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Another Piece In The Feldstein - Horioka Puzzle. Sabie Anca mihaela. Introduction.

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  • 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.
literature review
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
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
The Model
  • In line with the work of Giannone and Lenza (2004), the following representation of saving and investment rates will be considered:



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.

the model1
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,


the model2
The Model
  • Equations (3) and (4) could be rewritten in terms of observable saving and investment rates as:



where and .

the model3
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:




the data
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


oecd the between model
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
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 thesame 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
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 suggestthat all the corresponding effects are statistically significant.

the factor model
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%.


principal component analysis
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
Factor Augmented Panel Regression

The following factor augmented panel regression is estimated:

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.

factor augmented panel regression1
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 regression2
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.

economic interpretation of the principal components
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.

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.

other methods for estimating idiosyncratic equations
Other Methods for Estimating Idiosyncratic Equations
  • Since the factors didn’t explain muchof 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 .

other methods for estimating idiosyncratic equations1
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 zit 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;

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
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 effects1
Panel Regression with Cross-Country Fixed Effects

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.

The redundant fixed effects tests strongly reject the null hypotesis that the fixed effects coefficients are thesame across countries.

panel regression with country and period fixed effects1
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 suggestthat all the corresponding effects are statistically significant.

  • Overall, 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.
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