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NBER WORKING PAPER SERIES CAPITAL MOBILITY IN THE WORLD ECONOMY: THEORY AND MEASUREMENT Maurice Obstfeld Working Paper No. 1692 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 August 1985 The research reported here is part of the NBER's research program in International Studies and project in Productivity and Industrial Change in the World Economy. Any opinions expressed are those of the author and not those of the National Bureau of Economic Research. NBER Working Paper #1692 August 1985 Capital Mobility in the World Economy: Theory and Measurement ABSTRACT This paper is a critical assessment of some recent empirical evidence on the extent of international capital mobility. Its major conclusion is that while much of this evidence is difficult to interpret without ambiguity, it is consistent with a world economy in which the degree of capital mobility is high and increasing. Two main approaches to the measurement of capita]. mobility are discussed. The first, traditional, approach is based on comparing expected yields on assets located in different countries. The second, and more novel, approach is based on comparing national saving rates and domestic investment rates. Maurice Obstfeld Department of Economics Columbia University New York, NY 10027 (212) 280—5489 Introducti on I. Since real in terest rates around the war Id have risen era. and remained at levels unprecedented in the postwar While the he won dwi de nature increase in real rates awaits a full expi an ation, t e. Both widespr ead f i nanc i of the phenomenon is itself less of a puzzl on techn ol ogi es al have cr eated close industr i linkages among the financial market s of the al ized c oun tries. interriat ional ly mobile1 Economic theory suggests that if cap ital is move in a rates of return in different countri es will tend to synchronized fashion as inve stor toward assets offering relat i s conti nual ly shift their portfolios said to be high yiel ds. Capit al is vel y resident s may engage in mobile between two regions i f som e of their inter—regional Car r espon dingi asset trades. y, the de gr ee of capital sco pe which might mobility is measured by the scope for such trades, a be limited by transaction coits, How mobile is capital tax e S or off i ci al regu 1 ati ons. in t he wor 1 d ec onomy? E mpi ri cal research twa ma)Or ii nes. The first line into thi s question has proc eeded along S 4 resea rch is based on the comparison of expected yield on alternative ne of researc h, or iginated by assets. The second, and more novel, ii Fel dste in and Horioka 19B0) is based on saving and domestic investment rates. the cOffpa r i son of national lii an economy that is closed to nati onal saving and intert emporal trade with the outside world, overall dome st ic investment 'ust be equal bal anc e that is, the cur rent account of the i of payments must be zero. The FeldsteirvHor based on the premise that the degree f car r e 1 at i or a k a approach is bet ween saving and investment rates is therefore a barometer of the extent of capital mobility. Th is paper is critical a assessment of some recen t empir i cal evidence or the extent of inter national capi tal mobilit y. Free capi tal mobility is in general a necess ary condition for the ef + tional allocat ion of the world' s saving. i ci ent interna— The efficient all oca tion of risks in the w orld economy requ ires internati onal asset trade and the portfolio dive rsification it al lows. Further, the extent to whi ch capi— tal is mobile is important in a ssessing the e fficacy of financi al policies in op en economies, the incidence of certain taxes, and the impact on capi tal accumulation of changes in government and pri vate saving. The di scussion emphasi zes that concl usi ons about effici ency cannot be drawn from an y set 0 f empiri cal resul ts unless some b enchmar k model of an "eff icie n Similarly, posit i ye wor 1 d t economy is specif ied in advance. as well as normat ive conclu sions are extremel y sensitive to the emp in cal assumption s embedded in the benchmark model. The remain der of thi s paper is organized as follows: Section II de scr ibes recent wor k on the relation between measured rates of return on ass ets denomi nated in diff erent currencies. It is argued that in mo dels of any generali ty, the observed internati onal linkages between these r ates may be 1 oose ev en if there are no serious imperfections in world c api tal markets. The di scussion suggests that the tests most likely to be i nf ormative about the extent of capital mobility involve assets de nomi nat ed in the same currenc y but issued in di f f er en t political or regu 1 atory jun isdictions. Availab le evidence is con si stent with strong cross —border li nkages between OECD —country capital m arkets. Section III descri bes the Feldstein—Hori oka approach and r esul ts, and then presents a life-cycle model in which countries' saving and investment rates are correlated even though capital is perfectly mobile. A simulated regression using data generated by the model yields es— timates quite similar to those found by Feldstein arid ot her S. However, the policy implications differen t Horioka of the estimates from those that are usually drawn • For example, and are very + I scal policies that encoura ge saving have no effe ct on domestic capita 1 stocks in spite of the stron g statistical correlat ion between lon 9—run savi rig and inves tment rates. The empirical { indings of Feldstei n and Horioka are for the most part based on cross—s ectional c omparisons of countries saving and I nvestment rates over periods of five years or more. Sections IV through Vi of this paper explore the savi ng—in vest merit relation in a short—run, time— series context. Section IV develops a si mple open—economy model suitable for anal yz ing comovements between innovations in saving and innovations in invest merit. Both Feldstein (1983) and Murphy (1984) have used aggrega— tive I S—LPI models for this purpose but the modelling strategy here is differ ent in that the possibility of a saving—investment correlation is derive d explicitly from the maximi zing behavior of households and firms rather than imposed a priori. The model of section IV highli qhts the fact that data from na— income accounts do not yield an ac curate represent ation o + na- tiorial tional saving in a world where share s in the ownership of domest ic firms can be held by foreigners. Section V show s measur ed correlations between saving and ho this probi em can i ncrease i n vest m en t Section Vi presents estimates of th e tire-series bet wee n correlion quarterly changes in saving rates and in invest ment rates fr seven OECD countries. although these esti mates need to be interpreted with c autior, they provide empirical fact s with which macroeconomic theories must be consistent. The estimated correlation coefficients turn —4— out to be highest for economies which are either very large (the United States) or have had extensve c apital controls over much of the sample period (Japan). The y are smalle r for medium—sized countries, and may be insignificantly dif ferent from zero for the smallest economies. In all cases but those of the U.S. and Japan, the estimated saving—investment correlations over t he entire sa mple period considered differ sig— nificantly from the value of 1 that would obtain under complete capital for six of the seven countries, the measured cor— immobility. Further relation drops in t he period af ter 1972. An interpretation of the data consistent with the se findings is suggested. This interpretation, which postulates substant ial and incr easing capital mobility among OECD countries, receives i ndi re ct support from evidence on the United Kingdom under the pre—1914 gold st and ard. The papers m am II. con clusions are summarized in section VII. Inte rest, Exch ange Rates, and Inflation The international integrati on of natio nal financial markets im— plies important linkage s between the ret urns off ered by assets issued in different countries. Th ese links can be weak ened by transaction costs, taxes, capital controls sovereig n ri sk, and other market imperfections. Even in the absence of imperfecti ons, th e na ture of the 1 inkage depends on investors preferen ces and the stochastic structure of the world economy. The most stra i capital is the direct ghtf or ward c omp ar i approach t o evaluating the mobility of son of rates of return on ph ysical capital in various countries. Al thoug h such comparisons have been attempted (for example, by Harberqer (1978)) the problems of measuremen t, of diverse ta treatment, and of converting measured returns into a common numeraire, are severe. Much recent research has therefore limited itself t rather to comparing returns within a narrowly delimited group of rela— tivEly homomoeneous financial assets. It is convenient to mot ivate some of the recent empirical tests on international rate of return linkages b model of international nomina 1 inte r es t developing a simple two—good rate differenti als wi th ri sk - 4 averse investors. The model makes the point that many of the empi ri cal tests have unambiguous implic ati ons ab out capital mobil ity on ly un der some rather stringent assumpt ions. It the c ompar i sons mOst likely to be informative about the extent of international capital mobility involve assets denomi nated in the same currency but issued in different countries. There are two countries in the world, a "home" country and a 'foreign' country, each with its own, country—specific currency. On any date t, the domestic—money p rice of a unit of domestic currency to be deliver ed with cert ainty on date t+l is just 11(1 + where Rt is the domesti c nominal in terest r ate. The foreign nominal interest rate is similar ly defined, and the spot exchange rate, X, gives the price of a unit of foreign cur rency d elivered at time t in terms of a unit of home cur r enc y also deliv ered at time t. Note that the nominal interest rates thet ha ye just beer defined are risk—free nominal rates. Each country is special i:ed in the product i on of its characteristic output. The do ire s t i d e ot e E c—mon ey price of home output at time t is denoted P, while the I n d i vi f ore i g n — d u a 1 s cur r en c y price of foreign output. in the two countries have identical, time—separable utlity functions of the form wherr Ett. is e, orditional expectation based on time—t information, s lisa fixed subjective time—preference rate, c (c) is time—t con— 5 U l) pt i on o tho hose (fore ign) good, and the ins tantaneous util I ty is 4 unction u(. ,.) stricti y concave. Given these preferences, w hat condition s will characteri ze asset—market equili brium in the ab sence of imperfect ions? Consider th e position of a repres entative invest or. If there are no cash—in—advan ce constraints, he may use a domestic currency unit to i ncrease consumpti on of the home good to day, to increas e con— sumpti on tomorrow after a one—period investment in domestic—cur rency loans1 o r to 1 n crease cons umption tomorrow after a one—period i nvestment in forei gn—cur rency 1 oans; and in equilibrium, h e must be indif ferent among th ese three alt ernatives. Define u u(ct.c)i Then the implied in tertemporal arbit raqe conditions are u4 (c ,c /P (1) u = c,t c,t t = E t [(I+Rt )u c,t+l/Pt+l ) = 5E t [c1+R:)Xt+iuct+i/Pt+i)/Xt. Because the marginal rate of substitution between current consumption of home goods and current consumption of foreign goods foreign goods always equals the relative price of those goods, (2) u /u = c4,t c,t (1) implies that the indivi dual is also indifferent be tween consuming the foreign good today and shifting that consumption + orward a period through an investment in do mestic or foreign bonds. -3 The second equality i n (1) may be rewritten in a way that ii— lustrates the link between nominal interest rates and the exchange rate. Let CovtL) denote a covari ante conditional on time—t information. Then (1) implies that 1+R I + E (X Et(ut+i/Pt÷i)EtXi) —7- Expression (3) revea is that, absent imper fections, the nominal interest differential between the home and foreign currencies is two factors. First1 there is the expected currency against the foreign currency, Et depreciation determined by of the domestic Seconds there is the covariance term, whi ch may be interpreted as a risk premium. The intuition behind the covariance term in (3) is as fo 11 ow; The quantity ut+i/Pt+i measures the marginal consumption value o f the domestic currency at time t+1, the utility obtained then by sp ending another unit of home money to consume the domestic good. (By 2), this is the same as the u tility that would be obtained by spending the money to raise consumption of the foreign good. ] The greater is the covariance between the future ex change rate and the marginal consum ption value of domestic currency, the more effective is the foreign bond relative to the domestic bond as a hedge against cons umption risk. This i s because the stochastic payoff on foreign assets, in terms of domestic c urrency tends to be surprisin gly high when the consumption value of the currency is surprisingly high. rise in this covariance therefore leads to a fall i n the nominal i nterest rate on foreign bonds relative to that on domest ic bond;. when the ris p remium in (3) is zero, interest rates are linked by the uncovered interest parity condition (4> (R — R)/(1 + R) (Et(Xt +i) — which relates the interest d iff erential exclusively to expected depreciation. Under the assumpt ion that expectation; are rational, approximations to condition (4> have been tested extensively on recent data. These tests are unani mous in rejecting the condition as a charac— terization of asset—market equi 1 ibrium [see Cumby and Dbstfeld —8— Hansen and Hodrick (1980,1983), Hodrick and Srivastava 1981,1584), (i5S4,19B) , and the references therein]. But it should be clear that 6 the assumptions required to proceed from (3) to (4) are not innocuous. Most authors ha ye therefore regarded rejections of (4) as indicating the presence of a t ime—varying rationality or market imperfections. Because expectations (and, by implication, r isk premia) are not directly observable, this is just one of several pos sible assumptions on consumption risk premium rather than ir— interpretations. Only after making some strong prior expectations and the nature of the risk premium can one extract conclu sions about the functioning of international asset markets from test; of (4). 7 it noteworthy that the concept of uncovered interest parity may is be well defined. not always By using (2), one can manipulate (3) to obtain 1 + IC — 1 B; = + 1JX, whi ch is jus t cur rency If hol d bec ause 1/Et(X+i. only Et(1/Xt+i) equation Coy (u t c* I E tc*,t+i/F )E (1/X +1 t + t+1 3) viewed from the perspective of the foreign the risk pr emium in (5) is zer o, (4) will not generally by Jensen' s inequality, Et (1/ Xt+i) need not equal In fact unc overed interest par ity can be uniquely defined in a nonstocha stic "Siegel's paradox" environment. Th is 4 act is sometimes called (Sieg ml (1972)]. Tests of unco vered interest parity typically use interest rates on Euroc urrenc y deposi ts, which, unlike U.S. Treasury bills, are not widely believed to be free of default risk. This raises two further problems of interpretation. The first of these arises from the assumption underlying (3) that interest rates are risk free—rates. The second problem, which —9— is more serious, involves the question of whether inferences concerning international capital mobility can in fact be made from the tests. The pres ence of default risk indicates t hat the reasoning leading to (3) or (5) is not valid when ap plied to Eur ocurrency rates. The use of Eurocurrenc y rates is typically justified, however, by the argument that Eurocurre ncy deposits have id entical risk characteristics (at least when issued by the same bank). And indeed, a p articular formalization of this idea does yield (3) and (5). Suppose that the Eurobank honors its deposits with probability E t+1 on date t+1 but defaults with probability payl ng depositors 1 — random variabl e that assumes t he value 1 with probability val ue 0 with probability 1 — be a no co mpensation in that case. Let c1 and the Then the sto chastic payoff on cur r enc y Eurodeposits is Q t+1 (1 + Rt) with an expected value of II t+1 (1 + R t 1) = + Eur odep osits is If Qt+1 is 1 + t+1 while that on wit h an exp ected value of + R). distributed I ndependentl y of all other relevant variables, then conditions (3) and (5) follow exactly as bef ore. Of c ourse, a failure of the f oregoi ng independence assumpti on makes it even more difficult than o therwi se to interpret rejectio ns of condi tion (4). The second problem of interpretatiDn is th at tests of interest pan t y based exc 1 in for cation usi vel y on Eurocurrency rates 5imply may not yield any abou t the ex tent of capital mobility among countries. These tests typically assess the efficiency of arbitr age among deposits issued in a s inqle 1 ocal issued ir dif f i ty er ent (for example, London). (.inIe ss tests involve assets countries, they can tell us little ab out the ease with w hich re i dent s of those countries can engage in mt ertemporal trades This po nt would be irrelevant if nominal yields on assets derosinated in the same currency but issued in different oolitical —itj— 3 ur 4 or isdictions were equal. hut casual observation reveals discrepancies, reasons that may involve heterogeneity in terms of default risk3 soy ereiqn risk, and tax treatment, as well as existing capital controls and other financial regulations [see Aliber (1973) and Dooley and Isard (1980) indeed, any attempt to measure capital mobility using rates of return must b e based, not on a comparison of Eurocurrenc y rates, but on a comparison of nominal yi elds on 'onshore" and "offshor e" assets denominated i n the same cu rrency——for example, large dol lar certi ficates of deposit is sued by New V ork banks and those issued by London ba n k s. These rates g enerally do d iffer, as noted above, but fo r many cur renc i es they have ten ded to move t ogether in recent years [see Fieleke (1 982) chart 11. Johnsto n (1979) finds that after correction for differential financial req ulations, Eurodollar and Eurodeutschemar k rates are always quite close t o the interest rates paid on comparable liabilities of onshore banks (at least after 1973 for dollar rates a nd after mid—1973 for Dli rates). In a very careful study accounting for bid—ask spreads and the cost a f deposit insurance as w eli as differen tial reserve re— quirements, Kr eicher (1982) finds that over the 1975- 198C' period, the difference bet ween Eurodollar and U.S. certificate—of —deposit rates afforded banks little or no opportunit y for arbitrage Hartman (1984) presents evide nce of significant two—way feedback between Eurodollar deposit rates and interest rates on commercial paper issued in the U.S When ca pital controls are known to have been important, there are still links b etween onshore and offshore interest rates, but also some important di screpancies. Siavazzi and Pagano (1984) show that for France and Italy, these discrepancies have been largest around the time of -11-- exchange—rate realignments within the European Monetary System (EMS). In contrast, these authors find a close connection between onshore and offshore rates for Germany and the Netherlands, two EMS countries with essentially open capital markets. Rogoff (1985) also presents evidence that capital controls have helped the French and Italian authorities maintain EMS—linked exchange rates. Ito (1983) documents the existence of apparent arbitrage opportunities between Japanese Gensaki repurchase agreements and Eurocurrency deposits during the 1970s, when Japanese capital controls were stringent. However, he shows that these opportunities became very infrequent once Japanese capital markets were effectively opened in December 1980. 10 On the whole, therefore, data on onshore—offshore interest differentials imply a substantial degree of capital mobility among OECD countries. In the face of this strong evidence of efficient international portfolio allocation at each point in time, it is difficult to understand assertions that the allocation of portfolios over time somehow consistent with substantial arbitrage opportunities. No explicit mention has been made of the international linkage among expected real rates of interest, defined as nominal rates corrected for expected local price—level inflation. The reason is that the theory outlined above makes no strong predictions about real interest rates so defined. This point is illustrated through the assumption that the interest parity condition (4) holds. Define the domestic inflation — = rate as — 1. If 1 and the foreign inflation rate as 11 denotes the terms of trade XtF/Pt and if Ft/P are distributed independently, then (4) can be written (6) (Rt R/(1+R = [Et(tt+i)/7t)Et[(1+t+i/1+U*i)) -1. and I' Note that iin addition, the terms of trade are expected to remain constant over timp, (6) assumes the form (7) (R — R:)I(l+R:) = EtC(Iti * 1+11* )] which explains relative nominal interest rates by expected relative inflation rates. A very crude approximation to (7) is Rt — = Et(llt+i * Rt — * the usual statement of the international equality of expected real interest rat es. But even when (4) holds, the equality (7) leading to this approxi mati on follows only if one mak es some exceedingly strong assumptions, inc luding the assumpti on that the relative price of na— tional outpu ts f ollows a martingale pr oces s. This last assumption is sometimes ca 11 ed ex ante purchasing power parity, and while there is some support for it in the data, it can b e statistically rejected in see Cumby and Ubstfeld (1984)]. many cases The eq ual i ty of expect ed real rates has been tested, for both onshore and offshore nomi nal rates, in a series of papers by Hodrick 1979) Howard (1979 (1984), and Mishkin tions of Cumby and Mi shkin (1985), Cumby and Obstfeld (l984a, 19 84b) In li ght of the rather strong rejec— uncovered p arity and ex a nte p urchasing power parity, is it is not surp rising that most of these tests reject the hypothesis that expected real rates are equal acro ss cur rencies. Nonetheless1 the bi 1 atera 1 correlatio ns computed by Cumby and Mishkin (1985) show that ex ante rea I rates tend to move together, even when defined using onshore interest rates. Thei r finding r einforces the impression of significant capital mobility among OECD countries. III. Saving, Investment, and Capital Mobil ity While international comparisons of interest rates yield indirect evidence on the mobility o 4 capital among countries1 the connection between a c ountry's income and its expenditure yields a direct measure of the exte nt of its inter temporal trade with the rest o4 the world. When a coun try i s completely closed to capi t al may ements, its income necessarily equa is its spending on consumpti on and investment goods. In contrast, c ountr ies that are integrated into the w arId capital market may finance disc repancies between income and spend ing through inter na— tional borr owing In a pair or lending. of stimulating papers, Feldstein and Horiok a (1980) and 1983) have attempted to use measured discrepanci es between Feld stein national in comes and ependitur es to assess the degree of i nternational financial integrati on. To motivate their approach, let V denote national income, C private c onsumption, I domestic investment, and 6 government consumption. In an economy closed to international cap ital movements1 total national savi ng S = V — C — 6 necessarily equals domestic invest— ment I. The current account of the balance of payments =V is n ecesarily t r ad e, S (C + 1 — 4 6) S — given by I, zero in this case. For an economy open to external asset and I need not coincide and th eref ore can vary independently in equi librium. For example, when national saving exceeds domestic nyc stment,the C U S U lating economy is running a curr ent—account net claims on the rest of the world's future output. Th Fel d stein—Horioa iorld of perfect moveserits surplus and ac— analysis is predicated an the contention that in a capital mobili ty, movements in domestic in nat ioral saving wi Il be approximat ely investment and uncor related. s they —14— put it, "With perfect world capital mobility, there should be no relation between domesti c saving and domestic investment: saving in each country responds to the worldwide opportunities for investmen t while investment in that c ountry if financed by the worldwide pool of capital.' tFeldstein and Horioka (1980), p. 317.] The statistica 1 analysis in these papers is based on regression equations of the form (8) (116DM. = 1 0 4- i (816DM. 1 1 where 6DP is nominal gross domestic product, the left— and right—h and side variabi es are averages of annual ratios of gross nominal investment and saving t o GOP over periods ranging in length from five to twenty years, and t he index i ranges over a cross—section of DECO cou ntries. A finding that differs significantly from 0 is viewed as beinq incon— sistent with perfect capital mobility, while a value of to represent the case of complete capital immobility. = 1 is taken 11 Over t he period 1960—1974, for example, the least—squares estimate reported in Feldstein and Horioka (1980), table 2, is 0 = 0.035 = 0.887, (0.018) 0.91. R2 = (0. 074) Regressions using net, rather than gross, savi nç and investment yield estimates of even closer to 1. Because s repeatedly estimated to be significantly different from zero but not 5igni ficantl y different from 1, the authors conclude that capital mobi lity is rot perfect and that most of any increment to national saving ends up augmonting the domestic capital stock. The estimated vlus of is interpreted as 1 measurinq the effect o & sustained increase i n a country's saving rate on its investsert rats, The strong policy impl ication drawn from this — 15— interpretation is that policies to encourage domestic saving will have an effect on domestic investment that is essentially one—f or—one. I' The bal anc e of this section argues that the res ul ts reported in Feldstein and Nor i oka (1980) and in Feldstein (1983) do no t necessarily have any i mpl icati ons regarding t he extent of capital mobi lity. Common factors af fec ting both saving and investment rates may c au se these variables to be hi ghly correlated in cross—sectional d ata. But such high measured c or r el ati ons do not impl y that y shift in n atio nal saving, would be the regardless of its source, affects domestic investment, as case under capital immobility. A c orol I ary of this arg ume nt is that policies th at increase domestic sa ving rat es may have no effect on domestic in vestment rates even if regr essi ons like (8) yi eld large and 41 £ ,J statistical ly significant least—sq uares es timates of These points are established within the context a life—cycle model of sa ving and growth in the world ec onomy. The mod el is designed the longer to capture forces influencing savi ng and i term. First the theoretical predi cti ons of the model ar e established. These include a possibly positive cross—sectional correl ation between investment and saving rates1 but a zero ef fect on i nvest ment of policies that encourage savi n g within an i ndivi d ual cou ntry. Seco nd, it is demonstrated th rough simulate d re gressi on anal ysis that the theoretical model is capabi e of producing emp irical r esult 5 sim i reported in the Feldstein—Hor i Consi der o k a studi es. 1 ar to those 14 a 5mall open econ omy wh ich produces and consumes the single consumpt ion good avail able in the world. Individuals live for two periods and are endowed with a un it of I abor which is sold in the first period of life at a real wage w. The labor endowment of an 0 ld in— di vidual is 2ero, so all old—age cons umption is financed thr ough wealth - là— accumulated while younq. Wealth may be held in the form of domestic capital or in th form of an internationally—traded bond which costs one unit of the consumption good and pays its owner p units of consumption after a period. F is just the world rate of interest, and it is a parameter from the standpoint of the small economy. Output y is a function fR'in) of domestic capital and labor. H.,.) exhibits standard properties, including constant returns. The labor force is assumed to equal (l+g)t, and therefore grows at rate g. Labor cannot migrate across national boundaries. A unit of saving may be costlessly transformed into a unit of installed capital a period later, and capital depreciates in use at rate . by the conditions p + S = fk(k1n) wt = Equilibrium fn(ktntl is characterized and n = (1g)t the production function is taken to be of the form kmnlm, these equalities imply that for all t (9) k = (i+g) (u/p*F) 1/1—a t (10) w w = (11) Vt = Let (1—u (l+g)t(a/p+fl c denote an u/i—u individual s consumption in period t. Then the lifetime problem of an individual young at time (12) u(ct) + t is to maximize fiu(c+1) subject to the constraint (13) c + c+1/(l+r) r w. If it is assumed that the subjective time preference factor p equals l/l+p, maximization of (12) subject to (13) results in a preferred If -17- individual consumption path that is flat at the level (14) c = (1+p)wf(2+p) and the same for each member of each generat ion. net saving in this economy, Ag o req ate consists of the saving o the young plu s the (negative) saving of t he old: (15) St = (Hg (w — c) 4 Hg) t—1 [p(w — c) — c]. Equations (14) and (15) imply that (16) St = g(1+g) t—1 wI (2+p) and equat ions (10) and (11) may be combined with (16) to obtain the ratio of net saving to gross domestic product = (17) 6DPt) (g/1#g)[(1—u)/(2+p)3. Net investment (IS) I = ( — kt is given by = g( Hg) (a/p+fl 1/ 1-m according to (9). By (11), t19) It/6DPt g(ufp+E). The most important fact to note is that because a rise in the population growth rate g causes both the saving rate given in (17) and the investment rate given in (19) to rise, these variables can be corre— lated in a cross—section of countries, in spite of the perfect mobility of capital.1 Saving rates are increasing functions of population growth rates for the standard life—cycle reasons [as set forth in tiodigliani (1970), for example): the more quickly the economy grows, the lower the weight in the aggregate saving ratio of dissaving by the old. Invest— sent, however, depe nds on population growth for reasons that are uncon— nected with saving b e h a vi capital stock must i or: as the e+fectiv e la bor force increases, the ncrea se in proportion to mai ntain the equality between the net mar ginal product of capital and the world rate of return. It is reall ' the international immob ilit y of labor that is behind the saving—i nvestm ent correlation in this model. Nc.te, however that saving and investm ent rates will be negatively correlated in a cross—section al sample if gr owth rates are fairly uniform acr ass countries but there are wide disp arities in the values of capital's share a. Can the theoret ical mod el developed here yield regression results similar to those foun d by Eel dstein and Horioka (1980) and Feldstein (1983)? To answer thi 5 questi on the model was calibrated usi ng data on growth rates and the function al distribution of income for the seventeen OECD countries listed in tabl e 1 of Eeldstein (1983). In thi s model world economy, the li fespan o + a generation was taken to be a year, p was set at .1, and t was set at 1 (implying that capital is used up camp men t 1 etel y in produc tion). 4 scatter diagram for the saving and invest— rates generated by (17) and (19) is shown in figure 1. 16 Estimation of (8) by ordinary least squares using the simulated data set yields 0 0.006, (0.0(1) = 0.858, = 0.07. very cl ose (0.806) While the estimate of the si ope coeff icient is to those obtai ned in the literature, this para meter is impr eci sely estimated, and does not differ significantl y from 0 or 1. However that "Greece' is an extreme out 11 er in this sample figure 1 indicates (1 argel y because of 0.00500 0.0050 0.0100 o.oiso 0.0200 0.0250 Invs stmsnt rots I 0.00650 I Swedsn I • United Kingdom Germiny Italy • Denmark • • • Sellvm Austrafla Francs • 0.00950 I 31,1111 1 I 0.01100 I United St.,.. • Ireland Netherlands I (Simulatid data) 0.00800 I • Austria New Zealand Finland Ir•ecS Figure 0.01250 Saving rotS CIMdI -19— the un usually low share of employee compensation in national income, an art i a ct of severely distorted data). Omitting that -= 1.422, C.' 0. U 04 (0. 45) F observation 4. yields u.41. — In thi s equati or the esti mated slope coefficient is significantly dif— ferent from and insigni ficantly different from 1. The equation is therefore quite close to the type of result found in the Feldstein— Horioka literature, al though the is only about half as large as those typically reported there. The preceding the Fel dstein— Horioka findin gs are consistent with perf ect capital mobili ty. They also show that it i s ha:ardous to make predict ions on the basis of such regressions wi thout knowledge of the economic model underly mg the measured corre lation. It is true, in the theoretical model, that an increase in th e saving rate caused by an increase in the ec onomy 's investment growth rate wi 11 be associated with a ri se in the domestic rate. This fac t lies behind the large and significant slop e coefficient in the regress ions. But it does not follow that j ri se I n saving will be accompanied by an increase in investment. For eamp le, a rise in the saving rate in duced by tax policies that do not affect fir s will leave the investment rate unchanged any increment to saving abroad in that wi 1 I I ndeed flow case. The example warns us that the reg ress ion results, taken by therns elves, are an insufficient basis for pol icy for mul at ion. While th e foregoing counter—example is driven en ti growth1 it is investment not clear that growth alone can account r ly by economic f or the saving and rat es seen in the real—world data. Modigli ani 197 0), in a cross—country study, 4ind that growth rates are an import ant deter— irinant of saving rates. However, there is an increasing body of evidence —20 — flat lifc—cvcle considerations alone are insufficient to explain na— tional saving behavior in the U.S. hctli(:off Summers (1961)1. Feld stei n and Ho rioka (1960) test for the importance arid and ml sewher e [see, for example, cf growth by adding the rate income arowth to their basic equation (6). But while the t—statistic for the new regressor is 1.45, high correlation between saving and a investment rates remains. Summers (1965) finds a highly significant co efficient on population growth when that variable and the rate of income growth ar e added as regressors. An investment—saving correlation of 0.61 remains, but the Summers result contradicts the hypothesis that domestic inves tment depends only on domestic saving in the long run. It i s an open question whether more realistic intergenerational models, i n corp or at ing country—specific demographic and inst i tut i onal bequests as well as factors, can explain the observed behavior of current accounts over lon q periods. The preceding simulation example should not be taken as an e xpianation Feldatein—Horioka results. It should be taken as tions other than capital immobility are quite of the evidence that possible. expl ana— Future research should aim at identifying and testing the potential alternative e x p1 a n at on s. 17 I Another question that has not been answered i s why OECD current accounts have been so small rel ative to saving over most of the post— 1960 period [see Feldstein and Horioka ( 1980) Recall that the current account measures a country and the rest of the worId. and the fact that gross capital and F i el eke (1962)]. the net +1 ow of Both the resul ts flows have been lar ge capital between of this section sug gest that small current—account imbalances are n ot evidenc e of capi tal im mobility. A further r mason why small current ac counts need not imply capital immobi— lity is tt a countrys bilateral current account with respect to an individual trading partner not infrequently exceeds the difference between its t otal sa ving and invest ment. that definiti ons LI SeU reduce the me asu red lB Secti on V. below, points out in national I ncome statist ics may artificially var i a bility of current accou nts Howe'er, the em— pirical impor tan cc o + thi s distort ion is unknown at present. Tobin t1983) , Westp hal (19 83) Summers 1985) , and othe rs have suggested that governments m ay targ et th e current account over t he long run through fiscal measur es desi gned to offset changes in pri va te spending. The extent to whi ch small size of c er do genou s fiscal policy reaction urren t—account mb alances s responsible for the is, agai n an open question; Summers (1985) prese nts some inst rumental—variabl ee stimates that appear to support this e x p1 anati on. It s hould be reitera ted however, that the simulation re suits repor ted above show that a str ong cross—sectional savi ng—i nvest ment covar i ation is consistent with per fect capital mobility even in the absence of such current—account targeting. IV. Time—Ser in Covariation between Saving and Invest.ent: An Example Section III explored the i nterpretati on of cross—sectional cor - relations between long—run average saving and i nvestmen t rates. The Feldstein—Horioka reasoning impi ies also that the time— series correla— tion between changes in saving r ates and chan ges in mv estment rates should be zero as well if capitaI mobility is perfect. This section discusses this proposition at a theoretical 1 evel show ing that its validity will depend on the nat ure of the sho cks imping ing on the economy. The discussion serves as a backgroun d for the estimation of time—series saving—i nvestment correlations in section V 1, below. 4 simple intertemporal model of a small open econ omy illustrates one channel leading to a posi tive time—series correlati on between in— n novations in saving and innovations in investment. That channel is the response of both saving and investment to temporary shifts in the productivity of domestic capital and 1 a bor. Say ma and investment may move together in the short run even if domestic firms are entirely foreign owned. The essential reason for this co movement is again the fact that labor is not mobile across na tional b oundaries. An increase in domestic factor productivity therefore entails an increase in the domes— tic wage; and if this increase is suffi ciently transient, saving will rise as suppliers of labor spread it cv er all + uture periods. The model is deliberately kept as simple as possible; in par— ticular, a nonstochastic environment is assumed • While a stochastic setup would of course be necessary to develop r igorously the model s empirical implications, my goal here is merely to illustrate an aspect of the saving—investment link in open ec onomi es The possibly dif- ferent identities of the agents who make saving decisions and those who make investment decisions is highlighted below b y the presence of a stock market and value—maximizing firms. However the competitive equi— librium naturally I eads to the same allocation of resources that a central planner wou ld choose. A small open economy faces a perfect world capital market, In— dividuals consume a single good which may also be transformed into a unit of capital or lent abroad at the interest rate p. The world capital market is perfect i n the sense that individuals may lend or borrow any amount they wish at the rate r, subject to a lifetime budget constraint to be discussed bel ow. All loans are again denominated in units of the single consumption good. The represen t ative immortal consumer has a fixed labor endowment (normalized at uni t y) which he sells domestically at the wage rate w at tine t. H holds his nonhuean wealth at time t in the form of claims on foreianers (possibly neative) and shares ht (0 of the single domestic firm. ht s 1) in the profits Shares pay dividerds (and bonds pay inter- est) after a period. Let dt denote the dividends the domestic firm pays out in period t and the firms e—dividend (or end—of—period) market alue. Necessary conditions for the optimal individual consumption plan under perfect foresiaht may be derived by maximizing the consumers objective function (20) E u(ct) t—1 w subject to + (21) An implication + (1+p)btj — c Nt + bt (t 1). of the necessary conditions is that in a perfect— foresight equi librium, shares in the domestic firm offer a rate of return equal t o the wor Id interest rate: (22) (q +d — t+1 t+i 1/ = p. = l/(l+p) The si mplifying assumption yi elds the further implication that i ndividuals choose a perfectly flat consumption path. Consumption is flat at the highest constant level that allows the lifetime budget constraint (23) 1(1+p) t—1 (ct - wt) (q1+d1)h0+ (1+P)b to hold as an equality. The implied consumption function is 4 (1+p)b1 + Ej0 (1+p — w t+j (24) c for all t 1. —24— Consider next t he The firm is in labelled behaior of the repr esentative domestic + i r m. "dome'stict not because it is owned entirel y or even part by domestic r esidents, but because i ts capital cooperat es with domestic labor in the production of output. The firm chooses a progr am of production and mv estment that maximizes its beginning—of—p er value v, equal to the dividends. i od discounted present vol ue of current and future In the Mod igi iani —Mi 11cr environe ent that has been assumed, it makes no differenc e how the firm finances its investment. It is convenient to assume that the firm does so e ntirely through retained 20 earni ngs. Output at time t, yt, is a constant—returns f unc tion labor domestic capital and a factor—product i vi etftn) of ty disturbance Capital may be instal led costle ssly, and it depreci ate s in use at rate I. Installation takes a period, however, and instal led capital may not be removed from produ ction unti I the fall owing pen od. (In other words, the stock of capital unlike th e labor input, is a pre determined variable.) The firm's max i mand, the present discoun ted value of its stream of dividend pa yments Cdi!i may therefore be written: (25) v = r 0(l4p) [e+f(k+.tn+.) Equation (22) i mplies that v = q 4 - — kt+i+i + (l—flkt+.]. dt. The probl em's solution calls for investment and employment paths such that t F' (26) (27) &f n(k t,n I = t w t ——C— for all t (although the ;niti0l capital stoc( is not subject to choice). Notice that when rules (26) and (27) are followed, the ex—dividend value of the firm is given by (28) t the end of the market period, the firms value must equal the stock of capital that has been put in place to participate in next period's producti on. In equilibrium, the firms demand for labor equals the available domestic labor force; (29) 1. To be concrete, take once again the Cobb—Douglas case f (k,n) = kDn. Then the equilibrium capital stock and wage in each period are given by (30) kt = (31) (l_u)[u/p+t)tulm(et) Net saving in period t, denoted S, is given by (32) St = Let v = w + 81/lu (q + dt — 1)h1 + Pbti — c. Equations (22), (24), and (32) imply that along a perfect—foresight equilibrium path, ( St w — = (l_u)[m/p+flmfl - PEo(1+P)vt+]. Equation (30) implies that the perfect—foresiqht level of net investment in period t, is (34) It = kt+i - kt = (vt+i - Consider now an una nticipated rise in the productivity p araseter which had previously been expected to be constant at the level v. The shock occurs in period 1, and, as will be shown, it qenerally causes both national saving and domestic investee nt to causes in that pen od. Equations (33) and (34) which presuppose perfect foresight, a re ap- plicable after period 1 p rovided no furth er unanticipated dist urbances occur. But because k1 i s predetermined an d was chosen on the b asis of mistaken expectations, Si and I must be calculated from first pr in— ciples. I will assume that from period 1 onward, the productiv ity dis— turbance follows the path (35) Vt t For N V + At-.1 (V-1 — i.) (0 < A S 1). < 1, (35) represents a transitory increase in productivity from i' to v' that decays at rate A. For N = 1, the productivity increase is permanent. In period 0, fArms choose k1 so that the expected net marginal product of capital equals the world interest rate, vIUfk(kl,1) = p + g This leads to k1 = vLm/p+&)1lU. After v rises to v' in period 1, however, the capital stock rust remain fixed at k1 even though the the capital stock desired for period 2 rises. Net investment in period 1, equal to k2 — k1, is ther efore gi yen by = [u/p+S] 1/1—u Nv' — it) > o. Investment in all futur e periods is negative (when 7.. 7.. = 1) if < 1) or zero (when there are no further shock s. 4ccordinq to (14) and 17C time path of investment from period 2 on is S-i. C, = 1/F 31! 1[ Fiqure 2 j)t1 ) 0 3 (t 2>. illut rates the response of domestic investment to a temporary productivity in crease. What abou t the behavior of national savi ng? First—period consump— tion jumps to a level fully incor porating the information embodied in (35) while (as no ted earlier) remains at I ts predetermined level. Period I savin g S1 is therefore eq ual to w1 + (q1 + d1 — q0)h0 + pb0 C1, or, (36> S using 1'iA — 26> and (28) = (1/I+p)((w1 = (lf1+p){tw1 — + if pZ.1(1+p) w j+1 3 + (pfl[(v'/i> 1-a_1 )k1h0) is the component of saving due to deviations between the current real wage and the discount—rate weighted average of future wages. When the current wage exceeds the permanenU wage, for example, househ olds will tend to accumulate wealth in order to smooth their consu mpt ion over time. The second term in the braces in (36) reflects the wi ndfal 1 gain to stockholders caused by a temporar y deviation between the net marginal product of capital and the world of return p. Becau se c annot rate be adjusted until period 2, an unan- ticipated producti vity sh ock in period 1 leads to a deviation from the Perfect—foresight arbi tra ge condition (22). The resulting abnormal profits are expected to disappear next period, so only a fraction p/1+p of the windfall is consumed in period 1. To understand the response of aggregate saving, it is useful to consider each of the terms in (36) separately. The effect on saving of temporarily abnormal profits is It 0 Time 1 Figure 2 nitude is independent of the persistence parameter . Equation 3O) shows that thi s effect is given by (1 /1 +p) (p+V ((Ku' 1/ l+p)utalpfl However a/i—a (1—a) a — (Ku') v / 1 01] K h.) 1 0 v) )h0. the persistence parameter ?\ plays a key role in determin— ing the impact of wage movements on saving. When ? so that the 1, productivity s hock is permanent3 the period —i wage rise s to the level 1-a) (VI) iska = (1—a)(u/p4t] a/i—a Ku') shock wage and the wage (1—m)(a/p+f] i—a a V a/I—a which lies between the pre— V1 expect ed to prevail in all future periods (see equation (31)]. Since t he wage in p eriod 1 is there— fore below its permanent level, the +irst t arm in (36 equal to (1/1+ p) K 1-a) (a/pH 3a11-a1 (1) V a — V' is negative and If h.U = 1, all shares in the domestic +irm are domestically owned, net saving when =1 so that first—period is = Ku') 1—u u — (l—u)v' — v mu], a neoati ye (and probably small) n K 1; if and saving is zero from p eriod 2 on (see (33)]. If the only shocks h itting the economy are pr oductivity shocks which are perceived as perea nent, the time—series cor relation between saving and investment changes is likely to be negigible In the general case the t ime path of saving is SI = (i/1+P)(a/P+vJlaccl_(i_h0)Dac(VI a / 1—a St (I/l+p)la/p+f] (u' — lmua_V]_(l_a) EpXJ (l+p-) i v ' v)I(1 )ytl/Ki+px)] > U enouch (so that the disturbance is sufficiently transitory), (t -v))1 2), may now be positive. Since wages are expected to decline over time, the increase 2 — in w oer w 1 may be sufficiently larqe to induce savino even though w (I is lower than it would have been if the firm had correctly foreseen the d 0. Fgur e 3 depicts a saving per iod—1 prod uctivity i ncrease in p er i 0 pat h in which first—per iod saving i S p0 sitive. Th is may occur even if all shares ar e owned by foreigners in h h0 0), alth ouqh is increasing 0 Figures 2 and 3 t ogether make the point that investment and saving innovations can be posi tively correlated when both are c aused by tern— porary shifts in the domest tivity alter saving as i C well production function. Shift 5 in produc— as investment incentives by conferring a windfall gain or loss 0 n domes tic shareholders and chan ging the path of real wages. When shock s to the prod uction function are sufficently transient, saving and i nve stment Wi 11 move together in the short run. The purpose of t his section h as been to provide a single illustra— tive example, but it i s ci ear that factors other than productivity shocks can induce a po siti ye conrei ation between savin g and investment innovations. Suppose, for example, that production req uires as an input an imported good that is d istinct from t he output of t he domestic firm. If imports and capital ar e complements i n production, a temporary fall in the relative price of imports will sp ur investment and also encourage saving as households spre ad the temporar y increase in their real incomes over all future pen ods. Temporary chang es in the won d interest rate p (the intertemporal terms of trade) also cause simultaneous movements in saving and investment.21 V. Nati onal A Proble. with National Income Account Data income account (NIA) data provide notoriously poor proxies for th e economic concepts of saving and investment. For example, St 0 1 2 3 4 Figure 3 Time —3(1- purchase-s o consumer durables, which really represent investment, are treated in the accounts as current consumption. Since national product figures represent the nominal val ue of goods and ser vi ces produced by a countrys factors, as measured by real ned finan cial 11 ows, exchange— rate induced redistrib utions of w eal between n at ions do n ot enter into th the NIA definition of national in come or saving. Also i gnor ed are the chanoes in the real va lue of net ext e r nal debts due to i nfl ation [see, for example, Freedman (1979)3. The previous sec tions theo retical model suggests an additional data problem which is related to those associated with price—level variation. This prob 1mm is most acute for mx ch ange—rate ec ono ohms and in which a substantial share of domestic industry is forei gn owned, or in which much of domestic wealt h is held as shares in fore ign firms. In the former case, that in whi ch forei gners own domesti c shares, the correla— tion between the NIA mea sure of saving and invest ment will tend to be higher than that between the tru e value of saving and investaent. Continue to assume ther e is no government, as in section IV, and recall the definition of net saving i n that secti ons model [equation f7 ti— St - cit tt i + wt + (cit 4 — Ct. The defini tion of dividends dt and the fact that q = (28)) impl y that aggregate net saving may be writt en as (37) St = Since q + equals net t i on. — Vt lkt — + dt — q t-i 1(1 — = + ( k , 1) k — h ti ) + — Ct. (37) states that net saving output plus net factor payments from abroad minus consump— In contrast to (37) the NI definition of net sav1n. N1St, iqnores the capital ains on foreiqn securities accounted for by (37) and instead sets (38) NIASt = yt — •kt — ( t 4 d th ti The second line of + pbtj dt(i—ht + pb1 — c ) + t — Ct (: t+l — t (38) shows that NIS i s the sum of two components, the NIA concept of personal saving (which also ignores plus what is usual ly capital gains) defined as corporate savi ng, i.e., retained earn— ings. Regrouping t he terms on the second line of (8) shows that in the model of section IV, (39) N14S = S + (l_hti) — kt) itplying that the NIA definition of saving equals actual saving plus a term proportional when h 1, to net investment. so that all shares are domestical ly ow ned,the NIA concept of saving and true saving coincide in this model The reason is that corporate sa ving just equals the increase in th e firm s ex—dividend market value, so that when no shares are owned by fo rei gne rs, the addi— tion of corporate saving to personal saving corrects the 1 atter measure for the omission of capi tal gains from personal moo me. Bu t when h < 1, the addition of c orporate s aving to personal saving i nfl at es aggregate savi ng by i ncorrectl y counting as part of domestic i ncome capital gains that actual ly accrue to foreigners. The error equals the f raction of fore 1 gn—own ed shares tImes the firms net investment Equat ion (39) m akes clear that NIA convent ions may art f id ally Increase th cor relation betweer measured nation al saving an d domestic investment. Fara doxically, the magnitude of this distortion is greater the larger the share o4 domestic firms owned by foreigners, that is, the more open is t he economy to foreign portfolio investment. lndeed, in an integrated wor ld economy with full international portfolio diversifica— tion, we would ex pect domestic residents to own a negligible share of the domestic f irm when human—capital risk is approximately uncorrelated with the fir m s profitability. But if h 0, national income data for the economy o+ section IV would nonetheless show NIA net saving and investment as being perfectly correlated precisely when investment is totally un correlated with the economically relevant measure of saving. The prevalence of earnings retention as a means of financing corporate investment lends empirical significance to this problem. 2 But the magnitude of the errors involved is unknown. Gross capital flows between countries are very large even though net flows, as measured by current account imbalances, have been small (see section Ill). So while the problem may be of minor importance for the U.S., where the ratio of foreign—owned capital to total capital is low, it may be of greater importance in other economies. It should also be remembered that in reality, NIA saving differs from true saving not only because of capital gains on foreign—owned shares but because of unobserved capital gains on foreign shares owned by domestic residents. The effect of this additional discrepancy on the correlation between NIA saving and investment is theoretically ambiguous. VI. Saving and Investment in the Short Run: Time—Series Evidence This section presents estimated correlatio ns between quarterly changes in saving and investment rates, for seve n UECD countries, over the period since the restoration o4 currency convertibility in late 1958. Confidence intervals for tnese estimates a re also calculated. Ihe enpiricJ r&sults are consistent wit h a significant and increasing decree o{ capital mobility There are over the sample period. least four reaso ns why short—run time—series correla— at tion coefficients between changes i n saving and investment rates are of interest. First, and mo st important ¶ they provide a set of empirical recularites with whmch theoreti cal open—economy models must be consis— tent. These empir ical r egularities a iso suggest hypotheses that may inspire more powe rful t ests in the f uture. Second, estimation of the coefficients and their asymptotic di stributions permits an assessment of the significance of the ir difference from the value of 1 that would obtain under comp lete c apital immobi lity. Third, the results can provide scce guidance on the ap propr i ateness of pooling time—series observations on different cour tries, as in Feldst em strong mdi cation (1983). In fact, the data give a that such pooling is not appropriate. Fourth, even though (as was sh own in section IV) short—run saving and investment changes need not be unco rrelated und er perfect capital mobility, measures of thei r the forces that correl ation are likely to be unaffected by some of the may limi t prot racted current—account imbalances over longer periods. This is still insufficient to allow rigorous inference concerning a countr y' 5 opennes s to capital movements. But once the saving and in vest me nt rate dat a have been purged of movements caused by known common factor s, such as effective labor—force growth, the iden— tifying assum pt ions needed to permit such inference become more plausible. Of tion of some cours e, addition ml tests may ultimately lead to the rejec— or all of these i dentfying assumptions. The dat a used in estimat ing the correlations a re nomin al quarterly national—account data from the International Monetary Fund's Inter na— tional Financial Statistics data tape. The sample of countries was —34— dictated by the availability of quarterly data over a reasonably long sanp 1 e per iod; it cons sts of Austr all a , Atistri a, Republ 1 Co + K i For the at t e mp t Berma ny, Japan sa ke the Uni ted no Canada, the Federal and the Un i d a ted States. 24 of c omparabi 1 ity with the Fel dstei n—horjoka r esul ts, no the data wa s made to adjust to account for any of the potential problem s discussed in secti on V. In ad dition, gross rather than net saving and investment sen e s were u t il i:ed. Saving S was defined as gross n ational produc t (GNF consump tion. minus p ri vate plus go verneent Invest ment I was def in ed as g ross fixed capital f ormati on plu.s the change in st ocks. The corr e ations that were computed w ere between t(S/GNP) and t.( I /ON P), wher e L denot es a quarterly first dif— ference. The populati on val ue of th is correl ation will be labell ed p. Obtaining point est imates of the cont empor aneou s correlati ons p51 presents no difficulties. Under conditions spelled ou t in Fuller (1976)1 of the ts(S/ GNP) and chapter 6, which imply joi nt covariance sta ti onar i ty A(I/GNP) series, the sampl e correlations provide consi stent es- timates of the population correlations p51. Statisti cal inferenc e based on the est i mat ed an asymptotic distribution theory, however. Ass LI a(IIGNP) series are jointl y normal, let Sl j) = correlations requires me that the MSIGNF) and m15(—j) denote the and let unconditional populati on covar 1 ance Coy E s (SIGN F c1 L) denote the corresp onding sample covar ian observations. Denote the popul a tion aut ocovar = Var [a and m11(j); of cou rse, 0 Var[t(l/GNP)], and p51 = functions o{ £1 (0) I 0 11 ce based on a sample of T i a nces for the series by (S/ GNPU, ( 0 = 1. If the autocovariance the two series are absolutely summable, then (40) liST.ll Vartc51 (0)) Z r5(J)r11 Li) + Ej_SJ (J)c15(j) M —35.- [Fuller (T[Cç1 (197) theorem 6.5. 13. It can be shown that the random variable (0 — (0)3 has a limiting normal distribution with mean 0 and variance equal (41) JT(rj — to Fl tHannan 1970), theorem 143 chapter iV). Therefore p1 in distribution. From (41), th asymptotic standard error c-f r51 is just (42) M/To.s (0i i(0)3. The variances and a11(0) in (42) can be consistently es- timated by sample variances. It is tently ir also possible to estimate M consis- the time domain by truncating the infinite sums in (40) at as j that increases sufficiently quickly with sample size and sub- stituting sample covarlances for their population counterparts. However3 S.in;letun (19601 and Hodrick and Srivastava (1965) have suggested a frequency—domjrT procedure for estimating Fl that is more convenient from a computational point of view. That procedure is implemented in obtain- ing the standard error estimates reported below. Define the autocovariance matrix r61 (j) (43) m(j) = °Is 0(J) Then the spectral density matrix for the vector process at frequency i (44) sk) is given by (1121T) E '(u)e' 11 where i j-i. Direct computation using c43) and (44) shows that N can be written in the form (45) N = 2111 ssii + (V3du. Consistent estimates of the spectral density matrix s() may be used in "6 formula (45) to obtain a consistent estimate of M/ The results, for the entire sample available since the return to convertibility, are presented in table 1. A pronounced pattern emerges from these estimates. For the smallest countries, Australia and Austria, the contemporaneous correlation between t(SI6NF) and t(lIGNF) is low. In the case of Austria, r51 is statistically insignificant. For Canada, Germany, and the United Kingdom, the correlation coefficients are statistically significant but lower than the cross—sectional coefficients reported in the Feldstein— Horioka papers. Dn]y in the cases of Japan and the United States, with r51 values of 0.846 and 0.908 respectively, are the correlations of the same order of magnitude as the coefficients estimated by Feldstein and Horiok'a. Also, it is only in the cases of Japan and the U.S. that the estimated coefficients do not differ significantly from I, the theoretical value under complete capital immobility. However, the U.S. is the largest country in the world economy, while Japan has had extensive capital—account controls until very recently. The results of table 1 therefore suggest that the measured saving— investment correlation is an increasing function of country size. Except where capital controls were an important factor, the correlation is low for small countries, moderate for medium—sized countries, and high for the largest country. Harberger (1980) and Murphy (1984) have argued that the link between saving and investment will increase with country size Table 1 Estimated Correlations between Chanqes in Saving and Investment Rates (Quarterly Data) Country Sample Period Australia 60:! — 83:Iv 0.194 0.106 Austria 70:11 — 84.1 0.13: 0.195 Canada 59:! — 84:11 0.550 0.125 Lermany 60:111 — 84:11 0.649 0.133 Japan 59:1 — 83:IV 0.846 0.140 United Kingdom 59:1 — 84:11 0.604 0.166 United States 59:1 — 84:11 0.908 0.143 Standard Error because a ccurt'7 h or wor I at certainly C in world prices prows a; its share ci pro sented tiectes to influence the world interest rate and ati I itv anrot output prows. The es- inter pretati on, and be i ruterpreted as cv idence aoainst p erfect capi tal with here are consistent this ndsed, the evidence is ful lv consistent wi th a world in which tI!L!.I .1 capital mob iiity is substantial, but in which saving and investm ent changes can be significantly correlat ed for reasons 1 ike those d i scussed in section 1V and because of country si Se 27 IL 1 s interesting to compare th C results of table 1 to a pooled t I me —5cr i e s cross—section regression n Feldstein (1983), p. 136, which 1 correl ates year—to—year changes in th e rate with year—to—year i n vest men t changes in the saving rate. The slope coefficient in that regression is 0.Bt3 I! (wit h a standard error of 0.040) from whic h it is concluded that even year to year increases in saving tend to be associated with in- creases in domestic investment in the saving coun t ry by approximately Equal amou nts.h The evicence in table 1 shows tha t on a quarterly basis trere is c onsiderable heterogeneity a cross coLntr en with respect to the u niformity e;ontud e o this association. The as sumptior of the pool ing procedure is therefore im p t er pro of t the reported standaru error of estimat i the s c' ia -cnrrelati or properties is also ciifficult to It 1 a us i b 1 e. implicit in without a discussion on of the regr ess ion s error terms. S nce the br eel down of the post war systeit nc f.!ed e;change rates n l57 there has been an apparent i ncrease ic t he integration of world capital earl ets. Four set; of reasons are us u a 11 y given 4or this cieeloprrent. The first involves the di scant I nier' tc cap;tai cavernart t ing hat had impeded i nt er un:or fi:ed ecchar.po rates ciL t appearec' super f of r a 1 u o u the wioespread bar— tional money flows s under f Icr ible rat Ci. The second certer s on the emergence of the OPEC surpluses after art tho orowtb c{ world trade generally, develoornents that raisEc ounaro for the services of i nt 5 r fl a t i C' P a I 4 inanc al :nterseciaries. T he third set of reasons is related to technological chanqa jr the corn muni cat I UPS and dat a—processi nq areas. The fourth crc-c ems I ncr e a 5 ed multinatcnai corporate activit 28 These considerations suggest that the stochastic propert ies of the saving-investment process may have changed over time. To inves ti gate this possibility the samples were split at 1972:IV and the cor rd ati on coeHiclents were estimated separately over the sub—samples. The pr oce— dure was not carried out for hustri.a because the data on that countr y are available only from 1970.) Table 2 reports the results. jr all c ames except that of 4ustralia, r51 drops——sometimes dramatically——be t ween the earlier and later periods. This evidence is consistent with the widespread belief that the decree of international capital mobility increased after 1972:IV. Note that for the second sub—sample r51 reman-s more than two standard deviations below I for all countries other than Japan and the U.S. But once again, the high estimated correlations for these two countries can be ascribed to capital controls in the Japanese case and country Size in the U.S. case. Because the estimated correlations are higher before 1973: I and because smaller sample size results in less precise estimates, r51 lies within two standart errors of 1 more frequently in the first sub—sample than over the complete sanple. One further test can be conducted to help evaluate the argument that high values of r01 for the United States are a consequence of its size rather than capital i mmouil i ty. The Uni ted F ingdom occupied a similarly dominant position in the world economy during the pre—Worid War I gold-standard era, particularly from 1870 onward, and its experience then is often cited as the o Table 2 Estimated Savinu—Investeent Correlations up to and after 197:IV (Quarterly Data) after 72:IV Country r51 up to 72:IV Australia 0.095 (0.147) 0.331 (0.155) Canada 0.716 (0.193) 0.399 (0.143) Germany 0.747 (0.198) 0.536 (0.168) Japan 0.885 (0.184) 0.723 (0.190) United Kingdom 0.622 (0.196) 0.593 (0.235) United States 0.962 (0.191) 0.870 (0.207) Note: Standard errors appear in parentheses. ccrreiaton hc.t ecbiIit. rent ratec c\Er between changes in U.h. savinQ and invest— the Qoib—standard direct evidence that the U.S. results are consistent with substantial ta It1cti ii ty.' Ua1 data Eel nstein +rcIL 19 error d rqj and its asymptotic standard error were calcu— he estimate d correlation c oelficient is 0.722, with a standard I an of C: 199. Thi U.S. over t he those coefficient s not quite as high as that for the 1 float in g repor ted of r5 for the from 1, in 5 pite of the period. it follows that of the high value capit a! move gi en t. t ha t tent with substant 1 al 4 r o m undeniable mobility post wa r U.S. prcvi The picture ntrIe5 period, but it exceeds many of In addition, the coefficent does not 1 and 2. dur ing the go 1 d—standard inter neti 0 nal 0 0U enchanqe ra te n t ab les d1+er sign i+ i cant! y capital table 2. Say • the post war tests, lated. the U.k. coverinfl the period 1871—1912 were taken + or In most emerges and increasing capital cases the value of from t hese time series tests mobility among OECD saving—investment correlations are qu ite impl ied by complete cap ital immobility. are not, high corr ci at i 0 + C: t S or to Cnown is consis— can be asc ribed ei ther to Wh far en they large—coun try ef— off ic al restricti ons on i nternational asset trade. VII. Con clusi ens Cap tal ing mobility i n the wor ld asset yiel ds economy h as been measured by compar— across count r l es an d, more r ecently, comovements be tween savi ng and in vest duced by Eeldstein and Horioka (198:0) encounter se.ere considorahie identification merit probl . and by by studying e sec Felds tein (1983), may the of focusino attention directly on the determinants of intertesporal trade patterns. E:oth international interest—rate data and data on national saving and investment patterns are consistent with a world in which capi tal mobility is substantial, at least amon g OECD countr ies. In p articular quarterly time—series correlations bet ween changes in saving rates an d changes in investment rates are in mos t cases signi ficantly distant 4 r om the value of 1 that would prevail were capital enti rely imm obile ac r o cc national boundaries. The data are also consistent w ith the hypothes s that capital mobility has increased in recent years • Future researc h should aim to sharpen our knowledge by explai ning both the t i me—ser i es correlations reported above and the cross—sectional correlations em— phasized in the Feldstein—Horioka studies. Notes I thank Michael W. Klein for excellent research assistance and sugges— tions. Helpful co mments were made by Robert Cumb y, Michael Edeistein, Alberto Giovannin i, Robert Hodric k, Philippe Jor ion, Laurence Kotlikoff, Allan Meltzer, Fr ederic Mishkin, Kenneth Singlet on, Rene Stul:, and Lawrence Summers. All errors and opinions are my own responsibility. Financial support was provided by grants from th e National Science Foundation and th e Alfred F. Sloa n Foundation. 1. The synchronized nature of the rise in world real in terest rates is documented, for various Elanchard and Summers me a sure s of expected domestic i nflation, by 1984) and by Cumby and Mishkin 1985) 2. As noted by Kotlikoff (1984), there are special circumstances (such as those assumed in the static Heckscher—Ohlin trade model), in which —41— the international allocation of a given stock of productie factors can be efficient e yen in the absence of capi tal mobil i ty. Ohlin model! t his occurs when no country is speci ali z ed In the HecIscher— in production, so that factor prices are equal everywhe re. But w her capital is immobi— le, factor—pri ce equali:ation at a point in time doe s not imply that the world allocati on of resources is interte mporal I y dynamic Hecksc her—Ohlin models may entai 1 ef f icient. In addition, optimal ca pi tal —accumul ati on paths leading to a steady state in which one of t he countries is spe— ciali:ed (or b oth are) and factor prices differ i nte rnationally. 3. Some policy implications o + th is Ii ne of empi r non discussed in Obstfeld ( At TOt i cal research are Pro blems con nec ted with the taxation of interest paym ents remai n rel evant even when the group of assets studied is narrowed; see Howard and Johns on (1 982,1983). 4. Similar analyses appear in Hansen and Hodrick (1983), Hodrick and Sri vast ava (1984 Svensson (1 984). • •£700 nor Stul z Kouri / 'TOO Inn-v Lucas (1982), and Stockman and (1984) p rovi d es a useful survey of the theory of asset prici ng fr om an internati onal perspective. 5. In models with cash —in—advance constraint 5, (1) and (2) will not hold in general if nominal consumption expendi tur es cannot be predicted with certainty a p eriod in advance. St ockman and Svensson (1984) analyze a model of that type. I n contrast, (1) and (2) always hold in Lucass (1982) cash—i n— ad vanc e model . Eec ause the pr esent discussion is il— lustrative, I make no attempt to motivate th e existence of national mon i e 5. — 42— 6. Uncovered interest parity follows from (3. if the marqinal consump— tion value of domestic currency is distributed independently of the exchange rate. While it is d ifficult to assess this possibility in the present, partial—equilibrium setting general— equilibrium model s of Lucas (19 82) and Stockman an d Svenss on (1984) suggest that (4) is Un— likely to hold when there ar P outpL't shocks or domestic moneta ry shocks. Hansen and H odric k (1983) sh ow that (3) leads to a log—linear tion to (4) i nvol ving a time —i nvar i ant risk pr emium when all variables ar e joi ntly lognor mally d istri buted. empirically. ) If agents are risk ne utral , (4) a p pro x i ma — rel evant (They reject t his model h olds if the pr ice level and exchange rate are indep endently distributed [see Engel (1 984) and Frenkel and Rn in (1980)). The assum ption of ri sk neutrality may have implausible conse quences in general equilibniu it however. If the instan— taneous util ity f unction is linear and the same in each pen od, for example, mar ginal rates of substitution in consumption, and hence the terms of trade, must be fi xed. 7. There i 5 relat ively I ittle empirical work that attempts to model the risk premi urn expl icitly. Hansen and Hodrick 1983) test, and reject, some simpl e model s of mt ertemporal equilibri urn (s ee the previous footnote). Fr an ke 1 (1982) is unable to reject a tw 0—period mean—variance model based on a portfol i o of six currencies. Hodr ick and Erivastava (1984,1985) discuss emprical aspects of Lucas '5 (1 982) model. 8. The argument made above to justify ignoring default risk on Eurocur— rency deposits is inapplicable here because the deposits being compared are not issued by a single bank. Even when there is no currency r i s k nominal interest rates can therefore differ across national boundaries. L However he detec ted an increase in potenti al arbitrage profits over the period freT the end of 1980 to early 1982. part to inc reased co their requl a 1 0 the part of banks and r s. Frank el (1984) discusses recent measures opening Japanese capital mar kets ¶ 6i a t 0 He attributes this in van i spr eads and also presents evidence on interest differentials — i both the Fagano and Ito papers, like Kreicher's, account for bid—ask n calculating potential arbitrage profits. Ito also accounts for domes tic transaction taxes. 11. Since ng, a correl ati on coefficient, there is no reason for it to be less than This is b orne out by the simulated regressions reported later in this section. In what follows I sometimes refer to as a "correlation, II but it should be understood that 12. Feldstein and Horioka (1980) also present instrumental—variable estimates based on an explicit model of aggregate saving. They regard those results as supporting the conclusions reached earlier in their paper. Howeve r, interpreting (8) as a structural investment equation involves some potential specification errors. A number of studies have pursued the a pproach outlined in the text. Penati and Dooley (1984) and Fieleke (1982 obtain results consistent with those reported by Feldstein and Horioka. Capric and Howard (1984) find that the results are quite sen sitive to the period over which saving and investment rates are averaged, while Summers (1985) finds that the correlation between saving and investment rates falls dramatically when less—developed —44-- cc'untrieE arE included in thE sample. Eachs (1961,1953) carries out cross—sectional regress i on; c h n p es in domest ic 1 n Vol Vi n p investment in apparent current accounts, findings of 1 I cited capital G4i and 1/Y, concludina that have ha d large, negative effects on OECD contradi ction of mo bi 1 ity. However the Feldstei n—Hon o ka Sachss empirical r esul ts are subject t o the difficultie s of mt erpretati on outlined below i n connection wi th the Feldstein— Hor i oka findings. On the basis of an empirical sim ultane ous—equat i o n model of saving and investment, von Furstenberg 19 B 0) i n tern at i on a 1 by capi t al (lime (197 7), on fiscal def i concludes t hat the United St ates is quite open to movement Anothe r relate d approach is that taken wh o performs time— ser ies regr essions of trade balances cits for a large sample of count ries. Seve ral papers in the development literature att empt to measure the impact of capital inflow on saving and investment by regressing those variables on the current account. Leff and Sato (1954) discuss some econometric bi ases that may arise. 13. Fel dstein and Horioka (1950) recognize the potential importance of common factors affecting both saving and investment, but assert (p. 319) that th eir strong results place 'the burden of identifying such common causal factors' on proponents of the hypothesis that capital is interna ti onal I y mobile. The demonstration in this section that equally strong results can emerge in a world with perfect capital mobility hopefully redi str ibutes the burden more equitably. The empirical relevance of the forces driving this sections simulation example is discussed below. Summers (1955) points out that least—squares estimates of do not measure the effect of aggreqate saving on investment when fiscal policy systematically counteracts shifts in private spending. The theoretical At -'U-- possihiljt that exceeds 1, not ed Interpretation of this coefficient as saving that is ref1ectej above, seems inconsistent with the fraction of any tb increase in ic investment. 14. Buiter 19B1) has studied a two—coLintry version of the model employed here. effect in the model. I concentrate here (and in the theoretical model of section IV) on net saving and investment, rather than on the gross concepts em— phasized by Feldstein and Horioka (1980) and Feldstein (1983), because net concepts are the economically meaningful ones. s remarked above, those authors found even higher correlations between saving and invest— ,.ent ratios constructed from net measures. They ascri bed the higher correlation to a common lb. 6rowth rates g were taken to be average annual real 6DF growth rates over 1970—1979, as reported in the United Nations Statistical book, 1981, table 30. (The GDP growth rate for New Zealand was calculated from data reported in the International Monetary Funds tional Financial Statistics.) Labors sharp, 1—e, was calculated as the ratio of employee compensation to national income in 1970. These data were taken from OECD, National ccounts of OECD Countries, vol. II, 1974. No attempt was made to correct for the labor income of the self— employed, so the estimate of 1—u used is an underestimate of labors s h are the This b ias reduces saving rates relative to investment rates in S mul ated economy. —46- 17. One alternative explanation involves the economys intertemporal budget constraint, which states that to the change in the economy s n et current accounts must sum over time external assets. 1+ there is a ten- dency for the economys external assets to approach some steady—state level, as a result of residents consumption preferences [as in Obstfeld (1981)] or of the pattern of sho cks disturbing the economy, saving and investment will necessarily tend toward equality over long periods. Features of the tax system simul taneously affecting saving and invest— ment rates could also be part of an explanation. 18. For example, German ys current account balance in 1982 was DPi 6.6 billion but it ran a b ilateral current—account surplus of DPi 14.7 billion against France alone in that year. In all of the three years 1979—19 61, Ger&any ran historically large current—accoun t deficits, yet it was a net lender to France and other countries. [See Deutsche Eundes— bank (1 963).] This typ e of current—account behavior is inconsi stent with the ide a that overall current—account imbalances are lieited by con— siderat ions of soverei gn—risk exposure. I am indebted to Larry kotlikof+ for thi s observation. 19. Stockean and Svensson (1984) analyc e a stochastic two—country monetary model in which the investment decision in one of the countries is explicitly modelled. They also find that saving and investment may be positively correlated, but the mechani sas operating in their model stern from terms—of—trade effects and are di fferent from the one emphasized here. 20. Taken literally, this assumption may require that dividends be —4—- roati\c. i1 sour periods. I he possibility of negative dividends raises no conceptual difficulties, but for the sake of realism one might want to assume that shocks to te chnology, and henc e period—to—period changes in the capital stock, are" seal 21. Persoor, an d Even eson (19B5 to study the e f I fec t s 1 use an overlapping—oenerations framework of various terms—of—trade shocks on saving and n vest men t 22. The pr oblern is al so discussed by Stocksan and Svensson (1984), who show how I t distorts reported current—account data. be modified if the firm financed some investment through debt issue. In this case the difference betweem NIAS and S would be proportional to net investment mi nus corporate borrowing. The problem does not arise here wh en investment is financed exclusively through the issuance of new shares 24. These data, with t he exception of the Austrian data, were available only in seasonally—adj usted form. The estimates for Austria reported below based theoreti cally preferable seasonally—unadjusted data. 25. in the U.S. data, the government consumption variable includes government investment. This is not the case for the other countries, whose nati oral —income data are compiled according to the United Nations System of National 4cc ou n t s. -48- 26. Formula (45) appears in Fisnean (1969), p. 1 21. In the present application, the spectral density matri> was est imated at T equally spaced frequencies bet wee n —s and 11, where I is the number of observa— tions. Atriangula r mm ooth ing window of width me yen was used. An es— timate of Ii was th en c a 1 cu lated by summing the i ntegrand in (45) over '1 the I frequencies inult iplying ar.d the result by 27. Bummers (1985) per for ms a cr oss—sec t including sm all, 1 ems —d cv eloped countries in ci uded in the parameter is only - Fe 1 d st -7 I arge—countr y effect s are i ona I count r i em 4u'/T. regression on a sample in addition to the UECD ei n—Nor ioka studies. His estimate of the This evidence lends support to the view that in part respons ible for the Feldstein—Nor i o ha findings. 28. Bryant (1985) reviews the postwar growth of international financial intermediation. 29. Between 1870 and 1913, LI.I.. net foreign lending averaged 5.2 percent of ONE • a figure that is enormous by postwar standards (Edel stein 1962. I. The temptation to quote Keyness description of the per iod is i r r em i stible: The inhabitant of London could order by tel ping h is morning tea in bed, the various products of the eph one w h ol ee arth and in such quantity am he might see fit, and reasonably eKpe ct the r ear I y delivery upon his doorstep', he could at the same mo me n t an d by the same means adventure his wealth in the natural resources and new en- terp rises e v e n of any quarter of the world, and share, w:thou t cxc rti on or trouble, in their prospective fruits and advantages; or he could decide to couple the security of hs fortunes with the good faith of the - townspeople of or informatiw, might recommend. He could secure 1orthwith if he wished it, cheap and Comfortable means o transit to any country or climate without passport or other forsality, cCuld desatch his servant to the neighbouring office of a bank for such supply of the precious metals as might seem con'enient. and could then proceed abroad to foreign Quarters, without knowledge of their religion, language, or customs, bearing coined wealth upon hi person, and would consider himself greatly aggrieved and much surprised at the least Interference. But, most Important of all, he regarded this state of affairs permanent, except in the direction of further as normal, certa n, and improvement, and any deviation from it as aberrant, scandalous, and avoidable. (1919), C Keynes 9—10.] References P4liber, R.Z. (1973) The Interest Rate Parity Theorem: Journal of Political Economy, 81: Reinterpretation. 1451—1459. Blarchard, 0. J. and Summers, L.H. (1 984) Perspectives on High World Real Interest Rates. 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