Decio Coviello, EUI Microeconometrics/Labor lunch Florence, 10.02.2005

LEGAL ORIGINS,FINANCIAL DEVELOPMENT AND GROWTH:REVISITING THE EVIDENCE IN THE CASE OF WEAK IDENTIFICATION.

Decio Coviello, EUIMicroeconometrics/Labor lunchFlorence, 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:

iiii

iiii

XFinancey

cXbLegalaFinance

9560, 2

1

Cross-Country growth regression Barro et al. (2004)

Table 2: Strength of Legal Origins

Instruments Relevance:

How do we test ?

How large should the correlation be ?

How is it possible to assess whether the instruments are correlated enough with Finance ?

0' XZE

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., 85.1F

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) Under the null β = β0, (Spotted typo),

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):

kAR k

a 2

0 ~)(

Second Stage Results:

Results (1): Under Weak Instruments: bounded C.I.

C.I Lower Upper

Wald 0.7821 6.0864

AR

AR*

2.8571

2.836

8.5714

42.857

605.23

815.7

51.3

23

23

F

05

1015

Tes

t sta

tistic

and

crit

ical

val

ue

-50 0 50 100beta

ar arcrit

Confidence Region

Results (2): Under Very Weak Instruments: unbounded C.I. (Commercial-

Central Bank),

C.I Lower Upper

Wald 0.01486 18.5624

AR [5.7142,+Inf)

02

46

810

Test

sta

tistic

and

crit

ical

val

ue

-40 -20 0 20 40beta

ar arcrit

Confidence Region

605.23

815.7

85.1

23

23

F

Intuition 1:

The confidence regions for β consist of all the points s.t. the AR statistic is below the chi-square-k critical value (k is number of instruments)

Dufour (1997), shows that “any” valid confidence region in the (Very) weak-instrument 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

b

:as expressed becan Finance ofeffect theSo

,

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-i-Martin (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.

n

IV

GMM

GMM

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yZZZZXXZZZZX

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:estimator GMM steps twoefficient feasible The

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