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Oil, inflation, and financial markets Jiang, Haibo 2016

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Oil, Inflation, and Financial MarketsbyHaibo JiangBSc. Applied Mathematics, UESTC, 1997BCom. Finance, Concordia University, 2007MSc. Finance, Concordia University, 2009A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Business Administration)The University of British Columbia(Vancouver)July 2016© Haibo Jiang, 2016AbstractThe economy’s heavy dependence on fossil energy links oil prices to real economic activities, inflation,and financial markets. This dissertation studies the extent to which fluctuations in oil prices are related toinflation and the prices and expected returns of Treasury bonds.Chapter 2 shows that the correlation between U.S. core inflation and oil price changes exhibits a time-varying pattern since the 1970s. The significant resurgence of the positive correlation after the 2007 financialcrisis is puzzling, given the subdued macroeconomic impact of oil price shocks since the mid-1980s. A two-sector DSGE model illustrates that the relation between the price of oil and core inflation depends on thetype of shocks embedded in oil price changes. Oil supply shocks cause the price of oil and core inflation toco-move, whereas the aggregate demand shocks driven by economic growth lead to opposing changes in theprice of oil and core inflation. The economic mechanisms uncovered in the model and historical geopoliticalevents together provide a consistent and logical explanation of the time-varying correlations observed in thedata.Chapter 3 examines the economic impact of oil prices on Treasury bond returns. I find novel evidencethat growth rates of crude oil prices can explain contemporaneous excess returns on nominal U.S. Treasurybonds and inflation swaps, and also predict expected future excess returns on inflation swaps. Empiricalresults suggest that the impact of oil prices on nominal bonds is through the impact on expected inflation. Ithen build a two-sector New Keynesian model to study theoretical interactions between the economic driversof oil prices, expected inflation, and bond yields. The model shows that oil supply and demand shocks haveopposite impacts on bond yields and expected inflation. The conventional wisdom that high oil prices leadto high expected inflation and nominal yields is true only if high oil prices are driven by a negative shock tothe supply of oil. In contrast, when oil prices are driven by a positive shock to productivity growth, high oilprices can lead to low expected inflation and nominal yields.iiPrefaceThis dissertation is original, unpublished, independent work by the author, Haibo Jiang.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Reconciling the puzzling time-varying correlations between oil price changes and core infla-tion: The distinct roles of supply and demand shocks . . . . . . . . . . . . . . . . . . . . . . . 62.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Related literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Empirical facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.1 Data and summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.2 The puzzling time-varying correlations between core inflation and oil price changes . 142.3.3 Structural changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 A two-sector general equilibrium model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16iv2.4.2 Oil sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.3 Final consumption goods sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.4 Central bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4.5 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5 Oil price and core inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.1 Supply-demand diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.5.2 Positive and negative correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.6 Historical events, oil supply and demand shocks, and correlations . . . . . . . . . . . . . . . 202.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Oil prices, expected inflation, and bond returns . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2 Bond returns and oil prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.2 Excess returns on nominal bonds, TIPS, and breakeven inflation . . . . . . . . . . . 383.2.3 Excess returns on inflation swap rates . . . . . . . . . . . . . . . . . . . . . . . . . 393.3 A two-sector New Keynesian model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.2 Oil sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.3.3 Core goods sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.3.4 Central bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.5 Symmetric equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.6 Measures of inflation, yields, and inflation swaps . . . . . . . . . . . . . . . . . . . 473.4 Model solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4.2 Model moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.5 Oil prices, expected inflation, and bond yields . . . . . . . . . . . . . . . . . . . . . . . . . 513.5.1 Oil prices and three productivity shocks . . . . . . . . . . . . . . . . . . . . . . . . 513.5.2 Expected inflation, real yields, and nominal yields . . . . . . . . . . . . . . . . . . 533.5.3 Bond return regressions on simulated data . . . . . . . . . . . . . . . . . . . . . . . 55v3.5.4 Key economic mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.5.5 Term structure of nominal yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.5.6 Inflation risk premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Appendix A Equilibrium conditions of the two-sector general equilibrium model . . . . . . . . 83Appendix B Inflation swap contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Appendix C Latent factors of inflation swap contracts . . . . . . . . . . . . . . . . . . . . . . . 87Appendix D Equilibrium conditions of the two-sector New Keynesian model . . . . . . . . . . . 90D.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90D.2 The oil firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91D.3 The final goods firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92D.4 Intermediate goods firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92D.5 Market clearing conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93viList of TablesTable 2.1 Summary statistics of inflation series and oil price changes . . . . . . . . . . . . . . . . 24Table 2.2 Chow test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Table 2.3 List of geopolitical and economic events . . . . . . . . . . . . . . . . . . . . . . . . . . 26Table 3.1 Excess bond returns: Contemporaneous regressions . . . . . . . . . . . . . . . . . . . . 59Table 3.2 Excess bond returns: Predictive regressions . . . . . . . . . . . . . . . . . . . . . . . . . 60Table 3.3 Excess returns on inflation swap rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Table 3.4 Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Table 3.5 Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Table 3.6 Data and model implied statistics for alternative specifications . . . . . . . . . . . . . . . 64Table 3.7 Variance decompositions for the baseline model . . . . . . . . . . . . . . . . . . . . . . 65Table 3.8 Decomposition of the one-period inflation risk premium . . . . . . . . . . . . . . . . . . 66Table B.1 Summary statistics of the U.S. zero-coupon inflation swap rates . . . . . . . . . . . . . . 86Table C.1 Level and slope factors of inflation swap rates . . . . . . . . . . . . . . . . . . . . . . . 88viiList of FiguresFigure 2.1 Historical prices of crude oil and core inflation . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.2 The price of oil and world crude oil production . . . . . . . . . . . . . . . . . . . . . . 28Figure 2.3 Correlations between monthly core inflation and one-month lagged oil price changes . . 29Figure 2.4 A negative productivity shock in the oil sector . . . . . . . . . . . . . . . . . . . . . . . 30Figure 2.5 A positive productivity shock in the consumption goods sector . . . . . . . . . . . . . . 31Figure 2.6 U.S. energy intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32Figure 3.1 Inflation swap rates and crude oil spot price growth . . . . . . . . . . . . . . . . . . . . 67Figure 3.2 Standard deviations of changes in 10-year inflation swaps and growth rates of the nearest-to-maturity oil futures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 3.3 Impulse response functions to a negative oil productivity shock . . . . . . . . . . . . . . 69Figure 3.4 Impulse response functions to a positive short-run productivity shock . . . . . . . . . . 70Figure 3.5 Impulse response functions to a positive long-run productivity shock . . . . . . . . . . . 71Figure 3.6 Impulse response functions of 1-quarter and 5-year real yields to three productivity shocks 72Figure 3.7 Impulse response functions of 1-quarter and 5-year breakeven inflation rates to threeproductivity shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 3.8 Impulse response functions of 1-quarter and 5-year nominal yields to three productivityshocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 3.9 Inflation risk premia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Figure C.1 Loadings of the first three principal components of the inflation swap rates . . . . . . . . 89viiiAcknowledgmentsI am especially grateful for advice and encouragement from my advisor, Lorenzo Garlappi. I also thankmy committee members: Paul Beaudry, Murray Carlson, Jack Favilukis, Carolin Pflueger, and Georgios Sk-oulakis for their guidance and support. Warm thanks are also due to Adlai Fisher, Ron Giammarino, HernanOrtiz-Molina, and other finance faculty members and PhD students at UBC Sauder for their valuable com-ments and help. Special thanks go to Eduardo Schwartz, who sponsored and advised me as a visiting Ph.D.student at UCLA Anderson in 2013. In addition, I thank participants at the Northern Finance Association2014 and 2015 annual meetings and Brown Bag presentations at the Vancouver School of Economics atUBC and the Sauder School of Business at UBC for helpful suggestions and comments.My most important debt is to my family, especially my dear wife Xiuli Qi, who continue to support myacademic endeavors, with unending patience and unconditional support and love.Finally, I gratefully acknowledge financial support from the Social Sciences and Humanities ResearchCouncil of Canada (SSHRC) CGS Doctoral Fellowship and the Canadian Securities Institute (CSI) PhDScholarship.ixDedicationTo my dear wife, Xiuli QixChapter 1IntroductionThe connection between the price of crude oil and financial markets has attracted considerable attentionfrom investors and policymakers. A series of recent news articles, appeared in the Wall Street Journal andother financial presses, brought public attention to the pronounced reactions of stocks and Treasury bondmarkets to rises and falls in the price of oil.1 In addition, U.S. Fed and other central banks also typically payclose attention to oil price movements because oil price changes have a substantial effect on inflation and inparticular on energy inflation.The economy’s heavy dependence on fossil energy links oil prices to real economic activities and con-sequently to the aggregate price level and the financial markets. Petroleum and its derivative products, asthe main source of energy supply, are used for transportation and the production of a wide range of goodsand services. Global expenditures on petroleum account for about 4.5% of the world GDP. The average U.S.household spends about 4% of pre-tax income on gasoline for day-to-day transportation, and about 40% ofindustrial energy consumption is accounted for by oil.When the price of oil fluctuates, it affects households’ expenditure on gasoline and firms’ energy costs,and, to a large extent, influences aggregate consumption, production, and inflation. Thus oil price fluctua-tions inevitably have an effect on securities prices and monetary policies. Given the importance of oil to the1Examples of news articles on co-movements between stocks and oil include “Oil and stocks are moving tickfor tick” published on January 25, 2016 on CNBC (accessed on May 20, 2016 at http://www.cnbc.com/2016/01/25/oil-and-stocks-are-moving-tick-for-tick.html and “Is the link between stocks and oil breaking up?” published onApril 18, 2016 on the Wall Street Journal (accessed on May 20, 2016 at http://blogs.wsj.com/moneybeat/2016/04/18/is-the-link-between-stocks-and-oil-breaking-up/). Examples of news articles on the response of Treasury bonds to oilprice fluctuations include “U.S. Government bonds strengthen as oil slips: Yield curve flattest since January 2008”published on January 25, 2016 on the Wall Street Journal (accessed on May 20, 2016 at http://www.wsj.com/articles/u-s-government-bonds-strengthen-as-oil-slips-1453734373) and “US Treasury prices fall as oil buoyed” published on May 16,2016 on CNBC (accessed on May 20, 2016 at http://www.cnbc.com/2016/05/16/us-treasury-prices-fall-as-oil-buoyed.html).1macroeconomy, it is natural to study the extent to which fluctuations in oil prices are related to inflation andthe prices and expected returns of financial securities. Indeed, many studies, starting with Chen, Roll, andRoss (1986), have investigated the role of oil prices in stock returns.2 However, few papers have studied theimpact of oil prices on inflation and bond returns.3 This is especially surprising since intuition and empiricalobservations suggest an important link.The purpose of this dissertation is to fill this gap by studying the relationship between oil prices, inflation,and Treasury bond returns both empirically and theoretically. Specifically, Chapter 2 first documents apuzzling time-varying trend in correlations between U.S. core inflation and one-month lagged oil pricechanges from 1973 to 2015. The chapter then addresses the question of which economic mechanismsrationalize the observed time-varying correlations. Chapter 3 first addresses the question of whether theprice of oil price is a significant explanatory variable and predictor of excess returns on nominal Treasurybonds. Additionally, since oil price variations are widely thought to affect inflation, consumption, andoutput, I then examine whether oil prices are relevant determinants for expected inflation and real yields oninflation-indexed bonds.In general, this work is related to an extensive macroeconomic literature that studies the link betweenoil price shocks and the economy. Hamilton (1983) documents that oil price hikes precede 7 out of 8postwar U.S. recessions.4 This seminal paper triggers a series of studies that investigate the mechanisms oftransmission from oil price shocks to economic output.Recently, several papers document the muted impact of oil price shocks on the U.S. economy and otherdeveloped economies. The literature has explored different channels to rationalize this phenomenon. Blan-chard and Galı´ (2010) attribute a reduction in real wage rigidities, along with a reduction in the share ofenergy in production and a lack of adverse shocks, to the decline in the impact of oil shocks on inflationand economic activity. The channel of the asymmetric impact of oil price shocks on durable goods andnon-durable goods, which causes a large reduction in expenditures on durable goods, has been suggestedand empirically investigated (Dhawan and Jeske, 2008; Hamilton, 2008; Kilian and Park, 2009). Bernanke,Gertler, and Watson (1997) and Clark and Terry (2010), among others, show that monetary policy dramati-cally responds to oil price shocks and thus magnifies the impact of oil price shocks on the economy in the2Driesprong, Jacobsen, and Maat (2008), Kilian and Park (2009), Chiang, Hughen, and Sagi (2014), Jiang, Skoulakis, and Xue(2016), among others, find that oil prices impact stock returns.3Exceptions are studies by Kang, Ratti, and Yoon (2014) and Baker and Routledge (2015)4Hamilton (2011) updates the count at 10 out of 11.21970s and the 1980s, but has become less responsive to oil price shocks since the 2000s. However, Hamiltonand Herrera (2004) argue that monetary policy plays a much smaller role.The impact of oil price shocks on inflation also has been studied in the monetary literature. The literatureinvestigates the passthrough of oil price changes into inflation. The passthrough is usually estimated by thecoefficient of the oil price change in a regression of regressing inflation on oil price changes. The influence ofthe price of oil on inflation has declined from the 1970s to the 2000s. Clarke and Subramanian (2006) showthat core inflation in U.S. becomes less responsive to changes in energy prices. A decrease in energy intensityin the economy and in the exchange rate passthrough is attributed to the smaller magnitude of the influence(De Gregorio, Landerretche, Neilson, Broda, and Rigobon, 2007). Clark and Terry (2010) measure thepassthrough by allowing time-varying coefficients and volatilities and confirm findings in previous studies.Alarmingly, oil price fluctuations still have a substantial effect on the economy and the financial markets,as manifested by the most recent news articles on the pronounced reactions of stocks and Treasury bondmarkets to rises and falls in the price of oil, published in the period in January to May 2016.The perception of the nature of oil price shocks among economists has evolved. Oil price shocks wasthought to be exogenous and was associated with the disruption in supply of oil. Researchers commonlymodel oil prices as exogenous. However, this assumption is problematic, as pointed out by Rotemberg(2010) and Balke, Brown, and Yu¨cel (2011). Recently, researchers start to realize that not all oil priceshocks are the same. Kilian (2009) shows that oil price shocks are mostly driven by aggregate demandshocks instead of oil supply shocks in the period of 1975 to 2007. I take the simple view that oil pricesreflect fundamental supply and demand information in the world oil market.However, empirically identifying the intrinsic shocks embedded in the price of oil is challenging. Kilian(2009) proposes a VAR framework to decompose oil price changes, using data on world oil production andproxy for global real economic activities. Rapaport (2014) and Ready (2014) suggest to use informationfrom the stock market to distinguish supply and demand shocks in the oil market. Rapaport (2014) usesthe sign and magnitude of the correlation between daily oil price changes and stock market total returns toidentify shocks specific to the oil market and shocks that affect the overall economy. Ready (2014) proposesidentifying demand shocks by looking at the correlation between returns to oil firms and innovation in theVIX index.As pointed out by Sockin and Xiong (2014), a theoretical model can help us better understand theimpact of oil price shocks on the economy and the financial markets. The price of oil should be modeled3endogenously, and the demand side of the oil market should be emphasized.This dissertation highlights three unique features of the oil in the economy. First, an oil sector is explic-itly modeled in addition to the standard consumption goods sector. Second, oil is included in a household’sutility function, to capture the fact that households spend about 4% of their pre-tax income on gasoline fortransportation needs. In addition, household consumption of oil is assumed to be complementary to the con-sumption of core goods, as in Ready (2015). In particular, oil is complementary to the consumption of somedurable goods, such as motor vehicles. Third, oil is also used as an energy input in producing consumptiongoods, reflecting the fact that 40% of industrial energy comes from oil.This dissertation is related to a growing literature on studying determinants of nominal and real bondyield curves. Previous papers studying real rates, inflation expectations, and risk premia use latent factorterm structure models (Ang, Bekaert, and Wei, 2008; Chernov and Mueller, 2012; Haubrich, Pennacchi, andRitchken, 2012) and New Keynesian macro models (Kung, 2015; Hsu, Li, and Palomino, 2014). However,oil prices have not been considered in this literature. In chapter 3, the price of oil is treated as an explicitmacroeconomic risk factor. In addition, the chapter 3 builds on the New Keynesian model; moreover, itincludes an oil sector and incorporates the dual uses of oil to examine macroeconomic linkages among bondyields, inflation expectations, and supply and demand shocks in the oil markets.My research is also related to several empirical papers that document the connection between oil spot orfutures prices and U.S. Treasury bond returns. Kang, Ratti, and Yoon (2014) show that U.S. Treasury bondreturns deflated by the U.S. CPI are negatively associated with oil price shocks driven by global aggregatedemand for all industrial commodities. Baker and Routledge (2015) document that monthly excess returnson nominal U.S. Treasury bonds are higher when the slope of NYMEX WTI crude oil futures curve isnegative. Moreover, few papers study the impact of oil prices on long-term expected inflation, althoughnumerous studies examine the effect of oil prices on contemporaneous core inflation and total inflation, asreviewed in detail in Clark and Terry (2010). Celasun, Mihet, and Ratnovski (2012) find that oil futures priceshocks have a statistically significant impact on long-term breakeven inflation. In fact, both real rates andexpected inflation are important in understanding nominal bond yields (Duffee, 2014; Pflueger and Viceira,2015). I am the first to examine not only nominal bond yields as a whole, but also real bond yields andbreakeven inflation separately in relation to oil prices.Last, several recent papers have studied the impact of oil price shocks on equity returns. Driesprong,Jacobsen, and Maat (2008) find that increases in oil prices predict lower future stock returns. Kilian and4Park (2009) show that oil supply and demand shocks jointly explain 22% of the long-run variation in U.S.real stock returns. Chiang, Hughen, and Sagi (2014) demonstrate that oil risk factors explain the returns ofnon-oil portfolios. These papers highlight important implications of oil price risks for equity returns, butignore inflation. Unlike these papers, my focus is the impact of oil on inflation and bond yields.The dissertation is organized as follows. Chapter 2 studies the puzzling time-varying correlations be-tween core inflation and oil price changes. A two sector DSGE model is built to show the distinct impacts ofoil supply and demand shocks on oil prices and core inflation. Historical geopolitical events and economicdata are then used to reconcile the time-varying correlations. Chapter 3 focuses on the empirical and theo-retical relations between oil price, expected inflation, and bond returns. It provides novel empirical evidenceof the connection between oil prices, breakeven inflation, and real and nominal Treasury bond returns. Atwo-sector New Keynesian model illustrates theoretical predictions and replicates several key empirical re-sults. The responses of real yields, breakeven inflation, and nominal yields to increases in oil prices dependon the type of shocks that drive oil prices. Chapter 4 concludes.5Chapter 2Reconciling the puzzling time-varyingcorrelations between oil price changes andcore inflation: The distinct roles of supplyand demand shocks2.1 IntroductionThe correlation between oil price changes and inflation has been of great interest to pensioners, pensionfund managers, and monetary policymakers. Because oil price changes have a substantial effect on inflationand in particular on energy inflation, U.S. Fed and other central banks typically monitor oil price movementsclosely. Furthermore, inflation jumps destroy pensioners’ purchasing power and increase pension funds’payments and liabilities. The size of the pension entitlements of the private and public pension funds inthe U.S. is enormous, around $17.9 trillion dollars as of December 2014.1 Therefore, understanding themacroeconomic linkage between the price of oil and inflation is very important. The effectiveness of usingcrude oil futures to hedge inflation critically depends on the correlation between oil price changes andinflation (Gorton and Rouwenhorst, 2006). In addition, oil prices can be used to gauge information regardinginflation (Cheng and Xiong, 2014). The correlation is useful for central banks to filter out the underlying1Data on the pension funds are obtained from the Fed Reserve’s websites.6driving forces of inflation.Core inflation represents the change of the consumer price index (CPI) excluding food and energy. Theweight of CPI-core items in the CPI consumer basket is substantial, about 76%.2 As a result, core inflation isconsidered as a viable inflation target for monetary policy. Note that total inflation contains energy inflation,which is directly affected by oil price changes. The relationship between core inflation and oil prices is adistinct and clean measure of the inflationary impact of oil price shocks. However, how fluctuations in oilprices are related to core inflation is not straightforward.A time series of correlations between U.S. core inflation and one-month lagged oil price changes, com-puted using a five-year rolling estimation window, exhibits an interesting time-varying trend from 1973 to2015.3 The correlation declines from 1973 to the mid-1980s, and becomes small and sometimes negativebefore 2008; but it jumps up to a positive and high level again after 2008, and, interestingly, comes down toa low level from 2014. The decline in the correlation is consistent with the muted impact of oil price shockson the economy, as documented by Bernanke, Gertler, and Watson (1997), Hamilton (2008), Blanchard andGalı´ (2010), and Clark and Terry (2010), and others. Surprisingly, the correlation after the 2007 financialcrisis reverts to an equivalent level observed in the 1970s. The significant resurgence of the correlation ispuzzling because it defies easy explanations. For instance, the declining energy intensity in U.S. actuallypredicts a weaker relationship between oil price changes and core inflation.The purpose of this chapter is to study the relationship between oil prices and core inflation both em-pirically and theoretically. Specifically, I first address the question of whether there are structural breaks incorrelations between U.S. core inflation and oil price changes. I then examine which economic mechanismscan rationalize the observed puzzling pattern of the time-varying correlations.The connection between oil prices and inflation is through the indispensable use of oil in the economy.Oil, as the main source of energy supply, is used for transportation and the production of a wide range ofgoods and services. Statistical data from the U.S. Energy Information Administration show that about 4% ofpre-tax income of the average household is spent on gasoline for day-to-day transportation, and about 40%of industrial energy consumption is accounted for by oil in 2013. When the price of oil fluctuates, it affectshouseholds’ disposable income and firms’ energy costs, and, to a large extent, influences consumption, out-2The weights of CPI-energy and CPI-food items are around 8% and 16%, respectively.3One-month lag is used because it takes time for firms to adjust prices and production in response to oil price shocks. Thetime-varying trend is robust to contemporaneous or lagged correlations, to different lengths of rolling estimation window. Thetrend is also robust to other measures of the price of oil, such as the real price of oil, the PPI-crude oil price, and the CPI-energyindex.7put, and the aggregate price level. Thus oil price fluctuations naturally have an effect on inflation, valuationof financial products that are subject to inflation, and monetary policies.In my empirical analysis, besides estimating correlations, I also use a generalized Phillips curve model toassess the “passthrough” of oil price changes into core inflation. Chow tests show that two structural breaksin the relationship between oil price changes and core inflation occur in the mid-1980s and during the 2007financial crisis. The presence of structural breaks indicates that the relationship between core inflation andoil prices is not stable and has fundamentally changed over time.The perception of the nature of oil price shocks among economists has evolved. Oil price shocks wasthought to be exogenous and was associated with the disruption in the supply of oil. Recently, researchersstart to realize that not all oil price shocks are the same. Kilian (2009) shows that oil price shocks are mostlydriven by aggregate demand shocks instead of oil supply shocks. I take the simple view that oil prices reflectfundamental supply and demand information in the world oil market. Empirically identifying the intrinsicshocks embedded in the price of oil is challenging. Kilian (2009) proposes a VAR framework to decomposeoil price changes, using data on world oil production and proxy for global real economic activities. Rapaport(2014) and Ready (2014) suggest to use information from the stock market to distinguish supply and demandshocks in the oil market. As pointed out by Sockin and Xiong (2014), a theoretical model can help us betterunderstand the inflationary impact of oil price shocks.I use a two-sector general equilibrium model to illustrate the direct and indirect inflationary impact of oilprice shocks. The economy consists of an oil sector and a consumption goods sector. Oil is in households’utility function because gasoline is complementary to consumption goods, and oil is in firms’ productionfunctions because energy is needed to produce consumption goods. Oil supply shocks are modeled directlyby the total factor productivity shock in the oil sector, while oil demand shocks are triggered by the produc-tivity shock in the consumption goods sector, which in turn affects households’ demand for gasoline andfirms’ energy demand.In the model, when a negative productivity shock hits the oil sector, the oil price increases because ofthe oil shortage. The marginal cost of producing consumption goods increases because firms have to spendmore on energy input. As a result, the price of consumption goods rises. For a negative oil supply shock,both households and consumption goods firms are worse off.On the other hand, when a positive productivity shock hits the consumption goods sector, the output ofconsumption goods increases and the price of consumption goods decreases. When households consume8more consumption goods, they demand more for oil, because gasoline is complementary to consumptiongoods. Increased demand for oil from households pushes up the price of oil, because the supply of oil isinelastic in the short run. For a positive productivity shock in the consumption goods sector, households andfirms are better off, even though the oil price is higher.The economic mechanisms illustrated in the model is then used to rationalize the puzzling pattern of thecorrelations. Either oil supply disruptions in oil-producing nations or increased demand for oil, especiallyfrom fast-growing emerging economies, can drive up the price of oil. But the Consumer Price Index ofnon-energy goods and services rises when a higher oil price is driven by oil supply shocks, and falls whena higher oil price is driven by aggregate oil demand shocks. The correlation between oil price growth ratesand core inflation can be positive or negative, depending on the type of the underlying shocks. As a result,the correlation can be used to identify the types of oil price shocks.With the benefit of hindsight, I use historical geopolitical events and economic data to reconcile the time-varying trend of the historical correlation between core inflation and oil price changes. Oil supply shocksdue to geopolitical events in the period of 1973 to the mid-1980s have been widely documented, such as theArab embargo from December 1973 to March 1974, the Iranian revolution from May 1979 to July 1979,and the Iran-Iraq war from November 1980 to February 1981. The price of crude oil increased more than45% in each aforementioned historical event. Negative oil supply shocks were the main driver of the risingprice of oil during this period. U.S. core inflation reached its historic highest level during this period. Largeand positive correlations are observed, which is consistent with the passthrough of the supply-driven priceof oil.Correlations declined in the mid-1980s. This decline may be attributed to other channels, suggested byprevious studies, such as the reduced share of energy in production, the deregulation of the energy sector, aless accommodative monetary policy of shocks, the lack of adverse shocks, less rigid real wages, and foreignexchange rates.From the mid-1980s to 2008, correlations are were small, fluctuating around zero, because oil supplyand demand shocks co-exist. There were mild oil supply shocks resulting from unrest in Venezuela, GulfWar I, and Gulf War II from August 1990 to October 1990. In the same period, there was increased demandfor oil, especially from fast-growing emerging economies such as China and India. The IMF reports that theglobal real GDP grew more than 4.7% over the period of 2004-2007.4 In addition, the negative correlation4The data source is IMF World Economic Outlook Database.9observed in the period of 2004 to 2008 supports the view that the persistent rise in oil prices before 2008was driven by the increased oil demand from emerging economies. This provides an alternative explanationof the oil price hike other than the bubble view associated with the financialization of commodity futuresmarkets.Since the 2007 financial crisis, the correlations jumped to the positive and high level that was observedin the 1970s. Both positive oil supply shocks and weak oil demand shocks are responsible for the resurgenceof the correlations. The rapid development of shale oil in U.S. led to a positive shock to oil supply. Afterthe 2007 financial crisis, many economies around the globe entered recessions. As illustrated in the model,both positive oil supply and weak oil demand result in a stronger co-movement between oil price changesand core inflation. Last, the decline of correlations from 2014 is consistent with the burst of shale oil boom.This chapter makes three contributions to the literature. First, this chapter documents a new time-varying pattern of the correlation between core inflation and changes in the price of oil. The resurgenceof the correlations after the 2007 financial crisis is puzzling, in contrast to the economy’s declining energyintensity. Second, the puzzling pattern is reconciled by the distinct inflationary impact of oil supply shocksand demand shocks. The correlation between oil price fluctuations and core inflation is time-varying anddepends on the type of shocks in the oil market. This finding has useful implications for using oil futuresto hedge inflation. Third, the sign of the correlation between core inflation and oil price changes indicateswhether the intrinsic shocks embedded in the price of oil are supply shocks or aggregate demand shocks.This chapter provides a new method for identifying the type of oil price shocks.The chapter is organized as follows. The next section reviews related literature. Section 2.3 describesdata and presents empirical facts. A two sector DSGE model is presented in Section 2.4. Section 2.5analyzes model implications on inflation and the price of oil. Historical geopolitical events and economicdata are used to reconcile the time-varying correlations in Section 2.6. Section 2.7 concludes.2.2 Related literatureThis chapter is related to the new strand of literature that uncovers underlying economic shocks fromthe price of oil. Researchers commonly model oil prices as exogenous. However, this assumption is prob-lematic, as pointed out by Rotemberg (2010) and Balke, Brown, and Yu¨cel (2011). The price of crude oil isdetermined by the global supply and demand for oil, so oil price shocks are not exogenous shocks; rather,they reflect underlying fundamental shocks in the world economy.10However, empirically identifying intrinsic shocks underlying variations in the price of oil is challenging.Kilian (2009) uses a structural VAR framework to estimate demand and supply shocks in the global crude oilmarket by decomposing shocks to the real price of oil into oil supply shocks, aggregate demand shocks, andoil-specific demand shocks. He shows that from 1975 to 2007, major forces driving oil price shocks wereglobal aggregate demand shocks and precautionary demand shocks for crude oil. He suggests that the priceof oil should be modeled endogenously and that models of the endogenous price of oil should emphasize thedemand side of the oil market. Rapaport (2014) uses the sign and magnitude of the correlation between dailyoil price changes and stock market total returns to identify shocks specific to the oil market and shocks thataffect the overall economy. Ready (2014) proposes identifying demand shocks by looking at the correlationbetween returns to oil firms and innovation in the VIX index. This chapter suggests a new way to distinguishoil price shocks by examining the correlation between core inflation and oil price changes.This chapter is also related to the empirical literature that investigates the passthrough of oil prices intoinflation. The passthrough is usually estimated by the coefficient of the oil price change in a regression ofregressing inflation on oil price changes. The influence of the price of oil on inflation has declined fromthe 1970s to the 2000s. Clarke and Subramanian (2006) show that core inflation in U.S. becomes less re-sponsive to changes in energy prices. A decrease in energy intensity in the economy and in the exchangerate passthrough is attributed to the smaller magnitude of the influence (De Gregorio, Landerretche, Neil-son, Broda, and Rigobon, 2007). Clark and Terry (2010) measure the passthrough by allowing time-varyingcoefficients and volatilities and confirm findings in previous studies. Using a correlation measure to esti-mate the interdependence between core inflation and the price of oil, this chapter provides an alternativeexplanation of such a decline, investigating beyond the declined “passthrough”.In general, this work is related to an extensive macroeconomic literature that studies the link between oilprice shocks and the economy. Hamilton (1983) documents that oil price hikes precede 7 out of 8 postwarU.S. recessions, triggering a series of papers that investigate the mechanisms of transmission from oil priceshocks to economic output. Hamilton (2011) updates the count at 10 out of 11. Unlike oil price shocks in1970s, recent shocks from 2004 to 2007 are correlated with healthy global growth.To explain the muted impact of oil price shocks on the U.S. economy and other developed economies,the literature has explored different channels. Blanchard and Galı´ (2010) attribute a reduction in real wagerigidities, along with a reduction in the share of energy in production and a lack of adverse shocks, to thedecline in the impact of oil shocks on inflation and economic activity. The channel of the asymmetric impact11of oil price shocks on durable goods and non-durable goods, which causes a large reduction in expenditureson durable goods, has been suggested and empirically investigated (Dhawan and Jeske, 2008; Hamilton,2008; Kilian and Park, 2009). Bernanke, Gertler, and Watson (1997) and Clark and Terry (2010), amongothers, show that monetary policy dramatically responds to oil price shocks and thus magnifies the impactof oil price shocks on the economy in the 1970s and the 1980s, but has become less responsive to oil priceshocks since the 2000s. Hamilton and Herrera (2004) argue that monetary policy plays a much smaller role.My model differs from this line of research in that a separate oil sector is explicitly modeled and there is afeedback effect from the consumption goods sector to the oil sector.2.3 Empirical factsTwo approaches to measuring the relationship between core inflation and oil price changes are consid-ered. First, I present the correlation between historical core inflation and one-month lagged oil price growthrates. Second, I use a generalized Phillips curve model to assess the “passthrough” of oil prices into coreinflation. In addition, I conduct Chow tests of structural breaks in the impact of oil price changes on coreinflation.2.3.1 Data and summary statisticsI use the consumer price index to measure inflation. I obtain four series of monthly CPI for All UrbanConsumers (seasonally adjusted): all items, food, energy, and all items less food and energy from the websiteof the Bureau of Labor Statistics (BLS). I use CPI for all items, and CPI for all items less food and energyto estimate total inflation and core inflation.5 CPI excluding volatile food and energy items is called coreCPI, which measures more persistent underlying inflation. Ajello, Benzoni, and Chyruk (2012) documentthat average weights of CPI-energy, CPI-food, and CPI-core in the CPI consumer basket are 8%, 18%, and74% (8%, 15%, and 77%), respectively, for the sample period of 1962Q1–2011Q4 (1985Q1–2011Q4).The nominal price of oil is based on the refiner acquisition cost of imported crude oil, provided bythe U.S. Department of Energy since 1974.6 I extend these growth rates back to February 1973, usingthe dataset provided by Kilian (2009).7 Data on global oil production are obtained from the U.S. Energy5Alternatively, total inflation and core inflation could be measured by the Personal Consumption Expenditure (PCE) data fromthe Bureau of Economic Analysis (BEA). Ajello, Benzoni, and Chyruk (2012) also document that average weights on PCE-energy,PCE-food, and PCE-core are 6%, 12%, and 82% (5%, 9%, and 86%) for the sample period of 1962Q1–2011Q4 (1985Q1–2011Q4).6The producer price index (PPI) (WPU0561) for crude oil is another proxy for the nominal price of oil used by other papers. Asexpected, growth rates of the price of oil based on these two proxies are highly correlated.7Data are obtained from the AEA website at http://www.aeaweb.org/aer/data/june09/20070211 data.zip.12Information Administration. I use monthly data of world crude oil production for the period of January 1973to December 2015. The unit of monthly oil production is one thousand barrels per day, which is the dailyaverage of production over a month. The full sample period is from January 1973 to December 2015. Thestarting date of the sample period is constrained by the data availability for crude oil prices.Table 2.1 presents summary statistics of four series of inflation and the rates of oil price changes. Theinflation of three sub-indices has distinct characteristics. The core inflation series is very persistent andless volatile, while the energy inflation series is less persistent and very volatile. The volatility of oil pricechanges is 3 times larger than that of CPI-energy inflation and around 28 times that of core inflation. Com-paring three subsample periods, the average growth rate of the price of oil from March 1973 to July 1987(i.e., the pre-Greenspan period) is larger than those of two late subsample periods, and the kurtosis is aboutat least 3 times larger than those in the later period, meaning that more extreme oil price changes happenedin the 1970s and early 1980s.Figure 2.1 plots the historical real price of crude oil and core CPI inflation from February 1973 toDecember 2015. Core inflation is in the range of 3% to 13% from 1974 to 1983, and becomes smaller andless volatile starting from 1984. This stabilization of inflation is called the “great moderation.” The realprice of crude oil is much more volatile than core CPI inflation. Oil price hikes took place in a sequenceof geopolitical events: the Arab embargo from December 1973 to March 1974, the Iranian revolution fromMay 1979 to July 1979, the Iran-Iraq war from November 1980 to February 1981, Gulf War I from August1990 to October 1990, unrest in Venezuela and Gulf War II from November 2002 to March 2003.The steady rise of the price of oil from 2004 to 2008 is an unprecedented phenomenon. Hamilton (2013)argues that global economic growth from 2004 to 2007, over 4.7% of annual real GDP growth as estimatedby the IMF, is responsible for the accompanying increase in the price of oil. In particular, a group of newlyindustrialized economies, such as China and Indina, represent 69% of the increase in global oil consumption.Since 2008 the oil price has sharply declined and rapidly recovered.Figure 2.2 shows the historical world oil production along with the price of oil from 1973 to 2015.Starting in the 1980s, global oil production exhibits an upward trend, but the oil supply flattens out beginningin 2005. This stagnant oil supply impedes downward pressures on the price of oil.132.3.2 The puzzling time-varying correlations between core inflation and oil price changesI use correlations to estimate the empirical interdependence between core inflation and changes in theprice of oil. As it takes time for firms to adjust prices in response to oil price shocks, I measure the correlationbetween core inflation and one-month lagged oil price changes.Figure 2.3 plots the correlation between core inflation and one-month lagged rates of oil price changes,computed using a five-year rolling estimation window, over the sample period from March 1973 to Decem-ber 2015. The correlation (the solid line) is historically large and positive before 1983, becomes small andeven becomes negative for a substantial period from the early 1980s to 2007, and finally rises after 2008.The solid line exhibits a time-varying pattern. The jump of the correlations happens in the fourth quarter of2008. The magnitude of the correlation after the jump is close to that observed before the mid-1980s.In addition, I estimate correlations in three sub-sample periods: February 1973 to July 1987 (the Pre-Greenspan period), August 1987 to September 2007 (the Great Moderation period), and October 2007 toDecember 2015 (the Post-Crisis period), which are plotted as dotted lines in Figure 2.3. Three correlationsare 0.17 (significant at the 5% significance level), -0.09 (insignificant), and 0.16 (insignificant), respectively.I follow Fisher (1921) to test for the difference between two independent correlations.8 The z-tests of thedifferences between correlations of the Pre-Greenspan period and Post-Crisis period versus that of the GreatModeration period are 2.56 and 2.03, respectively. Both differences are significant at the 5% significancelevel.Last, the time-varying trend is robust to various measures of the price of oil, such as the real price of oil,the PPI-crude petroleum index, and the CPI-energy index.2.3.3 Structural changesAlternatively, I conduct Chow tests of structural change for the coefficients of lagged oil price changesin the following regression. I integrate the Chow test into a generalized Phillips curve model specified as8Howell (2012) provides details and textbook examples of this method on pages 284-5. Because the sampling distribution of acorrelation (denoted by r) is not approximately normal, the first step is to transfer r to a new variable r′ = 0.5ln(|1+ r|/|1− r|).The converted variable r′ is approximately normally distributed with the standard error sr′ = 1/√T −3, where T is the number ofobservations. The z-test is estimated by z = (r′1− r′2)/√1/(T1−3)+1/(T2−3), where T1 and T2 are the number of observationsof two correlations r1 and r2, respectively.14follows:piCt = β0+β1piCt−1+β2(yt− y¯t)+β3(yt−1− y¯t−1)+β4∆pot +β5∆pot−1+β6Dbreakdate+β7Dbreakdate∗∆pot−1+εt .(2.1)In the above regression equation, piC is the monthly core inflation rate. y is the monthly log industrialproduction index, and y¯ is the Hodrick-Prescott filtered trend of y. ∆po is the log growth of the monthlynominal price of oil. Dbreakdate is a dummy variable that takes a value of 0 before the known break date and1 thereafter. The coefficient β7 of the interaction term between the dummy and the lagged oil price changemeasures the difference of the impact of the lagged oil price change on core inflation before and after theknown break date.The results of Chow tests are presented in Table 2.2. Columns 1 and 2 show the existence of structuralchanges of the coefficients after July 1987 and after September 2007. The coefficients of the interactivevariable are significantly negative after July 1987, and are significantly positive after September 2007. Ialso conduct Chow tests on two different break dates: December 1983, when the U.S. inflation came downfrom its historic highest level, and September 2008, when crude oil prices started to drop after reaching ahistoric peak and Lehman Brothers filed for bankruptcy. Results in columns 3 and 4 show that the changesof coefficients are significant as well for these two different break dates.All these tests indicate that the relationship between core inflation and oil price changes in the 1970s toearly 1980s and after the 2007 financial crisis is different from that in the Great Moderation period. Thereare structural breaks in their relationship.However, how fluctuations in oil prices are related to core inflation is not straightforward. As not all oilprice shocks are the same (Kilian, 2009), I take the simple view that oil prices reflect fundamental supply anddemand information in the world oil market. As discussed in previous sections, empirically identifying theintrinsic shocks embedded in the price of oil is challenging. I build a theoretical model to better understandthe inflationary impact of oil price shocks.2.4 A two-sector general equilibrium modelI use a simple model to illustrate the basic intuition behind the economic mechanism that generatessimilar oil price shocks but has a distinct impact on inflation and economic fluctuations. The model featuresa competitive, frictionless economy, in which oil and final goods are produced by an oil sector and a final15goods sector, respectively. Oil is in the household’s utility function, as oil is considered complementaryto the consumption of other goods, and oil is used as input in the production of the final goods. Prices inthe model are endogenous and flexible. The supply shock in the oil market is modeled by the total factorproductivity shock in the oil sector. The demand shock in the oil market comes from aggregate demand foroil from the household and the final goods producer, both of which are driven by the total factor productivityshock in the final goods sector.I consider a closed economy, i.e., the global economy, because the oil market is a global market. Al-though the model is very simple, it captures the key feature of the oil consumption in the economy. Inaddition, supply and demand shocks are separately modeled. The production of oil and consumption goodsis greatly simplified, abstracting from many rich features in the oil market and the real economy. Overall,the two-sector general equilibrium model has the minimum number of elements but possesses all necessaryfeatures to address the different impact of oil supply and demand shocks on oil prices and core inflation.2.4.1 HouseholdsAn infinitely-lived representative household maximizes the expected utilityE0∞∑t=0β t [ξ (Ct)1−γ +(1−ξ )(OHt )1−γ ]1/(1−γ), 0 < β < 1, 0 < ξ < 1, γ > 0, (2.2)where β is the time discount factor, Ct the consumption of the final goods, and OHt is the consumption ofoil. The weight on oil in the utility function is measured by 1−ξ . The elasticity of substitution is equal to1/γ .9The household owns the capital used in the oil firm and in the final goods firm and receives rentalincome. In addition, the household can trade one-period riskless bonds available in zero net supply. Thebudget constraint is expressed asPCt Ct +POt OHt +Bt ≤ Rt−1Bt−1+RCt KCt +ROt KOt , (2.3)where Bt is the number of shares of bonds, RCt is the rental rate of the capital of the final goods firm KCt ,and ROt is the rental rate of the capital of the oil firm KOt . The one-period riskless bond costs one dollar incurrent period t and pays Rt next period, which is the gross nominal interest rate. In addition, the one-period9When γ = 1, one period felicity is given by the Cobb-Douglas form (Ct)ξ (OHt )1−ξ .16riskless bond price serves as the nume´raire in the model. PCt and POt are prices of the final goods and oil,respectively.2.4.2 Oil sectorThe oil is produced by a representative oil firm. The oil production function takes a simple formY Ot = ZOt KOt = ZOt , (2.4)where ZOt is the total factor productivity (TFP) in the oil sector and KOt is the capital and is normalized to 1:KOt ≡ 1. I assume that zot ≡ logZOt follows an AR(1) processzot = ρozot−1+ εot , (2.5)where εot ∼ N(0,σ2o ). The oil is sold at the price of POt , which is, in equilibrium, determined by the supplyand demand for oil from both households and the final goods firm.Given the prices POt and ROt , the oil firm maximizes its profitmaxKOt{ZOt KOt POt −ROt KOt }. (2.6)2.4.3 Final consumption goods sectorA representative final goods firm uses capital and oil to produce the final goods. The production functionis given byYCt = ZCt (KCt )α(OIt )1−α = ZCt (OIt )1−α , (2.7)where ZCt is the total-factor productivity (TFP), OIt is the amount of oil, and KCt is the capital and normalizedto 1: KCt ≡ 1. The share of oil in the production is measured by 1−α . Similarly, zct ≡ logZCt is assumed tofollow an AR(1) processzct = ρczct−1+ εct , (2.8)where εct ∼ N(0,σ2c ). In addition εct is assumed to be independent of εot .17Each period, the final goods firm maximizes its profitmaxKCt ,OIt{ZCt (KCt )α(OIt )1−αPCt −KCt RCt −OIt POt }, (2.9)subject to (2.7), taking the price and the rental rate as given.2.4.4 Central bankTo complete the model, a central bank follows a Taylor rule to set the nominal interest rate as followsit = logRt = ρ+φpipict , φpi > 1, (2.10)where ρ =−logβ and pict = log(PCt /PCt−1) is the inflation rate of the final goods price.As there is no friction in this simple model, the monetary policy does not affect real variables. However,nominal variables, such as prices and inflation, are not independent of the Taylor rule.2.4.5 EquilibriumThe optimal conditions of the household’s and two firms’ maximization problems are given in AppendixA. In the model, two total factor productivity shocks are exogenous, and capital in both firms is normalizedto 1. All other real and nominal variables are endogenous.2.5 Oil price and core inflationInstead of going through analytical solutions for the oil price and the final goods price, I use supply-demand diagrams in the oil market and the final goods market to illustrate the transmission of two produc-tivity shocks to two prices. I then discuss the co-movement between the price of oil price and the price ofthe consumption goods, which is corresponding to the price index of core inflation in the model.2.5.1 Supply-demand diagramsIn the diagram for the oil market, the oil supply curve is a vertical line because the production of oil isdetermined by the fixed level of the oil capital and by the exogenous productivity level. Demand for oil isthe sum of the demand from households and the demand from the final goods firm. The oil demand curve isa downward sloping. In the diagram for the consumption goods market, the supply curve of the final goods18is upward sloping, and the demand curve of the final goods is downward sloping.Figure 2.4 shows how a negative productivity shock in the oil firm affects the supply and demand of oiland the final goods and their prices. The output of oil decreases when a negative productivity shock hits theoil sector. The vertical supply curve of oil is shifted to the left. Everything else being equal, the negativeoil supply shock results in a higher oil price. Because the final goods firm needs the oil to produce the finalgoods, the higher oil price means a higher marginal production cost for the final goods. The final goods firmwill produce less and supply fewer final goods. The supply curve of the final goods is shifted to the left, sothe final goods price also goes up.Thus, a negative productivity shock in the oil firm leads to higher prices for both oil and the final goods.Oil price shocks originating from the supply side of oil lead to a positive correlation between the prices ofthe consumption goods and oil.Figure 2.5 shows that a positive productivity shock in the final goods sector leads to a lower price ofthe final goods but a higher price of oil. When productivity in the final goods firm increases, the marginalproduction cost decreases even if I assume that the final goods firm does not change its demand for energy.The final goods firm produces and supplies more of the final goods, so the supply curve of the final goodsis shifted to the right. Everything else being equal, the final goods are sold at lower prices. Householdsincrease their consumption of the final goods, given that the final goods are cheaper. Because of the incomeeffect and the complementarity of oil to the final goods (i.e., 1/γ < 1 in the utility function), householdswant to increase their consumption of oil.The change of the aggregate demand for oil needs further analysis, because the oil demand by the finalgoods firm could be lower. Assume that the final goods firm initially does not change its demand for oil. Asanalyzed above, the oil demand by households increases, so the aggregate oil demand increases. Given thatthe supply of oil does not change, the demand curve of oil is shifted to the right, resulting in a higher oilprice. Facing the increased costs of oil, the final goods firm decreases its demand for oil. Continuing thisanalysis, the oil price is adjusted high enough to clear the oil market, and the final goods price is adjustedlow enough to clear the final goods market.When the positive productivity shock hits the final goods market, the lower price of the final goods andthe higher price of oil are observed. But the higher oil price this time comes from the demand side of theoil market. Most important, the transmission mechanism from a positive innovation in productivity to theeconomy induces a negative correlation between core inflation and the oil price.192.5.2 Positive and negative correlationsTo sum up, the rise of the oil price can occur because of either a negative productivity shock in the oilfirm or a positive productivity shock in the final goods firm. However, the price of the final goods goes upfor a negative ZOt shock but goes down for a positive ZCt shock. As no food is considered in this model, thechange of the final goods price represents core inflation. Thus, the correlation between core inflation and anoil price change could be positive or negative depending on the underlying shocks that drive the oil price. Amixture of two types of TFP shocks can generate a very rich set of scenarios.Theoretically, positive or negative correlations, and small or large correlations, are all possible, depend-ing on which mechanism dominates the other. I examine the usefulness of the two mechanisms to helpexplain the time-varying trend discussed below.Next, the economic mechanisms are examined by using historical geopolitical events and economic datato explain the time-varying trend and structural breaks of the relationship between oil price changes andcore inflation.2.6 Historical events, oil supply and demand shocks, and correlationsWith the benefit of hindsight, I use historical geopolitical events and economic data to distinguish oilsupply shocks from global demand shocks in subsample periods. Table 2.3 lists oil-related geopoliticaland economic events from 1973 to 2015. I further utilize the identified types of oil shocks to reconcile thepuzzling time-varying pattern of correlations between U.S. core inflation and oil price changes.Oil supply shocks due to geopolitical events in the period of 1973 to the mid-1980s have been widelydocumented, including the Arab embargo from December 1973 to March 1974, the Iranian revolution fromMay 1979 to July 1979, and the Iran-Iraq war from November 1980 to February 1981. The price of crude oilincreased by more than 45% upon each of the aforementioned three historical events. Negative oil supplyshocks were the main driver of the rising price of oil in this period. U.S. core inflation reached its historichighest level during this period. Thus, a large and positive correlation of 0.17 is observed in the period ofMarch 1973 to July 1987, which is consistent with the proposed mechanism.Note that the correlation declines from the mid-1980s onward. It is argued that the decline may beattributed to other factors, suggested by previous studies, such as a reduced share of energy in production,deregulation of the energy sector, a less accommodative monetary policy of shocks, a lack of adverse shocks,20less rigid real wages, and foreign exchange rates.For instance, Figure 2.6 shows that energy intensity, measured by the total primary energy consumptionper dollar of GDP, halves from 1980 to 2010. As the share of petroleum in the overall economy declines,the price of crude oil has less influence on inflation. A smaller energy share in aggregate production helpsexplain lower correlations between inflation and oil prices from the 1970s to 2007, but it contradicts the riseof these correlations after the 2007 financial crisis, because the energy share does not increase after 2007.Over the course of the mid-1980s to 2003, Gulf War I from August 1990 to October 1990, the mild oilsupply shocks of Venezuelan unrest, and Gulf War II from November 2002 to March 2003 all took place.A handful of small oil supply shocks happened. Correspondingly, correlations were also small, fluctuatingaround zero as the supply and demand channels co-existed.The IMF reports that global real GDP grew by more than 4.7% over the period of 2004-2007.10 Fast-growing emerging economies, such as China and India, increased demand for oil. For instance, the shareof world total petroleum consumption consumed by China and India has persistently risen from 5% to15% from 1990 to 2013. This rise can be interpreted as the dominance of the aggregate demand channel.Correlations are negative over this period, although mostly not significantly different from zero.It is worth noting that the financialization of commodity markets also occurred in the period of 2004to 2008. The large inflow of investments to commodity futures markets triggered a heated debate aboutwhether commodity prices are distorted by the financialization. In particular, it is argued that speculationin futures markets led to a bubble in oil prices in 2007 and 2008. Although there is some evidence tosupport this bubble view, Fattouh, Kilian, and Mahadeva (2012), among many others, defend a fundamentalview that economic fundamentals, such as disruption to oil supply and increased global demand for oil,are responsible for the persistent run-up in oil prices. Interestingly, the empirical correlation between coreinflation and oil price changes in this period may shed some light on this debate. If the persistent rise inoil prices before 2008 was due to speculation in crude oil futures, it would lead to higher energy costs forconsumers and producers, i.e., like the scenario of a disruption in oil supply; consequently, as analyzed in themodel, the correlation between core inflation and oil prices should be positive and increasing. However, theobserved correlation is negative, which is inconsistent with the bubble view but in favor of the fundamentalview. Admittedly, as pointed out by Cheng and Xiong (2014), the two different views are not necessarily10The data source is IMF World Economic Outlook Database, which is accessible at http://www.imf.org/external/pubs/ft/weo/2014/01/weodata/index.aspx.21exclusive.After the 2007 financial crisis, economies across the world have fallen into recessions, followed byrecoveries. A lack of strong economic growth is apparent. Meanwhile, the U.S. domestic oil supply grewrapidly as the fracking technology improved and have been widely adopted. Because both positive supplyshocks and weaker demand shocks increase correlations in the model, these two facts together can explainthe positive correlations between core inflation and oil price changes after the 2007 financial crisis. Theresurgence of positive correlations cannot be explained by channels suggested in the literature, such as thereduced share of energy in the economy.Last, it is noticeable that the correlations decrease to small values from 2014. The decline in correlationsis consistent with the beginning of the burst of shale oil boom and the steady economic growth in U.S. andother major economies.In summary, the aforementioned historical events provide a consistent and logical explanation of thetime-varying correlations observed in the data. The above analysis supports the implications of the two-sector general equilibrium model.2.7 ConclusionThis chapter studies the macroeconomic linkage between the price of oil and core inflation, which shedslight on identifying intrinsic shocks in oil price shocks. I document that the correlation between U.S. coreinflation and changes in the price of oil exhibits a time-varying pattern from 1973 to 2015: being large andpositive before the mid-1980s, declining and then sometimes being negative for a substantial period of timefrom the mid-1980s to 2008, rising after 2008, and finally declining from 2014. Empirical results confirmthe presence of two structural breaks in correlations in the mid-1980s and during the 2007 financial crisis.I build a two-sector general equilibrium model to study the underlying economic mechanism and tofurther rationalize these facts. Theoretical analysis shows that the relation between the price of oil andinflation risk depends on the type of shocks embedded in oil price changes. Oil supply shocks cause theprice of oil and core inflation to co-move, whereas the aggregate demand shocks in the consumption goodssector lead to an opposing movement of the price of oil and core inflation. The implications of the modelare supported by the analysis of using historical events to explain the time-varying correlation observed inthe data.The implications from this chapter are practical for central banks and pension fund managers. The22sign of correlation indicates whether the intrinsic shocks embedded in the price of oil are supply shocks oraggregate demand shocks. This structural analysis provides a new method for identifying the type of oilprice shocks. In addition, the understanding of time-varying correlation based on the supply and demandshocks in the oil market can help investors to more effectively hedge inflation, and it can help central banksto better gauge information regarding inflation from oil price shocks.23Table 2.1: Summary statistics of inflation series and oil price changesThis table reports summary statistics for the inflation series on CPI, CPI-core, CPI-food, and CPI-energy,and oil price changes. The full sample period is from March 1973 to December 2015. Inflation ratesare annualized percent change. Oil price changes are expressed as annualized percent growth. The lasttwo columns are corresponding correlations with contemporaneous and 1-month lagged oil price changes,respectively. *, **, and *** denote significance of correlations at the 10%, 5%, and 1% level, respectively.Panel A: Full sample period: 1973.3 - 2015.12Central Moments Autocorrelation CorrelationMean SD Skew. Kurt. Min Max AC(1) AC(2) Cont. LaggedCPI 4.01 4.14 0.14 6.91 -21.25 21.72 0.64 0.47 0.44*** 0.43***CPI-core 3.97 3.10 1.60 5.97 -2.96 17.03 0.77 0.75 0.07* 0.08*CPI-food 3.97 5.13 3.79 35.92 -11.58 61.98 0.36 0.28 0.11** 0.13***CPI-energy 4.85 28.40 -0.91 13.44 -216.29 161.53 0.42 0.01 0.60*** 0.60***Oil price changes 4.52 90.93 -0.26 9.35 -439.88 541.11 0.48 0.14 – –Panel B: Subsample period: 1973.3 - 1987.7Central Moments Autocorrelation CorrelationMean SD Skew. Kurt. Min Max AC(1) AC(2) Cont. LaggedCPI 6.78 4.43 0.22 3.29 -6.56 21.72 0.64 0.58 0.42*** 0.43***CPI-core 6.76 3.63 0.60 3.43 -2.96 17.03 0.64 0.59 0.12 0.17**CPI-food 6.39 7.45 2.78 19.88 -11.58 61.98 0.28 0.21 0.21*** 0.20***CPI-energy 8.17 19.28 -0.74 7.13 -83.22 59.08 0.68 0.37 0.61*** 0.65***Oil price changes 9.65 71.79 1.46 27.10 -383.53 541.11 0.54 0.21 – –Panel C: Subsample period: 1987.8 - 2007.9Central Moments Autocorrelation CorrelationMean SD Skew. Kurt. Min Max AC(1) AC(2) Cont. LaggedCPI 3.01 2.58 0.34 7.12 -6.03 16.52 0.29 -0.11 0.39*** 0.45***CPI-core 2.89 1.42 0.58 3.49 0.00 7.79 0.42 0.42 -0.06 -0.09CPI-food 2.94 2.74 0.60 5.02 -5.23 15.97 0.20 0.03 0.03 0.11CPI-energy 4.59 27.95 0.59 7.73 -86.84 161.53 0.28 -0.22 0.46*** 0.56***Oil price changes 6.56 92.45 0.27 4.98 -237.22 459.66 0.37 0.01 – –Panel D: Subsample period: 2007.10 - 2015.12Central Moments Autocorrelation CorrelationMean SD Skew. Kurt. Min Max AC(1) AC(2) Cont. LaggedCPI 1.61 4.12 -1.92 12.62 -21.25 12.57 0.52 0.13 0.76*** 0.61***CPI-core 1.76 0.84 -0.52 3.65 -1.35 3.43 0.42 0.25 0.21** 0.16CPI-food 2.27 2.52 0.92 4.36 -2.06 11.23 0.59 0.56 0.00 0.07CPI-energy -0.33 40.01 -1.76 11.79 -216.29 114.80 0.46 0.10 0.78*** 0.63***Oil price changes -9.45 113.84 -1.51 6.17 -439.88 210.67 0.59 0.28 – –24Table 2.2: Chow testThis table presents results of Chow test. Core inflation is regressed on the lagged core inflation, contem-poraneous and lagged output gap, contemporaneous and lagged oil price changes, a dummy variable thatequals to 0 before a break date and 1 thereafter, and an interaction term between the dummy and the laggedoil price changes. piC is the monthly core inflation rate. y is the monthly log industrial production index. y¯is the Hodrick-Prescott filtered trend of y. ∆po represents the percentage change in the monthly nominal oilprice. The dummy variable of DpostVolcker equals 0 before July 1987 and 1 thereafter. The dummy variableof DpostCrisis equals 0 before September 2007 and 1 thereafter. The dummy variable of Dpost1983 equals0 before December 1983 and 1 thereafter. The dummy variable of DpostLehman equals 0 before September2008 and 1 thereafter. Newey-West standard errors with six lags are in parentheses. *, **, and *** denotesignificance at the 10%, 5%, and 1% level, respectively.(1) (2) (3) (4)piCt piCt piCt piCtpiCt−1 0.56*** 0.40*** 0.50*** 0.41***(0.06) (0.08) (0.07) (0.06)yt − y¯t 0.25 -0.14 0.28 0.00(0.20) (0.11) (0.19) (0.14)yt−1− y¯t−1 -0.12 0.19 -0.14 0.04(0.20) (0.12) (0.18) (0.14)∆pot -0.00 0.00 -0.01 0.00(0.01) (0.01) (0.01) (0.01)∆pot−1 0.05** -0.01 0.05 -0.01*(0.02) (0.01) (0.03) (0.01)DpostVolcker -1.74***(0.34)DpostVolcker ∗∆pot−1 -0.06***(0.02)DpostCrisis -0.66***(0.12)DpostCrisis ∗∆pot−1 0.02**(0.01)Dpost1983 -2.34***(0.45)Dpost1983 ∗∆pot−1 -0.06*(0.03)DpostLehman -0.75***(0.13)DpostLehman ∗∆pot−1 0.02**(0.01)Constant 2.98*** 1.73*** 3.82*** 1.78***(0.47) (0.19) (0.60) (0.18)Adj. R2 60% 30% 62% 30%Observations 414 341 426 384Sample period 1973.3-2007.9 1987.8-2015.12 1973.2-2008.9 1984.1-2015.1225Table 2.3: List of geopolitical and economic eventsOil prices are obtained from the website of U.S. Energy Information Administration. Hamilton (2013)provides the list of oil price shocks. Data on U.S. recessions are obtained from the NBER website. GDPdecline refers to the decrease of GDP measured from peak to trough.Panel A: Oil price shocksEvent Period Oil price increaseArab oil embargo Nov. 1973 - Feb. 1974 51%Iranian revolution May 1979 - Jan. 1980 57%Iran-Iraq War Nov. 1980 - Feb. 1981 45%Gulf War I Aug. 1990 - Oct. 1990 93%Venezuela unrest, Gulf War II Nov. 2002 - Mar. 2003 28%Strong demand, stagnant supply Feb. 2007 - Jun. 2008 145%Libyan Civil War Feb. 2011 - Oct. 2011 29%Panel B: U.S. recessionsEvent Period GDP decline1973-1975 recession Nov. 1973 - Mar. 1975 -3.2%1980 recession Jan. 1980 - Jul. 1980 -2.2%Early 1980s recession Jul. 1981 - Nov. 1982 -2.7%Early 1990s recession Jul. 1990 - Mar. 1991 -1.4%Early 2000s recession Mar. 2001 - Nov. 2001 -0.3%Great recession Dec. 2007 - Jun. 2009 -4.3%26197303 197603 197903 198203 198503 198803 199103 199403 199703 200003 200303 200603 200903 201203 201503010Arab oil embargo→ Iranian revolution→ ← Iran−Iraq war Gulf war I → Venezuela civil unrest,Gulf War II→ ← Libyan Civil WarCore CPI inflation and real oil pricesCore Inflation (percent)  Core CPI InflationReal Oil Price (CPI Base month: Jan. 1981)NBER recession0102030405060Real Oil Price ($ per barrel)DateFigure 2.1: Historical prices of crude oil and core inflation.The core CPI inflation series is monthly year-over-year rates. The real oil price is the refiners’ acquisition cost of imported crude oil deflated by CPIinflation with a base month of January 1981. The real oil price is chosen to show the comparable magnitude of oil price changes for the whole sampleperiod.2750000.0055000.0060000.0065000.0070000.0075000.0080000.0085000.001973021974051975081976111978021979051980081981111983021984051985081986111988021989051990081991111993021994051995081996111998021999052000082001112003022004052005082006112008022009052010082011112013022014052015080.0020.0040.0060.0080.00100.00120.00140.00Oil Production (thousand barrels per day)DateOil Price ($ per barrel)Historical Oil Prices and World Oil Production: 1973.2-2015.12Oil Prices (right axis) Oil Production (left axis)Figure 2.2: The price of oil and world crude oil production.The oil price refers to the refiners’ acquisition cost of imported crude oil. The world oil production is measured in the unit of thousand barrels per day.Both data are obtained from the website of U.S. Energy Information Administration.28197303 197603 197903 198203 198503 198803 199103 199403 199703 200003 200303 200603 200903 201203 201503−0.2−0.100.10.20.30.40.50.6Correlations between core CPI inflation and one−month lagged oil price changesDateCorrelation  Arab oil embargo→ Iranian revolution→ ← Iran−Iraq war Gulf war I → Venezuela civil unrest,Gulf War II→ ← Libyan Civil War5−Year Rolling WindowSubperiod 1973.3−1987.7Subperiod 1987.8−2008.9Subperiod 2008.10−2013.7NBER recessionFigure 2.3: Correlations between monthly core inflation and one-month lagged oil price changes.The core CPI inflation rates are an annualized percent estimated at a monthly frequency. The nominal oil price is the refiners’ acquisition cost ofimported crude oil. One month lagged oil price changes are used to reflect the time required for firms to respond to oil price changes.29Figure 2.4: A negative productivity shock zot in the oil sector.30Figure 2.5: A positive productivity shock zct in the consumption goods sector.310	  2000	  4000	  6000	  8000	  10000	  12000	  14000	  16000	  1980	   1985	   1990	   1995	   2000	   2005	   2010	  BTU	  per	  year	  (2005	  U.S.	  Dollor)	  Year	  U.S.	  Energy	  Intensity:	  Total	  primary	  energy	  consump@on	  per	  dollar	  of	  GDP	  Figure 2.6: U.S. energy intensity from 1980 to 2010.Energy intensity is measured by the total primary energy consumption per dollar of GDP. Data on U.S. energy intensity are obtained from the websiteof U.S. Energy Information Administration.32Chapter 3Oil prices, expected inflation, and bondreturns3.1 IntroductionOil is the single most important commodity in the world economy: global expenditures on petroleumaccount for about 4.5% of the world GDP. Oil is also a special commodity, because it is both consumed byhouseholds to meet their daily energy needs and used by firms as energy input to produce a wide range ofgoods and services.1 Given the importance of oil to the macroeconomy, it is natural to study the extent towhich fluctuations in oil prices are related to the prices and expected returns of financial securities. Indeed,many studies, starting with Chen, Roll, and Ross (1986), have investigated the role of oil prices in stockreturns.2 However, few papers have studied the impact of oil prices on bond prices and returns.3 Thisis especially surprising since intuition and casual empirical observations suggest an important link. Forinstance, one day after OPEC announced on November 27, 2014 that it would keep its production ceilingunchanged, the yield on 10-year U.S. Treasury bond fell 8 basis points, along with a sharp 10% drop in theWTI crude oil price.The purpose of this chapter is to fill this gap by studying the relationship between oil prices and bondreturns both empirically and theoretically. Specifically, I first address the question of whether the price of oil1The average U.S. household spends about 4% of pre-tax income on gasoline for day-to-day transportation, and about 40% ofindustrial energy consumption is accounted for by oil, according to data in 2013 from the U.S. Energy Information Administration.2Driesprong, Jacobsen, and Maat (2008), Kilian and Park (2009), Chiang, Hughen, and Sagi (2014), among others, find that oilprices impact stock returns.3Exceptions are studies by Kang, Ratti, and Yoon (2014) and Baker and Routledge (2015)33price is a significant explanatory variable and predictor of returns on nominal Treasury bonds in excess ofTreasury bills. Additionally, since oil price fluctuations are widely thought to affect inflation, consumption,and output, I then examine whether oil prices are relevant determinants for expected inflation and real yieldson inflation-indexed bonds.In my empirical analysis, I find novel evidence that high growth rates of crude oil spot prices can explainlow contemporaneous excess returns on nominal 10-year U.S. Treasury bonds, breakeven inflation (thedifference between nominal and real yields), and inflation swaps, which provide market-based measures ofexpected inflation.4 In addition, oil price growth can predict positive expected excess returns on breakeveninflation and inflation swap rates. Oil prices appear to provide incremental information above and beyondthe yield spread, which is a well-known predictor of excess bond returns.Understanding the connections between oil prices and bond yields proves to be very challenging, be-cause they depend on the underlying causes of oil price changes (Kilian, 2009). An oil price hike could bebad news for the economy if driven by a scarce oil supply, or good news if driven by a strong demand foroil due to economic growth. In addition, simply examining the relationship between nominal yields and oilprices might disguise valuable information. For example, the real rate component and breakeven inflationcomponent in nominal yields may respond differently to oil price changes.I build a two-sector New Keynesian model to study in a structural way the interactions between (i) supplyand demand shocks in the oil market, (ii) expected inflation, and (iii) nominal and real bond yields. I studyan economy where oil and core goods are produced in the oil sector and the core sector, respectively. Acritical feature of the model is that oil is included in households’ utility function and used as an input in theproduction of core goods as in Blanchard and Galı´ (2010). In addition, oil is assumed to be complementaryto core goods. The elasticity of substitution between oil and core goods is less than one, supported byempirical findings by Ready (2015). Both the complementarity between oil and core goods and the oil inputin production bind the oil sector and the core sector together. Thus higher oil prices could be driven by eithernegative productivity shocks in the oil sector or positive productivity shocks in the core goods sector.5 Theformer shock is the negative supply shock in the oil market, and the latter acts as the positive demand shock4I follow Pflueger and Viceira (2015) in estimating the liquidity premium present in the U.S. TIPS market and construct liquidity-adjusted TIPS yields and breakeven inflation rates. Inflation swaps data have been used by Haubrich, Pennacchi, and Ritchken(2012), Fleckenstein, Longstaff, and Lustig (2013, 2014), and others. Data on inflation swaps are available from July 2004 onward.5Hurricane Katrina in 2005 is a good example of a negative shock to oil supply, and the strong demand for oil in the period of2004 - 2007 from fast-growing emerging economies, such as China and India, is an example of a positive shock to oil demand dueto economic growth.34in the oil market.The model shows that the conventional wisdom that high oil prices are associated with high expectedinflation and high nominal bond yields is not always true. It is true only if high oil prices are driven bythe disruption to oil supply. If high oil prices are driven by oil demand shocks, the conventional wisdom iswrong.Let’s consider a positive shock to oil demand due to economic growth. The production of consumptiongoods increases because of economic growth. Households consume more consumption goods and alsodemand more oil. Therefore, the price of oil also goes up. However, the price of consumption goods goesdown because more consumption goods are available in the economy. Overall, expected total inflation islow. Because the aggregate economy performs well, real yields rise. Nominal yields become relatively lowso that nominal bond prices and returns become higher. For positive oil demand shocks due to economicgrowth, high oil prices are associated with low expected inflation and low nominal yields, in contrast to theconventional wisdom. The model shows that oil supply and demand shocks have opposite impacts on pricesand returns of Treasury bonds.The model is able to replicate the empirical fact that growth rates of oil prices can explain contempo-raneous excess returns on 10-year nominal bonds and breakeven inflation. Using simulated data from thebaseline model, I show that slope coefficients have the same signs and statistical significance levels. Inaddition, correlations between the growth in oil prices and changes in nominal yields in the baseline modelare close to those in the data.The model is also able to generate upward sloping nominal yields and sizable positive inflation riskpremia, because consumption growth is negatively correlated to CPI inflation. When consumption growthis lower, higher expected inflation makes nominal bonds less valuable. In addition, long-term nominalbonds have lower real payoffs than short-term bonds when expected long-term productivity growth is low.Therefore, buyers of nominal bonds demand higher nominal yields of long-term bonds to compensate forthe inflation risk. As in Hsu, Li, and Palomino (2014), both nominal price rigidities of core goods and realwage rigidities are crucial in generating the negative correlation between expected inflation and consumptiongrowth in the model.This chapter highlights that households’ direct consumption of oil and the oil input in production aretwo essential economic channels for explaining the dynamics between oil prices and bond yields. Variationsin oil prices have real effects on household consumption expenditures through distorting households’ dis-35cretionary incomes and affecting demand for core goods, which are complementary to oil (Hamilton, 2008;Edelstein and Kilian, 2009). Oil prices also directly affect the price of core goods through the marginal costof producing core goods, and influence core goods firms’ labor demands. The two channels together createthe dynamics among oil prices, consumption, and production, all of which determine endogenous inflation,nominal yields, and real yields in equilibrium.This chapter is related to a growing literature on studying determinants of nominal and real bond yieldcurves. Previous papers studying real rates, inflation expectations, and risk premia use latent factor termstructure models (Ang, Bekaert, and Wei, 2008; Chernov and Mueller, 2012; Haubrich, Pennacchi, andRitchken, 2012) and New Keynesian macro models (Kung, 2015; Hsu, Li, and Palomino, 2014). However,oil prices have not been considered in this literature. In this chapter, the price of oil is treated as an explicitmacroeconomic risk factor. In addition, this chapter builds on the New Keynesian model; moreover, itincludes an oil sector and incorporates the dual uses of oil to examine macroeconomic linkages among bondyields, inflation expectations, and supply and demand shocks in the oil markets.This chapter is also related to several empirical papers that document the connection between oil spot orfutures prices and U.S. Treasury bond returns. Kang, Ratti, and Yoon (2014) show that U.S. Treasury bondreturns deflated by the U.S. CPI are negatively associated with oil price shocks driven by global aggregatedemand for all industrial commodities. Baker and Routledge (2015) document that monthly excess returnson nominal U.S. Treasury bonds are higher when the slope of NYMEX WTI crude oil futures curve isnegative. Moreover, few papers study the impact of oil prices on long-term expected inflation, althoughnumerous studies examine the effect of oil prices on contemporaneous core inflation and total inflation, asreviewed in detail in Clark and Terry (2010). Celasun, Mihet, and Ratnovski (2012) find that oil futures priceshocks have a statistically significant impact on long-term breakeven inflation. In fact, both real rates andexpected inflation are important in understanding nominal bond yields (Duffee, 2014; Pflueger and Viceira,2015). This chapter is the first to examine not only nominal bond yields as a whole, but also real bond yieldsand breakeven inflation separately in relation to oil prices.Last, several recent papers have studied the impact of oil price shocks on equity returns. Driesprong,Jacobsen, and Maat (2008) find that increases in oil prices predict lower future stock returns. Kilian andPark (2009) show that oil supply and demand shocks jointly explain 22% of the long-run variation in U.S.real stock returns. Chiang, Hughen, and Sagi (2014) demonstrate that oil risk factors explain the returns ofnon-oil portfolios. These papers highlight important implications of oil price risks for equity returns, but36ignore inflation. Unlike these papers, my focus is the impact of oil on bond yields.I make three contributions to the literature. First, I present novel empirical evidence that crude oilprices have explanatory and incremental forecasting power for nominal and real bond returns and inflationswap rates. Empirical tests using data on TIPS and inflation swap rates provide richer information onunderstanding behaviors of components of nominal yields than those using data solely on nominal bonds.Second, I extend the New Keynesian model to investigate the theoretical relationships between nominal andreal yields, expected inflation, and oil supply and demand shocks. The model offers novel predictions andfurther highlights key economic transmission channels through which oil price shocks affect bond markets.Last, this chapter shows that oil prices are relevant risk factors for pricing nominal and inflation-indexedTreasury bonds and inflation swaps.The remainder of this chapter is organized as follows. Section 2 describes the data and presents empiricalresults. A two-sector New Keynesian model is presented in Section 3. Section 4 discusses model solutions.Theoretical analysis is conducted in Section 5. Section 6 concludes.3.2 Bond returns and oil pricesIn this section, I describe the data and then present empirical evidence of the explanatory and incrementalforecasting power of growth rates of crude oil prices for excess returns on nominal bonds, real bonds, andinflation swap rates. Inflation swap rates provide alternative market-based measures of breakeven inflation,compared to those inferred from the differences between nominal yields and real yields. A description ofinflation swap contracts is provided in Appendix B.3.2.1 DataI use yields on 10-year U.S. Treasury bonds, yields on 10-year U.S. inflation-indexed bonds called TIPS– Treasury Inflation Protected Securities, and 3-month short interest rates to construct bond excess returns.Excess returns on breakeven inflation rates are defined as the difference in excess returns between nominalbonds and TIPS. Data on 10-year nominal U.S. Treasury bond yields, liquidity adjusted 10-year U.S. TIPSyields, and liquidity adjusted breakeven inflation from June 1999 to December 2014 are from Pflueger andViceira (2015).6 TIPS yields and breakeven inflation are adjusted for the liquidity risk present in the TIPSmarket (for details, see Pflueger and Viceira (2015).)6I am very grateful to Carolin Pflueger for providing data constructed in Pflueger and Viceira (2015).37Inflation swap rates, as market-based measures of breakeven inflation, provide a rich dataset on inflationexpectations for various horizons. Inflation swap rates from July 2004 to December 2014 are obtained fromBloomberg. The tenors of inflation swap contracts are available in 1 to 10, 12, 15, 20, or 30 years. As the1-year, 2-year, 5-year, and 10-year maturities are the most common, empirical tests on inflation swap ratesfocus on these four contracts only.Crude oil spot prices are based on the refiners’ acquisition cost of crude oil from the U.S. Energy Infor-mation Administration (EIA) since January 1974. The NYMEX crude oil futures prices of the nearest-to-maturity contracts are from the U.S. EIA since 1986. The various inflation measures are constructed fromthe seasonally-adjusted Consumer Price Index and sub-indexes from the U.S. Bureau of Labor Statisticssince January 1947.The full sample period is from June 1999 to December 2014. The sample period is constrained by dataavailability for U.S. TIPS yields and the liquidity variables that are needed to estimate the liquidity premiumembedded in TIPS yields. In addition, empirical tests using inflation swap rates are run over the sub-sampleperiod from July 2004 to December 2014 due to the data availability for U.S. inflation swap rates.3.2.2 Excess returns on nominal bonds, TIPS, and breakeven inflationDo crude oil prices have explanatory and incremental forecasting power for bond returns? I use reduced-form regressions to address this question. The independent variable is the growth rate of crude oil spotprices, denoted by gOil . I also include two control variables. The first one is the term spread, which is awell-known predictor variable for bond returns (Ludvigson and Ng, 2009). Another one is the inflation ofthe CPI-All Items less Energy price index, which contains inflation-related information for the breakeveninflation component in the nominal bond yields.Excess bonds returns refer to one-period buy-and-hold returns in excess of Treasury bill rate. Ex-cess return of the n-period Treasury bond is defined as xr$t+1 = ny$n,t − (n− 1)y$n−1,t+1− y$1,t , where y$n,tis the nominal yield of the n-period at time t and y$1,t is the rate of the one-period nominal Treasurybills. Similarly, the liquidity-adjusted log excess return of the n-period inflation-indexed bond is definedas xrT IPSt+1 = nyT IPS,ad jn,t − (n− 1)yT IPS,ad jn−1,t+1 − yT IPS1,t , where yT IPS,ad jn,t is the liquidity-adjusted real yield of then-period TIPS at time t and yT IPS1,t is the yield of the one-period real bond. Because the TIPS market is lessliquid than the Treasury market, especially in the early years of the TIPS market and during the 2007 finan-cial crisis, TIPS yields are priced higher to compensate for the liquidity risk. The liquidity-adjusted TIPS38yield is estimated as yT IPS,ad jn,t = yT IPSn,t −Ln,t , where Ln,t is the liquidity premium, as in Pflueger and Viceira(2015). The liquidity-adjusted log excess breakeven return is defined as xrBEt+1 = xr$t+1−xrT IPSt+1 , representingthe log excess return of a portfolio that is long one nominal bond and short one TIPS bond with the samematurity.Table 3.1 Panel A shows the results of regressing the 3-month overlapping excess returns on nominalbonds, TIPS, and breakeven inflation using the corresponding term spread and the CPI-less energy inflation,and then adding the log growth of crude oil spot prices. Columns (1) and (3) show that oil price growth gOiltis a significant explanatory variable for contemporaneous excess returns on nominal bonds and breakeveninflation. Increases in the oil price tend to go along with decreases in the expected excess return on nominalbonds and breakeven inflation, implying that realized breakeven inflation and nominal yields are higher. Inaddition, gOilt contributes additional explanatory power over and beyond the term spread and the CPI-lessenergy inflation, as reflected by increases in the adjusted R2.Table 3.2 shows the results of predictive regressions. Column (1) shows that the lagged oil price growthgOilt−1 significantly forecasts the excess returns of nominal bonds. Column (3) shows that the oil price growthgOilt is a significant predictor for the excess returns of the breakeven inflation. Column (2) shows that gOiltand gOilt−1 have opposite predictions on excess returns on real bonds. In addition, gOilt and gOilt−1 contributeadditional forecasting power over and beyond the term spread and the CPI-less energy inflation, reflected byincreases in the adjusted R2. The forecasting power of gOilt is also economically significant. For instance,a 10% increase in oil price predicts a 0.5% increase in the expected excess return on breakeven inflation.Columns (4) to (6) present robustness checks of using the sum of gOilt and gOilt−1 as the regressor, in the spiritof Dimson beta. Results confirm that growth rates of oil prices have the strongest forecasting power forexcess returns on breakeven inflation.Because the expected nominal bond excess returns, the expected real bond excess returns, and the ex-pected excess returns on breakeven inflation could be viewed as nominal rate risk premia, real rate riskpremia, and inflation risk premia, respectively, the above forecasting regression results indicate that growthrates of oil prices are a significant predictor for nominal rate risk premia and inflation risk premia.3.2.3 Excess returns on inflation swap ratesTo gain some insight into the connection between oil prices and breakeven inflation of different matu-rities, I use data on inflation swap rates. Figure 3.1 plots inflation swap rates along with the log growth of39oil spot prices from July 2004 to December 2014. Inflation swap rates of different maturities co-move overtime, whereas short-term swap rates are more volatile than long-term swap rates. Most noticeably, swaprates co-move with crude oil prices starting in July 2008. All swap rates dropped in August 2008, the monthin which the U.S. refiners’ acquisition cost of crude oil started to drop after reaching the peak of $127 inJuly 2008. I also look at whether uncertainty in the oil market is associated with uncertainty in the inflationswap market. Figure 3.2 shows a striking co-movement between standard deviations of 10-year inflationswap rate changes and the log growth of the nearest-to-maturity oil futures prices, estimated by using dailyobservations in each month. I use the nearest-to-maturity oil futures prices as the proxy for spot pricesbecause crude oil spot prices are not available at a daily frequency. An analysis of latent factors of inflationswap rates is provided in Appendix C.In the same spirit of explaining and forecasting excess returns of breakeven inflation shown in column(3) in Table 3.1 Panel A and Table 3.2, I use oil price growth to explain and forecast excess returns onthese inflation swap rates. Table 3.3 shows results for both contemporaneous and predictive regressions for1-year, 2-year, 5-year, and 10-year inflation swap rates. Slope coefficients on gOilt have the same signs andsignificance levels as those in column (3) in Table 3.1 Panel A and Table 3.2.To sum up, the above regression results present novel empirical evidence that oil price changes containincremental information for bond returns and breakeven inflation. However, interpreting empirical evidenceis challenging, mainly because the economic signal of oil price changes is ambiguous. Kilian (2009) showsthat the impact of oil price shocks on the economy depends on the type of fundamental shocks that driveoil prices. In addition, empirical tests on real bond returns and inflation swap rates are constrained by theshort history of data on TIPS and inflation swap rates. All limited empirical evidence can benefit from atheoretical analysis. I proceed with examining the theoretical impact of shocks in the oil market on bondreturns and inflation expectations in a structural model.3.3 A two-sector New Keynesian modelThe modeling framework builds on the workhorse New Keynesian model (Galı´, 2008), which is the mostsuitable DSGE framework for analyzing nominal bond yields, real bond yields, and inflation processes; andtheir interactions with economic fluctuations.There are three important departures from the basic New Keynesian model. First, an oil sector is in-cluded in addition to the standard consumption goods sector. The two sectors are labelled as the oil sector40and the core sector. Oil and core goods are produced by a representative oil firm and monopolistic coregoods firms, respectively. The inflation of oil prices represents energy inflation, while the inflation of coregoods prices represents core inflation. Second, oil is included in a household’s utility function, to capturethe fact that households spend about 4% of their pre-tax income on gasoline for transportation needs. Inaddition, household consumption of oil is assumed to be complementary to the consumption of core goods,as in Ready (2015).7 Third, oil is also used as an energy input in core goods firms’ production functions,reflecting the fact that 40% of industrial energy comes from oil.The oil price is assumed to be flexible, consistent with the average duration of 10-18 days between pricechanges in retail gasoline and of 2.4 days in wholesale gasoline (Douglas and Herrera, 2010). The coregoods price is assumed to be sticky, supported by the fact of the average frequencies of 8 to 11 months ofprice changes of 350 product categories underlying the U.S. CPI (Nakamura and Steinsson, 2008). Last, theadjustment of real wages is assumed to be sluggish as in Blanchard and Galı´ (2007).The productivity shock in the energy sector represents the oil supply shock. The productivity shock inthe core sector is the supply shock in the core sector, but acts as demand shock in the oil market. Note thatdemand for oil comes from both households and core goods firms.3.3.1 HouseholdsAn infinitely-lived representative household has recursive utility (Epstein and Zin, 1989; Weil, 1989)Vt = (1−β )U(Xt ,Nt)1−ρ +β(EtV1−γ1−ρt+1) 1−ρ1−γ(3.1)where β is the time discount factor, γ is the relative risk aversion, and 1/ρ is the elasticity of inter-temporalsubstitution (EIS). The period utility U(Xt ,Nt) is given byU(Xt ,Nt) =(X1−ρt1−ρ −φκtN1+νt1+ν) 11−ρ, φ > 0, ν > 0 (3.2)where Xt is the consumption bundle of oil and the final core goods, Nt is households’ labor supply tointermediate core goods firms, and 1/ν is the Frisch elasticity of labor supply. The process κt is chosento ensure balanced growth and will be specified in the core goods sector below. As the households value7Oil is complementary to the consumption of some durable goods, such as motor vehicles. As the model does not distinguishbetween durable goods and non-durable goods, the complementarity of oil is modeled in a reduced form.41leisure, there is disutility from supplying labor to the intermediate goods firms.The consumption bundle is a constant elasticity of substitution (CES) aggregation of oil and the finalcore goods,Xt ≡ [(1−ξ )C1−1ηt +ξ (OHt )1− 1η ]11− 1η (3.3)where Ct is the final core goods, OHt is the consumption of oil by households, ξ measures the weight of OHtin the consumption bundle, and η measures the elasticity of substitution between oil and the consumptiongoods. The price of the consumption bundle is defined as PXt ≡ [(1−ξ )(PCt )1−η+ξ (POt )1−η ]1/(1−η), wherePCt and POt are the prices of the final core goods and oil, respectively. It can be shown that (1− ξ )CtPCt +ξOHt POt = XtPXt .The representative household is endowed with all the shares of the oil firm and core goods firms andreceives dividends from the oil sector and the core goods sector. The household chooses the optimal con-sumption of the final core goods and oil, the holding of bonds, and labor supply to maximize the utility givenin equation (3.1)maxCt ,OHt ,Bt ,NtVt , (3.4)subject to the intertemporal budget constraintXtPXt +Bt ≤ Bt−1Rt−1+WtNt +DCt +DOt (3.5)where Bt is the holding of the one-period riskless bond, Wt is the wage, and DCt and DOt are the dividendsfrom the intermediate core goods sector and the oil sector, respectively. In addition, households can tradeone-period riskless bonds available in zero net supply.The nume´raire in the model is the one-period riskless bond. The bond costs one dollar in the period tand pays Rt dollars in the next period t+1. Thus Rt corresponds to the gross nominal interest rate.Following Blanchard and Galı´ (2007), I model real wage rigidities in a reduced way without specifyingthe exact friction in the labor market. The process of real wages is given byWtPCt=(Wt−1PCt−1)ρw(−UN,tUC,t)1−ρw(3.6)where ρw is an index of real wage rigidities and−UN,t/UC,t is the marginal rate of intra-temporal substitution42between the labor supply and consumption of core goods. A high value of ρw indicates a more sluggishadjustment of real wages.The stochastic discount factor (SDF) is derived from the optimization of the household’s problem. Theone-period real SDF MRt,t+1 is the marginal rate of substitution between time t and time t+1MRt,t+1 = β(Xt+1Xt) 1η−ρ(Ct+1Ct)− 1η  V 1−ρt+1(EtV(1−γ)/(1−ρ)t+1)1/(1−γ)ρ−γ(3.7)The one-period nominal SDF is defined as M$t,t+1 ≡ MRt,t+1 PCtPCt+1. The SDF here also depends on householdgasoline consumption because Xt depends on the consumption of oil.3.3.2 Oil sectorA representative oil firm produces oil. As in Kogan, Livdan, and Yaron (2009), the oil productionfunction takes a simple formY Ot = ZOt KOt−1 (3.8)where KOt−1 is the installed capital, and ZOt is the total factor productivity (TFP) in the oil sector.I assume that zot ≡ logZOt follows an AR(1) processzot = ρozot−1+σoεot , (3.9)where εot ∼ i.i.d.N(0,1).The law of motion for capital is given byKOt = (1−δ o)KOt−1+ΦO(IOtKOt−1)KOt−1 (3.10)ΦO(IOtKOt−1)=bo1−1/ζ o(IOtKOt−1)1−1/ζ o+go (3.11)where IOt is the new investment, δ o is the depreciation rate of existing capital, and the functionΦO(IOt /KOt−1)is a positive, concave function, as in Jermann (1998). The parameter ζ o is the elasticity of the investmentcapital ratio with respect to Tobin’s q.43For the sake of simplicity, I abstract from the oil inventory and the oil cartel.8 Oil is sold to the interme-diate goods firms to produce intermediate goods and to the households for their consumption. Note that theoil price POt is flexible because the oil firm faces no price adjustment costs.Given the oil price of POt and the final core goods price of PCt , the oil firm chooses the optimal investmentto maximize its firm value:V Ot ≡maxIOtEt∞∑j=0M$t,t+ jDOt+ j (3.12)where DOt+ j ≡Y Ot+ jPOt+ j− IOt+ jPCt+ j is the dividend in period t+ j and M$t,t+ j is the nominal SDF derived fromthe household’s optimality conditions. The oil firm dividend goes to the household.3.3.3 Core goods sectorThe core goods sector is comprised of a final core goods firm and a continuum of monopolistic interme-diate core goods firms.Final core goodsA representative final core goods firm combines a continuum of intermediate core goods into the finalcore goods. The final core goods firm operates in a perfectly competitive market and thus is a price taker.The firm uses a constant elasticity of substitution (CES) production technology to produce the final coregoods.YCt ≡(∫ 10(YCt (i))ε−1ε di) εε−1(3.13)where YCt (i) is the quantity of intermediate core goods i, i ∈ [0,1]. The parameter ε measures the elasticityof substitution between intermediate core goods.The final core goods are either consumed by the household or used as investment for new capital by theoil firm and intermediate core goods firms.Ct + IOt +∫ 10ICt (i)di≤ YCt (3.14)where ICt (i) is the investment made by the intermediate core goods firm i.8Carlson, Khokher, and Titman (2007) and Kogan, Livdan, and Yaron (2009) do not consider these two features in their modelseither. Inventory is not critical in the model, but the presence of inventory can mitigate oil supply and demand shocks on oil spotprices.44Given the final core goods price of PCt and the price of intermediate core goods i of PCt (i), the final coregoods firm chooses the optimal demand of core goods i by maximizing its profit in each periodmaxYCt (i)PCt YCt −∫ 10PCt (i)YCt (i)di (3.15)Furthermore, the optimal demand for the intermediate core goods i can be expressed asYCt (i) =(PCt (i)PCt)−εYCt (3.16)Equations (3.13) and (3.16) together imply that the final core goods price is an aggregate price in-dex of intermediate core goods prices: PCt ≡ [∫ 10 (PCt (i))1−εdi]11−ε . Furthermore, it can be shown that∫ 10 PCt (i)YCt (i)di = PCt YCt .Intermediate core goodsIntermediate core goods are produced by a continuum of monopolistic firms indexed by i ∈ [0,1]. Theproduction of intermediate core goods i is given byYCt (i) = [KCt−1(i)]ω [ZCt Nt(i)]α [OIt (i)]1−α−ω (3.17)where ZCt is the common productivity across all intermediate core goods firms, KCt−1(i) is the capital, Nt(i)is the labor employed, and OIt (i) is the quantity of oil used in production. The oil share of production ismeasured by 1−α−ω .The law of motion for capital is given byKCt (i) = (1−δ c)KCt−1(i)+ΦC(ICt (i)KCt−1(i))KCt−1(i) (3.18)ΦC(ICt (i)KCt−1(i))=bc1−1/ζ c(ICt (i)KCt−1(i))1−1/ζ c+gc (3.19)where ICt (i) is the new investment, δ c is the depreciation rate of existing capital, and the functionΦC(ICt (i)/KCt−1(i))is a positive, concave function, as in Jermann (1998). The parameter ζ c represents the elasticity of the in-vestment capital ratio with respect to Tobin’s q.45Following Croce (2014), I assume that the productivity growth rate, ∆zct+1 ≡ log(ZCt+1/ZCt ), has a long-run risk component and a short-run risk component:∆zct+1 = xct +σcεct+1 (3.20)xct = ρxcxct−1+σxcεxct (3.21)where εct ∼ i.i.d.N(0,1) and εxct ∼ i.i.d.N(0,1). In addition, all shocks are assumed to be mutually indepen-dent.Following Rotemberg (1982) and Ireland (1997), I assume that each monopolistic firm changes its priceevery period but faces a real quadratic cost of price changes.Γ(PCt (i))≡ϑ2(PCt (i)piPCt−1(i)−1)2YCt (3.22)The parameter ϑ measures the degree of price stickiness, which is common to all intermediate core goodsfirms. The variable pi is the target gross core inflation rate in the steady state. If the price grows at the rateof target inflation, the cost of the price adjustment is zero. If ϑ = 0, there is no adjustment cost of pricechanges. Because of the quadratic cost of price changes, fewer final goods are available for consumptionand investment. The presence of nominal price rigidity leads to inefficiency.9As shown in (3.16), the optimal demand for the intermediate core goods i is downward-sloping, which isdetermined by the relative prices. Monopolistic firm i chooses the optimal price of its goods and the optimalinvestment to maximize its firm value:VCt (i)≡ maxPCt (i),ICt (i)∞∑j=0EtM$t,t+ jDCt+ j(i) (3.23)where DCt+ j(i)≡ YCt+ j(i)PCt+ j(i)−Ψt+ j(YCt+ j(i))−Γ(PCt+ j(i))PCt+ j− ICt+ j(i)PCt+ j is the dividend in period t + jand M$t,t+ j is the nominal SDF derived from the household’s optimality conditions. The production cost9An equivalent inflation dynamic can also be derived under the assumption of a staggered price-setting mechanism (Calvo,1983).Ascari, Castelnuovo, and Rossi (2011) discusses the similarities and differences between the two approaches. The Rotembergapproach is better than the Calvo approach for replicating the dynamics of inflation at the macro level. An advantage of theassumption of quadratic price adjustment costs is that it leads to a tractable symmetric equilibrium. Because of the presence ofnominal rigidity, real quantities depend on nominal prices and the nominal interest rate, which is governed by monetary policy.46functionΨt+ j(YCt+ j(i)) for a given level output YCt+ j(i) is defined below.Given the oil price POt and the wage Wt , the firm i chooses the optimal demand for labor and oil tominimize production cost:minNt(i),OIt (i)Ψ(YCt (i))≡WtNt(i)+OIt (i)POt .s.t. YCt (i) = [KCt−1(i)]ω [ZCt Nt(i)]α [OIt (i)]1−α−ω(3.24)Last, the process κt is defined as κt ≡ (ZCt−1)1−ρ to ensure balanced growth.3.3.4 Central bankTo complete the model, I assume that the central bank follows the Taylor rule in setting the nominalinterest rate.Rt = R¯(piCPItp¯i)φpi (YCtY¯)φy, φpi ≥ 0, φy ≥ 0 (3.25)where R¯, p¯i , and Y¯ are the gross interest rate, the target gross total inflation, and the output of core goods insteady state, respectively.3.3.5 Symmetric equilibriumThe equilibrium of the model is characterized by the solutions of the household’s problem (3.4), the oilfirm’s problem (3.12), the final core goods firm’s problem (3.15), and the intermediate core goods firms’problems (3.23). The first order conditions of these problems are presented in Appendix D.The equilibrium is symmetric. All intermediate core goods firms have identical cost minimizationproblems and value maximization problems. Thus, they choose the same optimal demand for labor andoil: Nt(i) = Nt and OIt (i) = OIt . Furthermore, they choose the same optimal selling price and investment:PCt (i) = PCt and ICt (i) = ICt . Finally, all markets are clear.3.3.6 Measures of inflation, yields, and inflation swapsThis sub-section first defines three measures of inflation and then uses the SDF to price nominal and realzero-coupon bonds and zero-coupon inflation swap contracts.47Inflation measuresIn the model, the core CPI price index, the energy CPI price index, and the CPI price index are repre-sented by the prices of the final core goods, oil, and the consumption bundle, respectively. Let piCt ≡ PCt /PCt−1denote core CPI inflation, piOt ≡ POt /POt−1 denote energy CPI inflation, and piCPIt ≡ PXt /PXt−1 denote CPI in-flation.To gain insight into relations of oil prices to core inflation, the core inflation equation can be expressedin the log-linearization form˜ct = βEt ˜ct+1+λψ˜t (3.26)where λ ≡ ε−1ϑ is decreasing in the index of price stickiness ϑ , ψt represents the real marginal costs ofproducing intermediate goods, and tilde variables denote the log deviation from steady state. Core inflationdepends on the expected inflation in the next period and the change of the real marginal production cost.The effect of oil price on core inflation is reflected through the real marginal costs of producing inter-mediate core goods.ψ˜t =1−α−ω1−ω p˜ot +α1−ω w˜t −11−ω z˜ct +ω1−ω (y˜ct − kct−1) (3.27)Yields and inflation swap ratesI use the pricing kernel derived from the optimality conditions of the household’s problem to valuezero-coupon nominal bonds, zero-coupon real bonds, and zero-coupon inflation swaps.The nominal yield of an n-year zero-coupon nominal Treasury bond and the real yield of an n-yearzero-coupon real Treasury bond are defined as:ynt =−1nEt(m$t,t+n)−12nVart(m$t,t+n) (3.28)rnt =−1nEt(mR,Xt,t+n)−12nVart(mR,Xt,t+n) (3.29)where m$t,t+n ≡ logM$t,t+n and mR,Xt,t+n ≡ logMR,Xt,t+n.The breakeven inflation rate is the difference in yield-to-maturity between an n-year zero-coupon nomi-48nal Treasury bond and an n-year zero-coupon real Treasury bond. The breakeven inflation rate measures then-year inflation swap rate.Alternatively, the zero-coupon inflation swap rate can be directly estimated. When an inflation swapcontract is initialized, the present value of expected cash flow at maturity should be zero. Assuming that thenotional amount is one dollar and that the inflation index refers to the CPI index, the zero-coupon inflationswap fixed rate snt is given by:0 =−Et [M$t,t+nensnt ]+Et [M$t,t+npiCPIt,t+n] (3.30)Note that snt is known at time t and that the real SDF MR,Xt,t+n ≡M$t,t+npiCPIt,t+n.The swap rate is further expressed as:snt =1nEt pˆiCPIt,t+n−12nVart pˆiCPIt,t+n+1nCovt(mR,Xt,t+n, pˆiCPIt,t+n) (3.31)where pˆiCPIt,t+n ≡ logpiCPIt,t+n is the log CPI inflation. On the right-hand side of the equation, the first term is theexpected inflation, the second term is the Jensen’s inequality adjustment of the expected inflation, and thethird term is the inflation risk premium.The swap rate (ignoring the Jensen’s inequality adjustment) consists of the inflation expectation and theinflation risk premium. If inflation is high in “bad” states, where marginal utility is high, the covarianceterm will be positive. If inflation is positively correlated with the real SDF, the inflation risk premium willbe positive and the swap rate will be higher than the expected inflation. The fixed receiver asks for a higherrate to compensate for the risk of the realization of unexpected high inflation in the “bad” states of the world.3.4 Model solutionIn this section, I discuss the choices of parameter values. The model is solved in Dynare using a second-order approximation at a quarterly frequency.3.4.1 ParametersTable 3.4 reports the parameter values used in the baseline calibration of the model. I choose parametervalues reported in previous studies whenever possible, or by matching the selected moments in the data.Parameters are grouped into four categories.49I choose a value of 0.997 for the time discount rate β , which corresponds to an annual real interest rateof 1.2% in the long run. Households prefer an early resolution of uncertainty. If the relative risk aversion γtakes a value of 10 and the elasticity of intertemporal substitution 1/ρ is set at 2, the nominal yield curveis slightly upward sloping and the 10-year inflation risk premium is about 8 basis points. In order to matchthe term spread of nominal yields, I also consider the RRA γ and the EIS 1/ρ of the values of 20 and 5,respectively, in some calibrations. The weight of oil in the consumption bundle ξ is set at 0.1, close to theweight of energy components in the CPI.10 The elasticity of substitution between oil and core goods η isset at 0.25, the same value as used in Ready (2015), implying complementarity between the two types ofconsumption. The real rage rigidity index ρw is set at 0.95 to be close to the ratio of σ(w)/σ(yc) = 0.44,a key moment of wages in the data. The labor supply N is fixed at 0.33 in the deterministic steady state sothat households spend one-third of their discretionary time working. The Frisch elasticity of labor supply ispinned down as 0.2498 by the the labor supply in the deterministic steady state.For most parameters associated with production functions, I follow related papers. The constant elas-ticity of substitution of intermediate core goods ε is set at 6 (which corresponds to a markup of 20%). Thedegree of capital adjustment cost (ζ o and ζ c) is set at 4.8, both in the oil sector and intermediate goodssector. Free parameters bo and go are chosen such that there is no adjustment cost for the oil sector in thedeterministic steady state. In particular, I set bo = (δ o)1/ζ o and go = 11−ζ o δo. Similarly, free parameters bcand gc are chosen such that there is no adjustment cost for the intermediate goods firms in the deterministicsteady state. In particular, I set bc = (δ c)1/ζ c and gc = 11−ζ c δc. I choose a higher value of 0.05 for thedepreciation rate of the oil capital δ o (which corresponds to an annualized rate of 20%). The depreciationrate of consumption goods capital δ c is equal to 0.02. The capital share ω and labor share of output α areset at 0.33 and 0.57, respectively. Thus the oil share of output 1−α−ω is equal to 0.1.11 I choose 25 forthe degree of price adjustment cost ϑ , which is close to the values suggested by Ireland (2000).Coefficients in the Taylor rule φpi and φy are set at 1.5 and 0.125, respectively, which are standard valuesin the monetary literature. The target inflation p¯i is set at 1.0092 (which corresponds to an annual inflationof 3.68%, close to the average U.S. core inflation).10Note that the parameter ξ measures the share of oil in the consumption bundle. The chosen value of 10% for ξ does notcontradict the fact that an average U.S. household spends 4% of pre-tax income on gasoline. The percentage of energy expenditureof all household expenditure is higher than 4% because of income tax and savings. Both theoretical analysis and model predictionsare robust to a wide range of parameter values of ξ .11As in the case of the parameter ξ , the oil share of output is also a key variable in the model, affecting many quantities in themodel. However, both theoretical analysis and model predictions are robust to a wide range of parameter values of 1−α−ω .50Parameter values of three productivity shocks are chosen to match the moments of the relative oil prices,core inflation, CPI inflation, 5-year nominal yields, and the term spread of 5-year nominal bonds.3.4.2 Model momentsMoments from data and the model are summarized in Table 3.5. The model is able to roughly match themoments of the relative oil prices, core inflation, CPI inflation, 5-year nominal yields, nominal yield spreadbetween 5-year and 1-quarter, and correlations between growth rates of oil prices and changes in yields andbreakeven inflation.Note that the focus of the chapter is not the term structure of nominal yields or the equity premium.Rather, reporting these moments illustrates that the model can generate with reasonable magnitude the fea-tures of nominal yields and equity returns. The term spread of 5-year nominal yields in the model is about58% of the values in the data. The inflation risk premium for 5-year nominal yields is 28 basis points.However, the volatility of 5-year nominal yields in the model is much smaller than that in the data, whichis a well-known problem in the literature. Although the model is not calibrated to match moments of equitypremium, the model generates a sizable equity premium.Last, the model is also able to match other key macroeconomic data, in addition to inflation data. Thebottom panel in Table 3.5 shows that the relative volatilities and autocorrelations of the final good con-sumption, wage, and output in the model are close to the empirical counterparts. In particular, the negativecorrelation between consumption growth and inflation from the model closely matches that in the data.3.5 Oil prices, expected inflation, and bond yieldsIn this section, I first discuss the economic drivers of oil prices: supply and demand shocks in the oilmarket. Afterwards, I examine how expected inflation, real yields, and nominal yields respond to supply anddemand shocks that drive oil prices. Last, I discuss key economic channels and the inflation risk premiumin the model.3.5.1 Oil prices and three productivity shocksThis sub-section analyzes the impulse response functions around the stochastic steady state to a negativeproductivity shock εot in the oil sector, a positive transitory productivity shock εct , and a positive permanentproductivity shock εxct in the core goods sector. The size of the shock is one standard deviation of each51shock. The impulse response functions plot the percentage deviation from the stochastic steady state. Inthe baseline solution of the model, the productivity zot process in the oil sector is transitory (ρo = 0.45) andvolatile (σo = 9.5% per quarter). The shock to the productivity growth εct is less volatile (σc = 1.2%) perquarter, and the process xc is persistent (ρxc = 0.9) and even less volatile (σxc = 0.17%).Figure 3.3 illustrates the response of a set of key variables to a negative productivity shock εot in theoil sector. For a 9.5% decrease in oil productivity, the real oil price jumps by 11%, which is a big pricehike. Core inflation also increases by 0.36%, because the rise in the oil price is passed on through the higherproduction cost of core goods. The relative change of the core goods price is small in part because the coregoods price is sticky, and in part because the share of oil in production is the smallest among all the factorsof production. Households greatly reduce oil consumption, with a sharp drop of 5.3%. The income effectleads to households demanding fewer core goods. Households consume fewer core goods, resulting in a2.5% drop. Even though the weight of oil in the CPI is only 0.1, CPI inflation still increases by roughly0.5% because of the 11% big jump in oil prices.Because households consume both less oil and fewer core goods, the economy after a big oil disruptionis in a “bad” state for households. If the oil supply disruption is transitory, oil production will graduallyrecover. The oil price and the core goods price revert to their long-run trends. One quarter later, the real oilprice drops by 5%, leading to a lower expected energy inflation. An initial big increase in realized energyinflation is followed by a decrease in expected energy inflation as a “correction” sets in. The impact of oilsupply on the economy disappears after 4 quarters.Figure 3.4 shows responses for a positive transitory productivity shock to εct (1.2% increase) in thecore goods sector. The productivity jumps to a higher level and stays there afterwards. The intermediatecore goods firms produce more and sell core goods at lower prices because the marginal production costdecreases. Core inflation decreases by 0.1% initially and gradually recovers to the long-run value. Given thelower prices of core goods, households consume more, in a nearly 0.3% increase. Meanwhile, householdsalso want to consume more oil because oil is complementary to the consumption of core goods. Because oilproduction is inelastic in the short run and the capital is predetermined in the last quarter, the oil price hasto rise to clear the oil market. The real oil price rises by 1%. Since the relative price of oil to core goodsincreases, the substitution effect mitigates the rising demand for oil due to the complementarity. Householdsbarely increase demand for oil by 0.07%. Overall, the magnitude of the rise in the oil price is mild, therealized CPI inflation decreases, and the expected CPI inflation remains below the long-run trend for about5225 quarters.Because households consume both more oil and consumption goods, the economy after a positive tran-sitory productivity shock in the core goods sector is a “good” state for households. When oil demand isdriven by economic growth, higher oil prices are accompanied by lower inflation and vice versa.Figure 3.5 shows different responses for a positive permanent productivity shock to εxct (0.17% increase)in the core goods sector. Because it is a positive shock to the growth rate of productivity and the processxc is very persistent, the level of productivity ZC keeps increasing for a substantial length of time. As theeconomy grows, intermediate core goods firms produce more and sell core goods at lower prices because themarginal production cost decreases. Core inflation decreases by 0.03% initially and keeps declining beforerecovering to the long-run value. Core goods firms increase their investment in new capital to maximize thebenefit of rising productivity. Because the expected consumption of core goods will be high in subsequentperiods, households reduce consumption by 0.7% in the first period. Meanwhile, households also consumeless oil in the first period because oil is complementary to consuming core goods. Because oil production isinelastic in the short run, real oil prices initially decrease to clear the oil market by 0.1%. As the productivitylevel ZC steadily increases, the output of core goods increases, and households increase their consumptionof core goods and oil. Real oil prices start to rise from the second period.Overall, the magnitude of the rise in the oil price is big and lasts for a very long time. Realized CPIinflation decreases and expected CPI inflation remains below the long-run trend for more than 40 quarters.Because households consume both more oil and consumption goods, the economy after a positive permanentproductivity shock in the core goods sector is a “good” state for households.Because the oil market is competitive, the oil price quickly responds to either type of shocks. On theother hand, core inflation gradually responds to shocks because of the presence of the nominal price rigidityof core goods and the real wage rigidity. In addition, the magnitude of the response of the gross core inflationrate is also determined by the parameter values of the oil share in production and the elasticity of substitutionbetween oil and consumption goods. In the model, a mixture of three types of productivity shocks cangenerate many rich dynamics among oil prices, inflation processes, and total consumption processes.3.5.2 Expected inflation, real yields, and nominal yieldsThis sub-section discusses how real yields, breakeven inflation, and nominal yields respond differentlyto each productivity shock. The impulse response functions plotted in Figure 3.6 to 3.8 highlight that the53impacts of oil price increases driven by three specific productivity shocks are different in terms of directions,magnitudes, and lengths.As shown in Figure 3.6, real yields of both maturities increase for all three productivity shocks. Theresponse of real yields to the negative productivity shock in the oil sector relies on the transitory property ofthe ZO process. Although the realized consumption of core goods and oil is lower, households will expecta positive overall consumption growth as productivity in the oil sector returns to normal. The responseof real yields to either transitory or permanent positive productivity shocks in the core goods sector isstraightforward. The growth rate of overall consumption is positive after either of the shocks. Because thexc process is very persistent, the effect of εxct shock on the real yields lasts over 25 quarters.Figure 3.7 plots impulse response functions of 1-quarter and 5-year breakeven inflation (i.e., inflationswap rates) to a negative productivity shock εot in the oil sector, a positive transitory productivity shock εct ,and a positive permanent productivity shock εxct in the core goods sector. When an oil supply shock occurs,breakeven inflation jumps because the expected inflation after the shock is positive, as discussed earlier.One-quarter breakeven inflation goes up significantly, while 5-year breakeven inflation slightly rises. Asthe productivity shock in the oil sector is transitory, the impact disappears after 5 periods. Figure 3.7 alsoillustrates that a positive transitory productivity shock εct in the core goods sector has a very small impacton breakeven inflation. Unlike the transitory shock εct , the positive permanent shock εxct has a big andlong-lasting impact on both 1-quarter and 5-year breakeven inflation.For a given maturity, the nominal yield is the sum of the real yield and breakeven inflation. Figure3.8 plots impulse response functions of the 1-quarter and 5-year nominal yields to a negative productivityshock εot in the oil sector, a positive transitory productivity shock εct , and a positive permanent productivityshock εxct in the core goods sector. For the negative productivity shock in the oil sector, the nominal yieldsunambiguously go up because both real yields and breakeven inflation positively respond to the shock.However, the response of nominal yields to productivity shocks in the core goods sector is ambiguous,depending on the relative magnitude of the positive responses of real yields and the negative responses ofbreakeven inflation. Under the calibration of the baseline model, nominal yields go down, especially inresponse to the permanent positive productivity shock.The conventional wisdom that high oil prices cause higher expected inflation and nominal yields is trueonly for the disruption in the oil supply. Admittedly, the above model predictions depend on the assumptionsof the properties of the three productivity shocks, and the model considers only three important productivity54shocks in the economy. Nevertheless, the model illustrates the necessity of identifying the type of shocksthat drive oil prices, and of decomposing nominal yields into real yields and breakeven inflation. Thisapproach provides a more informative analysis on the interaction between oil prices and bond yields.3.5.3 Bond return regressions on simulated dataSimilar to the empirical counterpart in Panel A, Table 3.1 Panel B shows the contemporaneous regres-sions of excess returns on 10-year nominal bonds, real bonds, and breakeven inflation on oil price growthrates using simulated data from the baseline model. The model is able to replicate the empirical slopecoefficients of the same signs and statistical significance levels while the R2 are fairly large.The coefficient on gOilt in columns (1) and (3) in the data and the model is negative and significant. Inthe model when the price of oil rises, breakeven inflation rises for productivity shocks in the oil sector butfalls for productivity shocks in the core goods sector. Similarly, nominal yield rises for oil supply shocksbut might rise or fall for productivity shocks in the core goods sectors. Higher nominal yields and higherbreakeven inflation lead to lower excess returns on nominal bonds and breakeven inflation, respectively.According to the model, contemporaneous regression results suggest that in the data productivity shocks inthe oil sector have larger effects than productivity growth shocks.In the model when the price of oil rises, real yields rise for all shocks. Excess returns on real bondsthus negatively respond to positive oil price growth, so the slope coefficient on oil price growth should benegative. In column (2), the coefficient on gOilt is negative in the data and in the model simulation. However,the negative slope coefficient in the model is significant, while it is insignificant in the data. This implies thatthe model predicts a stronger positive response of real yields to increases in oil prices than that presented inthe data.Because three productivity shocks are homoskedastic in the model, risk premia are constant over time.Thus the model is incapable of replicating the empirical predictive regressions presented in Table 3.2 .Time-varying volatility of productivity shocks will be considered in future research.3.5.4 Key economic mechanismsTo gain insight into the role of oil usage in households’ consumption and in firms’ production andthe importance of productivity shocks in both sectors, I estimate model implied statistics for alternativespecifications. Table 3.6 reports four cases. Column (3) shows that if oil is not included in the consumption55bundle, core and CPI inflation and 5-year nominal yields become much lower. This shows that oil pricessignificantly affect the level of inflation and nominal yields. If oil is not used as an input in core goodsfirms’ production, Column (4) shows that correlations between oil price growth and changes in nominalyields implied from the model are very different from those in the data. In addition, relative oil prices arevery volatile, and the term spread and 5-year inflation risk premium dramatically increase. This highlightsthat the direct connection between the two sectors can smooth shocks across sectors; the connection helpsto reconcile the empirical correlations between bond yields and oil prices.The last two columns in the table indicate that productivity shocks in the core sector alone fail to generatevolatile oil prices, and productivity shocks in the oil sector alone fail to generate sizable term spreads andthe inflation risk premium. To sum up, the dual roles of oil and shocks in the two sectors are necessary andimportant elements of the model.Table 3.7 reports unconditional variance decompositions for the baseline model. Consistent with theanalysis above, the productivity shock in the oil sector accounts for the majority of variation in relative oilprices, 1-quarter nominal yields, and 1-quarter real yields. On the other hand, the permanent productivityshock in the core goods sector is important for long-term nominal and real yields, breakeven inflation, andthe long-term inflation risk premium. Last, the transitory productivity shock in the core goods sector playsa smaller role.3.5.5 Term structure of nominal yieldsThe nominal yields curve is upward sloping in the model. The sluggish adjustment of real wages is akey real friction to generate the negative correlation between consumption growth and expected inflation,which in turn leads to the positive inflation risk premium and upward sloping nominal yields.12 The role ofreal wage rigidities in the context of the term structure of nominal yields has been examined in Hsu, Li, andPalomino (2014). However, this chapter incorporates the real wage rigidities in a simpler and reduced way.3.5.6 Inflation risk premiumTo gain some insight into the inflation risk premium, I examine the processes of the SDF and the inflationswap rate for one period only.12It is well known that standard dynamic stochastic general equilibrium models fail to generate the upward sloping nominalyields curves. Kung (2015) and Hsu, Li, and Palomino (2014) are the two exceptions.56First, project the log real SDF process mR,Xt,t+1 on the space spanned by the three productivity shocksmR,Xt,t+1 = EtmR,Xt,t+1−λ ot+1εot+1σo−λ ct+1εct+1σc−λ xct+1εxct+1σxc(3.32)where εot+1, εct+1, and εxct+1 defined in the model section are orthogonal to each other. The quantities λot+1,λ ct+1, and λxct+1 are the market prices of risk for the three productivity shocks, respectively.Similarly, project the log CPI inflation process pˆiCPIt,t+1 on the space spanned by the three productivityshocks:pˆiCPIt,t+1 = Et pˆiCPIt,t+1+βot+1εot+1+βct+1εct+1+βxct+1εxct+1. (3.33)Parameters λ and β can be estimated from the impulse responses of the real SDF and the CPI inflationto the three shocks. The market prices of risk are approximated by:λ ot+1 =−σo∂mR,Xt,t+1∂εot+1, λ ct+1 =−σc∂mR,Xt,t+1∂εct+1, λ xct+1 =−σo∂mR,Xt,t+1∂εxct+1. (3.34)The inflation betas are approximated by:β ot,t+1 =∂ pˆiCPIt,t+1∂εot+1, β ct,t+1 =∂ pˆiCPIt,t+1∂εct+1, β xct,t+1 =∂ pˆiCPIt,t+1∂εxct+1. (3.35)Finally, the inflation risk premium of the one-period inflation swap is given by:Covt(mR,Xt,t+1, pˆiCPIt,t+1) =−β ot+1σoλ ot+1−β ct+1σcλ ct+1−β xct+1σxcλ xct+1. (3.36)Table 3.8 presents the market price of risk and the one-period inflation risk premium for each shock,estimated from the impulse response functions of the real SDF and CPI. The market prices of risk perquarter are 0.11%, 0.23%, and 0.04% for productivity shocks εo in the oil sector, εc and εxc in the core goodssector, respectively. The betas of CPI inflation are negative for all three shocks. CPI inflation decreases for apositive oil supply shock and positive transitory or permanent innovations in productivity in the core goodssector. Households’ marginal utility moves along with CPI inflation: an economic environment with highCPI inflation is viewed as a “bad” state and vice versa. Therefore, the inflation risk premium is positive.The inflation risk premium for one quarter is 0.6 basis points, 1.7 basis points, and 0.9 basis points for theεo, εc , and εxc shocks, respectively. Thus the one-quarter inflation risk premium is 3.2 basis points in total.57In the model, the average values of the 5-year and 10-year inflation risk premium are 29 basis points and48 basis points per quarter, respectively. In the data, the 10-year inflation risk premia have an average ofabout 40 and 20 basis points per year for TIPS-based measures and inflation swap-based measures. Figure3.9 plots the inflation risk premia of 10-year inflation swap rates. The inflation risk premium is positive mostof the time and time varying, and was negative in late 2008 and early 2009.133.6 ConclusionI first provide novel empirical evidence of the connection between oil prices, breakeven inflation, andreal and nominal Treasury bond returns; I then build a two-sector New Keynesian model to study theirtheoretical relationships. The responses of real yields, breakeven inflation, and nominal yields to increasesin oil prices depend on the type of shocks that drive oil prices. The complementarity between oil and coregoods consumption and oil input in production are important economic channels for studying the dynamicsof oil prices and bond yields. Overall, the model is able to replicate several key empirical relationshipsbetween oil prices and bond yields. The model also generates upward sloping nominal yield curves andsizable positive inflation risk premia. For the sake of simplicity, the current version of the model considersthree productivity shocks only, omitting true demand shocks, such as preference shocks in the representativeagent’s utility function. Additional preference shocks and the time-varying volatility of productivity shockswill be considered in future research. The implications of the impact of oil price shocks on long-termexpected inflation are also useful for monetary policy and risk management.13I use the Survey of Professional Forecasters (SPF) CPI expectation as the proxy for expected inflation, which is available at aquarterly frequency. The inflation risk premia are estimated as the differences between liquidity adjusted breakeven inflation andthe 10-year inflation swap rate and the median of the SPF 10-year CPI.58Table 3.1: Excess bond returns: Contemporaneous regressionsIn Panel A, the log growth of crude oil spot prices is used to explain contemporaneous 3-month overlappingexcess returns on 10-year U.S. Treasury nominal bonds, 10-year U.S. inflation-indexed bonds (TIPS), andbreakeven inflation, in addition to the corresponding term spreads and the inflation of the CPI-All Itemsless Energy price index. Excess returns are defined in the text. The yield (breakeven inflation) term spreadis the difference between a 10-year and one-quarter yields (breakeven inflation). U.S. 10-year TIPS yieldsand breakeven inflation are liquidity-adjusted as in Pflueger and Viceira (2015). gOilt denotes the 3-monthoverlapping quarterly log growth of crude oil spot prices. piCPI excl. energyt is the quarterly inflation of theseasonally-adjusted Consumer Price Index - All Items less Energy. The sample period is 1999.6 - 2014.12.Standard errors are Newey-West adjusted with six lags. Panel B presents results of replicating contempo-raneous regressions using simulated data from the baseline model. Each simulation generates a series ofquarterly growth rates of oil prices, nominal yields, real yields, and breakeven inflation for 64 quarters.Regressions on these simulated data are repeated 3,000 times. Standard errors are reported in bracket. ***,**, and * denote statistical significance at the 1%, 5%, and 10% level, respectively.Panel A. Data(1) (2) (3)xr$t xrT IPSt xrBEtgOilt -0.08*** -0.03 -0.05***(0.02) (0.03) (0.01)Nominal term spreadt 2.45*(1.51)Liq. Ad j. T IPS term spreadt 2.37*(1.69)Liq. Ad j. breakeven term spreadt 1.28(1.47)piCPI excl. energyt 1.56 1.34 -0.09(3.07) (2.93) (1.39)Const. -0.00 -0.00 0.00(0.02) (0.02) (0.01)Adj. R2 (excl. gOil) 1.6% 0.5% 1.4%Adj. R2 (incl. gOil) 10.9% 2.5% 10.9%Panel B. Model(1) (2) (3)xr$t xrT IPSt xrBEtgOilt -0.16*** -0.06*** -0.09***(0.04) (0.01) (0.04)Nominal term spreadt -3.65**(1.67)T IPS term spreadt 0.97(0.59)Breakeven term spreadt -21.1***(5.99)piCPI coret -2.74* 0.09 -6.29***(1.48) (0.28) (2.07)Const. 0.03 -0.00 0.10***(0.01) (0.00) (0.03)R2 33.1% 60.8% 28.9%59Table 3.2: Excess bond returns: Predictive regressionsThe log growth of crude oil spot prices is used to forecast 3-month overlapping log excess returns on10-year U.S. Treasury nominal bonds, the liquidity-adjusted log excess returns on 10-year U.S. inflation-indexed bonds (TIPS), and the liquidity-adjusted log excess breakeven inflation returns, in addition to thecorresponding term spreads and the inflation of the CPI-All Items less Energy price index. Excess returnsare defined in the text. The yield (breakeven inflation) term spread is the difference between a 10-yearand one-quarter yields (breakeven inflation). U.S. 10-year nominal and liquidity-adjusted TIPS yields,liquidity-adjusted breakeven inflation, and the liquidity risk premium are from Pflueger and Viceira (2015).gOilt denotes the 3-month overlapping quarterly log growth of crude oil spot prices. piCPI excl. energyt is thequarterly inflation of the seasonally-adjusted Consumer Price Index - All Items less Energy. The sampleperiod is 1999.6 - 2014.12. Standard errors are Newey-West adjusted with six lags. ***, **, and * denotestatistical significance at the 1%, 5%, and 10% level, respectively.(1) (2) (3) (4) (5) (6)xr$t+1 xrT IPSt+1 xrBEt+1 xr$t+1 xrT IPSt+1 xrBEt+1gOilt 0.01 -0.04 0.05***(0.03) (0.02) (0.01)gOilt−1 0.04** 0.04** 0.01(0.02) (0.02) (0.01)gOilt +gOilt−1 0.03* -0.00 0.03***(0.01) (0.02) (0.01)Nominal term spreadt 4.76*** 4.76***(1.50) (1.53)Liq. Ad j. T IPS term spreadt 4.27*** 3.70**(1.58) (1.51)Liq. Ad j. breakeven term spreadt 5.87** 5.22***(1.58) (1.44)piCPI excl. energyt 5.61* 2.38 2.98** 5.70* 2.16 2.83**(3.19) (2.68) (1.25) (3.23) (2.70) (1.39)Const. -0.04* -0.02 -0.02*** -0.04* -0.01 -0.02***(0.02) (0.02) (0.01) (0.02) (0.02) (0.01)Adj. R2 (excl. gOil) 10.1% 4.4% 10.7% 10.1% 4.4% 10.7%Adj. R2 (incl. gOil) 12.5% 9.7% 21.5% 12.0% 3.9% 17.9%60Table 3.3: Excess returns on inflation swap ratesThe log growth of crude oil spot prices is used to explain contemporaneous and forecast expected future3-month overlapping excess returns on 1-, 2-, 5-, and 10-year inflation swaps, in addition to the inflationswap term spreads and the inflation of the CPI-All Items less Energy price index. The excess return ofn-period inflation swap is defined as xrnt+1 ≡ nsn,t − (n− 1)sn−1,t+1−EtpiCPIt+1 , where sn,t is the rate of then-period inflation swap and EtpiCPIt+1 is the expected CPI inflation from t to t+1. The quarterly expected CPIinflation EtpiCPIt+1 is estimated from the lagged CPI, the lagged output gap, and the lagged log growth of crudeoil prices in the past 12 months. The quarterly expected CPI inflation is the fitted value of the regressionpiCPIt+1 = β0+∑4j=1β pij piCPIt− j+1+∑4k=1βyk (yt−k+1− y¯t−k+1)+∑4l=1β ol gOilt−l+1+εt+1 in the period January 1982to December 2014. y is the quarterly log industrial production index from the U.S. Board of Governors ofthe Federal Reserve System. y¯ is the Hodrick-Prescott filtered trend of y. gOilt is the quarterly log growthof crude oil prices. The inflation term spread is the difference between 10-year inflation swap rate and one-quarter expected CPI inflation. piCPI excl. energyt is the quarterly inflation of the seasonally-adjusted ConsumerPrice Index - All Items less Energy. The sample period is July 2004 - December 2014. Newey-West standarderrors with six lags are in parentheses. ***, **, and * denote statistical significance at the 1%, 5%, and 10%level, respectively.Panel A. Contemporaneous(1) (2) (3) (4)xr1yt xr2yt xr5yt xr10ytgOilt -0.04*** -0.05*** -0.08*** -0.08***(0.01) (0.01) (0.02) (0.02)In f l. swap term spreadt -0.79*** -1.02** -1.22* -1.52(0.27) (0.46) (0.72) (1.18)piCPI excl. energyt 0.79** 0.92 0.16 0.41(0.36) (0.74) (1.14) (1.79)Const. -0.51** -0.48 0.09 0.11(0.21) (0.38) (0.59) (0.96)Obs. 123 123 123 123Adj. R2 49.6% 45.6% 46.8% 31.1%Panel B. Predictive(1) (2) (3) (4)xr1yt+1 xr2yt+1 xr5yt+1 xr10yt+1gOilt 0.01*** 0.02*** 0.03*** 0.04***(0.00) (0.01) (0.01) (0.01)gOilt−1 0.01** 0.01 0.02 0.03(0.01) (0.01) (0.02) (0.02)In f l. swap term spreadt -1.29*** -1.96*** -2.79** -2.81(0.39) (0.62) (1.24) (1.79)piCPI excl. energyt -0.39 -0.81 -2.40* -2.31*(0.66) (0.82) (1.23) (1.20)Const. -0.03 0.23 1.15 1.22(0.39) (0.51) (0.78) (0.75)Obs. 123 123 123 123Adj. R2 22.8% 19.9% 16.6% 13.6%61Table 3.4: Parameter valuesParameter values are at a quarterly frequency. Parameters are grouped into four categories: preferences,production, shocks, and monetary policy.Group Description Symbol ValuePreferencesTime discount rate β 0.997Relative risk aversion γ 10 (20)EIS 1/ρ 2 (5)Coefficient of disutility φ 3.6272Frisch elasticity of labor supply ν 0.2498Oil share of the consumption bundle ξ 0.1Elasticity of substitution of oil and core goods η 0.25Index of real wage rigidity ρw 0.95Labor supply in the DSS N 0.33ProductionCES of intermediate core goods ε 6Degree of price adjustment cost ϑ 25Degree of oil capital adjustment cost ζ o 4.8Degree of core goods capital adjustment cost ζ c 4.8Depreciation rate of oil capital δ o 0.05Depreciation rate of core goods capital δ c 0.02Capital share of output ω 0.33Labor share of output α 0.568Oil share of output 1−α−ω 0.102Shockszo-shock in the DSS z¯o 0AR(1) coefficient of zo-shock ρo 0.45Standard deviation of zo-shock σo 9.5%zc-shock in the DSS z¯c 0Standard deviation of SRR shock σc 1.2%AR(1) coefficient of LRR shock ρxc 0.9Standard deviation of LRR shock σxc 0.17%PolicyCore inflation target p¯i 1.0092Sensitivity of the interest rate to inflation φpi 1.5Sensitivity of the interest rate to output φy 0.12562Table 3.5: MomentsThis table reports the means, standard deviations, autocorrelations of growth reates of relative oil prices,core inflation, CPI inflation, 5-year nominal yields, yields spread between 5-year and 1-quarter, 5-yearinflation risk premium, and equity premium of the core goods sector from the data and the model. Thereported statistics from the data are numbers at a quarterly frequency for the period of 1987Q4 to 2014Q4.y40, y20, and y1 refer to 10-year, 5-year, and 1-quarter nominal yields, respectively. r40 and be40 refer to 10-year real yields and breakeven inflation, respectively. gOilt represents the growth rate of nominal oil prices.rc and r f refer to the aggregate equity return and the risk-free rate, respectively. The model is calibrated ata quarterly frequency.Data ModelRelative oil pricesE(∆log(POt /PCt )) 0.45% 0.02%σ(∆log(POt /PCt )) 18.48% 13.26%AC(∆log(POt /PCt )) 0.008 -0.219InflationE(piCt ) 0.64% 0.62%σ(piCt ) 0.29% 0.60%AC(piCt ) 0.717 0.619E(piCPIt ) 0.66% 0.62%σ(piCPIt ) 0.62% 0.67%AC(piCPIt ) 0.046 0.4475Y nominal yields, spread, inflation risk premiumE(y20) 1.17% 0.94%σ(y20) 1.16% 0.25%AC(y20) 0.951 0.887E(y20− y1) 0.31% 0.18%IRP(y20) 0.28%CorrelationsCorr(∆y20t ,gOilt ) 0.408 0.473Corr(∆y40t ,gOilt ) 0.397 0.386Corr(∆r40t ,gOilt ) 0.218 0.706Corr(∆be40t ,gOilt ) 0.389 0.133Equity premiumE(rc− r f ) 1.38% 0.86%σ(rc− r f ) 10.23% 1.98%Other macroeconomic momentsσ(c)/σ(yc) 0.51 0.91σ(w)/σ(yc) 0.44 0.64AC(c) 0.53 0.50AC(w) 0.36 0.87AC(yc) 0.57 0.68Corr(∆c,piCPI) -0.56 -0.4763Table 3.6: Data and model implied statistics for alternative specificationsThe table reports summary statistics for key variables from the data and the model with alternative speci-fications. y40, y20, and y1 refer to 10-year, 5-year, and 1-quarter nominal yields, respectively. r40 and be40refer to 10-year real yields and breakeven inflation, respectively. gOilt represents the growth rate of nominaloil prices. Column (2) is the baseline model. Column (3) refers to a specification that there is no oil inhouseholds’ utility function. Column (4) refers to a specification that there is no oil input in firms’ produc-tion function. Column (5) is the baseline model without the productivity shock in the oil sector, i.e., εo = 0.Column (6) is the baseline model without the productivity shock in the core sector, i.e., εc = 0 and εxc = 0.(1) (2) (3) (4) (5) (6)Data Baseline ξ = 0 1−α−ω = 0 εo = 0 εc = εxc = 0Relative oil pricesE(∆log(POt /PCt )) 0.45% 0.02% 0.00% 0.00% 0.00% 0.00%σ(∆log(POt /PCt )) 18.48% 13.26% 14.37% 34.06% 1.20% 12.83%AC(∆log(POt /PCt )) 0.008 -0.219 -0.268 -0.171 0.395 -0.209InflationE(piCt ) 0.64% 0.62% 0.21% 0.71% 0.64% 0.90%σ(piCt ) 0.29% 0.60% 0.55% 0.79% 0.46% 0.44%AC(piCt ) 0.717 0.619 0.661 0.931 0.965 0.585E(piCPIt ) 0.66% 0.62% 0.21% 0.71% 0.64% 0.90%σ(piCPIt ) 0.62% 0.67% 0.55% 0.85% 0.46% 0.52%AC(piCPIt ) 0.046 0.447 0.661 0.768 0.972 0.3515Y nominal yieldsE(y20) 1.17% 0.94% 0.45% 1.27% 0.96% 1.20%σ(y20) 1.16% 0.25% 0.23% 0.47% 0.31% 0.04%AC(y20) 0.951 0.887 0.961 0.954 0.976 0.428Yield spread: 5Y − 1QE(y20− y1) 0.31% 0.18% 0.14% 0.45% 0.18% 0.00%5Y inflation risk premiumIRP(y20) 0.28% 0.24% 0.59% 0.29% 0.00%CorrelationsCorr(∆y20t ,gOilt ) 0.408 0.473 0.622 0.126 -0.199 0.988Corr(∆y40t ,gOilt ) 0.397 0.386 0.514 0.109 -0.058 0.989Corr(∆r40t ,gOilt ) 0.218 0.706 0.648 0.671 0.109 0.981Corr(∆be40t ,gOilt ) 0.389 0.133 0.233 -0.023 -0.068 0.99764Table 3.7: Variance decompositions for the baseline modelThis table reports the unconditional variance decompositions for the baseline model for the three productiv-ity shocks εo, εc, and εxc. Variance decompositions are in percentage terms. The parameters values of thebaseline model are given in Table 3.4. y20 and y1 refer to 5-year and 1-quarter nominal yields, respectively.s20 and s1 refer to 5-year and 1-quarter breakeven inflation, respectively.εo εc εxcReal oil prices and inflationlog(POt /PCt ) 90.76 5.78 3.47piCPIt 54.15 5.73 40.12piCt 44.78 7.27 47.951Q and 5Y nominal yieldsy1 63.81 3.66 32.53y20 1.76 6.36 91.891Q and 5Y real yieldsr1 88.73 3.19 8.08r20 20.66 3.6 75.741Q and 5Y breakeven inflations1 11.52 8.36 80.13s20 0.22 5.35 94.431Q and 5Y inflation risk premiumIRP1 0.02 7.08 92.9IRP20 0.05 30.96 68.9965Table 3.8: Decomposition of the one-period inflation risk premiumThis table presents the market price of risk of three productivity shocks, the beta of CPI inflation, and theinflation risk premium for the base calibration. The prices of risk and the inflation risk premia are reportedat a quarterly frequency.Price of riskλ o 0.11%λ c 0.23%λ xc 0.04%Inflation betaβ o -0.05β c -0.07β xc -0.20Inflation risk premiumIRPo 0.6 bpsIRPc 1.7 bpsIRPxc 0.9 bps66-40.00%-30.00%-20.00%-10.00%0.00%10.00%20.00%30.00%-5-4-3-2-101234200407200410200501200504200507200510200601200604200607200610200701200704200707200710200801200804200807200810200901200904200907200910201001201004201007201010201101201104201107201110201201201204201207201210201301201304201307201310201401201404201407201410Log growth of crude oil spot prices Inflation swap rate (Annual %)Date1-year inflation swap rate2-year inflation swap rate5-year inflation swap rate10-year inflation swap rateLog growth of crude oil spot pricesFigure 3.1: Inflation swap rates and crude oil spot price growth.The figure plots the monthly U.S. zero-coupon inflation swap rates of 1-, 2-, 5-, 10-year maturities and the growth rate of crude oil prices from July2004 to December 2014. Inflation swap rates are expressed as annual percentage. Data on inflation swap rates are from Bloomberg. Crude oil spotprices are the U.S. refiners’ acquisition costs of crude oil from U.S. Energy Information Administration (EIA).6701234567800.020.040.060.080.10.120.140.160.18200408200411200502200505200508200511200602200605200608200611200702200705200708200711200802200805200808200811200902200905200908200911201002201005201008201011201102201105201108201111201202201205201208201211201302201305201308201311201402201405201408201411201502Std. of  the log  growth of the nearest oil futures prices (%)Std. of the 10-year inflation swap rate changes (%)DateStd. of the 10-year inflation swap rate changesStd. of the log growth of the nearest oil futures pricesFigure 3.2: Standard deviations of changes in 10-year inflation swaps and growth rates of the nearest-to-maturity oil futures.The standard deviations of changes in 10-year inflation swap rate changes and growth rates of the nearest-to-maturity NYMEX crude oil futures pricesare estimated based on daily observations within each month. Daily inflation swap rates are from Bloomberg. The NYMEX crude oil futures prices ofthe nearest contract are from the U.S. Energy Information Administration (EIA).680 10 20−3−2−10Consumption: core goods0 10 20−6−4−20Consumption: oil0 10 20−1.5−1−0.500.5Labor0 10 20051015Real oil prices0 10 2000.10.20.30.4Inflation: core0 10 2000.20.40.60.8Inflation: CPIFigure 3.3: Impulse response functions to a negative εot shock.This figure plots impulse response functions of core goods, households’ consumption of oil, labor supply, real oil prices (POt /PCt ), core inflation, andCPI inflation. The y-axis shows the percentage deviation. The size of εot shock is one standard deviation σo = 9.5%.690 20 4000.511.5Consumption: core goods0 20 4000.511.5Consumption: oil0 20 4000.511.5Labor0 20 4000.511.5Real oil prices0 20 40−0.15−0.1−0.0500.05Inflation: core0 20 40−0.1−0.0500.050.1Inflation: CPIFigure 3.4: Impulse response functions to a positive εct shock.This figure plots impulse response functions of core goods, households’ consumption of oil, labor supply, real oil prices (POt /PCt ), core inflation, andCPI inflation. The y-axis shows the percentage deviation. The size of the εct shock is one standard deviation σc = 1.2%.700 20 40−1012Consumption: core goods0 20 40−1012Consumption: oil0 20 4000.511.5Labor0 20 40−0.500.51Real oil prices0 20 40−0.1−0.08−0.06−0.04−0.020Inflation: core0 20 40−0.1−0.08−0.06−0.04−0.020Inflation: CPIFigure 3.5: Impulse response functions to a positive εxct shock.This figure plots impulse response functions of core goods, households’ consumption of oil, labor supply, real oil prices (POt /PCt ), core inflation, andCPI inflation. The y-axis shows the percentage deviation. The size of the εxct shock is one standard deviation σxc = 0.17%.710 5 10 15 20 25 30 35 4000.10.20.30.4Real yields: 1 quarter  Negative oil−sector prod. shockPositive core−sector transitory prod. shockPositive core−sector permanent prod. shock0 5 10 15 20 25 30 35 4000.010.020.03Real yields: 5 years  Negative oil−sector prod. shockPositive core−sector transitory prod. shockPositive core−sector permanent prod. shockFigure 3.6: Impulse response functions of 1-quarter and 5-year real yields to three productivity shocks. The size of each shock is one standarddeviation: σo = 9.5%, σc = 1.2%, and σxc = 0.17%.720 5 10 15 20 25 30 35 40−0.100.10.20.3Breakeven inflation: 1 quarter  Negative oil−sector prod. shockPositive core−sector transitory prod. shockPositive core−sector permanent prod. shock0 5 10 15 20 25 30 35 40−0.1−0.0500.050.1Breakeven inflation: 5 years  Negative oil−sector prod. shockPositive core−sector transitory prod. shockPositive core−sector permanent prod. shockFigure 3.7: Impulse response functions of 1-quarter and 5-year breakeven inflation rates to three productivity shocks. The size of each shock isone standard deviation: σo = 9.5%, σc = 1.2%, and σxc = 0.17%.730 5 10 15 20 25 30 35 40−0.200.20.40.6Nominal yields: 1 quarter  Negative oil−sector prod. shockPositive core−sector transitory prod. shockPositive core−sector permanent prod. shock0 5 10 15 20 25 30 35 40−0.1−0.0500.050.1Nominal yields: 5 years  Negative oil−sector prod. shockPositive core−sector transitory prod. shockPositive core−sector permanent prod. shockFigure 3.8: Impulse response functions of 1-quarter and 5-year nominal yields to three productivity shocks. The size of each shock is one standarddeviation: σo = 9.5%, σc = 1.2%, and σxc = 0.17%.74-80-60-40-20020406080100Basis	PointsQuarter10-Year	Inflation	Risk	PremiumLiq.	Adj.	Breakeven	 Infl.	- SPF	CPI	(Median) Swap	Rate	- SPF	CPI	(Median)Figure 3.9: Inflation risk premia.The solid line represents the inflation risk premia estimated from the difference between the liquidity-adjusted 10-year breakeven inflation and themedian of the forecasts for the Survey of Professional Forecast 10-year CPI from 1999Q2 to 2014Q4. The dashed line represents the inflation riskpremia estimated from the difference between the 10-year inflation swap rate and the median of the forecasts for the Survey of Professional Forecasters10-year CPI from 2004Q3 to 2014Q4. Data on the liquidity-adjusted 10-year breakeven inflation are from Pflueger and Viceira (2015). Data on theSurvey of Professional Forecasters 10-year CPI are from the Federal Reserve Bank of Philadelphia.75Chapter 4ConclusionThis dissertation studies the relationship between oil prices, inflation, and Treasury bond returns bothempirically and theoretically. Chapter 2 documents a puzzling time-varying trend in correlations betweenU.S. core inflation and one-month lagged oil price changes, which is the first time reported in the literature.The chapter then builds a two-sector general equilibrium model to show that oil supply and demands shocksare able to generate either co-movements or opposing movements between core inflation and oil prices. InChapter 3, I provide novel empirical evidence that the price of oil price is a significant explanatory variableand predictor of excess returns on nominal Treasury bonds. Additionally, I present theoretical analysis thatoil prices are relevant determinants for expected inflation and real yields on inflation-indexed bonds.Chapter 2 sheds light on understanding and identifying intrinsic shocks in oil price shocks. Empiricalresults confirm the presence of two structural breaks in correlations between U.S. core inflation and changesin oil prices in the mid-1980s and during the 2007 financial crisis. The resurgence of the correlations afterthe 2007 financial crisis is puzzling, in contrast to the economy’s declining energy intensity. Theoreticalanalysis shows that the relation between the price of oil and inflation risk depends on the type of shocksembedded in oil price changes. The economic mechanisms in the model and historical events togetherprovide a consistent and logical explanation of the time-varying correlations observed in the data.Chapter 3 highlights that the complementarity between oil and core goods consumption and oil inputin production are important economic channels for studying the dynamics of oil prices and bond yields.Overall, the two-sector New Keynesian model is able to replicate several key empirical relationships betweenoil prices and bond yields. The model also generates upward sloping nominal yield curves and sizablepositive inflation risk premia; it is well-known that these two features are very challenging to achieved in76macro-finance models. Empirical results suggest that the impact of oil prices on nominal bonds is throughthe impact on expected inflation. The model shows that oil supply and demand shocks have opposite impactson bond yields and expected inflation. The conventional wisdom that high oil prices lead to high expectedinflation and nominal yields is true only if high oil prices are driven by a negative shock to the supply of oil.In contrast, when oil prices are driven by a positive shock to productivity growth, high oil prices can lead tolow expected inflation and nominal yields.The connection between the oil market and the economy and the financial markets is complex in nature.The oil market is a global market. Oil prices are globally determined, and oil futures and other relatedfinancial products are traded at several international derivatives exchanges. Research on the area is tradi-tionally done in economic literature. Research from the finance perspective is still under-explored overall.My dissertation focuses on the impact of oil price changes on inflation, expected inflation, and Treasurybond returns, at the aggregate level.Chapter 2 has practical implications for central banks and pension fund managers. The sign of corre-lation indicates whether the intrinsic shocks embedded in the price of oil are supply shocks or aggregatedemand shocks. A better understanding of time-varying correlation based on the supply and demand shocksin the oil market can help investors to more effectively hedge inflation, and it can also help central banks tobetter gauge information regarding inflation from oil price shocks.In Chapter 3, empirical tests using data on TIPS and inflation swap rates provide richer information onunderstanding behaviors of components of nominal yields than those using data solely on nominal bonds.In addition, the chapter offers novel predictions and further highlights key economic transmission channelsthrough which oil price shocks affect bond markets. Most importantly, the chapter shows that oil pricesare relevant risk factors for pricing nominal and inflation-indexed Treasury bonds and inflation swaps. Theimplications of the impact of oil price shocks on long-term expected inflation are also useful for monetarypolicy and risk management.For the sake of simplicity, the model in Chapter 3 considers three productivity shocks only, omitting truedemand shocks, such as preference shocks in the representative agent’s utility function. Additional prefer-ence shocks and the time-varying volatility of productivity shocks will be considered in future research.Last, research from the international perspective will be interesting as well. For empirical tests, I useU.S. data on inflation, inflation swaps, and Treasury bonds. My choice is constrained by the availability ofdata on other countries. Nevertheless, using U.S. data is reasonable given that U.S. is the largest consumer77of oil and its financial markets is the largest in the world. 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An inflation swapis a bilateral contractual agreement. Inflation swap rates refer to the zero-coupon fixed rate leg against afloating leg on the CPI appreciation on U.S. Consumer Price Index for Urban Consumers, Not SeasonallyAdjusted (CPUR-NSA) over the maturity.The U.S. inflation swap market is an over-the-counter market andhas developed quickly in recent years. The U.S. Swap Data Repository (SDR) shows that the gross USDnotional volume is $12 to $20 billion per month.1 In practice, because the CPI index is known with a lag,the floating payment is estimated on inflation over the period starting three months before the start date andending three months before the termination date. The data on the inflation swap rates are available startingfrom July 2004 from Bloomberg.The zero-coupon inflation swap fixed rate consists of the expected inflation and the inflation risk pre-mium. Inflation swap rates are quoted as annually compounded rates. Table B.1 presents the summarystatistics of the inflation swap rates and rate spreads. The average inflation swap curve is upward sloping inthe period from July 2004 to December 2014.1Reported by Amir Khwaja from Clarus Financial Technology. The report is available at http://www.clarusft.com/inflation-swaps-what-the-data-shows/.85Table B.1: Summary statistics of the U.S. zero-coupon inflation swap ratesSwap rates are reported as annual percentage. The 1-, 2-, 5-, and 10-year maturities are the most common.The whole sample period is from July 2004 to December 2014.2004.7-2012.12 2004.7-2008.7 2008.8-2014.12Mean Std. Mean Std. Mean Std.1-year 1.71 1.28 2.69 0.42 1.09 1.262-year 1.90 0.96 2.68 0.34 1.40 0.895-year 2.29 0.54 2.74 0.19 2.00 0.4910-year 2.59 0.29 2.81 0.13 2.46 0.2920-year 2.78 0.29 2.98 0.14 2.65 0.2930-year 2.86 0.30 3.10 0.18 2.72 0.2610-year − 1-year 0.88 1.03 0.12 0.37 1.36 1.0386Appendix CLatent factors of inflation swap contractsI use principal components analysis to estimate latent factors that explain variations in inflation swaprates. Similar to the latent factors of nominal bond yields, the first three principal components (PCs) of the1-year, 2-year, 5-year, and 10-year inflation swap rates explain 95.5%, 3.7%, and 0.6% of the variation ofinflation swap rates, respectively. Because inflation swap rates for short maturities are more volatile thanfor long maturities, I first standardize swap rates by dividing the standard deviation of swap rates. I thenuse principal component analysis to estimate latent factors of standardized inflation swap rates. Based oncoefficient patterns of the first three principal components on the underlying swap contracts, as shown inFigure C.1, the first three PCs could be labelled as the level, slope, and curvature factors, respectively. Asthe first two PCs account for 99.2% of the variation, the following tests focus on the level and slope factors.Two tests are conducted to answer whether information contained in oil prices is useful for forecastingbreakeven inflation. First, are oil prices spanned by latent factors of inflation swap rates? It turns out thatthe log growth of crude oil spot prices is mostly not explained by latent factors of inflation swap rates.The adjusted R2 is 32.2% of the contemporaneous regression of oil price growth on the first three PCs (notshown). Second, the more interesting question is whether gOil can forecast latent factors over and abovethe information in inflation swap rates. Table C.1 shows the results of forecasting changes of the level andslope factors, the average of inflation swap rates, and the spread of inflation swap rates between 10-yearand 1-year. Oil price growth can significantly forecast the changes of the level factor, the average, and thespread. Increases in the adjusted R2 also show the incremental forecasting power of oil prices, except forthe slope factor.87Table C.1: Level and slope factors of inflation swap ratesThe change of the level and slope factors, the change of the average of inflation swap rates, and the changeof the spread of inflation swap rates are regressed on the lagged log growth of crude oil prices and thelagged level and slope factors. The level and slope factors are the first and the second principal componentsof 1-, 2-, 5-, and 10-year inflation swap rates from July 2004 to December 2014. ∆PCLevelt+1 and ∆PCSlopet+1denote the monthly change of level and slope factors, respectively. ∆st+1 represents the monthly changeof the average of 1-, 2-, 5-, and 10-year inflation swap rates. ∆Spread10y−1yt+1 is the monthly change of thespread between 10-year and 1-year inflation swap rates. gOilt is the log growth of monthly crude oil prices.The F-test for no predictability is shown. Newey-West standard errors with four lags are in parentheses. **and * denote statistical significance at the 1% and 5% levels.(1) (2) (3) (4)∆PCLevelt+1 ∆PCSlopet+1 ∆st+1 ∆Spread10y−1yt+1gOilt 0.04* -0.00 0.02* -0.02**(0.02) (0.00) (0.01) (0.01)PCLevelt -0.14** 0.03 -0.05** 0.04*(0.04) (0.02) (0.01) (0.02)PCSlopet 0.10 -0.43** -0.04 0.36(0.25) (0.12) (0.11) (0.18)Const. 1.70 -2.83** 0.15 1.83(1.50) (0.76) (0.64) (1.14)Obs. 124 124 124 124Adj. R2(PCs only) 2.7% 20.1% 2.8% 8.3%Adj. R2(PCs+gOil) 11.4% 19.2% 11.8% 13.3%F-ratio 4.95** 8.30** 5.11** 5.73**881 2 3 4 5 6 7 8 9 10−0.8−0.6−0.4−0.200.20.40.60.8TenorInflation swap rate factors  LevelSlopeCurvatureFigure C.1: Loadings of the first three principal components of the inflation swap rates.This figure plots the loadings of the first three principal components of the inflation swap rates of 1-, 2-,5-, and 10-year maturities.89Appendix DEquilibrium conditions of the two-sectorNew Keynesian modelD.1 HouseholdsThe Lagrangian of the household’s problem isL HH =V0+∞∑t=0µt{(1−β )U1−ρt +β(EtV1−γ1−ρt+1) 1−ρ1−γ−Vt}+∞∑t=0λt{Rt−1Bt−1+WtNt +DCt +DOt − (1−ξ )CtPCt −ξOHt POt −Bt}.(D.1)First order conditions with respect to choice variables Ct , OHt , Nt , and Bt give rise to the following equationsφκtNνtX1/η−ρt C−1/ηt=WtPCt(D.2)(OHtCt)−1/η=POtPCt(D.3)1 = Etβ(Xt+1Xt) 1η−ρ(Ct+1Ct)− 1η  V 1−ρt+1(EtV(1−γ)/(1−ρ)t+1)1/(1−γ)ρ−γPCtPCt+1Rt (D.4)Equation (D.2) represents the intratemporal relationship between consumption of core goods and labor90supply. Equation (D.3) describes the intratemporal substitution between oil and consumption of core goods.Equation (D.4) is the Euler equation for consumption of core goods.The nominal stochastic discount factor (SDF) M$t,t+1 is defined asM$t,t+1 ≡ β(Xt+1Xt) 1η−ρ(Ct+1Ct)− 1η  V 1−ρt+1(EtV(1−γ)/(1−ρ)t+1)1/(1−γ)ρ−γPCtPCt+1. (D.5)The real stochastic discount factor (SDF) MR,Ct,t+1, in the unit of core goods, could be defined asMR,Ct,t+1 = M$t,t+1PCt+1PCt. (D.6)Alternatively, the real SDF can also be expressed in the unit of the consumption bundleMR,Xt,t+1 ≡M$t,t+1PXt+1PXt. (D.7)D.2 The oil firmThe Lagrangian of the oil firm’s problem isL O = Et∞∑j=0M$t,t+ j{ZOt+ jKOt+ j−1POt+ j− IOt+ jPCt+ j +qot+ j[(1−δ o)KOt+ j−1+ϒO(IOt+ j,KOt+ j−1)−KOt+ j]}(D.8)where the Lagrangian multiplier qot is the shadow value of the capital (i.e., the Tobin’s q).The first order condition with respect to IOt isPCt = qot ΦOI (IOt ,KOt−1)KOt−1 (D.9)where ΦOI is the partial derivative of ΦO with respect to IOt .The first order condition with respect to KOt isqot = EtM$t,t+1{FOK (ZOt+1,KOt )POt+1+qot+1[(1−δ o)+ΦOK(IOt+1,KOt )KOt +ΦO(IOt+1,KOt )]}(D.10)where FOK (ZOt+1,Kt)≡ ZOt+1 and ΦOK is the partial derivative of ΦO with respect to KOt .91D.3 The final goods firmThe first order condition of the final firm’s problem is given in equation (3.16).D.4 Intermediate goods firmsThe Lagrangian of the intermediate goods firm’s problem isL C = Et∞∑j=0M$t,t+ j{[PCt+ j(i)YCt+ j(i)−Ψt+ j(YCt+ j(i))−PCt+ jϑ2(PCt+ j(i)piPCt+ j−1(i)−1)2YCt+ j−PCt+ jICt+ j(i)]+qct+ j[(1−δ c)KCt+ j−1+ϒC(ICt+ j,KCt+ j−1)−KCt+ j]}(D.11)where the Lagrangian multiplier qct is the shadow value of the capital (i.e., the Tobin’s q).The first order condition with respect to ICt isPCt = qctΦCI (ICt (i),KCt−1(i))KCt−1(i) (D.12)where ΦCI is the partial derivative of ΦC with respect to ICt .The first order condition with respect to KCt isqct = EtM$t,t+1{FCK (ZCt+1,KCt (i))PCt+1(i)+qct+1[(1−δ c)+ΦCK(ICt+1(i),KCt (i))KCt (i)+ΦC(ICt+1(i),KCt (i))]}(D.13)where FCK (ZCt+1,KCt (i)) is the marginal productivity of capital and ΦCK is the partial derivative of ΦC withrespect to KCt .The first order condition with respect to PCt (i) isPCt YCt[(1− ε)(PCt (i)PCt)−ε 1PCt+ψtε(PCt (i)PCt)−ε−1 1(PCt )2−ϑ(PCt (i)piPCt−1(i)−1)1piPCt−1(i)]+M$t,t+1PCt+1YCt+1ϑ(PCt+1(i)piPCt (i)−1)PCt+1(i)pi(PCt (i))2= 0(D.14)where ψt is the marginal cost defined in equation (D.18).In a symmetric equilibrium, equation (D.14) is rewritten asϑ(piCtpi−1)piCtpi= (1− ε)+ εψˆt +ϑEt{MR,Ct,t+1(piCt+1pi−1)piCt+1piYCt+1YCt}(D.15)92where ψˆt ≡ ψt/PCt is the real marginal cost and Mt,t+1 is the real SDF defined in equation (D.6).The first order condition of the cost minimization problem for a given level of output YCt (i) isαOIt (i)(1−α−ω)Nt(i) =WtPOt(D.16)Minimized cost function for a given level of output YCt (i) isΨ(YCt (i)) = (1−ω)α−α1−ω (1−α−ω)− 1−α−ω1−ω (ZCt )−α1−ω (KCt−1(i))− ω1−ω (Wt)α1−ω (POt )1−α−ω1−ω (YCt (i))11−ω .(D.17)Marginal cost function for a given level of output YCt (i) isψ(YCt (i))≡Ψ ′(YCt (i)) = α−α1−ω (1−α−ω)− 1−α−ω1−ω (ZCt )−α1−ω (KCt−1(i))− ω1−ω (Wt)α1−ω (POt )1−α−ω1−ω (YCt (i))ω1−ω .(D.18)D.5 Market clearing conditionsIn equilibrium, all markets are clear. The aggregate oil resource constraint isOHt +OIt = YOt . (D.19)In the symmetric equilibrium, the aggregate resource constraint of final consumption goods becomesCt + IOt + ICt =(1− ϑ2(piCtpi−1)2)YCt . (D.20)where piCt = PCt /PCt−1.93

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