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Modern Economy, 2012, 3, 695-711 http://dx.doi.org/10.4236/me.2012.35090 Published Online September 2012 (http://www.SciRP.org/journal/me) Welfare-Enhancing Accumulation of Foreign Reserves* Hiroya Akiba School of Political Science & Economics Waseda University, Tokyo, Japan Email: hiroyaakiba@hotmail.com Received December 14, 2011; revised February 14, 2012; accepted February 22, 2012 ABSTRACT This paper considers if huge accumulation of foreign reserves by some countries is optimal in a simple, intertemporal, and welfare maximization model with loss aversion. The optimality condition is shown to depend on several underlying parameters of the model. Configuration of output shocks and probability of bad state reveal that, controlling other pa- rameters, huge accumulation of foreign reserves of China and Japan is consistently interpreted as optimal within the model. We also consider if external debts serve as alternative optimal precautionary methods. The optimal precaution- ary saving is also shown to be welfare-enhancing with loss aversion. Keywords: Foreign Reserves; Loss Aversion; Precautionary Saving 1. Introduction It has been recognized that foreign reserve accumulation is costly for governments, and the costs must be com- pensated by the benefits from reserve holding. In the real world, foreign reserves have been accumulated, but the essential problem has not only been the accumulation itself, but also its uneven distribution across developed and developing nations. This uneven holding is a source of the unresolved issue called as the global imbalance (Corden [1], McKinnon [2] and Roubini [3]). For exam- ple, at the end of 2010, reserve of China and Japan con- stituted 2300 billion SDRs, more than 40 percent of the total world foreign reserves (minus gold). From historical data, foreign reserves of China and Japan have increased drastically by 11.4 and 2.4 times over the last decade (see Figures 1(a) and (b))1. If reserve holding is costly, it is also puzzling that such huge reserves have been accumulated by some countries, because the demand for reserves was believed to dimin- ish since the advent of the general floating from 1973. Contrary to this prediction, it is a historically observed fact that accumulation grew fast under exchange rate flexi- bility, known as the Frenkel’s paradox in the literature (Bastourre et al. [4] and Frenkel [5])2. The optimal level of foreign reserves is defined as the level that maximizes the (utility of) net benefit which is, in turn, defined as the difference between the total benefit and the total cost associated with reserve holding. How- ever, the optimal level has long been examined mainly from the cost side, while keeping the benefit side fixed consciously or unconsciously. There are several excellent surveys focusing on the minimization of the costs (Bah- mani-Oskooee et al. [6] and Flood et al. [7]). It has been a relatively new tendency to consider the optimal level from the benefit side. In the next Section 2, the author will present a non-exclusive survey of the recent litera- ture of the optimal reserves examined mainly from the benefit side. Although several rules of thumb have been proposed for practical level of foreign reserves for policy makers such as maintaining reserves equivalent to three months of imports or full coverage of total short-term foreign debt known as the “Greenspan-Guidotti” rule (Jeanne and Ran- cière [8,9]; Obstfeld et al. [10])3, recent literature based on rigorous optimization frameworks propose that foreign reserves are explained by such motivations as self-insura- nce (or precautionary motive or buffer stock; e.g., Aizen- man et al. [11-13], Cifarelli and Paladino [14]), financial *Ealier versions of this paper were presented at graduate workshops at Southwest University, Waseda University, and University of Paris. Com- ments and suggestions from Yunfeng Gao, Ivan Deseatnicov, Ruidong Gao, Hui-Ling Li, Yukihiro Iida, Hayato Nakata, Valerie Mignon, Cecile Couharde and other participants are gratefully acknowledged. My thanks also go to Jerry Weng for able research assistance. Any remainingerrors are my own. 1The source is the IMF-IFS On-line. The Figure makes it clear that for- eign reserves have been unevenly distributed, and the vector is now mov- ing clearly from advanced countries to emerging and developing coun- tries during the last decade (Figure 1(b)). 2According to Frenkel [5], central banks’ behavior did not change sub- stantially before and after the Bretton-Woods breakdown in 1973. Be- fore the breakdown, many of the exchange rate arrangements were adjustable peg, and they were managed (not pure) floating afterwards. 3Huge foreign reserves of China and Japan cover their imports for 8.3 and 6.5 quarters, respectively, as of December 2010. Also, their foreign reserves are more than 10.2 and 7.9 times larger than those suggested by the “Greenspan-Guidotti” rule, as of December 2010. For the rules o f thumb results for other Asian countries, see, e.g. Park and Estrada [18]. C opyright © 2012 SciRes. ME H. AKIBA 696 Foreign Reserve minus Gold (bil.SDR) 2001 Q1 2010 Q1 China,M.L.141.9 1622.6 Japan28.17 668.7 Taiwan87.8 233.8 Korea74.9 179.3 Hong Kon g 90.9 170.4 Brazil27.1 159.8 India31.9 172.2 Singapore61.5 129.8 1622.6 668.7 233.8 179.3 170.4 159.8 172.2 129.8 0 200 400 600 800 1000 1200 1400 1600 China,M.L. Japan Taiwan Korea Hong Kong Brazil Indi a Singapore 1800 2001 Q1 2010 Q1 Unit: Billion SD R (a) 0 10 20 30 40 50 60 70 Develop Asia Advanced Europe Middle East West He misphere Africa C&E Europe Emer & Develop 2001 Q1 2010 Q1 (b) Figure 1. (a) Large holders of foreign reserves. Data source: IMF-IFS on-line, accessed on April 28, 2011; (b) Regional dis- tribution of foreign reserves. Data source: see (a). stability “to support the overaly of holding foreign re- serves increases for a higher measure of loss aversion. A similar interpretation to the preceding case (1) applies to this case when the instantaneous (period) utility function f consumption. Since a mar- wise. Also, if (20) is evaluated at the initial point where α sitive to loss aversion. 27The Japanese average annual growth rate of the “lost two decades” (1992-2011) is only 0.87%. The lowest growth rate is –6.29% in 2009 (IMF-World Economic Outlook, April, 2011). According to Figure 2, utility is increased by reserve accumulation at a point where p= 0.6 and α = –0.6. This “indifference curve” shows the same utility for a lower p with a higher α. A similar indifference relation is observed in Figure 3 where, for example, p = 0.8 with α = –0.3. Thus, Japan is an example o f case (bthe Bloomsberg’s report dated April 21, 2011 (http://www.bloomm/news), the 28 J arch 11, 2011 is estimated as 16.9 trillion yen, about 3.5% o is closer to a linear function o ginal increase in loss aversion for a linear utility function implies a decrease in the expected utility level, the desir- ). Accroding to sberg.co “sovereign vulnerability index ranks Japan as the second most vulnerable”, next to Greece. The USA was ranked 5th. According to the press release by the Japanese Cnet Office dated une 24, 2011, the total loss incurred by the “Great East Japan Earth- quake” on M abi ability of holding foreign reserves increases than other- = 0, the whole expression reduces to 0, i.e. the desirabil- ity of holding foreign reserves as a buffer stock is insen- f t the end of 2010, while that of Chine was 49%. 11)). the 2010 nominal GDP (479.2 trillion yen). The Japanese foreign reserve ratio to GDP was 19% a (Author’s calculation based on the IMF’s World Economic Outlook (April, 20 Copyright © 2012 SciRes. ME H. AKIBA Copyright © 2012 SciRes. ME 706 ts o nel Fores) Table 1. Comparative statics results for benefi Pa Parameter R ( f foreign reserves (R) and external debts (B). A eign Reserv p 12 222 1 Uu FK pR p 1 1 σ 12 222 1FK Rp 1 1p Uu p α 12 2 1 Uu FK p Rp 1 1121p p φ 12 Uu FK 221 1Rp 1 1p p δ - β 2 1 21 1 uY UFK Bp 1 [11 21p Note: Evaluated at R = B = 0. Panel B nal Debts): No Defaulting B (International Debts): Defaulting* Parameter B (Internatio p 12 221 1 1 Uu FK pB p 2 21 2 pB 2 91 211 1 uFK p U σ 21 1p 12 22 Uu FK p B 2 1p 1 2 B 2 121 1 1 u pp FK p U α 2 2 1 11121 FK p pp p 1 U B u U B F 211 1211K pppp 1p 1 2 u φ 12 2 1 211 (1) Uu FK Rp pp 2 2211 11 1 u FKpp p p 1 R U δ - 2 2 1112 1 u pFK p 1 B U β 2 2 1 1111 21 B uFK p p 1 U 1 2 (121 11 U B 2 1 u p ) 1 11 F Kp p Note: Evaluated * at R = B = 0. means evaluated at rB = 0 and δ = 0. H. AKIBA 707 6.3. An Increase in α The third com crease in future output shock, which implies that outp is more uncertain as it fluctuates more widely. The increase in the fluctuation is reflan increase in α. Diffe entiating (18) partially with respect to α, and evaluating at the initial point where the historical level of foreign reserve accumulation is assumed zero and no output un- certainty (α = 0) yields: parative statics exercise is an effect of in- ut ected in r- 1 22 1 111 U R uY F K p pp 21p (21) which is ambiguous in sign, but positive for α > 0.083 under our assumption of = 2, σ = 1 and 12p at the autarky position. Thus, we arriplausible prediction that the desirability of holding foreign reserves is likely to increase when future outes more uncertain than otherwise. 6.4. An Increase in The fourth and the final exercise is an effect of increase itudes milar pro- cedure as in the previous cases, partial differentiation of (18) with respect to yields: ve at a put becom in the att towards risk, . Following a si 1 22 211 1 1 U R uYF Kpp p (22) Thus, if α is set to zero at autarky point, (22) is also zero. It is also positive for 13 if evaluated under our assumptions nd of σ = 1, = 2 a12p. The posi- tive value see it implies that the desir- ability of holdirves is stronger for a higher relative riskalso clear that (22) is posi- tive when σ = ms plausible, ng foreign rese aversion, 1, = 2 as . It is and 13p , regardless of α(>0), iming that reser becomes more desirable with relative risk aversion. In addition to those effects, it should be mentioned that an increase in β, the subjective discount factor, will ce- teris paribus increase the desirability of holding the op- timal level of foreign reserves for a precautionary pur- pose at the zero reserve level, on condition that (18) is unambiguously positive. This plausible implication is simi- lar to the one in Aizenman and Marion [12,13]. Our new finding is that all effects summarized in Equations (20)- (22) are further strengthened by an increase in β. 7. The Optimal International Debts nd compares ith the optimal R. When the state of nature is good, the government has no reason for defaulting, but it is t the government chooses to default when the state is bad. Thus, consumption in period 2 is changed to: plyve holding This section considers the optimal level of B, a it w assumed tha 22 11 111 111 1 HfB CFKrRrB I KrYCIBR (23-1) 2211 111 11 1 1 Lf CKrRIK rY CIBR (23-2) where (1 > δ > 0) is “the additional loss of output in au- tarky, a common feature in sovereign debts models” (Al- faro and Kanczuk [: p. 25). 7.1. Without Defaulting Following a similar procedure as we derived Equation (14) by assuming that the authority neither have external debts nor foreign reserves at the beginning of the first period, or alternatively the historical levels of external debts and foreign reserves are zero, the marginal benefit accru- ing from external debt holding is, for a non defaulting case: 25] 1 2 11 1 12 H HB LLB UuYpuYrr B puYrr (24) The private sector of this economy is assumed to choose their optimal levels of consumption and investment be- fore the monetary authority chooses B optimally. This implies that, for the optimal investment decision, I1, the same condition as Equation (13) is satisfied. Upon sub- stitution of (13), λH, and λL, into (24) yields: 2 1 2 2 1 111 111 B B uY U Bp pFKr pFKr (25) Evaluation of (25) with our assumption rB = 0 (Ai- zenman and Marion [3,4]) reduces (25) to: 1 22 1 11 1111 U B uY F K p pp (26) Thus, at the autarky point where p = 0.5, σ = 1 and = 2 as before, the optimal level of external debts is unam- biguously positive for α in between 0 and 0.795. Thus, it Copyright © 2012 SciRes. ME H. AKIBA 708 is optimal for the country to hold some external debts for this region of α. However, recalling that the optimal level of foreign reserves is zero for this region of α, we can see that this result is consistent with Alfaro and Kanczuk [25], arguing that the optimal level of foreign reserves is zero, while that of international debts is positive, bsed model output uncertainty being in be- llowing a similar procedure as before and using (23-2): a on their simulation. What we have found is that our uggests that their conclusion based on loss aversion also s is true for the extent of tween 0 < α < 0.795. For larger uncertainty α ≥ 0.795, the opposite conclusion is deduced; the optimal level of B is zero, while that of R is positive. 7.2. With Defaulting When the government chooses to default for a low output level due to a bad state, we can derive the marginal change at the autarky point, fo 2 1 2 1 111 111 B uY U Bp pFKr p (27) < α < 0.795, but also greater than (26), in from external debts is larger on-defaulting case. How- gaining credibility. 7.3. Effects of Exogenous Changes on the Optimal Debts with or without Default A similar procedure of comparative statics exercises for the optimal B yields the results summarized in Panel B of Ta metric result between R and B for non-defaulting case (the first column of Panel B). However, this symmetric nature is a natural consequence of the budget constraint (11’), in which R and B enter the constraint at the first period with opposite signs. Thus, since the marginal bene- fits of holding R (Equation (18)) or B (Equation (26)) are evaluated at the beginning of the first period at R = B = 0, that the defaulting 8. Precautionary Saving with Loss Aversion This section considers the optimal precautionary sav with loss or disappointment aversion in a simple two-period dynamic model under uncertainty. We simplify t vious model in section IV with an assumption of 0, and by disregarding production, and hence investment. Y2 – α. Thus, the problem faced by the government is to maximize (10’) with re- to the lifetime budget con- 2 11 1FK Evaluating at the initial autarky position with our as- sumption rB = 0 and, in addition δ = 0 reduces (27) to (see the Equation (28) below): This is not only positive as (26) with the same parame- ter values for 0 implying that a utility ga for defaulting case than for n ever, this larger utility gain with defaulting should not be emphasized, as the country in the longer-run will have a larger cost of inability to borrow from the world capital market for sometime before re ble 1. Several characteristics are outstanding from it. The first and the most noticeable characteristic is the sym- the comparative statics results of R and B must have the opposite signs for each other. In other words, they are “substitutes” each other in the sense of Alfaro and Kanc- zuk [25]. Secondly, as a comparison between defaulting (the first column of Panel B) and non-defaulting (the second col- umn) cases reveals, the comparative statics values are lar- ger in absolute value for the case of non-defaulting than defaulting (except the case of δ). This implies optimality of holding B is strengthened for a case for this one-shot game. Moreover, this observation is also consistent with that of Alfaro and Kanczuk [25] who observe that they are not “complete substitutes”. We confirm this characteristic in our model incorporating loss aversion. ing he pre- R = B = Outputs are assumed given exogenously, but the sec- ond-period endowment of output is stochastic by α as before, Y2H = Y2 + α and Y2L = spect to S (saving), subject straint 12 12 11CCr YYr , where S is de- fined by S = Y1 – C1. The first-order condition is: 12 2 11 1 11 H L uY SpuYrS puYrS (29) where 11 r is assumed equal to the discount rate, β. Expanding the marginal utilities around the neighbor- hood of S = 0 and α = 0 by Taylor series and approxi- mating them at the first and the second degree, it c shown that ( see the Equation (30) below): an be 2 1 21111 1 uY UFK p Bp 1[11 11p p (28) 2 11 1 111 12 HL dS uY rS pp ruY 2 211 121 uY rS pp 2 1 1 12 112 1 rpuY r 12 1r (30) Copyright © 2012 SciRes. ME H. AKIBA 709 where Ωi is the coefficient of Arrow-Pratt absolute risk aversion at time i 0uiui . The second term on thght-hand side is unambiguously voking the so-called Arr hypo g (or non-increasing) Ωi, since it . Thus, for a given positive second rtainty (α) is i e numerator of the ri positive (or non-negative), in thesis of decreasin lies that 0u 0pp ow’s imp ter 12 m, a sufficient, but not necessary, condition for sav- ings to increase by an increase in unce . The equation 12 0pp is a Figure 4. If the second, positive, term of (30) is negligibly small for a small α, the sign of (30) is dominated by the sig 12pp hyperbola in the p – σ plane as shown in n of (Aizenman [19]). In the absence of aversion (σ = 0), this implies that saving increases for loss 12p. But under loss aversion, it can be confirmed that saving increases for an even smaller probability of output loss; for example, when σ = 1 (Aizenman, 1998), the country saves more even for 13p for a precau- tionary purpose. As discussed earlier, we may be able to approximate p being somewhere in between 0.2 to 0.3 from preceding literature on the Early Warning System against currency crises. When p ≤ 0.3 the sufficient con- dition for dS > 0 is satisfied for σ < 1.3. An important implication is that our sufficient condition depicted in Figure 4 is likely to be satisfied, and thus, that the opti- mal precautionary saving under loss aversion is quite likely to be positive for plausible value of p according to empirical crisis episodes. 9. Conclusions This paper considers a t foreign reserves, with pa heory of the “optimal” level of rticular emphasis on the benefits derived from precautionary holding of reserves. Starting from a simple self-insurance model, we elaborate our analytical model in an intertemporal framework, and σ p 0 1/2 1/3 1 Figure 4. A sufficient condition for dS > 0. presuppose that policy makers are motivated by neither financial stability nor financial mercantilism, but actually by holding precautionary reserves because agents are loss Itn for surface depicted in Figures 2 and 3. Showing that the change in the welfare from the optimal level of foreign reserves under loss aversion depends crucially on the underlying parameter values (the probability of bad state, the Arrow-Pratt measure of relative risk aversion, the loss aversion rate, and the output uncertainty measure), we show how the present discounted level of welfare (U1) changes with configuration of the probability of bad state (p) and the output shock (α), controlling the rest of the two parameters. From the surface depicted in Figures 2 in the p-α-U1 space, we put forth our interpretation that huge accumulated foreign reserves observed in the actual historical data of China and Japan can be interpreted con- sistently within our intertemporal optimization model with loss aversion. Several comparative statics exercises for the condition of the optimal foreign reserves are examined with respect to the underlying exogenous parameters. It is argued that the optimal level of foreign reserves decreases with the probability of bad state. The reason rests on the fact that the total spending decreases if the country saves more for a precautionary purpose. However, it is also clear that this prediction crucially depends on the degree of risk aversion. A similar dependency is also observed in an- other comparative statics exercise with respect to loss aversion. Plausible effects of output shocks and the atti- tudes toward risk are also derived. Admitting that a country would not likely to make ex- ternal borrowing for a precautionary purpose, we also consider such a possibility, partly because of theoretical completeness and partly because such a case has been considered in the previous literature. Allowing for a pos- sibility of defaulting, we derive that similar optimality conditions with and without defaulting. The optimal precautionary saving is also considered directly from our intertemporal optimizing model with loss aversion. We have shown that, as long as the Ar- row’s hypothesis of non-increasing absolute risk aversion, the optimal level of precautionary saving is likely to be positive with historically observed parameter values. An important message drawn from the present invest- tigation is that foreign reserve accumulation observed in the real world is consistent with the rational behavior of a country which has been concerned with loss aversion and averse. is shown that the initial optimality conditio holding foreign reserves depends on the underlying pa- rameters of the model. Given the loss aversion parameter and the coefficient of relative risk aversion, the utility surface depends on the probability of bad state and the degree of output uncertainty, as summarized by a convex Copyright © 2012 SciRes. ME H. AKIBA 710 thus behaved optimally in a dynamic world with precau- tionary savings. REFERENCES [1] W. M. Corden, “Those Current Account Imbalance: A Sceptical View,” The World Economy, Vol. 30, No. 3, 2007, pp. 363-382. doi:10.1111/j.1467-9701.2007.01000.x [2] R. McKinnon, “Why China Should Keep Its Dollar Peg,” International Finance, Vol. 10, No. 1, 2007, pp. 43-70. doi:10.1111/j.1468-2362.2007.00195.x [3] N. Roubini, “Why China Should Abandon Its Dollar Peg,” International Finance, Vol. 10, No. 1, 2007, pp. 71- 89. doi:10.1111/j.1468-2362.2007.00197.x [4] D. Bastourre, J. Carrera and J. Ibarlucia, “What Is Driving Reserve Accumulation? A Dynamic Panel Data Ap- proach,” Review of International Economics, Vol. 17, No. 4, 2009, pp. 861-877. [5] J. A. Frenkel, “International Liquidity and Monetary Con- trol,” In: G. M. von Furstenberg, Ed., International Money and Credit: The Policy Roles, International Monetary Fund, Washington DC, 1983, pp. 65-109. [6] M. Bahmani-Oskooee and F. Brown, “Demand for Inter- national Reserves: A Review Article,” Applied Economics, Vol. 34, No. 10, 2002, pp. 1209-1226. doi:10.1080/00036840110096129 [7] R. Flood and N. Marion, “Holding International Reserves in an Era of High Capital Mobility,” IMF Working Paper WP/02/62, April 2002. [8] O. Jeanne and R. Rancière, “The Optimal Level of Inter- national Reserves for Emerging Market Countries: For- mulas and Applications,” IMF Working Papers WP/06/ R. Rancière, “The Op ld J C [11] J. Aizenmaeserve Uncertain 229, October 2006. [9] O. Jeanne and timal Level of Inter- national Reserves for Emerging Market Countries: A New Formula and Some Applications,” (Mimeographed), February 2009. [10] M. Obstfe,.. Shambaugh and A. M. Taylor, “Finan- cial Stability, the Trilemma, and International Reserves,” Unpublished Manuscript, January 2008. n and N. Marion, “Rty and the Supply of International Credit,” Journal of Money, Credit, and Banking, Vol. 34, No. 3, 2002, pp. 631-649. doi:10.1353/mcb.2002.0001 [12] J. Aizenman and N. Marion, “The High Demand for In- ional Reserves in the Far East: What Is Going on?” Journal of the Japanese and International Economies, l. 17, No. 3, 2003, pp. 370-400. 2009, pp. 525-543. [15] J. Aizenman and J. Lee, “Financial versus Monetary Mercantilism—Long-Run View of Large International Reserves Hoarding,” NBER Working Paper Series 12718, December 2006. [16] J. Aizenman and J. Lee, “International Reserves: Precau- tionary versus Mercantilist Views, Theory and Evi- dence,” Open Economies Review, Vol. 18, No. 2, 2007, pp. 191-214. doi:10.1007/s11079-007-9030-z [17] R. Chang and A. Velasco, “Financial Fragility and the Exchange Rate Regime,” Journal of Economic Theory, Vol. 92, No. 1, 2000, pp. 1-34. doi:10.1006/jeth.1999.2621 ng Asia Too Much Foreign Exchange Reserves? An Empirical Examination,” The Journal of Korean Economy, Vol. 11, No. 1, 2010, pp. 103-128. [19] J. Aizenman, “Buffer Stocks and Precautionary Savings th Loss A [18] D. Park and G. E. B. Estrada, “Does Developi wiversion,” Journal of International Money and Finance, Vol. 17, No. 6, 1998, pp. 931-947. doi:10.1016/S0261-5606(98)00035-7 [20] Y.-W. Cheung and R. Sengupta, “Accumulation of Re- serves and Keeping up with Joneses: The Case of LASTAM Economies,” International Review of Economics and Fi- nance, Vol. 20, No. 1, 2011, pp. 19-31. doi:10.1016/j.iref.2010.07.003 [21] H. R. Heller, “Optimal International Reserves,” Economic Journal, Vol. 76, No. 302, 1966, pp. 296-311. doi:10.2307/2229716 [22] J. A. Frenkel and B. Jovanovic, “Optimal Interna Reserves: A Stochastic Framework,” Economic Journal Vol. 91, No. 362, 1981, pp. 507-514. doi:10.2307/2232599 tional , [23] H. Akiba, Y. Iida and Y. Kitamura, “The Optimal Ex- change Rate Regime for a Small Country,” International Economics and Economic Policy, Vol. 6, No. 3, 2009, pp. 315-343. doi:10.1007/s10368-009-0140-5 [24] F. Gul, “A Theory of Disappointment Aversion,” Econo- metrica, Vol. 59, No. 3, 1991, pp. 667-686. doi:10.2307/2938223 [25] L. Alfaro and F. Kanczuk ment and Sover , “Optimal Reserve Manage- eign Debt,” Journal of International Eco- nomics, Vol. 77, No. 1, 2009, pp. 23-36. doi:10.1016/j.jinteco.2008.09.005 [26] D. D. Diamond and P. H. Dyvbig, “Bank Runs, Liquidity, and Deposit Insurance,” Journal of Political Economy, Vol. 91, No. 3, 1983, pp. 401-419. doi:10.1086/261155 [27] A. Tversky and D. Kahneman, “Loss Aversion in Risk- ternat Vo doi:10.1016/S0889-1583(03)00008-X [13] J. Aizenman and N. Marion, “International Reserve Hold- ings with Sovereign Risk and Costly Collection,” The Economic Journal, Vol. 114, No. 497, 2004, pp. 569-591. less Choice: A Preference-Dependent Model,” Quarterly Journal of Economics, Vol. 106, No. 4, 1991, pp. 1039- 1061. doi:10.2307/2937956 [28] M. Obstfeld and K. Rogoff, “Foundations of International Macroeconomics,” The MIT Press, Cambridge, 1996. [29] S. Han, S. Gupta and D. R. Lehmann, “Consumer Price Sensitivity and Price Thresholds,” Journal of Retailing, Vol. 77, No. 4, 2001, pp. 435-456. doi:10.1016/S0022-4359(01)00057-4 Tax doi:10.1111/j.1468-0297.2004.00232.x [14] G. Cifarelli and G. Paladino, “The Buffer Stock Model Redux? An Analysis the Dynamics of Foreign Reserve Accumulation,” Open Economies Review, Vol. 20, No. 4, Copyright © 2012 SciRes. ME H. AKIBA ME 711 [30] S. Benartzi and R. H. Thaler, “Myopic Loss Aversion and the Equity Premium Puzzle,” NBER Working Paper No. 4369, May 1993. [31] D. Kahneman, J. L. Knetsch and R. H. Thaler, “Experi- mental Tests of the Endowment Effect and the Coase Theorem,” Journal of Political Economy, Vol. 98, No. 6, 1990, pp. 1325-1348. doi:10.1086/261737 Copyright © 2012 SciRes. [32] A. Kraay, “Do High Interest Rates Defend Currencies during Speculative Attacks?” Journal of International Economics, Vol. 59, No. 2, 2003, pp. 271-321. doi:10.1016/S0022-1996(02)00021-1 [33] H. J. Edison, “Do Indicators of Financial Crises Work? An Evaluation of an Early Warning System,” Interna- tional Journal of Finance and Economics, Vol. 8, No. 1, 1972003, pp. 11-53. doi:10.1002/ijfe. [34] S. Budsayaplakorn, S. Dibooglu and I. Mathur, “Can Macroeconomic Indicators Predict a Currency Crisis? Evidence from Selected Southeast Asian Countries,” Emerging Markets Finance & Trade, Vol. 46, No. 6, 2010, pp. 5-21. [35] T. Ito and K. Orii, “Early Warning Systems of Currency Crises,” Public Policy Review, Vol. 5, No. 1, 2009, pp. 1- 24. [36] M. S. Kingl, L. Sarno and E. Sojli, “Timing Exchange Rates Using Order Flow: The Case of the Loonie,” Jour- nal of Banking & Finance, Vol. 34, No. 12, 2010, pp. 2917-2928. doi:10.1016/j.jbankfin.2010.02.016 Appendix tainty equivalent consumption, μ, i.e. the “expected dis- appointment”. This average loss below the certainty equi- valent consumpt This section recapitulates the definition of loss aversion as put forth in Aizenman [19] and Azenman and Marion [12], and clarifies the demand side of the economy (i.e. ex ion reflects the authority’s sentiment of “disappointment” (Aizenman [19]: p. 935). Equation (A-1) postulates that theutility equals the difference betweeected utility and are only two orresponds to a ts loss averse expected n the conventional exp pected utility) in the second period in more detail. The relationships between the degree of loss aversion (σ), the probabilities of bad and good states, (p, 1 – p), and the extra weights attached to utility in good and bad states (λH, λL) are presented. As it will be explained below, the definition of loss aversion is an application of the con- cept of risk aversion by subtracting the expected disap- pointment from the conventional expected utility. Assume that the policy authority possesses the ex- pected utility of uncertain consumption 2 s C in n states of nature, s 1,,n, denoted by 2 ;s WC in the second period. σ is called the loss aversion rate. Assume also that there is the “certainty equivalent” level of consumption μ, defined by 2 ;s WC u , where u is a conventional utility index with 0u and 0u . Then, loss aversion is defined by the existence of a positive parameter σ that satisfies: 2 22 2 ;s ss s C WC uCf CdsuuC a measure of loss aversion (σ) times the “expected dis- appointment”. Assume further that, for simplicity, there states of nature, C2H and C2L, where C2H c higher and C2L to a lower level of consumption with probability of 1 – p and p, respectively. Thus, p represen probability of bad state. Then, sincethe u(μ) does not depend on states of nature but a constant, it is straightfor- ward to derive W . Upon integration of (A-1) yields: 22 2 1 H L L WpuCpuC pW uC (A-2) and thus solving (A-2) for W yields: 22 11 1 H HLL W puCpuC (A-3) 2 22 2 2 | Pr s ss s s fC ds EuCEuuCC C 2s (A-1) where f is the probability density function of C2s, E is the expectation operator, and Pr(s) is the probability of state s. The term 2 |s Eu C where 1 Hpp and 11 Lpp . Note that λH and λL are non-linear with p, as in Tversky and Kahneman [27] and Benartzi and Thaler [30]. Note that they are both positive, λH = λL for p = 1/2, and 0 Hp and 0 Lp . Thus, the policy author- ity attaches a lower weight to 2 H uC , but a higher weight to 2 L uC for a higher probability of bad state. Finally, it should be mentioned that W reduces to the conventional expected utility when the loss aversion rate, σ, is zero. is the expected value of 2 s uuC , conditional on C2s below the cer- |