28
Introduction
In the literature of open-economy macroeconomics, defining and measuring capital mobility has been one of the most important issues. The traditional approach to testing the capital mobility hypothesis was proposed by the seminal paper of Feldstein and Horioka (1980). The idea behind their thesis is quite simple: if an economy is well internationally integrated, then, its accumulation of capital should not be constrained by national savings. The equation which summarizes their work is the following:
Feldstein and Horioka studied the relationship between saving and investment rates by using cross-section data for 16 OECD countries over the 1960-1974 period and concluded that 85% to 95% of the national saving was invested locally. The high correlation was interpreted as capital being immobile even among developed countries. This came to be known as the ‘‘Feldstein–Horioka puzzle’’
Their conclusion has sparked a huge literature on trying to explain this puzzle and to reconcile it with the overwhelming evidence of high capital mobility.
jjj si
Literature Review
The Feldstein-Horioka result of a high saving-investment association has remained remarkably robust in OECD cross-sections although the coefficient on saving has shown some tendency to decline over recent years. The result persists in panels and time-series and has been remarkably robust to the addition of other variables and different estimation methods in the OECD.
However, there is less evidence for a close relationship between saving and investment in non-OECD samples, particularly in less developed countries. Overall, the studies indicate that the degree of capital mobility is higher for developing economies.
As stressed by Blanchard and Giavazzi (2002), even in a fully integrated economy - an economy in which investment decisions do not depend on domestic saving - some shocks will move saving and investment in the same direction, generating a positive correlation between the two. If these shocks dominate, the correlation will be high.
The Feldstein-Horioka result may not be informative about capital mobility since a range of theoretical models can generate high saving-investment correlations even under perfect capital mobility (Coakley et al., (1998)).
Aims of the Paper
To investigate the existence of the saving-investment correlation in a group of developed economies, respectively 22 OECD countries and a group of developing economies, 10 Central and Eastern Europe countries;
To determine its evolution over time;
To investigate whether controlling for global shocks (either homogenously or heterogeneously transmitted across countries) could provide an explanation for the puzzle.
The Model
In line with the work of Giannone and Lenza (2004), the following representation of saving and investment rates will be considered:
idtjtr
Ijrt
Ijtj
idtjtr
Sjrt
Sjtj
IffI
SffS
,,,,1,1,
,,,,1,1,
...
...
(1)
(2)
where are few global factors affecting saving and investment rates of all countries while and are the idiosyncratic components of saving and investment rates that are assumed to be driven by idiosyncratic shocks. The factor loadings are country specific.
rif ti ,...,1,, idtjS ,
idtjI ,
),...1,,...,1(, ,, riNjIji
Sji
The Model
Following Feldstein and Horioka, the linear relationship between the idiosyncratic components represents the degree of capital mobility:
where β is the saving-retention coefficient conditional to idiosyncratic shocks or, in terms of long run fluctuations,
tjidtjj
idtj SI ,,, (3)
T
tj
idtjLj
T
t
idtj S
TI
T 1,
1,
11 (4)
The Model
Equations (3) and (4) could be rewritten in terms of observable saving and investment rates as:
j
T
ttr
Ljr
T
tt
Lj
T
ttjLj
T
ttj f
Tf
TS
TI
T
1,,
1,1,1
1,
1,
1...
111
tjtrjrtjtjjtj ffSI ,,,,1,1,, ... (5)
(6)
where and . )( ,,,Sji
Ijiji )( ,,,
SjiL
Iji
Lji
The Model
Methodologies commonly used in the Feldstein-Horioka debate:
Original long-run regression or the between model:
Panel regression with country fixed effects:
Panel regression with country fixed and common time effects, which assumes homogeneity in the transmission of global shocks:
j
T
ttjL
T
ttj S
TI
T
1,
1,
11
tjtjjtj SI ,,,
tjtjtjtj SI ,,,
(7)
(8)
(9)
The Data
The research focused on 2 groups of countries:
22 OECD countries: Australia, Austria, Belgium, Canada, Germany, Denmark, Spain, Finland, France, United Kingdom, Greece, Ireland, Iceland, Italy, Japan, Korea, Netherlands, Norway, New Zealand, Portugal, Sweden and United States.
10 CEE countries: Bulgaria, Czech Republic, Estonia, Latvia, Lithuania, Hungary, Poland, Romania, Slovakia and Slovenia.
Data frequency is annual and the sample ranges from 1970 to 2007 for the first panel, and from 1993 to 2008 for the second;
Investment is Gross Capital Formation. Saving is the sum of Consumption of Fixed Capital and Net Saving. Saving and investment rates are calculated as the ratio of Saving and Investment to GDP.
Data sources: OECD AMECO
OECD - The Between Model
Using Feldstein and Horioka’s original regression, the puzzle is further documented. Although the correlation has obviously decreased over time, all 3 saving-retention coefficients are high and significantly different from zero.
Therefore, even in the last two decades, the capital appears to be far from mobile among these OECD countries.
Panel Regression with Cross-Country Fixed Effects
Again, the results do not suggest that the puzzle has disappeared, decreasing only slightly when compared to the between model estimators.
For the last subsample though, there appears to be evidence of increased capital mobility, although the coefficient is still statistically different from zero.
The tests reject the null hypotesis that the fixed effects coefficients are the same across countries. This suggests that there is unobserved heterogeneity in the data and one should use a model with fixed effects.
Panel Regression with Country and Period Fixed Effects
This method relies on the quite strong assumption that the responses to the common factors are identical across individuals in the panel.
The results suggest that, even when controlling for global comovements by assuming homogeneity of their transmission mechanisms across countries, the saving retention coefficient is significantly reduced, even if it still remains statistically different from zero in all 3 samples.
The redundant fixed effects tests suggest that all the corresponding effects are statistically significant.
The Factor Model
In order to estimate equation (5) the global factors will be extracted directly from saving and investment rates by cross country aggregation (since the idiosyncratic components are driven by country or region specific shocks, by worldwide aggregation they are ruled out). As shown by Forni, Hallin, Lippi and Reichlin (2002), the unobserved factors can be estimated provided that the number of countries under analysis is large, and they are estimated by means of the first r principal components.
The criteria used for choosing the number of factors is the one proposed by Forni and Reichlin (1998), who suggest retaining only the principal components that explain more than a certain threshold percentage of the panel variance; following their example, the threshold is set at 10%.
(10)tjtrjrtjtjjtj ffSI ,,,,1,1,,
ˆ...ˆ
Principal Component Analysis
The first principal component explains about 54% and the second principal component about 15% of the variance of domestic saving and investment rates. Therefore, the first two principal components will be retained as they capture, overall, about 69% of the panel variance. The hypothesis of strong cross-country linkages between saving and investment rates of OECD countries is confirmed.
Factor Augmented Panel Regression
The results show that, once taken into account the heterogeneity of the transmission mechanism of global shocks, the Feldstein-Horioka coefficient only slightly decreases when estimated for the whole sample period or for the first subsample, but is considerably reduced, becoming insignificantly different from zero, for the last two decades. This suggests that assuming an homogenous transmission mechanism has biased upwards the estimated coefficient.
tjtjtjtjjtj ffSI ,,2,2,1,1,,ˆˆ
The following factor augmented panel regression is estimated:
Factor Augmented Panel Regression
Indeed, the homogeneity restriction is strongly rejected by the data, as the Wald tests confirm. Also, the high number of significant coefficients on the second principal component provides further evidence that the first factor was not able, alone, to account for the effects of global shocks on saving and investment rates in OECD countries.
** Significant at 5% level, * Significant at 10% level
Factor Augmented Panel Regression
In addition, by looking at the percentage of the variance of domestic saving and investment rates explained by global factors, it is obvious how their impact varies considerably across countries.
Investment
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Aus Aut Bel Can Den Fin Fra Ger Gre Ice Ire Ita J ap Kor Net Nzl Nor Por Spa Swe UK USA
First Factor Second Factor
Saving
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Aus Aut Bel Can Den Fin Fra Ger Gre Ice Ire Ita J ap Kor Net Nzl Nor Por Spa Swe UK USA
First Factor Second Factor
Economic Interpretation of the Principal Components
In order to find an economic interpretation for the principal components, we try to assess their relation with some economic aggregates. The first principal component is found to be very similar to global OECD investment rate, with a correlation coefficient of 0.86.
0.15
0.17
0.19
0.21
0.23
0.25
0.27
0.29
0.31
Global OECD Investment Ratio First Principal Component
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
G7 average l.t.interest rate Second principal component US l.t. interest rate
In what concerns the second principal component, one should search for an aggregate driven by global shocks but not collinear with the global OECD investment rate. Therefore, we try to assess its correlation with two proxies of the world interest rate, G7 long run interest rate and US long run interest rate, which are found to be 0.78, and 0.71, respectively.
Synthesis of the Results
Type of regression
Sample
1970-2007 1970-1989 1990-2007
Between model (Long Run Regression)0.59 0.68 0.41
[0.11] [0.11] [0.12]
Panel Regression with cross-section fixed effects
0.50 0.52 0.28
[0.03] [0.03] [0.03]
Panel Regression with cross-section and period fixed effects
0.32 0.40 0.23
[0.02] [0.03] [0.05]
Factor Augmented Panel Regression0.27 0.28 -0.03
[0.03] [0.05] [0.05]
Other Methods for Estimating Idiosyncratic Equations
Since the factors didn’t explain much of the correlation on the sample 1970-2007, the idiosyncratic relation was re-estimated using other two methods developed for filtering out unobservable common factors in the panel regression: the ‘common correlated effects’ (CCE) estimator of Pesaran (2006) and the ‘projected principal components’ (PPC) estimator of Greenaway-McGrevy, Han and Sul (2007).
Pesaran (2006) suggests filtering out common factors by including the cross-sectional averages of the regressand and regressors in the panel regression. His common correlated effects (CCE) estimator of β can be obtained by least squares estimation of the following regression:
where ; and are used as ‘proxies’ for the common factors to and .
ittixtiyitit excycxy ,,
N
i it
N
i titt xNxyNy1
1
1
1 ,
ity itx
Other Methods for Estimating Idiosyncratic Equations
The PPC estimator proposed by Greenaway-McGrevy, Han and Sul (2007) consists of:
estimation of the factor number using a modified Bai and Ng (2002) selection criteria;
For the panel the number of common factors ‘h’ can be estimated consistently by minimizing the information criterion.
Han et. al. suggest using instead of z it to account for possible serial correlation in the idiosyncratic error.
estimation of the common factors for each variable using the principal component method;
partialling out all common factors from each cross-sectional unit for each variable;
estimating the idiosyncratic equation;
TN
NT
NT
TNhhVhIC log)(log)(
N
i
N
ttzizit
iztz
FzNTF
hV1 1
2,,
,,
)(1
},{
min)(
0,,, )()()1()( ittzizizit zLAFLAAzLA
0,,, ittzizizit zFz
Results
Estimation 1970-2007Factor Augmented Panel
Regression0.27
[0.03]
Common Correlated Effects0.28
[0.11]
Projected Principal Component 0.23
[0.09]
In terms of point estimates, the coefficient is somewhat lower in the PPC case but overall, the results sustain the existence of a weakened, but significant correlation between saving and investment ratios for the whole time period.
Models’ Estimation for CEE Countries
The majority of the studies focusing on non-OECD samples show that there is less evidence for a close relationship between saving and investment in these economies, the savings coefficients for developing economies being generally smaller than those found for industrialized economies.
The between estimator though suggests that there is less than perfect capital mobility in the CEE countries:
Again, using Feldstein and Horioka’s original regression, there appears to be a high correlation between saving and investment rates even among this group of developing countries.
Panel Regression with Cross-Country Fixed Effects
The redundant fixed effects tests strongly reject the null hypotesis that the fixed effects coefficients are the same across countries.
The saving retention coefficient remains significant and comparable with the one estimated for the OECD countries for the last subsample, indicating that the CEE countries are neither perfectly integrated into nor perfectly separated from the world capital market, according to the Feldstein-Horioka criterion.
The result is also comparable to the one obtained by Kohler (2005), who finds a point estimate of 0.32 using a panel regression with cross-country fixed effects.
Panel Regression with Country and Period Fixed Effects
The Feldstein-Horioka coefficient becomes insignificantly different from zero when common time effects are assumed. The result may in fact suggest that the shocks are homogenously transmitted across the region, yielding similar effects on the countries in the panel.
This may be the sign that Eastern European countries’ financial markets are quite open and countries are able to invest without having to comply with the strict constraint of domestic saving.
The redundant fixed effects tests suggest that all the corresponding effects are statistically significant.
ConclusionsOverall, the results show that, irrespective of the method employed to test for the existence of the puzzle, the saving-investment correlation has decreased over time, therefore providing evidence of increased capital mobility in the recent years.
When allowing for heterogeneous responses of saving and investment rates to global shocks across OECD countries, the correlation between saving and investment decreases and becomes insignificantly different from zero in the last two decades. Imposing the homogeneity restriction (which is rejected by the data), biases upwards the estimated correlation.
The results from the CEE countries suggest that the shocks propagate homogenously across countries, and again, once controlling for these shocks, the saving-investment correlation is insignificant. Although future research using longer time series would have to further check these results, they yet suggest that these states are integrated into the international capital markets to a degree similar to other OECD countries. Problematic is that the panel approach only measures the degree of capital mobility for a group of countries and not for each country separately. Therefore, the degree of capital mobility might have been biased by a small number of highly integrated countries.
These findings are consistent with the empirical evidence that international capital mobility has increased in the last two decades, and that the Feldstein-Horioka puzzle seems to be de-emphasized.
References
• Adedeji, O. and Thornton, J. (2007), “International capital mobility: Evidence from panel cointegration tests”, Economics Letters, 99, 349–352
• Apergis, N. and Tsoumas, C. (2009), “A survey on the Feldstein-Horioka puzzle: what has been done and where we stand”, Research in Economics, Forthcoming. Also available at SSRN:http://ssrn.com/abstract=993736
• Artis, M. and Bayoumi, T. (1991), “Global Financial Integration and Current Account Imbalances”, in G. Alogoskoufis, L. Papademos and R. Portes (Eds.) External Constraints on Macroeconomic Policy: The European Experience, Cambridge: Cambridge University Press
• Bai, J. (2003), “Inferential Theory for Factor Models of Large Dimensions” Econometrica, 71, 135–171• Bai, J. (2004), “Estimating cross-section common stochastic trend in nonstationary panels,” Journal of Econometrics, 122, 137–183• Bai, J., and S. Ng (2002), “Determining the Number of Factors in Approximate Factor Models,” Econometrica, 70, 191–221• Bai, J., and S. Ng (2006), “Confidence intervals for diffusion index forecasts with a large number of predictors,” Econometrica, 74,
1133–1150• Barro, R. (1991), “World interest rate and investment,” NBER Working Paper 3849• Bayoumi, T. (1990), “Savings-Investment Correlations: Immobile Capital, Government Policy or Endogenous Behavior?”, IMF Staff
Papers, 27, 360-387• Blanchard, O., and F. Giavazzi (2002): “Current account deficits in the Euro Area: the end of the Feldstein-Horioka puzzle?”, Brookings
Papers on Economic Activity, 22, 147–209• Buch, Claudia M. (1999), “Capital Mobility and EU Enlargement”, Kiel Working Paper No. 908• Coakley, J., Fuertes, A. M. and Spagnolo, F. (2004) “Is the Feldstein-Horioka puzzle history?”, The Manchester School, 72, 569-590. • Coakley, J., Fuertes, A. M. and Spagnolo, F. (2002) ‘The Feldstein-Horioka puzzle is not as bad as you think,’ available at
http://repec.org/mmfc03/Coakley.pdf.• Coakley, J., F. Hasan and R. Smith (1999) “Saving, Investment and Capital Mobility in LDCs”, Review of International Economics, 7,
632-640. • Coakley, J., F. Kulasi, and R. Smith (1998): “The Feldstein-Horioka Puzzle and Capital Mobility: A Review”, International Journal of
Finance and Economics, 3(2), 169–88• Coakley, J., F. Kulasi, and R. Smith (1996) ‘Current Account Solvency and the Feldstein-Horioka Puzzle’, Economic Journal, 106, 620-
627.• Feldstein, M., and C. Horioka (1980), “Domestic saving and international capital flows”, Economic Journal, 90, 314–329• Forni, M., M. Hallin, M. Lippi, and L. Reichlin (2000), “The Generalized Dynamic Factor Model: identification and estimation”, Review of
Economics and Statistics, 82, 540–554• Forni, M., and L. Reichlin (1998), “Let’s get real: a factor analytic approach to business cycle dynamics”, Review of Economic Studies,
65, 452–473• Frankel, J. A. (1992), “Measuring International Capital Mobility - A Review”, American Economic Review, 82, 197-202• Giannone, D. and M. Lenza, (2004), “The Feldstein-Horioka Fact”, CEPR, Discussion Paper No. 4610
References
• Glick, R., and K. Rogoff (1995), “Global versus country-specific productivity shocks and the current account”, Journal of Monetary Economics, 35, 159–192
• Greenaway-McGrevy, R., C. Han, and D. Sul (2007), “Estimating and Testing Idiosyncratic Equations Using Cross-Section Dependent Panel Data: Application to Feldstein-Horioka Puzzle”, forthcoming, also available at: http://homes.eco.auckland.ac.nz/dsul013/working/working1.htm
• Katsimi, M. and T. Moutos (2007), “Human capital and the Feldstein-Horioka puzzle”, CESifo Working Paper Series No. 1914• Hogendorn C. (1998), “Capital Mobility in Historical Perspective”, Journal of Policy Modeling, 20(2), 141-161• Köhler, M. (2005), “International capital mobility and current account targeting in Central and Eastern European countries”, CEER,
Discussion Paper No. 05-51• Levy, D. (1995), “Investment-Savings Co-movement under Endogenous Fiscal Policy”, Open Economies Review, 6, 237-254• Obstfeld, M., and K. Rogoff (2000a), “The six major puzzle in international economics: is there a common cause?”, NBER Working
Paper 7777• Obstfeld, M., and K. Rogoff (2000b), “Perspectives on OECD economic integration. Global economic integration: Opportunities and
challenges”, Federal Reserve Bank of Kansas City, Annual Monetary Symposium• Obstfeld, M. (1998), “The Global Capital Market: Benefactor or Menace?”, NBER Working Papers, 6559• Obstfeld, M. and K. Rogoff (1995), “The Intertemporal Approach to the Current Account”, in G. M. Grossman and K. Rogoff (Eds.)
Handbook of International Economics, New York: North-Holland Publishing Co• Payne, J. and R. Kumazawa (2006), “Capital Mobility and the Feldstein-Horioka Puzzle: Re-Examination of Less Developed
Countries”, The Manchester School, 74, 610-616• Pesaran, M. H. (2006), “Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure”, Econometrica,
74(4), 967–1012• Rossini, G., and P. Zanghieri (2002) ‘A Simple Test of the Role of Foreign Direct Investment in the Feldstein-Horioka Puzzle’, Applied
Economics Letters, 10, 39-41.• Sachsida, A. and M. Caetano (2000), “The Feldstein-Horioka Puzzle Revisited”, Economics Letters, 68, 85-88• Sinha, T., and D. Sinha (2004), “The Mother of All Puzzles Would Not Go Away”, Economics Letters, 82, 259-267• Stock, J. H., and M. W. Watson (2002), “Macroeconomic Forecasting Using Diffusion Indexes”, Journal of Business and Economics
Statistics, 20, 147–162• Telatar, E., F. Telatar and N. Bolatoglu (2007), “A Regime Switching Approach to the Feldstein-Horioka Puzzle: Evidence from Some
European Countries”, Journal of Policy Modeling, 12, 523-533• Tesar, L. (1991), “Saving, Investment and International Capital Flows”, Journal of International Economics, 31, 55-78• Vamvakidis, A., and R. Wacziarg (1998), “Developing Countries and the Feldstein-Horioka Puzzle”, IMF Working Paper No. 98/2• Ventura, J. (2003), “Towards a theory of current account”, World Economy, pp. 483–512
