There are various factors has been stated in past literature. I would suggest for the following readings on this topic.

https://www.tandfonline.com/doi/abs/10.1080/00036846.2014.995360

https://pdfs.semanticscholar.org/47e9/8d19eb2aa75991cbfe97bbde38b03f7ff3b9.pdf

http://www.sciencedirect.com/science/article/pii/S0165410101000180

http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1987.tb04565.x/full

https://www.cambridge.org/core/journals/journal-of-financial-and-quantitative-analysis/article/div-classtitlethe-determinants-of-capital-structure-capital-market-oriented-versus-bank-oriented-institutionsdiv/0F08AA876248523B3D84E645178323DB

If by efficiency of capital markets you mean the costs of trading or transactions, access to capital as measured by market liquidity (i.e. traded volumes as proxy), and integrity of the market (i.e. legal framework and protection of property rights), you can do a number of cross section regressions of these variables against some of the measures under ease of doing business that are published by Transparency International, or Heritage Foundation's economic freedom indicators.  

The correlations tend to be positive for the following:

1. Higher transparency scores tend to lead to lower costs of transactions, access to capital or market liquidity.

2. Higher scores in "ease of doing business" tend to lead to higher scores in transparency measures.

By doing a two stage regression analysis, you could formulate a framework that could analyse 

 Have you ever read Daron Acemoglu?  He has also written a book on why nations fail. Well in short a good capital market is the one with the institutions. Let's say the one with the central bank etc. The macro economic variables are the ones affected I believe. The influence comes from within , a bit of a keynesian approach 

If by efficiency you mean prices reflecting all the information available publicly or privately, then information asymmetry & disclosure are the most important variables. Liquidity prevailing in the markets, and low transaction costs are other important variables.

For frontier markets - concentration of ownership structure of companies as one of determinant of market liquidity.

A good place to start is the Journal of Economic History, Volume 49, Issue 4, December 1989, pp. 803-832. "Constitutions and Commitment: The Evolution of Institutions Governing Public Choice in Seventeenth-Century England," by Douglass C. North and Barry R. Weingast.