CURRENT ACCOUNT DYNAMICS UNDER INFORMATION RIGIDITY AND IMPERFECT CAPITAL MOBILITY

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1 Discussion Pape No CURRENT ACCOUNT DYNAMICS UNDER INFORMATION RIGIDITY AND IMPERFECT CAPITAL MOBILITY Akihisa Shibata Mototsugu Shintani Takayuki Tsuuga July 2018 The Institute of Social and Economic Reseach Osaka Univesity 6-1 Mihogaoka, Ibaaki, Osaka , Japan

2 Cuent Account Dynamics unde Infomation Rigidity and Impefect Capital Mobility Akihisa Shibata y, Mototsugu Shintani z, and Takayuki Tsuuga x This daft: July 2018 Abstact The cuent account in developed counties is highly pesistent and volatile in compaison to output gowth. The standad intetempoal cuent account model with ational expectations (RE) fails to account fo the obseved cuent account dynamics togethe with pesistent changes in consumption. The RE model extended with impefect capital mobility by Shibata and Shintani (1998) can account fo pesistent changes in consumption, but only at the cost of the explanatoy powe fo the volatility of the cuent account. This pape eplaces RE in the intetempoal cuent account model with sticky infomation (SI) in which consumes ae inattentive to shocks to thei income and infequently adjust thei consumption. The SI model can bette explain a pesistent and volatile cuent account than the RE model but it ovepedicts the pesistence of changes in consumption. The SI model extended with impefect capital mobility almost fully explains cuent account dynamics and the pesistence of changes in consumption, if high degees of infomation igidity and impefect capital mobility ae taken into account. JEL Classi cations: E21, F21, F32, F41 Keywods: Capital mobility, Impefect infomation, Inattentiveness, Pemanent income hypothesis We thank Takashi Kano, Eiji Okano, Jun Nie, and semina and confeence paticipants at the Cabinet O ce (Govenment of Japan), Otau Univesity of Commece, Shiga Univesity, the Univesity of Tokyo, and the Asian Meeting of the Econometic Society, Annual Meeting of Japan Society of Monetay Economics, and Econometic Society Austalasian Meeting fo helpful comments and discussions. The authos geatly acknowledge the nancial suppot of Gant-in-aid fo Scienti c Reseach (16H02026, 15H05729, 15H05728, and 18K01684). Akihiko Ikeda povided excellent eseach assistance. All emaining eos ae ou own. y Kyoto Univesity; shibata@kie.kyoto-u.ac.jp. z Coesponding autho. The Univesity of Tokyo; shintani@econ.cast.u-tokyo.ac.jp. x Osaka Univesity; tsuuga@ise.osaka-u.ac.jp. 1

3 1 Intoduction The pesistent and volatile cuent account suplus and de cit have attacted the attention of eseaches and policymakes because they ae associated with a lage imbalance in intenational tade, o global capital in ows and out ows. Despite this consideable attention, the standad intetempoal cuent account (ICA) model has only limited success in accounting fo the pesistent and volatile cuent account. 1 A eason fo the limited success of the standad ICA model is that the model depends on the pemanent income hypothesis. Unde the pemanent income hypothesis, changes in consumption ae unpedictable, but the changes in consumption obseved in developed counties ae often pedictable. 2 Such pedictable changes in consumption have often been explained by hand-to-mouth consumes who have only limited access to nancial makets (e.g., Campbell and Mankiw 1989, 1990). 3 In the context of the ICA model, limited access to nancial makets means that intenational capital mobility is impefect. Shibata and Shintani (1998) study the ICA model with impefect intenational capital mobility. They estimate the degee of impefect capital mobility, which can be tanslated into the faction of hand-to-mouth consumes in the economy. The objective of this pape is to undestand theoetically how the ICA model can bette explain cuent account dynamics. The data of OECD counties indicate that the cuent account is much moe pesistent and volatile than net output gowth. 4 We show that the ICA model with ational expectations (RE) undepedicts the pesistence and volatility of the cuent account. As in Shibata and Shintani (1998), we intoduce impefect capital mobility by combining fowad-looking consumes and hand-to-mouth consumes. We ague that this hybid RE model can explain pesistent consumption gowth but achieve this pediction only at the cost of undemining the pedicted volatility of the cuent account. To bette explain cuent account dynamics, we eplace RE in the ICA model with sticky infomation (SI) as developed by Mankiw and Reis (2002, 2007) and Reis (2006). In the liteatue on the pemanent income hypothesis, a numbe of pevious studies have agued fo the ole of inattentiveness to shocks (e.g., Pischke, 1995, Sims, 2003, Reis, 2006, Caoll and Slacalek, 2007, Luo, 2008, Sims, 2010, Luo, Nie, and Young, 2015, and Gabaix, 2016, among othes). In these pevious studies, agents ae subject to infomation igidities and 1 See Nason and Roges (2006) and the efeence theein. 2 Caoll, Slacalek, and Somme (2011) povide obust evidence on the pesistence of consumption gowth. 3 Fo the intenational evidence on hand-to-mouth consumes, see Campbell and Mankiw (1991). The theoetical implications fo hand-to-mouth consumes have been exploed well in the geneal equilibium models (e.g., Galí, López-Salido and Vallés 2004, 2007 and Bilbiie 2008). 4 Net output in the ICA model is obtained by subtacting investment and govenment spending fom output. Fo a moe fomal de nition, see Section 2. 2

4 inattentive to income shocks. The esulting consumption does not follow a andom walk and the changes in consumption ae pedictable, depending on the degee of infomation igidity. Oveall, consumption dynamics with infomation igidities ae shown to t the data of aggegate consumption well, in compaison to the RE model. Following this line of eseach, we exploe cuent account dynamics unde the SI model, one of the simplest models of infomation igidity. Unde SI, consumes cannot update thei infomation with a constant pobability. Consequently, some consumes ae inattentive to news and such inattentive consumes stick to the consumption level planned in the past peiod. We demonstate that the SI model can explain a pesistent and volatile cuent account but it tends to ovepedict pesistent changes in consumption. We show that the hybid SI model that combines fowad-looking consumes with SI and hand-to-mouth consumes geneates modeately pesistent consumption gowth without undemining pedictions of the cuent account. If we allow fo a high degee of impefect infomation and impefect capital mobility, the hybid SI model can almost fully explain cuent account dynamics along with pesistent consumption gowth. At least two impotant ecent studies on open macoeconomy ae closely elated to ou wok in tems of the impotance of infomation igidity. 5 The st is Luo, Nie, and Young (2012) who extend the ICA model with ational inattention and obustness. 6 While ou pape is simila to theis in that economic agents in ou model impefectly obseve state vaiables, the pimay focus of Luo, Nie, and Young (2012) is on how obustness, that is, the uncetainty on the model economy, impoves the ICA model s pediction and its inteaction with ational inattention. 7 The othe impotant contibution is Ekinci (2017) who develops the geneal equilibium model unde SI. His analysis of SI is motivated by explaining the well-known puzzles in the two-county, open-economy models, such as the eal exchange 5 We also note that, apat fom infomation igidity, a numbe of the pevious studies have investigated explanations fo cuent account dynamics and ae thus closely elated to ou pape. Examples include Glick and Rogo (1995), Ghosh and Osty (1997), Begin and She in (2000), Işcan (2002), Gube (2004), Kunieda and Shibata (2005), and Kano (2008, 2009). 6 See also a ecent wok by Li, Luo, and Nie (2017) who use the ational inattention and study intenational consumption comovement puzzle. 7 Luo, Nie, and Young (2012) ague that the cuent account detended by the Hodick-Pescott (HP) lte tends to be less pesistent than the standad RE model pedicts. By contast, we ague that the cuent account scaled by net output tends to be moe pesistent than the standad RE model implies. On top of the de nition of vaiables, the di eence fom Luo, Nie, and Young s (2012) agument also stems fom di eence in the assumption on the stochastic pocess of net output. In paticula, while Luo, Nie, and Young (2012) focus on the case whee the net output detended by the HP lte follows a stationay AR(1) pocess o a andom walk, we conside the case whee net output gowth follows the AR(1) pocess so that a stochastic tend is always pesent as in othe pevious woks in the liteatue. Fo example, see She in and Woo (1990), Otto (1992), Ghosh (1995), Ghosh and Osty (1997), Begin and She in (2000), and Gube (2004). 3

5 ate volatility puzzle and the Backus-Smith puzzle. In contast, ou analysis of SI aims to undestand the pesistence and volatility of the cuent account in small open-economy models. 8 This pape is oganized as follows. In Section 2, we povide the evidence on cuent account dynamics. Section 3 eviews the RE model. We discuss that the model is di cult to econcile with the data. In Section 4, we descibe the SI model. Section 5 assesses the empiical pefomance of the SI and hybid SI models. Section 6 concludes ou analysis. 2 Evidence The data souce is the annual data fom 16 OECD counties ove taken fom the Intenational Financial Statistics of the Intenational Monetay Fund. The selected counties ae also included in the pevious empiical studies such as She in and Woo (1990), Ghosh (1995), and Shibata and Shintani (1998), among othes. Ou sample of developed counties includes Austalia, Austia, Belgium, Canada, Denmak, Finland, Fance, Gemany, Iceland, Italy, Japan, the Nethelands, Noway, Sweden, UK, and US. 9 Hee, cuent account data ae constucted fom goss national income minus the sum of the household nal consumption expenditue, goss capital fomation, and govenment nal consumption expenditue. 10 The net output is de ned by the goss domestic poduct (GDP) minus the sum of goss capital fomation and govenment nal consumption expenditue. Consumption is the household nal consumption expenditue, including non-po t institutions seving households. All the seies ae conveted to eal seies with the GDP de ato and measued in pe capita tems. 11 In ou empiical analysis, the cuent account is nomalized by the net output. This 8 See also Cucini, Shintani, and Tsuuga (2010) who assume SI and sticky pices in ms pice setting and explain the pesistence and volatility of good-level eal exchange ates. 9 We select these counties based on the following citeia: Fist, the numbe of obsevations of the cuent account exceeds 30. Second, the sample counties ae classi ed as ich counties based on Uibe and Schmitt- Gohé (2017). Thid, the mean gowth ate of net output ove is less than 4 pecent. The last citeion is employed because the numeical execise in Section 5 equies that the mean gowth ate of net output be low in compaison to the wold inteest ate. 10 The only exception is the Nethelands, whee goss national income is not available in the Intenational Financial Statistics. Fo this county, we take cuent account data based on Balance of Payments Manual Fifth edition (BPM5) fom the OECD website. To be consistent with the data souce, the data fom the OECD website is also used fo constucting the net output fo the Nethelands. 11 If we use quately data, net output and the cuent account constucted fom the seasonally-adjusted seies of the GDP, consumption, investment, and the govenment expenditue do not match the seasonallyadjusted seies of net output and the cuent account. Howeve, aw data (befoe the seasonal adjustment) ae not typically available so that seasonally adjusted seies of net output and the cuent account cannot be constucted fo many counties. Fo this eason, we do not use the quately data but focus on the analysis based on annual data. 4

6 nomalization is useful in descibing the cuent account dynamics, paticulaly when the gowth ate of net output is stationay. 12 A simila nomalization was st employed by Campbell and Deaton (1989) in the context of the optimal saving ate unde the pemanent income hypothesis when labo income gowth is stationay. Fo the same eason, we also expess changes in consumption as a faction of lagged net output. The same efomulation of consumption change has also been used by Shibata and Shintani (1998) in thei analysis of ICA model with impefect capital mobility. Table 1 assesses cuent account dynamics in the sample counties. In the table, we epot the coss-county aveage of pesistence and volatility of the cuent account, along with the pesistence of net output gowth and changes in consumption. The pesistence of the cuent account is measued by the st-ode autocoelation, denoted by data ca. 13 Volatility is measued by the standad deviation atio of the cuent account to net output gowth. We denote the volatility measue by Vca data. In this measue, when the cuent account is moe volatile than the net output gowth, Vca data exceeds one. Table 1 indicates that the cuent account is much moe pesistent and volatile than the net output gowth. We see that the obseved pesistence of the cuent account ( data ca ) is 0.82, which is much moe pesistent than that of the net output gowth of 0.16 ( data ). While the table epots, fo bevity, only the pesistence aveaged acoss counties, these inequalities ae peseved fo all single-county data. When we examine the volatility, the cuent account is about twice as volatile as the net output gowth. In tems of the singlecounty data, the volatility of the cuent account in all counties except fo Japan exceeds unity. We note that the pesistence of changes in consumption ( data ) deviates fom zeo, and is 0.25 on aveage. c 3 The RE models In this section, we pesent RE models, focusing on the pesistence and volatility of the cuent account. 3.1 Setup Conside a small open economy inhabited by a continuum of identical consumes located in a unit inteval. A consume s lifetime expected utility is E t P 1 j=0 j u (C t+j ) whee C t denotes 12 We emove the stochastic tend in the net output by the log di eence athe than Hodick-Pescott lte, in contast to Luo, Nie, and Young (2012). 13 Hee, we measue the st-ode autocoelation using the OLS estimato of the AR(1) model. 5

7 consumption and is the discount facto satisfying 2 (0; 1). Also, E t [] epesents the expectations opeato conditional on the infomation available in peiod t. Following Uibe and Schmitt-Gohé (2017), we specify u () as u (C t ) = 0:5 C t C 2, whee C is the bliss point so that C t < C fo all t. The consumes ow budget constaint is A t+j+1 = (1 + )A t+j + X t+j C t+j ; (1) fo all j > 0. Hee, A t denotes foeign asset holdings at the beginning of peiod t. In this budget constaint, consumes have access to pefect intenational capital makets whee capital can be saved o boowed at a constant wold inteest ate. To facilitate the analysis, we assume that the ate of time pefeence is equal to : = 1= (1 + ). Finally, X t is the exogenous stochastic endowment which we can also intepet as net output. The st-ode condition implies that C t = E t C t+j fo j = 1; 2; :::. The optimal consumption is given by C t = A t + X p t ; (2) whee X p t is the non- nancial pemanent income given by X p t = [= (1 + )] P 1 j=0 (1 + ) j E t X t+j. Changes in consumption ae calculated as C t+1 = E t+1 Xt+1, p whee E t+1 denotes a change in the expectations opeato de ned by E t+1 = E t+1 E t. This equation means that consumption between peiods t and t + 1 changes only if changes in the pemanent income ae ecognized by consumes. By the fundamental balance-of-payments identity, the cuent account CA t equals changes in the county s net foeign assets (i.e., CA t A t+1 A t ). Theefoe, using (1) and (2), we have CA t = X t X p t = (1 + ) j E t X t+j ; (3) j=1 meaning that the cuent account is minus the pesent discounted value of futue expected changes in the net output. It is staightfowad to extend this standad RE model with impefect capital mobility. Shibata and Shintani (1998) conside consumes with limited access to the intenational capital maket, as in Campbell and Mankiw (1989, 1990). A faction 1 of consumes have pefect access to intenational capital makets and thei consumption is detemined by (2). The emaining faction 2 [0; 1) of consumes hold neithe intenational nancial assets no liabilities: They ae hand-to-mouth consumes who consume all endowment within a single peiod. When we intoduce the hand-to-mouth consume into the RE model, we call this model the hybid RE model. Denoting the aggegate consumption in the hybid model 6

8 by Ct HY, we expess Ct HY = (1 ) C t + X t. Likewise, let CA HY t be the cuent account in the hybid model. Because hand-to-mouth consumes do not hold intenational nancial assets, CA HY t becomes CA HY t = (1 ) CA t : (4) This implies that the magnitude of the cuent account changes is small compaed to the case of pefect capital mobility descibed by (3). We thus call the degee of impefect capital mobility. 3.2 Chaacteizing the RE models We chaacteize the pue and hybid RE models using (3) and (4). We look at theoetical pedictions fo the pesistence and volatility of the cuent account unde the assumption of AR(1) pocess of the net output gowth. Let g t ln (X t =X t 1 ) be the net output gowth. Assume that g t = (1 ) + g t 1 + " t, whee " t i:i:d: (0; 2 ) and jj < 1. As discussed in Campbell and Deaton (1989), this assumption of the stationay net output gowth ate equies some efomulation of vaiables. In paticula, to ensue the stationaity of the cuent account, we divide both sides of (3) by X t. We obtain ca t CA t =X t = P 1 j=1 (1 + ) j E t (X t+j =X t ). While we will evaluate the model with 6= 0 in Section 5, we tempoaily set = 0 only fo expositional puposes. In this case, the st-ode appoximation of ca t yields ca t ' (1 + ) j E t g t+j = j=1 1 + g t: (5) The left column of Table 2 summaizes the chaacteization of the RE model s pedictions. The popotionality of ca t to g t in (5) implies that the pesistence of ca t should be the same as that of g t, namely, ca =. It also implies that the pedicted volatility is given by V ca = sd (ca t ) =sd (g t ) = = (1 + ). Fom Hall s andom walk hypothesis, it is evident that changes in consumption ae seially uncoelated in the RE model. In ou case with efomulation of vaiables, we de ne c t+1 C t+1 =X t. These newly de ned (nomalized) changes in consumption can be expessed as c t+1 = E t+1 X p t+1=x t ' [(1 + ) = (1 + )] "t+1 by the st-ode appoximation. Since " t is independent and identically distibuted, the pedicted pesistence of changes in consumption is zeo, namely, c = 0. These pedictions of the pue RE model ae inconsistent with the evidence in Section 2. While the model pedicts that ca =, the data suggests that data ca > data, as indicated in Table 1. It also fails to explain the volatility of the cuent account, if we ecall Vca data ' 2. 7

9 Fo the pue RE model to geneate V ca ' 2, taking the wold inteest ate as given, it equies a su ciently lage value of. Fo example, if = 0:04, needs to be as lage as 0:69, as opposed to the data of data = 0: Note also that seially uncoelated changes in consumption, c = 0; is against the data, data c > 0. The hybid RE model can geneate bette pedictions fo the pesistence of changes in consumption (see the ight column of Table 2). Again, denoting c HY t+1 C HY t+1 =X t, we have c HY t+1 ' (1 ) c t+1 + g t+1 in the hybid RE model. Since g t+1 is seially coelated, the assumption of impefect capital mobility leads to pedictable changes in consumption. The esulting HY c takes a fom of HY c = 0 6= 0, whee 0 is a function of and the second moments of c t and g t (see the footnote of Table 2 fo the analytical expession). The impovement can be made at least without in uencing the pedicted pesistence of the cuent account. Because CA HY t = (1 ) CA t fom (4), ca HY t = (1 ) ca t = (1 ) = (1 + ) g t, whee ca HY t CA HY t =X t. The popotionality of ca HY t to ca t means that the st-ode autocoelation of ca HY t is unchanged in compaison to the pue RE model: HY ca = ca =. Howeve, the bette pediction fo the pesistence of changes in consumption is achieved at the cost of undemining the pedicted volatility of the cuent account. The above popotionality also implies that Vca HY = (1 ) V ca, whee Vca HY sd ca HY t =sd (gt ). Since 2 [0; 1), the volatility of ca HY t is dampened by. Theefoe, fo the hybid RE model to geneate V ca ' 2, the hybid model needs an even lage value of than the pue RE model. Fo example, if = 0:04 and = 0:50, the hybid RE model equies that = 0:83, which is lage than 0.69 equied in the pue RE model The SI models To impove pedictions of the ICA model, we eplace RE in the ICA model with SI. In this section, we leave the detailed maximization poblem of the SI model to Appendix A.1 and focus on how the cuent account dynamics ae descibed in the SI model. 4.1 Setup Let us assume that, in evey peiod, only andomly selected 1! faction of consumes update thei infomation set and that the emaining faction! 2 [0; 1) of consumes do not 14 Solving V ca ' 2 = = (1 + ) fo yields ' 2 (1 + ) =3. When = 0:04, tuns to be Solving Vca HY ' 2 = (1 ) = (1 + ) fo yields = 2 (1 + ) = (3 ). If we evaluate it at = 0:04 and = 0:50, ' 0:83. 8

10 update thei infomation set. We call! the degee of infomation igidity. Ou assumption simpli es the SI model of consumption by Reis (2006), who consides endogenous infequent infomation updating. 16 Despite the simpli cation, as we will late show, the model pedictions ae vey simila to Reis (2006). Given infequently updated infomation, consumes make decisions as ationally as they can. Suppose that a consume updated his infomation in peiod t and does not obtain new infomation in t + 1. In this case, he does not change his consumption in peiod t + 1 since he ecognizes no changes in the pemanent income. He sticks to a consumption plan that he could make in peiod t. Theefoe, if the infomation is not updated in peiod t + 1, any shock in peiod t + 1 is unecognized and absobed by the consume s saving. Reis (2006) efes to consumes who stick to thei consumption plans as inattentive consumes. Moe fomally, an inattentive consume who has peiod-t infomation chooses the ex ante optimal plan of consumption fc t+j;j g 1 j=0, whee C t+j;j is consumption chosen fo peiod t + j with j-peiod delay of infomation. Note that C t;0 epesents consumption that the consume enjoys in peiod t with full infomation. This C t;0 must be the same as the optimal consumption unde the RE model. If the consume does not eceive new infomation until peiod t + j, the consume chooses C t+j;j that was planned in peiod t. Note also that C t+j;j = C t;0 is satis ed because the inattentive consume peceives no changes in his pemanent income. Theefoe, fo j = 1; 2; :::, we have C t+j;j = C t;0 = A t + X p t : (6) Let S t+j;j be changes in the foeign asset holdings of the consume in peiod t+j, conditional that his infomation was updated in peiod t but has not been updated until peiod t + j. Then, S t+j;j is given by S t+j;j = A t+j + X t+j C t+j;j ; (7) whee A t+j follows (1) evaluated at C t+j = C t+j;j. That is, A t+j+1 = (1 + ) A t+j + X t+j C t+j;j. While S t+j;j in (7) looks simila to the cuent account in the RE model, they need to be distinguished in two aspects. Fist, S t+j;j absobs all changes in endowment between t and t + j, togethe with etuns of the unintended change in the foeign asset holdings. Using 16 In Reis (2006), consumes face the cost of obtaining and pocessing infomation and decide whethe to update thei infomation and ecompute the optimal consumption plan. In ou setting, the infomation updating is exogenously given. 9

11 (6), we can ewite S t+j;j as S t+j;j = (A t+j A t ) + X t+j X p t = (A t+j + ::: + A t+1 ) + X t+j + ::: + X t+1 + S t;0, fo j = 0; 1; 2; :::; (8) whee S t;0 = X t X p t which equals the cuent account unde the RE model. Unde SI, the inattentive consume s consumption (C t+j;j ) does not espond to the unecognized changes in endowment between peiods t and t + j. In (8), saving absobs all unecognized changes in endowment X t+1, X t+2,:::, X t+j. Accodingly, changes in the inattentive consume s foeign asset holdings also include etuns fom the unecognized changes in endowment (i.e., (A t+j + ::: + A t+1 )). We ewite (8) ecusively as 17 S t+j;j = (1 + ) S t+j 1;j 1 + X t+j fo j = 1; 2; 3; :::: (9) The second aspect that should be distinguished fom the cuent account in the RE model is that changes in foeign asset holdings di e acoss inattentive consumes, depending on how they update thei infomation. To obtain the cuent account in the SI model, we need to aggegate individual foeign asset holdings acoss all inattentive consumes. Based on the assumption of infomation updating, the cuent account in the SI model is CA t = (1!)! k S t;k ; (10) whee S t;k is the peiod-t changes in the inattentive consume s foeign assets based on the infomation in peiod t k. Using (9), S t;k can also be witten as k=0 S t;k = (1 + ) S t 1;k 1 + X t ; (11) whee S t k;0 = X t k X p t k. It is again staightfowad to extend the SI model with impefect capital mobility. The aggegate consumption is given by C HY t = (1 ) C t + X t and the cuent account is given by in the hybid SI model so that (4) continues to hold. 18 CA HY t = (1 ) CA t (12) 17 See Appendix A Reis (2006) also povides the micofoundation fo (12). In paticula, consumes may stick to saving plans and let thei consumption espond to unecognized shocks to endowment, instead of sticking to consumption 10

12 4.2 Chaacteizing the SI models We chaacteize the SI and the hybid SI models using (10) (12). We establish popositions fo the cuent account and changes in consumption unde the pue SI model. We then discuss the hybid SI model Pesistence and volatility of the cuent account The following poposition descibes cuent account dynamics unde the pue SI model: Poposition 1 Suppose that inattentive consumes update thei infomation with the pobability of 1! evey peiod. Suppose also that the degee of infomation igidity! is su ciently low such that! (1 + ) < 1. Then, the cuent account is given by CA t =! CA t 1 + (1!) S t;0 +!X t ; (13) whee S t;0 = X t X p t and! =! (1 + ). Futhemoe, suppose that the net output gowth follows a covaiance-stationay AR(1) 1 + " t, whee " t i:i:d: (0; 2 ). Then, ca t can be appoxi- pocess with mean zeo: g t = g t mated by the AR(2) pocess: Poof : See the Appendix A.3. ca t = (! + ) ca t 1 (! ) ca t 2 +! 1 + " t: (14) The st pat of Poposition 1 tells us that the cuent account is witten as the st-ode di eence equation with the two diving foces. The st diving foce is S t;0, changes in foeign asset holdings unde full infomation. The impact of S t;0 becomes weake as! becomes highe. The second diving foce is X t. A faction! of inattentive consumes with old infomation let thei saving absob unecognized shocks to endowment. Fo this eason, X t appeas in (13) with its coe cient!. Also, ecall that the e ect of unecognized changes in endowment on CA t is caied ove to the subsequent peiods with inteest eanings. Theefoe, plans and letting thei saving espond to shocks. He efes to such consumes as inattentive saves. Reis (2006) shows that, if the costs of planning ae not too small, it is optimal fo inattentive saves not to e-plan thei savings at all. This esult suggests that inattentive saves behave like consumes without any access to the intenational capital maket, since thei consumption is pefectly coelated with endowment. If the initial assets of inattentive saves ae zeo, the pesence of inattentive saves epoduces the same equation as (12). 11

13 as! =! (1 + ) inceases, the coe cient on CA t 1 becomes lage, making CA t moe pesistent. Tuning to the second pat of the poposition, ca t follows the AR(2) pocess, genealizing (5) in the RE model. Indeed, substituting! =! (1 + ) = 0 in (13) esults in the AR(1) pocess ca t = ca t 1 = (1 + ) " t. Compaing ca t = = (1 + ) P 1 j=0 j " t j with g t = P 1 j=0 j " t j implies ca t = = (1 + ) g t, epoducing (5). The pesistence of ca t is now inceasing in! so that the pue SI model can geneate a pesistent cuent account even when net output gowth is not pesistent. In paticula, the st-ode autocoelation of ca t is calculated as (! + ) = (1 +! ) fom (14) as long as! 6=. The left panel of Figue 1 shows the st-ode autocoelation of the cuent account against!. 19 The blue line is the pesistence unde = 0:20, while the ed line is that unde = 0:80. We econ m that pesistence of the cuent account inceases with!, egadless of the value of, except fo the case of! =. If! happens to equal, the coe cient on " t is zeo in (14) and the cuent account is constant fo all t. Ou esult on the pesistence of the cuent account can be summaized in the next coollay: Coollay 1 cuent account ca t is given by Unde the pue SI model with = 0, the st-ode autocoelation of the ca =! + 1 +! ; (15) and is always geate than ca = unde the pue RE model, as long as! 6=. We move on to volatility of the cuent account in the SI model. Equation (14) implies the following coollay: Coollay 2 Unde the pue SI model with = 0, the volatility of the cuent account V ca = sd (ca t ) =sd (g t ) is given by s s 1 +! V ca = (! ) 2 (1! ) [1 (! ) 2 ] (1 + ) 2 : (16) The middle panel of Figue 1 plots the volatility against!. The volatility deceases with! if! < and inceases with! if! >. When = 0:20, the volatility inceases with! ove a wide ange of!. Theefoe, even when takes a low value as in the data, the SI model can geneate a volatile cuent account with a lage value of!. By contast, as shown in the ed line, when = 0:80, the volatility inceases with! ove a vey naow ange of!. 19 Hee, we set = 0:04 to plot the cuves. We also choose the ange of! 2 [0; 0:96], which ensues the stationaity of the cuent account. 12

14 4.2.2 Pesistence of consumption gowth It is wothwhile discussing pesistent changes in consumption in the SI model. Using the model with endogenous infequent infomation updating, Reis (2006) demonstates that his SI model of consumption can successfully geneate pedictable changes in consumption. We con m pesistent changes in consumption unde exogenous infequent infomation updating. In the next poposition, we analytically deive the stochastic pocess of c t+1 : Poposition 2 Suppose that inattentive consumes update thei infomation with the pobability of 1! evey peiod. Suppose also that the degee of infomation igidity! is su ciently low such that! (1 + ) < 1. Then, changes in the consumption ae given by C t+1 =! C t + (1!) E t+1 X p t+1: (17) Futhemoe, suppose that net output gowth follows a covaiance-stationay AR(1) pocess with mean zeo: g t = g t by the AR(1) pocess: Poof : See the Appendix A " t, whee " t i:i:d: (0; 2 ). Then, c t+1 can be appoximated c t+1 =! c t + (1!) " t+1: (18) As is clea in (18), the pesistence of changes in consumption citically depends on!. In the ight panel of Figue 1, we plot the st-ode autocoelation of c t. It has a one-to-one elationship with!. Fo example, when! = 0:80 and = 0:04, c = (1 + )! = 0:83. We summaize this esult in the following coollay: Coollay 3 Unde the pue SI model with = 0, the st-ode autocoelation of c t is given by c =!, and is always geate than c = 0 unde the pue RE model. We have two additional emaks on changes in consumption. Fist, not supisingly, the dynamic popeties of changes in consumption ae vey close to those in Reis (2006). His poposition 2 states that, when the maximum length of time duing which consumes ae inattentive is q peiods, changes in consumption follow the MA(q) pocess with monotonically deceasing MA coe cients. In ou SI model, the maximum length of time of being inattentive is in nity and the MA(1) epesentation of the AR(1) pocess (18) implies that MA coe cients ae exponentially decaying. 13

15 Second, as Reis (2006) agues, the epesentative-agent habit fomation model can be an altenative explanation fo pesistent changes in consumption. It can be shown analytically that the cuent account in the habit fomation model is the obsevational equivalent to the cuent account in the SI model. In paticula, if the peiod utility in the habit fomation model is given by u(c t C t 1 ) and the habit paamete is equal to!, the cuent account in the habit fomation model follows the same stochastic pocess as that in ou SI model. Theefoe, the two models ae indistinguishable in the aggegate data. 20 In the mico data, howeve, thee ae mixed evidence fo the pesence of habit fomation. 21 In addition, while the stuctue of SI models suggest disageements about expectations, some empiical studies based on the mico suvey data suppot such disageements about expectations on main economic vaiables. Fo example, Doven, Fitsche, and Slacalek (2012) epot disageement among pofessionals fo main economic indicatos including GDP gowth in G7 counties. Mankiw, Reis, and Wolfes (2003) and Coibion, Goodnichenko, and Kuma (2018) nd much stonge disageement among economic agents such as households and ms than among pofessional foecastes. While Gube (2004) nds that the epesentative-agent habit fomation model pefoms bette than the model without habits in pedicting the cuent account dynamics, the bette pefomance of his model may also e ect the pesence of SI. An advantage of ou SI model is that the explanation based on SI is boadly in line with the above evidence fom the mico data Impulse esponses To bette undestand the cuent account in the SI model, it is helpful to investigate the impulse esponse functions. Figue 2 plots the impulse esponse functions of g t, ca t, and c t to one unit incease in " t. The leftmost panel points to the impulse esponse of g t. Hee we set at 0:20, so the esponse of g t decays quickly. In the middle and ight panels, we compae the esponse of ca t and c t unde the RE model (! = 0) and the SI model (! = 0:20 o 0:80). Let us st conside the impulse esponse functions of ca t and c t unde the RE model (! = 0). As shown in the blue line in the middle panel of Figue 2, the cuent account declines in esponse to " t. Because the shock has a positive pemanent e ect on endowment, consumes pemanent income inceases moe than the cuent endowment. In this case, inceases in consumption at the impact peiod ae lage than those in endowment at the 20 See also Caoll, Slacalek, and Somme (2011) fo the similaity between the habit fomation model and thei sticky expectations model. 21 Fo example, see Dynan (2000) and Guaiglia and Rossi (2002) among othes. 14

16 same peiod. As a esult, the economy uns cuent account de cits. How do the impulse esponses di e in the SI model (! > 0)? When! = 0:20, the cuent account is nealy constant, as the coe cient on " t in (14) is close to zeo. To peceive the intuition, ecall that inattentive consumes let thei saving absob unecognized shocks between peiods of planning. Even though a pemanent e ect on endowment inceases the pemanent income of all consumes, some consumes do not educe thei saving. Instead, they unintentionally incease thei foeign asset holdings. The unintended inceases in foeign asset holdings o set eductions in foeign asset holdings esulting fom a pemanent shock to endowment. If the degee of infomation igidity is su ciently high (e.g.,! = 0:8), the cuent account inceases. In esponse to a positive shock " t, unintended inceases in foeign asset holdings exceed deceases in foeign asset holdings. In this case, the inceases in consumption ae smalle than those in endowment at the impact peiod. As a esult, the economy uns the cuent account suplus The hybid SI model Figue 3 plots the pesistence and volatility of the cuent account and the pesistence of changes in consumption against! unde the pue and hybid SI models. In the gue, we set = 0:50 fo the hybid SI model. The value is boowed fom the simple aveage of estimates in Shibata and Shintani (1998) who estimate of 11 developed counties. The popotionality of ca HY t to ca t is fully peseved in the hybid SI model. The elationship of HY ca = ca continues to hold in the hybid SI model, and the cuve fo HY ca taces out the upwad-sloping cuve fo ca in the left panel of Figue 3. Theefoe, HY ca can also be high unde infomation igidity. This esult is summaized in the following coollay: Coollay 4 cuent account ca HY t the pue SI model. Unde the hybid SI model with = 0, the st-ode autocoelation of the is given by HY ca = (! + ) = (1 +! ) and is the same as that unde Tuning to the volatility of the cuent account, the popotionality of ca HY t to ca t continues to imply that Vca HY = (1 ) V ca. The dashed line coesponds to the hybid SI model with = 0:50, while the solid line points to the pue SI model (i.e., = 0). The dashed line in the middle panel of Figue 3 indicates that the volatility of the cuent account in the hybid SI model is educed in compaison to the solid line. Howeve, V ca on the ight-hand side can incease with! as long as! 2 (= (1 + ) ; 1), as in the case of the pue SI model. 15

17 When takes a low value and! is su ciently lage, the cuent account can be volatile in the hybid SI model. coollay: The analytical expession fo V HY ca is povided by the following Coollay 5 Unde the hybid SI model with = 0, the volatility of the cuent account = sd ca HY t =sd (gt ) is given by V HY ca V HY ca = (1 ) V ca = (1 ) s 1 +! (1! ) [1 (! ) 2 ] s (! ) 2 (1 + ) 2 : (19) How can we descibe the pesistence of changes in the aggegate consumption in the hybid SI model? Recall that changes in the aggegate consumption c HY t+1 is a convex combination of c t+1 and g t+1. We demonstate that pesistence of changes in the aggegate consumption is a weighted aveage of pesistence of c t and g t, that is,! and. analytical expession fo the pesistence of changes in consumption in the hybid SI model is summaized by the following coollay: The Coollay 6 Unde the hybid SI model with = 0, the st-ode autocoelation of c t is given by the weighted aveage of! and : whee 2 [0; 1] is a weight given by HY c = (1 )! + ; (20) = (; ;!) = Poof : See the Appendix A.5. 2 V a (g t ) + (1 ) Cov (g t ; c t ) (1 ) 2 V a (c t ) + 2 (1 ) Cov (g t ; c t ) + 2 V a (g t ) : (21) The pesistence of changes in the aggegate consumption in the hybid SI model no longe has a one-to-one elationship with!. The exteme ight panel of Figue 3 plots the pesistence of changes in the aggegate consumption in the pue and the hybid SI models. When! is low, the dashed line is located above the solid line, inceasing the oveall pesistence of changes in the aggegate consumption by means of the pesistence of net output gowth. When! is lage, the dashed line is located below the solid line, peventing the oveall pesistence fom inceasing. 22 In othe wods, impefect capital mobility beaks the tight link 22 The dashed line in the ight panel of Figue 3 also shows that the pesistence of changes in the aggegate 16

18 between the pesistence of changes in consumption and the degee of infomation igidity. 5 Assessment of the SI models This section assesses the SI models in compaison to the RE models. 5.1 Methodology We begin by slightly genealizing the pue SI model with the possibility of the non-zeo mean gowth ate of g t, i.e., 6= 0. While this genealization does not a ect the steady state of c t, the steady state value of ca t is no longe zeo. 23 To addess the non-zeo steady state, it would be convenient to de ne c^a t and ^g t by c^a t ca t E (ca t ) and ^g t g t, espectively. The following poposition genealizes the second pat of Popositions 1 and 2: Poposition 3 Suppose that infomation igidity is pesent as in Popositions 1 and 2. Suppose also that net output gowth follows a covaiance-stationay AR(1) pocess with nonzeo mean: g t = (1 ) + g t 1 + " t, whee " t i:i:d: (0; 2 ). Assume that and! ae both su ciently low such that < and!! (1 + ) = (1 + ) < 1. The stochastic pocess of c^a t and c t+1 can be appoximated by c^a t =! + c^a t 1! c^a t 2 +! (1 + ) = (1 + ) " t; (22) and c t+1 =! c t + (1!) espectively. Poof : See the Appendix A.6. (1 + ) (1 + ) 1 + (1 + ) " t+1; (23) Hee we impose a estiction that the net output gows at a slowe ate than the foeign asset holdings: <. We equie this assumption to ensue the stationaity of the non- nancial pemanent income scaled by the net output. 24 A positive slightly deceases consumption deceases with!, even though an incease in! geneally aises the pesistence of c t, which is included in c HY t. The decline occus because the weight in (20) inceases as!! See (34) in Appendix A.3.2. If the net output has a positive deteministic tend, the economy is sustainable unde the cuent account de cit in the steady state. 24 To undestand the stationaity, conside the non- nancial pemanent income scaled by the net output, X p t =X t = = (1 + ) P 1 j=0 (1 + ) j E t (X t+j =X t ) = = (1 + ) + = (1 + ) P 1 j=1 (1 + ) j Pj i E t hexp k=1 g t+k. In the nonstochastic steady state, the non- nancial 17

19 the pesistence of the cuent account and consumption gowth, since a highe negatively in uences!. Obviously, these esults ae applicable to the RE models and can be extended to the hybid SI model. Befoe we discuss the pefomance of the SI models, let us quickly econ m the poo pefomance of the RE models unde nonzeo. Table 3 summaizes pedictions of the pue and hybid RE models fo the theoetical moments. The left panel epots the pedictions of the pue RE model. They ae inconsistent with the actual moments (shown in the most ight panel) even if nonzeo is taken into account. The pedicted pesistence of the cuent account is 0.16 on the coss-county aveage, which is much lowe than the obseved pesistence of The pedicted volatility is 0.44 on aveage, again much lowe than the data of Of couse, changes in consumption have no pesistence unde = 0. The poo pefomance can also be econ med unde = 0:5. As we discussed in Section 3, the hybid RE model can geneate seially coelated changes in consumption at the cost of undemining the pedicted volatility of the cuent account. While the pesistence of changes in consumption is slightly positive (0.05 on aveage) due to impefect capital mobility, the pedicted volatility of the cuent account is educed fom 0.44 in the pue RE model to 0.22 in the hybid RE model. To assess the SI models, we estimate! and using the data of 16 developed OECD counties listed in Table 1, athe than using pe-speci ed values of! and. We obtain! and to match the theoetical moments of the pesistence and volatility of the cuent account and the pesistence of changes in consumption with the sample moments in each county. Let f () be a vecto of distances between the theoetical and sample moments fo the pesistence and volatility of the cuent account and the pesistence of changes in consumption, whee denotes the vecto of paamete consisting of! and. In the case of the hybid SI model, fo example, f () = 0. HY ca () data ca ; Vca HY () Vca data ; HY c () data c Using the data of cat and c t in each county, we obtain the weighting matix ^W fom the invese of the bootstap 0. covaiance matix of ; V data ; data 25 The objective function Q () to be minimized is data ca de ned by the quadatic fom: ca c Q () = f () 0 ^W f () : When minimizing Q (), we impose the estiction that! 2 [0; (1 + ) = (1 + )) to ensue pemanent income scaled by the net output educes to = (1 + ) P 1 j=0 [(1 + ) = (1 + )]j. Fo this expession to be non-explosive, must be lowe than. See also Campbell and Deaton (1989). 25 A block bootstap method with a block length of fou is employed to compute the bootstap covaiance matix. 18

20 that! < 1 fo both of the pue and hybid SI models. We futhe impose the estiction that = 0 in the pue SI model and 2 [0; 1) in the hybid SI model, espectively. The minimizes of Q () ae denoted by ~ = (~!; 0) 0 fo the fome and ^ = (^!; ^) 0 fo the latte, espectively. 5.2 Pedictions of the SI models The left panel of Table 4 shows the pedictions of the pue SI model and the middle panel pesents those of the hybid SI model. The two models pedictions ae based on ou estimates of! and, which we will discuss in the next section. Fo compaison, the ight panel again epots the actual moments fom the OECD counties. Let us st conside the pue SI model. compaison to the RE models in Table 3. Oveall, it exhibits a geat impovement in Fo example, the pue SI model can almost fully account fo the thee tageted moments in the Nethelands. In paticula, the pedicted moments ae ( ca ; V ca ; c ) = (0:83; 2:05; 0:76), as opposed to the actual moments: ; V data ; data = (0:85; 2:07; 0:74). The SI model also pefoms well in othe counties, data ca ca c though all moments ae not fully explained. Fo example, the pedicted moments in Denmak ae ( ca ; V ca ; c ) = (0:77; 1:75; 0:78), while the actual moments ae (0:94; 3:73; 0:20). This outcome is a emakable impovement in pedictions elative to the RE models, because the RE models pedict ( ca ; V ca ; c ) = ( 0:01; 0:02; 0:00) and HY ca ; Vca HY ; HY c = ( 0:01; 0:01; 0:01). While the pue SI model emakably impoves pedictions of the cuent account, it tends to ovepedict the pesistence of changes in consumption. In paticula, c is 0.65 in the coss-county aveage but the actual pesistence is only 0.25, which is much lowe than in the model. The ovepediction stems fom the one-to-one elationship of c =! =! (1 + ) = (1 + ) in (23). That is, although a lage! helps the SI model explain the pesistence and volatility of the cuent account, the one-to-one elationship between c and! also inceases the pesistence of changes in consumption fa beyond the obseved pesistence. The hybid SI model beaks the tight link. The middle panel of Table 4 pesents the theoetical moments geneated by the hybid SI model. The hybid SI model continues to pedict a pesistent and volatile cuent account but now with a modeate degee of pesistent consumption gowth. In the example of Denmak, the pediction of the hybid SI model is HY ca ; Vca HY ; HY c = (0:98; 3:83; 0:21) as opposed to the data of (0:94; 3:73; 0:20). In tems of the coss-county aveage, the pedicted pesistence and volatility of the cuent account is 0.94 and 2.39, espectively. Unlike that in the pue SI model, the pedicted pesistence of 19

21 changes in consumption is now suppessed to 0.34, which is faily close to the data of It may not be supising that impefect capital mobility leads to the good pefomance of the SI model because the hybid SI model has one additional fee paamete. Howeve, impefect capital mobility alone does not necessaily impove the pedictions, unless infomation igidity is incopoated. When we estimate in the hybid RE model with the same objective function, the estimated tuns out to be zeo in 11 out of 16 counties. 26 In ou execise, the impovement of pedictions ae achieved only unde the infomation igidity. 5.3 Degees of infomation igidity and impefect capital mobility While the hybid SI model achieves a faily good model pefomance, we should note a caveat in the estimated values of! and. The hybid SI model can achieve good pefomance unde elatively high degees of infomation igidity and impefect capital mobility. Table 5 shows! and that ae estimated fo each county in the two SI models. On aveage, ^! is 0.64 in the pue SI model and 0.89 in the hybid SI model. These values imply that the aveage duation of holding infomation until the next update is 2.8 yeas in the pue SI model and is 9.1 yeas in the hybid SI model. 27 The latte value seems extemely lage compaed to the aveage duation estimate of 1.3 yeas obtained by Mankiw and Reis (2007). We also note that an impovement with the hybid SI model elies on a high degee of impefect capital mobility in some counties. While ^ is only 0.08 in the Nethelands, it is almost one in Belgium and Gemany unde the paamete estiction of 2 [0; 1). Oveall, howeve, the coss-county aveage of ^ is This aveage is not extemely high in the consumption liteatue though it may be consideed to be high compaed to the estimates of some pevious studies. 28 Fo single county s estimates, they ae statistically signi cant in many counties. In the ight panel of Table 5, we epot Q( ~ ) Q(^), the di eence between the objective functions evaluated at ~ and ^. The di eence is asymptotically distibuted as 2 (1) unde the null hypothesis of = 0. In 11 out of 16 counties, is found to be statistically signi cant at the conventional signi cance level. An intepetation of the high degees of infomation igidity and impefect capital mobility may be that the ICA model does not allow fo othe possible fictions and that the 26 The counties in which the estimated is zeo ae Austalia, Austia, Belgium, Canada, Denmak, Finland, Iceland, Italy, Japan, Noway, and Sweden. We also nd that the estimated tuns out to be unity in fou counties of Fance, Gemany, the Nethelands, and the UK. 27 Given the annual data, the aveage duation of holding infomation until the next update can be computed fom (1 0:64) 1 = 2:8 and (1 0:89) 1 = 9:1. 28 Fo example, Campbell and Mankiw (1990) use the US data and estimate to ange between 0.30 and Reis (2006) estimates, consideing SI explicitly. His estimate of is quite low, a value between 0.05 and

22 estimated paametes may e ect such fictions outside the model. Theefoe, while the SI model continues to be a pomising appoach to explaining the cuent account, intoducing othe types of fictions and/o shocks into SI model may esult in moe easonable estimates fo the degees of infomation igidity and impefect capital mobility. 6 Conclusions This pape extends the intetempoal cuent account (ICA) model with sticky infomation (SI). In ou ICA model, consumes ae inattentive to shock to net output and infequently update thei infomation, as developed by Mankiw and Reis (2002, 2007) and Reis (2006). Unde the assumption that a pemanent shock to net output dives the cuent account, the ational expectations model fails to pedict a pesistent and volatile cuent account as well as pesistent changes in consumption. In ou SI models, infomation igidity impoves the pedicted pesistence and volatility of the cuent account. If the SI model is extended with impefect capital mobility as in Shibata and Shintani (1998), ou SI model exhibits a faily good pefomance in pedicting changes in consumption as well as the cuent account. In paticula, the SI model almost pefectly explains the data of the 16 OECD counties if the degees of infomation igidities and impefect capital mobility ae su ciently high. Ou analysis also suggests that these fictions may need to be intoduced into a iche model of the cuent account to educe too much eliance on impefect infomation and impefect capital mobility. Towad this end, it may be impotant to conside the poduction economy and to include othe fictions in the ICA model. 29 Consideation of othe shocks, such as the wold inteest ate shock and the exchange ate shock, may also be helpful. 30 Extending the ICA model in these diections unde infomation igidity would be an impotant step fo futue eseach. Refeences [1] Begin, P. R. and S. M. She in (2000). Inteest ates, exchange ates and pesent value models of the cuent account, Economic Jounal, 110 (463), pp [2] Bilbiie, F. O. (2008). Limited asset makets paticipation, monetay policy and (inveted) aggegate demand logic, Jounal of Economic Theoy, 140 (1), pp One of the most impotant avenues of eseach may be the geneal equilibium model with SI by Ekinci (2017), although he focuses on a two-county model athe than on small open economies. 30 Fo example, see Begin and She in (2000) and Kano (2009). 21