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The long-run relationship between house prices and income: evidence from local housing markets.

Article Excerpt
Many in the housing literature argue that house prices and income are cointegrated. I show that the data do not support this view. Standard tests using 27 years of national-level data do not find evidence of cointegration. However, standard tests for cointegration have low power, especially in small samples. I use panel-data tests for cointegration that are more powerful than their time-series counterparts to test for cointegration in a panel of 95 metro areas over 23 years. Using a bootstrap approach to allow for cross-correlations in city-level house-price shocks, I show that even these more powerful tests do not reject the hypothesis of no cointegration. Thus the error-correction specification for house prices and income commonly found in the literature may be inappropriate.

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In the second half of the 1980s, real house prices rose about 3% per year. (1) Then in 1990 alone, real prices tumbled almost 5%. Prices continued to fall, on balance, through the end of 1994, reversing more than half of the gains posted in the late 1980s; prices did not return to their 1989 level until almost 10 years later. Many coastal cities experienced even wilder swings: Real house prices rose about 65% in Los Angeles and about 45% in Boston in the second half of the 1980s, only to fall 30% in Los Angeles and 20% in Boston during the next 5 years.

Many real-estate market observers think that housing prices got too far ahead of fundamentals in the 1980s-especially in many coastal cities--and that the poor performance of house prices during the first half of the 1990s was the inevitable aftermath. Real house prices have risen rapidly in recent years, sparking fears that the housing market is once again overvalued.

Of particular concern to many is the fact that house-price gains have dwarfed per capita income gains since 1998. As can be seen in Figure 1, the ratio of house prices to per capita personal income moved up rapidly beginning in the late 1990s after trending down for most of the previous 20 years. (2) More specifically, from the middle of 1997 to the middle of 2002, real house prices rose about 28% while real per capita personal income rose about 15%. In contrast, during the previous 20-year period, real house prices rose only 8% while real per capita income rose 35%. The recent performance of house prices relative to income is taken as evidence by some that house prices are out of line with "fundamentals" and that prices must stagnate or fall to allow income to catch up.

[FIGURE 1 OMITTED]

This idea is commonly formalized in the housing literature by positing a cointegrating relationship between house prices and fundamentals such as income and then estimating an error-correction specification (Abraham and Hendershott 1996, Malpezzi 1999, Capozza et al. 2002, Meen 2002). That is, house prices and income are thought to be linked by a stable long-run relationship; they may drift apart temporarily, but their tendency is to return to their long-run equilibrium.

The purpose of this article is to test this view of the housing market. If prices and income are cointegrated, then the gap between the two may be a useful indicator of when house prices are above or below their equilibrium values and therefore a useful predictor of future house-price changes. Conversely, if prices, income and other fundamentals such as interest rates and construction costs are not cointegrated, then the error-correction specifications common in the literature are inappropriate, and house prices need not stagnate or fall just because they have grown more quickly than has income of late. (3)

Many researchers simply assume that house prices and fundamentals are cointegrated (Abraham and Hendershott 1996, Capozza et al. 2002). Others implicitly assume that they are not (Poterba 1991). Meen (2002) is the only study I am aware of that tests for cointegration of prices and fundamentals using national-level data. His reported tests do not find evidence for cointegration at conventional significance levels. However, Meen argues that the test statistics are "near" their critical values, and therefore he concludes that prices and fundamentals are cointegrated. One contribution of this article is to show that using 27 years of national-level data, one does not find evidence that prices, income and other fundamentals are cointegrated. Thus my results, if not my interpretation, are in accord with Meen, and they suggest that it is inappropriate to model house-price dynamics using an error-correction specification.

However, cointegration tests are known to have low power, particularly in small samples (Banerjee 1999). A time span of 27 years may be too short to estimate what may be a genuine long-run relationship with slow adjustment. Starting with Quah (1990) and Levin and Lin (1992), researchers have developed panel tests for unit roots and cointegration that are more powerful than their standard time-series counterparts. The second, and main, contribution of this article is to apply the recently developed tests of Pedroni (1999) and Maddala and Wu (1999) to a panel of 95 U.S. cities over 23 years. I show that even these more powerful tests cannot reject the hypothesis that prices and income are not cointegrated. My results contradict those of Malpezzi (1999), which found that one can reject the null of no cointegration in a similar panel. However, Malpezzi used a panel unit root test, which overstates the likelihood of cointegration because it ignores the first-stage estimation in his residuals-based cointegration test.

The rest of this article is organized as follows. In the following section, I briefly describe a simple stock-flow model of housing. The purpose of the model is to motivate why prices, per capita income and perhaps other variables might be cointegrated. I then describe the national-level data and show that there is little evidence for cointegration using Engle and Granger's (1987) augmented Dickey-Fuller (ADF) test. City-level tests...

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