# The Feldstein-Horioka puzzle and exchange rate regimes: Evidence from cointegration tests

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Panayotis Alexakis.

1. INTRODUCTION

One of the most challenging and contro\.ersiaf topic\ in the interna- tional finance literature over recent years is the relationship between investment and saving decisions in an environment of virtually inte- grated capital markets. The majority of the studies dealing with the subject utilize as a benchmark the article by Fetdstein and Horioka ( 1980) who showed that perfect capitrtl mobility conditions contribute to the lack of any relation between saving and investment decisions. In other words. savings in one countrv tend to remain there for investment purposes in an environn ;

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rtes amsng one aii that tl7e capital n7arkst in P rate systen7 nas characterize controls are ill (free) eurocurren ever, we believe 177arkets foHow/e in the U.S. cas U.S. ii7 1978 and th (sed also Figurr: 2 that displays intcre mid otfshore dollar markets during cim4deration ); as a rations (Edge carp) wtfre allowed to freely expand their work in international capital markets. In other words. the xed exchange rate syst437-r wb asshated with extensive capital an exchange controls that contributed the presence of a significant relationship between

ent decisions. At the same time, the relaxation of

FELDSTEIN-HORIOKA PUZZLE -if? i

P. Akxahis and N. Aptxgis

between saving and investment decisions in the United States as were defined in the innovative ,trticle oi Feldstein and Horioka Q 1 kfore and after the collapse of the fixed-exchange-rate regime. A general equilibriuln opti artificial (model) data technique is used to reveal w between savings and i

investment and sa arlalysis. splitting our sa through 1973 and some concluding re

This secti0n intrsdfnces ;a dyn ates m0del data f0f saving an cansists of idenkal. infinitely sumption (C) and investment (1

C denotes sea3 consumption. 1 leis the individuals (constant) subjecti

In other wlords, the representative in discsuntied flaw of

he strictly quasi-concave and twice differentiable. with all of its elements being normaI goods.

At the same time. the individual Paces a sequence of constraints. In particular. there is a resource constraint that dictates that

cIFIP[ C, + I, -I- CA, + - = GF*- I

Pt Y, -; tK,+, - K,, + -.

P, t2,

where Y = output production, 1 = investment decisions, CA = the current account. K = the capital stock, e = the exchange rate, F = foreign bonds (which pay one dollar at t + 1). PF = the price of foreign bonds (= /t> 1 + .T+I = the fureiq c terest rate.

In other words. Equation Z indicates. among other things. that our qent h;lr access to i 1 m.xkets ;tnd is aGowed to Invest i ~~t~~~~t~~~~~~!~ trltded 5 maxi tion process is taken over all st

function such as

with L = bf serviced a aMImed to follow a

mean zero and variance 0;.

At the same time uaO faces the following constraint:

Equation 5 descri atisn of total time into leisure and working time. Finally, the Oaw of motion for domestic capital shows that

where. I = gross investment. and 6 = the rate of depreciation, with 0

364 P. Alex&is and N. Apergis

CJc I - L,) = b U(C,) Y,IL, (9)

In order to exploit the information provided from the first-order conditions, we have utilized a specific form of the utiliry function, namely,

u c. II = CW 1 Yaz

Y l t 101

where. a,, a2 are positive parameters with 0 < a,, a2 < 1 and c a, = 1, while y is a risk wersion paranleter with y # 0.

i

E SOLUTION TECHNIQUE

Dynamic pragramming for studying dynamic optimization. Fo intertemporal decisions involve seiei3in the state of the economy, as desctibed by CA,, and Pt. However, during the fixed exchange rate e e variable et ceases to be an important state variabk f the model; in other u*t;rds. e, = e. Give of the utility function, obtaining closed form solutions is very difficult. Instead. a numerical procedure is used derive the equilibrium p ess of the artificial economy. Th;e meth uced by Bertsekas ( 1976) and utilized in dynamic macroeconomic els by Sargent ( 19

generates artificial time s la using a Monte C 144 sets (76 for the first period and 63 for

time series data (of which we calculated the e) for our relevant variables by feeding our

model with u,,, artificial values which are identically and indepen- dently distributed with mean zero and standard deviation of 0.0149. The last figure emerged from the estimation of Equation 4

L, = o.o09e, - 0. IO4 t,_, (0.61) (2.99) 01)

R = 0. I9 Standard-Deviation of Residuals = 0.0 I49

with z being Solow residuals, and numbers in parentheses t-statistic values.

At the same time, in order to make use of the state variable Ft+ we need to compute its value (at least in the first round) for the iteration process. Therefore, Equation 2 in steady state yields

FEILDSTUW-iORIOKA PCZ!lE a5

Then solving for F we obtain

P F = CC + I + CA - Y, c ePf _ , )

The aforementioned recursive problem was solved with the assis- tance of the Fortran larguage in conjunction with the Irtternationa]

athematical 69r Statistical (1 S) Library software. The algorithm converged after nine (9) iterations when the mode1 was hit with random technology disturbances.

However. to compute the equilibrium of the model. we need to the values for a set of parameters. The ( deep) parameters of

y are b, aI. ;~t?% B. OE, 6. y. The Generafized-Method- ) te::hnique proposed by Hansen 4 1982) is used. In

his article. he proposes and implements an economic estimation that avoids the theoretical requirements of an plicit representation of the stochastic equilibrium. Some other meth . that is. limited informa- tion methods. specify the decision rukes of an individual without specifying the (deep) parameters that describe preferences (of individ- uals and of corporations). The utilization of the GMM technique gives the optimal solution for the deep parameters of the model. For the empirical purposes of this section. we make use of the fohowing starting values for the deep parameters of the model: p = I. y = I. b = 0.3. a1 = 0.3. a2 = 0.7. e = 0.025 (Craine. 1975). 6 = 0.04. The data considered correspond to quarterly observations for the period 1955 through 1990 [splitting our sample into two time periods, 195543 and 1974-90. generated different values for the (deep) parameters]. Appendix A provides details of the data and their sources. Appendix B provides the associated instrument set of the derived Euler equations ot our model. The results are shown in Tables 2 and 3 both of which reveal that our mode1 performs relatively well (in both time periods). since the esttmated (deep) parameters are characterized by low standard errors. In other words. the values of the x2 statistic indicate that the overall performance of our model is relatively satisfactory. Following the estimation of the (deep parame- ters of the model, we generated artificial (modei) data for the afore- mentioned variables.

Feldstein and Horioka (1980) tested t eir pu=le or cb capital mobilit;/ hypothesis by regressing investment rates against

466 P. Alexakis and N. Apergis

Table 2: GMM estimates. Time period: 19SSql through 1973q4

WSQ iy 5 Y 81 82 b xZ(DF)= SLb

I 0.9% 0.01s 0.030 I 25 0.33 0.67 0.16s 2. Ia31 28.77

(0.12) (0.076) (0.065) ~0.31~ (1.02, (0.57) (0.1161 2 0.963 0.016 0.032 1.36 a.34 0. 0.66 2.14(3) 29.19

(0.14) (0.07~~ (0.072~ (0.35) (0.99) rO.64b (0.118) 3 0.97 I 0.016 0.029 I.37 0.35 0.6s 0.65 2.26(3, -34.5 I

(0.15) (0.102) (0.087) (0.40) (0.971 (0.60) (0.125)

Note: Numbers in parentheses de dard ewors. For the empirical purposes of our article. we made use of the values that corns ird step since the algorithm converged after three iterations. GMM values wew obtained with the assistance of the RATS wfware.

saving rates. Specifically, they regressed the gross domestic invest- ment to gross domestic nst the gross domestic savings to gross domes Under perfect capital immobility. the coeffic expected to be very close to one. In contrast, a coefficient nat significantly different from zero would be an indication of perfect capital mobility. However, as was explained in the introductory section, we employ two innovations in this article in contrast to the original Iuticle of Felstein and Horioka ( 1980). First. we test the perfect capital mobility between two differ-

te regimes, for example, under the Bretton-Woods nge rate system ( 195Sql through 1973q4) and under the

floating exchange rate system ( 19749 1 through 199Qq4) that followed i;cre collapse of the Bretton-Woods regime. Second, in order to deter- mine whether there is a strong linear combination of the high variance

Table 3: GMM estimates. Time period: 197Jq I through 199Oq4

Lw Q 6 Y 21 a2 b xZ(DF) SL

I 0.980 O.OI9 0.035 I .87 0.28 0.7 I 0.67 2.35(3, 19.?f (0.001) (0.135) (0.087) (0.03; (0.M) (0.65 1 ~0.125;

7 0.989 0.022 0.037 I .96 0.33 0.66 0.65 2.46(3) 39.97 (0.002) (0.133) (0.074) (0.04) (0.84) (0.59) (0.122)

3 0.994 0.022 0.037 I .99 0.34 0.66 0.64 2.43( 3) 36.38 (0.002 1 (0.130) (0.079) (0.01) (0.80) (0.53) (O.IZl)

Notes: Same as per Table 2.

FELDSTEIN-HORIOKA PUZZLE 367

Table 4: Stationxity tea. Time period: 195Sq I through I972q-l

S/Y ratios that balance each other out and leave a random term that is stationary, we make use of the cointegra- tion technique (in addition, a simple regression between S/Y and I/Y does not take into consideration the problem of simultaneity).

First. we test for stationarity. The investigation concerning station- arity is related to the tests for unit roots. It is cruciaf for the cointegration tests that the series are differentiated the correct number of times. Tables 4 and 5 present the results of Dickey-Fuller unit root tests on the first differences in the levels of the two variables WY and IN). The results indicate that both of the variables are integrated of degree one. in other words. both exhibit stationarity after beino t differentiated once.

Next, we proceed with cointegration tests that revealed some inter- esting results shown in Table 6. As it is shown in Table 6. the two ratios (I/Y and S/Y) are cointegrated during the first period while they

Table 5: Stationarity testh. Time pa-~od: 11 W4q 1 through 199Oq-l

SY 4 -4.17 -3.50 IY 4 -1.1 I -3.50

168 P. Alexakis and N. Apergis

Table 6: Cointegration Tests

Cointegrating regression: (I/Y) = k, + Ii, (S/Y) + E

The augmented Dickey-Fuller (ADF) test:

AE, = -q-x,_1 + CY,AE+,

Time period k, k, Rr Cl-u Critical values

ofg(n=lOO)

lc)SSql-107244 0.i I !).Or) I4 0.27 2.1 4.-w X77( I ;i ) 2. I7(5% )

2.84( I05 )

1974q I - l99oq2 0.17 0.0565 0.52 I .9 2.08

,Yott*: The number of lags in the ADF test wa 4 in both tinw pcriad~ and H;L~ c4nlatcd

lath the ;lssimncc 01 the Akaihc criterion. Critical ~duc\ for q wtxc ohtuincd trom En@

and Grangcr ( 1987 ).

Durbin-Watson statistic.

hSipniticant at all three lcwls ( I Y4. 5%. IOc;i ). thus. WL reject the null hypothesis of cointegration.

are not cointegrated in the second time period. In other words. there seems to exist a close relationship between saving and investment decisions durinp the era of the fixed exchange rate regime. Such a s_? strong relationship is probably due to the presence of intensive capital controls reducing the likelihood that a domestic investment project could be undertaken independently of domestic saving conditions. In contrast, during the era of the floating exchange rate regime, such a relationship seems to disappear, an outcome that could very easily be attributed to the massive relaxation of the aforementioned capital controls. In such a libera; environment, a domestic investment project could be easily financed by savings undertaken internationally.

6. CONCLUDING REMARKS, POLICY IMPLICATIONS, AND SUGGESTION!3 FOR FURTHER RESEARCH

The purpose of this article has been to examine the relationship between savings and investment decisions under two different ex- change rate environments, namely, the Bretton-Woods era and thet floating exchange rate era. To this end, a dynamic programming model was constructed that was capable of generating artificial (model) data, through Ii-hich we tested the existence of a relationship between the previously mentioned decisions within the Feldstein- Horioka puzzle framework. The results that emerged displayed the c

FELDSTEIN-HOKIOKA PUZZLE -SW

presence of such a relationship only in the former exchange r;lte er;t. Such a strorg relationship seems to be supported by the presence of extensive capital controls prevailing during that time period. The disappearance of that relationship is easily attributed to the relaxation of those controls.

A policy implication that has emerged from the empirical analysis of this paper is the fact that the international financial system is characterized by capital market integration tendencies. NIany studies [for example. La1 and Wolf ( 1986) and World Bank ( 1985)] point out that the international financial markets have tended to be mere inte- grated. particularly following the collapse of the Bretton-Woods system. Therefore. in a world of integrated capital marke;s. savings. and investment are not related to each other and the former flow into a pool of global savings. In the case of the United States. investment has increased over the last 15 years but was not compensated by a simultaneous increase in private savings (mainly due to the govem- ment deficit). The hysterisis in private savings with regard to private investment created a deficit in the U.S. trade balance. I-Iowever, the presence of integrated international capital markets allowed the inhib- ited finance of the above trade-balance deficit by attracting savings funds from the pool of global savings. In other words. an increase in savings in one country would tend to offer funds to the world capital market. Finally, the allocation of world savings would depend on investment demand and international interest differentials.

Another important implication of our results is the enhanced role of the interest rate mechanism in a framework of international integrated capital markets. Therefore, policy makers in all countries will have to implement the control of the mechanism mentioned before very carefully and definitely not for exchange rate purposes.

Our analysis has been characterized by the absence of an active government sector within the model framework and of how various policies (tax and/or government spending. interventions in the foreign exchange market) could have exploited that relationship. Our results stress the need to investigate the role of fiscal policy in conjunction with the aforementioned relationship.

Therefore, a future research objective could be to carry out empiri- cal analysis in a $ynamic programming framework that will have incorporated governmental economic policy (fiscal) decisions. actions regarding the close-form relationship between savings and investment decisions.

P. Alexakis and N. Apergis

REFERENCES

Grain. Roger ( 1975 ) I...

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