Abstract
This paper proposes a probabilistic model based on comovements and nonlinearities useful to assess the type of shock affecting each phase of the business cycle. By providing simultaneous inferences on the phases of real activity and inflation cycles, contractionary episodes are dated and categorized into demand, supply and mix recessions. The impact of shocks originated in the housing market over the business cycle is also assessed, finding that recessions are usually accompanied by housing deflationary pressures, while expansions are mainly influenced by housing demand shocks, with the only exception occurred during the period surrounding the “Great Recession,” affected by expansionary housing supply shocks.
Acknowledgment
Thanks to Maximo Camacho, Gabriel Perez-Quiros, the editor and an anonymous referee for valuable comments and suggestions. Thanks to the participants at 20th Symposium of the Society for Nonlinear Dynamics and Econometrics, 31st Annual International Symposium on Forecasting, Quantitative Economics Doctorate Jamboree and internal seminar series at the University of Alicante for discussions that improved the content of this paper. The views expressed in this paper are those of the author and do not represent the views of the Bank of Canada.
Appendix
It is assumed that m=2, and k=0. Focusing first on the real activity versus inflation model, according to the eleven-variable model used in the empirical application, the measurement equation, yt=Hβt+et, with et~N(0,R), is
where R is a matrix of zeroes. The notation of the variables is defined as: GDP is real GDP, IND is industrial production, PIN is real personal income less transfers, SAL is real manufacturing trading sales, PAY is total non-farm labor, DEF is deflator of GDP, CPI is consumer price index, PPI is producer price index, GSC is Standard and Poor’s GSCI non-energy commodities price index, OIL is spot oil price, and HCN hourly compensation in the non-farm business sector.
The transition equation,
where Q is a diagonal matrix in which the entries inside the main diagonal are collected in the vector
For the real activity versus housing prices model, the measurement and transition equations follow the same reasoning as in Equations (A.1) and (A.2), respectively. The main change, apart from adjusting the appropriate dimension of the matrices for 10 observed indicators, is that vector yt, as defined in Equation (A.1), is replaced by
The notation of the housing price indicators is defined as: PDI is Price deflator index of new single-family houses under construction, CMH is Conventional Mortgage Home Price Index, ATP is FHFA All-transactions Price Index, POI is FHFA Purchase-only Index, SPC is S&P Case-Shiller-10-cities Home Price Index.
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