Cross-sectional estimation in STATA by Binam Ghimire

1. Cross-sectional estimation in STATA by BinamGhimire

2. Learning Objectives • Cross sectional regression in Stata • Wald test for joint significance

3. Theory • Many papers have provided evidence of a positive relationship between financial development and economic growth. • Theses papers have mainly applied cross sectional estimation (average effect) to empirically prove the above relationship

4. Theory • Cross-sectional estimation: Beck et al. (2004) paper shows positive relationship between banks, stock market and economic growth. • Next slide shows the output of cross sectional estimation in Beck et al. (p 430, 2004)

5. Learning Objectives • Cross sectional regression in Stata • Wald test for joint significance

6. File to import for practice • Data from Beck et al. (2004) • Download the data from www.banksandmarkets.wordpress.com • You can note that the name of the countries have been converted into numbers. (Stata wont recognise the names therefore you must convert them into numbers).

7. Importing the file • To import the data in stata: copy and paste from excel into Data Editor as follows • Data - Data Editor and paste the copied cells. You should have copied all the cells inside the worksheet “main” i.e. all 40 observations for all 9 variables including the country column) (Or you can import the file using various options available in Stata: File - Import)

8. Converting data into natural logs • Generate the natural log of the variables to avoid the affect of the outliers using the “gen” command as follows • In the stata command box type gen lnvariablename =log(variablename) for some variables you should apply gen lnvariablename=log(1+variablename) • Press enter each time a gen command is written. • You should convert 8 variables into natural log so 8 times gen command to be applied as follows • gen lnstart=log(start), gen lnschool=log(1+school) gen lngov=log(gov), gen lntrade=log(trade), gen lnpi=log(1+pi), gen lnbmp=log(1+bmp), gen lnpriv=log(priv), gen lntor=log(tor)

9. Converting data into natural logs • If you make any mistake while generating natural logs you can drop the generated variable by using the drop command – e.g. drop lnstart to delete the generated lnstart. • You can generate the variable again as shown in previous slide using the gen command

10. Pooled cross sectional regression • Now run the cross-sectional pooled regression estimates using the regress command: regress growth lnstartlnschoollnprivlntor • It should look like the output in next slide. This is the output of regression 1, simple conditioning information set of Beck et al. (2004) where the authors have included the initial real GDP per capita to control for convergence and the average years of schooling to control for human capital accumulation.

11. Pooled cross sectional regression

12. Importing Data from Excel into Stata2. Pooled estimate • In the policy conditioning information set, authors use the simple conditioning information set plus either (i) the black market premium, (ii) the share of exports and imports to GDP, (iii) the inflation rate or (iv) the ratio of government expenditures to GDP. • The regression command for each of the above regressions are as follows : regress growth lnstartlnschoollngovlnprivlntor regress growth lnstartlnschoollntradelnprivlntor regress growth lnstartlnschoollnpilnprivlntor regress growth lnstartlnschoollnbmplnprivlntor • The outputs are similar to regression 2, 3, 4 and 5 of Beck et al. (2004). They are provided in the next 4 slides.

13. Pooled cross sectional regression, Beck et al. (2004) regression 2

14. Pooled cross sectional regression, Beck et al. (2004) regression 3

15. Pooled cross sectional regression, Beck et al. (2004) regression 4

16. Pooled cross sectional regression, Beck et al. (2004) regression 5

17. Result: • The OLS regressions demonstrate a strong positive association between stock market development, bank development, and economic growth. Both bank development (bank credit represented by lnpriv) and stock market development (turnover ratio represented by lntor) enter each of the five regressions significantly at the 0.05 significance level.

18. Wald test: • Wald Test can be used to test the joint significance of a subset of coefficients. • Here we can test the two variables from Beck et al. (2004): lnpriv and lntor. • The null hypothesis is H0: θ is 0 (Ho: b1=b2=0) and hence the variables are not providing meaningful results. The alternative hypothesis is H0: θ is greater or less than 1 (H1: b1=b2 ≠0) , which means the variables are jointly significant and give a meaningful result. • In the regression result lnpriv and lntor are individually significant based on t-tests with very low p values. But to test that they are jointly significant we can perform the Wald test

19. Wald test: • The command is • Test lnprivlntor • The result is shown in the slide next

20. Wald test:

21. Wald test: • F static at 17.67 with p value of 0.0000 means they are jointly significant • The F static of 10.15 and p value of 0.0000 shown in the regression output is also the indicator of the joint significance for ALL independent variables. This means when we perform Wald test for all independent variables in the first regression equation, the output would be similar to the F static in OLS equation above (F= 10.15 and = 0.0000). See next slide to check this

22. Wald test:

23. Thank You

24. Reference(s): • BECK, T. and LEVINE, R. 2004. Stock Markets, Banks, and Growth: Panel Evidence. Journal of Banking & Finance, 28, 3, 423-442. • GUJARATI, D. N. 2003. Basic Econometrics, New York, McGraw-Hill Education.