Dynamic price–volume causality in the American housing market: A signal of market conditions

North American Journal of Economics and Finance 48 (2019) 385–400

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Dynamic price–volume causality in the American housing market: A signal of market conditions I-Chun Tsai

T

⁎

Department of Finance, National University of Kaohsiung, Taiwan

ARTICLE INFO

ABSTRACT

Keywords: American housing market Price–volume relationship Causality Price discovery function Price rigidity

This study analyzes the dynamic price–volume causality in the American housing market using the average price and transaction volume of existing houses in the United States from January 1999 to December 2015. A rolling window sample is used for estimation in the bootstrap Granger causality test. The results reveal that the transaction volume tends to be informative during price rigidity. In particular, the housing price tends to lag the volume when the information on housing price decreases is required for market correction. The housing price tends to be informative during volume rigidity, particularly during the substantial increase in housing price and the reduced transaction volume caused by the sellers’ reluctance to sell. The dynamic causality estimation explains that the price–volume relationship varies according to market conditions. Under normal circumstances, both the price and volume efficiently react to the information without a lead–lag relationship between the two. However, during a housing market boom or downturn, a lead–lag relationship between price and volume exists. This paper infers that the existence of a lead–lag relationship between price and volume can be a signal of housing market conditions.

1. Introduction In classical economics theory, market equilibrium occurs when the stability between price and volume is established. The price–volume change represents market participants’ reactions and adjustments during an economic shock. Therefore, the price and volume information and the relationship between their mutual adjustments has long been a critical issue in the study of asset markets. Among asset markets, the price–volume relationship in the stock market was the first to be analyzed (Osborne, 1959). Two theoretical models interpreting the price–volume relationship in the stock market were proposed in the 1970s: the sequential information arrival model (Copeland, 1976) and the mixture of distributions hypothesis (Clark, 1973; Epps & Epps, 1976). Karpoff (1987) reviews the possible causes of the price–volume relationship and proposes four imperative reasons for studying the price–volume relationship in financial markets: to understand the structure of financial markets, because it is beneficial to event studies, to understand price distribution, and because of its implications for research into futures and options markets. Studies of the price–volume relationship in the housing market were developed later than those in the stock market, and the level of discussion in the housing market research is not as in-depth as that in the stock market research. Empirical studies on price–volume relationship in the housing market have exhibited inconsistent results. For example, Miller and Sklarz (1986) reveal that transaction volume signals future price movements in the Hawaiian housing market. Subsequent studies that have found the price discovery ⁎

Address: Department of Finance, National University of Kaohsiung, No. 700, Kaohsiung University Rd., Nanzih District, 811. Kaohsiung, Taiwan. E-mail address: [email protected].

https://doi.org/10.1016/j.najef.2019.03.010 Received 16 August 2018; Received in revised form 9 March 2019; Accepted 12 March 2019 Available online 13 March 2019 1062-9408/ © 2019 Elsevier Inc. All rights reserved.

North American Journal of Economics and Finance 48 (2019) 385–400

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function of transaction volume include Berkovec and Goodman (1996), Hort (2000), and Shi et al. (2010). Stein (1995) reveals that the current transaction volume in American existing home sales is correlated to the price change rate in the previous year, indicating the predictive function of price on transaction volume. Zhou (1997) also observes a lead of American housing price over transaction volume. Leung and Feng (2005) observe that the price and volume in Hong Kong office buildings are adjusted synchronously without a lead–lag relationship. Leung et al. (2002) report that examples of price leading volume, volume leading price, and no lead–lag relationship have all existed in past samples of the residential housing market in Hong Kong. The inconsistent price–volume relationship may be attributed to variation in housing types and locations. Tsai and Peng (2016) find there are Linear and nonlinear dynamic relationships between housing prices and trading volumes, and propose that estimating the behavior of housing prices through a linear model can result in underestimating the information reflected by housing returns. The latest studies, such as Huang et al. (2018) and Leung and Tse (2017), assume a new perspective and use proxy variables to describe price factors’ relationships with liquidity or transactions in the housing market. Huang et al. (2018) build an on-the-house search model and show that the rent-toprice ratio and the turnover rate are jointly determined in equilibrium; the results suggests significantly negative effects of turnover and popularity on rent-price ratios. Leung and Tse (2017) build a model by adding arbitraging middlemen – investors who attempt to profit from buying low and selling high – to a housing market search model. There can be multiple equilibria in the model of Leung and Tse (2017). In one equilibrium, most transactions are intermediated, resulting in rapid turnover and high housing prices; in another equilibrium, few houses are bought and sold by flippers, then turnover is slow and prices are moderate. These empirical results of price–volume causality may demonstrate the status of a particular market. The three theories of price–volume causality in the housing market are the downpayment model (Stein, 1995), the search model (Berkovec & Goodman, 1996), and the loss-aversion model (Genesove & Mayer, 2001). All three theories describe the price–volume correlation differently. This study estimates the dynamic price–volume causality in the American housing market, objectively measure the change in price and volume information, and assess what types of market conditions are led by price or volume. The abundance of studies in the price–volume relationship in stock market may be attributed to the high volatility of the business cycle. With investors in the stock market being plentiful, both market bubbles and crashes exhibit substantial influences on an economy, and any information related to trading variables in the stock market is an urgent issue for discussion. Since the collapse of the United States housing market (the subprime mortgage crisis) in 2007, all factors that can be used to monitor the stability or current status of the housing market have also become crucial research topics. For example, Iacoviello and Neri (2010) study sources and consequences of fluctuations in the housing market. Research in price and volume changes can not only facilitate understanding of their informativeness, but can also be used to speculate on market conditions. In addition, an increasing number of studies on housing market issues have proposed evidence revealing price–volume characteristics different from those in the stock market. For example, the trading lags in the housing market in both the downpayment and search models do not occur in the stock market. Although Empirical studies (e.g. Phillips et al., 2015; Pavlidis et al., 2016) have been able to prove that the irrational exuberance proposed by Akerlof and Shiller (2009) is a common occurrence in the stock market and housing market, the irrational behaviors in the loss-aversion model are more frequent in the housing market than in the stock market because of the consumption characteristics of real estate. In addition, the endogenous regime‐switching mechanisms have been shown to be existed in the housing markets, such as the models of Chen and Leung (2008) and Chen et al. (2015),1 and the subsequent empirical works, such as Chang et al. (2011, 2012, 2013). Therefore, further research on the price–volume relationship favors understanding the characteristics of the housing market. Conventional estimating methods of causality are often limited by the sample size for dynamic estimation. The present study employs the bootstrap method to mitigate the biases that often occur in small samples, and verifies the temporal causality estimation using a rolling window analysis. Therefore, the present study does not subjectively predict the timing of causal structural changes, but instead presents it with an objective estimation, and examines the possible causes and market conditions related to the causal relationships. The rest of the paper is organized as follows: Section 2 is a literature review of price–volume relationship and the research background of the present study, section 3 details the research methodology, section 4 describes the samples and discusses the empirical results, and section 5 concludes the study. 2. Literature review and background There is a myriad of literature regarding price–volume correlations in other financial markets; the stock market in particular. From an information-flow or information-asymmetry perspective, previous studies have proposed three hypotheses to elucidate the lead–lag relationship between stock prices and volumes. First, sequential information arrival models involve the use of trading volumes as a proxy variable for arrived information (Copeland, 1976), and can provide explanations for the presence of a causal relation between stock prices and trading volume. Secondly, the mixture of distributions hypothesis that elucidates stock return distribution (Epps & Epps, 1976; and Clark, 1973). However, these two studies made dissimilar proposals. Epps and Epps (1976) proposed that trading volume can be used to measure the degree of disagreement among traders, the greater disagreement among traders, the larger the level of trading volume. Hence, the model suggests a positive causal relation from trading volume to absolute 1 However, there is a difference between these two models. In the model of Chen and Leung (2008), the “regime change” is driven by a change in the credit market conditions, whereas Chen et al. (2015) proposed that the “regime change” is driven by government policy changes and the change of expectation of the private sector.

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Table 1 The different price–volume relationships derived from three models. Author

Sample and period

Research results

Stein (1995): Downpayment model Zhou (1997) Ho et al. (2008) Clayton et al. (2010)

U.S., 1970M1 ∼ 1994M 12 Hong Kong, 1987 ∼ 2004 U.S., 1990Q2 ∼ 2000Q2

Price Volume (price affects sales significantly and sales affects price weakly) Price Volume Price Volume (decreases in house prices reduce market turnover, but increases in house prices do not have significant effects)

Volume Volume

Price Price

Genesove and Mayer (2001): Lossaversion model Engelhardt (2003)

Volume cities) Volume test)

Price (there is a strong causality between price and volume for large

Tsai and Peng (2016)

Swedish, 1981M 1 ∼ 1993M 7 Hong Kong, 1991M 7 ∼ 1998M 11 New Zealand, 1994M1 ∼ 2004 M12 U.S., 19991M1 ∼ 2014M12

U.S., 1985 ∼ 1996

This study does not directly discuss the leading–lagging relationship between price and volume, however, the results support the inference derived from the Loss-aversion model.

U.S., 1981Q1 ∼ 2011Q3 Hong Kong, 2011M11 ∼ 2012M10

Price Price

U.S., 1968 ∼ 2011

Uncertain (the leading–lagging relationship between price and volume can vary with region and data frequency)

Berkovec and Goodman (1996): Traditional Search model Hort (2000) Leung et al. (2002) Shi et al. (2010)

New search model Leung and Tse (2017) Huang et al. (2018) Uncertain Akkoyun et al. (2013)

Price (linear causality test) Volume

Price (nonlinear causality

Volume Volume

stock returns. On the other hand, Clark (1973) viewed trading volume as a proxy for the speed of information flow, that affects contemporaneous stock returns and volume. A third explanation is the asymmetric information hypothesis. The hypothesis attribute asymmetry in the price–volume relation to differences in expectation formation by traders (Moosa and Korczak, 1999). In contrast with the research on financial markets, research and discussions concerning the price–volume correlations in the property market are rare. One reason for this phenomenon is that data on the real estate cannot be as easily obtained as that of securities. However, the difficulty of data obtaining does not indicate the insignificance of the studies on the price–volume correlations in the property market. More and more scholars have been devoted to research on the price–volume correlations in the property market in recent years. Three main models have been proposed for interpreting the price–volume relationship in the housing market: The downpayment model, the search model, and the loss-aversion model. In the downpayment model (Stein, 1995), the price drop during a housing market downturn reduces the value of a household asset and the household’s ability to pay for the downpayment, thereby limiting the ability to purchase a new house. Consequently, both the buying demand and transaction volume decrease. In the search model (Berkovec & Goodman, 1996), trade occurs only when the seller’s offer price is equal to, or below, the buyer’s reservation price, or the buyer will keep searching for a house within budget. Therefore, the transaction volume represents the level of market demand. When the market receives a negative demand shock, the decreased transaction volume causes sellers to adopt price drops, leading to decreased transaction prices. In the loss-aversion model (Genesove & Mayer, 2001), when the sellers’ disposition effect of avoiding losses exists, the buyers’ low offer prices during the housing market downturn reduces the sellers’ willingness to sell their properties, resulting in decreased transaction volume. Table 1 is a list that briefly describes the different price–volume relationships derived from three models, and the empirical studies that support the use of each of the models. As we can see in Table 1, in the price–volume relationship during a market downturn, the search model indicates that the transaction volume leads the price, the downpayment model indicates that the price reacts to the negative shock and subsequently reflects the transaction volume, and the loss-aversion model argues that both price and volume decrease during a market downturn. Scenarios in which volumes lead prices (the search model) or vice versa (the downpayment and loss-aversion models) can potentially occur in housing markets. In other words, prices and volumes should have a mutual lead–lag relationship. However, this relationship is only found under specific market conditions. For example, loss aversion can easily occur during a market recession, resulting in different findings of the relationship between housing prices and volumes obtained by previous empirical studies. Additionally, one new theory on housing price discusses how the private sector reacts to government interference. For example, Chen et al. (2015) study the stabilization effect of monetary policy reacting to asset price, and propose that since the monetary authority may change the policy and how people form expectation to it could lead to regime‐switching dynamics in house price.2 Zhou (2016) studies the 2004–2015 transaction data of the Shanghai housing market to investigate the market dynamics under 2

The results are consistent to the evidence presented in Chang et al. (2011, 2012, 2013). 387

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frequent policy changes, and notices that the market often overreacts when a policy change occurs. Wong et al. (2016) analyze the transmission mechanism of a loan-to-value policy to financial stability by providing the findings from Hong Kong, and the findings show that the direct pass-through rate of the LTV policy to the property market is weak. These studies clearly indicate that governmental policies can affect the trend of housing price, which can either underreact or overreact. Therefore, the price–volume relationship can also be affected by the current status of the market. For example, Zhang et al. (2015) analyzes the 2005–2013 housing price and transaction volume data of 35 metropolitan areas to determine whether the Purchase Restriction Order enforced in China can shift the price–volume relationship. The results reveal that, in the case of coastal cities, price change was a significant leading indicator of transaction volume before the Purchase Restriction Order was enforced, and that leading relationship disappeared after the enforcement of the Order. This could be attributed to the intervention that was imposed on the market, which affected the informativeness of transaction price, thereby changing the price–volume relationship. According to the aforementioned theories, the price and volume reactions during an economic shock cause the leads or lags observed in the empirical results. Therefore, information lag does not occur under normal circumstances (i.e., without a shock) because the price and volume in the housing market should be synchronously adjusted, similar to those in the stock market. Leung (2014) argues that, when government interference and market imperfection are excluded, housing prices can exhibit an endogenous process of self‐correction. Tsai (2014) claims that both price and volume are critical characteristic variables of housing transactions, and both can adjust themselves to reach equilibrium achieve a balance. However, because supply in the housing market has a time lag, the market’s self-correcting behavior in the wake of an exogenous impact can possibly be achieved through either price or volume. Oikarinen (2012) notices that transaction volume reflects demand faster than price. Information lag might occur during an economic shock because the restricted price and volume exhibit a short-term rigidity. For example, Tsai (2018) use a simple housing market supply–demand model to show that the presence of housing market imbalance, or excess supply, depends on the informativeness of housing prices, and find information between regional housing markets is either transferred through price or volume. If the data used in empirical studies are mostly from normal circumstances, the results should yield no lead–lag relationships between price and volume. However, data containing restricted sellers (the loss-aversion model) or buyers (the downpayment model) are prone to price or volume inefficiency, resulting in information lags. Therefore, through a dynamic causal model, the present study aims to interpret the relationship between the market conditions during the sampling period and the empirical results. Recent studies have also focused on the direction of price influence, for example, Yiu, et al. (2008) noticed that price fluctuation could affect the volume negatively, and the incremental liquidity could reduce the risk from price error, as well as the risk premium of the buyers. Thus the interplay between the price and volume is obvious. Clayton, et al. (2010) conducted an empirical study on 114 housing markets in the U.S. between 1990 and 2002, observing the interplay between price and volume, but discovered that the effect of the price leading volume is asymmetric; when the price declined, the volume would decline, whereas the volume kept stable when the price rose. Hence, the present study verifies whether the empirical results support the hypothesis by observing the direction of the correlation coefficient in statistically significant causalities. 3. Empirical methodology To estimate the price–volume relationship in the housing market, this study employs a bivariate vector autoregressive (VAR) model, where HP is the home price change and TV is the transaction volume change. The VAR model can be written in matrix form as

HPt TVt

=

10 20

+

11 (L)

12 (L)

21 (L)

22 (L)

HPt TVt

+

1t

(1)

2t

i , j = 1, 2 and L is the lag operator. where ij (L) = ij, c The Granger causality test is a commonly used method for verifying the short-term causality between economic variables. The Granger noncausality is defined as the inability of the information collection containing lagging items of variable A to predict variable B . If the estimated statistic significantly rejects the null hypothesis of the Granger noncausality, variable A causes variable B (i.e., variable A leads variable B). According to Eq. (1), the null hypothesis of the housing price not causing a change in transaction volume is p+1 c=1

H0 :

12,1

=

12,2

Lc ,

=

=

12, p

=0

(2)

and the null hypothesis of the transaction volume change not causing the housing price is

H0 :

21,1

=

21,2

=

=

21, p

=0

(3)

Because the coefficients of one lagging period and p lagging periods are both zero, the statistics in the joint restriction tests (i.e., the Wald statistics and the likelihood ratio statistics) are used for the causality test. In addition to the conventional Wald test, the present study also uses the bootstrap method to test Eqs. (2) and (3). Shukur and Mantalos (2000) observe biases in small- and medium-sized samples when they test the Granger noncausality using the Wald test. Shukur and Mantalos (2004) confirm that the critical values constructed by the residual-based bootstrap method can improve the testability of the causality test. Mantalos and Shukur (1998) also observe the consistency of the critical values obtained by the residual-based bootstrap method. Nyakabawo et al. (2015) analyze causality between real house price and real GDP per capita in the US by using bootstrap Granger non-causality test 388

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based on a fixed-size rolling-window. To rigorously estimate the price–volume relationship and avoid biases caused by the small sample size, the present study also conducts the causality test using the residual-based bootstrap method. The bootstrap is first proposed by Efron (1979), and constructs the critical values and p values using the resampling distribution of the empirical data. For the sake of simplicity, Eq. (3) can be written as follows: (4)

Y= X+ where

Y

is

the

vector

of

the

independent

variable

(i.e.,

Y=

HPt ), TVt

X

is

the

explanatory

variable

(i.e.,

X = 0 + (L ) Y , (L ) = L + + ), and L is the lag operator. The present study uses the restricted model (i.e., the null-hypothesis model) and estimates the coefficient using the ordinary least squares (OLS) method to obtain the following equation: L2

= YX ' (X 'X )

+L p

(5)

1

After the estimated coefficient is inserted, the OLS residuals can be obtained from the following equation:

=Y

(6)

X

Through the mean adjusted OLS residuals, the statistics for the causality test are obtained. The bootstrap statistics restricted by the null hypothesis are obtained after repetitions of these steps, and can be used for empirical distribution.3 Because the bootstrap method can alleviate potential biases in small samples, the relationship between the variables can be estimated using either the entire sample or a fraction of the sample. The rolling window subsamples can estimate the temporal causality and the causal dynamics. Let k denote the size of the rolling window, then apply the bootstrap causality test to rolling window subsamples for t= k + 1, k, ., . = k , k + 1, T . Subsequently, the change of the estimating coefficient is illustrated according to the confidence intervals estimated by the bootstrap method. 4. Empirical results We use the nominal average sales price and trading volume of existing single-family homes, published by the National Association of Realtors. The data is monthly and from January 1999 to December 2015. We investigate the housing market of the entire USA. The data used in this study are adjusted by season through the moving average method,4 and all data are presented as natural logarithms during the empirical estimation. Table 2 shows the brief statistics and the unit root test results of the variables, and Fig. 1 illustrates the price and volume trends during all sample periods. Fig. 1 demonstrates that both the price and volume had a common rising trend before 2005. However, the transaction volume rises gradually, whereas the price rises substantially after 2002. At the end of 2005, both the price and volume exhibited a reversed trend. The maximum average housing price occurred in October 2005, whereas the maximum transaction volume occurred in September 2005. Therefore, the transaction volume started declining a month before the average housing price did. In October 2005, the transaction volume decreased from 615 thousand units to 557 thousand units, a −9.4% monthly decrease, whereas the housing price in November 2005 decreased by 0.53%. In addition, the volume exhibited a larger market correction than the price did in the housing market downturn beginning in 2005. From September 2005 to November 2008, the transaction volume was corrected by 51.86%, whereas the price was corrected by 16.51%. Fig. 1 also demonstrates that when the housing market began to recover in 2010, the price and volume react differently. The housing price began to rise in June 2010 whereas the transaction volume did not begin to rise until August 2010. In addition, except for some minor corrections during 2012, the housing price continued to rise until the end of 2015, approaching the high point of 2005. Transaction volume, however, did not recover to the level of the previous housing boom in 2004–2005. The unit root test in Table 2 reveals that both the housing price and transaction volume are first-order integrated series. The test result using the initial data with two variables reveals that both the price and volume are nonstationary sequences. However, after the bivariate data are estimated using the first-order differentiation, both the housing price and transaction volume become stationary data. Because the initial data of price and volume are both first-order integrated and both generally exhibit a matching temporal trend, as shown in Fig. 1, a long-term cointegration relationship between price and volume is observed. Table 3 shows the estimation results of the price–volume cointegration. Table 3 shows the results of the bivariate cointegration test developed by Engle and Granger (1987). The results reveal that the housing price and transaction volume do not exhibit an integrated linear relationship regardless of which one is set as the dependent variable. Because Engle and Granger (1987) do not consider a long-term nonlinear, asymmetric, or structure-changing relationship, the results in Table 3 do not represent a disassociation between price and volume. The results in Table 3 imply that the price and 3

The numbers of repetitions in past studies have had an increasing trend. For example, Horowitz (1994) conducts 100 repetitions, Davidson and MacKinnon (1999) conduct 1000 repetitions, and Balcilar and Ozdemir (2013) conduct 2000 repetitions. The present study conducts 10,000 repetitions. 4 The steps of the method are as following. First we compute the centered moving average of the series, then compute the seasonal indices, and adjust the seasonal indices so that they multiply to one. Then we compute the seasonal factors as the ratio of the seasonal index to the geometric mean of the indices. The seasonally adjusted series can be obtained by dividing the series by the seasonal factors. 389

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Table 2 Simple statistics and unit root tests.

Simple statistics Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis PP unit root tests Original data Differenced data

HP

TV

227,697 225,996 276,322 166,460 30,851 −0.3198 2.0589

432,419 423,591 615,004 279,199 75,099 0.4509 2.5037

−1.5876 (0.4871) −12.9048 (0.0000)

−2.4443 (0.1310) −20.4937 (0.0000)

Notes: HP denotes housing price, and TV denotes trading volume. PP test is adopted for testing the null hypothesis of a unit root in the series. The intercept is included in the testing equation, and the lag length of the unit root models is selected by using the Schwarz information criterion. The entry in parenthesis stands for the p-value.

700,000 600,000 500,000 400,000 300,000 200,000 100,000

2000

2002

2004

2006

Housing price

2008

2010

2012

2014

Trading volume

Fig. 1. The price and volume trends during all sample periods. Table 3 Cointegration test. Dependent

tau-statistic

p-value

z-statistic

p-value

HP TV

−1.9224 −1.3587

0.5694 0.8132

−3.5457 −3.8491

0.8413 0.8195

Notes: HP denotes housing price, and TV denotes trading volume. Cointegration test is adopted for testing the null hypothesis of there is no cointegrating relationship existed.

volume do not exhibit a common trend in the long term because the price–volume relationship is either short-term or changes over time. Therefore, the present study investigates the mutual adjustment between the two variables through short-term and dynamic causalities. Because both the VAR model and the causality test require stationary sequences, the first-order differentiated data (i.e., the return rate of housing price and transaction volume change) are employed for subsequent analysis of the price–volume relationship. Table 4 shows the estimated results using the VAR model. The results support the hypothesis of market efficiency because the housing price exhibits efficiency and is not related to past price–volume information. The transaction volume change lags the autocorrelation from one, two, and four periods (i.e., months) earlier, and is influenced by the housing price two periods earlier. The 390

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Table 4 Vector Autoregression Estimates. TV

HP

HPt

1

HPt

2

HPt

3

HPt

4

TVt

1

TVt

2

TVt

3

TVt

4

Constant Adj. R-squared

0.0955 [1.3296] −0.0157 [−0.2185] 0.0658 [0.9145] 0.1388 [1.9317] 0.0108 [0.6210] 0.0273 [1.4913] −0.0002 [−0.0102] −0.0241 [−1.3636] 0.0018 [1.7431] 0.0256

−0.0116 [−0.0397] 0.8468*** [2.8912] −0.3895 [−1.3279] 0.2174 [0.7421] −0.3179*** [−4.4886] −0.2534*** [−3.3906] 0.0701 [0.9300] −0.2763*** [−3.8348] −0.0011 [−0.2598] 0.2317

Notes: HP denotes housing price change, and TV denotes transaction volume change. The lag length of the estimated models is selected by using the Schwarz information criterion. The entry in parenthesis stands for the t-statistics. *** indicates significance at the 1% level.

negative autocorrelation of the volume change may be attributed to housing demand. When an increased number of housing units in high demand are traded in a certain period (i.e., there is increased transaction volume), the demand of the remaining housing units decreases, resulting in a decrease in transaction volume change in the following periods. A housing price increase leads to an increased transaction volume after two months, with a 1% increase in housing price leading to a 0.84% increase in transaction volume after two months. Therefore, the transaction volume change is substantially influenced by the housing price. The transaction volume not only exhibits a price discovery function, but also lags the housing price. Table 5 shows the test results of Eqs. (2) and (3) using the model in Table 4. The conventional causality test results in Table 5 reveal that the housing price is not influenced by past changes of transaction volume, but that the housing price significantly leads the reaction of transaction volume change. The results in Table 5 imply that in the American housing market, the price is more informative than the volume during the sampling period. According to the estimated results of the VAR model in Table 4, the direction of influence of the price–volume relationship in Fig. 2 is drawn using the impulse response analysis. Fig. 2 demonstrates that when either the housing price or the change of transaction volume experiences a shock of one standard deviation, the direction of influence of the other variable is positive. However, the impulse response of the volume change influenced by the housing price shock is more obvious than the opposite, particularly two periods after the shock occurs. The volume change exhibits minimal influence on the housing price, and the influence approaches zero in a short amount of time. Both the estimated positive influence of price on volume in Table 4, and the estimated results of the impulse response in Fig. 2, match the theoretical models in past studies, although the transaction volume is not as informative as that estimated in past studies. Table 5 Pairwise Granger Causality Tests. Null Hypothesis Monthly data TV does not Granger Cause HP HP does not Granger Cause TV Panel data TV does not Granger Cause HP HP does not Granger Cause TV Quarterly data TV does not Granger Cause HP HP does not Granger Cause TV The C-S home price index (Panel data) TV does not Granger Cause HP HP does not Granger Cause TV

F-Statistic

p-value

1.2660 2.4325

0.2849 0.0490

1.0432 3.7275

0.3528 0.0245

5.7973 43.5804

0.0050 0.0000

0.6102 0.0837

0.5433 0.9197

Notes: HP denotes housing price change, and TV denotes transaction volume change. The lag length of the estimated models is selected by using the Schwarz information criterion. 391

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Accumulated Response of Housing Price to Cholesky One S.D. Volume Innovation .006 .004 .002 .000 -.002 -.004 -.006

1

2

3

4

5

6

7

8

9

10

Accumulated Response of Volume to Cholesky One S.D. Housing Price Innovation .024 .020 .016 .012 .008 .004 .000 -.004 -.008

1

2

3

4

5

6

7

8

9

10

Fig. 2. Impulse response.

To compare the different price–volume relationships under varied sampling structures, Table 5 presents the results derived from panel data and from quarterly data. The results from panel data cover four regions of the United States (Northeast, Midwest, South, and West) during the same time span (January 1999 to December 2015), whereas the results from quarterly data represent different data frequencies from the first quarter of 1999 to the fourth quarter of 2015. In addition, Table 5 also includes a comparison of estimation results derived from panel data of another dataset: The S&P/Case-Shiller Home Price Indices for 20 major metropolitan areas in the United States between January 1999 to December 2015.5 In Table 5, the estimation results derived from panel data conform to the nationwide results from the United States, suggesting that price has greater informativeness. By contrast, in the estimation results derived from quarterly data, both housing price and transaction volume either lead or lag each other, suggesting that transaction volume also has informativeness. Long-term transaction volume has greater informativeness than short-term transaction volume; this phenomenon showcases information rigidity in shortterm transaction volume. As we can see in Table 5, the estimation results derived from the Case–Shiller home price index show that there is no significant causality between the price and volume data. This might be because that the Case–Shiller home price index 5

The home price indices and home price sales are obtained from the S&P Dow Jones Indices website. 392

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.06 .04 .02 .00 -.02 -.04 -.06 00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

Recursive Residuals of Housing Return Model 2 S.E. .2

.1

.0

-.1

-.2

-.3

00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

Recursive Residuals of Volume Variation Model 2 S.E. Fig. 3. Recursive residuals of the causality estimation model.

provides the quantitative data for the matching index instead of the complete transaction data. The results in Table 5, however, do not consider the change in the price–volume relationship during the sampling period. If the price–volume information changes according to the market condition as described in past studies, the linear model of the estimated causality may exhibit structural changes, leading to misestimated causality. To verify the goodness of fit of the linear model, the recursive residuals for the causality estimation model are illustrated in Fig. 3. Brown et al. (1975) argue that if the estimated coefficient in a linear model does not exhibit structural changes, the recursive residuals are independent and identically distributed. Fig. 3 demonstrates that the linear model of the estimated influence of transaction volume change on housing price exhibited remarkable errors in 2009, whereas that of the housing price on transaction volume change exhibited remarkable errors in 2010. During these two periods, the recursive residuals exceeded the confidence interval, which may not be consistent with the hypothesis of the absence of structural changes. To further verify the change in the price–volume relationship, the multiple breakpoint test proposed by Bai and Perron (2003) is used for subsequent estimation. Table 6 shows the structural changes of the coefficients in the two causality models in which the housing price and volume change are set as the dependent variable. Table 6 reveals that when the housing price is set as the dependent variable (i.e., the linear model for estimating the influence of volume change on housing price), the coefficient exhibits 393

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Table 6 Multiple breakpoint tests. Dependent Variable

TV

HP

Break Test

F-statistic

Scaled F-statistic

Critical Value

F-statistic

Scaled F-statistic

Critical Value

0 vs. 1 1 vs. 2 2 vs. 3 Break dates

3.3583 3.0916 2.4352 Sequential

30.2251 27.8241 21.9165 Repartition

25.65 27.66 28.91

1.9319

17.3873

25.65

1 2

2006 M02 2009 M05

2006 M01 2009 M05

Notes: HP denotes housing price change, and TV denotes transaction volume change. Table 7 Bootstrap p-value. Null Hypothesis

TV does not Granger Cause HP HP does not Granger Cause TV

F-Statistic

p-value

1.2660 2.4325

0.2750 0.0459

Notes: HP denotes housing price change, and TV denotes transaction volume change.

significant structural changes. Therefore, the results in Tables 4 and 5 may underestimate the influence of the transaction volume. Table 6 reveals that the null hypotheses with zero and one structural change are rejected significantly, and the two structural changes in the estimating model of the housing price occurred in February 2006 and May 2009. Table 6 also reveals that when the transaction volume is set as the dependent variable, there are no structural changes in the linear model. The significant lead of housing price on volume change observed in Tables 4 and 5 may be attributed to the absence of significant structural changes in the linear model. Both Fig. 3 and Table 6 imply that structural changes occur in the price–volume relationship, and may underestimate the informativeness of the transaction volume. However, neither Fig. 3 nor Table 6 provides a clear point of structural change to reestimate the causality through cutoff sampling because the timing of structural changes may depend on the observed dependent variable and the tested statistics. For a more rigorous cutoff sampling result without subjective or preset time points, the bootstrap method is employed to comprehensively estimate the price–volume causality because it solves the problem of small sample sizes without the need to preset the time points of structural changes. The dynamic price–volume relationship can be observed using the rolling window samples for estimation. Table 7 lists the causality test results using the bootstrap method. Both Tables 5 and 7 estimate the causality using the entire dataset with similar results. Table 7 also reveals that the price leads the volume, but the volume does not lead the price. Subsequently, the 36-month causality test is estimated using the rolling window sample.6 Fig. 4 shows the p values of the temporal causality test. Because the p values are estimated using a 36-month dataset, the midpoint of the 36-month sample denotes the estimated time point on the X axis to demonstrate whether causality significantly exists during the 36-month span, similar to what past studies have conducted. Therefore, the p value in June 2000 corresponds to the estimated result from January 1999 to December 2001, as shown in Fig. 4. The two test results in Fig. 4 respectively correspond to (a) the influence of housing price on volume change and (b) the influence of volume change on housing price. In Fig. 4, the lower the p value is, the more significantly rejected the null hypothesis of noncausality is. In addition, horizontal lines of 0.1 are labeled to demonstrate which periods exhibit significant causalities. Fig. 4(a) shows that the three midpoints where the housing price significantly leads the volume change (p < .05) consist of June–October 2000, January–June 2014, and November 2004–February 2005. Fig. 4(b) shows that the three midpoints where the volume change significantly leads the housing price consist of July 2000, February 2005, and November 2005–February 2006. The dynamics of the price–volume relationship in the present study can be obtained through the comparison of the results in Fig. 4(a) and (b). Beginning in the second half of 2000, the price and volume exhibited a back-and-forth lead–lag relationship, but the housing price leads the volume more noticeably. The housing price also led the volume change from November 2004 to January 2005. The price and volume were back-and-forth again in February 2005. From November 2005 to February 2006, only the volume leads the price. Finally, the price led the volume from January to June 2014. The results in Fig. 4 and the housing price–volume trends in Fig. 1 reveal that the price–volume dynamic is correlated to the business cycle. Neither the price nor the volume lags in a steady market climate. The price or volume may exhibit rigidity only during economic shocks, resulting in one lagging the other. The housing price unilaterally leads the volume change when the volume exhibits rigidity. The two midpoints of the sample in November 2004–January 2005 and January–June 2014 represent the price booms in the 6 Past studies have set the rolling sample size at 40 (Aye et al., 2014, Balcilar & Ozdemir, 2013). Because the present study uses the monthly data in a 3-year span, the rolling sample size is set at 36.

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1.0

0.8

0.6

0.4

0.2

0.0 00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

13

14

(a) p-value: the influence of housing price on volume change 1.0

0.8

0.6

0.4

0.2

0.0 00

01

02

03

04

05

06

07

08

09

10

11

12

(b) p-value: the influence of volume change on housing price Fig. 4. Bootstrap p-value.

sampling period. The former represents the price increase of 23.62% from May 2003 to July 2007, whereas the latter represents the price increase of 18.04% from July 2012 to December 2015. However, the transaction volumes in both periods are rigid and without a substantial increase. The transaction value unilaterally leads the housing price when the price exhibits rigidity. The midpoint from November 2005 to February 2006 represents the price increase of 10.23% from May 2004 to August 2007. However, the housing market begins to recover at the end of 2015 with a price increase of 16% from a decrease of 5.41% in October 2015. During the housing market downturn, the transaction volume is substantially corrected and begins leading the price because the price rigidity led by negative information forms the price discovery function of the transaction volume during this period. To further interpret the correlation between the price–volume relationship and the business cycle, Figs. 5 and 6 illustrate the market performance of the first and second occurrences of the price leading the volume, respectively. Fig. 7 illustrates the market performance when the volume leads the price. Figs. 5 and 6 reveal that the price unilaterally leads the volume when the price substantially increases, and the volume stays rigid during the beginning of a market boom. Fig. 7 demonstrates that the volume unilaterally leads the price when the volume rapidly decreases and the rigid price decreases slowly during the beginning of a market downturn. The estimated results in the present study verify the three effects of the theoretical models. When the price unilaterally leads the volume, the downpayment model can be used for interpretation. When the housing price increases in a market boom, the increased 395

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House price

Trading Volume

280,000

640,000

270,000

600,000

260,000 250,000

560,000

240,000

520,000

230,000 480,000

220,000 210,000

440,000 II

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Housing return

II

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Volume Variation

.03

.12

.02

.08

.01

.04

.00

.00

-.01

-.04

-.02

-.08

-.03

-.12 II

III 2003

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III 2003

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Fig. 5. The first occurrence of the price leading the volume.

household asset enables the buyers to afford the downpayment, thus increasing the buying demand. However, without a substantial increase in the housing supply, the transaction volume cannot be synchronously increased, resulting in volume rigidity. When the volume unilaterally leads the price, the search model can be employed to interpret the demand change. In addition, the phenomenon supports the inference of the loss-aversion model. When the housing market downturn occurs, homeowners who purchase at high prices in the previous wave are reluctant to sell, and tend to wait for a future price increase. Therefore, the houses stay in the market for an extended time, and the transaction volume rapidly decreases, whereas the price remains rigid. Additionally, the search model can also explain the volume rigidity at the beginning of a housing market boom. The buyer’s reservation price may not substantially increase while the sellers are reluctant to sell. Therefore, the housing supply cannot be increased, resulting in mismatches between buyers and sellers. The aforementioned inferences reveal that the influence should be positive regardless of whether the price unilaterally leads the volume or the volume unilaterally leads the price. When the transaction volume remains rigid during a market boom, the housing price increases first, followed by an increase in the volume. When the price remains rigid during a market downturn, the transaction volume rapidly decreases, followed by a rapid price decrease. Under normal circumstances in the absence of rigidity, both the price and volume volatilities reflect real-time economic information. The influences become nonsignificant to each other and may not always be positive. Fig. 8 illustrates the dynamic estimated coefficient of the price–volume relationship. Fig. 8(a) illustrates the sum of the coefficients when the price leads the volume, whereas Fig. 8(b) illustrates those when the volume leads the price. The X axis in Fig. 8 also denotes the midpoints of the samples during the sampling period. Although the coefficients in Fig. 8 change substantially, unlike the results in Table 4, the p values in Fig. 8 are nonsignificant in most periods. Therefore, the occurrences of unilateral leads are labeled in the shadowed areas in Fig. 8 to observe the direction of price–volume correlation in various market conditions in Figs. 5–7. Fig. 8(a) demonstrates that when the price unilaterally affects the volume during a market boom, all sums of coefficients are positive. Fig. 8(b) demonstrates that when the volume unilaterally affects the price during a market downturn, all sums of coefficients are also positive. Fig. 8 demonstrates that under various market conditions estimated in the present study, the lead–lag relationship between the price and volume supports the inferences of the aforementioned theoretical models. Changes in these coefficients and their significance may cause underestimation of causality when only one model is used for estimation. Using data from a different period may also yield negative causality which does not match the theoretical models. 396

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House price

Trading Volume

270,000

480,000 460,000

260,000

440,000

250,000

420,000 240,000

400,000

230,000

380,000

220,000

360,000 III

IV

I

2012

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2013

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IV

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Housing return

II

III

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II

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2015

Volume Variation

.04

.2

.03 .1

.02 .01

.0

.00 -.01

-.1

-.02 -.03

-.2 III

IV

2012

I

II

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IV

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Fig. 6. The second occurrence of the price leading the volume.

5. Conclusion This study analyzes the dynamic price–volume causality in the American housing market using the average price and transaction volume of existing houses in the United States from January 1999 to December 2015. The bootstrap method is employed to estimate the temporal price–volume causality of the rolling window sample. The conventional causality test results reveal that the housing price unilaterally leads the transaction volume, whereas the transaction volume does not exhibit a price discovery function. Inconsistency with past studies may be attributed to structural changes in the empirical model. When the multiple breakpoint test is used, the influence of trading volume variations on housing price from February 2006 to May 2009 exhibit significant structural changes. The rolling window samples are used for estimation of the bootstrap Granger causality test. The obtained dynamic price–volume causality during the sampling period reveals the occurrences of price unilaterally leading volume, volume unilaterally leading price, and constant lead changes between the two in various periods. In addition, the dynamic of the price–volume relationship is correlated to the business cycle. Under normal circumstances, neither the price nor the volume exhibit information lags. The price or volume may exhibit rigidity only during an economic shock, resulting in one variable lagging the other. When the price unilaterally leads the volume at the beginning of a market boom, the price increases substantially and the volume remains rigid. When the volume unilaterally leads the price at the beginning of a market downturn, the volume rapidly decreases and the rigid price only decreases slowly. The empirical results in this study verify the inferences of the theoretical models. When the housing market starts to boom, increased household wealth increases the affordability of downpayment and the buying demand. However, the buyer’s reservation price does not substantially increase accordingly, which coupled with the sellers’ reluctance to sell leads to an inability to increase the housing supply. Without a substantial increase in the housing supply, the transaction volume cannot be synchronously increased, resulting in volume rigidity. Therefore, the downpayment model can be employed to interpret the price leading the volume. When a housing market downturn occurs, homeowners who purchased at high prices in the previous wave are reluctant to sell, and tend to wait for a future price increase. Therefore, the houses stay in the market for an extended time, and the transaction volume rapidly decreases whereas the price remains rigid. The transaction volume information supports the loss-aversion model. Finally, when the price unilaterally affects the volume during a market boom, all sums of the coefficients are positive. When the volume 397

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House price

Trading Volume

280,000

650,000 600,000

270,000

550,000

260,000

500,000 250,000

450,000

240,000

400,000

230,000

350,000 II

III

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IV

I

2004

II

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2005

Housing return

II

III

IV

I

2006

II

III

2007

Volume Variation

.03

.08

.02

.04

.01

.00

.00

-.04

-.01

-.08

-.02

-.12

-.03

-.16 II

III 2004

IV

I

II

III

2005

IV

I

II

III

2006

IV

I

II

III

II

2007

III 2004

IV

I

II

III

2005

IV

I

II

III

2006

IV

I

II

III

2007

Fig. 7. The market performance when the volume leads the price.

unilaterally affects the price during a market downturn, all sums of the coefficients are also positive. However, using only one model for estimation may cause underestimation of the causality. Using data from a different period may also yield negative causality which does not match the theoretical models. Through an objective estimation of the dynamic price–volume relationship, this study verifies that both the downpayment and loss-aversion effects exist in certain market conditions, resulting in changes in the price–volume relationship. The increasingly varying market conditions substantially affect civilian wealth, and the efficiency and information of the housing market variables deserve further exploration. This study observes that the housing price rigidity in a housing market downturn may lead to misjudging market changes. Both the government and real estate traders must pay extra attention to information on substantially decreased transaction volumes and implement response measures in advance. The three models that are used to explain the price–volume relationship in the housing market (the downpayment model, the search model, and the loss-aversion model) have all been supported by empirical studies employing different samples. Moreover, recent dynamic behaviors, such as governmental interference and housing price’s corresponding informativeness, have been found to explain certain market behaviors. This paper also infers that the existence of a lead–lag relationship between price and volume can be a signal of housing market conditions. The results are consistent with the endogenous regime‐switching models. Both these facts suggest that the price–volume relationship can change with time, and what an individual model is able to explain probably only represents a piece of the whole picture in the price–volume relationship. If future studies are able to find more suitable proxy variables to decipher the effects reflected in the different models, a more thorough quantification of the price–volume relationship can be formalized for further analysis.

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15 10 5 0 -5 -10 -15 00

01

02

03

04

05

06

07

sum

08

lower

09

10

11

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13

14

upper

(a) sum of coefficients: the influence of housing price on volume change 1.2 0.8 0.4 0.0 -0.4 -0.8 -1.2 00

01

02

03

04

05

06

07

Sum

08

lower

09

10

11

12

13

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upper

(b) sum of coefficients: the influence of volume change on housing price Fig. 8. Sum of coefficients.

Acknowledgements I am immensely grateful to Professor Hamid Beladi (Editor) and the two anonymous referees for the constructive comments of this paper. Funding from the Ministry of Science and Technology of Taiwan under Project No. MOST-107-2410-H-390-016-MY3 has enabled the continuation of this research and the dissemination of these results. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.najef.2019.03.010.

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