افزایش ارزش (استهلاک) مسکن و رفاه صاحبان مسکن

This paper extends Frank’s (2006) very simple model to analyze the welfare effects of appreciation and depreciation in a world with borrowing, property taxes, and moving costs. It is shown that appreciation can make homeowners worse off but that even when there is a property tax depreciation can not make homeowners who intend to stay in their house worse off. Our model provides a simple framework that can be used discuss the rationale for alternative policies to aid homeowners during periods of both appreciation and depreciation.

From the late 1990s through 2005 low interest rates, new exotic mortgage instruments and real estate speculation led to increased residential appreciation. The rise in market values led to increased residential property tax assessments and widespread citizen protests. In response many states adopted government programs that gave property tax breaks to homeowners whose parcels had appreciated especially rapidly (see Dye et al., 2006; Haveman and Sexton, 2008). Beginning in mid-2006 a rapid and widespread decline in housing prices occurred and there was considerable discussion about appropriate government programs to protect housing equity. Appreciation provoked the greatest controversy in areas where the market value of homes rose despite the fact that perceived structure and neighborhood quality were unchanged. Thus, we can view the change as a pure increase in user cost. Frank’s (2006) wonderfully simple model shows that, starting from a fixed bundle of housing and a composite good, either an increase (appreciation) or a decrease (depreciation) in the price of housing makes an owner better off (pp. 166–167).2 The appreciation result is intuitive but the case with depreciation is not. This result may seem paradoxical but the intuition behind it is that, once purchased, housing and the composite good become endowments that can be costlessly maintained even when relative prices change. Frank’s logic exercise is an amusing and useful teaching tool but also raises an important and timely question: under what conditions are real world consumers made better (or worse) off by changes in housing prices? This short paper provides some additional intuition about this question by adding three real world complexities-borrowing, moving costs and property taxes-to Frank’s model. The rest of the paper is organized as follows: Section 2 recapitulates Frank’s (2006) model, Section 3 revises the model to add borrowing and moving costs, and property taxes are considered in Section 4. Application to some issues raised in recent literature is discussed in Section 5. Some potential extensions are considered in Section 6 and concluding remarks are discussed in Section 7.

Frank (2006) provides a paradoxical example that demonstrates that housing appreciation and depreciation both benefit owners. We add more structure to the model by considering the remaining mortgage balance, moving costs, and property taxes and show that appreciation can make homeowners either better or worse off, depending on the relative size of the remaining mortgage balance, moving costs, property taxes, and the benefits from altering consumption bundles when relative prices change. Surprisingly, however we show that when there is depreciation and a property tax Frank’s counter-intuitive result holds and the homeowner must be better off whether she moves or stays. These results could be used to partially justify some government programs to mitigate increases in property tax payments resulting from rapid housing appreciation on equity grounds, especially for households that have high moving costs. These results also might justify a gradual phase-in of assessment reductions during periods of housing price depreciation. Of course, the total effect of these programs could still be negative since recent studies (Haveman and Sexton, 2008) find that programs to cushion property tax assessment increases often have unwanted efficiency or equity effects.