Dear Ali

Bank efficiency, a measure of bank performance, should be influenced by 'real GDP growth rate' not 'real GDP'.

'Real GDP' itself is a stock variable and should have no direct impact on bank efficiency. The determinants of real GDP are aggregate consumption, capital expenditure(investments), government expenditure and net exports/import. From this, you can clearly see that real GDP do not contribute to bank efficiency in a defined way.

When you talk about GDP per capital, what do you mean? GDP per capital is a measure of 'economic development', not economic growth. And GDP per capital is calculated as real GDP divided by total population. Now, the two components that determine GDP per capital: 'real GDP' and 'population' do not separately have any impact on bank efficiency or bank performance. For instance, increase/decrease in population do not directly affect bank performance/efficiency in any predictable way. Similarly, increase/decrease in real GDP do not directly affect bank performance/efficiency. Now, you can see why you find conflicting results. 

I reckon that the appropriate variable to use should be 'real GDP growth rate'. Positive GDP growth reflect periods of economic prosperity while negative GDP growth reflect economic downturn/recession. In the economic literature, a positive relation between bank efficiency and 'GDP growth' (economic boom) is expected because during good economic times (positive GDP growth), banks tend to have lower NPLs, lower operating costs; thus have improved efficiency etc. and vice versa. This is why you should probably consider to re-run your regression with 'real GDP growth rate' not 'real GDP' nor 'real GDP per capital'. 'Real GDP' by itself is a stock variable and do not have any relation to bank efficiency.

Additionally, from an econometric point of view, adding 'real GDP' and GDP per capita into the model already creates multicollinearity and serial-correlation issues because 'GDP per capita' is clearly dependent on 'real GDP'. 

Finally, if you are happy to proceed with your analysis after the above explanation, I recommend that you replace the real GDP variable with GDP growth rate. Because the latter measures changing economic conditions, and it is now clear that bank efficiency would be affected by changing economic conditions. 

Hope this helps.

Regards

Peterson.

I do not know why is this happening but from an econometric viewpoint, as Peterson suggested, real GDP and GDP per capital must not be both included in the same model because this will create a multicollinearity problem and serial correlation problem.