Owners\u27 Equivalent Rent and the Consumer Price Index: 30 Years and Counting

The objective of the Consumer Price Index (CPI) is to measure the change in expenditures required to maintain a given standard of living. For expenditures on houses, this leads to a measurement objective that focuses on the shelter services provided by a house over a period of time. A house is a capital asset that provides a flow of services over a substantial period of time, not a one-time consumption item. The Bureau of Labor Statistics (BLS) explored two major approaches to determine how to estimate the cost of shelter services for owner-occupied dwellings. The first approach attempts to estimate the flow of shelter services for an owned dwelling from items related to living in it. This approach is called “user cost” and includes items such as real estate taxes, insurance, and an interest estimate based on the market value of the house. The second approach attempts to estimate the flow of services for an owner dwelling based on market rents for rented dwellings. This research led to a method referred to as “rental equivalence.” This method measures the rate of change in the amount an owner would need to pay in order to rent on the open market. It is based on actual market rents collected from a sample of renter-occupied housing units that are identified to be representative of owner-occupied housing. On October 27, 1981, Commissioner Janet Norwood announced that BLS would convert the CPI for All Urban Consumers (CPI-U) to a rental equivalence measure for homeowner costs, effective with data for January 1983. The CPI for Urban Wage Earners and Clerical Workers (CPI-W) would be converted to the new method, effective with the January 1985 data. This announcement was consistent with general BLS practice of giving at least 1-year’s notice before making a major methodological change. The change also meant that the CPI-U for 1983 and 1984—the first years the CPI was to be used in the escalation of personal income tax brackets and exemptions—would use the new methodology. The longer period of notice for the CPI-W was provided, because the CPI-W continued to be the primary index used in cost-of-living adjustments in collective bargaining agreements and in the escalation of government entitlement payments. It was felt that sufficient time needed to be provided for users to adapt to the change. The transition to the new method was smooth, in large part, owing to the open way it was done and the extensive public information effort

The combinatorial Mandelbrot set as the quotient of the space of geolaminations

We interpret the combinatorial Mandelbrot set in terms of \it{quadratic laminations} (equivalence relations $\sim$ on the unit circle invariant under $\sigma_2$). To each lamination we associate a particular {\em geolamination} (the collection $\mathcal{L}_\sim$ of points of the circle and edges of convex hulls of $\sim$-equivalence classes) so that the closure of the set of all of them is a compact metric space with the Hausdorff metric. Two such geolaminations are said to be {\em minor equivalent} if their {\em minors} (images of their longest chords) intersect. We show that the corresponding quotient space of this topological space is homeomorphic to the boundary of the combinatorial Mandelbrot set. To each equivalence class of these geolaminations we associate a unique lamination and its topological polynomial so that this interpretation can be viewed as a way to endow the space of all quadratic topological polynomials with a suitable topology.Comment: 28 pages; in the new version a few typos are corrected; to appear in Contemporary Mathematic