Download The orthogonal deviations GMM dynamic panel estimator

Academy of Economic Studies, Bucharest
Doctoral School of Finance and Banking
AN ANALYSIS OF THE CONDITIONING ROLE OF FINANCIAL
DEVELOPMENT ON THE IMPACT OF EXCHANGE RATE
VOLATILITY ON ECONOMIC GROWTH
Supervisor:
PhD. Univ. Professor Moisă Altăr
M. Sc. Student:
Petre Dicu
Bucharest
July 2009
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This paper examines the influence of real effective exchange rate
volatility on GDP per capita growth rate and the way this impact
depends on the level of financial development of the countries;
It follows the specification of Aghion, P., P. Bacchetta, R.
Ranciere and K. Rogoff (2006) (with regard to regression,
variables and estimation techniques);
It conducts a dynamic balanced panel data analysis using GMM
dynamic panel data estimators;
It employs a data set for the non-EMU EU countries for a time
period of 10 years (1999 - 2008).
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Structure of the presentation
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The estimated model specification
Estimation techniques
Results of analysis and comparisons
Conclusions
Tests
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The model tested using real data closely follows Aghion, P., P.
Bachetta, R. Ranciere and K. Rogoff (2006)
yi,t - yi,t-1= (α – 1)yi,t-1 + β1eri,t + β2pci,t*eri,t + β3pci,t + γ1gei,t +
γ2iri,t + γ3oti,t + γ4popi,t + µt + ηi + vi,t
(1)
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yi,t = real GDP per capita,
eri,t = real effective exchange rate volatility,
pci,t = financial development (private credit to GDP),
gei,t = government expenditure,
iri,t = inflation,
oti,t = openness to trade,
popi,t = population growth rate,
ηi = an unobserved individual-specific time-invariant effect for each
country,
vi,t = the disturbance term,
µt = a time specific effect,
The series are in logarithms.
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The overall coefficient of eri,t (the volatility of real exchange rate)
is a linear function of pci,t (the financial development):
Equation (1) can be written as:
yi,t - yi,t-1= (α – 1)yi,t-1 + [β1 + β2pci,t]eri,t + β3pci,t + γ1gei,t + γ2iri,t
+ γ3oti,t + γ4popi,t + µt + ηi + vi,t
(2)
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The assumption β1 < 0 and β2 > 0 shows a level of threshold for
financial development: pc* = - (β1 / β2), meaning that
∂ (yi,t - yi,t-1)/ ∂ (eri,t) = β1 + β2pci,t > 0 for pci,t > pc* = - (β1 / β2) and
∂ (yi,t - yi,t-1)/ ∂ (eri,t) = β1 + β2pci,t < 0 for pci,t < pc* = - (β1 / β2)
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GMM estimators are used to address the issue of endogeneity
in explanatory variables
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I used 2 estimators:
 The GMM dynamic panel data estimators developed in
Arellano, M. and S. Bond (1991) and Arellano, M. and O.
Bover (1995),
 Both estimators are based on the assumption of no serial
correlation (or limited serial correlation) in the errors,
 Both are included in Eviews 6,
 They deal with the time specific effect by applying period
dummy variables,
 They deal with the country specific effect in different ways,
as presented below.
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The GMM estimator from Arellano, M. and S. Bond (1991)
(“The first difference GMM dynamic panel estimator”)
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The one-step estimator developed in Arellano, M. and S. Bond
(1991):
 This one step estimator is robust to heteroskedasticity over
individuals and over time (Arellano M. and S. Bond (1991),
p 285);
 The regressions are estimated in first differences;
 Differencing the equations is the way the country specific
effect is eliminated, since for each country i, Δηi = 0.
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The GMM estimator from Arellano, M. and O. Bover (1995)
(“The orthogonal deviations GMM dynamic panel estimator”)
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The orthogonal deviations estimator developed in Arellano, M.
and O. Bover (1995):
 The transformation that eliminates the individual effect is
applied to the first T-1 equations;
 It consists of subtracting the mean of the remaining future
observations available for each period and using time
weights (presented in Arellano, M. and O. Bover (1995), pp
41 and 42);
 The regressions remain in levels.
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Estimations and comparisons versus similar estimations in
Aghion, P., P. Bachetta, R. Ranciere and K. Rogoff (2006):
Coefficients of variables:
Table 2,
column
[2.2][1]
Table 2,
column
[2.4][2]
First
difference
GMM
estimation
Orthogonal
deviations
GMM
estimation 1
Orthogonal
deviations
GMM
estimation 2
Real exchange rate volatility
-3.124
(1.204)
-3.319
(1.208)
-6.6068
(4.891)
-2.6785
(1.4214)
***
-4.6800
(1.9684)
**
Financial development * real exchange
rate volatility
0.677
(0.262)
0.706
(0.277)
1.4609
(1.2378)
0.3162
(0.3626)
0.9004
(0.4907)
***
Initial per capita GDP
-0.530
(0.474)
-0.828
(0.404)
-0.2611
(0.0866)
*
-0.1555
(0.0210)
*
-0.0886
(0.0387)
**
0.53
0.86
Sargan p-values
0.241
0.187
0.30
* means significant at 1%, ** means significant at 5% and *** means significant at 10%
[1] Aghion, P., P. Bacchetta, R. Ranciere and K. Rogoff (2006), p35
[2] Aghion, P., P. Bacchetta, R. Ranciere and K. Rogoff (2006), p35
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The results are better with the orthogonal deviations GMM
estimator in terms of smaller s.e., coefficient and Sargan p-values
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Estimation results summary:
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The orthogonal deviations GMM estimators yield more significant
results;
(This is in line with the observation in Blundell, R. and S. Bond (1998) (p
115) that the widely used first difference GMM dynamic panel data estimator can
be less precise when the autoregressive parameter in the regression is moderately
large:
The estimated regression: yi,t - yi,t-1= (α – 1)yi,t-1 + …  yi,t = αyi,t-1 + …
In the estimations, α – 1 belongs to {-0.2611; -0.1555; -0.0886} => large
values for α)
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Results presented in the last two columns in the comparative table
above indicate that exchange rate volatility has a significant negative
impact on economic growth, but only the estimations in the last column
indicate a positive and significant interaction term of real exchange rate
volatility and financial development; those estimations in the last
column are also most reliable among my results, as they result from
using the best specified of all estimators.
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Threshold level analysis:
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For the “orthogonal deviations” estimation with significant
coefficient for the interaction term, the computed threshold
level = 4.68/0.9 = 5.2 => a ratio of e5.2 ≈ 1.81 private credit to
GDP, which is a high rate, suggesting it could be biased
upwards (supportive of this are the threshold levels of private
credit to GDP estimated in Aghion, P., P. Bacchetta, R.
Ranciere and K. Rogoff (2006), p 35 - which are 1.01 and 1.10
- significantly smaller than 1.81
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Conclusions
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In the analysis of this paper, instead of looking at an individual effect of
exchange rate volatility on growth, an interaction term between volatility of
the real effective exchange rate and the financial development level was
also used, as in Aghion, P., P. Bacchetta, R. Ranciere and K. Rogoff (2006)
The balanced panel data analysis partly validated the predictions set in the
objectives of this paper.
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The orthogonal deviations GMM estimators provide evidence that the real
effective exchange rate volatility influences the economic growth rate;
The first difference GMM estimator’s results are inconclusive;
The best specified GMM estimator employed yielded results similar to the
ones in Aghion, P., P. Bacchetta, R. Ranciere and K. Rogoff (2006):
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It provided evidence that the real effective exchange rate volatility
influences the economic growth rate and there is a threshold effect of the
level of financial development, below which the volatility of the real
exchange rate diminishes growth and above which the exchange rate
volatility becomes growth enhancing and that the level of financial
development should be taken into account when a country chooses to adopt
a more flexible or a more fixed exchange rate system.
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Tests employed - exemplified on the best estimator
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Sargan test – for instruments validity
 Under the null hypothesis that the overidentifying restrictions are valid, the
Sargan
statistic
(J-statistic)
is
distributed χ2(d.f. = instrument rank –
number of estimated coefficients,
including time dummies);
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all tests, the over-identifying
restrictions seem to be valid,
considering that J-statistic < critical χ2
value => the null will not be rejected;
 The p-values show that the validity of
the instruments (the null hypothesis)
can not be rejected and, in the last
estimation, the high value (0.86)
suggests almost certain acceptance of
the null hypothesis (that the variables
are valid).
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Tests employed - exemplified on the first difference estimator
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Wald test of joint significance of the
independent variables
 Under the null of no relationship, the
Wald statistic is asymptotically
distributed as χ2(k), where k = the
number of estimated coefficients
(excluding the time dummies);
 The
test is robust to general
heteroskedasticity (Arellano, M. and S.
Bond (1991), p 292; Blundell, Richard and
Stephen Bond (1998), p139; Windmeijer,
Frank (2005), pp 42 and 43);
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For all tests, the Wald statistic >>
critical χ2 value => the null will be
rejected => a joint significance of the
variables used in the regression. Pvalues of 0.000 confirm that;
Individual coefficient tests can be
made, with similar conclusions.
The Wald statistic = 86.11
χ2(8, 5%) = 15.507
p-value = 0.000
The Sargan and Wald tests are also tests presented in Aghion, P., P. Bacchetta,
R. Ranciere and K. Rogoff (2006), whose benchmark specification I follow.
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Testing for error serial correlation - exemplified on the first
difference estimator
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Since both GMM estimators I use are
based on the assumption of limited or no
serial correlation of errors, I applied a
simple test using the residuals from the
GMM estimated equations. I regressed the
residuals against their first lag using a
panel LS estimator. The results are that
errors are not autocorrelated.
For α% significance, the criteria are:
DW > DW(U, α%) => the error
terms are not positively autocorrelated,
and
(4 – DW) > DW(U, α%) => the
error
terms
are
not
negatively
autocorrelated. (the critical values of the
statistics are taken from Greene, William
H. (2003), p 958, Table G.6)
For all three estimations the result is that
the errors are not positively nor negatively
autocorrelated
We can also assume the noncorrelation of
error terms by looking at the values of
adjusted R square, which are very small
(close to zero).
DW = 1.843594 > 1.63
4 – DW = 2.156406 > 1.63
DW (U, 5%, nr of regressors excluding intercept =
1, observations = 66) = 1.63
Adjusted R-square = 0.021369 << 1
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Selected Bibliography
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Aghion, Philippe, Philippe Bacchetta, Romain Ranciere, and Kenneth Rogoff, “Exchange Rate Volatility
and Productivity Growth: The Role of Financial Development”, Center for Economic Policy Research,
Discussion Paper no. 5629, April 2006
Arellano, Manuel and Stephen Bond, “Some Tests of Specification for Panel Data: Monte Carlo Evidence
and an Application to Employment Equations”, The Review of Economic Studies, vol. 58, no. 2, 277-297,
April 1991
Arellano, Manuel and Olympia Bover, “Another Look at the Instrumental Variable Estimation of Errorcomponents Models”, Journal of Econometrics 68, 29-51, 1995
Blundell, Richard and Stephen Bond, “Initial Conditions and Moment Restrictions in Dynamic Panel Data
Models”, Journal of Econometrics 87, 115-143, 1998
Bond, Stephen R., “Dynamic Panel Data Models: A Guide to Micro Data Methods and Practice”, CeMMAP
Working Paper 09, April 2002
Dubas, Justin M., Byung-Joo Lee, and Nelson C. Mark, “Effective Exchange Rate Classifications and
Growth”, NBER Working Paper 11272, April 2005
Husain, Aasim M., Ashoka Mody, and Kenneth Rogoff, “Exchange Rate Regime Durability and
Performance in Developing versus Advanced Economies”, Journal of Monetary Economics 52, 35-64, 2005
Levine, Ross, Norman Loayza, and Thorsten Beck, “Financial Intermediation and Growth: Causality and
Causes”, Journal of Monetary Economics 46, 31-77, 2000
Levy-Yeyati, Eduardo and Federico Sturzenegger, “To Float or to Fix: Evidence on the Impact of Exchange
Rate Regimes on Growth”, The American Economic Review, vol. 93, no. 4, pp. 1173-1193, Nov. 2003
Rogoff, Kenneth, Aasim M. Husain, Ashoka Mody, Robin Brooks and Nienke Oomes, “Evolution and
Performance of Exchange Rate Regimes”, IMF Working Paper 243, Dec. 2003
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Back up slides
The choice of instrumental variables 1/2
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For the regressors I mention the following possibilities:
endogenous (correlated with current and past shocks, but
uncorrelated with future shocks); predetermined (correlated
with past shocks and uncorrelated with present and future
shocks) or strictly exogenous (uncorrelated with past, present
or future shocks);
In the assumption of lack of serial correlation, than values of
the dependent variable lagged 2 and longer are valid
instruments for the regressions in first differences (Arellano,
M. and S. Bond (1991), p 278); so are lagged values of 2 or
higher order of endogenous regressors in first differenced
equations; the predetermined ones from the lag -1 and higher
order, and the strictly exogenous can be used for all lags
(Bond, Stephen R. (2002), p16; Windmeijer, Frank (2005);
Arellano, M. and S. Bond (1991), p 280).
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The choice of instrumental variables 2/2
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For the orthogonal deviations estimators, the transformation
ensures that lags of predetermined variables are valid
instruments in the transformed equations and that if the
original vi,t are not autocorrelated, than so are the transformed
errors;
As with the first difference estimator, limited or lack of serial
dependence in vi,t allow for lags of the dependent variable to
be predetermined variables in the model and thus to be used as
valid instruments.
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Tests employed - exemplified on the best estimator for AR(4)
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The Breusch-Godfrey test for
errors serial correlation, using the
F statistic:
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P-value (F-statistic) = 0.187853 > 0.1
=> the null hypothesis (that errors are
uncorrelated) can not be rejected ;
F-stat = 1.77 <= 2.943 = critical F
(v11=, v2=10) => H0 accepted (errors
uncorrelated);
Also by looking at the adjusted Rsquare, the very small value indicates a
misspecified regression, implying the
noncorrelation in error terms;
Similar tests can be conducted for
AR(r) for all the estimations conducted
in this paper’s application.
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