The convergence of regional house prices in the USA in the context of the stress testing of financial institutions

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I studied the convergence of regional house prices to national prices in USA by analyzing time-series of house price indices of 9 Census Divisions. I found the evidence of the convergence in some parts of the country using asymmetric unit root tests. The fact that the evidence of the convergence is not present in large parts of the country raises an issue of execution and interpretation of results of Federal Reserve Bank's annual stress testing of the US banking system.