Does a portfolio with direct real estate provide stronger diversification than portfolios of stocks and REITs?

General Topic: Direct Real Estate Performance
Data set: Commercial real price indices from Real Capital Analytics (RCA). https://www.rcanalytics.com/. Stock and REIT
data.
Research Question: Does a portfolio with direct real estate provide stronger diversification than portfolios of stocks and REITs?
Direct real estate is perceived as an asset class that is difficult to add to a portfolio (high transaction costs, low liquidity), but the diversification benefits could outweigh the costs. REITs have generally been used as a proxy for real estate, but research has shown REITs tend to correlate more to the stock market than one would expect from real estate. What can an allocation to direct real estate do for a portfolio? And what works better within a country, diversification over regions or over property types?
The estimation of direct real estate indices is a challenge on its own. Increased availability of transaction data however makes it possible to create an international set of direct real estate indices. Estimation of real estate indices is an optional addition to the research subject.
Methodologies:
Required: The jennrich test, test for differences in correlation matrices; constructing and comparison of efficient frontiers
Starting Literature:
Bailey, M. J., R. F. Muth, and H. O. Nourse (1963). A regression method for real estate price index construction. Journal of the American Statistical Association 58, 933–942.
Value indices of commercial real estate: a comparison of index construction methods. JD Fisher, DM Geltner, RB Webb – The journal of real estate finance and economics, 1994
Seiler, M.J., Webb, J.R. & Myer, F.C.N. Diversification Issues in Real Estate Investment. Journal of Real Estate Literature 7, 163–179 (1999).
Eichholtz, P.M.A., Hoesli, M., MacGregor, B.D. and Nanthakumaran, N. (1995), “Real estate portfolio diversification by property type and region”, Journal of Property Finance, Vol. 6 No. 3, pp. 39-59
Piet M.A. Eichholtz (1996) Does International Diversification Work Better for Real Estate than for Stocks and Bonds?, Financial Analysts Journal, 52:1, 56-62
Mitchell Conover, Swint Friday & Stacy Sirmans (2002) Diversification Benefits from Foreign Real Estate Investments, Journal of Real Estate Portfolio Management, 8:1, 17-25
My slot:
Is international diversification more effective for direct real estate than for Stocks and REITS?
– Global selection: 2007-2020.
Main difficulties: Matching data with other sources, small count econometrics