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How Do We Determine Which Housing Market Allows Greater Mobility

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How Do We Determine Which Housing Market Allows Greater Mobility

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    1. How Do We Determine Which Housing Market Allows Greater Mobility? Danny Ben-Shahar Technion Israel Institute of Technology and Eyal Sulganik The Interdisciplinary Center, Israel

    2. MOTIVATION How do we determine which housing market allows greater mobility? Rank the mobility in a given market over time (time series) Rank the mobility among markets at a given time-period (cross section)

    3. INTUITION Consider an information matrix P where the current states are considered as signals about the past states P = An entry Pij of an information matrix P is the conditional probability that state sj has emerged as a signal from a past state si (where i refers to a row and j refers to a column in the matrix).

    4. INTUITION

    5. INTUITION Suppose, instead, that P is a transition (mobility) matrix: P = An entry Pij of a mobility matrix P is the conditional probability that a vacancy starting at housing status si will end up at housing status sj at the end of the period. Then,

    6. INTUITION

    7. OBJECTIVE Explore the implications of the proposed mobility measure to vacancy chains; Explore possible links between the proposed mobility measure and other mobility measures that appear in the literature.

    8. OUTLINE OF PRESENTATION Brief literature review; Background vacancy chains; Selected results; Summary.

    9. LITERATURE REVIEW On mobility measures: Prais (1955), Shorrocks (1978), Brumelle and Gerchak (1982), Conlisk (1990), Dardanoni (1993), Parker and Rougier (2001), and Ben-Shahar and Sulganik (forthcoming).

    10. LITERATURE REVIEW On vacancy chains in the general literature: Robson et al. (1999) and Lanaspa et al. (2003) in urban studies; Felsenstein and Persky (forthcoming) in labor studies; Weissburg et al. (1991) in ecology; Chase and Dewitt (1988) in life science; Sorensen (1983) in education systems; Stewman (1988) in criminology; Chase (1991) presents an overview of vacancy chain literature.

    11. LITERATURE REVIEW On vacancy chains in real estate: Kristof (1965), Adams (1973), and Watson (1974) are among the firsts to consider vacancy chains emerging from new construction; Lansing et al. (1969), racster et al. (1971), and Brueggeman et al. (1972) were among the first to suggest the use of vacancy chain models in order to assess the effectiveness of possible housing policy programs; Others: Marullo (1985); Hua (1989); and Emmi and Magnusson (1995).

    12. BACKGROUND Vacancy chains: Given the vacancy transition matrix P, P = Suppose s3 is the only absorbing state, then = and

    13. BACKGROUND is the vacancy chain. An entry of the matrix represents the expected number of times that a vacancy emerging from state i will appear in state j before it is absorbed.

    14. RESULTS Proposition 1: For any two triangular vacancy transition matrices Q and P, if Q is more mobile than P (i.e., Q=PR), then for all i.

    15. RESULTS Example: Suppose that P = Q = such that Q=PR R = and thus Q is more mobile then P.

    16. RESULTS P = =

    17. RESULTS Q = =

    18. RESULTS

    19. RESULTS Proposition 2: For doubly stochastic transition matrices P and Q, if Q is more mobile than P (i.e., Q=PR) and R is doubly stochastic, then the sum of the entries in the column of vacancy chain of RP is greater or equal to the sum of the entries in the respective column of the vacancy chain of Q.

    20. RESULTS Proposition 3: If is a strictly row diagonally dominant matrix (i.e., ), then the vacancy chain matrix is a strictly diagonally dominant of its column entries (i.e., for all i and j).

    21. RESULTS Corollary: If for all i (i.e., any vacancy that emerges in status i is always associated with a change of status), then is strictly diagonally dominant in its columns (that is, for all i and j).

    22. RESULTS Proposition 4: For any two triangular transition matrices Q and P, if Q is more mobile than P (i.e., Q=PR), then . Following Conlisk and Sommers (1979), Shorrocks (1978), and McFarland (1981), a greater second largest eigenvalue is associated with a greater speed of convergence of a transition matrix to its equilibrium (i.e., to a constant row matrix).

    23. RESULTS Proposition 5: For any normal transition matrices P and Q and a doubly stochastic matrix R, if Q is more mobile than P (i.e., Q=PR), then . Consistent with Parker and Rougier (2001) mobility measure.

    24. Summary We develop a link between the literature on mobility measures and the vacancy chain literature; We derive implications of the mobility measure Q=PR for vacancy chains;

    25. THE END

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