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1
Another Piece In The Feldstein - Horioka Puzzle
Sabie Anca mihaela
2
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 FeldsteinHorioka
  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.

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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)).

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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.

5
The Model

• In line with the work of Giannone and Lenza
  (2004), the following representation of saving
  and investment rates will be considered

6
The Model

• Following Feldstein and Horioka, the linear
  relationship between the idiosyncratic components
  represents the degree of capital mobility

where ß is the saving-retention coefficient
conditional to idiosyncratic shocks or, in terms
of long run fluctuations,
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The Model

• Equations (3) and (4) could be rewritten in terms
  of observable saving and investment rates as

(5)
(6)
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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

(7)
(8)
(9)
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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

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OECD - The Between Model
Using Feldstein and Horiokas 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.
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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.
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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.

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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)
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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.

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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.
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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
17
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.

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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.
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Synthesis of the Results
Type of regression   Sample     Sample     Sample  
Type of regression 1970-2007 1970-1989 1990-2007
Between model (Long Run Regression) 0.59 0.68 0.41
Between model (Long Run Regression) 0.11 0.11 0.12
Panel Regression with cross-section fixed effects 0.50 0.52 0.28
Panel Regression with cross-section fixed effects 0.03 0.03 0.03
Panel Regression with cross-section and period fixed effects 0.32 0.40 0.23
Panel Regression with cross-section and period fixed effects 0.02 0.03 0.05
Factor Augmented Panel Regression 0.27 0.28 -0.03
Factor Augmented Panel Regression 0.03 0.05 0.05
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Other Methods for Estimating Idiosyncratic
Equations

• Since the factors didnt 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 ß can be obtained by least squares
  estimation of the following regression
• where
  and are used as proxies for the
  common factors to and .

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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

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Results
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.
Estimation 1970-2007
Factor Augmented Panel Regression 0.27
Factor Augmented Panel Regression 0.03
Common Correlated Effects 0.28
Common Correlated Effects 0.11
Projected Principal Component 0.23
Projected Principal Component 0.09
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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 Horiokas original
regression, there appears to be a high
correlation between saving and investment rates
even among this group of developing countries.
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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 the same across countries.
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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.
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Conclusions

• 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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