Hi Salsabil Shaikh, you can use panel data analysis with dummy variable interaction model.

Best 

Irfan Sofi

Economist 

Just Jobs Network, New Delhi India

Dear Salsabil, my understanding is that you want to make a cross-country analysis about the possible relationship between investment types and economic growth, introducing the effects of corruption on possible outcomes. First I would suggest to clearly identify the variables to be used and check data availability (I would not include foreign aid unless you have data on related investments). Regarding corruption, you could use global indicators like Transparency International´s Corruption Perception Index or the Worldwide Governance Indicators from the World Bank, or the International Country Risk Guide corruption index (ICRG).  I think the quality and availability of data is a key issue before choosing the "right" methodology. The theory and conceptual review is also very important to understand the possible links between investment and growth in presence of corruption. I would suggest you review Daron Acemoglou´s work on these topics. Below you will find some papers. At the end, which methodology to choose would depend on the theoretical approach and data quality. If there is sound theory and good data, a basic regression analysis might be useful.

http://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1022&context=econ_workingpaper

http://jbsq.org/wp-content/uploads/2013/06/June_2013_9.pdf

http://www.gsmi-ijgb.com/Documents/JEDMITFM%20V6%20N2%20P05%20Adela%20SHERA%20-Economic%20Growth.pdf

panel co-integration and VECM

Luis Rivera suggests a good list of literature from where more literature can be found. But since corruption has a hidden component, econometric  studies may not reveal all truth about interaction with growth.

First of all, there are different types of corruption. If a small government servant gets a bribe, he is likely to use it for domestic consumption. This influences distribution, but may not influence economic growth (he still demands domestic goods for consumption).

If corruption takes place when foreign aid is used for too much inefficient investment (like this happens in many African countries), GDP can grow due to investment, but some part of it goes to private pockets via bribes. Yes, inefficient investment makes long term growth path lower (because creation of new physical capital is not sufficient), but in short term those bribes are likely to be consumed domestically, so aggregate domestic demand does not drop much.

The worst case for the country is when bribes are huge and they move finally to offshore accounts of few super-rich corrupted officials, and never return to work for domestic economy. In this case we can observe negative growth and increasing indebtness of a country. This was very much the case of Russia in 1990s, when it has accumulated huge debt accompanied with negative economic growth in 1992-1998.

I do not know how you will find some evidence about the structure of corruption in a particular country. Perhaps some case investigations by journalists may help, but this is only visible part of an iceberg. Accounting for capital flight, especially unofficial, may help.

GMM y MC2E. You can use Instrumens variables. For example La Porta (1999) for MC2E. The corruption is endogenous with economic growth for a long time. 

Dutta y Sobel (2016) ejemplo GMM.

If the time is short, for example one or two year, you can use PLS. This method is not yet ready to correct the endogeneity, but they are in it. You can try to use MC2E with PLS.

You may try a book on India's Black economy by Arun Kumar  from Penguin .

I am assuming you have already done some review of the vast literature. Before you proceed any further, let me ask you about the contribution of your planned research. Thinking through this question will help you decide on your estimation methodology.   

Ideally, you would need some sort of quasi-experiment to tease out this difference (with or without corruption). However, that this clearly not available. Particularly, since you would like to have multiple countries in your analysis. Then, you need to make sure that you capture (as best as you can) causality (i.e., use GMM or an IV estimator) and control for all possible explanations to reduce the potential for omitted variables. The problems with this kind of analysis are (1) it is difficult to do a good (convincing) job econometric stand point (i.e., which estimator to use, which instrument is good enough, etc.) and (2) all these indexes (CPI, WGI) are very raw approximations which do not vary much over time and are highly correlated with other such aggregated variables (e.g., institutional quality, human capital, etc.) which should be controlled for in a growth regression, making it more difficult to isolate and estimate successfully these effects. What about focusing on fewer countries where you can clearly identify some sort of external shock (policy change) that affects corruption? Then you can examine these effects in a before-after scenario maybe using some difference-in difference approach. Good luck!

Helo,Salsabil,ranking wise could be expenditure,stock market,FDI and foreign aid.To gather information on corruption better to assess based on gaps in increase expenditure.