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Keywords:

  • Stock returns;
  • Housing returns;
  • Inflation;
  • Inflation illusion;
  • Structural VAR

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

The inflation illusion hypothesis of Modigliani and Cohn (1979) has received renewed attention in explaining a negative relation not only between stock returns and inflation but also between housing returns and inflation. We reexamine the empirical relation in general and the validity of the inflation illusion hypothesis in particular using data from the US, the UK and Korea. We find three key results. (1) The negative relation is particularly strong in recession periods, indicating that the relation is sensitive to business cycles. (2) There are two regimes with positive and negative asset returns and inflation relations for all three countries, and the two-regime relation is found not only for the stock return–inflation relation but also for the housing return–inflation relation. This finding is at odds with the inflation illusion hypothesis because the hypothesis anticipates only a negative relation for both positive inflation and negative inflation. (3) Housing returns Granger-cause inflation, and their dynamic net effect on inflation is significantly positive for all three countries. This is at odds with the inflation illusion hypothesis, which anticipates inflation being related to negative returns. Overall, we find limited evidence for the inflation illusion hypothesis. If there is inflation illusion, only a small fraction of investors suffer from it.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

The relation between asset returns and inflation has been investigated extensively. In particular, given various economic stimulus packages and the central bank's expansionary monetary measures during this economic downturn, there seems little doubt about the possibility of forthcoming inflation, and the relation between asset returns and inflation becomes a more relevant issue. Contrary to the conventional view and the Fisher (1930) hypothesis, many empirical studies find a negative relation between inflation and real stock returns (RSRs) in post-war data from the US and other countries (e.g. Bodie, 1976; Jaffe and Mandelker, 1976; Fama and Schwert, 1977; Nelson and Schwert, 1977; Geske and Roll, 1983; Gultekin, 1983; Lee, 1989; Marshall, 1992; Hess and Lee, 1999).

Several hypotheses have been proposed to explain the observed negative relation between stock returns and inflation. Modigliani and Cohn (1979) propose the inflation illusion hypothesis, which maintains that stock market investors are subject to inflation illusion. This hypothesis has been extended and applied by Ritter and Warr (2002), Campbell and Vuolteenaho (2004), Cohen et al. (2005), Thomas and Zhang (2007), Chen et al. (2009) and Wei and Joutz (2009). Feldstein (1980) proposes the tax hypothesis to explain the inverse relation between higher inflation and lower share prices. Fama (1981, 1983) proposes the proxy hypothesis. Given that inflation affects value by way of its effect on the risk premium, Brandt and Wang (2003) propose the time-varying risk aversion hypothesis.

Substantial increases in housing prices in recent years have been followed by a collapse. These housing price fluctuations and potential inefficiency are documented in Case and Shiller (1989, 1990), Shiller (2005) and Brunnermeier and Julliard (2008). In particular, Brunnermeier and Julliard (2008) suggest that among potential reasons for the housing market inefficiency, money illusion is a strong explanation because frictions make it difficult for investors to arbitrage away possible mispricing. They identify an empirical proxy for mispricing in the housing market, which is largely explained by movements in inflation, and thus find empirical support for the inflation illusion hypothesis. They show that a reduction in inflation can generate substantial increases in housing prices when agents are subject to money illusion.

Given the recent renewed interest in the inflation illusion hypothesis both in the stock market and the housing market, we reexamine whether the relation between stock market return and inflation and the relation between housing return and inflation are indeed mainly due to inflation illusion. Traditionally in the US and other countries, residential real estate has been the principal asset held in most private portfolios. Therefore, it is important and interesting to examine whether real estate and stocks provide a good inflation hedge. To address this question and provide new insights into the relationship, we propose an alternative, more general identification method of the various types of forces that drive the asset return–inflation relation, and we reevaluate various hypotheses including the inflation illusion hypothesis.

Our major findings and contribution to the literature can be summarized by comparing with those in Hess and Lee (1999). Hess and Lee (1999) examine the relation between stock returns and inflation with two types of disturbances—supply shocks and demand shocks—to explain mainly pre-war period positive relations and post-war period negative relations in the US. They identify the supply and demand shocks based on a bivariate vector autoregressive (VAR) model. Our paper extends their study in several respects. First, we examine the negative relation not only between stock returns and inflation but also between housing returns and inflation using data from the US, the UK and Korea. Second, by extending structural VAR identification into a more general context, we identify the positive and negative inflation and the complement and substitution effects between the two asset returns—stocks and housing—as well as the supply and demand shocks. Based on complement and substitution identification, we find that the two assets are weak complements rather than substitutes. Third, using the general identification method, we find that there are two regimes with positive and negative asset returns and inflation relations for all three countries, and the two regime relations are found not only for the stock return–inflation relation but also for the housing return–inflation relation. Fourth, we confirm the findings in Hess and Lee (1999)—that the identification of aggregate supply and aggregate demand shocks can explain a negative stock return–inflation. However, we find that this cannot explain the negative relation between housing returns and inflation. Fifth, we find that business cycles are a factor in the relations. In particular, the negative relation is mainly due to the relation in recession periods rather than the relation in expansion periods for all three countries. Sixth, based on causality tests, we find that housing returns Granger- cause inflation and the dynamic net effect of housing returns on inflation is significantly positive for all three countries, which suggests a potential wealth effect. Seventh, while we find that both the stock return–inflation relation and the housing return–inflation relation are negative for all three countries in short run, housing tends to preserve their real value against inflation in the long run for all three countries, but stocks are an inflation hedge in the long run only for the US and the UK. Finally, based on our dynamic framework, we examine the empirical validity of the inflation illusion hypothesis, which has received renewed attention recently.

For our empirical analyses, in addition to the two major economies—the US and the UK—we include Korea partly because it was one of the representative developing countries hosting the G-20 meeting in 2010 and partly because residential housing in Korea constitutes the largest portion of household wealth in the world.1 According to a recent analysis, the value of primary residence (in the case of owner-occupants) and renters' money deposit (in the case of renters) in Korea was about five times financial assets and represented 83% of the total household wealth in 2001 (Kim, 2004; Yoo, 2004). Hence it would be interesting to see whether developing countries such as Korea show different empirical relations from the US and the UK.

This paper is organized as follows. In Section 'Related Literature', we introduce and review various hypotheses that are used to explain the relation between the two types of asset returns (i.e. stock returns and housing returns) and inflation. In Section 'Preliminary Empirical Relations', as our motivation, we provide brief preliminary empirical relations between the two types of asset returns and inflation. In Section 'Identification Based on a Bivariate Time-Series Representation', we provide our empirical method, a VAR model, to provide new insights into the relation. Empirical results are presented in Section 'Empirical Results and Implications'. Further analyses introducing business cycle effects and dynamic causal relation analyses are presented in Section 'Further Analyses', and we conclude the paper in Section 'Summary and Concluding Remarks'.

2. Related Literature

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

Analyses of the inflation hedging properties of stocks have produced anomalous results, with stocks offering a perverse hedge against inflation. To explain the observed negative stock return–inflation relation, Modigliani and Cohn (1979) propose the inflation illusion hypothesis, which explains that stock market investors are subject to inflation illusion so that when inflation rises, they tend to discount expected future earnings and dividends more heavily by using higher nominal interest rates. As a result, stock prices are undervalued when inflation is high and they become overvalued when inflation falls. According to the proxy hypothesis proposed by Fama (1981, 1983), high expected inflation proxies for slower expected economic growth. That is, a positive association between stock returns and real activity, combined with a negative association between inflation and real activity based on a money demand model, leads to spurious negative relations between stock returns and inflation. The proxy hypothesis has been extended by Geske and Roll (1983), who emphasize the link between monetization of government deficits and a fiscal and monetary policy.2 Brandt and Wang (2003) propose the time-varying risk aversion hypothesis, which maintains that inflation makes investors more risk averse, driving up the equity premium and thus the real discount rate.

Several studies show that there are two factors affecting the stock return–inflation relation: supply shocks and demand shocks. They show that the stock return–inflation relation depends on the source of inflation (e.g. Geske and Roll, 1983; Danthine and Donaldson, 1986; Lee, 1989). Stock returns can be negatively correlated with inflation, especially when the source of inflation is related to non-monetary factors such as real output shocks (e.g. Danthine and Donaldson, 1986; Stulz, 1986; Marshall, 1992; Bakshi and Chen, 1996).3 Hess and Lee (1999) propose the two-regime hypothesis by applying a structural bivariate VAR model and identifying aggregate demand and supply shocks that drive the stock return–inflation relation.4

Recently, Modigliani and Cohn's (1979) inflation illusion hypothesis has received renewed interest. Ritter and Warr (2002) find that the bull market that began in 1982 was due in part to equities being undervalued, whose cause is cognitive valuation errors of levered stocks in the presence of inflation and mistakes in the use of nominal and real capitalization rates. Campbell and Vuolteenaho (2004) revisit the issue of the stock price–inflation relation based on a time-series decomposition of the loglinear dividend yield model and provide strong support for Modigliani and Cohn's (1979) inflation illusion hypothesis.5 Cohen et al. (2005) present cross-sectional evidence supporting Modigliani and Cohn's hypothesis by simultaneously examining the future returns of Treasury bills, safe stocks and risky stocks to distinguish inflation illusion from any change in the attitudes of investors toward risk.

However, some studies cast doubt on the empirical validity of the inflation illusion hypothesis. Thomas and Zhang (2007) find that the results in Campbell and Vuolteenaho (2004) are sensitive to model specifications: the sample period studied, the proxy used for expected inflation, the use of dividends versus earnings yields and the VAR methodology employed. They claim that it is premature to conclude that the market confuses real and nominal growth rates and suffers from massive inflation illusion. Chen et al. (2009) find that the money illusion hypothesis of Modigliani and Cohn (1979) may explain the level, but not the volatility, of mispricing in the US market (see also Wei and Joutz, 2009).6

Economists think that real estate should provide a good inflation hedge. However, empirical results have been mixed. The balance of evidence from the private commercial real estate market points to property acting as only a partial inflation hedge. For US markets, Hartzell et al. (1987) analyze appraisal-based Commercial Real Estate Fund returns and find coefficients in excess of one for both expected and unexpected inflation. However, using owner-occupied homes, income-producing real estate and Real Estate Investment Trust (REIT), Gyourko and Linneman (1988) obtain mixed results.7 For other countries, Newell (1996) finds that Australian private real estate only partially hedges both expected and unexpected inflation. Limmack and Ward (1988) report that UK property sectors hedge expected, but not unexpected, inflation. Hoesli et al. (1997) examine UK real estate, and they obtain coefficients significantly less than one, with those relating to unexpected inflation being negatively signed. Barber et al. (1997) use a structural time series approach and find that UK real estate provides, at best, a weak hedge against changes in underlying inflation but no hedge against shocks that change price levels or against irregular price fluctuations. Stevenson and Murray (1999) examine the inflation hedging ability of the commercial real estate sector in the Republic of Ireland and do not find evidence to support the hypothesis that real estate acts as an effective inflation hedge over the period 1985–1996. Using Hong Kong data for 1998–2006, Glascock et al. (2008) find that real estate assets in Hong Kong are not a good hedge against inflation, in both the short term and long term.

Several studies focus on the relation between securitized real estate market returns and inflation because it is difficult to obtain high-quality, high-frequency real estate return data and appraisal-based returns may not be very reliable. Regarding US REITs, studies tend to find the lack of a positive relation between inflation and REIT returns with coefficients that are negative or non-significant. Examples include Brueggeman et al. (1984), Gyourko and Linneman (1988), Goebel and Kim (1989), Murphy and Kleiman (1989), Titman and Warga (1986), Park et al. (1990) and Larsen and McQueen (1995).8 As in most prior research, Chatrath and Liang (1998) also find no evidence that REIT returns are positively related to temporary or permanent components of inflation measures. For other countries, Hoesli et al. (1997) do not find evidence that UK property companies hedge components of inflation. Liu et al. (1997) investigate whether real estate securities continue to act as a perverse inflation hedge in foreign countries given security design differences. They find that real estate securities provide a worse hedge against inflation relative to common stocks in some countries and are comparable to stocks in other countries.

Overall, prior studies tend to find mixed results for the relation between real estate returns and inflation and that real estate returns are only a partial hedge against inflation. The findings vary across periods and countries, depending on the components of returns and conditioning variables that are included in the models. This may be, to some extent, due to the lack of a reliable, high-quality, comprehensive, real estate performance measure and to potential structural breaks in sample periods. The findings suggest that private real estate acts as a partial hedge against some components of inflation, while public, securitized real estate seems to exhibit the negative relationships found in common stock markets (see also Hoesli et al., 2008).9

As for testing the hypotheses for the relation between housing market returns and inflation, Darrat and Glascock (1989) explicitly address the proxy hypothesis, modeling monetary policy and financial variables, in particular, movements in federal budget deficits. They argue that budget deficits are linked to increases in uncertainty, equity premia and bond returns, and hence, to real estate returns. Their property data set contains a mixture of REITs, building firms and taxable real estate investors.10 In addition to the application of the proxy hypothesis, the inflation illusion hypothesis has been applied recently Brunnermeier and Julliard (2008) examine potential mispricing in the housing market, focusing on the price–rent ratio. Specifically, regarding the role of money illusion, Brunnermeier and Julliard (2008) state: “For example, people who simply base the decision of whether to rent or buy a house on a comparison between monthly rent and monthly payment of a fixed nominal interest rate mortgage suffer from money illusion. They mistakenly assume that real and nominal interest rates move in lockstep. Hence, they wrongly attribute a decrease in inflation to a decline in the real interest rate and consequently underestimate the real cost of future mortgage payments. Therefore, they cause an upward pressure on housing prices when inflation declines.” Piazzesi and Schneider (2007) consider asset pricing in a general equilibrium model in which some, but not all, agents suffer from inflation illusion. Illusionary investors mistake changes in nominal interest rates for changes in real rates, while smart investors understand the Fisher (1930) equation. The presence of smart investors ensures that the equilibrium nominal interest rate moves with expected inflation. The model also predicts a non-monotonic relationship between the price-to-rent ratio on housing and nominal interest rates.

3. Preliminary Empirical Relations

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

For our analysis, we use data from the US, the UK and Korea. For stock market price indexes, we use the MSCI USA, the MSCI UK and the KOREA SE COMPOSITE (KOSPI). For housing price indexes, we use quarterly residential property indexes, specifically, the Ofheo House Price Index from the Office of Federal Housing Enterprise for the US; the Nationwide House Price Index of all properties from the Nationwide Anglia Building Society for the UK; and the Nationwide Price Index of all apartments from Kookmin Bank for Korea. The consumer price indexes (CPIs) (not seasonally adjusted) for all countries are originally from the International Monetary Fund's International Financial Statistics. The data are quarterly and the sample periods are January 1975 to April 2008 for the US; January 1982 to March 2008 for the UK; and January 1987 to April 2008 for Korea. Except for the Korean housing price index, the data are obtained from Datastream.

Real estate returns derive from both income and capital appreciation. Here, we focus on capital appreciation returns (i.e. changes in the housing price index) partly because reliable rent indexes corresponding to housing price indexes are not readily available for these countries and because we want to be consistent with the treatment of stock market returns.

Table 1 shows regression coefficients and cross correlations between asset returns and inflation for the US, the UK and Korea. We report not only contemporaneous correlations but also cross correlations with one lag and one lead to allow for potential mismatches in timing in the compilation of the data. The regression for the US shows that while RSRs are weakly negatively related to inflation, real housing returns (RHRs) are strongly negatively related to inflation, which confirms the findings in previous studies. If asset returns are a perfect hedge against inflation, we expect the regression coefficient of nominal returns on inflation to be one, and that of real returns to be zero. Cross correlations also show that RSRs and RHRs are negatively correlated with inflation. A similar observation is made for the UK and Korea, while there is some variation in the magnitude of correlations in each country.

Table 1. Regressions and cross correlations
Dependent variableConstantINFR2 barCross-correlations with INF(tk)
−101
  1. SR, nominal stock return; RSR, real stock return; HR, nominal housing return; RHR, real housing return; INF, inflation rate.*** , ** and * denote significance at the 1%, 5% and 10% levels, respectively.

Panel A: The US
Sample period: February 1975 to April 2008
SR2.01400.0223−0.0075−0.05540.0024−0.0350
1.24640.0179    
HR1.10800.22680.02660.4090**0.1839**0.1222
9.76052.0836    
RSR2.0140−0.97770.0036−0.1174−0.1051−0.0971
1.2464−0.7873    
RHR1.1080−0.77320.2838−0.0525−0.5377**−0.2985**
9.7605−7.1018    
Panel B: The UK
Sample period: March 1982 to March 2008
SR2.2715−0.1039−0.00970.0014−0.0104−0.0899
2.0307−0.1402    
HR1.42620.46850.0097−0.05140.1390−0.1798**
3.95611.2657    
RSR2.2715−1.10390.0025−0.0005−0.1102−0.0912
2.0307−1.4893    
RHR1.4262−0.53150.0152−0.0567−0.1573**−0.1848**
3.9560−1.4356    
Panel C: Korea
Sample period: April 1987 to April 2008
SR4.4146−1.7246−0.0043−0.1974**−0.0882−0.3197***
1.1488−0.6686    
HR1.23170.2843−0.00600.1664*0.0781−0.1393
1.79910.4638    
RSR4.4146−2.72460.0072−0.2058**−0.1385−0.3275***
1.1488−1.0562    
RHR1.2317−0.71570.01520.1127−0.1934**−0.1881*
1.7991−1.1674    

4. Identification Based on a Bivariate Time-Series Representation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

4.1. A Bivariate Model: Under-Identification of the Model

In this section, we briefly discuss the structural VAR identification and introduce various alternative ways of identifying distinct disturbances in the asset return–inflation relation. Consider a 2 × 1 vector, Zt, consisting of real asset returns (e.g. RSRs or RHRs), Rt, and the rate of inflation, πt (or INFt), that is, Zt = [Rt, πt,]′. By the Wold theorem, Zt has the following bivariate moving average representation (BMAR):

  • display math(1)

where Rt = real asset returns (e.g. stock returns or housing returns); πt (or INFt) = inflation rate; et is a 2 × 1 vector of disturbances (or shocks) consisting of e1t and e2t; L is the lag operator (i.e. Lnxt = xt−n); Bij(L) for i, j = 1, 2 is a polynomial in the lag operator L (i.e. inline image; and the disturbances are orthonormalized, that is, Var(et) = I.

This representation implies that real asset returns (e.g. stock returns or housing returns) and inflation are driven by two types of disturbances (or shocks), e1t and e2t. The time paths of the dynamic effects of the two types of disturbances on real asset returns and inflation are implied by the coefficients of the polynomials inline image for i, j = 1, 2 and k = 1, 2, 3,…., that is, inline image measures the effect of ej on the i-th variable in k periods.

The BMAR model [i.e. estimates of B(L)] in equation (1) is derived by inverting a bivariate vector autoregression (BVAR). By estimating the following BVAR of Zt = [Rt, πt]′:

  • display math(2)

where A(L) = [Aij(L)] = [∑k aijk Lk−1] for i, j = 1, 2, ut = [u1t, u2t]′ = ZtE (Zt|Zts, s ≥ 1) with Var(ut) = Ω, we obtain estimates of A(L) and Ω. By inverting this BVAR of Zt, we derive a BMAR of Zt:

  • display math(3)

where I is the identity matrix of rank 2.

Estimates of B(L) in equation (1) can be obtained by noticing that:

  • display math(4)

and that:

  • display math(5)

Using equations (4), (5) implies that:

  • display math(6)

Since estimates of A(L) are obtained by estimates of the BVAR in equation (2), to calculate B(L), we only need an estimate of B0. This can be obtained by taking the variance of each side of equation (4):

  • display math(7)

Here we obtain three restrictions for the four elements of B0: b110, b120, b210, b220. This implies that we need an additional restriction for the bivariate model to achieve just-identification.

4.2. Various Identifying Restrictions

4.2.1. The Positive and Negative Inflation Identification

In this paper, we consider three ways of identifying the two distinct types of shocks, depending on the focus of the analysis. The first method is to identify the two types of shocks as positive and negative shocks to inflation. This is to examine whether both positive and negative inflation shocks drive a negative asset return–inflation relation or if they drive two distinct (i.e. positive and negative) relations.11 According to the inflation illusion hypothesis, stock prices are undervalued when inflation is high and become overvalued when inflation falls. Therefore, the inflation illusion hypothesis anticipates that both positive and negative inflation shocks drive only a negative asset return–inflation relation. However, the two regime hypothesis anticipates the two (i.e. positive and negative) asset return–inflation relations.

For this purpose, we define the BMAR model of Z1t = [πt, Rt]′ = B(L) et, where coefficient b1j0 measures the effect of the j-th shock on the first variable (i.e. inflation in this model) contemporaneously (i.e. k = 0). We identify a positive inflation shock et+ and a negative inflation shock et by imposing an identifying restriction that the two shocks affect inflation with the same magnitude but with an opposite sign:

  • display math(8)

on the BMAR model of Z1t = [πt, Rt]′ = B(L) et.12 Given that we focus on the identification of a positive inflation shock et+ and a negative inflation shock et, we define the vector Z1t = [πt, Rt]′ with inflation rate πt as the first variable.

4.2.2. Permanent and Temporary Restrictions

The second method is to identify the two types of shocks as permanent and temporary shocks. This is motivated by various theoretical studies mentioned in Section 'Related Literature' and the findings in Hess and Lee (1999). The latter provide a theoretical model showing that there are aggregate supply and aggregate demand shocks that affect the relation between stock returns and inflation. To empirically identify the two shocks, following Blanchard and Quah (1989), Hess and Lee (1999) use a structural VAR identification method by relating permanent and temporary disturbances to aggregate supply and aggregate demand shocks, respectively. We extend this identification method to examine whether the permanent and temporary shocks provide new insights into the housing return–inflation relation in addition to the stock return–inflation relation.

When we define the BMAR model of Z2t = [Rt, πt]′ = B(L) et, coefficient b12k measures the effect of the second shock (e.g. demand shock) on the first variable (i.e. asset return Rt) after k periods. Therefore, the identifying restriction for the temporary shocks (say e2) is represented by the restriction that the coefficients in B12(L) add up to zero:

  • display math(9)

which implies that the cumulative effect of e2 on Rt is zero.

Given the relation between the MAR coefficients B(L) and VAR coefficients A(L) in equation (6), the restriction on the MAR coefficients in equation (9) is implemented by imposing the following restriction on the VAR coefficients:

  • display math(10)

This provides an additional restriction on the relation between the BMAR coefficients b120 and b220 given the estimates of the bivariate VAR, A12(1) and A22(1).

4.2.3. The Complement and Substitution Effect Identification

The third identifying restriction we consider is to determine whether the two asset returns, stock returns and housing returns, are characterized by either a complement relation or a substitution relation over time. In asset allocation, stocks and real estate, together with bonds, are among the major asset classes. The price of real estate may covary with stock prices because the prices of these assets are driven by common underlying economic factors such as the discount factor. However, real estate may serve as a hedge during periods of volatile stock markets, and investors distribute their investments among various classes of assets. Therefore, stocks and real estate can be either complements or substitutes, and the relation between stocks and real estate can provide a new insight into the relation between asset returns and inflation.

For this, we consider a BMAR model of two asset returns: Z3t = [SRt, HRt]′ = B(L) et, where SRt and HRt denote stock returns and housing returns, respectively. Here, we identify the substitution effect and its disturbances, which we denote as ets, by imposing the following restriction: by definition, the substitution effect disturbance affects stock and housing returns in an opposite manner. In practice, however, we cannot impose a general inequality restriction because it is too broad to be implemented, and the opposite movement of stock and housing returns need not occur in the same period. As such, we take an alternative, more flexible approach by assuming that its long-term effect on stock returns is the negative of its long-term effect on housing returns. That is, we identify the substitution disturbance ets as having effects on stock returns and housing returns in such a way that the sum of the long-term effects on the two returns over time adds up to zero. Given that the substitution effect is measured in a flexible time span (i.e. over time), it is also related to the intertemporal substitution. On the other hand, in the absence of such a restriction, the complement (or income) effect disturbance, ety, is allowed to affect both returns in the same direction.13

Since MAR coefficients b12k and b22k measure the effect of the second shock on stock returns (SRt) and housing returns (HRt) after k periods, respectively, the above restriction on the substitution disturbance is represented by the restriction that the coefficients in B12(L) and B22(L) add up to zero:

  • display math(11)

where Bij(L)|L=1 = Bij(1) = ∑k bijk represents the cumulative effect of the j-th disturbance on the i-th variable over time. With this restriction imposed on the BMAR Z3t = [SRt, HRt]′ = B(L)et, we now identify the second shock as the substitution shock, ets, and the remaining shock as the complement (or income) shock, ety.

Given the relation between the MAR and VAR coefficients in equation (6), B(L) = [IA(L)L]−1 B0, the restriction on the MAR coefficients in equation (11) is implemented by imposing the following restriction on the VAR coefficients:

  • display math(12)

This provides an additional restriction on the relation between the BMAR coefficients b120 and b220 given estimates of the BVAR, A11(1), A12(1), A21(1) and A22(1).

4.3. A Measure of the Relative Importance of Each Effect

Although we identify the two distinct shocks and components of asset returns and inflation (or two asset returns) that drive the relation in two directions, what we observe in the economy is only one relation, which can be thought of as their net effect. For example, while we identify that positive inflation shocks drive a negative asset return–inflation relation and negative inflation shocks drive a positive asset return–inflation relation, we observe only a negative relation in the economy and we understand this as a net effect of the interaction between the two types of shocks based on their relative importance. That is, we claim that the observed sign of the correlation depends on the relative importance of each effect. Therefore, we need to establish a measure of the relative importance of each effect.

Such a measure would be based on the fraction of (forecast error) variance in each variable explained by each type of disturbance. For example,

  • display math(13)

measures the fraction of the forecast error variance in the first variable in the BMAR (e.g. asset returns) explained by the first type of disturbance because the MAR coefficient b1jk measures the effect of e1 (for j = 1) or e2 (for j = 2) on the first variable in the BMAR Zt. Therefore,

  • display math(14)

will measure the relative importance of the first type of disturbance that explains variances in the two variables in Zt. Similarly,

  • display math(15)

will measure the relative importance of the second type of disturbance that explains variances in the two variables in Zt.14

5. Empirical Results and Implications

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

5.1. Bivariate Model Identification of Positive and Negative Shocks to Inflation

As discussed above, the motivation for the positive and negative inflation shocks is to examine the presence of the two regimes that drive both positive and negative relations between asset returns and inflation. If we find that both positive and negative inflations drive only a negative relation between asset returns and inflation, this provides evidence for the inflation illusion hypothesis.

As discussed in Section 'The Positive and Negative Inflation Identification', we implement the identification of positive and negative inflation (INF) shocks on the BMAR model of Z1t = [πt, Rt]′ = B(L) et by imposing the restriction b110 + b120 = 0 in equation (8). The estimation results are presented in Table 2. Figures 1, 2 and 3 in Panels A, B and C of Table 2 present the dynamic effects of positive and negative inflation on inflation and stock returns and housing returns for the US, the UK and Korea, respectively.

Table 2. Bivariate model identification of positive and negative shocksThumbnail image of

For the US, we observe from Figure 1.1 in Panel A.1 that positive and negative shocks to inflation have an asymmetric dynamic effect of the same magnitude initially on inflation as expected from the identification restriction b110 + b120 = 0. Figure 1.2 shows that both positive and negative inflation shocks have negative effects on stock returns initially. This implies that the positive inflation shock drives a negative contemporaneous correlation between RSRs and INF, while the negative inflation shock drives a positive contemporaneous correlation. Further, we find in Figure 1.2 that the effect of the positive inflation shock on stock returns is stronger than that of the negative shock in absolute value, which implies that the positive inflation shock dominates and we observe a negative correlation between stock returns and inflation as a net effect. This is confirmed in Table 2.1, which shows that initially the positive and negative inflation shocks explain 68% and 32% of one-quarter forecast error variance of stock returns, respectively. This shows that positive inflation shocks that drive a negative contemporaneous correlation dominate negative inflation shocks.

These findings indicate, among other things, that there are two distinct forces that drive positive and negative relations between stock returns and inflation for the US sample period. Further, the positive inflation shock that drives a negative correlation dominates, and as a result we observe a negative correlation. This implies that the inflation illusion hypothesis that anticipates only a negative relation between stock returns and inflation isn't easily compatible with this finding.

Now we turn to the relation between housing returns and inflation for the US. We observe from Figure 1.3 in Panel A.2 of Table 2 that positive and negative shocks to inflation have an asymmetric dynamic effect of the same magnitude initially on inflation as expected from the identification restriction b110 + b120 = 0. Figure 1.4 shows that both positive and negative inflation shocks have negative effects on housing returns initially. This implies that the positive inflation shock drives a negative contemporaneous correlation between RHR and INF, while the negative inflation shock drives a positive correlation. Further, we find that the effect of the positive inflation shock on housing returns is dominantly stronger than that of the negative shock in absolute value, which implies that the positive inflation shock dominates and we observe a negative correlation between housing returns and inflation as a net effect. This is confirmed in Table 2.2, which shows that initially the positive and negative inflation shocks explain 99.6% and 0.4% of one-quarter forecast error variance of housing returns, respectively.

As in the stock return–inflation relation, these findings indicate that there are two distinct forces that drive positive and negative relations between housing returns and inflation for the US. Further, the positive inflation shock that drives a negative correlation dominates, and as a result we observe a negative correlation. This implies that the inflation illusion hypothesis that anticipates only a negative relation between housing returns and inflation isn't easily compatible with this finding.

For the UK, we have a very similar finding. In Figure 2.1 in Panel B.1, we observe asymmetric positive and negative inflation shocks of the same initial magnitude by construction. In Figure 2.2, we observe that both inflation shocks have negative effects on UK stock returns, and the positive inflation shock that drives a negative relation between stock returns and inflation dominates the negative inflation shock that drives a positive relation. The dominance of the positive inflation is confirmed in Table 2.3, which shows that initially the positive and negative inflation shocks explain 64% and 36% of one-quarter forecast error variance of stock returns, respectively.

In Figure 2.3 in Panel B.2, we again observe asymmetric positive and negative inflation shocks of the same initial magnitude by construction. In Figure 2.4, we observe that both inflation shocks have negative effects on UK housing returns, and the positive inflation shock that drives a negative relation between housing returns and inflation dominates the negative inflation shock that drives a positive relation. Again, the dominance of positive inflation is confirmed in Table 2.4, which shows that initially the positive and negative inflation shocks explain 68% and 32% of one-quarter forecast error variance of housing returns, respectively.

For Korea, there is a very similar finding for the stock return–inflation relation and the housing return–inflation relation. For the three countries, there are some common findings. There are two distinct forces that drive positive and negative relations between asset returns (e.g. stock returns and housing returns) and inflation for the given sample periods. The positive inflation shock that drives a negative relation between asset returns and inflation dominates the negative inflation shock that drives a positive relation. As a result, we observe, as a net effect, a negative relation between stock returns (or housing returns) and inflation in each country for the sample period. This implies that the inflation illusion hypothesis that anticipates only a negative relation may have a hard time explaining these findings, and instead the two-regime hypothesis seems more appealing.

5.2. Identification of Permanent and Temporary Shocks

5.2.1. Bivariate Model Identification

As discussed in Section 'Permanent and Temporary Restrictions', we implement the identification of the permanent (e.g. aggregate supply) and temporary (e.g. aggregate demand) shocks on the bivariate model of Z2t = [Rt, πt]′ = B(L) et. The estimation results are presented in Table 3. Panel A shows the permanent/temporary decomposition results for RSR and INF, Z2t = [Rt, πt]′ = [RSR, INF]′, while Panel B shows the results for RHRs and INF, Z2t = [Rt, πt]′ = [RHR, INF]′ using US data from February 1976 to April 2008.

Table 3. Bivariate model identification of permanent and temporary shockThumbnail image of

For the sample period 1976–2008, we observe that, as in previous studies (e.g. Hess and Lee, 1999), permanent (e.g. aggregate supply) shocks drive a negative correlation between RSR and INF (see Figure 1.1 in Panel A), while temporary (e.g. aggregate demand) shocks drive a positive correlation (see Figure 1.2 in Panel A). Further, the permanent shocks are slightly more important than the temporary shocks [e.g. 102% (= 60% + 42%) versus 98% (= 40% + 58%) in the first quarter] in explaining RSR and INF.

When we replicate the analysis for the shorter sub-sample period of 1975–1999, excluding recent years (results not reported here to save space), we find qualitatively similar results: permanent (e.g. aggregate supply) shocks drive a negative correlation between RSR and INF, while temporary (e.g. aggregate demand) shocks drive a positive correlation. Further, for this sample period, the permanent shocks are more important than the temporary shocks in the first quarter (e.g. 115% versus 85%), and even in the long run the permanent shocks remain more important (e.g. 119% versus 81% in 6 years). This implies that in recent years, the temporary shocks, which drive a positive relation, become more important over time in the RSR and INF relation.

Now we turn to the housing return–inflation relation presented in Panel B of Table 3, Z2t = [Rt, πt]′ = [RHR, INF]′. For the sample period 1976–2008, unlike the case of the RSR–INF relation, both the permanent (e.g. aggregate supply) shocks and temporary (e.g. aggregate demand) shocks drive a negative correlation between RHR and INF. Further, for this sample period, the permanent shocks are slightly more important than the temporary shocks in the first quarter [e.g. 109% (= 20% + 89%) versus 91% (= 80% + 11%)], but in the long run the temporary shocks become more important (e.g. 68% versus 132% in 6 years). This implies, among other things, that the RHR and INF are strongly negatively related.

When we replicate the analysis for the shorter sub-sample period of 1975–1999, excluding recent years, we find qualitatively similar results in that both shocks drive a negative relation between RHR and INF; and the two shocks are equally important in a one-quarter horizon (e.g. 99.6% versus 100.3%) but in the long run, the temporary shocks dominate (e.g. 41% versus 159%). That is, in recent years, the temporary (e.g. aggregate demand) shocks, which also drive a negative relation in this case, become more important over time in the RHR–INF relation in the long horizon.

Hess and Lee (1999) provide a model that identifies the permanent and temporary components in stock returns and inflation as aggregate supply and aggregate demand components, respectively. However, it is not clear whether we can apply the same identifying restriction to the bivariate model of housing returns and inflation. This is partly because it is not clear whether the permanent and temporary shocks to housing returns represent economy-wide aggregate supply and demand shocks, respectively. To further examine this issue, we introduce a trivariate model consisting of RSR, INF and RHR in the next section, and we identify the permanent and temporary shocks with respect to stock market returns to see whether the shocks can explain the relation between housing returns and inflation.15

5.2.2. Trivariate Model Identification

Specifically, we consider the following trivariate model of Zt = [RSRt, INFt, RHRt]′:

  • display math(16)

where RSRt is real stock return, INFt is inflation rate, and RHRt is real housing return. For identification, we impose the following restrictions:

  • display math(17)

With these restrictions, the model identifies inline image and inline image as permanent, temporary and housing shocks, respectively. That is, the trivariate model identifies inline image and inline image as permanent and temporary shocks in the context of the bivariate model of stock returns and inflation, and inline image as the housing market-specific shocks that are not related to stock market and inflation shocks. As a result, B33(L) eth is part of RHR that is not related to RSR and INF.

The estimation results for the US are presented in Panel A of Table 4. We observe that the permanent (e.g. aggregate supply) shock ep drives a negative RSR–INF relation in Figure 1.1, and the temporary (e.g. aggregate demand) shock et drives a positive RSR–INF relation in Figure 1.2, as in the bivariate model discussed above. This finding is consistent with that of Hess and Lee (1999). However, both the permanent (e.g. aggregate supply) shock ep and the temporary (e.g. aggregate demand) shock et drive a negative RHR–INF relation as in the bivariate model. Further, we find that about 40–45% of the forecast error variance of RHR is explained by its own innovation eth over horizons, which is quite substantial.

Table 4. Trivariate model identification of permanent and temporary shocks to RSRThumbnail image of

Overall, we find that there are two distinct types of shocks driving the RSR–INF relation, but we do not find two distinct shocks driving the RHR–INF relation based on permanent and temporary identification. So, this VAR identification result suggests that the inflation illusion hypothesis, which anticipates only a negative relation between asset returns and inflation, is inconsistent with the RSR–INF relation but can be possibly compatible with the RHR–INF relation.

However, this finding may not be fully compatible with the inflation illusion hypothesis. With a positive permanent shock (e.g. aggregate supply shock), output increases and inflation declines, and both RSR and RHR increase in Figure 1.1 of Panel A so we don't need inflation illusion for this relation. However, with a positive temporary (e.g. aggregate demand or specifically monetary) shock, output increases and inflation increases, but higher inflation does not push real interest rates high enough to reduce RSR due to an inflation illusion. However, it does lead real interest rates high enough to decrease RHR due to an inflation illusion (see Figure 1.2 of Panel A). Again, we may need some asymmetric inflation illusion for the stock market and the housing market, or we need a third factor to explain the negative INF–RHR relation.

However, for the UK we see somewhat different results. In Panel B of Table 4, we observe that permanent shock ep drives a negative RSR–INF relation in Figure 2.1, and the temporary shock et also drives a negative RSR–INF relation in Figure 2.2. This finding is not consistent with either the findings in Hess and Lee (1999) or the case of the US. The permanent shock ep drives a negative RHR–INF relation in Figure 2.1, and the temporary shock et also drives a negative RHR–INF relation in Figure 2.2. These findings imply that both permanent and temporary shocks drive a negative relation between asset returns and inflation for the UK, although we find in the previous section that there are two types of shocks that drive positive and negative relations between asset return and inflation in the UK. This suggests that permanent and temporary identification does not provide new insight into the relation for the UK. Further, we find that about 56–92% of the forecast error variance of RHR is explained by its own innovation eth over horizons, which suggests that there is a third factor that can explain housing market returns other than stock market-related aggregate supply and aggregate demand shocks.

We implement a similar procedure for Korean data and find results very similar to those of the US. In Panel C of Table 4, we observe that permanent shock ep drives a negative RSR–INF relation in Figure 3.1, and temporary shock et drives a positive RSR–INF relation in Figure 3.2. Again, this finding is consistent with the findings in Hess and Lee (1999), in that aggregate supply shock (permanent shock) drives a negative RSR–INF relation, and aggregate demand shock (temporary shock) drives a positive RSR–INF relation.

However, as in the case of the US, both ep (e.g. aggregate supply shock) and et (e.g. aggregate demand shock) drive a negative RHR–INF relation. Further, we find that about 70–86% of the forecast error variance of RHR is explained by its own innovation eth over horizons, which suggests that there is a third factor that can explain housing market returns other than stock market-related aggregate demand and aggregate supply shocks.

Overall, and as in previous studies, we find that permanent (e.g. aggregate supply) and temporary (e.g. aggregate demand) shock identification helps provide insights into the stock return–inflation relation. However, this provides little insight into the housing return–inflation relation partly because both the permanent and temporary shocks drive a negative relation between housing returns and inflation. This may be related to the finding in Table 1 that housing returns and inflation are strongly negatively correlated. One way to understand this finding is that with an increased temporary shock (e.g. aggregate demand) and inflationary pressure, nominal interest rates increase and housing demand declines, resulting in the temporary shocks driving a negative housing return–inflation relation. In addition, there seems to be another factor that drives the RHR–INF relation, which warrants further analysis.

5.3. Stocks and Housing: Substitutes or Complements?

As discussed above, we investigate whether two asset classes—stocks and housing—are substitutes or complements to better understand the dynamic relation between the two assets. For this purpose, we consider a BMAR model of two assets: Z3t = [RSRt, RHRt]′ = B(L) et, where RSRt denotes (real) stock returns and RHRt denotes (real) housing returns.

As a preliminary step, we look at the regression coefficient of stock returns on housing returns and cross correlations between the two returns. The estimation results are reported in Table 5. Panel A shows that for the US, nominal stock returns (SR) and nominal housing returns (HR) are positively but insignificantly related by both the regression coefficient and correlations, and a similar observation is made for RSRs and RHRs.16 Similar positive but insignificant relations between the two returns are observed for the UK and Korea.

Table 5. Regressions and cross-correlations
Dependent variable (Y)ConstantIndependent variable (X)R2 barCross-correlations with X(t−k)
101
  1. SR, nominal stock return; RSR, real stock return; HR, nominal housing return; RHR, real housing return. ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively.

Panel A: The US
Sample period: February 1975 to April 2008
SR HR    
 1.26140.5765−0.00160.03200.07680.0645
 1.12120.9614    
RSR RHR    
 0.75470.78740.00740.09760.12170.0849
 1.11451.3041    
Panel B: The UK
Sample period: March 1982 to March 2008
SR HR    
 2.11820.0294−0.00970.11810.0099−0.0308
 1.98600.0824    
RSR RHR    
 1.14830.0848−0.00900.13510.02860.0015
 1.30750.2315    
Panel C: Korea
Sample period: April 1987 to April 2008
SR HR    
 2.06790.2450−0.01010.2283**0.04560.0447
 0.84790.3778    
RSR RHR    
 1.13650.4156−0.00600.2859***0.07820.1239
 0.55440.6737    

The identification and estimation results for the complement and substitution shocks for the US, the UK and Korea are presented in Table 6. We find that the complement shock drives a positive initial contemporaneous relation between RSR and RHR, while the substitution shock drives a negative initial contemporaneous relation for all three countries. We also find that, initially, the complement shock is relatively more important than the substitution shocks. The complement and substitution shocks initially (i.e. one-quarter ahead forecast error decomposition) explain 105% versus 95% for the US, 106% versus 94% for the UK, and 101% versus 99% for Korea. A relatively marginal difference between the two types of shocks in their explanatory power implies that the correlations between stock and housing returns are weakly positive. Overall, we find that stock returns and housing returns are weakly positively correlated and can be thought of as complementary rather than substitutes, although the relation is relatively weak.

Table 6. Bivariate model identification of complement and substitution shocksThumbnail image of

6. Further Analyses

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

6.1. Further Analyses With the Business Cycle Effect

In investigating the asset return–inflation relation, an interesting issue is whether the relation is time-varying, and particularly whether the relation is sensitive to the business cycle. As pointed out by Fama (1990), of the many possible forces that drive stock market movement, real economic activities, which are highly related to asset pricing factors and are represented by business cycles, can be an important factor in the asset return–inflation relation. In this section, we examine how business cycles affect the asset return–inflation relation over time. For this purpose, we use a dummy variable approach to control for business cycles. Using the NBER business cycle classification, we define a dummy variable, D, as 1 if the economy is expanding and 0 otherwise.

Specifically, we estimate the following regression:

  • display math(18)

where Rt denotes various asset returns (SR, HR, RSR, RHR).

We report the estimation results and simple statistics (e.g. mean and variance) for these variables in expansion and contraction (or recession) periods in Table 7. For the US in Panel A, during the recession period, inflation is higher and more volatile but stock returns and housing returns are lower and more volatile. In particular, both real returns (RSR and RHR) are negative during recessions. The housing return–inflation relation is quite sensitive to business cycles while the stock return–inflation relation remains just a little sensitive. Nominal housing returns are positively related to inflation during the expansion period; and RHRs are negatively related to inflation in both periods, but more strongly negatively related in recessions. Therefore, the negative housing return–inflation relation observed in Panel A of Table 1 seems mainly due to the recession period relation.

Table 7. Regressions and cross-correlations with business cycle
Panel A: The US
Sample period: February 1975 to April 2008
A.1 Simple statistics
VariableMean (variance)
Whole periodExpansion periodRecession period
INF1.0486 1.01351.2769
(0.7337)(0.6391)(3.6085)
SR2.03742.5193−1.0953
(62.838)(51.306)(132.978)
HR1.34581.49030.4069
(1.1160)(1.2321)(1.4205)
RSR0.98881.5058−2.3722
(63.5391)(52.3437)(130.072)
RHR0.29730.4768−0.8700
(1.5169)(1.0686)(3.7062)
A.2 Regression and correlation coefficients
Dependent variableConstant D t INF t (1−Dt)INFtR2 bar Cross-correlations with INF(tk)
−101
SR2.0617 −0.04880.1090 −0.0150 D t INF t 0.1040−0.0074−0.1052
(1.3846)(−0.0466)(0.0605) (1−Dt)INFt−0.1800**0.01090.0696
HR0.9186 0.5092 −0.1177 0.1380 D t INF t 0.4571***0.3813***0.3216**
(6.2927)(3.5064)(−0.7389) (1−Dt)INFt0.0147−0.1820**−0.1942**
RSR2.0616−1.0488 −0.8910−0.0038 D t INF t 0.0645−0.0753−0.1634**
(1.3845)(−1.0010)(−0.4949) (1−Dt)INFt−0.2142**−0.04890.0554
RHR0.9186 −0.4908 −1.1177 0.3658 D t INF t 0.1401*−0.1129−0.1048
(6.2927)(−3.3794)(−7.016) (1−Dt)INFt−0.2151**−0.5429***−0.2561***
SR1 and HR1     −0.04350.0553−0.0195
SR0 and HR0     0.11030.10450.3684***
RSR1 and RHR1     −0.08610.11730.0218
RSR0 and RHR0     0.2715***0.05130.0724
Panel B The UK
Sample period: April 1982 to March 2008
B.1 Simple statistics
VariableMean (variance)
Whole periodExpansion periodRecession period
INF0.9465 0.94830.9294
 (0.6557)(0.7674)(1.2148)
SR2.17312.6091 −1.9253
 (64.9644)(58.8038)(113.705)
HR1.86972.1322−0.5983
 (7.4481)(6.8101)(11.1172)
RSR1.22671.6609−2.8548
 (65.7564)(59.0936)(119.7319)
RHR0.92321.1839−1.5277
 (7.4893)(6.2868)(15.4922)
B.2 Regression and correlation coefficients
Dependent variableConstant D t π t (1−Dt) πtR2 bar Cross-correlations with πt(t−k)
SR2.3961 0.1276 −3.7178 0.0069 D t INF t 0.09850.0560−0.0671
(2.1594)(0.1761)(−1.3490) (1−Dt)INFt−0.2368**−0.1612*−0.0497
HR1.5237 0.6497 −2.3592 0.1418 D t INF t 0.07450.2785***−0.0562
(4.0837)(1.6244)(−3.2362) (1−Dt)INFt−0.3034***−0.3493***−0.2889***
RSR2.3960 −0.8724 −4.7178 0.0188 D t INF t 0.1059−0.0356−0.0682
(2.1594)(−1.2043)(−1.7118) (1−Dt)INFt−0.2591***−0.1745*−0.0500
RHR1.5237 −0.3503 −3.3592 0.1465 D t INF t 0.09790.0074−0.0606
(4.0837)(−0.8760)(−4.6079) (1−Dt)INFt−0.3729***−0.3905***−2.2900***
SR1 and HR1     0.0791−0.0567−0.0434
SR0 and HR0     0.2317**0.2185**−0.2077**
RSR1 and RHR1     0.0687−0.0649−0.0704
RSR0 and RHR0     0.3475***0.3012***−0.1271
Panel C Korea
Sample period: January 1988 to April 2008
C.1 Simple statistics
VariableMean (variance)
Whole periodExpansion periodRecession period
INF1.13971.04031.2508
(0.8765)(0.9054)(2.6279)
SR2.44912.7731−1.6126
(335.1926)(300.9269)(399.5826)
HR1.55581.24613.0995
(11.6180)(11.2730)(14.8527)
RSR1.30941.7328−2.8635
(339.0922)(302.6754)(417.4064)
RHR0.41610.20581.8487
(11.9960)(11.6301)(8.4593)
C.2 Regression and correlation coefficients
Dependent variableConstant D t π t (1−Dt) πtR2 bar Cross-correlations with πt(t−k)
  1. Dt = 1 for expansion period, and Dt = 0 for contraction period; SR1 (RSR1), nominal (real) stock return in expansion; SR0 (RSR0), nominal (real) stock return in recession; HR1 (RHR1), nominal (real) housing return in expansion; HR0 (RHR0), nominal (real) housing return in recession; Total obs. = 135; Expansion: 117 obs. (86.7%); contraction 18 obs. (13.3%). ***, ** and * denote significance at the 1%, 5% and 10% levels, respectively. t-stat is given below.

SR4.1843−1.0502 −4.6648 −0.0054 D t INF t −0.1830*−0.0123−0.2548**
(1.1001)(−0.3946)(−1.8798) (1−Dt)INFt−0.0265−0.1272−0.1120
HR1.3021 0.0784 1.1822 0.0119 D t INF t 0.0639−0.0344−0.1882*
(1.9473)(0.1206)(3.0282) (1−Dt)INFt0.1725*0.1878*0.0794
RSR4.1843−2.0502 −5.6648 0.0061 D t INF t −0.1869*−0.0539−0.2602**
(1.1001)(−0.7704)(−2.2828) (1−Dt)INFt−0.0341−0.1423−0.1161
RHR1.3020−0.92150.1822 0.0430 D t INF t 0.0364−0.2555**−0.2218**
(1.9473)(−1.4183)(0.4666) (1−Dt)INFt0.12830.10040.0533
SR1 and HR1     0.1820*0.06620.0263
SR0 and HR0     0.0441−0.00790.3301***
RSR1 and RHR1     0.2514**0.08280.0882
RSR0 and RHR0     −0.03210.08600.4536***

For the UK, in Panel B of Table 7, during the recession period, inflation is somewhat lower and more volatile, and stock returns and housing returns are lower (negative) and more volatile. Unlike the US, both the stock return–inflation relation and the housing return–inflation relation are sensitive to business cycles. Both returns are strongly negatively related to inflation in recessions. This implies that during recessions, while inflation rate changes little, stock markets and housing markets decline substantially, resulting in a strong negative relation between returns and inflation. Therefore, the negative asset return–inflation relation in the UK, observed in Panel B of Table 1, seems mainly due also to the recession period relation.

For Korea, as seen in Panel C of Table 7, during the recession period, inflation is higher and more volatile, as in the US case. However, stock returns are higher in the expansion period but housing returns are higher in the recession period. In particular, stock returns are negative while housing returns remain positive during recessions. As a result, during recession periods, stock returns are negatively related to inflation, while housing returns are not. Therefore, the negative stock return–inflation relation in Korea observed in Panel C of Table 1 seems mainly due to the recession period relation. Overall, we find that the negative asset return–inflation relations for the sample period of the three countries are primarily due to the relations in recession periods rather than periods of expansion, except for the housing return–inflation relation in Korea.

We also look at correlations between the two asset returns to see whether a weak positive correlation between the two asset returns is sensitive to business cycles. For the US, stock and housing returns tend to move more strongly together in recession periods than in expansion periods. Therefore, a positive correlation between the two returns seems mainly due to the relation in recession periods. A similar observation is made for the UK. However, we don't find a necessarily stronger correlation in recession periods for Korea.17

6.2. Further Analyses Based on the Causal Relation Tests

To further examine dynamic relations between asset returns and inflation, we investigate dynamic causal relations between asset returns and inflation and between the two asset returns (stock returns and housing returns). For this, we use the Granger-causality test based on the following trivariate VARs with k lags:

  • display math(19)

where RSRt is (real) stock return, πt is inflation rate, and RHRt is (real) housing return. In the stock return equation, inflation Granger-causes stock return if the null hypothesis that lagged coefficients λ1ks (= 1, 2, …, K) are zero is rejected. Similarly, housing return Granger-causes stock return if the null hypothesis that lagged coefficients γ1ks (= 1, 2, …, K) are zero is rejected. In the inflation equation, stock return Granger-causes inflation if the null hypothesis that lagged coefficients β2ks are zero is rejected. Similarly, housing return Granger-causes inflation if the null hypothesis that lagged coefficients γ2ks (= 1, 2, …, K) are zero is rejected.18

In addition to the Granger-causality tests, we also test the cumulative (net) effect of asset return on inflation and vice versa. In the stock return equation, if the null hypothesis that the sum of the lagged coefficients λ1ks, inline image, is zero is rejected, inflation has a cumulative (net) effect on the asset returns. The tests on the sum of the lagged coefficients allow us to identify the dynamic net effect of inflation on asset returns and vice versa.

The estimation results are presented in Table 8. Based on a preliminary test considering both the Akaike (1973) information criterion and the Schwarz (1978) information criterion, we choose lag number k = 4. The first two columns contain the results for the US. In the RSR regression, neither RHR nor inflation Granger-causes (or leads) RSR in the US. This is not surprising in that it is very hard to find any variable that Granger-causes stock returns as long as the market is efficient. In the RHR regression, we find that neither RSR nor inflation Granger-causes RHR. Therefore, we find that between stock returns and housing returns, there is no Granger-causal relation. In particular, stock returns, which represent an important leading economic indicator, do not have any additional predictive power for housing returns in the presence of lagged values of RHR. We do not find any significant evidence of inflation Granger-causing either stock or housing returns.

Table 8. Causality tests
 The USThe UKKorea
χ2(4) value (t-stat)Signif.χ2(4) value (t-stat)Signif.χ2(4) value (t-stat)Signif.
  1. RSR, real stock return; RHR, real housing return; INF, inflation rate.

RSR regression:
H0: RHR[RIGHTWARDS ARROW]RSR:
Each coeff. = 04.49390.34334.52320.339819.10290.0007
Sum of coeff. = 0−0.4715 0.6057−0.0524 0.9004−1.1820 0.0813
(−0.5162) (−0.1252) (−0.7429) 
H0: INF[RIGHTWARDS ARROW]RSR:
Each coeff. = 02.84050.58498.08980.088320.51630.0004
Sum of coeff. = 0−1.14080.31791.2604 0.4839−1.8802 0.6065
(−0.9987) (0.7001) (−0.5150) 
RHR regression:
H0: RSR[RIGHTWARDS ARROW]RHR:
Each coeff. = 02.20140.69887.34630.11876.51450.1639
Sum of coeff. = 00.0009 0.9704−0.0168 0.72630.0048 0.9129
(0.0371) (−0.3500) (0.1094) 
H0: INF[RIGHTWARDS ARROW]RHR:
Each coeff. = 07.76810.100520.10050.00055.13580.2736
Sum of coeff. = 0−0.2122 0.3175−0.8587 0.0406−0.4842 0.5548
(−0.9996) (−2.0478) (−0.5905) 
INF regression:
H0: RSR[RIGHTWARDS ARROW]INF:
Each coeff. = 06.03120.19684.46910.34625.11420.2758
Sum of coeff. = 00.0196 0.1579−0.0097 0.4752−0.01380.2007
(1.4121) (−0.7140) (−1.2794) 
H0: RHR[RIGHTWARDS ARROW]INF:
Each coeff. = 019.87690.000517.32790.001713.55430.0089
Sum of coeff. = 00.2961 0.00110.0847 0.00090.1019 0.0062
(3.2566) (3.3211) (2.7347) 

In the inflation regression, we find that housing returns (RHR) Granger-cause inflation and their net effect on inflation is positive. However, stock returns (RSR) do not Granger-cause inflation. That is, a higher housing return leads to a subsequent higher inflation. This suggests a potential housing wealth effect in that a higher housing price anticipates (or leads to) higher spending by households and higher inflation. This finding is consistent with the finding in Goodhart and Hofmann (2008), who also find that housing price movements do provide useful extra information on future inflation, with equity prices and the yield spread being somewhat less informative. The positive effect of housing returns on inflation seems at odds with the inflation illusion hypothesis because the hypothesis anticipates a negative relation between asset returns and inflation.

Overall, we find for the US that inflation does not Granger-cause either stock returns or housing returns. Instead, we find that housing returns (RHR) Granger-cause inflation and the effect is positive over time, which seems to be at odds with the prediction from the inflation illusion hypothesis, at least for the housing return–inflation relation. We do not find that stock returns Granger-cause inflation.

The second two columns contain the results for the UK. In the RSR regression, RHR does not Granger-cause RSR. However, inflation Granger-causes (or leads to) RSR in the UK, although its net effect on RSR is insignificantly positive. This is quite surprising in that inflation contains some information about future RSRs. In the RHR regression, RSR does not Granger-cause RHR. Therefore, we find that between stock returns and housing returns, there is no Granger-causal relation in the UK as in the US. However, inflation Granger-causes RHR and its net effect is negative. This finding seems compatible with the inflation illusion hypothesis in that current inflation anticipates future lower housing returns. Therefore, we find some evidence for the inflation illusion hypothesis for the housing market, but little evidence for the stock market in the UK.

In the inflation regression, we find that stock returns (RSR) do not Granger-cause inflation. However, housing returns (RHR) Granger-cause inflation, and their net effect on inflation is positive. Again this suggests a potential housing wealth effect in that higher housing prices anticipate (or lead to) higher spending by households and higher inflation. The positive effect of housing returns on inflation seems at odds with the inflation illusion hypothesis because the hypothesis anticipates a negative relation between asset returns and inflation. Overall, we find some evidence both in favor of and at odds with the inflation illusion hypothesis for the UK.

The last two columns contain the results for Korea. In the RSR regression, RHR Granger-causes RSR and its net effect is negative. Inflation also Granger-causes RSR, but its net effect is insignificantly negative. The finding that RSR is Granger-caused by both RHR and inflation is rather unusual from the market efficiency perspective. In particular, the finding that RHR has a negative effect on RSR indicates that although there is a mild complement effect between stocks and housing, as discussed above, there may be some intertemporal substitution effect over time in Korea. In the RHR regression, neither RSR nor inflation Granger-causes RHR. So in some sense, the housing market tends to be more informationally efficient than the stock market in Korea.

In the inflation regression, we find that stock returns (RSR) do not Granger-cause inflation. However, housing returns (RHR) Granger-cause inflation, and their net effect on inflation is positive. Again, this suggests a potential housing wealth effect in Korea. The positive effect of housing returns on inflation seems at odds with the inflation illusion hypothesis. Overall, we find little evidence for the inflation illusion hypothesis for Korea, and housing markets contain much information even for the stock market in Korea.

6.3. Long-Term Relation Between Asset Returns and Inflation

We have examined the short-term relation between two types of asset returns and inflation based on various empirical analyses. Another interesting question in the relation is whether the two assets have been a long-term inflation hedge. To answer this question, we plot stock index, housing index and CPI over the sample period for the three countries. Figures in Table 9 show that for the US, both stocks and housing were a hedge against inflation for the sample period 1975–2008, although for some sub-sample periods they were not. In particular, for the last 33 years, stocks were a better inflation hedge than housing. For the UK, both stocks and housing were a pretty good hedge against inflation for the sample period 1982–2008. In particular, by the end of the 26-year sample period, both turn out to be similarly good hedges.

Table 9. Long-term relation between asset returns and inflationThumbnail image of

Korea shows a somewhat different picture. For the sample period 1987–2008, housing turns out to be a hedge against inflation although for some sub-periods (e.g. around 2000 after the Asian financial crisis) it was not. However, stocks in Korea turn out not to be a good hedge against inflation by the end of the 21-year sample period and for a substantial part of the sub-periods.

Overall, both stocks and housing are relatively good hedges over the long term against inflation in both the US and the UK, but in Korea only housing outperforms inflation. The finding of the long-term inflation hedge is consistent with several previous studies. Boudoukh and Richardson (1993) find that the Fisher (1930) equation holds in the long run (5-year horizon) but not in the short run (see also Boudoukh et al., 1994).19 Using new and existing house prices, as well as the CPI (excluding housing costs) for the period 1968–2000, Anari and Kolari (2002) find that house prices are a stable inflation hedge in the long run. Goetzmann and Valaitis (2006) use a very comprehensive database of commercial real estate properties (the National Property Index compiled by the National Council of Real Estate Investment Fiduciaries, NCREIF), and they find evidence that real estate is a relatively good asset to use as an inflation hedge, particularly over the long term.

7. Summary and Concluding Remarks

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References

We have examined the relation between two types of assets—stocks and housing—and inflation for the US, the UK and Korea based on various dynamic analyses. Our findings can be summarized as follows. First, we find that both the stock return–inflation relation and the housing return–inflation relation are negative for all three countries. Business cycles are a factor in the relations. In particular, the negative relation is mainly due to the relation in recession periods rather than the relation in expansion periods for all three countries.

Second, based on the positive and negative inflation identification, there are two regimes with positive and negative asset returns and inflation relations for all three countries. The two-regime relation is found not only for the stock return–inflation relation but also for the housing return–inflation relation. This finding is at odds with the prediction from the inflation illusion hypothesis because the hypothesis anticipates only a negative relation for both positive inflation and negative inflation. This finding is more closely related to the two-regime hypothesis that assumes the presence of at least two forces that drive the asset return–inflation relation.

Third, and as found in previous studies, based on permanent/temporary shock identification with the interpretation of permanent shocks representing aggregate supply shocks and temporary shocks representing aggregate demand shocks, a negative stock return–inflation is found. However, both types of shocks drive a negative relation between housing returns and inflation. This is confirmed using both bivariate and trivariate model identification, which warrants further analysis to find factors driving the housing return–inflation relation. One explanation is to introduce the role of interest rates. Given the findings of the two regimes based on positive and negative inflation identification, this suggests that while permanent (e.g. aggregate supply) shocks drive a negative relation between asset returns and inflation relation, temporary shocks (e.g. aggregate demand shocks) may have two conflicting effects on asset returns because of the opposite effects from output and interest rates. For example, an increase in money supply leads to higher output and income, which in turn leads to a higher housing demand; but higher interest rates with inflation lead to a lower demand for housing. If the latter effect is greater than the former (i.e. if housing is more sensitive to interest rates than to income), we observe a negative housing return and inflation relation due to the temporary (e.g. aggregate demand) shocks.

Fourth, based on complement/substitution identification, the two assets are weak complements rather than substitutes. We further find that stock returns and housing returns tend to move more strongly together in recession periods than in expansion periods for the US and the UK.

Fifth, further analyses based on causality tests indicate that housing returns Granger-cause inflation and their dynamic net effect on inflation is significantly positive for all three countries. This result is at odds with the inflation illusion hypothesis, which anticipates inflation being related to negative returns; but this result is consistent with the housing wealth effect in that higher housing returns lead to higher spending with subsequent higher inflation.

Further, we note that the negative short-term relation between asset returns and inflation does not necessarily mean that the two assets are not an inflation hedge in the long run. We find that housing tends to preserve their real value against inflation in the long run for all three countries, but stocks are an inflation hedge in the long run only for the US and the UK. In future studies, we may need to introduce interest rates into the model to see their role in the relations.

Overall, we find only limited evidence in favor of the inflation illusion hypothesis, which is consistent with recent studies that cast doubt on the empirical validity of the hypothesis (e.g. Thomas and Zhang, 2007; Chen et al., 2009; Wei and Joutz, 2009). As discussed by Piazzesi and Schneider (2007), one way to understand these findings is to acknowledge that not all investors suffer from inflation illusion and as a result we may anticipate a non-monotonic relation between asset returns and inflation.

Notes
  1. 1

    The ratio of non-financial assets, which included dwellings and land, to household assets in 2007 was 57.5% for the US, 67.8% for the UK, 56.0% for Switzerland, 71.1% for Japan, 77.4% for Germany, 81.8 for France, 60.9% for Canada, and 83.7% for Korea. For details, see http://stats.oecd.org/. Our initial attempt to include Japan in our empirical analyses was hindered by the limited availability of housing return data. For Japan, only semi-annual housing return is available.

  2. 2

    It has been recognized that the observed negative stock return–inflation relation is not a direct causal relation but reflects other more fundamental relations in the economy (e.g. James et al., 1985; Kaul, 1987, 1990; Lee, 1992).

  3. 3

    Empirical studies further find a positive relation between stock returns and inflation in the pre-war period; in other words, the stock return–inflation relation is time-varying. To reconcile a positive pre-war and a negative post-war correlation, Kaul (1987, 1990) introduces the equilibrium process in the monetary sector in relation to real activity and Kaul and Seyhun (1990) emphasize supply shocks in the 1970s.

  4. 4

    See also Fama and Schwert (1977) and Lee (2003) for the inclusion of interest rates in the relation.

  5. 5

    Wei (2010) explores an explanation for the positive association between inflation and dividend yields with no inflation illusion involved. To achieve this goal, she builds a dynamic general equilibrium New-Keynesian model to study the relation between inflation and dividend yields.

  6. 6

    However, Chen et al. (2009) find that the stock resale option hypothesis of Scheinkman and Xiong (2003), which stems from heterogeneous beliefs about future dividend growth rates and short-sale constraints, can explain both the level and the volatility of mispricing.

  7. 7

    Other studies include Wurtzebach et al. (1991), Miles and McCue (1982), and Sirmans and Sirmans (1987).

  8. 8

    For example, Murphy and Kleiman (1989) run regressions both with and without the market index on the right-hand side and find observed significant negative coefficients for inflation sensitivity in the former but coefficients that are indistinguishable from zero in the latter.

  9. 9

    Hoesli et al. (2008) also point out that in researching the inflation hedging qualities of commercial (investment) real estate, a distinction needs to be made between private and public assets. In both cases, there are conceptual and data-related issues.

  10. 10

    Glascock et al. (2002) revisit this model using a Vector Error Correction Model, and they find significant negative coefficients for general and expected inflation and a negative but insignificant coefficient for unexpected inflation.

  11. 11

    Bharat and Wahab (2008) find an asymmetric relation between stock returns and inflation. By partitioning their sample period into subsamples of high and low inflation regimes, they find an inverse relation between stock returns and inflation forecasts during only low inflation periods, while a positive relation is detected through high inflation periods. In combination, results from both high and low inflation regimes suggest that stocks have delivered favorable inflation protection. While Bharat and Wahab (2008) find asymmetric relations using sub-sample periods and Wei and Joutz (2009) find evidence for structural instability over time focusing on the stock return–inflation relation, we identify the simultaneous presence of two forces that drive positive and negative relations between stock returns and inflation and housing returns and inflation for any sample period we consider. Then, we show that we only observe the net effect, usually the negative relation for our sample periods, depending on the relative importance of the two relations (or forces).

  12. 12

    As discussed above, in general we have the restriction B0 B0′ = Ω for the identification of the MAR coefficient, and to just-identify we add the restriction b110 + b120 = 0 on B0, that is, we obtain:

    • display math

    Specifically, we proceed as follows. First, we estimate inline image, where σ11 > 0, σ22 > 0 from the estimation of the bivariate VAR Z2t in equation (2). Second, from the restriction inline image, we obtain three equations:

    • display math(a)
    • display math(b)
    • display math(c)

    From (b) and (c), we find:

    • display math

    Then, we can calculate the remaining three elements of inline image inline image. Once coefficients of A(L) and B0 are estimated, we can obtain estimates of the MAR coefficients B(L) using the relation in equation (6): B(L) = [IA(L)L]−1 B0.

  13. 13

    The restriction on the substitution disturbance, ets, may help assure its opposite impact on the two types of returns. However, the question of how to guarantee that the complement (or income) effect disturbance will affect the two types of returns in the same direction remains. Here, we simply take the position that, in the absence of such a restriction, the complement effect disturbance, ety, is allowed to affect both market returns in the same direction. As such, it seems that there is no stringent restriction that guarantees the effects of the complement disturbance. As discussed in the text, the bivariate VAR model is under-identified, requiring only one additional restriction. If we impose an additional restriction on the complement effect disturbance, we have an over-identifying restriction, which needs to be tested for its empirical validity. Given this problem, we take the position in this paper that we impose a just-identifying restriction (on the substitution effect disturbance) and see whether the outcome will show that the complement effect disturbances affect both returns in the same direction.

  14. 14

    As an alternative measure, one may consider

    • display math

    to measure the relative importance of the first type of disturbance that explains variances in the two variables in the BMAR. The problem with such a measure is that it ignores the size of variances of the two variables in the system by mixing the two. For example, although the first type of disturbance explains 40% of variance in the first variable and 80% of variance in the second variable, the above measure may provide less than 50% of the relative importance (say the variance of the first variable is four times that of the second variable), which seems unreasonable.

  15. 15

    To conserve space, we do not report the bivariate model estimation and identification results for the UK and Korea. Instead, we report the results for the UK and Korea using a trivariate model estimation and identification in the next section.

  16. 16

    When we regress the housing price index (RHP or HP) on the stock price index (RSP or SP) for the US, we find a significant positive relation:

    • display math

    This indicates that housing prices tend to covary with stock prices over time in the US. A similar relation is found for the UK and Korea.

  17. 17

    One reason for the somewhat different result in business cycles for Korea is that Korea may have different business cycle periods than the US.

  18. 18

    We implement bivariate models to test Granger-causality among the variables. We find results very similar to those from the trivariate models. To save space, we do not report the bivariate test results.

  19. 19

    Boudoukh et al. (1994) show that the short-term failure of the Fisher equation is due to industry output cycles being correlated with expected inflation.

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  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Related Literature
  5. 3. Preliminary Empirical Relations
  6. 4. Identification Based on a Bivariate Time-Series Representation
  7. 5. Empirical Results and Implications
  8. 6. Further Analyses
  9. 7. Summary and Concluding Remarks
  10. References
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