the feldstein–horioka puzzle revisited: a monte carlo study

Journal of International Money and Finance 24 (2005) 1143e1149www.elsevier.com/locate/econbase

The FeldsteineHorioka puzzle revisited:A Monte Carlo study

Guglielmo Maria Caporale a,*, Ekaterini Panopoulou b, Nikitas Pittis b

a Brunel University, Uxbridge, Middlesex UB8 3PH, UKb Department of Banking and Financial Management, University of Piraeus,

Karaoli e Dimitriou 80, 18534 Piraeus, Greece

Abstract

This study revisits the FeldsteineHorioka (FH) puzzle by employing a variety of asymptotically effi-cient cointegration estimators, and by using the critical values obtained from Monte Carlo simulations totest the hypothesis of a unit retention coefficient. This leads to a lower rejection of the null than standardcritical values would have implied. Despite ample evidence supporting the FH result, there appears to beconsiderable heterogeneity in terms of the savingseinvestment association, and only 25% of the 23 OECDcountries we examine can be characterised as open economies in the FH sense. Whether or not one sub-scribes to the FH interpretation, the FH result does not appear to be robust.� 2005 Elsevier Ltd. All rights reserved.

JEL classification: C15; C32; F21

Keywords: International capital mobility; FeldsteineHorioka puzzle; Cointegration; Estimators;Monte Carlo simulations

1. Introduction

The high correlation between national savings and investment rates across OECD countriesis one of the best-established facts in international economics. In their seminal cross-sectionstudy, Feldstein and Horioka (1980) (FH henceforth) argued that this is inconsistent with per-fect capital mobility, which should imply no strong relation between domestic savings and do-mestic investment. The FH result is clearly a ‘‘puzzle’’ in the presence of highly integrated

* Corresponding author. Tel.: C44 1895 266713; fax: C44 1895 269770.

E-mail address: [email protected] (G.M. Caporale).

0261-5606/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jimonfin.2005.08.003

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1144 G.M. Caporale et al. / Journal of International Money and Finance 24 (2005) 1143e1149

financial markets, and has been questioned both on empirical and theoretical grounds. Forinstance, it has been shown that even in the presence of perfect capital mobility a highsavingseinvestment correlation can arise because of productivity shocks, positively autocorre-lated domestic and foreign technology shocks, or a particular varianceecovariance structureof exogenous shocks.

This paper makes an empirical contribution to the literature on the FH puzzle. It focuses onthe FH ‘‘result’’, as opposed to the FH ‘‘interpretation’’,1 i.e. it examines the robustness of theirfindings rather than asking the question whether a high savingseinvestment (SeI) correlationdoes indeed reflect low capital mobility. We take a time-series as opposed to a cross-sectionapproach since the SeI correlation differs across countries depending on the nature of the dis-turbances and the structure of the economy, and the use of long-term averages causes an upwardbias in capital mobility correlations. Also, cross-section estimates might be significantly affectedby outliers (e.g., countries with capital controls) and sample selection bias, and are not informa-tive about the key question of how much of an increase in saving is truly translated into domesticinvestment.

Unlike most previous time-series studies, the present one examines the robustness of the FHresult across countries and across estimators under the maintained hypothesis that savings andinvestment are cointegrated. Furthermore, it carries out Monte Carlo simulations to obtain thesmall-sample distributions of the t-statistics associated with the estimators under consideration,thereby using the finite sample rather than the asymptotic critical values for hypothesis testing.A few researchers had used asymptotically efficient cointegration estimators (see, e.g., Ma-mingi, 1997), or compared the properties of some estimators (see, e.g., Ho, 2002), but oursis the first systematic and comprehensive analysis based on the statistical features of the actualseries. The layout of the paper is as follows. Section 2 describes the data and reports the esti-mation results. Section 3 discusses the Monte Carlo simulations. Section 4 offers some conclud-ing remarks.

2. Estimation results

Our sample comprises 23 OECD countries (16 of which were examined by FH). The datasource is the IMF’s International Financial Statistics, CD-ROM/December 1999. For the major-ity of the countries the sample period goes from 1948 to 1998.2 We used annual rather thanquarterly data (to avoid interpolation and seasonality issues, and also because short-term capitalmovements should be less important at the annual frequency). Gross (rather than net) savingand investment were chosen as they respond to worldwide yield differentials; also, depreciationmeasures are inevitably inaccurate. Gross saving was constructed subtracting private and gov-ernment consumption from GNP. Gross investment was defined as gross capital fixed formationplus change in stocks. Other variable definitions are also standard.

As a first step, we carried out standard unit-root tests. On the whole, the results (not re-ported) broadly confirm those of other studies, i.e. saving and investment ratios seem to be in-tegrated of order 1: I(1). Thus, we proceeded to test for cointegration using both the Johansen

1 See Coakley et al. (1996) for this distinction.2 The countries considered are the following (with the first year of the sample in brackets if different from 1948):

Australia (1951), Austria, Belgium (1953), Canada, Denmark (1950), Finland (1950), France (1950), Germany

(1950), Greece, Iceland (1950), Ireland, Italy (1951), Japan (1955), Luxembourg (1950), Netherlands (1950), New Zea-

land, Norway (1949), Portugal (1953), Spain (1954), Sweden (1950), Switzerland, UK, US.

1145G.M. Caporale et al. / Journal of International Money and Finance 24 (2005) 1143e1149

methodology by estimating a VAR(1) model and the two-step EngleeGranger procedure. Theresults (not reported) indicate that the two series are cointegrated, although the evidence wasfragile in the case of Belgium, Denmark, Finland and Norway. OLS estimation of the cointe-grating coefficient, though superconsistent, would not be optimal for statistical inference, in thepresence of nuisance parameters in the asymptotic distribution of the OLS estimator that stemfrom possible long-run endogeneity and serial correlation of the cointegration error (see Phil-lips and Hansen, 1990) e an asymptotically efficient cointegration estimator should be choseninstead. In addition to the system-based maximum likelihood Johansen estimator, we used thefollowing single-equation estimators for the SeI coefficient (q): OLS; four different versions ofFMLS (Fully Modified Least Squares e see Phillips and Hansen, 1990), with both standard andprewhitened residuals and parametric (Andrews, 1991) and non-parametric (Newey and West,1994) methods for selecting the optimal bandwidth; DOLS (Dynamic Ordinary Least Squares esee Stock and Watson, 1993); DGLS (Dynamic Generalised Least Squares); ADL (Autore-gressive Dynamic Linear) (1,2) and (4,4); AADL (Augmented Autoregressive Dynamic Linear)(1,2,1) and (4,4,4).

The savings retention coefficient q, its standard error and the t-statistics were obtained inorder to test the hypothesis that qZ 1. The average, lowest and highest estimates of the coin-tegrating coefficient for each country are reported in Table 1 (see Caporale et al., 2003, fordetailed results for individual countries). As can be seen, the average coefficients rangefrom �0.104 to 1.319. One-third of the countries have a coefficient between 0.7 and 1 (Austria,France, Greece, Iceland, Japan, Netherlands, Sweden and the UK), indicating capital immobil-ity according to the FH interpretation, and thus representing quite closed economies. Seven

Table 1

Estimated coefficients and rejection percentages

Country Estimate % Rejection (Monte

Carlo critical values)

% Rejection (asymptotic

critical values)Average min max

Australia 0.648 0.283 0.847 8 27

Austria 0.865 0.739 1.022 8 45

Belgium 0.576 0.508 0.697 58 82

Canada 0.566 0.268 0.802 58 73

Denmark 0.625 0.225 1.003 8 18

Finland 1.319 0.883 2.559 8 0

France 0.903 0.856 0.958 0 9

Germany 0.672 0.506 0.870 8 55

Greece 0.888 0.844 0.918 8 73

Iceland 0.938 0.724 1.136 0 9

Ireland 1.032 0.265 2.944 0 27

Italy 1.087 0.928 1.534 0 0

Japan 0.859 0.83 1.047 0 0

Luxembourg �0.103 �0.164 �0.023 100 100

Netherlands 0.862 0.423 1.315 0 9

New Zealand 1.03 0.673 1.376 0 9

Norway �0.075 �0.192 0.108 83 100

Portugal 0.300 0.093 0.438 8 73

Spain �0.104 �1.022 0.209 42 91

Sweden 0.75 0.486 1.401 0 27

Switzerland 1.016 0.837 1.053 0 0

UK 0.882 0.800 0.994 0 0

US 0.469 0.044 1.199 67 64


countries (Australia, Belgium, Canada, Denmark, Germany, Portugal and the US) have averagecoefficients between 0 and 0.7, hence exhibiting some degree of capital mobility, with less than70% of domestic saving being invested in the same country. Luxembourg, Norway and Spainhave a negative savings retention coefficient, the first country usually being excluded fromcross-section studies as an outlier due to the size of its financial and banking sector, the secondbecause of its large industrial sector. Finally, five countries (Finland, Ireland, Italy, New Zea-land and Switzerland) produced estimates above 1, indicating that investment systematicallyexceeds savings. Fig. 1 shows the ‘‘distribution’’ and the ‘‘descriptive statistics’’ of the sampleof estimated coefficients. On average, the FH coefficient is 0.71, although the estimates rangebetween �1.02 and 2.94. The mode of the distribution is close to one, providing evidence tosupport the ‘‘puzzle’’ (though many coefficients are not significant). We also divided the esti-mates in 14 categories (see Table 2). It can be seen that over 30% of the coefficients are be-tween 0.8 and 1, while 60% of them range between 0.6 and 1.2, very close to a unitcoefficient. Next we discuss the Monte Carlo simulations.

3. Monte Carlo simulations

Using GAUSS routines, we conducted a Monte Carlo study to obtain the 2.5% and 97.5%points of the empirical distribution of the t-statistics for each estimator in each of the 23 coun-tries. This is necessary to draw valid statistical inference, as standard asymptotic distributionsare not likely to apply in this case. The Data Generating Process (DGP) was assumed to be thefollowing:

ItZqStCu1t;

DStZu2t for tZ1;2;.;T

0

20

40

60

80

100

-1 0 1 2 3

Descriptive Statistics

Observations 276 Mean 0.705328Median 0.801000Maximum 2.944000MinimumStd.Dev. 0.453904Skewness 0.023851Kurtosis 6.336788

Jarque-Bera 128.0690Probability 0.000000

-1.021500

Fig. 1. Distribution of estimated coefficients.


where It and St are the investment and saving rate, respectively, and utZðu1t; u2tÞ0 followsa VAR(1) process:

utZAut�1Cet; etzNiidð0;SÞ:

Given the annual frequency of the data, one lag should be sufficient to capture the dynamics.This is confirmed by misspecification tests (not reported). Estimates of the 2! 2 A matrix, andof the varianceecovariance matrix of the DGP (needed for each country) were obtained as fol-lows. First, we estimated the FH equation and saved the residuals (u1t); then we ran an AR(1)regression for St, also saving the residuals (u2t). Using the series u1t and u2t, we estimateda VAR(1) and consequently the matrix and the varianceecovariance matrix. These estimateswere used for the Monte Carlo simulations, and the exact distribution of each estimator foreach country was obtained. The analysis was conducted under the maintained assumption ofcointegration, evidence for which we had found (see Section 2).3 It is clear that there is a shiftin the empirical distributions compared to the Standard Normal. Using the critical values fromthe latter as a benchmark for rejection of the null hypothesis that qZ 1 would have resulted ina higher percentage of rejections (see Table 1). It should also be noted that the standard errorsof the estimates are big, resulting in low t-statistics and non-rejection of the null hypothesis,despite the fact that the estimated coefficient is considerably lower than unity.

The percentages of rejection for each country are shown in Table 1. On the basis of theseresults, and adopting the FH interpretation, one would conclude that Belgium, Canada, Luxem-bourg, Norway, Spain and USA are countries with high capital mobility, while the rest seem tohave a savings retention coefficient close to unity. More in detail, the OECD countries would be

Table 2

Distribution of estimates

Value Count Percent Cumulative count Cumulative percent

[�1.2, �1) 1 0.36 1 0.36

[�1, �0.8) 1 0.36 2 0.72

[�0.2, 0) 22 7.97 24 8.70

[0, 0.2) 15 5.43 39 14.13

[0.2, 0.4) 22 7.97 61 22.10

[0.4, 0.6) 29 10.51 90 32.61

[0.6, 0.8) 48 17.39 138 50.00

[0.8, 1) 85 30.80 223 80.80

[1, 1.2) 32 11.59 255 92.39

[1.2, 1.4) 12 4.35 267 96.74

[1.4, 1.6) 5 1.81 272 98.55

[1.8, 2) 2 0.72 274 99.28

[2.4, 2.6) 1 0.36 275 99.64

[2.8, 3) 1 0.36 276 100.00

Total 276 100.00 276 100.00

Notes: Included observations: 276. Number of categories: 14.

3 Clearly, if ut were instead I(1), which would imply no cointegration between savings and investment, the regressions

would be ‘‘spurious’’ and the estimates invalid e the transition matrix for the errors in the VAR(1) would have an ei-

genvalue equal to unity, which would radically change the simulation results. But we report robust evidence of cointe-

gration, with the exception of four countries, where this is less clear-cut.


categorized as follows in terms of capital mobility: Austria, France, Greece, Iceland, Japan,Netherlands, Sweden and the UK display capital immobility (0.75! q! 1); Australia, Bel-gium, Canada, Denmark, and Germany display medium capital mobility (0.5! q! 0.75); Por-tugal and the United States display capital mobility (0! q! 0.5); Finland, Ireland, Italy, NewZealand and Switzerland have an FH coefficient greater than 1; Luxembourg, Norway andSpain display a negative correlation between the savings and investment ratios.

The percentages of rejection per estimator using both the asymptotic critical values and theones obtained from our Monte Carlo simulations are shown in Table 3. It is clear that the OLSestimator rejects more often than the other estimators (whether using the asymptotic or theMonte Carlo values), while the ADL (1,2), AADL (1,2,1) and the AADL (4,4,4) accept the hy-pothesis that qZ 1 more frequently.

4. Conclusions

A number of papers have questioned both the FH result (i.e. the robustness of the savingseinvestment association), and the FH interpretation (i.e. its implying little or no capital mobility).This study has re-examined the former in a sample of 23 OECD countries adopting a time-se-ries approach. Unlike earlier contributions, we have employed a variety of estimators, whichcorrect for both serial correlation and long-run endogeneity to estimate the savings retentioncoefficient. Further, we have tested the hypothesis of a unit coefficient using the critical valuesobtained from Monte Carlo simulations, which replicated the statistical processes followed bythe investment and saving series. This led to a lower rejection of the FH hypothesis than stan-dard critical values would have implied.

On the whole, we found ample evidence supporting the FH result. However, there appears tobe considerable heterogeneity across countries in terms of the savingseinvestment association,with both estimates and percentages of rejection varying substantially. Only 25% of the 23OECD countries examined can be characterised as open economies in the FH sense (as highrejection percentages are found for only six countries based on the finite sample critical values),the others displaying a variety of degrees of ‘lower’ capital mobility. Whether or not one sub-scribes to the FH interpretation, the FH result itself does not seem to be robust.

Acknowledgements

We are grateful to two anonymous referees and participants in the 2002 Royal EconomicSociety Conference, University of Warwick, Coventry, UK, 25e27 March 2002, the 2003

Table 3

Rejection percentages for each estimator

Estimator % Rejection (Monte

Carlo critical values)

% Rejection

(asymptotic

critical values)

Estimator % Rejection

(Monte Carlo

critical values)

% Rejection

(asymptotic

critical values)

OLS 43 78 DGLS 26 30

FM-S-A 26 48 ADL (1,2) 9 13

FM-S-NW 30 48 AADL (1,2,1) 9 13

FM-PW-A 22 52 ADL (4,4) 13 30

FM-PW-NW 26 48 AADL (4,4,4) 4 26

DOLS 26 52 Johansen 13 26


MODSIM Congress, Townsville, Australia, 13e17 July 2003, and seminars at the University ofAuckland, University of Waikato, Reserve Bank of New Zealand, Victoria University of Wel-lington, Otago University, University of Canterbury, Curtin University of Technology and Uni-versity of Western Australia for useful comments and suggestions.

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the feldstein–horioka puzzle revisited: a monte carlo study

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