North American Journal of Economics and Finance 34 (2015) 187–214 Contents lists available at ScienceDirect North American Journal of Economics and Finance Review What do scientists know about inflation hedging? Stephan Arnold, Benjamin R. Auer ∗ University of Leipzig, Department of Finance, Germany a r t i c l e i n f o Article history: Received 8 June 2015 Received in revised form 28 August 2015 Accepted 31 August 2015 Available online 30 September 2015 JEL classification: G10 G11 G15 Keywords: Hedge Inflation Stocks Gold Fixed income Real estate a b s t r a c t In this article, we give an overview of the state of scientific knowledge on inflation hedging. Specifically, we distill the results of several decades of research analysing the relationship between major asset classes (common stocks, gold, fixed income securities, real estate) and inflation. Even though previous studies have brought forth important facts characterising the interplay of asset returns and inflation rates (e.g., time-dependency, asymmetry, outlier-sensitivity and a tendency towards long-term but limited short-term inflation protection), there is still no consensus on the subject because sample, data and methodology issues preclude strict comparison of most studies. Thus, from a synthesis of the insights gained from our review, we also outline possible directions for future research that may help to establish consensus among researchers. © 2015 Elsevier Inc. All rights reserved. Contents 1. 2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Some basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 2.1. Inflation measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 2.2. Inflation hedge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 2.3. Fisher hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 ∗ Corresponding author at: University of Leipzig, Department of Finance, Grimmaische Straße 13-15, 04109 Leipzig, Germany. Tel.: +49 341 97 33 672; fax: +49 341 97 33 679. E-mail address: auer@wifa.uni-leipzig.de (B.R. Auer). http://dx.doi.org/10.1016/j.najef.2015.08.005 1062-9408/© 2015 Elsevier Inc. All rights reserved. 188 3. 4. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 2.4. Extended Fisher hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 2.5. Further extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Asset returns and inflation: a synthesis of empirical evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Common stocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 3.1. Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 3.2. Fixed income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 3.3. Real estate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 3.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 1. Introduction Nearly 40 years ago, Lintner (1975) argued that ‘few matters are of more serious concern to students of finance and to members of the financial community than the impacts of inflation on our financial institutions and markets and its implications for investment policy’. This view that inflation is one of the predominant financial concerns for both academics and practitioners originated in the heyday of American inflation in the 1970s and is just as important today as it was then. Inflation forecasts now indicate new increases in price levels in the near future, driven by higher food and energy costs resulting from a reverse of recent influences (e.g. depressed oil prices) that contributed to a phase of rather low US inflation (see Barclays Research Centre, www.wealth.barclays.com). Inflation acceleration in emerging markets is likely to be larger than in developed countries because of the much greater importance of food in their economies and their stronger rates of growth (see Amenc, Martellini, & Ziemann, 2009). As a result of these trends and the knowledge about historic impacts of inflation on the economy, inflation hedging has become a concern of vital importance not only for private investors, who see inflation as a direct threat to their purchasing power, but also for pension funds, whose pension payments are indexed to consumer prices. In previous decades, scientific studies have examined the interplay between asset returns and inflation rates in order to identify assets that can protect investors from inflation. Typically, the media attribute an inflation-hedging ability to common stocks, gold, fixed income securities and real estate. However, does empirical evidence support this view? Do these assets hedge both expected and unexpected components of the rate of inflation? Can they provide inflation protection in the short run and the long run? Is the hedging effectiveness stable over time and economic states, or does it depend on the sample under analysis? Because each study has its own answer to these and related questions, there is no consensus on whether these assets can hedge against inflation. This is because studies differ in their data sources, sample period and frequency, country coverage and/or econometric methodology. In order to systematise the evidence, this article offers a comprehensive overview of what academics know about inflation hedging. That is, we summarise important characteristics of asset–inflation relationships scientific research has identified. This will allow us to answer the questions stated above and identify gaps in the literature that may be filled by future research. We will not discuss the macroeconomic prerequisites or econometric methodology used in the studies reviewed here; we will, however, assess the direct inflation hedging properties of single assets.1 We focus on common stocks, gold, fixed income securities and real estate because these assets have received the most significant attention in the literature.2 1 Detailed descriptions of all methods mentioned in our review can be found in Tsay (2005) and Greene (2008). There are of course other potential inflation hedges such as private equity or infrastructure. However, so far there is no data of sufficient quality, time-span and frequency that allows reasonable econometric analysis (see Rödel & Rothballer, 2012). This is not true for assets like general commodities or hedge funds but, in comparison to our four asset classes, they have received only little attention in the inflation hedging literature. Thus, the few existing studies (summarized by Rödel, 2012) do not allow similarly deep overall conclusions. 2 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 189 The remainder of our article is organised as follows. Section 2 reviews the concepts that are required to study whether an asset can hedge against inflation. We define the terms inflation and inflation hedging and discuss variants of the Fisher hypothesis linking asset returns and inflation. This is because most research on inflation hedging is based on the latter hypothesis. Section 3 discusses the most influential peer-reviewed articles and working papers. For each of the traditional asset classes common stocks, gold, fixed income securities and real estate, we screen the literature for answers to the question of whether they are effective inflation hedges. For comparative purposes, we supplement our discussion with tables documenting the differences in the time-frames, datasets and methodologies used in the studies and indicating their results (hedge, no hedge, mixed results). Finally, Section 4 concludes and reveals gaps in the literature that might be interesting for future research. 2. Some basic concepts 2.1. Inflation measurement Because inflation is defined as ‘a process of continuously rising prices, or equivalently, of a continuously falling value of money’ (see Parkin, 2008), a natural way to measure inflation is to use growth rates of representative consumer price indices (CPIs). Even though there are significant conceptual shortcomings with this approach (e.g., lagged announcements, international differences in measurement and the fact that CPI estimates are unlikely to constitute an adequate representation of the relevant price changes for a particular investor), CPIs have become the most frequently used proxies for inflation (see Tables 1–3). A smaller number of studies uses production price indices (PPI), wholesale price indices (WPI), retail price indices (RPI) or GDP deflators. Depending on the data frequency used in empirical studies, either monthly, quarterly, bi-annual or annual period-to-period percentage changes are used as inflation rates. 2.2. Inflation hedge There are three possible definitions of inflation hedging (see Bodie, 1976). In the first one, a security is called an inflation hedge if it eliminates or at least reduces the possibility that the real return on the security will fall below some specified floor value such as zero. A second definition measures the hedging effectiveness of a security as the proportional reduction in the variance of the real returns on a default-free bond attainable by combining the security and the bond. Finally, the last definition, which has been used in almost all empirical studies of inflation hedging, states that an asset is an inflation hedge if its real return is independent of the rate of inflation, implying a positive correlation between the nominal return of the hedging asset and inflation. A correlation of 1 is called a perfect hedge because price increases are perfectly compensated by corresponding asset returns. If an asset does not provide a perfect hedge, a stable positive return-inflation relation can still make the asset valuable because, in this case, adequate hedge ratios theoretically allow its use as an effective hedge. However, because hedge ratio-based hedging can induce high transaction costs for retail investors (see Bekaert & Wang, 2010), high magnitudes of co-movement are of higher practical use than small ones being levered. 2.3. Fisher hypothesis Fisher (1930) was the first who formally stated the hypothetical relationship between asset returns and inflation. He noted that the nominal interest rate can be expressed as the sum of an expected real return and an expected inflation rate. Fama and Schwert (1977) point out that the proposition that expected nominal returns contain market assessments of expected inflation rates can be applied to all assets. Thus, if the information available at time t − 1 is processed efficiently, the market will set the price of any asset j so that the expected nominal return Et−1 (rjtn ) on the asset from t − 1 to t is the sum of the appropriate equilibrium expected real return Et−1 (rjtr ) and the best possible assessment of the expected inflation rate Et−1 (t ) from t − 1 to t. Formally, this means that Et−1 (rjtn ) = Et−1 (rjtr ) + Et−1 (t ) (1) 190 Table 1 Stocks as a hedge against inflation. Period (frequency) Region (data) Inflation proxy Econometric methodology Jaffe and Mandelker (1976) Bodie (1976) 1953–1971 (monthly) CPI, WPI OLS regression CPI OLS regression Nelson (1976) 1953–1974 (monthly) CPI OLS regression Fama and Schwert (1977) Gultekin (1983a) 1953–1971 (semi-annual, quarterly, monthly) USA (Lawrence Fisher index) USA (portfolios of NYSE common stocks) USA (Scholes index, S&P 500 index) USA (portfolios of NYSE common stocks) 26 countries (IMF stock market indices) CPI OLS regression CPI OLS regression Gultekin (1983b) 1952–1979 (semi-annual, annual) USA (Dow Jones Industrial Average index, S&P 500 index) CPI, WPI OLS regression Boudoukh and Richardson (1993) 1802–1990 (annual) USA, UK (individual portfolios) CPI Cochran and Defina (1993) 1947–1989 (quarterly) USA (S&P 500 index) Consumption deflator OLS and instrumental-variable regressions, GMM Cointegration techniques (ADF), ECM Solnik and Solnik (1997) 1958–1996 (monthly) USA, Germany, France, Netherlands, UK, Switzerland, Japan, Canada (MSCI indices) CPI OLS and instrumental-variable regressions, GMM, joint testing of all countries Ely and Robinson (1997) 1957–1992 (quarterly) 16 industrialised countries (IMF stock indices) CPI, PPI, GDP deflator Cointegration techniques (ADF, KPSS, Johansen), VECM Lothian and Simaan (1998) 1973–1994 (annual) 23 OECD countries (IMF stock indices) CPI, CLI OLS regression (with long period arithmetic averages of log differences) Schotman and Schweitzer (2000) – – – Nine scenarios with parameter estimates based on previous studies. Lothian and McCarthy (2001) 1790–2000 (annual) 14 OECD countries (IMF stock indices) CPI, CLI Cointegration techniques (ADF, PP) Kolari and Anari (2001) 1953–1998 (monthly) USA, Canada, UK, France, Germany, Japan (major stock indices) CPI Cointegration techniques (ADF, Johansen), VAR models 1953–1972 (annual, quarterly, monthly) 1947–1979 (monthly) Hedge? S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Study 1922–1997 (annual) USA, Denmark (S&P Composite index, Copenhagen stock exchange portfolio) CPI, GDP deflator VAR model for one-period returns and inflation Spyrou (2004) 1989–2000 (monthly) 10 major emerging markets (Datastream total stock market indices) CPI OLS regression Ahmed and Cardinale (2005) 1919–2002 (annual, monthly) USA, UK, Japan, Germany (GFD stock indices) CPI OLS regression, cointegration techniques (Johansen), VAR, Granger causality Luintel and Paudyal (2006) 1955–2002 (monthly) UK (Financial Times all share index and industry sub-groups) RPI Cointegration techniques (Johansen, ADF, KPSS) Alagidede and Panagiotidis (2010) 1980–2007 (monthly) Egypt, Kenya, Morocco, Nigeria, South Africa, Tunisia (IMF stock indices) CPI OLS regression, cointegration techniques (PP, Breitung, KPSS), VECM Kim and Ryoo (2011) 1900–2009 (monthly) USA (Dow Jones Industrial Average index, S&P 500 index) CPI Cointegration techniques (ADF), threshold VECM Rödel (2012, 2014) 1950–2010 (annual) 45 countries (GFD stock indices) CPI Panel regression with country fixed effects, cointegration techniques (KPSS) Abbreviations: ADF: augmented Dickey–Fuller test; CLI: cost-of-living index; CPI: consumer price index; ECM: error correction model; GDP: gross domestic product; GFD: global financial data; GMM: generalised method of moments; IMF: International Monetary Fund; KPSS: Kwiatkowski–Phillips–Schmidt–Shin test; MCSI: Morgan Stanley Capital International; NYSE: New York stock exchange; OLS: ordinary least squares; PP: Phillips–Perron test; RPI: retail price index; VAR: vector autoregression; VECM: vector error correction model; WPI: wholesale and indicate evidence for and against an inflation hedging property, respectively, whereas represents mixed or inconclusive results. price index. The symbols S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Engsted and Tanggaard (2002) 191 192 Table 2 Gold as a hedge against inflation. Period (frequency) Region (data) Inflation proxy Econometric methodology Chua and Woodward (1982) 1975–1980 (monthly, semi-annual) CPI OLS regression Brown and Howe (1987) 1975–1983 (monthly) Canada, Germany, Japan, Switzerland, UK, USA (London PM fixing) USA (Wallstreet Journal gold prices, COMEX gold futures) CPI OLS regression Jaffe (1989) 1971–1987 (monthly, quarterly) CPI OLS regression Mahdavi and Zhou (1997) 1970–1994 (monthly, quarterly) CPI Cointegration techniques (ADF, PP, KPSS), VECM Taylor (1998) 1914–1996 (monthly) USA (Handy/Harmann and Knight-Ridder Financial) CPI OLS and LAD regression, Huber M-estimation, cointegration techniques (DF, ADF) Ghosh et al. (2004) 1976–1999 (monthly) USA, Worldwide (unspecified) CPI, RPI Cointegration techniques (ADF, Johansen) Levin et al. (2006) 1976–2005 (monthly) USA, Worldwide (unspecified) CPI Cointegration techniques (DF, Johansen), VECM McCown and Zimmerman (2006) 1970–2003 (monthly) USA (Wallstreet Journal gold prices) CPI CAPM-based multifactor model, cointegration techniques (DF, KPSS, Johansen) Worthington and Pahlavani (2007) 1945–2006 (monthly) USA (GFD gold prices) CPI Cointegration techniques with endogenous structural breaks McCown and Zimmerman (2007) Blose (2010) 1970–2006 (monthly) USA (Wallstreet Journal gold prices) USA (London PM fixing) CPI CAPM-based multifactor model, correlation analysis Non-linear regression Rubbaniy et al. (2011) 1985–2010 (monthly) Baur (2011) 1979–2010 (monthly) Wang et al. (2011) 1971–2010 (monthly) USA, Japan (London PM fixing) CPI Linear and non-linear cointegration techniques, threshold VECM, causality tests Beckmann and Czudaj (2013) 1970–2011 (monthly) CPI, PPI Markov-switching VECM Erb and Harvey (2013) 1975–2011 (monthly) USA, UK, Euro Area, Japan (London PM fixing) USA (London PM fixing) CPI Descriptive analysis, OLS regression Batten et al. (2014) 1985–2012 (monthly) USA (London PM fixing) CPI Kalman filter regressions, cointegration techniques (ADF, KPSS, Johansen, Saikkonnen–Lütkepohl), ECM, Granger causality 1988–2008 (monthly) USA (London PM fixing, gold stocks) USA (London PM fixing) Germany (London PM fixing) USA (London AM fixing) CPI CPI CPI Hedge? Asymmetric CAPM-based multifactor model, cointegration techniques (ADF, KPSS, Johansen) Asymmetric GARCH model Abbreviations: AM: ante meridiem; APT: arbitrage pricing theory; ADF: augmented Dickey–Fuller test; CAPM: capital asset pricing model; COMEX: (New York) Commodities Exchange; CPI: consumer price index; DF: Dickey–Fuller test; ECM: error correction model; GARCH: generalised autoregressive conditional heteroscedasticity; GFD: global financial data; KPSS: Kwiatkowski–Phillips–Schmidt–Shin test; LAD: least absolute deviation; OLS: ordinary least squares; PM: post meridiem; PP: Phillips–Perron test; RPI: retail price index; VECM: vector and indicate evidence for and against an inflation hedging property; respectively, whereas represents mixed or inconclusive results. error correction model. The symbols S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Study Table 3 Real estate as a hedge against inflation. Period (frequency) Region (data) Inflation proxy Econometric methodology Tarbert (1996) 1978–1995 (semi-annual, quarterly) UK (commercial property) CPI Cointegration techniques (CDW, ADF), Granger causality Barkham et al. (1996) 1982–1994 (monthly) UK (Richard Ellis all property index) RPI Cointegration techniques (ADF, PP, KPSS, Johansen), VECM, Granger causality Matysiak et al. (1996) Chatrath and Liang (1998) 1964–1993 (annual, quarterly) 1972–1995 (monthly, quarterly) UK (commercial property) USA (equity, mortgage and hybrid REITs; all NAREIT) RPI CPI, treasury bill rates Cointegration techniques (ADF, Johansen) OLS regression, cointegration techniques (DF, PP, Johansen) Ganesan and Chiang (1998) 1984–1994 (quarterly) Hong Kong (office, commercial, industrial, residential real estate, property stocks) CPI OLS regression, cointegration techniques (DF) Anari and Kolari (2002) 1968–2000 (monthly) USA (new and existing home prices) CPI minus housing costs Recursive OLS regression, Cointegration techniques (ARDL) Glascock et al. (2002) 1970–1995 (monthly) CPI Adrangi et al. (2004) 1972–1999 (monthly) USA (NAREIT total return index) USA (equity and mortgage REITs; both NAREIT) CPI Cointegration techniques (PP), VECM, Granger causality OLS regression with Chow tests, cointegration techniques (DF, ADF, PP, Johansen) Simpson et al. (2007) 1981–2002 (monthly) USA (publicly traded equity REITs from CRSP) CPI Fixed-effect pooled regression Le Moigne and Viveiros (2008) 1973–2007 (annual, quarterly) Canada (apartment, industrial, office, retail, and mixed use real estate) CPI OLS regression, cointegration techniques (ADF, PP) Hoesli et al. (2008) 1977–2003 (quarterly) USA, UK (private and public commercial real estate) CPI, RPI Cointegration techniques (ADF, PP), ECM Amenc et al. (2009) 1973–2007 (quarterly) USA (NAREIT total return index) CPI Cointegration techniques (ADF, Johansen), VECM, VAR, Monte Carlo simulation Hardin et al. (2012) 1980–2008 (monthly) USA (REIT stock prices, CRSP/Ziman databases) CPI OLS regression, VAR model Lee and Lee (2012) 1972–2007 (monthly) USA (NAREIT total return index, CRSP/Ziman databases) CPI OLS regression, cointegration techniques (DOLS, PP, Johansen) Park and Bang (2012) 2002–2010 (quarterly) Korea (commercial real estate) CPI OLS regression, cointegration techniques (DOLS, DF, ADF, Johansen), VECM, Granger causality Obereiner and Kurzrock (2012) 1992–2009 (monthly) Germany (real estate funds, special funds, real estate stocks) CPI Cointegration techniques (ADF, PP, Johansen) Hedge? 193 Abbreviations: ADF: augmented Dickey–Fuller test; CDW: cointegrating Durbin–Watson statistic; CRSP: Center for Research in Security Prices; CPI: consumer price index; DF: Dickey-Fuller test; DOLS: dynamic ordinary least squares; ECM: error correction model; KPSS: Kwiatkowski–Phillips–Schmidt–Shin test; NAREIT: National Association of Real Estate Investment Trusts; OLS: ordinary least squares; PP: Phillips–Perron test; REIT: real estate investment trust; RPI: retail price index; VAR: vector autoregression; VECM: vector error correction model. The and indicate evidence for and against an inflation hedging property, respectively, whereas represents mixed or inconclusive results. symbols S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Study 194 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Tests of the hypothesis that the expected real return and expected inflation vary independently (and jointly that the market is efficient) require some way to quantify Et−1 (t ). For example, we could derive an empirical measure of the expected inflation rate from (i) well-known theoretical relations in the treasury bill market (see Fama, 1975; Fama & Schwert, 1977), (ii) survey measures (e.g., Consensus inflation forecasts), (iii) time-series models, and (iv) information contained in marketable securities (e.g., inflation swaps and inflation-linked bonds) or (v) simply use realised inflation as a rational forecast for future inflation (see Lintner, 1975; Rödel, 2012). Given a suitable measure, we can estimate the regression model rjtn = ˛j + ˇj E t−1 (t ) + εjt (2) Because a standard regression estimates the conditional expected value of the dependent variable as a function of the independent variable, a ˇj estimate that is not significantly different from one is consistent with the hypothesis that the expected nominal return of asset j varies in one-to-one correspondence with the expected inflation rate and thus acts as a perfect hedge. Of course, because of (1) this is also consistent with the hypothesis that the expected real return on the asset and the expected inflation are unrelated (see Fama & Schwert, 1977). 2.4. Extended Fisher hypothesis While Fisher (1930) incorporates only expected inflation Et−1 (t ), Fama and Schwert (1977) extend (2) by also considering unexpected inflation t − Et−1 (t ), which leads to the regression equation rjtn = ˛j + ˇj Et−1 (t ) + j [t − Et−1 (t )] + jt (3) In this framework, an asset j is a perfect hedge against expected inflation (unexpected inflation) if ˇj ( j ) is not significantly different from one.3 A partial hedge is given for significant parameter values between 0 and 1. Negative values of ˇj and j suggest that the asset acts as a ‘perverse hedge’ against inflation. This means that an inflation hedge can be obtained only by shorting the asset. 2.5. Further extensions Other scholars propose using a version of the Fisher model that takes taxes into account. Investors are liable for paying income and capital gain taxes; this is why the nominal return rate should include the effects of both taxes and inflation. Therefore, the elasticity factors in this tax-augmented version of the Fisher model should be significantly above unity (see Luintel & Paudyal, 2006). Of course other models can also capture the link between returns and inflation (see, for example, Bekaert & Engstrom, 2010; McCown & Zimmerman, 2007; Rubbaniy, Lee, & Verschoor, 2011). However, most studies of inflation hedging rely on Fisher-type relations. They all claim that any type of asset should act as a hedge against inflation because expected nominal returns should efficiently adjust to new information about the level of goods prices. 3. Asset returns and inflation: a synthesis of empirical evidence 3.1. Common stocks From a theoretical perspective, two important reasons make stocks good hedges against inflation (see Lintner, 1975). First, equities represent claims against real assets whose values are expected to keep pace with changes in purchasing power. Second, firms leverage their capital and are net debtors on average. Thus, shareholders would benefit from unexpected inflation as the firm’s 3 This does not imply zero or small variance of real returns since inflation might explain only a small fraction of the variation in nominal returns. The variance of the error term, which in this case is the variance of the real return, might be large relative to the variance of inflation (see Fama & Schwert, 1977). S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 195 long-term commitments to pay fixed nominal amounts decrease in real value (the debtor-creditor hypothesis).4 In recent years, the empirical analysis of stocks’ ability to protect investors from inflation-related losses in purchasing power has received considerable attention in the academic literature. The most important studies in the field are summarised in Table 1, which is limited to articles published after 1970. Earlier studies, summarised by Roll (1972) and Nelson (1976), which resort either to anecdotal evidence or use simple regression analysis, agreed on the proposition that the return of common stocks co-moves with inflation in a one-to-one relation as predicted by the Fisher model. Bodie (1976) wrote a seminal study of inflation hedging. Using New York Stock Exchange (NYSE) equity returns from the Center for Research in Security Prices (CRSP) with holding periods of one month, three months and one year and the CPI from the US Bureau of Labour Statistics for 1953–1972, he draws the surprising conclusion that equities appear to be a perverse inflation hedge since in the short run their returns are negatively related to both expected and unexpected inflation. He concludes that stocks must be sold short in order to be used as inflation hedges. This puzzling result is by no means an isolated finding. Nelson (1976), Jaffe and Mandelker (1976), Fama and Schwert (1977) and Gultekin (1983b) all confirm the negative relation between stock returns and the inflation rate in the short run. Jaffe and Mandelker (1976) analyse an extended sample covering almost one century of data, from 1876 to 1971. Using consumer and wholesale prices for measuring inflation and the Lawrence Fisher index (an equally weighted portfolio of all securities listed on the NYSE) for capturing US stock returns, they show that stock returns appear to be independent of inflation over this long period. However, they point out that this result may be biased by flawed data because the CPI published by the Bureau of Labour Statistics has been of reasonable quality only after a substantial upgrading of its sampling procedures in 1953. In a separate analysis of the period from 1953 to 1971, Jaffe and Mandelker (1976) confirm that stock returns are significantly negatively related to inflation. In a study of 26 countries, Gultekin (1983a) also finds that there is a consistent lack of positive relation between stock returns and inflation in most countries. Interestingly, these results hold irrespective of the three proxies he used for expected inflation: (i) contemporaneous inflation, (ii) short-term interest rates, and (iii) expected and unexpected components of inflation decomposed by ARIMA models. Finally, the multi-asset study of Fama and Schwert (1977) analysing the extended Fisher model for US common stocks, US government bonds and bills, private residential real estate and labour income, concludes that there is no explanation for the negative relationship between stock returns and the inflation rate from 1953 to 1971. A potential rationale for the anomalous behaviour of stock returns was provided four years later. Fama (1981) argues that there is no direct interaction between inflation and stock returns because the former simply acts as a proxy for real economic trends (the proxy hypothesis). On the one hand, stocks benefit from higher expected economic activity. On the other hand, increasing inflation leads to lower economic activity due to the short-term non-neutrality of money. Hence, changes in inflation signal changes in economic activity. The negative relation between stock returns and inflation might therefore be spurious.5 Subsequent studies offered several alternative explanations for the difference between theory (Fisher model) and practice (stocks perform poorly during inflationary periods). Their main ideas are, for example, that the spurious relation between the two variables may be linked to debt monetisation (see Geske & Roll, 1983), equilibrium processes in the monetary sector (see Kaul, 1987) or the role of a firm’s financing costs (see Lintner, 1975).6 4 However, unexpected inflation may also trigger shocks to aggregate output that can harm the hedging effectiveness of stocks. 5 This proxy hypothesis has been both supported and rejected in several follow-up studies (see Cochran & Defina, 1993). 6 For additional explanations (including the so-called money illusion hypothesis) see the study of Wilcox (2012) which is based on the findings of Modigliani and Cohn (1979). 196 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Another explanation of the puzzling relationship between stock returns and inflation is linked to the properties of the analysed time series and the econometric approaches used for testing hedging effectiveness. First, the Fisher effect describes a long-run phenomenon but most of the earlier studies cover only small samples. Thus, more recent studies suggest that using longer time series (see Solnik & Solnik, 1997) or cumulative stock returns (see Schotman & Schweitzer, 2000) can increase confidence in the findings. Second, measurement error in inflation introduces classic errors in variables problem into the standard OLS estimations of Fisher-type models which need to be addressed by instrumental variable regression (see Boudoukh & Richardson, 1993). Third, stock returns and inflation rates exhibit special time-series properties. Inflation is a slow-moving and persistent process, with much lower variance than stock returns. This negatively influences correlation tests between the two variables (see Madsen, 2007) because non-stationary variables introduce the problem of spurious regression, which is the detection of significant relationships even though none exist (see Granger, Hyung, & Jeon, 2001). To circumvent this problem, recent studies search for cointegration between stock returns and inflation.7 If the two variables are non-stationary but cointegrated, (2) may be interpreted as a cointegrating regression, reflecting an equilibrium relationship between nominal interest rates and inflation. Hence, a finding of cointegration combined with a slope parameter not significantly different from one is supportive of a long-run Fisher relationship.8,9 Because cointegrating regressions only consider long-term dynamics, they are usually supplemented by error correction models (ECM). They have been proposed by Granger (1983) and Engle and Granger (1987) and are designed to capture both short-term and long-term effects of one time series on another (see Cochran & Defina, 1993; Tarbert, 1996). In other words, ECM model short-run transitory changes as deviations from the longrun relationship. Studies published since the 1990s have explored these methodological issues and produced a more diverse picture than those of the 1970s and 1980s. Boudoukh and Richardson (1993) used longer time series. They collected almost 200 years of data – from 1802 to 1990 – for the US and the UK. Instrumental variable regression with past inflation rates and short- and long-term interest rates as instruments as well as OLS regressions show that long-horizon nominal stock returns are positively related to both ex ante and ex post long-term inflation. The ex ante Fisher coefficient at the 5-year horizon ranges from 0.38 to 2.07 in case of the instrumental variable regression depending on the instrument. OLS regression shows an ex post Fisher coefficient of 0.52 over the sample period and similar results for the two sub-periods from 1870 to 1990 and 1914 to 1990. This intriguing finding of a positive relationship between stock returns and inflation in the long run has been confirmed by Solnik and Solnik (1997) and Lothian and Simaan (1998) using panel data of eight and 23 advanced economies, respectively. Similar to Boudoukh and Richardson (1993), Solnik and Solnik (1997) test the Fisher model by means of an instrumental variable approach (with the 3-month bill rate, long-term bond rate, past 3-month and 1-year inflation rates as instruments). The comparably short period of 38 years is econometrically compensated by a cross-section of eight major countries. They find that the Fisher model holds at a 1-year holding period horizon. Even for horizons of less than 12 months the Fisher model is not rejected. The magnitude of the coefficient lends stronger support at longer horizons, though. Lothian and Simaan (1998) find that average stock returns co-move with inflation in the long run in almost all 23 OECD countries examined. The two variables are also positively correlated across countries. Lothian and McCarthy (2001) also extend the time-series dimension and cover data for the US and the UK from 1790 to 2000 and for 14 OECD countries (including the US and the UK) from 1945 until 7 Simply using first differences as regression variables could solve the problem of spurious regression but eliminates long-run information that is crucial in measuring the Fisher effect (see Hendry, 1986). 8 However, traditional cointegration tests exhibit two major problems: First, they have low power to reject the null hypothesis of non-stationarity for variables that are persistent but follow a stationary process (see DeJong, Nankervis, Savin, & Whiteman, 1992). Second, size distortions and moving-average components in the underlying data generating process might impair their results (see Lütkepohl & Saikkonen, 1999; Perron & Ng, 1996; Schwert, 1987, 1989). 9 Note that, unfortunately, there is no consensus in the literature on whether inflation rates are non-stationary or stationary (see Charemza et al., 2005; Culver & Papell, 1997). Therefore, studies on inflation hedging can differ in terms of which variable (CPI growth rates or CPI levels) they use to test for a long-run relationship via cointegration methodology. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 hier 197 1999. Using cointegration tests, OECD panel data and the long series for the US and the UK provide robust evidence that equity prices, in fact, keep pace with movements in the overall price level. For shorter horizons, they find a negative relationship between the two quantities. In the same year, Kolari and Anari (2001) tested the long-run Fisher effect for six major economies (the US, Canada, the UK, France, Germany and Japan) for a time span comparable to Lothian and McCarthy (2001). They show that the long-run elasticity of stock prices with respect to inflation ranges from 1.04 to 1.65, which tends to support the Fisher effect. Furthermore, in an impulse-response analysis, the time path of the response of stock prices to a shock in goods prices exhibits an initial negative response, which turns positive over long horizons. This helps to reconcile previous short-run and long-run evidence and reveals that stock prices have a long memory with respect to inflation shocks, so investors should expect stocks to be a good inflation hedge over a long holding period.10 Schotman and Schweitzer (2000) explicitly cover the horizon sensitivity of the hedging property of stocks. They develop nine theoretical hedging scenarios with different parameter values for inflation persistence, the Fisher effect, and the inflation beta of stocks. Assuming that these scenarios are equally likely, they show that stocks provide a hedge against inflation if the investor’s investment horizon is 15 years or longer. Institutional investors such as insurance companies or pension funds with long-term liabilities often buy high duration investments to reduce the asset-liability mismatch in portfolios. Thus, they are less concerned about the short-run relation between stock returns and inflation. Schotman and Schweitzer (2000) note that the persistence of inflation is a crucial parameter for determining an effective hedge ratio. They also highlight that the role of horizon effects for hedgers is an important shortcoming of classic Fisher regression estimates. This is because within the Fisher framework hedging coefficients are estimated for only one specific investment period. Among the first authors to apply ECM in an inflation hedging context are Cochran and Defina (1993). For US data from 1947 to 1989 they show that real stock returns are not independent of inflation. Hence, US stocks do not provide a long-term hedge. On the contrary, expected and unexpected components of the inflation rate have a negative effect on real stock returns. Ely and Robinson (1997) rely on a more general error correction approach. They employ a vector error correction model (VECM) – a special case of the vector autoregressive model (VAR) for variables that are stationary in their differences – because it allows the simultaneous consideration of multiple variables (the inclusion of variables that might play a role in the interaction of returns and inflation). While the error correction terms in the VECM account for short-term deviations from long-term equilibrium relationships among the variables, impulse response functions can be derived from the VECM to estimate the response of returns and inflation to changes in other included variables (such as measures of monetary policy or real output). With quarterly data from 1957 to 1992 for 16 industrialised countries, Ely and Robinson (1997) find that stocks maintain their real value relative to goods prices and this conclusion generally does not depend on the source of the inflation shock (real or monetary sector). The only exception are the US where stocks do not maintain their value relative to goods prices following real output shocks.11 In order to assess the hedging properties of US and Danish stocks, Engsted and Tanggaard (2002) measure multi-period expected returns and inflation from a VAR model involving only one-period variables. They find that Danish stock returns co-move with expected inflation in the long run but not at short horizons. For US stocks, however, the relationship between expected returns and inflation is quite weak at all horizons. Thus, in contrast to Boudoukh and Richardson (1993), the Fisher model does not perform better as the horizon increases in the US case. However, it does so for Danish stocks. Ahmed and Cardinale (2005) analyse data of different inflation regimes from 1919 to 2002 comprising the US, the UK, Germany and Japan. Although evidence for a cointegration relation is mixed – depending on horizons, methods and countries – equities tend to be a partial inflation hedge, even at long horizons. Equities appear to react asymmetrically to high or low inflation. In the short run (one 10 Knif, Kolari, and Pynnönen (2008) note that summing positive an negative inflation shocks tends to wash out or mute the effects on inflation news on stock returns. They show that, depending on the economic state, positive and negative inflation shocks can produce a variety of stock market reactions. 11 However, note that the analysis of Ely and Robinson (1997) is not fully equivalent to testing if stocks provide a hedge against inflation because it is based on stock price indices not including dividends. 198 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 year), equity returns have been significantly higher at times of ‘normal’ inflation (up to three percent) but lower in case of deflation or very high inflation (with the exception of Japan). Hence, equities do not offer protection when it is most needed. The same point has been made by Kim and Ryoo (2011) who conclude that stock returns and inflation show asymmetric adjustments to the long-run equilibrium depending on the period (high vs. low inflation regime). By means of a threshold VECM with two regimes they allow for asymmetric adjustments of stock returns and expected inflation towards the long-run equilibrium. Within a sample period of more than 200 years, US common stocks have been a hedge against inflation since the early 1980s. This coincides with the decline in the volatility of US inflation and other macroeconomic fundamentals, the ‘Great Moderation’. With more stable inflation rates it is more likely that inflation expectations become more accurate, potentially leading to a better hedging performance. Luintel and Paudyal (2006) disaggregate approximately 50 years of UK data to challenge the Fisher hypothesis for the country as a whole as well as for seven industry groups. The levels of UK stocks and the RPI are cointegrated both in aggregate and disaggregate data. Accounting for taxes, goods price elasticities are significantly above unity with the exception of the mineral extraction industry. Hence, British stocks not only provide an inflation hedge in the long run but also compensate for the loss in the real wealth of tax-paying investors. Finally, in a study of 45 developed and emerging markets, Rödel (2012, 2014) makes the interesting finding that international equities are superior to domestic equities as inflation hedges. To summarise the current state of scientific knowledge, we can state that stocks appear to perform poorly during inflationary periods in the short run since they are negatively related to changes in the rate of inflation. This is confirmed by early studies based on OLS techniques as well as by more recent ones adopting more sophisticated approaches. However, since the 1990s, several articles have presented more favourable evidence on the relation between equity returns and inflation. Even though there is still no consensus on the hedging properties of stocks, most of the recent studies find a longrun stock-inflation equilibrium implying that stocks do provide a hedge at horizons of at least five years. 3.2. Gold Especially in the aftermath of the 2008 financial crisis, gold has attracted significant attention in the scientific community (see Lucey, 2011). This is mainly because gold has a variety of features that make it a desirable asset (see Worthington & Pahlavani, 2007). First of all, gold’s intrinsic value neither depends on prospective cash flows nor carries a default risk. Second, gold is universally acceptable and scarce. Third, the relative inelasticity of the gold supply and the observed counter-cyclical demand qualify gold as a store of value. Finally, and probably most importantly, a protection property is commonly attributed to gold by many investors, individuals and the media. There are four streams in the literature on the economic and financial aspects of gold: forecasting the gold price, event studies and tests for the market efficiency hypothesis, determinants of the price for gold and the capability of gold to act as a diversifier, hedge or safe haven.12 The latter group is of particular interest for our review because it covers the questions of whether the price of gold moves along with higher inflation or whether it is unaffected by the level of goods prices because of factors such as carrying costs (see Blose, 2010). Research on common stocks subsumes inflation protection under the term ‘hedge’. In the analysis of interrelations between gold and other markets, Baur and Lucey (2010) have introduced more useful 12 For reviews of these literature strands, see Worthington and Pahlavani (2007) and O’Connor, Lucey, Batten, and Baur (2015). More recent articles on the issue of modelling and forecasting gold prices are Shafiee and Topal (2010), Białkowski, Bohl, Stephan, and Wisniewski (in press) and Baur, Beckmann, and Czudaj (2014). Charles, Darné, and Kim (in press) analyse gold market efficiency, Tully and Lucey (2007) the economic determinants of gold prices. Baur and McDermott (2010), Coudert and RaymondFeingold (2011), Ciner, Gurdgiev, and Lucey (2013), Pullen, Benson, and Faff (2014), Beckmann, Berger, and Czudaj (2015) and Lucey and Li (2015) investigate the role of gold as a hedge against risks other than inflation (such as market and currency risks, interest rate changes or the oil price shocks). Spierdijk and Umar (2014) and Zhou (2014) focus on aggregate commodity futures indices (including energy, industrial metals and precious metals) to evaluate their inflation hedging potential. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 199 operational definitions of hedging properties. They state that ‘a hedge is defined as an asset that is uncorrelated or negatively correlated with another asset or portfolio on average’ whereas a diversifier is ‘positively (but not perfectly) correlated with another asset or portfolio on average’ and a safe haven is ‘uncorrelated or negatively correlated with another asset or portfolio in times of market stress or turmoil’.13 Hence, a hedge can reduce losses on average but might exhibit a positive correlation when protection is most needed. In contrast, safe haven assets do not co-move with other assets or indices in crisis periods but provide tail risk insurance. They possess either positive or negative correlation during calmer periods.14 Even though these definitions are of high practical importance, they have found only limited attention in the analysis of the gold–inflation relationship (but highly frequent use in the analysis of the relationship between gold and other assets). However, they are sometimes implemented indirectly by considering different inflation regimes in which the gold–inflation relation may show different characteristics. The studies listed in Table 2 empirically examine the gold–inflation relation. In light of the rising awareness of inflation risks in the 1970s, Chua and Woodward (1982) were among the first to extend the inflation hedging literature on stocks to the gold market. Using monthly and bi-annual data of six industrialised countries they find that, with the exception of the US, gold has been neither a complete nor partial hedge against domestic inflation. However, the fact that gold was fixed at different levels under the Bretton Woods system and trading was prohibited in the US before 1975 limits the investigation period (1975–1980) and the validity of this study. In a larger sample (1975–1983) for the US, Brown and Howe (1987) find that, in the short run, hedged cash positions (the investor purchases gold and simultaneously sells a future contract), do not keep up with inflation. Jaffe (1989) analyses the returns of gold and gold stocks from 1971 to 1987 within a multi-asset framework and provides the first evidence of gold being a diversifier. The returns are found to be independent of those of other assets which suggests that a portfolio benefits from a share of gold in it. However, he adds that gold should not be relied upon as an effective inflation hedge because of insignificant Fisher regression results and low coefficients of determination (R2 ) between 0.4% and 5.8%. These limited and even contradictory initial findings have been reexamined in follow-up studies (mostly focusing on the US market) with longer time spans and improved econometric methodology. Mahdavi and Zhou (1997) investigate the relationship between gold prices and the CPI by means of an ECM.15 Controlling for economic and financial conditions (measured by the real gross domestic product and short-term interest rates), they find that gold is a poor out-of-sample forecasting variable for inflation. Potential explanations of this finding are linked to the facts that first, the short-term movement in the price of gold is much more volatile than the general price level and that second, the CPI basket tends to adjust more slowly to new information. In contrast to a broader basket of commodities, gold was not cointegrated with the CPI from 1970 to 1994. Hence, the two variables may drift apart not only in the short run but also in the long run which impedes using gold as an inflation hedge. With longer time series covering 82 years, Taylor (1998) examines the inflation hedging ability of the four precious metals: gold, silver, platinum and palladium.16 The hypothesis of non-stationary residuals (in regressions of monthly gold returns on ex post inflation rates) could not be rejected for the entire period from 1914 to 1996 implying that gold is not a long-run hedge against inflation. However, gold and the other precious metals were hedges before 1939 and around the second OPEC oil crisis in 1979. Thus, hedging properties appear to vary over time, indicating the need to take into account structural breaks when analysing the gold–inflation relation. 13 Baur and McDermott (2010) extend these definitions by distinguishing a strong hedge (safe haven), which is negatively correlated with other assets, from a weak hedge (safe haven), which is uncorrelated with other assets on average (in times of stress). 14 Lucey and Li (2015) present a list of assets, currencies and even whole countries that have all been referred to as safe havens with respect to various risks. 15 The results of earlier studies analysing a cointegration relation are different depending on the stationarity test and sample period (see Mahdavi & Zhou, 1997). 16 Jastram (2009) uses the most extensive sample studied so far by analysing the annual change of gold and goods prices in the US and the UK from 1560 to 2007 and 1808 to 2007, respectively. Unfortunately, his study has been heavily criticised because of its mere descriptive nature and other flaws (see Hautcoeur, 2010). 200 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Structural breaks occur for a variety of reasons: economic and financial crises, changes in policy, regime shifts or institutional changes. In either case, classic cointegration tests can yield spurious results because the presence of structural breaks makes it harder to reject the null of no cointegration.17 To avoid such bias, Worthington and Pahlavani (2007) explicitly consider the role of structural breaks in cointegration testing. Employing the unit root test proposed by Zivot and Andrews (2002) and a cointegration test proposed by Saikkonen and Lütkepohl (2000a, 2000b, 2000c), they estimate the timing of significant breaks rather than assuming the timing to be exogenous. In addition, the sample period from 1945 to 2006 is scaled down to the period after 1973 when market forces rather than the fixed or two-tiered gold system determined gold prices. The most significant structural breaks for gold (and inflation) were found in 1973 and 1979, coinciding with the first and second OPEC oil crises. Cointegration between gold prices and the US CPI was found for different econometric specifications, indicating that gold can indeed serve as an inflation hedge in the long run. In order to explain the theoretical conditions under which gold hedges changes in goods prices, Ghosh, Levin, MacMillan, and Wright (2004) present a model of the long-run determinants of the gold price. They show that, in a competitive market with gold producers as profit maximisers, the price of gold equals the marginal extraction cost which in turn equals the marginal cost of leasing gold from central banks. As long as the costs associated with extracting gold rise at the general rate of inflation, the price of gold will rise at the general rate of inflation and gold can be regarded as an inflation hedge. Changes in the gold lease rate, the real interest rate, convenience yield, default risk, the covariance of gold returns with other assets and the dollar/world exchange rate18 disturb this equilibrium relationship and generate short-run price volatility. Using data from 1976 to 1999, Ghosh et al. (2004) find empirical support for their model and a long-run relationship between the US RPI and the gold price. The implied elasticity of this relationship is consistent with the view that gold is a long-run hedge against inflation. Levin, Montagnoli, and Wright (2006) provide a further analysis of the nature of short-run and long-run gold movements. With monthly data from 1976 to 2005 they show that gold co-moves with the US price level (but not with world inflation) in a statistically significant one-to-one relationship. Their estimated ECM implies that gold reverses slowly to the long-term equilibrium (it takes about five years to eliminate two-thirds of the deviation from this equilibrium). The factors responsible for short-term deviations from the equilibrium are US inflation, US inflation volatility and credit risk (positively related to gold prices) as well as the US dollar tradeweighted exchange rate and the gold lease rate (negatively related). With US data from 1970 to 2003, McCown and Zimmerman (2006) examine the role of gold as a diversifier or hedge. In the context of a CAPM-based multifactor model containing various risk factors (including market risk, default and term spreads, changes in industrial production, and changes in inflation), gold yields a market beta that is statistically indifferent from zero indicating that an investment in gold adds no systematic risk to an investor’s portfolio.19 Furthermore, gold (and silver) prices and the CPI are found to be cointegrated. In a subsequent study over a similar period, McCown and Zimmerman (2007) provide evidence of a positive correlation between gold and expected future inflation (measured by the yield spread between nominal US Treasury securities and the US Treasury Inflation Protected Securities). Correlation tends to rise as the horizon increases from one month to five years. Besides noting that gold resembles a useful indicator of expected inflation, the authors conclude that gold hedges inflation, especially at longer horizons. While the studies discussed so far assume that the relationship between the price of gold and inflation is symmetric, a new strand of the literature suggests that it should be asymmetric. That is, a change in the rate of inflation has less or more effect on the price of gold depending on the state of financial markets.20 Studies following this logic use threshold regressions, asymmetric GARCH 17 For references covering the econometric problem of unit root tests with endogenous structural breaks, see Worthington and Pahlavani (2007). 18 The world exchange rate is the nominal major currencies Dollar index of the Federal Reserve Board. 19 A sub-period analysis shows that negative betas occur in the high-inflation phase of the 1970s whereas the betas are positive between 1980 and 2006. 20 Not only the state of the financial markets but also the business cycle, mechanisms of the price adjustment or transaction costs may cause asymmetries in the gold-inflation relation (see Wang et al., 2011). S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 201 models, non-linear cointegration tests or threshold VECM because theses econometric approaches can account for asymmetry. Taking into account earlier evidence of unstable relations between gold and inflation recent studies also supplement their empirical analysis by applying Kalman filter regressions or Markov switching models. Wang, Lee, and Thi (2011) apply linear and non-linear cointegration tests (as proposed by Enders & Siklos, 2001) to analyse the inflation hedging ability of gold in the long run and threshold VECM to also cover the short-run perspective. They find that, between 1971 and 2010, gold and the CPI in the US (in Japan) show linear, symmetric (non-linear, asymmetric) cointegration. Hence, using gold as an inflation hedge is almost absolutely effective in the US in the long run, however, only partially effective in Japan. The hedging ability in the short run depends on the adjustment momentum between prices (low- vs. high-momentum regime). In low-momentum regimes, gold cannot be a hedge against inflation in either the US or Japan. However, under high-momentum regimes, gold returns are able to hedge against inflation in the US, whereas price rigidity in Japan causes the price of gold to not fully hedge against inflation in the short run. While most studies focus on the US market, Rubbaniy et al. (2011) take a European perspective by examining gold’s role as a hedge against different risk factors in Germany. They build on the work of McCown and Zimmerman (2006) and confirm their finding that gold bears no market risk. Rubbaniy et al. (2011) extend the approach of McCown and Zimmerman (2006) by using GARCH and threshold GARCH specifications for the error terms of the multifactor model to account for volatility clustering and by adding a market sentiment variable which allows testing of whether or not the estimated factor coefficients are conditional on the state of the economy. The factor exposures indeed differ during stable and crisis periods (negative sentiment coefficient for gold in times of crisis while it has no predictive power in stable periods) implying that from 1985 to 2010 the gold price rises when the economic sentiment index declines. Thus, gold positions act as safe havens in times of distrust. Furthermore, the study shows that gold (but not silver and palladium) is cointegrated with the German CPI and thus is the only metal providing a long-run inflation hedge to German investors. Also extending the country focus beyond the US, Beckmann and Czudaj (2013) cover 41 years of data for the US, the UK, the Euro area and Japan, and report further evidence that the gold–inflation relation is characterised by instability. By means of Markov switching VECM the authors allow for regimes since shifts in the adjustment parameters between short-term deviations from the longterm equilibrium are incorporated. They find that the hedging effectiveness with regard to the CPI is stronger than for the PPI. Furthermore, it is stronger in the US and the UK than in the Euro area and Japan. Because fluctuations in the price of gold converge towards the long-run equilibrium at varying speeds depending on the regime, returning to the long-run relationship can take several years. Once again, this illustrates that time horizons matter for inflation hedging. Even though most of the studies discussed so far suggest co-movement of gold and inflation over long time horizons, recent studies (see Batten, Ciner, & Lucey, 2014; Baur, 2011; Blose, 2010; Erb & Harvey, 2013) are more skeptical about a positive relationship between gold and inflation, albeit for different reasons. Blose (2010) proposes two theories concerning the impact of expected inflation on the price of gold: the expected inflation hypothesis (EIH), which states that higher inflation expectations will increase the demand for gold and thus its price, and the carrying cost hypothesis (CCH), which states that changes in inflation expectations will not affect gold prices because higher inflation expectations cause interest rates to rise which implies that the costs of holding gold increase. The data basis for testing these hypotheses consists of inflation forecasts (monthly Consensus estimates published by the Wall Street Journal prior to the CPI announcement) as a proxy for expected inflation and unexpected inflation measured by the difference between announced and forecasted inflation. Using non-linear regressions and a sample of more than 20 years, Blose (2010) shows that surprises in the CPI do not affect gold spot prices.21 In other words, if the price of gold changes, the changes are not caused by changes in expectations about future inflation. Thus, investors cannot determine market inflation expectations by examining the price of gold. 21 With this result, Blose (2010) confirms the findings of Adrangi, Chatrath, and Raffiee (2003) that unexpected inflation does not affect gold prices. However, Adrangi et al. (2003) show that expected inflation does influence gold prices. 202 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Baur (2011) examines the properties of gold (hedge against exchange rate risks, interest rate changes and inflation) in a model that captures simultaneous influences. He criticises that most of the studies reporting evidence on these properties use simple regression frameworks and therefore assume that other variables potentially affecting the price of gold either do not exist or are at least stable over time. Using a multiple regression framework for US data from 1979 to 2010, Baur (2011) finds that the evidence for gold as an inflation hedge is at best weak (in contrast to the US dollar and commodity prices that are hedged by gold). The author first estimates the isolated impacts on gold prices by means of simple regressions and, in a second step, uses multiple regressions to show that the hedging ability of gold loses strength and significance when interactions among the independent variables are controlled for. Erb and Harvey (2013) observe that a single outlier in the data, namely the year 1980, might account for the positive relationship between gold and inflation documented in earlier studies. After excluding this outlier, little evidence can be found that gold was an effective hedge against unexpected inflation from 1975 to 2011 (neither in the short run nor the long run). Moreover, gold does not always provide tail risk insurance during highly inflationary periods (safe haven property). Finally, changes in the US inflation series in the early 1980s also played a role in the relation between gold and inflation (see Kim & Ryoo, 2011). Stock and Watson (1999, 2007) and Atkeson and Ohanian (2001) find a significant structural break in US inflation around 1984 which coincides with the onset of the ‘Great Moderation’. For this reason, Batten et al. (2014) restrict their analysis to 1985–2012 to examine the relation between gold price and CPI and arrive at three important findings based on the most sophisticated statistical methodology considering all features of the relation identified in the literature. First, they find no cointegration between the two variables. The evidence is robust to different cointegration tests and structural breaks. Second, the Kalman filter regressions point out that the sensitivity of the gold price to changes in goods prices declines in the 1990s and increases in the 2000s which is the underlying reason why the hypothesis of a stable and stationary, i.e. cointegrating, relation is rejected. Third, Granger causality tests reveal that the inflation sensitivity of gold increases with lower short- and long-term interest rates. This is consistent with the notion that monetary easing fuels higher inflation expectations which then increase the demand for gold. Hence, investors seeking protection against inflation should look at these underlying macroeconomic factors that generate time-variation in the relation between gold prices and inflation in order to evaluate gold’s hedging potential. Summarising the evidence on the empirical relationship between gold and inflation, we can say that most of the earlier studies in the field report evidence that gold prices and inflation are cointegrated while more recent work published after the financial crisis in 2008 presents a less favourable picture. The latter studies show that the link between gold and inflation is either non-existent, merely driven by outliers or strongly time-dependent. In some periods, gold has outperformed inflation, while in other periods gold has failed to match it. 3.3. Fixed income To judge the inflation-hedging ability of fixed income securities, we can collect evidence from two literature strands. The first strand concentrates on analysing the Fisher effect by testing the relationship between interest rates, i.e., the returns of short-term sovereign debt (money market instruments or bills with a maturity of less than one year) and inflation. Thus, they implicitly analyse hedging ability and mainly neglect bond returns (see Mishkin, 1992). The second strand explicitly tests for an inflation hedging ability and covers bills, standard bonds and inflation-linked bonds (ILB).22 We start with a brief discussion of the first strand of literature. In general, early studies find only limited empirical support for the validity of the Fisher hypothesis for interest rates. Some studies suggest and provide theoretical rationales for a Fisher coefficient significantly different from unity. Mundell (1963) and Tobin (1965) argue for partial interest rate adjustment, i.e., ˇ < 1, where a certain 22 Because there are already literature reviews covering the first strand of literature and the second strand only consists of a handful of important studies, this section does not require an overview table of relevant studies. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 203 level of anticipated inflation raises nominal interest rates by less than the rate of inflation. Inflation reduces real wealth, which could lead to a portfolio shift out of nominal assets and into real assets, which in turn puts pressure on real interest rates.23 Although this effect opposes the Fisher (1930) theory, it is in line with his empirical observations because, he argues, that ‘when the cost of living is not stable, the rate of interest takes the appreciation and depreciation into account to some extent, but only slightly, and, in general, indirectly’. Carmichael and Stebbing (1983) even propose an inverse one-for-one relationship between after-tax real interest rates and inflation. The conceptual antipodes of an inverse Fisher effect are Darby (1975) and Taylor (1993). Taylor (1993) argues for monetary policy rules rather than discretionary interventions of monetary authorities. In his opinion, nominal interest rates tend to overestimate inflationary pressure which is why nominal rates may overshoot actual inflation. In other words, he predicts a positive relation ˇ > 1. Darby’s (1975) tax-augmented version also postulates Fisher coefficients above unity since investors must be compensated for their tax burden. A one-percentage point increase in expected inflation would then increase nominal rates by 1/(1 − ) percentage points with being an investor’s marginal tax rate on nominal interest income.24 Several other early empirical studies examine inflation and interest rates in the context of inflation forecasting and the efficient market hypothesis. As summarised by Fama (1975), early findings indicate that the market fails to forecast inflation rates. There are no relationships between interest rates at time t and the subsequent rates of inflation. However, there is a clear link between current interest rates and past inflation which would support the Fisher hypothesis. Analysing one- to six-month US treasury bills, Fama (1975) presents evidence that the Fisher hypothesis holds in the short run. Since real interest rates are constant from 1953 to 1971, variations in nominal rates arise from changes in expected inflation. Unlike the majority of studies at that time, he does find relationships between nominal interest rates and subsequently observed inflation rates. His findings support the notion of an efficient capital market in the sense that nominal interest rates always incorporate and reflect all relevant information about future inflation rates.25 There are at least two rationales why the unexpected component after inflation announcements should lead to a change in interest rates. Unexpected inflation might trigger higher inflation expectations in the future (expected inflation hypothesis) or monetary authorities are expected to tighten their policy in response to unexpected inflation (policy anticipation hypothesis). Indeed, Urich and Wachtel (1984) show that short-term interest rates are positively related to unexpected inflation announcements measured by changes in the PPI while this effect is not observable in the CPI. Smirlock (1986) reports a significant positive response of long-term bond markets to unexpected inflation. Moreover, the short- and long-term responses are immediate which supports market efficiency. Starting with Rose (1988), the empirical literature has tested whether interest rates and inflation contain a unit root because stationary real interest rates imply that they are independent of inflation and thus support the Fisher hypothesis. Neely and Rapach (2008) published a comprehensive review of 29 studies covering the long-run properties of real interest rates; only four examine both ex ante real rates (EARR) and ex post real rates (EPRR), and the remaining 25 studies analyse only EPRR.26 The reviewed studies were published between 1988 and 2008 and use monthly or quarterly data. While most of them focus on the US market, others mainly employ panel data from industrialised countries such as a set of OECD countries or the G7.27 Although the evidence concerning (non-)stationarity of interest rates and inflation is mixed, there are a few commonalties. First, the majority of studies fails to reject a unit root for nominal interest rates as well as inflation. Second, EARR appear to be stationary. 23 Evans and Lewis (1995) present additional theoretical explanations such as liquidity premiums in general equilibrium models or output shocks. Crowder and Hoffman (1996) provide references for empirical findings on the Mundell–Tobin effect. 24 Allowing for tax effects, the estimated coefficient should be in the range of 1.3–1.4 for a tax rate around 25% (see Summers, 1983). 25 Fama (1975) has been challenged mainly for statistical reasons such as low testing power (see Nelson & Schwert, 1977) and dependency on the particular sample period (see Mishkin, 1984). Relaxing the stationarity assumption of Fama’s OLS regressions, Garbade and Wachtel (1978) conclude that the real rate of interest varied over the sample period from 1953 to 1971. 26 Studies on real interest rate persistence after 2008 include Yoon (2010), Haug, Beyer, and Dewald (2011), Tsong and Lee (2013) and Haug (2014). 27 The only exception is Lai (1997, 2008) who analyzes eight industrialised and developing countries each. 204 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 However, this conclusion should be treated with caution because of the limited number of reviewed studies. Third, the findings with respect to EPRR are puzzling since a rejection of a unit root is found by almost the same number of studies that present evidence of non-stationary EPRR. One possible explanation for this observation is regime-dependent behaviour of EPRR (see Garcia & Perron, 1996). Fourth, non-linear cointegration (see Christopoulos & León-Ledesma, 2007; Lai, 1997; Maki, 2003; Million, 2004; Sun & Phillips, 2004) and the comprehension of structural breaks (see Bai & Perron, 2003; Caporale & Grier, 2000; Clemente, Montañés, & Reyes, 1998; Lai, 2004, 2008; Rapach & Wohar, 2005) have become popular in more recent studies and tend to support stationary EPRR and (at least fractional) cointegration between nominal interest rates and inflation. Turning to our second strand of literature that directly analyses inflation hedging with fixed income securities, the seminal study by Fama and Schwert (1977) finds that US government bills and bonds are a complete hedge only against expected inflation. Unexpected inflation has a strong negative relationship with ex post returns. The magnitude of the effect increases with terms to maturity since long-term bonds have more future periods that require adjustments in expected nominal returns. Bekaert and Wang (2010) make the same point, stating that bonds fail to hedge unexpected inflation. In a cross-section of 45 countries with annual government bond returns from 1970 to 2010, 17 out of 19 statistically significant inflation betas of bond returns are negative, ranging from around 0 to −3. The hedging coefficients improve as the horizon increases. Since substantial inflation shocks are inimical to the portfolio returns of bond holders, it is no surprise that the bond markets of developed countries outperform emerging economies which regularly suffer periods of high inflation. The instability of the real rate of return on bills over long periods of time as well as the poor inflation hedging characteristics of bonds gave rise to the new class of ILB which link principal payments and/or coupon payments to a specific measure of inflation.28 The benefits of ILB are that (i) a new long-term real safe asset exists, (ii) financial markets become more complete due to additional possible payoff structures and improved real-time market information, and we have (iii) debt savings due to positive inflation risk premiums, (vi) predictable real financing costs and (v) a reduction of the incentive for governments to inflate their debt (see Garcia & Van Rixtel, 2007). In a portfolio context, ILB exhibit a low correlation with other asset classes and a lower volatility of real returns (see Kothari & Shanken, 2004; Swinkels, 2012). However, some drawbacks of ILB are that the ILB market still accounts for only a small proportion of government debt leading to poor liquidity compared to standard bonds and the costs associated with issuing ILB are higher than for standard bonds. Moreover, a particular inflation index may not match the inflation exposure of an investor because the index measurement may be biased or lagged (see Bekaert & Wang, 2010; Campbell & Shiller, 1996). Amenc et al. (2009) show that if short-term liability risk hedging is the sole focus in a framework where liabilities are indexed with respect to inflation, the optimal asset allocation consists of investing 100% into an inflation-indexed bond portfolio. Brière and Signori (2012) examine the asset return dynamics of cash, nominal bonds, ILB, equities, real estate and precious metals by means of a VAR model for varying investment horizons from 1 month to 30 years. Despite the authors’ focus on intertemporal portfolio decisions, they also report findings for individual assets. They show that the inflation hedging properties of nominal bonds and ILB strongly differ depending on the regime (1973 to 1990 or 1991 to 2010) and hedging horizon. In the first regime, nominal bond returns show negative correlation coefficients with inflation up to −0.7 at all horizons, whereas ILB coefficients become positive for horizons greater than five years. In the second regime, both types of bonds show positive coefficients for horizons around eight to ten years. The study is complemented by an analysis of shortfall probabilities according to which nominal bonds performed well with a probability of not achieving the inflation target of 7% (first regime) and 0% (second regime) at 30-year horizons. This performance may be explained by the significant fall in the inflation risk premium due to persistent disinflation. In short, the literature studying the interplay of interest rates and inflation has not been accompanied by a comparable quantity of studies that explicitly test the inflation hedging effectiveness of 28 For a comprehensive discussion of ILB (market development, issuance and information extraction from ILB), see Garcia and Van Rixtel (2007). S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 205 fixed income securities. State dependent behaviour and structural breaks in time series of real interest rates impede the detection of cointegration between nominal interest rates and inflation. Bills and bonds with fixed principal or coupon payments are vulnerable to inflation shocks. They show negative correlation with inflation in the short run but have some potential as inflation hedges in the very long run. ILB bonds technically protect investors against inflation. However, scarce liquidity and limited available maturities confine their use for investors. ILB unfold their inherent advantages (low correlation with other asset classes, low real return volatility) mainly in a portfolio context. 3.4. Real estate Because of the shortcomings of ILB markets, most investors continue to rely on the indirect hedging properties of traditional asset classes. Real estate is the last of these asset classes that we discuss in our review. It is a heterogeneous asset class that comprises diverse investment vehicles. Research on the inflation hedging properties of real estate has to differentiate between private and public real estate, residential and commercial properties as well as indirect (securitised) and direct (income-producing) means of participating in the real estate sector. The rationale for a potential hedging property, however, does not differ. Real estate represents an underlying value and its returns derive from both income (rents might be adjusted in line with the general price level) and capital appreciation (due to higher demand, for example through real output growth). One determinant of the inflation sensitivity of real estate is the lease structure including the length of the lease agreement, indexed escalations and pass-through of expenses (see Huang & Hudson-Wilson, 2007; Le Moigne & Viveiros, 2008). The identification of other major influences on the inflation hedging effectiveness of real estate is the subject of current empirical work. In the analysis of private and public real estate, we encounter the general problem that price information on real estate markets is often deficient (in quality and quantity), because of a lack of transparency or an insufficient number of trades which impedes market tracking and thereby research in general. This is especially true of private real estate and the reason why researchers often resort to appraisal-based indices. Appraisers base their estimates of the market value of a real estate property on past and current information about fundamental variables and transactions. The problems associated with an appraisal-based approach in which information must be extracted from noisy transaction prices can be subsumed under the term ‘appraisal smoothing’.29 It occurs not only in the appraisal process itself at the disaggregate (property) level, but also at the aggregate level due to the frequency of aggregation (time lags). Examining the relationship between real estate returns and inflation on the basis of appraisals may be biased by the fact that appraisers tend to adjust the property value estimate made in t − 1 by an inflation factor when estimating the value of a property in t. Hence, it is hardly surprising that positive coefficients are found when such returns are regressed on inflation. However, there is still no consensus on whether return series should be ‘unsmoothed’ because the revision of time series itself may produce misleading results regarding the inflation hedging ability of real estate (see Le Moigne & Viveiros, 2008). In general, direct real estate (ownership without financial vehicles) has several disadvantages, such as large required fund outlays, lack of a central market, need for local market knowledge, low liquidity, high transaction costs, maintenance expenditures and management requirements (see Wilson & Zurbruegg, 2003). These drawbacks, in conjunction with the difficulties posed by low frequency data and questions about the reliability of appraisal-based returns have drawn academics’ attention to securitised real estate markets and have given rise to the introduction of real estate investment trusts (REITs) that pool the funds of investors in order to invest in income-producing mortgages, real estate properties, joint ventures and other hybrid structures. REITs can be subdivided into mortgage REITs, which hold mortgages and construction loans, and equity REITs, which specialise in income-producing properties (see Chen & Tzang, 1988). REITs and real estate stocks should be treated separately from the discussion in Section 3.1 because (i) the underlying assets of REITs are primarily real estate, because 29 Geltner, MacGregor, and Schwann (2003) provide an overview of the estimation of market values by appraisers and the informational efficiency of the public and private real estate markets. 206 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 (ii) although evidence suggests that REITs tend to behave more like common stocks than like real estate, the equity component of REITs might be declining (see Adrangi, Chatrath, & Raffiee, 2004), and because (iii) REITs possess stable cashflows due to high dividend payouts, a feature that differs from stocks.30 Starting with Fama and Schwert (1977) the inflation hedging property of real estate has received considerable attention in the literature. Because other scholars have already summarised the early results, we have structured our review as follows. We first discuss the initial findings of Fama and Schwert (1977) and summarise the results from the overviews of Simpson, Ramchander, and Webb (2007) and Hoesli, Lizieri, and MacGregor (2008). We then review the most important recent studies using more advanced statistical methodology (see Table 3). Fama and Schwert (1977) use transaction-based real estate returns for the US market (the home purchase price component of the CPI) and find that nominal real estate returns co-move in a one-to-one relation with inflation. Specifically, they show that private residential real estate can provide an effective hedge against both expected and unexpected inflation. Although the findings of follow-up studies differ with respect to the hedging coefficients, they show that private real estate can be a good hedge against expected inflation.31 However, in most cases, the hedging coefficients regarding the rate of inflation are significantly less than 1 and indicate only a partial hedge. Furthermore, they present evidence that even though private real estate offers hedges against expected inflation, it fails to hedge against unanticipated inflation shocks (see Simpson et al., 2007). The question of whether these findings also hold for securitised forms of real estate and the issue of data-related shortcomings of unsecuritised real estate introduced a new strand of literature using REIT returns. Interestingly, early findings for securitised real estate resemble those for stocks from the late 1970s. REIT returns appear to be a perverse hedge against inflation (negative or insignificant hedging coefficients), in sharp contrast to the partial hedging properties of unsecuritised real estate. However, most early studies of inflation hedging with REITs test the Fama and Schwert (1977) model or its extensions based on ‘deficient’ OLS approaches.32 The negative or insignificant relationship between REIT returns and inflation has been documented for various sample periods and countries and remained largely unexplained until more recent research based on advanced econometric models (such as cointegration techniques) shed light on the subject. These approaches that are able to differentiate between any long-run equilibrium and short-run dynamic adjustments provided potential explanations including (i) spurious regression, (ii) differences in information processing between REITs and direct real estate, (iii) long- and short-run dynamics, (vi) regime dependency and (v) asymmetric adjustments of REIT returns to inflation (see Hoesli et al., 2008). However, also note that a long-term equilibrium relationship between real estate and inflation must not necessarily imply a hedge at long horizons because real estate may influence inflation. This introduces endogenity biases whose problems have to be addressed by instrumental variable estimation. Turning to our review of studies using methodologies beyond simple OLS regressions, we start with Tarbert (1996). Based on quarterly and semi-annual data from 1978 to 1995, he finds no evidence of a long-term hedging ability of British commercial real estate. Cointegration tests do not yield evidence for any stable relationship between commercial property and inflation. This result has been confirmed by Stevenson (1999) who employs both an OLS-based Fama and Schwert (1977) framework to examine commercial and residential property in the UK (mixed evidence concerning 30 If a large number of REITs become included in stock indices that are negatively correlated with inflation in the short run, this could weaken the hedging function of REITs, as the volatility from the stock market can overweigh the stability of REIT dividend payments over time (see Hardin et al., 2012). 31 Appraisal-based returns, as used in Hartzell, Hekman, and Miles (1987), tend to yield higher hedging coefficients than transaction-based returns or returns that are corrected for appraisal smoothing. 32 For example, Yobaccio, Rubens, and Ketcham (1995) propose a modified Fama and Schwert (1977) approach termed capital asset pricing model under uncertain inflation (CAPMUI), which relates expected real returns to inflationary expectations. Tarbert (1996) challenges their findings that are based on static regression approaches because they cannot capture slow adjustments of the real estate markets to changes in inflation. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 207 inflation hedging) and cointegration analysis (neither residential nor commercial property is cointegrated with inflation between 1983 and 1995). However, Barkham, Ward, and Henry (1996) and Matysiak, Hoesli, MacGregor, and Nanthakumaran (1996) provide contradictory results, implying that British direct real estate does hedge inflation measured by the RPI in the long run. By means of unit root, maximal eigen values and trace tests, Matysiak et al. (1996) show that while commercial real estate does not hedge inflation in the short run, there is a long-term inflation hedging characteristic of direct real estate in contrast to property shares. Barkham et al. (1996) conclude that real estate returns and inflation are cointegrated with persistent deviations from the equilibrium. Furthermore, inflation appears to Granger-cause real estate but real estate does not Granger-cause inflation. The findings in countries other than the UK also tend to favour an equilibrium between real estate returns and inflation over longer horizons. Anari and Kolari (2002), Park and Bang (2012) and Obereiner and Kurzrock (2012) all find direct real estate to be cointegrated with inflation in the US, Korea and Germany, respectively. Based on both autoregressive distributed lag (ARDL) models and recursive regressions, Anari and Kolari (2002) find Fisher coefficients that are consistently above unity, ranging from 1.08 to 1.42 in the US between 1968 and 2000. Although Korean direct real estate markets lack reliable, long and transaction-based time series,33 Park and Bang (2012) show that, contrary to listed real estate which provides a hedge only over longer horizons, appraisal-based commercial real estate provides a hedge against inflation, both in the short run and in the long run. Finally, Obereiner and Kurzrock (2012) examine three indirect real estate investment vehicles in Germany from 1992 to 2009: open-end funds, special funds and real estate stocks. The returns are almost independent of inflation in the short run. However, causality tests and different cointegration models suggest that indirect real estate provides a long-run hedge. The studies of Ganesan and Chiang (1998), Glascock, Lu, and So (2000, 2002), Hoesli et al. (2008), Le Moigne and Viveiros (2008) and Hardin, Jiang, and Wu (2012) advocate that the inflation hedging ability of real estate depends on the specific type of real estate asset, is regime-dependent or (dis)appears over time. For example, the findings of Ganesan and Chiang (1998) based on the Fama and Schwert (1977) framework differ widely depending on the type of real estate. Commercial and residential real estate in Hong Kong possesses good hedging properties with respect to expected and unexpected components of inflation in the sample period of 1984–1994, whereas other private real estate and property stocks fail to hedge inflation in the short run. In the long run, only property stocks were found to be cointegrated with inflation. Glascock et al. (2002) consider three potential rationales for the negative relationship between REIT returns and inflation in the literature that contradicts the alleged hedging property of direct real estate. First, REITs might be better at processing information than the general real estate sector, thus instantaneously reflecting future economic prospects. Second, the usage of data that contain more recent rather than future information could bias unsecuritised real estate returns. Third, improper econometric approaches may reverse the causal relationships between REIT returns and inflation. Introducing monetary regimes, the authors show that the perverse inflation hedging property of REITs is attributable merely to changes in monetary policy and therefore spurious. REIT returns seem to anticipate (Granger-cause) changes in expected and unexpected inflation. A similar approach that combines the proxy hypothesis framework with a long-run framework (covering the linkages between inflation, asset returns as well as macroeconomic and monetary variables) has been taken by Hoesli et al. (2008) for US and UK data from 1977 to 2003. According to their study, real estate returns are positively linked to expected inflation, but not to (unanticipated) inflation shocks. The adjustment to changes in inflation is gradual, implying that real estate does not always offer short-term protection.34 Inflation is positively linked to private and public commercial 33 While initially there has been much attention to American and British real estate markets, Asian markets have become the focus of recent interest. This entails new obstacles such as a lack of privatised real estate markets and limited access to investment opportunities. China, for instance, faced a gradual renunciation from a welfare-based approach to a market-based approach not until the late 1990s (see Zhou & Clements, 2010). 34 This finding is in line with the unfavourable (moderate) short-run (long-run) hedging ability identified by Froot (1995), Hoevenaars, Molenaar, Schotman, and Steenkamp (2008), Amenc et al. (2009) and Brière and Signori (2012) in a multi-asset 208 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 real estate once the impact of macroeconomic and monetary variables is considered, a result that holds for the UK and the US. Real estate returns hedge expected inflation one-to-one whereas the coefficients for unexpected inflation are either negative or insignificant. Private real estate appears to outperform public market assets in the sense that privately-owned real estate exhibits significant coefficients for both expected and unexpected inflation. Like Glascock et al. (2002), Lee and Lee (2012) base their study on a US total return REIT index. By means of dynamic OLS models (DOLS) they show that REITs serve as a hedge against expected inflation only after a structural break in 1993, where a tax reform made large-scale investments in REITs more desirable to institutional investors. Furthermore, they highlight that the hedging capability of REITs is driven by large-cap REITs but small-cap REITs fail to hedge inflation once isolated from the influence of large REITs. Hardin et al. (2012) also take into account the structural break in the US by splitting the sample period into two sub-periods (1980–1992 and 1993–2008) in order to obtain robust evidence on real estate stocks and REITs. By employing dividend yield composition, the authors show that, while both inflation illusion and hedging effects exist in REITs, the effect of inflation illusion seems to dominate throughout the entire sample period, from 1980 to 2008. Their results support the Modigliani and Cohn (1979) hypothesis that investors cannot quickly reconcile the changes in discount rates and dividend growth rates associated with inflation into stock prices. Thus, even though we might observe that REIT stock prices are negatively related to expected inflation, REITs compensate investors for the expected component of inflation via the dividend growth rate. Le Moigne and Viveiros (2008) examine how a variety of Canadian real estate types (by property type and province) hedge against inflation based on unsmoothed real estate returns from 1973 to 2007. They find that Canadian real estate acted as an inflation hedge over the sample period but also that this inflation-hedging ability has disappeared since the mid-1980s. To check for robustness, the tests are repeated for two subperiods (1973–1991 and 1992–2007) that coincide with the introduction of an inflation targeting policy by the Bank of Canada aiming to maintain inflation in the 1–3% range. The findings confirm the argument of Stevenson and Murray (1999) that real estate loses its protection against inflation in regimes with low rates of inflation. While Chatrath and Liang (1998) and Adrangi et al. (2004) support the traditional notion that REITs do not hedge inflation (in contrast to direct real estate) with almost identical sample periods from 1972 to 1995 and 1972 to 1999, respectively, Simpson et al. (2007) consider the asymmetric behaviour of REIT returns in explaining the alleged perverse inflation behaviour of REITs. Based on monthly data for 195 publicly traded equity REITs (EREITs) between 1981 and 2002, they use fixed-effect pooled regressions to allow for firm-specific differences via different intercept terms for each cross-section of the analysis. The authors conclude that the response of EREIT returns to inflation is asymmetric. In other words, when expected and unexpected inflation are separated into positive and negative changes, results indicate that EREIT returns rise in response to both increases and decreases in inflation. Rather than attributing the traditionally found negative relation to proxy effects or regime dependence, Simpson et al. (2007) claim that it is in fact this asymmetric adjustment of returns in conjunction with monetary policy effects that explain the puzzling behaviour. The findings of previous studies would then be nothing but ‘an artefact of the methodology they employ, which implicitly assumes symmetrical responses of EREIT returns to inflation’. In summary, empirical evidence indicates that even though direct real estate features severe datarelated and practical shortcomings, it is regarded as an (at least partial) inflation hedge by earlier studies that rely mainly on static regression approaches. In contrast, early studies of REIT returns have found a negative relation to inflation. With the advent of cointegration approaches in the real estate literature in the 1990s, the evidence on the inflation-hedging properties of real estate assets has become more ambiguous. Cointegration techniques as well as causality tests in more recent studies perspective where the focus of interested in how an asset reduces inflation exposure of a portfolio when it is added to the portfolio. It is supplemented by Bekaert and Wang (2010) showing that real estate consistently underperforms stocks in hedging expected and unexpected inflation. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 209 have produced mixed results on whether direct and indirect real estate is capable of hedging inflation. In particular, the choice of the sample period, inflation regime dependency, the type of real estate and asymmetries in the reaction of real estate returns to inflation news appear to play a crucial role in the interplay of real estate returns and the rate of inflation. 4. Conclusion Recent research has directed considerable effort towards answering the important question of whether investments in certain assets can shield investors from inflation risk. In this line of scientific work, the basic feature of interest is the interplay between asset returns and inflation rates because a positive relationship implies that asset returns (fully or partially) compensate a rising inflation rate. Similar to other fields, studies evolve by application of more advanced econometric techniques, by considering previously detected data features (such as structural breaks and time-dependency of variables) or by extension to new countries or longer time-spans. This process naturally leads to a wide variety of (potentially conflicting) results that require structuring in order to draw overall conclusions. Reviewing the literature on the inflation hedging properties of the four major assets (asset classes) stocks, gold, fixed income securities, and real estate, we provide such a structure that allows the detection of changing perceptions of the effectiveness of inflation hedging over time and to identify gaps that might be addressed in future research. Overall, our review describes the state of scientific knowledge concerning the link between asset returns and inflation. Most of the recent studies, using more sophisticated statistical methodology than the seminal studies in the field, find a long-run equilibrium between common stocks and inflation implying an effective inflation hedge at horizons of five years or more. In contrast, gold, typically advertised by the media as an ideal hedge because of its historically documented ability to rise in times of recession or financial turmoil, does not seem to offer such protection. Studies published in the aftermath of the financial crisis in 2008 report strong time variations in the gold–inflation linkage caused by structural breaks, different strength of the link depending on the investment horizon or even argue that outliers are the sole reason for historically documented positive relationships. As far as fixed income securities are concerned, nominal bills and bonds cannot hedge against inflation shocks. Inflation-linked bonds are designed to protect investors against inflation but scarce liquidity and limited available maturities restrain investors from using them. Finally, while the overall picture suggests that real estate might be an (at least partial) inflation hedge especially in the long run, several technical issues limit the validity of previously published results. While the analysis of direct real estate suffers from severe data-related and practical shortcomings, the more favourable indirect instrument of REITs also provides only a mixed picture because, for example, state dependence and asymmetric price reactions play a crucial role in the interplay of real estate returns and the rate of inflation. Given that even the most recent studies have produced partially conflicting results, how should future research proceed? To obtain a clear answer on the inflation-hedging question, we need a full-scale analysis that covers all relevant dimensions and crucial impact factors identified in previous studies. First, it has to encompass all asset classes (stocks, gold, fixed income securities and real estate) simultaneously in order to allow a direct comparison of results and identify which asset can be regarded as the best hedge. As far as the analysis of common stocks is concerned, it would be interesting to supplement the typical use of stock marked indices by the direct use of highly liquid individual stocks because they are typical components of private investors’ portfolios and because this way index construction methodologies cannot distort results. Second, we should focus on the safe haven property rather than a general hedging property because the latter offers protection only on average but not necessarily in times when it is most needed: in phases of high inflation. Besides considering this inflation regime dependency, it is also important to take into account other kinds of structural breaks such as periods of fixed gold prices, significant advancements in inflation measurement, regulatory changes in REITs markets or crucial financial turbulences. Third, the asset classes should not be analysed in an isolated context linked to only inflation. We require a system that models interactions between the different asset classes and also other variables that might influence returns (e.g. macroeconomic variables). Of 210 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 course such a system has to allow for long-term equilibria and short-term deviations thereof. Fourth, especially for real estate, data flaws have to be ruled out (e.g. by concentrating on REITs only). Furthermore, potential endogenity biases related to the interaction of housing and goods prices have to be addressed. Fifth, to obtain not only country-specific evidence, we have to consider a representative cross-section of markets. Finally, the analysis should cover several investment horizons in order to distinguish short-term from long-term inflation protection. Considering all these aspects allows giving a profound answer to the question of when, where and to what extend investments in stocks, gold, fixed income securities and real estate can shield investors from inflation risk. Given today’s situation of close to zero interest rates, we might expect that bills cannot protect against inflation and arising bubbles in stock and real estate markets (especially in Europe) that are the result of money shifts from bills to stocks and real estate have a crucial effect on the historically documented hedging ability of these assets. Acknowledgement We thank an anonymous reviewer for valuable comments and suggestions. References Adrangi, B., Chatrath, A., & Raffiee, K. (2003). Economic activity, inflation, and hedging: The case of gold and silver investments. Journal of Wealth Management, 6(2), 60–77. Adrangi, B., Chatrath, A., & Raffiee, K. (2004). REIT investments and hedging against inflation. Journal of Real Estate Portfolio Management, 10(2), 97–112. Ahmed, S., & Cardinale, M. (2005). Does inflation matter for equity returns? Journal of Asset Management, 6(4), 259–273. Alagidede, P., & Panagiotidis, T. (2010). Can common stocks provide a hedge against inflation? Evidence from African countries. Review of Financial Economics, 19(3), 91–100. Amenc, N., Martellini, L., & Ziemann, V. (2009). Inflation-hedging properties of real assets and implications for asset-liability management decisions. Journal of Portfolio Management, 35(4), 94–110. Anari, A., & Kolari, J. (2002). House prices and inflation. Real Estate Economics, 30(1), 67–84. Atkeson, A., & Ohanian, L. E. (2001). Are Phillips curves useful for forecasting inflation? Federal Reserve Bank of Minneapolis Quarterly Review, 25(1), 2–11. Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1–22. Barkham, R. J., Ward, C. W., & Henry, O. T. (1996). The inflation-hedging characteristics of UK property. Journal of Property Finance, 7(1), 62–76. Batten, J. A., Ciner, C., & Lucey, B. M. (2014). On the economic determinants of the gold–inflation relation. Resources Policy, 41, 101–108. Baur, D. G. (2011). Explanatory mining for gold: Contrasting evidence from simple and multiple regressions. Resources Policy, 36(3), 265–275. Baur, D. G., Beckmann, J., & Czudaj, R. (2014). Gold price forecasts in a dynamic model averaging framework: Have the determinants changed over time? Ruhr Economic Papers No. 506. Baur, D. G., & Lucey, B. M. (2010). Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review, 45(2), 217–229. Baur, D. G., & McDermott, T. K. (2010). Is gold a safe haven? International evidence. Journal of Banking & Finance, 34(8), 1886–1898. Beckmann, J., Berger, T., & Czudaj, R. (2015). Does gold act as a hedge or a safe haven for stocks? A smooth transition approach. Economic Modelling, 48, 16–24. Beckmann, J., & Czudaj, R. (2013). Gold as an inflation hedge in a time-varying coefficient framework. North American Journal of Economics and Finance, 24, 208–222. Bekaert, G., & Engstrom, E. (2010). Inflation and the stock market: Understanding the Fed model. Journal of Monetary Economics, 57(3), 278–294. Bekaert, G., & Wang, X. (2010). Inflation risk and the inflation risk premium. Economic Policy, 25(64), 755–806. Białkowski, J. P., Bohl, M. T., Stephan, P. M., & Wisniewski, T. P. (2014). The gold price in times of crisis. International Review of Financial Analysis (in press). Blose, L. E. (2010). Gold prices, cost of carry, and expected inflation. Journal of Economics and Business, 62(1), 35–47. Bodie, Z. (1976). Common stocks as a hedge against inflation. Journal of Finance, 31(2), 459–470. Boudoukh, J., & Richardson, M. (1993). Stock returns and inflation: A long-horizon perspective. American Economic Review, 83(5), 1346–1355. Brière, M., & Signori, O. (2012). Inflation-hedging portfolios: Economic regimes matter. Journal of Portfolio Management, 38(4), 43–58. Brown, K. C., & Howe, J. S. (1987). On the use of gold as a fixed income security. Financial Analysts Journal, 43(4), 73–76. Campbell, J. Y., & Shiller, R. J. (1996). A scorecard for indexed government debt. NBER Macroeconomics Annual, 11, 155–208. Caporale, T., & Grier, K. B. (2000). Political regime change and the real interest rate. Journal of Money, Credit and Banking, 32(3), 320–334. Carmichael, J., & Stebbing, P. W. (1983). Fisher’s paradox and the theory of interest. American Economic Review, 73(4), 619–630. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 211 Charemza, W. W., Hristova, D., & Burridge, P. (2005). Is inflation stationary? Applied Economics, 37(8), 901–903. Charles, A., Darné, O., & Kim, J. H. (2015). Will precious metals shine? A market efficiency perspective. International Review of Financial Analysis (in press). Chatrath, A., & Liang, Y. (1998). REITs and inflation: A long-run perspective. Journal of Real Estate Research, 16(3), 311–326. Chen, K., & Tzang, D. (1988). Interest-rate sensitivity of real estate investment trusts. Journal of Real Estate Research, 3(3), 13–22. Christopoulos, D. K., & León-Ledesma, M. A. (2007). A long-run non-linear approach to the Fisher effect. Journal of Money, Credit and Banking, 39(2–3), 543–559. Chua, J., & Woodward, R. S. (1982). Gold as an inflation hedge: A comparative study of six major industrial countries. Journal of Business Finance & Accounting, 9(2), 191–197. Ciner, C., Gurdgiev, C., & Lucey, B. M. (2013). Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates. International Review of Financial Analysis, 29, 202–211. Clemente, J., Montañés, A., & Reyes, M. (1998). Testing for a unit root in variables with a double change in the mean. Economics Letters, 59(2), 175–182. Cochran, S. J., & Defina, R. H. (1993). Inflation’s negative effects on real stock prices: New evidence and a test of the proxy effect hypothesis. Applied Economics, 25(2), 263–274. Coudert, V., & Raymond-Feingold, H. (2011). Gold and financial assets: Are there any safe havens in bear markets? Economics Bulletin, 31(2), 1613–1622. Crowder, W. J., & Hoffman, D. L. (1996). The long-run relationship between nominal interest rates and inflation: The Fisher equation revisited. Journal of Money, Credit and Banking, 28(1), 102–118. Culver, S. E., & Papell, D. H. (1997). Is there a unit root in the inflation rate? Evidence from sequential break and panel data models. Journal of Applied Econometrics, 12, 435–444. Darby, M. R. (1975). The financial and tax effects of monetary policy on interest rates. Economic Inquiry, 13(2), 266–276. DeJong, D. N., Nankervis, J. C., Savin, N. E., & Whiteman, C. H. (1992). The power problems of unit root test in time series with autoregressive errors. Journal of Econometrics, 53(1), 323–343. Ely, D. P., & Robinson, K. J. (1997). Are stocks a hedge against inflation? International evidence using a long-run approach. Journal of International Money and Finance, 16(1), 141–167. Enders, W., & Siklos, P. L. (2001). Cointegration and threshold adjustment. Journal of Business & Economic Statistics, 19(2), 166–176. Engle, R. F., & Granger, C. W. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. Engsted, T., & Tanggaard, C. (2002). The relation between asset returns and inflation at short and long horizons. Journal of International Financial Markets, Institutions and Money, 12(2), 101–118. Erb, C. B., & Harvey, C. R. (2013). The golden dilemma. Financial Analysts Journal, 69(4), 10–42. Evans, M. D., & Lewis, K. K. (1995). Do expected shifts in inflation affect estimates of the long-run Fisher relation? Journal of Finance, 50(1), 225–253. Fama, E. F. (1975). Short-term interest rates as predictors of inflation. American Economic Review, 65(3), 269–282. Fama, E. F. (1981). Stock returns, real activity, inflation, and money. American Economic Review, 71(4), 545–565. Fama, E. F., & Schwert, G. W. (1977). Asset returns and inflation. Journal of Financial Economics, 5(2), 115–146. Fisher, I. (1930). The theory of interest. New York: Macmillan Company. Froot, K. A. (1995). Hedging portfolios with real assets. Journal of Portfolio Management, 21(4), 60–77. Ganesan, S., & Chiang, Y. (1998). The inflation-hedging characteristics of real and financial assets in Hong Kong. Journal of Real Estate Portfolio Management, 4(1), 55–67. Garbade, K., & Wachtel, P. (1978). Time variation in the relationship between inflation and interest rates. Journal of Monetary Economics, 4(4), 755–765. Garcia, J. A., & Van Rixtel, A. A. (2007). Inflation-linked bonds from a central bank perspective. ECB Occasional Paper No. 62. Garcia, R., & Perron, P. (1996). An analysis of the real interest rate under regime shifts. Review of Economics and Statistics, 78(1), 111–125. Geltner, D., MacGregor, B. D., & Schwann, G. M. (2003). Appraisal smoothing and price discovery in real estate markets. Urban Studies, 40(5-6), 1047–1064. Geske, R., & Roll, R. (1983). The fiscal and monetary linkage between stock returns and inflation. Journal of Finance, 38(1), 1–33. Ghosh, D., Levin, E. J., MacMillan, P., & Wright, R. E. (2004). Gold as an inflation hedge? Studies in Economics and Finance, 22(1), 1–25. Glascock, J. L., Lu, C., & So, R. W. (2000). Further evidence on the integration of REIT, bond, and stock returns. Journal of Real Estate Finance and Economics, 20(2), 177–194. Glascock, J. L., Lu, C., & So, R. W. (2002). REIT returns and inflation: Perverse or reverse causality effects? Journal of Real Estate Finance and Economics, 24(3), 301–317. Greene, W. H. (2008). Econometric analysis (6th ed.). Upper Saddle River: Person Education. Granger, C. W. (1983). Co-integrated variables and error correction models. University of California Discussion Paper No. 83–113. Granger, C. W., Hyung, N., & Jeon, Y. (2001). Spurious regressions with stationary series. Applied Economics, 33(7), 899–904. Gultekin, N. B. (1983a). Stock market returns and inflation forecasts. Journal of Finance, 38(3), 663–673. Gultekin, N. B. (1983b). Stock market returns and inflation: Evidence from other countries. Journal of Finance, 38(1), 49–65. Hardin, W. G., III, Jiang, X., & Wu, Z. (2012). REIT stock prices with inflation hedging and illusion. Journal of Real Estate Finance and Economics, 45(1), 262–287. Hartzell, D., Hekman, J. S., & Miles, M. E. (1987). Real estate returns and inflation. Real Estate Economics, 15(1), 617–637. Haug, A. A., Beyer, A., & Dewald, W. (2011). Structural breaks and the Fisher effect. B.E. Journal of Macroeconomics, 11(1), 1–31. Haug, A. A. (2014). On real interest rate persistence: The role of breaks. Applied Economics, 46(10), 1058–1066. Hautcoeur, P., & Jastram, R. W. (2010). The golden constant. Journal of Economics, 100(2), 189–190. Hendry, D. F. (1986). Econometric modelling with cointegrated variables: An overview. Oxford Bulletin of Economics and Statistics, 48(3), 201–212. 212 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Hoesli, M., Lizieri, C., & MacGregor, B. (2008). The inflation hedging characteristics of US and UK investments: A multi-factor error correction approach. Journal of Real Estate Finance and Economics, 36(2), 183–206. Hoevenaars, R. P., Molenaar, R. D., Schotman, P. C., & Steenkamp, T. B. (2008). Strategic asset allocation with liabilities: Beyond stocks and bonds. Journal of Economic Dynamics and Control, 32(9), 2939–2970. Huang, H., & Hudson-Wilson, S. (2007). Private commercial real estate equity returns and inflation. Journal of Portfolio Management, 33(5), 63–73. Jaffe, J. F. (1989). Gold and gold stocks as investments for institutional portfolios. Financial Analysts Journal, 45(2), 53–59. Jaffe, J. F., & Mandelker, G. (1976). The Fisher effect for risky assets: An empirical investigation. Journal of Finance, 31(2), 447–458. Jastram, R. W. (2009). The golden constant: The English and American experience 1560–2007. Cheltenham: Edward Elgar Publishing. Kaul, G. (1987). Stock returns and inflation: The role of the monetary sector. Journal of Financial Economics, 18(2), 253–276. Kim, J. H., & Ryoo, H. H. (2011). Common stocks as a hedge against inflation: Evidence from century-long US data. Economics Letters, 113(2), 168–171. Knif, J., Kolari, J., & Pynnönen, S. (2008). Stock market reaction to good and bad inflation news. Journal of Financial Research, 31(2), 141–166. Kolari, J. W., & Anari, A. (2001). Stock prices and inflation. Journal of Financial Research, 24(4), 587–602. Kothari, S., & Shanken, J. (2004). Asset allocation with inflation-protected bonds. Financial Analysts Journal, 60(1), 54–70. Lai, K. S. (1997). Long-term persistence in the real interest rate: Some evidence of a fractional unit root. International Journal of Finance and Economics, 2(3), 225–235. Lai, K. S. (2004). On structural shifts and stationarity of the ex ante real interest rate. International Review of Economics and Finance, 13(2), 217–228. Lai, K. S. (2008). The puzzling unit root in the real interest rate and its inconsistency with intertemporal consumption behavior. Journal of International Money and Finance, 27(1), 140–155. Lee, M., & Lee, M. (2012). Long-run inflation-hedging properties of United State equity real estate investment trusts (REITs): Before and after the structural break in the 1990. African Journal of Business Management, 6(6), 2162–2168. Le Moigne, C., & Viveiros, É. (2008). Private real estate as an inflation hedge: An updated look with a global perspective. Journal of Real Estate Portfolio Management, 14(4), 263–286. Levin, E. J., Montagnoli, A., & Wright, R. E. (2006). Short-run and long-run determinants of the price of gold. World Gold Council Research Study No. 32. Lintner, J. (1975). Inflation and security returns. Journal of Finance, 30(2), 259–280. Lothian, J. R., & McCarthy, C. H. (2001). Equity returns and inflation: The puzzlingly long lags. Research in Finance and Banking, 2, 149–166. Lothian, J. R., & Simaan, Y. (1998). International financial relations under the current float: Evidence from panel data. Open Economies Review, 9(4), 293–313. Lucey, B. M. (2011). What do academics think they know about gold. Alchemist, 62, 12–14. Lucey, B. M., & Li, S. (2015). What precious metals act as safe havens, and when? Some US evidence. Applied Economics Letters, 22(1), 35–45. Luintel, K. B., & Paudyal, K. (2006). Are common stocks a hedge against inflation? Journal of Financial Research, 29(1), 1–19. Lütkepohl, H., & Saikkonen, P. (1999). Order selection in testing for the cointegrating rank of a VAR process. In R. F. Engle, & H. White (Eds.), Cointegration, causality, and forecasting. A Festschrift in Honor of Clive W.J. Granger (pp. 168–199). Oxford: Oxford University Press. Madsen, J. B. (2007). Pitfalls in estimates of the relationship between stock returns and inflation. Empirical Economics, 33(1), 1–21. Mahdavi, S., & Zhou, S. (1997). Gold and commodity prices as leading indicators of inflation: Tests of long-run relationship and predictive performance. Journal of Economics and Business, 49(5), 475–489. Maki, D. (2003). Nonparametric cointegration analysis of the nominal interest rate and expected inflation rate. Economics Letters, 81(3), 349–354. Matysiak, G., Hoesli, M., MacGregor, B., & Nanthakumaran, N. (1996). The long-term inflation-hedging characteristics of UK commercial property. Journal of Property Finance, 7(1), 50–61. McCown, J. R., & Zimmerman, J. R. (2006). Is gold a zero-beta asset? Analysis of the investment potential of precious metals. Oklahoma City University Working Paper. McCown, J. R., & Zimmerman, J. R. (2007). Analysis of the investment potential and inflation-hedging ability of precious metals. Oklahoma City University Working Paper. Million, N. (2004). Central bank’s interventions and the Fisher hypothesis: A threshold cointegration investigation. Economic Modelling, 21(6), 1051–1064. Mishkin, F. S. (1984). The real interest rate: A multi-country empirical study. Canadian Journal of Economics, 17(2), 283–311. Mishkin, F. S. (1992). Is the Fisher effect for real? A reexamination of the relationship between inflation and interest rates. Journal of Monetary Economics, 30(2), 195–215. Modigliani, F., & Cohn, R. A. (1979). Inflation, rational valuation and the market. Financial Analysts Journal, 35(2), 24–44. Mundell, R. (1963). Inflation and real interest. Journal of Political Economy, 71(3), 280–283. Neely, C. J., & Rapach, D. E. (2008). Real interest rate persistence: Evidence and implications. Federal Reserve Bank of St. Louis Review, 90(6), 609–641. Nelson, C. R., & Schwert, G. W. (1977). Short-term interest rates as predictors of inflation: On testing the hypothesis that the real rate of interest is constant. American Economic Review, 67(3), 478–486. Nelson, C. R. (1976). Inflation and rates of return on common stocks. Journal of Finance, 31(2), 471–483. O’Connor, F. A., Lucey, B. M., Batten, J. A., & Baur, D. G. (2015). The financial economics of gold – A survey. International Review of Financial Analysis (in press). Obereiner, D., & Kurzrock, B. (2012). Inflation-hedging properties of indirect real estate investments in Germany. Journal of Property Investment and Finance, 30(3), 218–240. Park, Y. W., & Bang, D. W. (2012). Direct commercial real estate as an inflation hedge: Korean evidence. Journal of Real Estate Portfolio Management, 18(2), 187–203. S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 213 Parkin, M. (2008). Inflation. In S. N. Durlauf, & L. E. Blume (Eds.), The New Palgrave Dictionary of Economics. Basingstoke: Palgrave Macmillan. Perron, P., & Ng, S. (1996). Useful modifications to some unit root tests with dependent errors and their local asymptotic properties. Review of Economic Studies, 63(3), 435–463. Pullen, T., Benson, K., & Faff, R. (2014). A comparative analysis of the investment characteristics of alternative gold assets. Abacus, 50(1), 76–92. Rapach, D. E., & Wohar, M. E. (2005). Regime changes in international real interest rates: Are they a monetary phenomenon? Journal of Money, Credit and Banking, 37(5), 887–906. Roll, R. (1972). Interest rates on monetary assets and commodity price index changes. Journal of Finance, 27(2), 251–277. Rose, A. K. (1988). Is the real interest rate stable? Journal of Finance, 43(5), 1095–1112. Rubbaniy, G., Lee, K. T., & Verschoor, W. F. (2011). Metal investments: Distrust killer or inflation hedging? 24th Australasian Finance and Banking Conference Paper. Rödel, M. G. (2012). Inflation hedging. An empirical analysis on inflation nonlinearities, infrastructure, and international equities (PhD Thesis). Technical University of Munich. Rödel, M. G. (2014). Inflation hedging with international equities. Journal of Portfolio Management, 40(2), 41–53. Rödel, M. G., & Rothballer, C. (2012). Infrastructure as hedge against inflation – Fact or fantasy? Journal of Alternative Investments, 15, 110–123. Saikkonen, P., & Lütkepohl, H. (2000a). Testing for the cointegrating rank of a VAR process with an intercept. Econometric Theory, 16(3), 373–406. Saikkonen, P., & Lütkepohl, H. (2000b). Testing for the cointegrating rank of a VAR process with structural shifts. Journal of Business and Economic Statistics, 18(4), 451–464. Saikkonen, P., & Lütkepohl, H. (2000c). Trend adjustment prior to testing for the cointegrating rank of a vector autoregressive process. Journal of Time Series Analysis, 21, 435–456. Schotman, P. C., & Schweitzer, M. (2000). Horizon sensitivity of the inflation hedge of stocks. Journal of Empirical Finance, 7(3), 301–315. Schwert, G. W. (1987). Effects of model specification on tests for unit roots in macroeconomic data. Journal of Monetary Economics, 20(1), 73–103. Schwert, G. W. (1989). Tests for unit roots: A Monte Carlo investigation. Journal of Business & Economic Statistics, 7(2), 147–159. Shafiee, S., & Topal, E. (2010). An overview of global gold market and gold price forecasting. Resources Policy, 35(3), 178–189. Simpson, M. W., Ramchander, S., & Webb, J. R. (2007). The asymmetric response of equity REIT returns to inflation. Journal of Real Estate Finance and Economics, 34(4), 513–529. Smirlock, M. (1986). Inflation announcements and financial market reaction: Evidence from the long-term bond market. Review of Economics and Statistics, 68(2), 329–333. Solnik, B., & Solnik, V. (1997). A multi-country test of the Fisher model for stock returns. Journal of International Financial Markets, Institutions and Money, 7(4), 289–301. Spierdijk, L., & Umar, Z. (2014). Are commodity futures a good hedge against inflation? Journal of Investment Strategies, 3(2), 35–57. Spyrou, S. I. (2004). Are stocks a good hedge against inflation? Evidence from emerging markets. Applied Economics, 36(1), 41–48. Stevenson, S. (1999). The performance and inflation hedging ability of regional housing markets. Journal of Property Investment and Finance, 17(3), 239–260. Stevenson, S., & Murray, L. (1999). An examination of the inflation hedging ability of Irish real estate. Journal of Real Estate Portfolio Management, 5(1), 59–69. Stock, J. H., & Watson, M. W. (1999). Forecasting inflation. Journal of Monetary Economics, 44(2), 293–335. Stock, J. H., & Watson, M. W. (2007). Why has US inflation become harder to forecast? Journal of Money, Credit and Banking, 39(1), 3–33. Summers, L. H. (1983). In J. Tobin (Ed.), The non-adjustment of nominal interest rates: A study of the Fisher effect (2nd ed., pp. 201–241). Washington, DC: Symposium in honor of Arthur Okun, Brookings Institution. Sun, Y., & Phillips, P. C. (2004). Understanding the Fisher equation. Journal of Applied Econometrics, 19(7), 869–886. Swinkels, L. (2012). Emerging market inflation-linked bonds. Financial Analysts Journal, 68(5), 38–56. Tarbert, H. (1996). Is commercial property a hedge against inflation? A cointegration approach. Journal of Property Finance, 7(1), 77–98. Taylor, J. B. (1993). Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy, 39, 195–214. Taylor, N. J. (1998). Precious metals and inflation. Applied Financial Economics, 8(2), 201–210. Tobin, J. (1965). Money and economic growth. Econometrica, 33(4), 671–684. Tsay, R. S. (2005). Analysis of financial time series. Hoboken: John Wiley & Sons. Tsong, C., & Lee, C. (2013). Quantile cointegration analysis of the Fisher hypothesis. Journal of Macroeconomics, 35, 186–198. Tully, E., & Lucey, B. M. (2007). A power GARCH examination of the gold market. Research in International Business and Finance, 21(2), 316–325. Urich, T., & Wachtel, P. (1984). The effects of inflation and money supply announcements on interest rates. Journal of Finance, 39(4), 1177–1188. Wang, K., Lee, Y., & Thi, T. N. (2011). Time and place where gold acts as an inflation hedge: An application of long-run and short-run threshold model. Economic Modelling, 28(3), 806–819. Wilcox, S. E. (2012). Equity valuation and inflation: A review. Research Foundation Literature Reviews, 7(1), 1–23. Wilson, P. J., & Zurbruegg, R. (2003). International diversification of real estate assets: Is it worth it? Evidence from the literature. Journal of Real Estate Literature, 11(3), 257–278. Worthington, A. C., & Pahlavani, M. (2007). Gold investment as an inflationary hedge: Cointegration evidence with allowance for endogenous structural breaks. Applied Financial Economics Letters, 3(4), 259–262. Yobaccio, E., Rubens, J. H., & Ketcham, D. C. (1995). The inflation-hedging properties of risk assets: The case of REITs. Journal of Real Estate Research, 10(3), 279–296. Yoon, G. (2010). Does nonlinearity help resolve the Fisher effect puzzle? Applied Economics Letters, 17(8), 823–828. 214 S. Arnold, B.R. Auer / North American Journal of Economics and Finance 34 (2015) 187–214 Zhou, X., & Clements, S. (2010). The inflation hedging ability of real estate in China. Journal of Real Estate Portfolio Management, 16(3), 267–277. Zhou, Z. (2014). Commodity futures as a hedge against inflation: An application of Markov-switching cointegration and errorcorrection modeling. Bocconi University Working Paper. Zivot, E., & Andrews, D. W. K. (2002). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 20(1), 25–44.