Essays on Applied Macro and Micro Econometrics

Transcription

1 UNIVERSITY OF CALGARY Essays on Applied Macro and Micro Econometrics by Ali Jadidzadeh A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ECONOMICS CALGARY, ALBERTA December, 2015 Ali Jadidzadeh 2015

2 Abstract This thesis consists of three essays on applied macro and micro econometrics. The first essay examines the interactions and co-movements between the crude oil and natural gas markets with multivariate time series analysis. The second essay investigates interfuel substitution and the demand for a limited number of energy goods with proper microeconomic foundations. The last essay augments the approach used in the second essay for a large number of goods and services in the market for money. An abstract of each essay follows. In essay 1, I employ a structural Vector AutoRegressive model to disentangle demand and supply shocks in the global crude oil market and investigate their effects on the real price of natural gas in the United States. I identify the model by assuming that innovations to the real price of crude oil are predetermined with respect to the natural gas market and show that close to 45% of the variation in the real price of natural gas can be attributed to structural supply and demand shocks in the global crude oil market. Essay 2 focuses on the aggregate demand for electricity, natural gas, and light fuel oil in Canada as a whole and six of its provinces in the residential, commercial, and industrial sectors. I employ the locally flexible normalized quadratic (NQ) expenditure and cost functions and provide evidence consistent with neoclassical microeconomic theory. My results indicate limited substitutability between electricity and natural gas, but strong substitutability between light fuel oil and each of electricity and natural gas in most cases. Essay 3 uses a highly-disaggregated demand system to estimate the degree of substitutability among monetary assets and to address the issue of optimal monetary aggregation in the United States. I address the problems of dimensionality and nonlinearity, estimating a very detailed monetary asset demand system encompassing the full range of assets based on the NQ expenditure function. I believe that our estimates of disaggregated monetary demand responses are of importance in resolving paradoxes associated with the measureii

3 ment of money, in solving the Barnett critique, and in understanding the effects of potential monetary policy actions.

4 Acknowledgments Foremost, I would like to express my sincere gratitude to Professor Apostolos Serletis for his supervision and mentorship of my academic development. I am very grateful for the countless hours he has spent supporting my PhD study and research. With his patience, motivation, and immense knowledge, he has helped to shape my academic future. I would also like to thank the rest of my thesis committee Professor Herbert Emery and Professor David Walls for their insightful comments and encouragement, but also for their questions which incented me to widen my research from various perspectives. My sincere thanks also goes to all of the professors at the Department of Economics whose thoughtful comments and suggestions guided my studies and research along the way. I am grateful to my colleagues who always provided me with advice and encouragement. Finally, I would like to thank my parents and my wife for supporting me spiritually throughout my life and academic career. iv

5 This thesis is dedicated to my parents and my wife for their love, endless support and encouragement

6 Table of Contents Abstract ii Acknowledgments iv Table of Contents vi List of Tables viii List of Figures x Overview xi 1 HOW DOES THE U.S. NATURAL GAS MARKET REACT TO DEMAND AND SUPPLY SHOCKS IN THE CRUDE OIL MARKET? Introduction Data The Structural VAR Model Structural VAR Estimates Conclusion SECTORAL INTERFUEL SUBSTITUTION IN CANADA: AN APPLICA- TION OF NQ FLEXIBLE FUNCTIONAL FORMS Introduction The Structure of Production and Preferences Normalized Quadratic Functional Forms The NQ Expenditure Function The NQ Cost Function Econometric Considerations Data Empirical Evidence Residential Sector Commercial Sector Industrial Sector Comparison with Other Studies Conclusion THE DEMAND FOR LIQUID ASSETS AND OPTIMAL MONETARY AG- GREGATION: EVIDENCE FROM A DISAGGREGATED DEMAND SYS- TEM BASED ON THE NQ EXPENDITURE FUNCTION Introduction The Structure of Preferences The Expenditure Function Approach The NQ Expenditure Function Econometric Considerations The Data Empirical Evidence Separability and Demand Analysis The Optimal Level of Monetary Aggregation Conclusion Bibliography vi

7 A Tables B Figures vii

8 List of Tables 1.1 Percent Contribution of Supply and Demand Shocks in the Crude Oil Market to the Overall Variability of the Real Crude Oil Price Percent Contribution of Supply and Demand Shocks in the Crude Oil Market to the Overall Variability of the Real Natural Gas Price Residential Sector Allen Own-Price Elasticities and Morishima Elasticities of Substitution Commercial Sector Allen Own-Price Elasticities and Morishima Elasticities of Substitution Industrial Sector Allen Own-Price Elasticities and Morishima Elasticities of Substitution A summary of Flexible Functional Forms Interfuel Substitution Studies A Summary of Flexible Functional Forms Estimation of Liquid Asset Demands The Components of Monetary Aggregates NQ Parameter Estimates Expenditure and Own- and Cross-Price Elasticities Allen Elasticities of Substitution Morishima Elasticities of Substitution A.1 NQ Parameter Estimates for the Residential Sector in Canada A.2 NQ Parameter Estimates for the Residential Sector in Quebec A.3 NQ Parameter Estimates for the Residential Sector in Ontario A.4 NQ Parameter Estimates for the Residential Sector in Manitoba A.5 NQ Parameter Estimates for the Residential Sector in Saskatchewan A.6 NQ Parameter Estimates for the Residential Sector in Alberta A.7 NQ Parameter Estimates for the Residential Sector in British Columbia A.8 NQ Parameter Estimates for the Commercial Sector in Canada A.9 NQ Parameter Estimates for the Commercial Sector in Quebec A.10 NQ Parameter Estimates for the Commercial Sector in Ontario A.11 NQ Parameter Estimates for the Commercial Sector in Manitoba A.12 NQ Parameter Estimates for the Commercial Sector in Saskatchewan A.13 NQ Parameter Estimates for the Commercial Sector in Alberta A.14 NQ Parameter Estimates for the Commercial Sector in British Columbia.. 95 A.15 NQ Parameter Estimates for the Industrial Sector in Canada A.16 NQ Parameter Estimates for the Industrial Sector in Quebec A.17 NQ Parameter Estimates for the Industrial Sector in Ontario A.18 NQ Parameter Estimates for the Industrial Sector in Manitoba A.19 NQ Parameter Estimates for the Industrial Sector in Saskatchewan A.20 NQ Parameter Estimates for the Industrial Sector in Alberta A.21 NQ Parameter Estimates for the Industrial Sector in British Columbia A.22 Own- and Cross-Price Elasticities: The Residential Sectors A.23 Allen Elasticities of Substitution: The Residential Sectors viii

9 A.24 Own- and Cross-Price Elasticities: The Commercial Sectors A.25 Allen Elasticities of Substitution: The Commercial Sectors A.26 Own- and Cross-Price Elasticities: The Industrial Sectors A.27 Allen Elasticities of Substitution: The Industrial Sectors ix

10 List of Figures and Illustrations 1.1 Crude Oil and Natural Gas Prices, 1976:1 2012: Historical Evolution of the Series, 1976:1 2012: Responses of the Real Price of Crude Oil (Upper Panel) and the Real Price of Natural Gas (Lower Panel) to One-Standard Deviation Structural Shocks: Point Estimates with One- and Two-Standard Error Bands Cumulative Responses of the Real Price of Crude Oil (Upper Panel) and the Real Price of Natural Gas (Lower Panel) to One-Standard Deviation Structural Shocks: Point Estimates with One- and Two-Standard Error Bands Historical Decomposition of the Real Price of Crude Oil Historical Decomposition of the Real Price of Natural Gas Per Capita Electricity Consumption: Residential Sectors Per Capita Natural Gas Consumption: Residential Sectors Per Capita Light Fuel Oil Consumption: Residential Sectors Average Electricity Prices: Residential Sectors Average Natural Gas Prices: Residential Sectors Average Light Fuel Oil Prices: Residential Sectors The Weakly Separable Relation u (x) = u ( x 1, u 1 (x 2, x 3, x 4, x 5 ) ) The Weakly Separable Relation u (x) = u [ x 1, u 1 ( x 2, x 3, f(x 4, x 5 ) )] The Weakly Separable Relation u (x) = u [ x 1, u 1 ( f 1 (x 2, x 3 ), f 2 (x 4, x 5 ) )].. 73 B.1 Aggregate Electricity Consumption: Commercial Sectors B.2 Aggregate Natural Gas Consumption: Commercial Sectors B.3 Aggregate Light Fuel Oil Consumption: Commercial Sectors B.4 Average Electricity Prices: Commercial Sectors B.5 Average Natrual Gas Prices: Commercial Sectors B.6 Average Light Fuel Oil Prices: Commercial Sectors B.7 Aggregate Electricity Consumption: Industrial Sectors B.8 Aggregate Natural Gas Consumption: Industrial Sectors B.9 Aggregate Light Fuel Oil Consumption: Industrial Sectors B.10 Average Electricity Prices: Industrial Sectors B.11 Average Natural Gas Prices: Industrial Sectors B.12 Average Light Fuel Oil Prices: Industrial Sectors x

11 Overview This thesis applies different macro and micro econometric approaches to investigate the interaction and relationship between goods in different markets. With regards to the macro econometric approach, I employ a multivariate time series method, structural Vector AutoRegressive (VAR), to examine the interaction between the crude oil and natural gas prices in the first chapter. Chapters 2 and 3 use recent state-of-the art advances in micro econometrics to address the relationship between energy goods and monetary assets, respectively. In particular, I use the normalized quadratic (NQ) functional forms with proper microeconomic foundations to estimate the demand and elasticities for energy goods and monetary assets. The first chapter undertakes a macro econometrics approach to answer two questions: Do natural gas prices in the United States react to crude oil price shocks? and does the response of natural gas prices depend on the source of the shock in the crude oil market? In order to answer these questions, I follow Kilian (2009) and treat the price of crude oil as endogenous and disentangle the causes underlying oil price shocks in a structural VAR frame work. In particular, I model changes in the real price of crude oil as arising from three different sources; shocks to the global supply of crude oil, shocks to the global demand for all industrial commodities (including crude oil) that are driven by the global business cycle, and oil-market specific demand shocks (also referred to as precautionary demand shocks). I augment Kilian s (2009) structural VAR model to include the real price of natural gas, and to investigate the response of the real price of natural gas to structural shocks in the crude oil market. I identify the model by assuming that innovations to the real price of crude oil are predetermined with respect to the natural gas market. I show that the response of the real price of natural gas may differ greatly depending on the underlying cause of the oil price shock. Further, I demonstrate that close to 45% of the variation in the real price of natural gas can be attributed to structural supply and aggregate demand shocks in the global crude xi

12 oil market. I additionally show that shocks in the natural gas market account for about 55% of the long run variability of the real price of natural gas, thus causing episodic decoupling of the real price of natural gas from the real price of crude oil. In the second chapter, I investigate the interfuel substitution and the demand for for electricity, natural gas, and light fuel oil in Canada as a whole and six of its provinces Quebec, Ontario, Manitoba, Saskatchewan, Alberta, and British Columbia in the residential, commercial, and industrial sectors. My objective is to provide updated empirical work using methodological improvements of the past twenty years, and to improve the understanding of how changing energy prices and incomes will influence interfuel substitution and the demand for energy in the future. In order to achieve this, I use duality theory and the demand systems approach based on neoclassical consumer and firm theories which allow me to estimate the demand for electricity, natural gas, and light fuel oil in a systems framework. I use a locally flexible demand system derived from the expenditure/cost function of the representative consumer/firm. Moreover, motivated by the widespread practice of ignoring the theoretical regularity conditions of neoclassical microeconomic theory, I approximate the unknown underlying expenditure function using a flexible functional form that allows the imposition of global curvature without losing its flexibility property. In particular, in the case of the commercial and industrial sectors I use the normalized quadratic (NQ) cost function, introduced by Diewert and Wales (1987), and in the case of the residential sector energy demand I use the NQ expenditure function, introduced by Diewert and Wales (1988). I find that the Morishima interfuel elasticities of substitution are in general positive and statistically significant. The results indicate limited substitutability between electricity and natural gas, but strong substitutability between light fuel oil and each of electricity and natural gas in most cases. Chapter 3 addresses the limitation of the existing literature, which has generally been carried out in the context of highly-aggregated demand systems. Aggregation tends to dra-

13 matically reduce the number of goods. Thus, the existing empirical evidence based on small, highly-aggregated demand systems is unrepresentative of the substitutability/complementarity and separability relationships among different goods of related markets. In this regard, I model the demand for all 15 monetary assets in the United States based on the locally flexible normalized quadratic (NQ) expenditure function. I treat the concavity property as a maintained hypothesis and provide evidence consistent with neoclassical microeconomic theory, as suggested by Barnett (2002). I believe that my estimates of disaggregated monetary demand responses are of importance in resolving paradoxes associated with the measurement of money, in solving the Barnett critique, and in understanding the effects of potential monetary policy actions. I provide evidence against what Barnett (1982, 2015) refers to as the Linearity Condition, consistent with much of the earlier literature that was based on small, highly aggregated (and thus restricted) demand systems. It means that the simple-sum monetary aggregates used by the Federal Reserve (and other central banks around the world) are inconsistent with neoclassical microeconomic theory, and therefore should be abandoned. In chapter 3, I also address the issue of optimal monetary aggregation by (assuming that money has positive value in equilibrium, implying the existence of a monetary services aggregator function) using disaggregated monetary demand responses to determine empirically monetary asset groupings consistent with the optimizing behavior of economic agents. In doing so, I test for the appropriateness of the aggregation assumptions that underlie the various monetary aggregates published by the Federal Reserve. I reject the necessary and sufficient conditions for all the money measures published by the Federal Reserve. I conclude that I have nothing to lose by using the highest level aggregate among those that are in the admissible hierarchy, as Barnett (2015, p. 32) puts it. Thus, the Centre for Financial Stability Divisia M4 monetary aggregate is the broadest and most theoretically consistent measure of money in the United States today. xiii

14 Chapter 1 HOW DOES THE U.S. NATURAL GAS MARKET REACT TO DEMAND AND SUPPLY SHOCKS IN THE CRUDE OIL MARKET? 1.1 Introduction I answer two questions in this chapter. Do natural gas prices in the United States react to crude oil price shocks? Does the response depend on the source of the shock in the crude oil market? Economic theory suggests that crude oil prices and natural gas prices are linked through both demand and supply. With regards to demand, crude oil is not consumed directly but is used as a factor of production in the refining industry in the production of gasoline, diesel, heating oil, and jet fuel. There are interactions between the crude oil market and the natural gas market because natural gas competes with heating oil in the residential and commercial heating markets and is also used interchangeably with residual and distillate fuels in the industrial and electricity generation sectors. With regards to supply, the relationship between the crude oil and natural gas markets is more complicated, because natural gas is found in two basic forms associated natural gas and non-associated natural gas. The former is a coproduct of crude as it occurs in crude oil reservoirs whereas the latter is not in contact with crude oil. Although associated natural gas accounts for a small fraction of natural gas production in the United States, the liquefaction of natural gas and its delivery from remote producing areas to large consuming areas suggests that crude oil and natural gas prices are related. For example, as can be seen in Figure 1.1, crude oil and natural gas prices in the United States (from the US Department of Energy) in general move together over time, but they decouple episodically in response to deregulation, technological 1

15 Price of crude oil ($/barrel) Oil price Natural gas price Price of natural gas ($/barrel) Figure 1.1: Crude Oil and Natural Gas Prices, 1976:1 2012:12 change, and major policy changes. Over the years, a large number of studies have sought to investigate whether the price of crude oil is an important determinant of the natural gas price. See, for example, Serletis and Herbert (1999), Pindyck (2003), Panagioditis and Rutledge (2004), and Brown and Yücel (2008), among others. This literature employs time series models, specifically cointegration models and tests, to examine the long run equilibrium relationship between crude oil and natural gas prices. Among those, some studies such as Yücel and Guo (1994), Pindyck (2003), Brown and Yücel (2008), and Asche et al. (2006) show that the relationship between the oil price and the natural gas price is stable and asymmetric in a way that the oil price predominantly drives the natural gas price, but not the other way around. In contrast, other studies find that there is no relationship, or a very weak relationship between the two prices. For example Serletis and Rangel-Ruiz (2004) suggest that because of oil and gas deregulation in the United States, West Texas Intermediate (WTI) crude oil prices and Henry Hub natural gas prices do not have shared stochastic trends. Similarly, Bachmeier and Griffin (2006) conclude that, in the very long run, there is no relationship between the 2

16 prices of primary energy goods, including crude oil and natural gas. In this chapter I build on Kilian (2009) and Kilian and Park (2009) and estimate the global crude oil market model of Kilian (2009), augmented with the real price of natural gas, in order to investigate the relationship between crude oil and natural gas prices. In doing so, I depart from the earlier literature that mostly treats the price of oil as exogenous and does not identify the causes underlying oil price shocks. I follow Kilian (2009) and Kilian and Park (2009) and treat the price of crude oil as endogenous and disentangle the causes underlying oil price shocks. In particular, I model changes in the real price of crude oil as arising from three different sources: shocks to the global supply of crude oil, shocks to the global demand for all industrial commodities (including crude oil) that are driven by the global business cycle, and oil-market specific demand shocks (also referred to as precautionary demand shocks). I augment Kilian s (2009) structural Vector AutoRegressive (VAR) model to include the real price of natural gas, and investigate the response of the real price of natural gas to structural shocks in the crude oil market. I show (using monthly data over the period from 1976:1 to 2012:12) that in the long run, an average of 45% of the variability of the real natural gas price in the United States can be attributed to structural shocks that drive the global crude oil market, suggesting that crude oil market fundamentals are an important determinant of natural gas prices. In particular, I show that oil supply shocks, shocks to the global demand for all industrial commodities that are driven by the global business cycle, and oil-market specific demand shocks (also referred to as precautionary demand shocks) have made big contributions to the real price of natural gas in the United States, as they account for about 45% of the long run variability of the real price of natural gas. I show that the responses of the real price of natural gas vary depending on the cause of the oil price shock, with aggregate demand shocks and precautionary demand shock accounting for most of the variation. I also show that shocks in the natural gas market (such as supply disruptions, deregulation, and major policy changes) account for about 55% 3

17 of the long run variability of the real price of natural gas, thus causing episodic decoupling of the real price of natural gas from the real price of crude oil. This chapter is organized as follows. Section 1.2 discusses the data and provides some graphical representations. Sections 1.3 and 1.4 describe the empirical method and present the results. The final section concludes the chapter. 1.2 Data I consider a structural VAR model based on monthly time series data for the United States, over the period from 1976:1 to 2012:12 (a total of 444 observations), for z t = ( prod t, rea t, rpo t, rpg t ), where prod t is the percent change in global crude oil production, rea t is a measure of real economic activity, rpo t is the real price of oil, and rpg t is the real price of natural gas. Regarding the percent change in global crude oil production, prod t, I use the oil production data from the U.S. Department of Energy to compute the log differences of world crude oil production in millions of barrels pumped per day (and averaged by month). I use Kilian s (2009) detrended real freight rate index to measure the component of real economic activity (rea t ) that drives demand for industrial commodities in global markets. As noted by Kilian (2009), this index is constructed from dry cargo single voyage ocean freight rates and is deflated by the U.S. Consumer Price Index (CPI) to express it in real terms. The real freight rate index is linearly detrended to remove long-term trends and thus represent the global business cycle. See Kilian (2009) for more details regarding the construction of this measure of global real economic activity. Finally, I divide the U.S. composite refiners acquisition cost of crude oil (RAC), as compiled by the U.S. Department of Energy, by the U.S. CPI to obtain the real price of crude oil, rpo t, and I divide the U.S. natural gas wellhead price, as compiled by the U.S. Department of Energy, by the U.S. CPI to obtain the real price of natural gas, rpg t. 4

18 The fact that global oil production enters the VAR model in percent changes, prod t, and the measure of real economic activity, rea t, is expressed as percent deviations from trend, suggests that I should be using the first differences of the natural logs of the real crude oil and natural gas prices in order to have consistent variables in the VAR system of equations. I note that the logged real crude oil and natural gas prices are not very informative regarding their unit root properties, although they should be stationary if each of the nominal crude oil and natural gas price cointegrates with the U.S. consumer price index. In this regard, as Lütkepohl and Netšunajev (2014) point out, overdifferencing may be more harmful than including a unit root series in levels, and to be on the safe side, I follow Kilian (2009), Kilian and Park (2009), and Lütkepohl and Netšunajev (2014) and use the log levels of the real crude oil and natural gas prices. Figure 1.2 shows the historical evolution of the series (the percent change in global crude oil production, prod t, real economic activity, rea t, log real oil price, rpo t, and log real natural gas price, rpg t ) over the sample period. 1.3 The Structural VAR Model The structural VAR representation based on Kilian (2009) and Kilian and Park (2009) and is Bz t = γ + p Γ i z t i + ε t (1.1) i=1 where γ is a parameter vector, B and Γ i denote the contemporaneous and lagged coefficient matrices, respectively, and ε t is a vector of serially and mutually uncorrelated structural ( ). innovations, ε t =, ε rea, ε rpo, ε rpg ε prod t t t t Assuming that B 1 exists, the reduced-form representation of equation (1.1) is p z t = α + A i z t i + e t (1.2) i=1 where α = B 1 γ, A i = B 1 Γ i, and the reduced form innovations, e t, are linear combinations of the structural shocks, ε t, e t = B 1 ε t. I estimate the reduced-form (1.2) and recover the 5

19 Percent change in global crude oil production ( Prod) Log detrended index of real economic activity (rea) Log of real price of crude oil (rpo) Log of real U.S. price of natural gas (rpg) Figure 1.2: Historical Evolution of the Series, 1976:1 2012:12 structural shocks, ε t, by imposing zero (exclusion) restrictions on the elements of B. Then I use the structural moving average representation of the model to infer the impulse responses. Since the natural gas market is assumed to be regional and segmented while the price of crude oil is determined in global markets, I follow Kilian and Park (2009) and impose a block-recursive structure on the contemporaneous relationship between the reduced-form VAR innovations and the underlying structural disturbances. In particular, I assume that B 1 has a recursive structure such that the reduced-form innovations, e t, can be decomposed 6

20 according to e t = B 1 ε t, as follows e prod t b e rea t b 21 b e t = e rpo t b 31 b 32 b 33 0 b 41 b 42 b 43 b 44 e rpg t oil supply shock εt aggregate demand shock εt oil specific demand shock εt other shocks to natural gas price εt. (1.3) I can think of model (1.3) as being composed of two blocks, with the first block, consisting of the first three equations, describing the global crude oil market and the second block, consisting of only the last equation, describing the natural gas market. As in Kilian (2009) and Kilian and Park (2009), I attribute fluctuations in the real price of oil to three structural shocks: shocks to the global supply of crude oil, referred to as oil supply shocks, shocks to the global demand for all industrial commodities (including crude oil) that are driven by the global business cycle, referred to as aggregate demand shocks, and an oil-market specific demand shock, referred to as oil-specific demand shock or precautionary demand shock, designed to capture shifts in precautionary demand for crude oil in response to increased uncertainty about future oil supply shortfalls see also Alquist and Kilian (2009) for more details. The structural shock in the second block is not a true structural shock, but an innovation to natural gas prices not driven by global crude oil demand or supply shocks. The identification scheme is consistent with a global crude oil market characterized by a vertical short-run supply curve and a downward sloping short-run demand curve. In particular, the block-recursive structure implies that crude oil supply does not simultaneously react to oil demand shocks. For example, the three exclusion restrictions in the first row of B 1 (b 12 = b 13 = b 14 = 0) imply that real economic activity, the real price of crude oil, and the real price of natural gas do not have a contemporaneous effects on oil supply, but only affect it with a lag. This assumption is consistent with the notion that only exogenous events, such as conflicts in the Middle east, affect oil production. The restrictions b 23 = b 24 = 0 imply that oil-specific demand shocks and other shocks to the natural gas price do not have 7

21 a contemporaneous effect on the global business cycle, but affect it only with a lag. The third equation of the first block implies that the real price of oil changes instantaneously in response to unanticipated oil supply shocks (that shift the vertical supply curve), as well as to both aggregate demand shocks and oil-specific demand shocks (that shift the demand curve), but that the real price of oil does not contemporaneously react to the real natural gas price (so that b 34 = 0). Finally, the nonzero elements in the last row of the B 1 matrix imply that global crude oil production, global real activity, and the real price of oil are treated as predetermined with respect to the natural gas price, meaning that all three oil supply and oil demand shocks have contemporaneous effects on the real natural gas price. 1.4 Structural VAR Estimates As suggested by Kilian (2009), I assume p = 24 in (1.2) to account for the low frequency comovement between the real price of oil and global economic activity, and estimate the reduced form VAR by the least squares method. I then use the resulting estimates to construct the structural VAR representation of the model and calculate impulse response functions to onestandard deviation shocks, together with one- and two- standard error bands, based on the recursive-design wild bootstrap of Gonçalves and Kilian (2004). My main objective is to investigate the effects of structural shocks in the crude oil market on natural gas prices in the United States. In the upper panel of Figure 1.3 I review the responses of the real price of crude oil to each of the three structural shocks in the crude oil market the oil supply shock, the aggregate demand shock, and the oil-specific demand shock. Point estimates are indicated by solid lines and one-standard error and two-standard error bands are indicated by dashed and dotted lines, respectively. As in Kilian (2009) and Kilian and Park (2009), I normalize the oil supply shock to represent a negative (one-standard deviation) shock and normalize the aggregate demand and oil-market specific demand shocks to represent positive shocks, so that all three 8

22 shocks would tend to generate an increase in the real price of crude oil. As can be seen in Figure 1.3, the three structural shocks in the crude oil market have very different effects on the real price of crude oil (in the upper panel) and the real price of natural gas (in the lower panel). For example, an unexpected decline in the supply of crude oil has a transitory positive effect within the first year on the real price of oil while it has a sustained positive effect on the real price of natural gas after one year, based on one-standard error bands (these shocks have insignificant effect on both prices based on two-standard error bands); an unexpected increase in global demand causes an immediate and sustained increase in the real price of both crude oil and natural gas, although the response of the real price of natural gas is episodically insignificant in some months based on two-standard error bands; whereas an unexpected increase in the precautionary demand for oil causes immediate and sustained increases in both prices. The forecast-error-variance decompositions in Tables 1.1 and 1.2 quantify the effects of the structural shocks on the real price of crude oil and the real price of natural gas, respectively. Although in the short-run the effects of the three structural shocks in the crude oil market on the real natural gas prices (see Table 1.2) are negligible (for example, the combined explanatory power of these shocks on impact is less than 1% of the variation of the real crude oil and natural gas prices), the explanatory power increases as the forecast horizon increases. In the long run, the oil supply shock, the aggregate demand shock, and the oil-market specific demand shock together account for about 92% of the variability in the real price of crude oil and for about 45% of the variability in the real price of natural gas. This suggests that structural shocks in the global crude oil market are an important fundamental for the natural gas market in the United States, with the largest contributor being precautionary demand shocks (accounting for about 16% of the long-run variation in the real natural gas price), followed by aggregate demand shocks (accounting for about 16%), and oil supply shocks (accounting for about 13%). 9

23 Oil supply shock Aggregate demand shock Oil specific demand shock Real price of oil Real price of natural gas Oil supply shock Aggregate demand shock Oil specific demand shock Figure 1.3: Responses of the Real Price of Crude Oil (Upper Panel) and the Real Price of Natural Gas (Lower Panel) to One-Standard Deviation Structural Shocks: Point Estimates with One- and Two-Standard Error Bands. Table 1.1: Percent Contribution of Supply and Demand Shocks in the Crude Oil Market to the Overall Variability of the Real Crude Oil Price. Shock Horizon Oil supply Aggregate demand Oil-specific demand Other Note: Based on variance decomposition of the structural VAR model (1). 10

24 Table 1.2: Percent Contribution of Supply and Demand Shocks in the Crude Oil Market to the Overall Variability of the Real Natural Gas Price. Shock Horizon Oil supply Aggregate demand Oil-specific demand Other Note: Based on variance decomposition of the structural VAR model (1). The impulse responses reported in Figure 1.3 show the timing and magnitude of the responses of the real price of crude oil and the real price of natural gas to one-time structural shocks in the crude oil market. In Figure 1.4 I report (in the same fashion as in Figure 1.3) the cumulative impulse responses of the real price of crude oil and the real price of natural gas to each of the three supply and demand shocks in the crude oil market. Figure 1.4 shows that the cumulative impulse responses of the real natural gas price depend on the underlying cause of the increase in the real price of crude oil. This first graph on the lower panel of Figure 1.4 shows that shocks to the supply of crude oil have no impact on the real price of natural gas (the estimated impulse response function is never statistically distinguishable from zero). The graph in the middle shows that an unexpected increase in the demand for industrial commodities produces an immediate, positive and significant increase in the natural gas price based on one-standard error bands. Finally, the response of the real price of natural gas to a shock in the precautionary demand for crude oil is positive and statistically significant according to the one-standard error bands. In Figures 1.5 and 1.6 I present the historical decomposition of the cumulative contribution of each of the structural shocks on the real price of crude oil and the real price of natural gas, respectively. Figure 1.5 suggests that oil supply shocks (in the first graph) have made small contributions to the real price of crude oil whereas aggregate demand shocks (in the graph in the middle) and oil-market specific demand shocks (in the third graph) have 11

25 Real price of oil Oil supply shock Aggregate demand shock Oil specific demand shock Oil supply shock Aggregate demand shock Oil specific demand shock Real price of natural gas Figure 1.4: Cumulative Responses of the Real Price of Crude Oil (Upper Panel) and the Real Price of Natural Gas (Lower Panel) to One-Standard Deviation Structural Shocks: Point Estimates with One- and Two-Standard Error Bands. 12

26 Cumulative effect of oil supply shock on real price of crude oil Cumulative effect of aggregate demand shock on real price of crude oil Cumulative effect of oil market specific demand shock on real price of crude oil Figure 1.5: Historical Decomposition of the Real Price of Crude Oil. made the biggest contributions. Moreover, consistent with Kilian (2009) and Kilian and Park (2009), I find that although the aggregate demand shocks caused long swings in the real price of crude oil, the oil-market specific demand shock is mainly responsible for the sharp increases and decreases in the real price of crude oil. As Kilian (2009, p. 1062) puts it, this fact is consistent with the view that precautionary demand shocks may reflect rapid shifts in the market s assessment of the uncertainty about future oil supply shortfalls. Finally, the historical decomposition of fluctuations in the real price of natural gas in Figure 1.6 suggests that historically the real price of natural gas has been driven by a combination of structural shocks in the crude oil market (mainly, real economic activity and precautionary demand shocks) and natural gas market specific shocks. In fact, the real price of natural gas and the real price of crude oil move together if the source of fluctuations is one 13

27 of the structural shocks in the crude oil market an oil supply shock, an aggregate demand shock, or an oil-specific demand shock. The real price of natural gas may decouple from the real price of crude oil (as shown in Figure 1.1) when there are changes in the fundamental influences of the natural gas price, such as, for example, weather conditions, seasonal effects, supply disruptions, storage activity, and imports of liquefied natural gas Cumulative effect of oil supply shock on real price of natural gas Cumulative effect of aggregate demand shock on real price of natural gas Cumulative effect of oil market specific demand shock on real price of natural gas Cumulative effect of other shocks on real price of natural gas Figure 1.6: Historical Decomposition of the Real Price of Natural Gas. 14

28 In fact, the recent fluctuations in the real price of natural gas (see Figure 1.1) were mostly driven by other shocks in the natural gas market. For example, the supply disruptions in the European natural gas markets due to the Arab Spring and the civil war in Libya in the spring of 2011, the Russian-Ukrainian gas transit dispute in January 2009, and the suspension of Russian gas exports in February 2012, as well as the development of shale gas production after 2009 in the United States are all captured by the other shocks to the real price of natural gas in the last graph of Figure Conclusion I have used the global crude oil market model of Kilian (2009) to disentangle the causes underlying crude oil price shocks and investigate the response of natural gas prices in the United States to changes in the price of crude oil. The results, based on an identified structural VAR and monthly data over the period from 1976:1 to 2012:12, show that the response of the real price of natural gas may differ greatly depending on the underlying cause of the oil price shock. I show that close to 45% of the variation in the real price of natural gas can be attributed to structural supply and aggregate demand shocks in the global crude oil market. I also show that shocks in the natural gas market account for about 55% of the long run variability of the real price of natural gas, thus causing episodic decoupling of the real price of natural gas from the real price of crude oil. 15

29 Chapter 2 SECTORAL INTERFUEL SUBSTITUTION IN CANADA: AN APPLICATION OF NQ FLEXIBLE FUNCTIONAL FORMS with Apostolos Serletis 2.1 Introduction Over the years, there have been two major approaches to the investigation of interfuel substitution (energy elasticities) and the demand for energy. One approach uses cointegration techniques and error-correction models to estimate long-run and short-run demand elasticities, respectively. Although this approach deals with econometric regularity issues, it lacks proper microeconomic foundations see, for example, Bentzen and Engsted (1993) and Hunt and Manning (1989). The other approach allows the estimation in a systems context assuming a flexible functional form for the aggregator function based on the dual approach to demand system generation developed by Diewert (1974). Using recent methodological advances in microeconometrics, this approach allows us to achieve theoretical regularity (in terms of curvature, positivity, and monotonicity of neoclassical microeconomic theory). It is difficult, however, to simultaneously achieve econometric regularity (in terms of stationary equation errors), because the combination of nonstationary data and nonlinear estimation in large demand systems is an extremely difficult issue and has not yet been addressed in the literature. The flexible functional forms approach was pioneered by Berndt and Wood (1975), Fuss (1977), and Pindyck (1979) in the context of interfactor and interfuel substitution. It involves 16

30 the specification of a differentiable form for the cost function, the application of Shephard s (1953) lemma to derive the cost share equations, and the use of relevant data to estimate the parameters and compute the relevant elasticity measures like the income elasticities, the own- and cross-price elasticities, and the Allen and Morishima elasticities of substitution. However, the major contributions in this area are quite dated, since their data incorporate observations before the 1970s. Moreover, most of these studies have ignored the theoretical regularity conditions of neoclassical microeconomic theory or the authors do not report the results of full regularity checks. In contrast recent papers by Serletis et al. (2010, 2011) and Chang and Serletis (2014) address the theoretical regularity conditions and produce meaningful inference consistent with the theory. In this study we take the flexible functional forms approach to examine interfuel substitution possibilities in energy demand within the residential, commercial, and industrial sectors in Canada as a whole and six of its provinces Quebec, Ontario, Manitoba, Saskatchewan, Alberta, and British Columbia as data limitations make it impossible to deal with all provinces. We focus on electricity, natural gas, and light fuel oil, ignoring energy forms with low shares in total energy expenditure like heavy fuel oil, kerosene, wood, and liquefied natural gas. Our objective is to provide updated empirical work using methodological improvements of the past twenty years, and improve our understanding of how changing energy prices and incomes will influence interfuel substitution and the demand for energy in the future. To achieve this, we use recent state-of-the art advances in microeconometrics. In particular, we use duality theory and the demand systems approach based on neoclassical consumer and firm theories which allows us to estimate the demand for electricity, natural gas, and light fuel oil in a systems framework. We also use a locally flexible demand system derived from the expenditure/cost function of the representative consumer/firm. Moreover, we are motivated by the widespread practice of ignoring the theoretical regularity conditions of 17

31 neoclassical microeconomic theory and approximate the unknown underlying expenditure function using a flexible functional form that allows the imposition of global curvature without losing its flexibility property. In particular, in the case of the commercial and industrial sectors we use the normalized quadratic (NQ) cost function, introduced by Diewert and Wales (1987), and in the case of the residential sector energy demand we use the NQ expenditure function, introduced by Diewert and Wales (1988). The NQ cost function has also been used recently by Serletis et al. (2010, 2011), but the NQ expenditure function is (to our knowledge) used for the first time in the empirical energy demand literature. It is to be noted that McKitrick (1998) also used NQ functional forms to estimate consumer demand and producer input demand in the context of computable general equilibrium models in Canada. The rest of this chapter is organized as follows. Section 2.2 sketches out related neoclassical theory and applied consumption and production analyses. Section 2.3 presents the NQ expenditure and cost functions and derives the associated systems of consumer demand and input demand functions. Section 2.4 discusses related econometric issues, paying explicit attention to the singularity problem and the imposition of global concavity. Section 2.5 discusses the data and Section 2.6 presents the empirical results for each of the residential, commercial, and industrial sectors. Section 2.7 compares the reported results to those obtained in analyses performed by others, and the final section concludes the chapter. 2.2 The Structure of Production and Preferences The econometric approach requires certain assumptions about the structure of production and preferences. We assume that the group of n energy inputs in the production context (or goods in the consumer context) is homothetically weakly separable from the non-energy forms in the underlying aggregator function f (production function in producer theory or 18

32 utility function in utility theory). Therefore, the aggregator function f has the form Q = f (E (x), M) (2.1) where Q is gross output (or utility, u), E( ) is a homothetic aggregator function over the n energy inputs (or goods), x = (x 1,..., x n ), and M is a vector of non-energy inputs (or goods). The requirement of weak separability in x is that the marginal rate of substitution between any two components of x does not depend upon the value of M. Under these assumptions and duality theorems [see Diewert (1974)], the corresponding cost function (or expenditure function in utility theory) can be written as C = g (P E (p), p M, Q) where p = (p 1,..., p n ) is the corresponding price vector of the n forms of energy, p M that of non-energy forms, and P E (.) is an energy price aggregator function which is a homothetic function and can represented by a unit cost or expenditure function. Our objective is to estimate a system of demand equations for the residential sector and a system of input demands for each of the commercial and industrial sectors and produce inference consistent with neoclassical microeconomic theory. To do so, we use flexible functional forms capable of approximating an arbitrary twice continuously differentiable function to the second order at an arbitrary point in the domain. Moreover, the flexible functional forms that we use allow for the imposition of global curvature without losing their flexibility property. 2.3 Normalized Quadratic Functional Forms We use the NQ expenditure function, developed by Diewert and Wales (1988), to investigate interfuel substitution possibilities in energy demand within the residential sector and the NQ cost function, developed by Diewert and Wales (1987), to investigate interfuel substitution possibilities in energy demand within the commercial and industrial sectors. In what follows, 19