ΛN /ΛD , where ΛN = λ(1−λ)Cov(∆ct , gt )+λ2 V ar(gt ) and ΛD = (1−λ)2 V ar(∆ct )+2λ(1−λ)Cov(∆ct , gt ) + λ2 V ar(gt ). The variances and covariance are given by V ar(∆ct ) = [(1 + r)/(1 + r − φ)]2 σ 2 ,V ar(gt ) = [1/(1 − φ2 )]σ 2 , and Cov(∆ct , gt ) = [(1 + r)/(1 + r − φ)]σ 2 .

40

Table 3: Predictions of the RE models (µ ̸= 0)
RE modelHybrid RE model

OECD data

ρca

Vca

ρ∆c

ρHY
ca

HY
Vca

ρHY
∆c

ρdata
ca

data
Vca

ρdata
∆c

Australia

0.13

0.25

0.00

0.13

0.13

0.04

0.44

1.26

0.16

Austria

0.03

0.07

0.00

0.03

0.03

0.01

0.88

1.89

-0.02

Belgium

-0.01

0.01

0.00

-0.01

0.01

0.00

0.78

2.50

-0.29

Canada

0.30

0.61

0.00

0.30

0.30

0.10

0.81

1.52

0.39

Denmark

-0.01

0.02

0.00

-0.01

0.01

-0.01

0.94

3.73

0.20

Finland

0.17

0.37

0.00

0.17

0.18

0.05

0.92

2.77

0.34

France

0.17

0.28

0.00

0.17

0.14

0.06

0.93

3.45

0.49

Germany

0.15

0.36

0.00

0.15

0.18

0.04

0.95

2.20

0.11

Iceland

-0.16

0.23

0.00

-0.16

0.12

-0.06

0.71

2.32

0.25

Italy

0.44

1.10

0.00

0.44

0.55

0.13

0.68

1.42

0.34

Japan

0.17

0.37

0.00

0.17

0.19

0.05

0.75

0.89

0.01

The Netherlands

0.20

0.42

0.00

0.20

0.21

0.06

0.85

2.07

0.74

Norway

0.17

0.40

0.00

0.17

0.20

0.05

0.84

2.48

0.26

Sweden

0.05

0.09

0.00

0.05

0.05

0.02

0.95

2.96

0.12

United Kingdom

0.43

1.44

0.00

0.43

0.72

0.10

0.91

3.76

0.45

United States

0.37

1.04

0.00

0.37

0.52

0.10

0.76

1.47

0.41

Mean

0.16

0.44

0.00

0.16

0.22

0.05

0.82

2.29

0.25

Note: The moments of the current account and changes in consumption predicted by the RE model (theleft panel), the hybrid RE model (the middle panel) and the actual moments (the right panel). Each panel
reports the persistence of the current account (in the ﬁrst column), the volatility of the current account(in the second column), and the persistence of changes in consumption (in the third column), respectively.
Here, the current account and changes in consumption are scaled by the net output and net output growthis assumed to follow AR(1) process with the mean growth rate µdata and persistence of φdata . The mean
growth rates of net output in the data (µdata ) are 1.76, 1.86, 1.47, 1.23, 1.26, 1.80, 1.27, 2.10, 1.66, 1.28,
1.81, 1.66, 1.94, 1.66, 2.00, and 1.81 percent in the order of countries shown in the table. The value of φ used
for the predictions can be conﬁrmed from ρca in the ﬁrst column of the left panel because the persistenceof the current account is predicted to equal that of net output growth in the RE models. In the hybrid RE
model shown in the middle panel, λ is set to 0.5.

41

Table 4: Predictions of the SI models (µ ̸= 0)
SI modelHybrid SI model

OECD data

ρca

Vca

ρ∆c

ρHY
ca

HY
Vca

ρHY
∆c

ρdata
ca

data
Vca

ρdata
∆c

Australia

0.59

0.91

0.50

0.59

0.91

0.50

0.44

1.26

0.16

Austria

0.70

1.74

0.69

0.98

2.04

0.08

0.88

1.89

-0.02

Belgium

0.43

0.75

0.44

1.00

2.93

0.00

0.78

2.50

-0.29

Canada

0.82

1.31

0.69

0.94

1.55

0.47

0.81

1.52

0.39

Denmark

0.77

1.75

0.78

0.98

3.83

0.21

0.94

3.73

0.20

Finland

0.89

3.18

0.85

0.96

2.81

0.37

0.92

2.77

0.34

France

0.90

2.70

0.86

0.97

3.45

0.50

0.93

3.45

0.49

Germany

0.59

0.99

0.48

1.00

2.20

0.15

0.95

2.20

0.11

Iceland

0.80

2.40

0.85

0.90

2.45

0.28

0.71

2.32

0.25

Italy

0.51

0.90

0.10

0.98

1.69

0.48

0.68

1.42

0.34

Japan

0.61

0.85

0.49

0.93

0.99

0.24

0.75

0.89

0.01

The Netherlands

0.83

2.05

0.76

0.85

2.07

0.74

0.85

2.07

0.74

Norway

0.79

2.05

0.72

0.96

2.69

0.31

0.84

2.48

0.26

Sweden

0.85

2.64

0.84

0.98

2.98

0.13

0.95

2.96

0.12

United Kingdom

0.86

1.58

0.68

1.00

3.96

0.46

0.91

3.76

0.45

United States

0.83

1.45

0.67

0.96

1.68

0.48

0.76

1.47

0.41

Mean

0.74

1.70

0.65

0.94

2.39

0.34

0.82

2.29

0.25

Note: The moments of the current account and changes in consumption predicted by the SI model (the left
panel), the hybrid SI model (the middle panel) and the actual moments (the right panel). The SI modelin the left panel is based on ω̃ that minimizes the objective function Q(θ) under a restriction λ = 0. The
objective function Q(θ) is deﬁned in the main text. The hybrid SI model is based on unrestricted estimatesω̂ and λ̂. The right panel reproduces the right panel of Table 3 to facilitate comparisons with the models.
See the footnote of Table 3 for the other detail.

42

Table 5: Estimates of ω and λ and Q(θ) in the SI models
SI modelHybrid SI model

H0 : λ = 0

ω̃

Q(θ̃)

ω̂

λ̂

Q(θ̂)

Q(θ̃) − Q(θ̂)

Australia

0.49

9.95

0.49

0.00

9.95

0.00

Austria

0.67

16.93

0.96

0.75

0.85

16.08**

Belgium

0.43

43.43

0.98

1.00

8.14

35.29**

Canada

0.67

3.74

0.87

0.55

1.49

2.25

Denmark

0.76

20.63

0.95

0.41

0.12

20.51**

Finland

0.83

5.27

0.92

0.52

0.14

5.13*

France

0.84

9.04

0.93

0.34

0.14

8.90**

Germany

0.47

17.64

0.98

0.99

0.30

17.35**

Iceland

0.83

13.78

0.91

0.32

1.53

12.26**

Italy

0.09

5.35

0.94

0.77

4.57

0.78

Japan

0.48

10.72

0.89

0.78

3.61

7.11**

Netherlands

0.74

0.04

0.76

0.08

0.00

0.03

Norway

0.71

10.29

0.93

0.60

1.36

8.93**

Sweden

0.82

25.43

0.96

0.63

0.08

25.35**

United Kingdom

0.67

6.20

0.97

0.81

0.66

5.54*

United States

0.65

4.18

0.89

0.67

2.61

1.57

Mean

0.63

12.66

0.89

0.58

2.22

10.44

Note: Estimates of the degree of information rigidity and the degree of imperfect capital mobility in the
SI models. The left panel (SI model) presents ω̃ under a restriction λ = 0 and the value of the objectivefunction Q(θ̃) under the same restriction. The middle panel (Hybrid SI model) shows unrestricted estimatesω̂ and λ̂ and Q(θ̂), where θ̂ = (ω̂, λ̂)′ . The right panel reports the test statistic for the null hypothesis of
λ = 0. The asterisks * and ** indicate that the null hypothesis is rejected at the ﬁve percent and the one
percent signiﬁcance level, respectively.

43