Hello everyone,

I am exploring whether the hypothesis that above a certain threshold financial depth yields negative results for economic growth. For this purpose, I take the quadratic term of my variable of interest, namely bank credit to the private sector. First I estimate the simple OLS with robust standard errors, which shows that there is indeed a quadratic relationship and that upon a certain threshold financial depth has a negative impact on growth.

reg gr linitial prcreditBI prcreditBI2 log_trade log_govsize log_school log_infl , robust

Linear regression Number of obs = 64
F(7, 56) = 8.36
Prob > F = 0.0000
R-squared = 0.5037
Root MSE = 1.1029

------------------------------------------------------------------------------
| Robust
gr | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
linitial | -.9851453 .335963 -2.93 0.005 -1.65816 -.3121306
prcreditBI | 6.026801 2.051998 2.94 0.005 1.916155 10.13745
prcreditBI2 | -3.052359 .9509696 -3.21 0.002 -4.95738 -1.147338
log_trade | -.001041 .2636371 -0.00 0.997 -.5291696 .5270876
log_govsize | -1.297607 .5570733 -2.33 0.023 -2.413559 -.1816553
log_school | 2.171247 .8182169 2.65 0.010 .532161 3.810332
log_infl | .0640021 .1290749 0.50 0.622 -.1945661 .3225703
_cons | 7.712365 1.98893 3.88 0.000 3.72806 11.69667

As you can see the coefficient of prcreditBI2 becomes negative. Nevertheless, I do not know how to find the exact threshold when bank credit to the private sector starts yielding a negative effect on growth (e.g credit to the private sector starts yielding negative effects on growth when it reaches 80%of GDP). Can somebody help me with this?

Thank you!