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LEGAL ORIGINS,
FINANCIAL DEVELOPMENT AND GROWTH:
REVISITING THE EVIDENCE IN THE CASE OF
WEAK IDENTIFICATION.
Decio Coviello, EUI
Microeconometrics/Labor lunch
Florence, 10.02.2005
Paper’s “fil rouge” is:
“Financial Intermediation and Growth:
Causality and Causes”
By Levine R., Loayza N. and Beck T, JME (2000)
The Original Paper:

IV Cross-Country Growth Regressions
(Heteroskedasticity),



Finance is considered as the only endogenous
regressor,
Legal Origin is the exogenous component of
Financial Development,
Endeavors to determine the causal effect of finance
on growth.
Aims:
 Replicate authors’ results (Table 3),

Evaluate the strength of Legal Origins (not
done in the paper,Table 2 is not enough:
wrong s.e.),

To assess when, under weak instruments, it
is still possible to identify the effects of
Finance on Growth.
Main Results:



Legal Origins are Weak Instruments,
Once applying test robust to weak
instruments, second stage inference
procedure, are confirmed the positive effects
of finance on growth but,
There are cases in which there is near
identification.
The Econometric Specification:
1
Financei  a  Legali b  X i c  i
2
yi , 6095    Financei  X i   i
Cross-Country growth regression Barro et al. (2004)
Table 2: Strength of Legal Origins
Instruments Relevance:
EZ ' X   0

How do we test

How large should the correlation be ?

?
How is it possible to assess whether the instruments
are correlated enough with Finance ?
Basic References:

Staiger and Stock, EEA (1997),

Stock and Yogo, NBER t0284 (2002/2004).
Problems with Weak Instruments


Small sample bias toward the inconsistency
of OLS estimator,
Non normality of the IV estimator in both
small and large samples (Bound et al. 329.000
observations in the Angrist-Krueger quarter of birth framework.),


Unreliable t-tests statistics, Nelson and Startz (1990)
Small Confidence Intervals
A toolkit:

Hall et al. (1996), showed in Monte Carlo
simulaiton the F-distribution is inadequate to
test H0: b=0,

Stock and Yogo (2004):
Compare the first stages F-Stat with ad hoc
critical values tabulated.
Detection Procedure

First Stage F-statistics of the excluded
Instruments,
from the first stage regressions of Finance on the
dummies for Legal Origins and the X’s,
(Do not use the p-value of the first stage regressions),
Only Legal Origins are the excluded instruments for
Finance,
First Stages F-Statistics
The p-value is computed for
an F, while it is shown that
the F-stat of the first stage
is a non central chi2.
My results in details (1):

For all the specifications F in [0.79 5.73]

While the rule of thumb threshold is F>10,

Two kind of weak Instruments:
Weak: for Priv.Cre and Liq.Liab, F > 1.85
Very Weak: for Comm.Cent., F  1.85
Second Stage Inference Procedure
(1):



Test robust to weak instruments:
1) Klibergen (2003),
2) Moreira (2004),
3) Anderson-Rubin (1949)
(1)+(2) under weak instruments asymphtotic
(K=fixed and N goes to Infinity),
(3) is the most powerful with few instruments,
see Dufour (1997).
Second Stage Inference Procedure (2)
a
a) Under the null β = β0, AR(  0 ) ~
(Spotted typo),
 k2
k
b) it does not depend on Z’X,
c) C.I by inverting the statistic,
d) The cuts-points can be computed by solving
(a,b,c depend on the data and critical values):
Second Stage Results:
Results (1):

Under Weak Instruments: bounded C.I.
Wald
0.7821 6.0864
AR
AR*
2.8571 8.5714
2.836 42.857
5
Upper
10
Lower
Test statistic and critical value
C.I
15
Confidence Region
 3 2  7.815
32
3
 2.605
0
F  3.51
-50
0
50
beta
ar
arcrit
100
Results (2):

Under Very Weak Instruments: unbounded C.I. (CommercialCentral Bank),
10
Confidence Region
F  1.85
 3 2  7.815
3
3
2
6
[5.7142,+Inf)
0
AR
4
Wald 0.01486 18.5624
8
Upper
2
Lower
Test statistic and critical value
C.I
 2.605
-40
-20
0
beta
ar
20
arcrit
40
Intuition 1:


The confidence regions for β consist of all the
points s.t. the AR statistic is below the chisquare-k critical value (k is number of
instruments)
Dufour (1997), shows that “any” valid
confidence region in the (Very) weakinstrument case must cover the whole real
line with non-zero probability,+ Zivot,Startz
and Nelson (1998).
Intuition 2:
If we substitute (1) into (2)….
   b,
So the effect of Finance can be expressed as :


b
Conclusions and Future Ideas:



The Statistical tools used are not powerful
enough to accept or reject the null of no
effects of finance,
Robusteness check on X’s using Sala-iMartin (2004).
focus on the assumed heteroskedasticity to
gain identification by looking at second
moments (IH),
Variable Definition (1):


Y= Average growth rate of real per capita
GDP
Finance (period averages):
1) LL= currency+demand and interest-bearing liabilities of
banks and non-bank financial intermediaries divided by
GDP
2) Com-Centr=bank assets divided by commercial bank
plus central bank assets. Society’s savings allocation,
3) Priv= is the value of credits by “financial intermediaries
to the private sector divided by GDP.
Variable Definition (2):

Legal=Dummy variables for British, French,
German and Scandinavian legal origin,
spread primarily through conquest and imperialism.

X:
1)Simple: lnGDP60 and lnEdu60
2)Policy: (1) + gov.size, infla, black mkt,
exchange rate, trade (period avg)
3)Full: (1)+(2)+ revolutions,assass, ethnic
GMM:



Authors’ claim is heteroskedasticity of unknown form:
No test is performed,
No stress of small sample problems given the
requirements of GMM, 71 observations.
The feasible efficient two steps GMM estimator :
1
ˆ Z ),
Ŝ 
(Z ' 
N
ˆ Z ) 1 Z ' X ) 1 ( X ' Z ( Z ' 
ˆ Z ) 1 Z ' y ),
ˆ
 ( X ' Z (Z ' 
GMM
ˆ Z ) 1 Z ' X ),
V (  GMM )  ( X ' Z ( Z ' 
ˆ

IV
 uˆ1
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





uˆ1






uˆ n 
