Decio Coviello, EUI Microeconometrics/Labor lunch Florence, 10.02.2005

1. 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

2. Paper’s “fil rouge” is: “Financial Intermediation and Growth: Causality and Causes” By Levine R., Loayza N. and Beck T, JME (2000)

3. 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.

4. 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.

5. 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.

6. The Econometric Specification: Cross-Country growth regression Barro et al. (2004)

7. Table 2: Strength of Legal Origins

8. 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 ?

9. Basic References: • Staiger and Stock, EEA (1997), • Stock and Yogo, NBER t0284 (2002/2004).

10. 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

11. 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.

12. 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,

13. 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.

14. 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.,

15. 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).

16. 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):

17. Second Stage Results:

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

19. Results (2): Under Very Weak Instruments: unbounded C.I. (Commercial-Central Bank),

20. 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).

21. Intuition 2: If we substitute (1) into (2)….

22. 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),

23. 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.

24. 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

25. 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.