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Housing prices and transaction volume
Journal of Housing Economics 22 (2013) 119–134
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Journal of Housing Economics journal homepage: www.elsevier.com/locate/jhec
Housing prices and transaction volume q H. Cagri Akkoyun, Yavuz Arslan, Birol Kanik ⇑ Central Bank of Turkey, Istiklal Cad. No.: 10, Ulus, Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 9 April 2012 Available online 28 February 2013 JEL classification: G1 R2 R3
a b s t r a c t We use annual, quarterly and monthly data from the US to show that the correlation between housing prices and transaction volume (number of existing houses sold) differs across different frequencies. While the correlation is high at the low frequencies it declines to the levels close to zero at high frequencies. Granger causality tests for different frequencies show that the way of causality in housing market changes from region to region. Our findings provide a litmus test for the existing theories that are proposed to explain the positive correlation between transaction volume and housing prices. Ó 2013 Elsevier Inc. All rights reserved.
Keywords: Housing prices Transaction volume Dynamic correlation Low frequency High frequency
1. Introduction In this paper, we use US data to analyze the relationship between housing prices and transaction volume at different frequencies. Our analyses provide several tests to evaluate the theories offered to explain the comovement of housing prices and transaction volume documented in the literature. The first test in our analysis utilizes the different correlations observed at different frequencies. The theories proposed in the literature generate positive comovement at higher frequencies (in the short run) but generate negative comovement or non at lower frequencies (in the long run). In this respect, we investigate the relationship between housing prices and transactions by using spectral analysis to reveal how much different frequencies contribute to
q We thank Abdullah Yavas, Umit Ozlale and Charles Leung for valuable comments. The views expressed are those of the authors and should not be attributed to the Central Bank of the Republic of Turkey. ⇑ Corresponding author. E-mail addresses: [email protected] (H.C. Akkoyun), yavuz. [email protected] (Y. Arslan), [email protected] (B. Kanik).
1051-1377/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jhe.2013.02.001
the correlation. Since both theories and data have implications about the correlation at different frequencies our paper proposes a new way of testing the existing theories in the literature which generate the comovement of housing prices and transaction volume. In addition to the correlation analysis we also explore the direction of the causality between the two series by using Granger causality test at different frequencies. This is important to evaluate the theories because the direction of causality between housing prices and transactions differs depending on the mechanism of the models. For our analysis we use annual, quarterly and monthly housing prices and transaction volume data from the US. We use HP and band-pass filters and dynamic correlations to obtain the correlations of the two series at different frequencies. In our analysis we show that the largest part of the positive correlation between housing prices and transaction volume comes from the low frequency components. However, at higher frequencies the correlation becomes smaller and sometimes negative. We, also, find that for the quarterly data at high frequency the way of causality between the two series is from transactions to housing prices. Our results are slightly
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different from Leung et al. (2002) findings which reveal the same relation at business cycle frequency. On the other hand, for the monthly data we do not find a way of causality dominating the other. For some cities transactions cause prices and for some cities prices cause transactions. There are also cities where both prices and transactions cause each other. While Granger causality tests provides small support for the search models, non of the theoretical models proposed passes the dynamic correlation test. Hence, our analysis poses a challenge for the existing theories. The paper is organized as follows. In Section 2 we provide a brief summary of the literature about housing prices and transaction volume and discuss what those theoretical models imply about the correlation of the two variables at different frequencies. In Section 3 we give a brief description of the spectral method. We describe our data set in Section 4. We provide the results and explain our findings in Section 5. Section 6 concludes. 2. Housing prices and transaction volume: theory and evidence There are numerous influential articles in the literature that document and analyze the relationship between housing prices and transaction volume in the housing market. On the empirical front, Stein (1995) finds a positive relation between the percentage change in real sales prices for existing single family homes and transaction volume for the period 1968–1992 in the US. Andrew and Meen (2003) report positive correlation for the same two variables for the UK data. On the other hand, Follain and Velz (1995) find a negative relationship between the level of house prices and the transaction volume. Hort (2000), however, does not find a robust pattern of these variables using simple regressions of housing prices on the level of transactions volume for Swedish housing market but finds a robust negative results after introducing regional and time dummies.1 The empirical findings we mentioned above (either positive or negative correlation) contradict with the Lucas’ (1978) result which asserts that there will be no correlation between prices and transactions in an environment with rational agents and perfect capital markets. The theoretical models that are developed to explain this puzzling feature of the data can be classified into three main groups.2 The first group is pioneered by Stein (1995) and advanced by Ortalo-Magne and Rady (2006) and uses the down-payment requirement in the housing market as an explanation of the positive correlation between the two series. Main driving force of this theory is the posit that for repeat buyers, a big portion of their down-payment is coming from the proceeds of the sale of their existing homes. The theory suggests that as housing prices increase it becomes easier to finance the down-payment requirement with an increase in the liquidity of current homeowners. Hence, 1 Leung and Feng (2005) shows commercial property behaves very differently from the residential property. 2 Although the empirical evidence is mixed, the theoretical models developed so far are developed to explain the positive correlation.
transaction volume increases. The second group uses search and matching frictions to model the housing market. Berkovec and Goodman (1996) and Wheaton (1990) show that with search and matching frictions their model can generate a positive comovement in housing prices and transaction volume. Recently, Ngai and Tenreyro (2010) use a similar model to explain the seasonality in housing prices and transaction volume that they document in the US and the UK data. The third group uses behavioral approach to explain the comovement. Genesove and Mayer (2001) argue that in the data, households who experience housing price losses tend to ask higher prices compared to the others. This behavior, which is consistent with loss averse preferences, causes prices to sluggishly adjust to the equilibrium price. It is this sluggishness in the housing prices that causes the decline in transaction volume in this theory.3,4 The theories proposed in the literature generate positive comovement at the higher frequencies but does not generate positive comovement at lower frequencies. To illustrate our point, suppose that housing prices fall permanently in all the models discussed above. A permanent fall in housing prices corresponds to a low frequency movement in housing prices. The mechanism in Stein (1995) and Ortalo-Magne and Rady (2006) generates positive correlation in the short run but no correlation in the long run since after the initial decline in housing prices consumers accumulate enough wealth for the down-payment and then they will be able to move later. In the long run, transaction volume returns to the initial value while housing prices stay low. As a consequence, housing prices and transaction volume have no correlation at low frequencies since there will be a symmetric effect when housing prices increase. In case of the mechanism in Genesove and Mayer (2001), over time as sellers with higher prices (remember that loss averse agents post higher prices then the market prices) sell their houses their negative effect on transactions disappears. As a result, transaction volume decreases in the short run but then increases back to its earlier value implying no correlation in the long run. For the search models proposed, a decline in the housing prices at lower frequencies results in a smaller number of houses built which decreases the vacancy rate (1 minus number of households divided by number of housing units). As vacancy rate decreases, sales time also decreases, whereas transaction volume increases (see for example Figs. 1 and 2 in Wheaton (1990)).5 Hence, for these types of search models, there is a negative correlation between housing prices and transaction volume at lower frequencies.6 Given the high and low frequency predictions of the models we
3 Leung and Tsang (2011) develops a model with loss averse agents by exploiting the idea of Genesove and Mayer (2001). 4 Another theory that explains the relation is presented in Arslan (2013) where the rigidities in the housing and the mortgage market are the main driving forces. 5 We specifically consider search and matching models only as in Berkovec and Goodman (1996) and Wheaton (1990). 6 Besides these models, there are new developments in search and matching literature that models give different results. Peterson (2009) introduce behavioral inefficiency into a textbook search model to produce positive correlation between housing prices and transaction volume at lower frequencies.
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Panel A. HP-filtered annual data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.79 and 3.14 (highlighted) captures business cycles.
explore whether these predictions are consistent with the data.
3. Spectral analysis In this section we provide a brief description of the spectral methods that we adapt in our analysis. Most of the time series have complex structures and can be decomposed into many frequency components by using filtering techniques. Decomposition enables us to explore the relation between two series at different frequencies. In the economics literature, for example, King and Watson (1994) show that the negative correlation between unemployment and inflation appears to be strong in businesscycle frequencies even though it is hard to see the same pattern in the original inflation and unemployment time series. Ramsey and Lampart (1998) explain the anomalies
in the permanent income hypothesis by decomposing a series into a number of frequency levels and conclude that permanent income hypothesis is more evident in the long run. To analyze the relationship between housing prices and transactions at different frequencies, we use the concept of dynamic correlation which is proposed by Croux et al. (2001) and band-pass filter introduced by Christiano and Fitzgerald (2003). The necessary measure to obtain dynamic correlation is the cross spectrum. Basically, cross spectrum is defined as the frequency domain representation of the covariance of two series. One necessary condition is that the series should be stationary. To stationarize our data we use HP filter. We can denote cross spectrum of price (p) and transaction (tr) as
Cp;tr ðxÞ ¼
1 X
cp;tr ðtÞeixt
t¼1
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Panel B. HP-filtered quarterly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.20 and 1.03 (highlighted) captures the business cycle.
Table 2 Band-pass filtered quarterly data, correlations.
Table 1 Band-pass filtered annual data, correlations. Region
Business cycle
Low frequency
US Northeast Midwest South West
0.43 0.19 0.65 0.57 0.04
0.85 0.79 0.86 0.63 0.81
Note: FMHPI is used for price series. Business cycle frequency corresponds to 2–8 years. Low frequency corresponds to 8 or more years
Region
High frequency
Business cycle
Low frequency
US Northeast Midwest South West
0.06 0.18 0.04 0.14 0.08
0.45 0.74 0.63 0.60 0.18
0.86 0.72 0.97 0.82 0.42
Notes: FMHPI is used for price series. High frequency corresponds to 2–6 quarters. Business cycle frequency corresponds to 6–32 quarters. Low frequency corresponds to more than 32 quarters.
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Panel C. (Part 1): HP-filtered monthly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.1 and 0.35 (highlighted) captures the business cycle.
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Panel C. (Part 2)
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Panel C. (Part 2)
Table 3 Band-pass filtered monthly data, correlations. City
High frequency
Business cycle
Low frequency
Phoenix Los Angeles San Diego San Francisco Denver DC Miami Tampa Atlanta Chicago Boston Detroit Minneapolis Charlotte Vegas New York Cleveland Portland Seattle Case-Shiller 10 City Case-Shiller 20 City
0.06 0.04 0.06 0.09 0.22 0.31 0.14 0.19 0.17 0.25 0.02 0.12 0.22 0.03 0.08 0.12 0.10 0.13 0.22 0.15 0.09
0.15 0.01 0.16 0.21 0.41 0.63 0.15 0.40 0.37 0.37 0.36 0.23 0.10 0.40 0.30 0.70 0.62 0.45 0.44 0.21 0.15
0.91 0.04 0.10 0.20 0.30 0.80 0.28 0.32 0.78 0.92 0.20 0.89 0.97 0.79 0.82 0.76 0.78 0.59 0.51 0.30 0.24
0.09
0.27
0.57
Average
Notes: Case-Shiller data is used. High frequency corresponds to 2–18 months. Business cycle frequency corresponds to 18–96 months. Low frequency corresponds to more than 96 months.
Table 4 Annual data granger causality test results. Region
The way of causality
Business cycle
Low frequency
US
prices ) transactions transactions ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices
5.63⁄ (0.00) 2.58 (0.09) 12.27⁄(0.00) 1.13 (0.34) 6.61⁄ (0.00) 13.02⁄ (0.00) 6.71⁄ (0.00) 3.96⁄ (0.03) 1.66 (0.21) 2.79 (0.08)
5.08⁄ (0.00) 2.93 (0.07) 1.55 (0.23) 3.24⁄ (0.05) 2.87 (0.07) 4.34⁄ (0.02) 6.68⁄ (0.00) 0.13 (0.87) 3.61⁄ (0.04) 7.82⁄ (0.00)
Northeast Midwest South West
Notes: F statistics are listed. The significance levels are in parentheses. High frequency captures 2–6 quarters, business cycle frequency captures 6–32 quarters and low frequency captures more than 32 quarters. Significance at 5% level.
⁄
where cp,tr is the cross covariance function and x is the angular frequency. The dynamic correlation for price and transaction at frequency x defined as:
C p;tr ðxÞ ffi qp;tr ðxÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sp ðxÞStr ðxÞ
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Table 5 Quarterly data granger causality test results. Region
The way of causality
High frequency
Business cycle
Low frequency
US
prices ) transactions transactions ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices
0.25 (0.62) 9.69⁄ (0.00) 1.02 (0.32) 9.08⁄ (0.00) 0.84 (0.37) 10.03⁄ (0.00) 1.12 (0.30) 14.97⁄ (0.00) 3.43⁄ (0.02) 10.25⁄ (0.00)
31.08⁄ (0.00) 31.92⁄(0.00) 59.80⁄ (0.00) 58.97⁄ (0.00) 21.60⁄ (0.00) 14.49⁄ (0.00) 32.57⁄ (0.00) 14.68⁄ (0.00) 34.79⁄ (0.00) 164.66⁄ (0.00)
61.48⁄ 49.31⁄ 13.80⁄ 23.76⁄ 25.25⁄ 11.08⁄ 64.19⁄ 58.05⁄ 15.75⁄ 39.52⁄
Northeast Midwest South West
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Notes: F statistics are listed. The significance levels are in parentheses. High frequency captures 2–6 quarters, business cycle frequency captures 6–32 quarters and low frequency captures more than 32 quarters. ⁄ Significance at 5% level.
Table 6 Monthly data granger causality test results. Region
The way of causality
High frequency
Business cycle
Low frequency
Phoenix
prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices
1.064 (0.30) 8.64⁄ (0.00) 2.49 (0.12) 0.24 (0.62) 0.19 (0.67) 1.94 (0.16) 9.58 ⁄ (0.00) 5.76⁄ (0.00) 4.71⁄ (0.03) 3.05 (0.08) 2.19 (0.14) 4.87⁄ (0.03) 0.36 (0.55) 0.14 (0.72) 1.73 (0.19) 0.58 (0.45) 11.21⁄ (0.00) 0.68 (0.41) 1.68 (0.20) 1.66 (0.20) 4.73⁄ (0.01) 1.42 (0.24) 6.02⁄ (0.01) 1.41⁄ (0.02) 0.91 (0.34) 0.12 (0.73) 2.72 (0.10) 0.92 (0.34) 8.03 ⁄ (0.00) 10.39 (0.00) 1.15 (0.28) 5.37⁄ (0.02) 0.48 (0.49) 0.67 (0.41) 0.83 (0.36) 2.43 (0.12) 0.03 (0.86) 4.78⁄ (0.03) 0.31 (0.86) 0.96 (0.42) 0.03 (0.99) 1.63⁄ (0.17)
57.95⁄ (0.00) 50.56⁄ (0.00) 22.94⁄ (0.00) 143.80⁄ (0.00) 3.97⁄ (0.02) 56.86⁄ (0.00) 27.50⁄ (0.00) 53.15⁄ (0.00) 5.36⁄ (0.00) 3.33 (0.07) 13.38⁄ (0.00) 74.16⁄ (0.00) 12.94⁄ (0.00) 123.23⁄ (0.00) 16.59⁄ (0.00) 60.35⁄ (0.00) 36.84⁄ (0.00) 45.14⁄ (0.00) 29.15⁄ (0.00) 25.99⁄ (0.00) 7.21⁄ (0.00) 59.10⁄ (0.00) 23.29⁄ (0.00) 4.54⁄ (0.03) 13.46⁄ (0.00) 13.52⁄ (0.00) 16.90⁄ (0.00) 144.53⁄ (0.00) 24.71⁄ (0.00) 205.83⁄ (0.00) 13.15⁄ (0.00) 19.82⁄ (0.00) 5.55⁄ (0.00) 9.10⁄ (0.00) 6.09⁄ (0.00) 15.34⁄ (0.00) 8.05⁄ (0.00) 35.71⁄ (0.00) 17.52⁄ (0.00) 5.36⁄ (0.00) 1.70 (0.15) 12.69⁄ (0.00)
0.57 (0.45) 12.51⁄ (0.00) 5.10⁄ (0.02) 6.85⁄ (0.00) 2.74 0.10 5.43⁄ (0.00) 23.47⁄ (0.00) 8.26⁄ (0.00) 1.90 (0.17) 2.95⁄ (0.05) 14.49⁄ (0.00) 6.27⁄ (0.00) 5.45⁄ (0.00) 17.11⁄ (0.00) 2.79 (0.10) 8.02⁄ (0.00) 5.47⁄ (0.00) 9.32⁄ (0.00) 6.69⁄ (0.00) 23.74⁄ (0.00) 6.17⁄ (0.00) 1.51 (0.22) 106.81⁄ (0.00) 10.49⁄ (0.00) 2.52 (0.11) 13.99⁄ (0.00) 7.91⁄ (0.00) 5.81⁄ (0.00) 12.78⁄ (0.00) 32.54⁄ (0.00) 0.66 (0.42) 15.39⁄ (0.00) 0.81 (0.37) 167.54⁄ (0.00) 6.81⁄ (0.00) 62.07⁄ (0.00) 1.97 (0.16) 12.71⁄ (0.00) 2.77 (0.06) 39.94⁄ (0.00) 82.61⁄ (0.00) 96.59⁄ (0.00)
Los Angeles San Diego San Francisco Denver Washington DC Miami Tampa Atlanta Chicago Boston Detroit Minneapolis Charlotte Las Vegas New York Cleveland Portland Seattle Case-Shiller 10 City Case-Shiller 20 City
Notes: High frequency captures 2–18 months, business cycle frequency captures 18–96 month and low frequency captures more than 96 months. Significance at 5% level.
⁄
where Sp(x) and Str(x) are the spectra of prices and transactions at frequency x, respectively, and Cp,tr(x) is the
cospectrum. Cp,tr(x) is the real part of cross spectrum i.e. Cp,tr(x) = Re{C p,tr(x)}. Dynamic correlation can be thought
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Panel D. First-differenced annual data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.79 and 3.14 (highlighted) captures business cycles.
as the normalized form of cospectrum with Sp(.) and Str(.). Specifically, as Corsetti et al. (2012) point it out, the cospectrum measures the portion of the covariance between two series that is attributable to cycles of a given frequency x. For example, take two monthly series xt and yt such that covariance cx,y(t) of xt and yt is high at t = 4k where k 2 Nþ . Then we expect cospectrum to generate peaks in frequencies that corresponds to 4k month cycles where k 2 Nþ that means that 4k month cycles of xt and yt are correlated and the correlation at 4k month cycles are higher than the correlations at other cycles. However, it is generally hard to detect the dominating cycles of the correlation of two series from the cross covariance values. At this point, cospectrum helps us to assess the source of correlation. In addition to the dynamic correlation we use another spectral method to highlight the relationship between housing prices and transactions for robustness. We use
the band-pass filter developed by Christiano and Fitzgerald (2003) to decompose the series into low, business cycle and high frequency components and measure the correlations for each component between housing prices and transactions. 4. Data The annual data that we use consists of existing singlefamily home sales (transactions) and prices for the US and four regions: Northeast, Midwest, South, and West. Data covers the period between 1968 and 2009 except for 1989.7 We use sales data from National Association of Realtors (NAR).8 As house prices, we use quality adjusted prices 7
The data for 1989 is missing. For robustness, we also performed our analysis with transactions divided by the population. Since the results are very similar we provide the one that uses transactions only. 8
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Panel E. First-differenced quarterly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to 1 standard deviation by Fisher transformation. Frequency between 0.20 and 1.03 (highlighted) captures the business cycle.
from Freddie-Mac House Price Index (FMHPI). Annual house prices are deflated for the US and each region by non-seasonally adjusted CPI. Quarterly transaction data includes sales of single-family homes and townhomes for the US and four main regions for the 1999Q1–2011Q1 period. House price data is the FMHPI data. We deflate the nominal prices by using 3month average non-seasonally adjusted CPI for the US and four regions. (Source: Bloomberg: ETSLTOTL Index, METRUS index and Freddie-Mac). We use S&P Case-Shiller prices and ‘‘sales pair’’ data for our monthly analysis.9 In their methodology, for a house sold in a region at a given period, if an earlier transaction is found, the two transactions are paired and are considered a ‘‘paired sale’’. From construction, this methodology is used to form existing house prices, as for a new house there 9 We do not include Dallas to our analysis since the data starts from 1991 with a very limited amount of transactions.
would not be an earlier transaction. As long as the number of first time sold houses do not dominate the market ‘‘sales pair’’ data can be used as a measure of number of transactions in that region.10 In addition to the metropolitan areas data we also use the Case-Shiller 10 and 20 composite indices. We sum the transactions of corresponding metropolitan areas to obtain the transactions data of composite indices. Seasonally adjusted monthly prices are deflated by seasonally adjusted CPI. We, also, seasonally adjust quarterly data.
5. Correlations 5.1. Annual data We start our analysis with annual data. We measure the dynamic correlations of the HP-filtered series for the US 10
Number of new houses sold is around 10% percent of total houses sold.
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Panel F. (Part 1): First-differenced monthly data, dynamic correlations. (Part 2). Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to 1 standard deviation by Fisher transformation. Frequency between 0.1 and 0.35 (highlighted) captures the business cycle.
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Panel F. (Part 2)
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Panel G. FMHPI and NAR HP-filtered annual data, dynamic correlations Notes: correlations are at the y and frequencies are at the x axis. Frequency between 0.79 and 3.14 (highlighted) captures business cycles.
and four regions.11 Panel A summarizes our results.12 It shows that there are high correlations of transaction volume and housing prices for every region at the lower frequencies (unshaded areas). However, it declines significantly as frequency increases and even goes to zero for the West. The declining correlations between housing prices and transaction volume as frequencies increase, cast doubt on the theories which try to explain the positive correlation between the two series. For robustness, we use the band-pass filter to decompose the two series into low and high frequency components and calculate the correlations between housing
11 We, also, provide the dynamic correlations of first-differenced data in the Appendix which shows similar pattern, however, all correlations are more volatile. 12 We use k = 100 for annual data, k = 1600 for quarterly data, k = 14,400 for monthly data, which are standard in literature.
prices and transactions for each components. With annual data, the high frequency component corresponds to the business cycle frequency (which is 2–8 years) and the low frequency component corresponds to the cycles of 8 or more years. We find that correlations at the low frequency is much higher than the business cycle frequency which is consistent with the results of the dynamic correlation analysis (see Table 1). 5.2. Quarterly data With quarterly data, we do the same exercises that we did with the annual data. Similar to the annual results, dynamic correlations are significantly positive and reach to highest levels at low frequencies, except for the West. Correlations are close to zero, are even negative for some regions, for the frequencies that correspond to business cycle frequency. Correlations turn to be positive at very
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Panel H. FMHPI and NAR HP-filtered quarterly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Frequency between 0.2 and 1.03 (highlighted) captures business cycles.
high frequencies except for the Northeast but still lower than the low frequency levels. When we decompose the series by the band-pass filter, correlations are smallest at the highest frequency except for the West and highest at the lowest frequency except for the Northeast (see Table 2). Without decomposition, the correlation between two series is on average 0.5 for the quarterly data (Panel B). 5.3. Monthly data The dynamic correlations analysis that we perform with monthly data confirms our earlier findings indicate that the correlations are in general higher at the lower frequencies. In figures presented in Panel C, due to the nature of the dynamic correlations exercise with the monthly data, the region with the lowest frequency is small and the region with the highest frequency is large. Hence, at first, it
may be difficult to observe from the figures that correlations are lower at the lowest frequency. Nevertheless, in figures of Panel C the correlations at lower frequencies (closer to the origin of each figure) are higher on average. As we did for quarterly and annual data, we use the band-pass filter to decompose the series into different frequency components. With monthly data we are able to decompose the series into three frequencies; high frequency (2-18 months), business cycle frequency (18-96 months) and low frequency (96 months and more). In Table 3 we report our results. Our results confirm our earlier findings with quarterly and annual data. The correlations are, in general, higher at the lower frequencies and lower at the higher frequencies. The average of the correlation of prices and transaction volume across cities at low frequencies is 0.57. At the business cycle frequencies this average is 0.27 and at the high frequencies it is 0.09. However, we should note that there is considerable
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heterogeneity across cities. In Western metropolitan areas of Phoenix, Los Angeles, San Diego and San Francisco the correlation is either negative or very close to zero at all frequencies. For the other metropolitan areas, almost for every one correlation increases as frequency increases.
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pect to see support for the models, the direction of causality is balanced. The Ganger causality tests we performed provide a partial support for the search and matching models. 7. Conclusion
6. Causality In the previous section, the relationship between housing prices and transactions is analyzed by using dynamic correlations. However, this analysis does not imply any causality between the two variables. The developed theories that try to explain the relationship between the two variables also generate a direction of causality between two variables. For instance, Stein’s (1995) down-payment theory explains the decline in transaction with a decline in housing prices. The decrease in housing prices causes a fraction of sellers not to move due to their reduced capability of paying the down-payment of new homes. Genesove and Mayer (2001) use loss aversion behavior that homeowners are less willing to sell their homes in falling market to avoid losses. The direction of causality is again, from prices to transactions. On the other hand, Berkovec and Goodman (1996) and Wheaton (1990) have search and matching models in which transactions cause the housing prices. In this section, we investigate the relationship between housing prices and transactions by using the Granger causality test. First, we decompose the series into high, business cycle and low frequencies and then apply the Granger causality test to investigate the relationship between two variables at different frequencies. Tables 4–6 show the Granger causality test results for the annual, quarterly and monthly data, respectively. With annual data it is not possible to see high frequency Granger causality test results. For the business cycle frequency prices Granger cause transactions in almost all regions, except for the West. On the other hand, for the low frequency transactions Granger cause prices in West, Midwest and Northeast regions. For the quarterly data at high frequency (2–6 quarters), transactions Granger cause prices. At the business cycle and lower frequencies both series Granger cause each other. As in the earlier parts of the paper we argued that high frequencies are the frequencies where the models proposed in the literature have something to say, we discover that the findings of the Granger causality exercise with the quarterly data to be consistent with the search and matching models. With the monthly data at high frequency, for 6 cities transactions Granger cause prices, for 6 cities prices cause transactions, and for 2 cities both series Granger cause each other. At the business cycle frequencies both series Granger cause each other for every city except Denver. For Denver prices cause transactions. At low frequencies, for 18 cities transactions Granger cause prices and for 11 cities prices cause transactions. For 9 of the cities both series Granger cause the other. The Granger causality test results for the monthly data does not provide any support to any model. Especially for the high frequency, where we ex-
In this paper, we use HP and band-pass filters, dynamic correlation to study the relationship between the housing prices and transaction volume in at different frequencies in the US data. We show that low frequency component is the major driver of the positive correlation. We also find that the way of causality at high frequency between the two series is from transactions to housing prices when we use quarterly regional data. For the monthly city-level data we do not find any direction. Taken together, we conclude that these findings pose a challenge for the current theories which claim to explain the positive correlation between two series. Appendix A In the Appendix we perform several robustness exercises. In the main text we use HP filter when we do dynamic correlation analysis. Figures in Panels D, E and F shows the results of the same exercise when we use first difference. Our main result does not change. At the low frequencies there is high correlation and at the higher frequencies there is low correlation. In Panels G and H we show that whether we use quality controlled prices (FMHPI) or median prices (NAR) the conclusion of the paper does not change. Dynamic correlation figures are very similar in both cases. References Arslan, Y., 2013. Interest rate fluctuations and equilibrium in the housing market. Unpublished manuscript. Andrew, M., Meen, G., 2003, House Price Appreciation, Transactions and Structural Change in the British Housing Market: A Macroeconomic Perspective. Berkovec, J., Goodman, J., 1996. Turnover as a measure of demand for existing homes. Real Estate Economics 24, 421–440. Christiano, J., Fitzgerald, T., 2003. The band pass filter. International Economic Review 44 (2). Corsetti, G., Dedola, L., Viani, F., 2012. The international risk-sharing puzzle is at business cycle and lower frequency. Canadian Journal of Economics 45 (2), 448–471. Croux, C., Forni, M., Reichlin, L., 2001. A measure of comovement for economic variables: theory and empirics. Review of Economics and Statistics 83 (2), 232–241. Follain, J., Velz, O., 1995. Incorporating the number of existing home sales into a structural model of the market for owner-occupied housing. Journal of Housing Economics 4, 93–117. Genesove, D., Mayer, C., 2001. Loss aversion and seller behavior: evidence from the housing market. The Quarterly Journal of Economics. Hort, K., 2000. Prices and turnover in the market for owner-occupied homes. Regional Science and Urban Economics 30, 99–119. King, R.G., Watson, M.W., 1994. The post-war U.S. phillips curve: a revisionist econometric history. Carnegie–Rochester Conference Series on Public Policy 41 (1), 157–219. Leung, C.K.Y., Lau, G.C.K., Leong, Y.C.F., 2002. Testing alternative theories of the property price-trading volume correlation. Journal of Real Estate Research 23 (3), 253–263. Leung, C.K.Y., Feng, D., 2005. What drives the property price-trading volume correlation? Evidence from a commercial real estate market. Journal of Real Estate Finance and Economics 31 (2), 241–255.
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Leung, T.C., Tsang, K.P., 2011. Anchoring and loss aversion in the housing market: implications on price dynamics. Hong Kong Institute for Monetary Research, WP 282011. Lucas, R., 1978. Asset prices in an exchange economy. Econometrica 46, 1426–1445. Ngai, R., Tenreyro, S., 2010. Hot and Cold Seasons in the Housing Market. London School of Economics, CEP, CEPR, Working Paper. Ortalo-Magne, R., Rady, S., 2006. Housing market dynamics: on the contribution of income shocks and credit constraints. The Review of Economic Studies 73, 459–485.
Peterson, B.M., 2009. Fooled by Search: Housing Prices, Turnover and Bubbles. CAEPR Working Paper, No.004. Ramsey, J., Lampart, C., 1998. The composition of economic relationships by timescale using wavelets. Macroeconomic Dynamics 2, 49– 71. Stein, J., 1995. Prices and trading volume in the housing market: a model with downpayment effects. Quarterly Journal of Economics 110, 379– 405. Wheaton, W., 1990. Vacancy, search, and prices in a housing market matching model. Journal of Political Economy 98, 1270–1292.
Contents lists available at SciVerse ScienceDirect
Journal of Housing Economics journal homepage: www.elsevier.com/locate/jhec
Housing prices and transaction volume q H. Cagri Akkoyun, Yavuz Arslan, Birol Kanik ⇑ Central Bank of Turkey, Istiklal Cad. No.: 10, Ulus, Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 9 April 2012 Available online 28 February 2013 JEL classification: G1 R2 R3
a b s t r a c t We use annual, quarterly and monthly data from the US to show that the correlation between housing prices and transaction volume (number of existing houses sold) differs across different frequencies. While the correlation is high at the low frequencies it declines to the levels close to zero at high frequencies. Granger causality tests for different frequencies show that the way of causality in housing market changes from region to region. Our findings provide a litmus test for the existing theories that are proposed to explain the positive correlation between transaction volume and housing prices. Ó 2013 Elsevier Inc. All rights reserved.
Keywords: Housing prices Transaction volume Dynamic correlation Low frequency High frequency
1. Introduction In this paper, we use US data to analyze the relationship between housing prices and transaction volume at different frequencies. Our analyses provide several tests to evaluate the theories offered to explain the comovement of housing prices and transaction volume documented in the literature. The first test in our analysis utilizes the different correlations observed at different frequencies. The theories proposed in the literature generate positive comovement at higher frequencies (in the short run) but generate negative comovement or non at lower frequencies (in the long run). In this respect, we investigate the relationship between housing prices and transactions by using spectral analysis to reveal how much different frequencies contribute to
q We thank Abdullah Yavas, Umit Ozlale and Charles Leung for valuable comments. The views expressed are those of the authors and should not be attributed to the Central Bank of the Republic of Turkey. ⇑ Corresponding author. E-mail addresses: [email protected] (H.C. Akkoyun), yavuz. [email protected] (Y. Arslan), [email protected] (B. Kanik).
1051-1377/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jhe.2013.02.001
the correlation. Since both theories and data have implications about the correlation at different frequencies our paper proposes a new way of testing the existing theories in the literature which generate the comovement of housing prices and transaction volume. In addition to the correlation analysis we also explore the direction of the causality between the two series by using Granger causality test at different frequencies. This is important to evaluate the theories because the direction of causality between housing prices and transactions differs depending on the mechanism of the models. For our analysis we use annual, quarterly and monthly housing prices and transaction volume data from the US. We use HP and band-pass filters and dynamic correlations to obtain the correlations of the two series at different frequencies. In our analysis we show that the largest part of the positive correlation between housing prices and transaction volume comes from the low frequency components. However, at higher frequencies the correlation becomes smaller and sometimes negative. We, also, find that for the quarterly data at high frequency the way of causality between the two series is from transactions to housing prices. Our results are slightly
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different from Leung et al. (2002) findings which reveal the same relation at business cycle frequency. On the other hand, for the monthly data we do not find a way of causality dominating the other. For some cities transactions cause prices and for some cities prices cause transactions. There are also cities where both prices and transactions cause each other. While Granger causality tests provides small support for the search models, non of the theoretical models proposed passes the dynamic correlation test. Hence, our analysis poses a challenge for the existing theories. The paper is organized as follows. In Section 2 we provide a brief summary of the literature about housing prices and transaction volume and discuss what those theoretical models imply about the correlation of the two variables at different frequencies. In Section 3 we give a brief description of the spectral method. We describe our data set in Section 4. We provide the results and explain our findings in Section 5. Section 6 concludes. 2. Housing prices and transaction volume: theory and evidence There are numerous influential articles in the literature that document and analyze the relationship between housing prices and transaction volume in the housing market. On the empirical front, Stein (1995) finds a positive relation between the percentage change in real sales prices for existing single family homes and transaction volume for the period 1968–1992 in the US. Andrew and Meen (2003) report positive correlation for the same two variables for the UK data. On the other hand, Follain and Velz (1995) find a negative relationship between the level of house prices and the transaction volume. Hort (2000), however, does not find a robust pattern of these variables using simple regressions of housing prices on the level of transactions volume for Swedish housing market but finds a robust negative results after introducing regional and time dummies.1 The empirical findings we mentioned above (either positive or negative correlation) contradict with the Lucas’ (1978) result which asserts that there will be no correlation between prices and transactions in an environment with rational agents and perfect capital markets. The theoretical models that are developed to explain this puzzling feature of the data can be classified into three main groups.2 The first group is pioneered by Stein (1995) and advanced by Ortalo-Magne and Rady (2006) and uses the down-payment requirement in the housing market as an explanation of the positive correlation between the two series. Main driving force of this theory is the posit that for repeat buyers, a big portion of their down-payment is coming from the proceeds of the sale of their existing homes. The theory suggests that as housing prices increase it becomes easier to finance the down-payment requirement with an increase in the liquidity of current homeowners. Hence, 1 Leung and Feng (2005) shows commercial property behaves very differently from the residential property. 2 Although the empirical evidence is mixed, the theoretical models developed so far are developed to explain the positive correlation.
transaction volume increases. The second group uses search and matching frictions to model the housing market. Berkovec and Goodman (1996) and Wheaton (1990) show that with search and matching frictions their model can generate a positive comovement in housing prices and transaction volume. Recently, Ngai and Tenreyro (2010) use a similar model to explain the seasonality in housing prices and transaction volume that they document in the US and the UK data. The third group uses behavioral approach to explain the comovement. Genesove and Mayer (2001) argue that in the data, households who experience housing price losses tend to ask higher prices compared to the others. This behavior, which is consistent with loss averse preferences, causes prices to sluggishly adjust to the equilibrium price. It is this sluggishness in the housing prices that causes the decline in transaction volume in this theory.3,4 The theories proposed in the literature generate positive comovement at the higher frequencies but does not generate positive comovement at lower frequencies. To illustrate our point, suppose that housing prices fall permanently in all the models discussed above. A permanent fall in housing prices corresponds to a low frequency movement in housing prices. The mechanism in Stein (1995) and Ortalo-Magne and Rady (2006) generates positive correlation in the short run but no correlation in the long run since after the initial decline in housing prices consumers accumulate enough wealth for the down-payment and then they will be able to move later. In the long run, transaction volume returns to the initial value while housing prices stay low. As a consequence, housing prices and transaction volume have no correlation at low frequencies since there will be a symmetric effect when housing prices increase. In case of the mechanism in Genesove and Mayer (2001), over time as sellers with higher prices (remember that loss averse agents post higher prices then the market prices) sell their houses their negative effect on transactions disappears. As a result, transaction volume decreases in the short run but then increases back to its earlier value implying no correlation in the long run. For the search models proposed, a decline in the housing prices at lower frequencies results in a smaller number of houses built which decreases the vacancy rate (1 minus number of households divided by number of housing units). As vacancy rate decreases, sales time also decreases, whereas transaction volume increases (see for example Figs. 1 and 2 in Wheaton (1990)).5 Hence, for these types of search models, there is a negative correlation between housing prices and transaction volume at lower frequencies.6 Given the high and low frequency predictions of the models we
3 Leung and Tsang (2011) develops a model with loss averse agents by exploiting the idea of Genesove and Mayer (2001). 4 Another theory that explains the relation is presented in Arslan (2013) where the rigidities in the housing and the mortgage market are the main driving forces. 5 We specifically consider search and matching models only as in Berkovec and Goodman (1996) and Wheaton (1990). 6 Besides these models, there are new developments in search and matching literature that models give different results. Peterson (2009) introduce behavioral inefficiency into a textbook search model to produce positive correlation between housing prices and transaction volume at lower frequencies.
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Panel A. HP-filtered annual data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.79 and 3.14 (highlighted) captures business cycles.
explore whether these predictions are consistent with the data.
3. Spectral analysis In this section we provide a brief description of the spectral methods that we adapt in our analysis. Most of the time series have complex structures and can be decomposed into many frequency components by using filtering techniques. Decomposition enables us to explore the relation between two series at different frequencies. In the economics literature, for example, King and Watson (1994) show that the negative correlation between unemployment and inflation appears to be strong in businesscycle frequencies even though it is hard to see the same pattern in the original inflation and unemployment time series. Ramsey and Lampart (1998) explain the anomalies
in the permanent income hypothesis by decomposing a series into a number of frequency levels and conclude that permanent income hypothesis is more evident in the long run. To analyze the relationship between housing prices and transactions at different frequencies, we use the concept of dynamic correlation which is proposed by Croux et al. (2001) and band-pass filter introduced by Christiano and Fitzgerald (2003). The necessary measure to obtain dynamic correlation is the cross spectrum. Basically, cross spectrum is defined as the frequency domain representation of the covariance of two series. One necessary condition is that the series should be stationary. To stationarize our data we use HP filter. We can denote cross spectrum of price (p) and transaction (tr) as
Cp;tr ðxÞ ¼
1 X
cp;tr ðtÞeixt
t¼1
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Panel B. HP-filtered quarterly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.20 and 1.03 (highlighted) captures the business cycle.
Table 2 Band-pass filtered quarterly data, correlations.
Table 1 Band-pass filtered annual data, correlations. Region
Business cycle
Low frequency
US Northeast Midwest South West
0.43 0.19 0.65 0.57 0.04
0.85 0.79 0.86 0.63 0.81
Note: FMHPI is used for price series. Business cycle frequency corresponds to 2–8 years. Low frequency corresponds to 8 or more years
Region
High frequency
Business cycle
Low frequency
US Northeast Midwest South West
0.06 0.18 0.04 0.14 0.08
0.45 0.74 0.63 0.60 0.18
0.86 0.72 0.97 0.82 0.42
Notes: FMHPI is used for price series. High frequency corresponds to 2–6 quarters. Business cycle frequency corresponds to 6–32 quarters. Low frequency corresponds to more than 32 quarters.
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Panel C. (Part 1): HP-filtered monthly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.1 and 0.35 (highlighted) captures the business cycle.
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Panel C. (Part 2)
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Panel C. (Part 2)
Table 3 Band-pass filtered monthly data, correlations. City
High frequency
Business cycle
Low frequency
Phoenix Los Angeles San Diego San Francisco Denver DC Miami Tampa Atlanta Chicago Boston Detroit Minneapolis Charlotte Vegas New York Cleveland Portland Seattle Case-Shiller 10 City Case-Shiller 20 City
0.06 0.04 0.06 0.09 0.22 0.31 0.14 0.19 0.17 0.25 0.02 0.12 0.22 0.03 0.08 0.12 0.10 0.13 0.22 0.15 0.09
0.15 0.01 0.16 0.21 0.41 0.63 0.15 0.40 0.37 0.37 0.36 0.23 0.10 0.40 0.30 0.70 0.62 0.45 0.44 0.21 0.15
0.91 0.04 0.10 0.20 0.30 0.80 0.28 0.32 0.78 0.92 0.20 0.89 0.97 0.79 0.82 0.76 0.78 0.59 0.51 0.30 0.24
0.09
0.27
0.57
Average
Notes: Case-Shiller data is used. High frequency corresponds to 2–18 months. Business cycle frequency corresponds to 18–96 months. Low frequency corresponds to more than 96 months.
Table 4 Annual data granger causality test results. Region
The way of causality
Business cycle
Low frequency
US
prices ) transactions transactions ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices
5.63⁄ (0.00) 2.58 (0.09) 12.27⁄(0.00) 1.13 (0.34) 6.61⁄ (0.00) 13.02⁄ (0.00) 6.71⁄ (0.00) 3.96⁄ (0.03) 1.66 (0.21) 2.79 (0.08)
5.08⁄ (0.00) 2.93 (0.07) 1.55 (0.23) 3.24⁄ (0.05) 2.87 (0.07) 4.34⁄ (0.02) 6.68⁄ (0.00) 0.13 (0.87) 3.61⁄ (0.04) 7.82⁄ (0.00)
Northeast Midwest South West
Notes: F statistics are listed. The significance levels are in parentheses. High frequency captures 2–6 quarters, business cycle frequency captures 6–32 quarters and low frequency captures more than 32 quarters. Significance at 5% level.
⁄
where cp,tr is the cross covariance function and x is the angular frequency. The dynamic correlation for price and transaction at frequency x defined as:
C p;tr ðxÞ ffi qp;tr ðxÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sp ðxÞStr ðxÞ
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Table 5 Quarterly data granger causality test results. Region
The way of causality
High frequency
Business cycle
Low frequency
US
prices ) transactions transactions ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices prices ) transactions transaction ) prices
0.25 (0.62) 9.69⁄ (0.00) 1.02 (0.32) 9.08⁄ (0.00) 0.84 (0.37) 10.03⁄ (0.00) 1.12 (0.30) 14.97⁄ (0.00) 3.43⁄ (0.02) 10.25⁄ (0.00)
31.08⁄ (0.00) 31.92⁄(0.00) 59.80⁄ (0.00) 58.97⁄ (0.00) 21.60⁄ (0.00) 14.49⁄ (0.00) 32.57⁄ (0.00) 14.68⁄ (0.00) 34.79⁄ (0.00) 164.66⁄ (0.00)
61.48⁄ 49.31⁄ 13.80⁄ 23.76⁄ 25.25⁄ 11.08⁄ 64.19⁄ 58.05⁄ 15.75⁄ 39.52⁄
Northeast Midwest South West
(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)
Notes: F statistics are listed. The significance levels are in parentheses. High frequency captures 2–6 quarters, business cycle frequency captures 6–32 quarters and low frequency captures more than 32 quarters. ⁄ Significance at 5% level.
Table 6 Monthly data granger causality test results. Region
The way of causality
High frequency
Business cycle
Low frequency
Phoenix
prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices prices ) transactions transactions ) prices
1.064 (0.30) 8.64⁄ (0.00) 2.49 (0.12) 0.24 (0.62) 0.19 (0.67) 1.94 (0.16) 9.58 ⁄ (0.00) 5.76⁄ (0.00) 4.71⁄ (0.03) 3.05 (0.08) 2.19 (0.14) 4.87⁄ (0.03) 0.36 (0.55) 0.14 (0.72) 1.73 (0.19) 0.58 (0.45) 11.21⁄ (0.00) 0.68 (0.41) 1.68 (0.20) 1.66 (0.20) 4.73⁄ (0.01) 1.42 (0.24) 6.02⁄ (0.01) 1.41⁄ (0.02) 0.91 (0.34) 0.12 (0.73) 2.72 (0.10) 0.92 (0.34) 8.03 ⁄ (0.00) 10.39 (0.00) 1.15 (0.28) 5.37⁄ (0.02) 0.48 (0.49) 0.67 (0.41) 0.83 (0.36) 2.43 (0.12) 0.03 (0.86) 4.78⁄ (0.03) 0.31 (0.86) 0.96 (0.42) 0.03 (0.99) 1.63⁄ (0.17)
57.95⁄ (0.00) 50.56⁄ (0.00) 22.94⁄ (0.00) 143.80⁄ (0.00) 3.97⁄ (0.02) 56.86⁄ (0.00) 27.50⁄ (0.00) 53.15⁄ (0.00) 5.36⁄ (0.00) 3.33 (0.07) 13.38⁄ (0.00) 74.16⁄ (0.00) 12.94⁄ (0.00) 123.23⁄ (0.00) 16.59⁄ (0.00) 60.35⁄ (0.00) 36.84⁄ (0.00) 45.14⁄ (0.00) 29.15⁄ (0.00) 25.99⁄ (0.00) 7.21⁄ (0.00) 59.10⁄ (0.00) 23.29⁄ (0.00) 4.54⁄ (0.03) 13.46⁄ (0.00) 13.52⁄ (0.00) 16.90⁄ (0.00) 144.53⁄ (0.00) 24.71⁄ (0.00) 205.83⁄ (0.00) 13.15⁄ (0.00) 19.82⁄ (0.00) 5.55⁄ (0.00) 9.10⁄ (0.00) 6.09⁄ (0.00) 15.34⁄ (0.00) 8.05⁄ (0.00) 35.71⁄ (0.00) 17.52⁄ (0.00) 5.36⁄ (0.00) 1.70 (0.15) 12.69⁄ (0.00)
0.57 (0.45) 12.51⁄ (0.00) 5.10⁄ (0.02) 6.85⁄ (0.00) 2.74 0.10 5.43⁄ (0.00) 23.47⁄ (0.00) 8.26⁄ (0.00) 1.90 (0.17) 2.95⁄ (0.05) 14.49⁄ (0.00) 6.27⁄ (0.00) 5.45⁄ (0.00) 17.11⁄ (0.00) 2.79 (0.10) 8.02⁄ (0.00) 5.47⁄ (0.00) 9.32⁄ (0.00) 6.69⁄ (0.00) 23.74⁄ (0.00) 6.17⁄ (0.00) 1.51 (0.22) 106.81⁄ (0.00) 10.49⁄ (0.00) 2.52 (0.11) 13.99⁄ (0.00) 7.91⁄ (0.00) 5.81⁄ (0.00) 12.78⁄ (0.00) 32.54⁄ (0.00) 0.66 (0.42) 15.39⁄ (0.00) 0.81 (0.37) 167.54⁄ (0.00) 6.81⁄ (0.00) 62.07⁄ (0.00) 1.97 (0.16) 12.71⁄ (0.00) 2.77 (0.06) 39.94⁄ (0.00) 82.61⁄ (0.00) 96.59⁄ (0.00)
Los Angeles San Diego San Francisco Denver Washington DC Miami Tampa Atlanta Chicago Boston Detroit Minneapolis Charlotte Las Vegas New York Cleveland Portland Seattle Case-Shiller 10 City Case-Shiller 20 City
Notes: High frequency captures 2–18 months, business cycle frequency captures 18–96 month and low frequency captures more than 96 months. Significance at 5% level.
⁄
where Sp(x) and Str(x) are the spectra of prices and transactions at frequency x, respectively, and Cp,tr(x) is the
cospectrum. Cp,tr(x) is the real part of cross spectrum i.e. Cp,tr(x) = Re{C p,tr(x)}. Dynamic correlation can be thought
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Panel D. First-differenced annual data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to one standard deviation by Fisher transformation. Frequency between 0.79 and 3.14 (highlighted) captures business cycles.
as the normalized form of cospectrum with Sp(.) and Str(.). Specifically, as Corsetti et al. (2012) point it out, the cospectrum measures the portion of the covariance between two series that is attributable to cycles of a given frequency x. For example, take two monthly series xt and yt such that covariance cx,y(t) of xt and yt is high at t = 4k where k 2 Nþ . Then we expect cospectrum to generate peaks in frequencies that corresponds to 4k month cycles where k 2 Nþ that means that 4k month cycles of xt and yt are correlated and the correlation at 4k month cycles are higher than the correlations at other cycles. However, it is generally hard to detect the dominating cycles of the correlation of two series from the cross covariance values. At this point, cospectrum helps us to assess the source of correlation. In addition to the dynamic correlation we use another spectral method to highlight the relationship between housing prices and transactions for robustness. We use
the band-pass filter developed by Christiano and Fitzgerald (2003) to decompose the series into low, business cycle and high frequency components and measure the correlations for each component between housing prices and transactions. 4. Data The annual data that we use consists of existing singlefamily home sales (transactions) and prices for the US and four regions: Northeast, Midwest, South, and West. Data covers the period between 1968 and 2009 except for 1989.7 We use sales data from National Association of Realtors (NAR).8 As house prices, we use quality adjusted prices 7
The data for 1989 is missing. For robustness, we also performed our analysis with transactions divided by the population. Since the results are very similar we provide the one that uses transactions only. 8
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Panel E. First-differenced quarterly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to 1 standard deviation by Fisher transformation. Frequency between 0.20 and 1.03 (highlighted) captures the business cycle.
from Freddie-Mac House Price Index (FMHPI). Annual house prices are deflated for the US and each region by non-seasonally adjusted CPI. Quarterly transaction data includes sales of single-family homes and townhomes for the US and four main regions for the 1999Q1–2011Q1 period. House price data is the FMHPI data. We deflate the nominal prices by using 3month average non-seasonally adjusted CPI for the US and four regions. (Source: Bloomberg: ETSLTOTL Index, METRUS index and Freddie-Mac). We use S&P Case-Shiller prices and ‘‘sales pair’’ data for our monthly analysis.9 In their methodology, for a house sold in a region at a given period, if an earlier transaction is found, the two transactions are paired and are considered a ‘‘paired sale’’. From construction, this methodology is used to form existing house prices, as for a new house there 9 We do not include Dallas to our analysis since the data starts from 1991 with a very limited amount of transactions.
would not be an earlier transaction. As long as the number of first time sold houses do not dominate the market ‘‘sales pair’’ data can be used as a measure of number of transactions in that region.10 In addition to the metropolitan areas data we also use the Case-Shiller 10 and 20 composite indices. We sum the transactions of corresponding metropolitan areas to obtain the transactions data of composite indices. Seasonally adjusted monthly prices are deflated by seasonally adjusted CPI. We, also, seasonally adjust quarterly data.
5. Correlations 5.1. Annual data We start our analysis with annual data. We measure the dynamic correlations of the HP-filtered series for the US 10
Number of new houses sold is around 10% percent of total houses sold.
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Panel F. (Part 1): First-differenced monthly data, dynamic correlations. (Part 2). Notes: correlations are at the y and frequencies are at the x axis. Dashed lines correspond to 1 standard deviation by Fisher transformation. Frequency between 0.1 and 0.35 (highlighted) captures the business cycle.
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Panel F. (Part 2)
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Panel G. FMHPI and NAR HP-filtered annual data, dynamic correlations Notes: correlations are at the y and frequencies are at the x axis. Frequency between 0.79 and 3.14 (highlighted) captures business cycles.
and four regions.11 Panel A summarizes our results.12 It shows that there are high correlations of transaction volume and housing prices for every region at the lower frequencies (unshaded areas). However, it declines significantly as frequency increases and even goes to zero for the West. The declining correlations between housing prices and transaction volume as frequencies increase, cast doubt on the theories which try to explain the positive correlation between the two series. For robustness, we use the band-pass filter to decompose the two series into low and high frequency components and calculate the correlations between housing
11 We, also, provide the dynamic correlations of first-differenced data in the Appendix which shows similar pattern, however, all correlations are more volatile. 12 We use k = 100 for annual data, k = 1600 for quarterly data, k = 14,400 for monthly data, which are standard in literature.
prices and transactions for each components. With annual data, the high frequency component corresponds to the business cycle frequency (which is 2–8 years) and the low frequency component corresponds to the cycles of 8 or more years. We find that correlations at the low frequency is much higher than the business cycle frequency which is consistent with the results of the dynamic correlation analysis (see Table 1). 5.2. Quarterly data With quarterly data, we do the same exercises that we did with the annual data. Similar to the annual results, dynamic correlations are significantly positive and reach to highest levels at low frequencies, except for the West. Correlations are close to zero, are even negative for some regions, for the frequencies that correspond to business cycle frequency. Correlations turn to be positive at very
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Panel H. FMHPI and NAR HP-filtered quarterly data, dynamic correlations. Notes: correlations are at the y and frequencies are at the x axis. Frequency between 0.2 and 1.03 (highlighted) captures business cycles.
high frequencies except for the Northeast but still lower than the low frequency levels. When we decompose the series by the band-pass filter, correlations are smallest at the highest frequency except for the West and highest at the lowest frequency except for the Northeast (see Table 2). Without decomposition, the correlation between two series is on average 0.5 for the quarterly data (Panel B). 5.3. Monthly data The dynamic correlations analysis that we perform with monthly data confirms our earlier findings indicate that the correlations are in general higher at the lower frequencies. In figures presented in Panel C, due to the nature of the dynamic correlations exercise with the monthly data, the region with the lowest frequency is small and the region with the highest frequency is large. Hence, at first, it
may be difficult to observe from the figures that correlations are lower at the lowest frequency. Nevertheless, in figures of Panel C the correlations at lower frequencies (closer to the origin of each figure) are higher on average. As we did for quarterly and annual data, we use the band-pass filter to decompose the series into different frequency components. With monthly data we are able to decompose the series into three frequencies; high frequency (2-18 months), business cycle frequency (18-96 months) and low frequency (96 months and more). In Table 3 we report our results. Our results confirm our earlier findings with quarterly and annual data. The correlations are, in general, higher at the lower frequencies and lower at the higher frequencies. The average of the correlation of prices and transaction volume across cities at low frequencies is 0.57. At the business cycle frequencies this average is 0.27 and at the high frequencies it is 0.09. However, we should note that there is considerable
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heterogeneity across cities. In Western metropolitan areas of Phoenix, Los Angeles, San Diego and San Francisco the correlation is either negative or very close to zero at all frequencies. For the other metropolitan areas, almost for every one correlation increases as frequency increases.
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pect to see support for the models, the direction of causality is balanced. The Ganger causality tests we performed provide a partial support for the search and matching models. 7. Conclusion
6. Causality In the previous section, the relationship between housing prices and transactions is analyzed by using dynamic correlations. However, this analysis does not imply any causality between the two variables. The developed theories that try to explain the relationship between the two variables also generate a direction of causality between two variables. For instance, Stein’s (1995) down-payment theory explains the decline in transaction with a decline in housing prices. The decrease in housing prices causes a fraction of sellers not to move due to their reduced capability of paying the down-payment of new homes. Genesove and Mayer (2001) use loss aversion behavior that homeowners are less willing to sell their homes in falling market to avoid losses. The direction of causality is again, from prices to transactions. On the other hand, Berkovec and Goodman (1996) and Wheaton (1990) have search and matching models in which transactions cause the housing prices. In this section, we investigate the relationship between housing prices and transactions by using the Granger causality test. First, we decompose the series into high, business cycle and low frequencies and then apply the Granger causality test to investigate the relationship between two variables at different frequencies. Tables 4–6 show the Granger causality test results for the annual, quarterly and monthly data, respectively. With annual data it is not possible to see high frequency Granger causality test results. For the business cycle frequency prices Granger cause transactions in almost all regions, except for the West. On the other hand, for the low frequency transactions Granger cause prices in West, Midwest and Northeast regions. For the quarterly data at high frequency (2–6 quarters), transactions Granger cause prices. At the business cycle and lower frequencies both series Granger cause each other. As in the earlier parts of the paper we argued that high frequencies are the frequencies where the models proposed in the literature have something to say, we discover that the findings of the Granger causality exercise with the quarterly data to be consistent with the search and matching models. With the monthly data at high frequency, for 6 cities transactions Granger cause prices, for 6 cities prices cause transactions, and for 2 cities both series Granger cause each other. At the business cycle frequencies both series Granger cause each other for every city except Denver. For Denver prices cause transactions. At low frequencies, for 18 cities transactions Granger cause prices and for 11 cities prices cause transactions. For 9 of the cities both series Granger cause the other. The Granger causality test results for the monthly data does not provide any support to any model. Especially for the high frequency, where we ex-
In this paper, we use HP and band-pass filters, dynamic correlation to study the relationship between the housing prices and transaction volume in at different frequencies in the US data. We show that low frequency component is the major driver of the positive correlation. We also find that the way of causality at high frequency between the two series is from transactions to housing prices when we use quarterly regional data. For the monthly city-level data we do not find any direction. Taken together, we conclude that these findings pose a challenge for the current theories which claim to explain the positive correlation between two series. Appendix A In the Appendix we perform several robustness exercises. In the main text we use HP filter when we do dynamic correlation analysis. Figures in Panels D, E and F shows the results of the same exercise when we use first difference. Our main result does not change. At the low frequencies there is high correlation and at the higher frequencies there is low correlation. In Panels G and H we show that whether we use quality controlled prices (FMHPI) or median prices (NAR) the conclusion of the paper does not change. Dynamic correlation figures are very similar in both cases. References Arslan, Y., 2013. Interest rate fluctuations and equilibrium in the housing market. Unpublished manuscript. Andrew, M., Meen, G., 2003, House Price Appreciation, Transactions and Structural Change in the British Housing Market: A Macroeconomic Perspective. Berkovec, J., Goodman, J., 1996. Turnover as a measure of demand for existing homes. Real Estate Economics 24, 421–440. Christiano, J., Fitzgerald, T., 2003. The band pass filter. International Economic Review 44 (2). Corsetti, G., Dedola, L., Viani, F., 2012. The international risk-sharing puzzle is at business cycle and lower frequency. Canadian Journal of Economics 45 (2), 448–471. Croux, C., Forni, M., Reichlin, L., 2001. A measure of comovement for economic variables: theory and empirics. Review of Economics and Statistics 83 (2), 232–241. Follain, J., Velz, O., 1995. Incorporating the number of existing home sales into a structural model of the market for owner-occupied housing. Journal of Housing Economics 4, 93–117. Genesove, D., Mayer, C., 2001. Loss aversion and seller behavior: evidence from the housing market. The Quarterly Journal of Economics. Hort, K., 2000. Prices and turnover in the market for owner-occupied homes. Regional Science and Urban Economics 30, 99–119. King, R.G., Watson, M.W., 1994. The post-war U.S. phillips curve: a revisionist econometric history. Carnegie–Rochester Conference Series on Public Policy 41 (1), 157–219. Leung, C.K.Y., Lau, G.C.K., Leong, Y.C.F., 2002. Testing alternative theories of the property price-trading volume correlation. Journal of Real Estate Research 23 (3), 253–263. Leung, C.K.Y., Feng, D., 2005. What drives the property price-trading volume correlation? Evidence from a commercial real estate market. Journal of Real Estate Finance and Economics 31 (2), 241–255.
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