How the financial market can dampen the effects of commodity price shocks

European Economic Review 121 (2020) 103340

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How the financial market can dampen the effects of commodity price shocksR Myunghyun Kim1 Bank of Korea, Sogong Annex, 55 Namdaemunno, Jung-Gu, Seoul 04531, Republic of Korea

a r t i c l e

i n f o

Article history: Received 30 September 2019 Accepted 1 November 2019 Available online 11 November 2019 Keywords: Commodities as an asset Commodity price shocks Commodity derivatives Financial accelerator

a b s t r a c t Commodities have begun to function as an asset class during the past decade, as trading in commodity derivatives has increased massively since the mid-20 0 0s. This paper studies the role of commodities as an asset class in accounting for the recently lessened impacts of commodity price shocks on the U.S. economy, by constructing a model with a financial accelerator and with financial intermediaries that own two assets tied to commodities as well as to capital. Simulation results of the model show that financial intermediaries’ holdings of commodities as assets have contributed to the recent reduction in the effects of commodity price shocks. © 2019 Elsevier B.V. All rights reserved.

1. Introduction It is generally accepted that there is an inverse relationship between the prices of commodities such as oil, wheat, basic metals, etc. and the economy: when commodity prices fall, the economic effects of this are positive. This is because a fall in commodity prices leads to a decrease in living costs and an increase in real income. Moreover, when commodity prices fall, firms using commodities as inputs benefit from the low input prices. Many studies have confirmed this inverse relationship between commodity prices (especially oil prices) and the economy. Hamilton (1983) presents evidence supporting the proposition that oil price shocks contributed to almost every U.S. recession over the 1948-72 period. Burbidge and Harrison (1984), Rotemberg and Woodford (1996), Cuñado and de Gracia (2003) and Leduc and Sill (2004) also show that an increase in oil prices brings about declines in industrial production or in output. However, there is other literature providing evidence that energy price shocks have little effect on the economy. For example, Kim and Loungani (1992) include energy in a real business cycle model with exogenous energy prices and find that the inclusion of energy price shocks increases output volatility only modestly. Dhawan and Jeske (2008) obtain similar R This paper is a substantially revised version of the first chapter of my DPhil thesis at the University of Oxford and Bank of Korea Working Paper No.2018-28. E-mail address: [email protected] 1 I am very grateful to Andrea Ferrero and David Vines for their guidance and advice. I wish to thank the editor (Florin O. Bilbiie), the associate editor and the referee for their detailed, thoughtful and constructive comments and suggestions. I also thank Guido Ascari, David Cook, Kook Ka, Junsang Lee, Paul Luk, John Muellbauer, Gulcin Ozkan, Segye Shin, Rick van der Ploeg and seminar participants at the University of Oxford, the Korea Energy Economics Institute, the Bank of Korea, the 7th International Symposium on Environment and Energy Finance Issues, and 2019 Korea Money and Finance Association for their helpful comments. I gratefully acknowledge the excellent research assistance provided by Junha Park. I base the VAR analysis on Ambrogio CesaBianchi’s Matlab VAR Toolboox 2.0. Any errors remaining are my own. The views expressed are those of the author and do not necessarily reflect the views of the Bank of Korea.

https://doi.org/10.1016/j.euroecorev.2019.103340 0014-2921/© 2019 Elsevier B.V. All rights reserved.

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M. Kim / European Economic Review 121 (2020) 103340

Fig. 1. Commodity derivative contracts. Notes: The values in (a) are the year-end notional amounts of commodity derivative contracts for commercial banks, savings associations and trust companies holding derivatives in the U.S. The values in (b) are the quarter-end notional amounts in the U.S. futures market including index investment greater than or equal to 0.5 billion U.S. dollars. Source: Sources: Quarterly Report on Bank Trading and Derivatives Activities, Office of the Comptroller of the Currency, U.S. Department of the Treasury and U.S. Commodity Futures Trading Commission (CFTC).

results by extending the model of Kim and Loungani (1992). Krugman (2016) also argues that the assumed relationship does not hold, since for example spending for investment falls quickly when oil prices plunge, as a lot of it is tied to oil prices. More importantly, according to some literature, when more recent data is used, the relationship between commodity prices and macroeconomic variables is found to be insignificant or attenuated. Using vector autoregressions (VARs) over the 1970–83 and 1984–2006 periods, Blanchard and Galí (2010) conclude that oil prices had a much lower impact on inflation and output in the second period than they did in the first. According to them, this was due to the lack of concurrent adverse shocks, the smaller share of oil in the economy, more flexible labor markets and improvements in monetary policy during the second period. Segal (2011), Baumeister and Peersman (2013) and Katayama (2013), etc. also find that the rises in oil prices during the recent period have had little influence on the economy.2 Something that is not discussed in the above literatures is the fact that trading in commodity derivatives tied to commodity prices has increased massively since the mid-20 0 0s3 (see (a) in Fig. 1). Moreover, the value of net long position of commodity derivative contracts in the U.S. futures market have been positive (see (b) in Fig. 1).4 As a result, commodities have in recent years begun to function as an asset class, which may have contributed to the aforementioned weakened relationship as well. Specifically, suppose that firms produce goods by using commodities, capital and labor as inputs, and financial intermediaries (FIs) own two assets – one tied to the capital of firms and the other to commodities. The net worths of FIs will then be affected by the returns on capital and commodities, both of which depend on changes in commodity prices. For instance, a fall in commodity prices will reduce firms’ input costs and their outputs will hence rise, which will lead to an increased return on capital. In contrast, the commodity price decline will lead directly to a decreased return on commodities as well. Under this environment, if commodity prices decrease, the net worths of FIs will rise by less than in a case in which they hold only capital. This will lead to a smaller increase in FIs’ demand for investment, which will partly offset the positive impact of the fall in commodity prices on the economy. However, it is impossible to capture the linkage between commodity prices and the net worths of FIs or FI profitability with the existing models, since these models omit the role of commodities as an asset class. For example, Bernanke et al. (1999) (hereafter BGG) assume that entrepreneurs borrow money from FIs to purchase capital and are leveraged. In their model, owing to the existence of the counter-cyclical external finance premium, when an adverse productivity shock hits the economy, the price of capital falls more initially, which amplifies and propagates the shock to the economy, compared to the frictionless models (the financial accelerator). Similarly, other studies also do not consider commodities as an asset class, and in their models FIs or entrepreneurs hold only assets tied to capital (see Gertler and Karadi, 2011; Christiano et al., 2014; etc.). There are also models that do contain two assets for FIs or entrepreneurs, but they mainly extend the framework of BGG to two-country models and the two assets are thus capital at home and capital in foreign countries (see Ueda, 2012; and Dedola and Lombardo, 2012). In any case, the existing models consider FIs or entrepreneurs to hold only assets tied to capital.

2 Contrary to this literature, Kilian (2009) concludes that the reason why the recent increases in oil prices have not been followed by a U.S. recession is that they were due to strong demand for oil thanks to the booming world economy rather than to oil supply disruptions. 3 Basu and Gavin (2011) explain well why many financial intermediaries have added commodity derivatives as an asset class to their portfolios. The first reason is the search for higher yields; when the returns on safe assets are low, intermediaries tend to choose riskier assets. Second, they use commodity derivatives to hedge against equity risks in line with the negative correlation between equity and commodity returns. 4 The data from the CFTC is only available for the December 2007-October 2015 period.

M. Kim / European Economic Review 121 (2020) 103340

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This paper begins by providing empirical evidence that since the mid-20 0 0s the influence of commodity prices on U.S. economic activity has declined and their impact on FI profitability has become stronger. Using a structural VAR (SVAR), I show that the responses of U.S. industrial production to a decrease in the real oil price, triggered by a positive oil supply shock, are positive and statistically significant during the pre-2005 period, but smaller and insignificant during the post2005 period. I then present estimation results based on panel data for major U.S. FIs which show that during the latter period oil supply shocks that lead to changes in commodity prices have had stronger effects on FI profitability than during the former period. Building on the empirical evidence, I extend the model with the financial accelerator, developed by BGG, by adding FIs that invest in assets tied to both commodities and capital. I use this model to show that if FIs can hold two assets, tied to commodities as well as to the capital of firms, then the effects of a negative commodity price shock on the economy will be attenuated. The simulation results of the model reveal that the responses of macroeconomic variables to a negative commodity price shock are weaker than those in a model without FIs’ investment in commodities. Based on these results, I conclude that commodities as an asset class play a substantial role in the reduced impacts of commodity price shocks. The remainder of the paper is organized as follows. Section 2 provides the empirical evidence that the impacts of commodity prices on the U.S. economy have weakened and their effects on FI profitability have strengthened since the mid20 0 0s. Section 3 describes the model in which FIs invest in two assets tied both to capital and to commodities. Section 4 presents the simulation results of the model, and explains why its inclusion of commodities as an asset class is important and relevant. Section 5 concludes the paper. 2. Empirical evidence In this section, using an SVAR, I first provide evidence that the effects of commodity prices on U.S. economic activity have been attenuated since the mid-20 0 0s when trading of commodity derivatives increased rapidly. I then show using data for major U.S. FIs that the impacts of commodity prices on FI profitability have become stronger since the mid-20 0 0s. 2.1. Declining effects of commodity prices In order to show that the influence of commodity prices on U.S. economic activity has weakened since 2005, I estimate a four-variable SVAR. Since the sources of commodity price changes are different over time5 and, as pointed out in Kilian (2009) and Peersman and Van Robays (2009), the effects of commodity price changes on economic activity are different depending on their sources, comparing the impacts of innovations to commodity prices on U.S. economic activity in the pre-2005 period and in the post-2005 period is not appropriate. To compare the impacts of commodity price changes during the two periods, we should consider the impacts of commodity price changes that are caused by supply or commodity-specific demand shocks, which can be unambiguously compared over time. However, this requires production data which is not available for all commodities. Hence, in this section I use oil price and world oil production instead of the equivalent data for all commodities and compare the effects of changes in the real oil price caused by an oil supply shock (innovation to world oil production) on U.S. economic activity. Since the weight of oil price in the commodity price index is the largest and oil is generally regarded as the main driver of commodity prices, oil data should be representative of data for all commodities. As in Baumeister and Peersman (2013), the four variables used in the SVAR are world oil production, the real oil price, U.S. consumer prices, and U.S. industrial production.6 The full sample period is January 1990 to December 2018. To examine whether the effects of oil price changes have weakened since the mid-20 0 0s when commodities began to function as an asset class, I divide the full sample period into two: January 1990 to December 20 04 (pre-20 05 period) and January 2005 to December 2018 (post-2005 period).7 In order to compare the effects during the two periods, I consider an oil supply shock normalized to decrease the real oil price by 10% in the initial period. For the identification of structural oil supply shocks, I use sign restrictions as in Baumeister and Peersman (2013). Specifically, a positive oil supply shock increases world oil production and decreases the real oil price for six months.8 With regards to the responses of industrial production and consumer prices, there are no constraints. The lag length is set to sixteen months based on the Akaike information criterion. The median impulse responses of the four variables to a 10% decrease in the real oil price, triggered by a positive oil supply shock, in the two sample periods are presented in Fig. 2. For the pre-2005 subsample, U.S. industrial production rises and the increase is statistically significant. In contrast, in the post-2005 period the effect of a fall in the real oil price 5

For example, in the 1970s, oil price increases were typically driven by supply, while in the 20 0 0s they were mainly driven by demand. All variables are natural logarithms, and consumer prices and industrial production are seasonally adjusted series. The source of the industrial production and consumer prices is the Federal Reserve Economic Data (FRED) of the St. Louis Fed, and that of world oil production is the U.S. Energy Information Administration (EIA). The real oil price is obtained from nominal oil prices, whose source is the World Bank, deflating by the U.S. CPI. 7 The pre-2005 period starts at 1990 because many papers such as Baumeister and Peersman (2013) find a break in the effects of oil price changes on economic activity around the mid-1980s. Specifically, after the mid-1980s the effects have weakened. 8 This is consistent with the results in Kilian (2009) in which a negative oil supply shock leads to a statistically significant increase in the real oil price for about six months. 6

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M. Kim / European Economic Review 121 (2020) 103340

Fig. 2. Median impulse responses. Notes: Figures are median impulse responses to a positive oil supply shock normalized to a 10% decrease in the real price of oil. The dashed lines are the 5th and 95th percentile error bands. The horizon is monthly.

M. Kim / European Economic Review 121 (2020) 103340

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on U.S. industrial production disappears. That is, the response of the production for the latter subsample is not statistically significant and is smaller compared to that for the former subsample. Since the muted response of U.S. industrial production for the post-2005 period could be due to a sharp rise in shale oil production since around 2011, I also estimate the same SVAR for the Euro area,9 which is an oil-importing region and is not affected by shale oil production.10 The estimation results, which are presented in the Online appendix, show that the effects of a 10% fall in the real oil price caused by a positive oil supply shock on industrial production in the Euro area also become weaker for the post-2005 period compared to the pre-2005 period. In a nutshell, these results provide evidence that the effects of commodity price changes on U.S. economic activity have weakened since 2005, as commodities have begun to function as an asset class. 2.2. Effects of commodity prices on FI profitability In this section, I analyze whether the impacts of commodity prices on FI profitability have become stronger since 2005. To do so, I use detailed, annual U.S. FI-level data from the Federal Deposit Insurance Corporation (FDIC) together with several macro variables.11 As explained in the previous section, the impacts of commodity prices vary depending on their sources, and the sources vary over time. Hence, in this section, I use the annual average of the monthly oil supply shocks from the SVAR in the previous section, rather than commodity prices. In addition, I consider the period 1992–2010 as the sample period, even though the data used in this section is available to 2018. This is because if we include the period 2011–2018, when the production of shale oil increased massively, in the sample period, the estimation results might be distorted. Following Borio et al. (2017) and Kohlscheen et al. (2018), I regress a measure of FI profitability on various FI-specific and macro variables. I use the pretax return on assets as a measure of FI profitability as well as oil supply shocks. Specifically, the following dynamic panel data model is estimated.

ROAi,t = ϑi + α ROAi,t−1 + β1 OSt + β2 (OSt × Dt ) + γ Yi,t + δXt + εi,t , where ROA is the pretax return on assets, ϑi is a FI fixed effect, OS denotes the oil supply shocks, and D is a dummy variable whose value is 1 after 2005. Y is a vector of FI-specific variables consisting of size (natural logarithm of total assets), capital ratio (ratio of total equity capital to total assets), liquidity (ratio of securities to total assets) and efficiency (ratio of noninterest incomes to noninterest expenses). X is a vector of macro variables, which includes the 3-month Treasury bill rate, the 10-year government bond yield, the growth rate of nominal GDP and CPI inflation.12 The global financial crisis dummy which takes the value of 1 in the period 2008–2010 is also included in X. The subscripts i and t denote FIs and years, respectively. I use the data for 73 major U.S. FIs among the top 100 U.S. banks in terms of asset size. The 73 major U.S. FIs are those whose data is available at least from 1995 from the FDIC. I estimate the above dynamic panel data model using the System Generalized Method of Moments (GMM) methodology developed by Arellano and Bover (1995) and Blundell and Bond (1998). Since sample FIs are large, their profitability could have an effect on macro variables. FI-specific variables could also have been affected by profitability. Therefore, I treat all explanatory variables with the exception of the oil supply shocks, the dummy variable and the interaction term between the oil supply shocks and dummy variable for the period 2005–2010 (OSt × Dt ) as endogenous in choosing an instrument set.13 Since the purpose of this analysis is to examine whether the effect of commodity price changes on FI profitability became stronger after 2005, the focus is on the interaction term. That is, I focus on the sign and significance of the coefficient of the interaction term β 2 . We expect that the sign of β 2 would be negative, because an increase in oil supply shocks leads to a fall in commodity prices. Therefore, if β 2 is negative and statistically significant, this suggests that the impact of commodity prices on FI profitability has become stronger since 2005. The third column in Table 1 provides the estimation results. The coefficient of the interaction term β 2 is negative and statistically significant at the 1% level. This result clearly shows that the influence of commodity prices on FI profitability has strengthened since 2005. In short, the estimation results in this section clearly provide empirical support for the hypothesis that since 2005, when commodities began to function as an asset class, FIs have been more strongly affected by commodity price changes than before 2005. 9 Since the nominal oil price is expressed in U.S. dollars, for the real oil price in the Euro area I multiply the nominal oil price by the exchange rate expressed per U.S. dollar and deflate by CPI in the Euro area. The source of consumer prices in the Euro area is the FRED, and that of industrial production and the exchange rate in the Euro area is the OECD Monthly Economic Indicators. 10 A different way to exclude the impacts of shale oil production would be to set the period January 2005 to December 2010 as the post-2005 period. With this approach, however, the sample size for the post-2005 period is too small to properly estimate the SVAR. 11 One simple way to show that the effects of commodity prices on FI profitability have strengthened during the post-2005 period is to include FI profitability in the SVAR model in the previous section and to compare the responses of FI profitability to commodity price changes. However, many studies such as Alessandri and Nelson (2013), Borio et al. (2017) and Kohlscheen et al. (2018) find that bank-specific characteristics such as size and liquidity, as well as macro variables such as GDP and interest rates, have significant effects on bank profitability. Hence, using bank-level panel data would seem to be more appropriate. 12 The sources of the FI-specific variables and macro variables are the FDIC and the FRED, respectively. 13 In order to limit instrument proliferation, which can weaken the Hansen test, I reduce lags for instruments and collapse the instrument set as recommended by Roodman (2009).

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M. Kim / European Economic Review 121 (2020) 103340 Table 1 Estimation results. Explanatory variables

Dependent variable: FI profitability (pretax return on assets)

Oil Supply Shock × Post-2005 dummy

-0.6191∗ ∗ ∗ (0.1048) 0.0179 (0.0230)

Oil Supply Shock 3-month Treasury rate 10-year bond yield GDP growth CPI inflation Global financial crisis dummy Log of total assets Capital ratio Liquidity Efficiency

0.7147∗ ∗ ∗ (0.0762) 73 16 0.580 0.212

Lagged dependent variable Number of FIs Number of instruments AB test for AR(2) (p-values) Hansen test (p-values) Notes: Robust standard errors are reported in parentheses. means the Arellano-Bond test.

∗∗∗

and

∗∗

-0.4687∗ ∗ ∗ (0.1448) -0.0202 (0.0476) -0.0287 (0.0329) -0.0124 (0.0597) 0.0946∗ ∗ ∗ (0.0284) -0.0391 (0.0382) -0.3449∗ ∗ (0.1541) 0.0092 (0.0318) 0.0170 (0.0322) 0.0044 (0.0036) 0.0012∗ ∗ ∗ (0.0003) 0.5946∗ ∗ ∗ (0.0519) 73 66 0.491 0.190

denote significance at the 1% and 5% level, respectively. AB test

3. The model In this section I describe the model14 with a financial accelerator and FIs investing in two assets – tied to capital and to commodities. The model is very close to that of BGG. The main differences between them are that in this model firms use commodities as well as labor and capital as inputs to produce goods, and that FIs invest not only in the shares in capital issued by firms but also in commodities. As usual in the literature such as Kim and Loungani (1992) and Wei (2003), commodities need to be imported at an exogenous price.

3.1. Financial market The framework of the financial market is closely related to that of Gertler and Karadi (2011). Specifically, firms issue shares to acquire funds that are necessary for purchasing capital for production, and there is no friction in the process of firms obtaining funding from FIs. Only FIs face credit constraints in obtaining funds from investors. There are two kinds of contracts in the financial market: loan contracts between FIs and investors, and share contracts between firms and FIs.15 FIs have their own net worth, N, which is not sufficient for investing in commodities and in shares in capital issued by firms. FIs thus enter into loan contracts with investors in order to borrow money. As in BGG, FIs face idiosyncratic shocks, ω, to their returns. Therefore, the ex post gross return to investment of FI F , where RF i ∈ {1, 2, , ∞} is equal to ωi Rt+1 is the ex post aggregate return to investment of FIs. ln ω follows a normal t+1 distribution with mean − 12 σ 2 and variance σ 2 , and under this assumption, E[ω] = 1. The CDF of ω is F( · ) and the PDF is f( · ). ω is i.i.d. across time and across FIs. 3.1.1. Loan contract between FIs and investors As in BGG, the costly state verification is assumed. Since the return on FIs’ investment is subject to the idiosyncratic shock, ω, if investors wish to observe the shock for a specific FI, they have to pay a monitoring cost, which is a fixed fraction, μ, of the entire wealth of the FI.

14 15

See Online appendix for details of the model. Since there are no frictions in the share contracts between FIs and firms, the contracts are not described.

M. Kim / European Economic Review 121 (2020) 103340

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Fig. 3. FI’s balance sheet.

In each period, FI i wishes to invest Qt Si,t in shares in capital issued by firms, and pt xFi,t in commodities.16 S is the quantity of the shares in capital issued by the firms, Q is the price of each share which is equal to the price of each unit of capital, xF is the units of the composite commodity used noncommercially, and p is the price of one unit of the composite commodity. Therefore, FI i needs to borrow Qt Si,t + pt xFi,t − Ni,t+1 from investors. Accordingly, the FI’s balance sheet is as given in Fig. 3.





FI i has to repay to investors the principal and interest, Zi,t+1 Qt Si,t + pt xFi,t − Ni,t+1 , where Zi,t+1 is the gross non-default loan rate, if it does not default. If it defaults, investors that lend money to FI i pay the monitoring cost and take the entire wealth of FI i. Since this is the standard debt contract, there exists a threshold value of the shocks, ω ¯ i , for FI i (see Townsend, 1979). If ωi ≥ ω¯ i , then FI i makes enough profit to repay the investors, whilst if ωi < ω¯ i , it defaults. Then, ω¯ i,t+1 is such that F ω¯ i,t+1 Rt+1 (Qt Si,t + pt xFi,t ) = Zi,t+1 (Qt Si,t + pt xFi,t − Ni,t+1 ).

(1)

Denote (ω ¯ i ) ∈ (0, 1 ) the share of the returns on FI i’s investment that goes to the investors. Then, (ω ¯i = i+  ω¯ G (ω ¯ i )RF (QSi + pxFi ) + (1 − F (ω ¯ i ) )Zi (QSi + pxFi − Ni ) holds, where G(ω ¯ i ) = 0 i ω f (ω )dω. Using Eq. (1), this becomes (ω ¯ i) = G (ω ¯ i ) + (1 − F ( ω ¯ i ) )ω ¯ i . Finally, considering the monitoring cost, the net share of the returns to FI i going to investors is

)RF (QS

(ω¯ i ) = (ω¯ i ) − μG(ω¯ i ).

pxFi )

(2)

Unless the expected profit of the contract is higher than the risk free rate, R, investors do not participate in the contract. Therefore, the expected participation constraint is F Et [(ω ¯ i,t+1 )Rt+1 (Qt Si,t + pt xFi,t )] = Rt+1 (Qt Si,t + pt xFi,t − Ni,t+1 ),

(3)

where Et is the expectations operation conditional on the information at t. FIs choose the expenditure on investment, Qt Si,t + pt xFi,t , and the threshold values of the idiosyncratic shocks, ω ¯ i,t+1 , so as to maximize their expected profits, Et F Et [Rt+1 ]

Rt+1



= Et







F 1 − (ω ¯ i,t+1 ) Rt+1 ( Qt Si,t + pt xFi,t ) . The first-order condition is



ω (ω¯ i,t+1 ) , (1 − (ω¯ i,t+1 ) )ω (ω¯ i,t+1 ) + ω (ω¯ i,t+1 )(ω¯ i,t+1 )

(· ) ·) where ω (· ) = ∂ ∂ω , ω (· ) = ∂ ( ∂ω , and

F ] Et [Rt+1 Rt+1

(4)

is called the external finance premium.

3.1.2. Aggregation of the loan contract Since the left-hand side of Eq. (4) is determined exogenously to the financial market, every FI’s choice for Et [ω ¯ i,t+1 ] is the same. Thus, Eq. (4) can be aggregated: F Et [Rt+1 ]

Rt+1



= Et



ω (ω¯ t+1 ) . (1 − (ω¯ t+1 ) )ω (ω¯ t+1 ) + ω (ω¯ t+1 )(ω¯ t+1 )

(5)

Aggregating the expected participation constraints, Eq. (3), yields F Et [(ω ¯ t+1 )Rt+1 (Qt St + pt xtF )] = Rt+1 (Qt St + pt xtF − Nt+1 ),

where St =



i Si,t ,

xtF

=



F i xi,t

and Nt+1 =



i

(6)

Ni,t+1 . Using Eqs. (5) and (6), the relationship between FIs’ leverage, (Qt St +

pt xtF )/Nt+1 , and the external finance premium can be obtained: F Et [Rt+1 ] Qt St + pt xtF =ℵ , Nt+1 Rt+1

where ℵ = Et



{(1− (ω¯ t+1 ))ω (ω¯ t+1 )+ ω (ω¯ t+1 )(ω¯ t+1 )} (1− (ω¯ t+1 ))ω (ω¯ t+1 ) ω (ω¯ t+1 )

(7)

 2

. Since the numerator of ℵ is positive, 1 − (ω ¯ t+1 ) > 0, ω (ω ¯ t+1 ) > 0

and ω (ω ¯ t+1 ) > 0, ℵ > 0. Therefore, leverage is increasing in the external finance premium. 16

In this section, the subscript i also denotes FIs.

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3.1.3. FIs’ commodity investment Now, suppose that the composite commodity is storable, and that in period t FIs buy xtF units of the composite commodity at pt and sell them at pt+1 in period t + 1. As in Unalmis et al., 2012, FIs also need to cover the storage costs, κ + ϕ2 xtF , of storing one unit of the composite commodity, where κ < 0 reflects the convenience yield. Since it is assumed that ϕ > 0, the storage costs are increasing in xtF . FIs’ expected profit from investing pt xtF in period t can be written as bEt [ pt+1 ]xtF Rt+1

  − pt xtF 1 + κ + ϕ2 xtF , where 1 − b > 0 is the wasted amount of the composite commodity in storage. Maximizing

the expected profit yields the demand for commodity investment:

xtF =

bEt [ pt+1 ] (1 + κ ) − . ϕ pt Rt+1 ϕ

(8)

Accordingly, the realized return to FIs’ investment in commodities, Rtx , is

Rtx =

bpt − pt−1 Rt



κ+

ϕ 2

F xt−1 .

(9)

For convenience, I define τ t as the ratio of FIs’ commodity investment pt xtF to their share investment Qt St :17

τt = pt xtF /Qt St .

(10)

Note that since each FI shares the identical rational expectation with other FIs, each FI’s choice for τ t is the same. Thus, the aggregate return to investment of FIs is

RtF =

1 (RK + τt Rtx ), 1 + τt t

(11)

where RtK is the return on FIs’ investment in the shares in capital issued by firms. 3.1.4. Dynamic behavior of net worth The aggregate net worth of FIs depends on their aggregate earnings from the above contracts, and from their labor incomes, since it is assumed that FIs inelastically supply one unit of labor to operating firms. Let Vt be the aggregate earnings of FIs from the above contract. Then, the aggregate net worth of FIs evolves according to

Nt+1 = γ F Vt + WF,t ,

(12)

− (ω ¯ t ) )RtF (Qt−1 St−1

F ) pt−1 xt−1

γF

where Vt = (1 + and WF,t is the labor incomes of FIs. Let be the survival probability for FIs. When an FI quits its business it consumes all of its net worth, and the consumption of quitting FIs is thus

CtF = (1 − γ F )Vt .

(13)

3.2. The rest of the economy 3.2.1. Household A representative household chooses consumption, labor supply and real lending so as to maximize its utility. For simplicity, log utility function of consumption and separability between consumption and labor are assumed. The utility function is

U = E0

∞ 



β t ln Ct −

t=0

1+χ

LC,t

1+χ



,

(14)

where Ct is consumption, LC,t is the labor supply by households, β is the discount factor, and χ is the inverse of Frisch elasticity of labor supply.18 The budget constraint is

Ct + Bt+1 = Wt LC,t + Rt Bt + t ,

(15)

where Bt is the real lending, Wt is the real wage, Rt is the real return from lending, and t is the real profits remitted by firms. The first order conditions of a representative household’s utility maximization problem are

1 = β Et

C t

Ct+1 χ

Wt = Ct LC,t .



Rt+1 ,

(16) (17)

Eq. (16) is the Euler equation, and Eq. (17) is the condition of intratemporal substitution between consumption and labor. If τt = 0 for all t, FIs invest all available funds in the shares in capital issued by firms, as in BGG. Some papers such as Bodenstein et al. (2011) assume that households consume commodities. However, for simplicity, I do not consider commodity consumption in the model, since it does not play a notable role in generating the results of this paper. 17

18

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3.2.2. Final goods firms There is a continuum of intermediate goods firms indexed by j ∈ [0, 1]. They produce differentiated intermediate goods, Yt (j), at prices Pt (j). Final goods firms bundle intermediate goods to produce final goods according to the following CES technology:



Yt =

1

0

Yt ( j )

ε −1 ε

ε  ε−1

,

dj

(18)

where ε > 1 is the elasticity of substitution among intermediate goods. From the profit maximization problem, the demand for each intermediate good is



Yt ( j ) =

Pt ( j ) Pt

−ε

Yt ,

(19)

and the corresponding price index is



Pt =

1 0

Pt ( j )1−ε dj

 1−1 ε

.

(20)

3.2.3. Intermediate goods firms A typical intermediate goods firm produces output using capital, labor and commodities. The production function is a nested CES with constant returns to scale, following Kim and Loungani (1992) and Dhawan and Jeske (2008): α

Yt ( j ) = At {(1 − a )Kt ( j )−ν + axt ( j )−ν }− ν Lt ( j )1−α ,

(21)

where x(j) is the units of the composite commodity used in production, K(j) is the capital inputs, and 1 − α is the labor ς share of income. The parameter a determines the importance of the commodities. The parameter ν is equal to 1− ς , where ς is the elasticity of substitution between capital and commodities. A is the common productivity, and follows an AR(1) process as usual:

ln At = ρA ln At−1 + ut ,

(22)

where ut is the productivity shock. As in BGG, Lt (j) is a composite of the labor that is supplied by households (LC,t (j)) and FIs (LF,t (j)). Lt (j) is expressed by

Lt ( j ) = LC,t ( j )1−F LF,t ( j )F .

(23)

In each period, intermediate goods firms issue shares in order to purchase capital for production, which means that

Qt Kt+1 = Qt St .

(24)

Firms purchase capital at the end of period t − 1 to produce goods in period t, and sell the non-depreciated capital back to the capital goods producers at the end of period t. The first-order conditions of the cost minimization problem are

Wt = (1 − α )(1 − F )mct WF,t = (1 − α )F mct

t Yt



RtK =

LF,t

t Yt LC,t

,

(25)

,

(26)



1 t Yt (1 − δ )Q t + α (1 − a )mct Kt−ν −1 , Qt−1 (1 − a )Kt−ν + axt−ν

pt = aα mct xt−ν −1

t Yt , (1 − a )Kt−ν + axt−ν

where δ is the depreciation rate, mct is the real marginal cost, and t =

(27) (28)  1 Pt ( j ) −ε 0

Pt

dj is the price dispersion term.

Commodity prices are determined exogenously, and follow AR(1) as in Wei (2003):

ln pt = ρ ln pt−1 + ηt ,

(29)

where ηt is the commodity price shocks. Firms set prices based on Calvo price-setting. In each period, a fraction, 1 − θ , of firms adjust their prices. This means that the probability a firm will be stuck with a price for one period is θ . Thus, the first-order condition for the optimal reset price, PtO , is

PtO

=

ε

ε−1

Et

∞

−1 ε Y (βθ )hCt+ mct+h Pt+ h t+h h . −1 ε −1 h (βθ ) Ct+h Pt+h Yt+h

h=0 Et ∞ h=0

(30)

Accordingly, the price index evolves according to



Pt = (1 − θ )PtO

1−ε

1 −ε + θ Pt−1

 1−1 ε

.

(31)

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M. Kim / European Economic Review 121 (2020) 103340 Table 2 Parameter values. Parameter

Value

Parameter

Value

β χ δ ξ α ε θ F

0.99 3 0.025 2.5 0.36 6 0.75 0.01 0.97 -0.08

ϕ ν

0.3 0.7 0.006 0.046 0.178 0.902 0.8 1.5 0.1 0.976

b

κ

a

σ μ γF ρI φπ φY ρ

3.2.4. Capital goods producers The capital goods producers use their technology to convert final goods to capital goods. In each period they buy It of final goods and (1 − δ )Kt of used capital from firms. They then produce new capital goods, Kt+1 . Thus, the capital goods producer’s problem is the following:

max Qt Kt+1 − (1 − δ )Qt Kt − It , Kt+1

subject to the law of motion for capital

Kt+1 = (1 − δ )Kt + It −

ξ (Kt+1 − Kt )2 2

Kt

,

(32)

where ξ is the parameter associated with the adjustment costs. The first-order condition gives the price of capital:

Qt = 1 − ξ + ξ

Kt+1 . Kt

(33)

3.2.5. Monetary policy and resource constraint The monetary authority follows a standard Taylor-type rule,

it = (1 − ρI )i + ρI it−1 + (1 − ρI ){φπ (πt − π ) + φY (ln Yt − ln Yt−1 )},

(34)

where it is the nominal interest rate, and πt = Pt /Pt−1 . The variables without time subscript t denote their steady state values. The Fisher equation, Rt+1 = Et [it /πt+1 ], gives the relationship between the nominal and real interest rates. In each period, all produced goods are used for either consumption, investment, purchase of commodities by firms for production, commodity investment by FIs, or the monitoring costs of investors. Thus, the resource constraint is given by F F Yt = Ct + CtF + It + pt xt + pt (xtF − bxt−1 ) + μG(ω¯ t )RtF (Qt−1 Kt + pt−1 xt−1 ).

(35)

The last term is the monitoring cost of investors.19 4. Model analysis 4.1. Calibration The parameter values are given in Table 2. The calibration is based on quarterly U.S. data. First of all, the CFTC and FRED data show that during the Q4 2007 to Q3 2015 period the value of FIs’ net long position of commodity derivative contracts was on average 1.1% of the remaining total assets. τ is therefore set to 0.011, which means that in the steady state FIs invest 1.1% of the amount that they invest in the shares in capital issued by firms in commodities. I also consider one more case for τ = 0 in which FIs invest only in the shares in capital issued by firms. By considering two cases for τ , I can show how the responses of the macroeconomic variables to a negative commodity price shock change as FIs invest in commodities. In keeping with much of the literature, the discount factor, β , is 0.99, the inverse of Frisch elasticity of labor supply, χ , is set to 3, the depreciation rate, δ , is assumed to be 0.025, the parameter associated with capital adjustment costs, ξ , is 2.5, and the labor share of income, 1 − α , is equal to 0.64. The elasticity of substitution between intermediate inputs, ε , is set to 6, and the probability that a price does not adjust, θ , is assumed to be 0.75. Following BGG, the share of FIs’ labor inputs, F , is 0.01, the rate of failure of FIs, F (ω ¯ ), is 0.03/4, and the steady state risk spread, RK − R, is assumed to be 0.01. I assume that the steady state leverage, (K + xF )/N, is 10, which matches the 19 Note that, according to BGG, CtF and the monitoring cost have relatively low weights under any reasonable parameterization of the model, and thus have no recognizable effects on the dynamics.

M. Kim / European Economic Review 121 (2020) 103340

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average ratio of total assets to total equity capital of all U.S. banks for the period 1995–2017 from the FDIC data. Hence, the steady state ratio of capital to the FIs’ net worth, K/N, is equal to 10/(1 + τ ) and that of commodity investment to net worth, xF /N, is 10τ /(1 + τ ) as in Eq. (10). The parameter for the surviving amount of commodities stored, b, is assumed to be 0.97 which matches the estimation results of Deaton and Laroque (1996) that annual deterioration rate of commodities in storage is around 12%. The convenience yield, κ , and the parameter associated with the storage costs, ϕ , are set to satisfy RK = Rx . As in Kim and Loungani (1992), I assume that the parameter related to the elasticity of substitution between capital and commodity inputs in production, ν , is 0.7. The steady state capital/commodity ratio, K/x, is assumed to be 126.2.20 Accordingly, the parameter related to the importance of commodities in production, a, is 0.006, which is determined by the values of K/x, RK , δ and ν from Eqs. (27) and (28) in the steady state. Using the definition of the log-normal distribution, the steady state expected participation constraint and first-order condition of the FI’s problem, the steady state threshold value of the idiosyncratic shocks, ω ¯ , and the variance of ln ω, σ 2 , can be obtained. Therefore, the monitoring cost, μ, and the probability of survival for FIs, γ F , can be calculated. σ is 0.046, μ is 0.178, and γ F is 0.902. The parameters in the monetary policy rule are consistent with the standard literature. The autoregressive parameter, ρ I , is 0.8, the policy weight on inflation, φ π , is set to 1.5, and the policy weight on the output gap, φ Y , is 0.1. Finally, the autoregressive parameter in commodity price, ρ , is equal to 0.976 which is estimated using Bayesian techniques.21

4.2. Effects of a negative commodity price shock This section shows how the model responds to a negative commodity price shock. By conducting this analysis, the way in which the existence of commodities as an asset class can dampen the effects of commodity price shocks on the economy can be shown. Fig. 4 presents the responses of the model, with two values of τ , to a negative 1% deviation shock to commodity prices. First, consider the case of τt = τ = 0 for all t, in which FIs invest only in the shares in capital issued by firms. Since a negative commodity price shock leads to a fall in firms’ input costs, their demands for both commodities and capital increase. Thus, the price of capital, Q, jumps, which leads to a rise in FIs’ returns on investment in the shares in capital issued by firms, RK . Since from Eq. (11) the FIs’ aggregate return on investment, RF , is equal to RK when τt = 0, RF increases. Due to the realized participation constraint, Eq. (6), a rise in RF brings about a fall in the threshold value of the idiosyncratic shocks, ω ¯ , since  ω > 0. Because RF and the share of the profits going to FIs in the loan contract, 1 − (ω ¯ ), increase (Γω > 0), the net worth of FIs, N, rises in accordance with Eq. (12). Therefore, owing to the increases in N and in the demand for capital, the investment goes up and output thus expands. However, since when τ = 0.011 (τ t = 0) the shock brings about a fall in the FIs’ returns on investment in commodities, Rx , RF rises by less. The smaller rise in RF leads to a smaller decrease in ω ¯ , and 1 − (ω ¯ ) thus rises by less. Given the smaller increases in RF and 1 − (ω ¯ ), N also rises by less. FIs’ investment in the shares in capital issued by firms thus increases by less. Although demand for capital grows due to a fall in commodity prices, investment rises by less than when τt = 0 owing to the smaller increase in N. Output therefore increases by less than the case of τt = 0. In short, if FIs hold the assets tied to commodities, N increases by less, and thus investment and output rise by less. To summarize, if FIs own assets tied to commodities, investment and output will increase to a lesser extent following a negative commodity price shock. This is mainly because a fall in commodity prices causes not only an increase in the returns to FIs’ investments in assets tied to capital, but also a fall in their returns on investment in commodities. As a result, FIs’ returns on total investment go up by less than in the models in which FIs hold only assets associated with capital, and their net worth hence rises by less. Thus, considering that commodities have begun to function as an asset class since the mid20 0 0s, and that according to the empirical evidence in Section 2 the impacts of commodity price shocks have weakened since the mid-20 0 0s, these results are consistent with the hypothesis that commodities as an asset class have played an important role in the recently reduced impacts of commodity price shocks on the economy.

4.3. Importance and relevance of commodities as an asset class The importance and relevance of commodities as an asset class in this model result from the fact that by investing in commodities, FIs can hedge against the risks to their investments in the shares in capital issued by firms stemming from commodity price shocks.

20 This is different from Kim and Loungani (1992), who assume that the steady state capital/energy ratio is 200. However, in this model firms use all commodities, rather than only energy. Considering that the weight of energy in the IMF’s commodity price index is 0.631, 200 × 0.631 = 126.2 as the steady state capital/commodity ratio seems appropriate. 21 Demeaned commodity price index divided by GDP deflator for the period Q1 1960 to Q2 2018 is used as demeaned real commodity prices. A Beta distribution, 0.96 and 0.05 are used as the prior distribution, mean and standard deviation, respectively, and posterior mean and 90% confidence interval are 0.9763 and [0.9584, 0.9997] respectively.

12

M. Kim / European Economic Review 121 (2020) 103340

Fig. 4. Responses of the model to a negative commodity price shock.

M. Kim / European Economic Review 121 (2020) 103340

13

To be specific, the demand for commodities in production, x, is decreasing in commodity prices, and the return to capital, RK , is increasing in x. Hence, RK is decreasing in commodity prices. However, the return on commodity investment, Rx , is increasing in commodity prices. Therefore, RK and Rx react in opposite directions to changes in commodity prices, which enables FIs to hedge against the risks from commodity price shocks to their investments in the shares in capital issued by firms by investing in commodities. For instance, a rise in commodity prices will lead to an increase in Rx by Eq. (9), but to a fall in RK by Eqs. (27) and (28). If FIs do not invest in commodities, their returns on investment, RF , will fall. In this model, however, since FIs hold commodities as an asset, RF declines, due to a rise in Rx , by less than when they do not hold any commodities as an asset, i.e. when FIs invest in commodities their returns on investment fluctuate by less in response to commodity price shocks. The existence of commodities as an asset class in this model is very consistent with the fact that FIs use commodity derivatives to hedge against equity risks, which is noted in the literature such as Basu and Gavin (2011). In models in which FIs invest only in capital, their returns on investment depend solely on the returns to capital, and there are no instruments with which FIs can diversify the risk of investment associated with capital. In this model FIs do have such instruments, however, and this model is thus more relevant than others in considering the existence of commodities as an instrument for hedging by FIs. 5. Conclusion This paper has developed a model with a financial accelerator and FIs investing in two assets – tied to capital and to commodities – by extending the model of BGG to explain the role of commodities as an asset class in the recently declined effects of commodity price shocks on the economy. The simulation results of the model show that FIs’ investment in commodities has been an important factor explaining these recently reduced impacts of commodity price shocks. A negative commodity price shock causes both a rise in the return on FIs’ investments in assets tied to capital and a fall in the return on their investments in commodities. In models such as BGG, in which there is no asset tied to commodities, there is only the former effect and the net worth of FIs thus increases. In this model, however, in which FIs invest in commodities as assets also, both effects exist and the net worth of FIs therefore rises by less. As a consequence, FIs’ investment in the shares in capital issued by firms increases by less, which results in smaller responses of the economy to commodity price shocks; i.e. the presence of commodities as an asset class makes the economy less volatile in response to commodity price shocks. The existence of commodities as an asset class in this model is moreover consistent with the fact that FIs use commodity derivatives to hedge against equity risk. Specifically, since the returns to capital and to commodities react in the opposite directions when commodity prices change, FIs can hedge against the risk of investment in the shares in capital issued by firms to commodity price shocks by investing in commodities. It should finally be noted that this paper does not study policy effects on the economy. However, the framework in this model allows such analyses with simple extensions, and it would be interesting to see future research that studies how policy effects change and to analyze the optimal policies to commodity price shocks when commodities as an asset class are present in the model. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.euroecorev.2019. 103340. References Alessandri, P., Nelson, B.D., 2013. Simple banking: profitability and the yield curve. J. Money Credit Bank. 47, 143–175. Arellano, M., Bover, O., 1995. Another look at the instrumental variable estimation of error-components models. J. Econ. 68, 29–51. Basu, P., Gavin, W.T., 2011. What explains the growth in commodity derivatives? Federal Reserve Bank of St. Louis Rev. 93, 37–48. Baumeister, C., Peersman, G., 2013. Time-varying effects of oil supply shocks on the us economy. Am. Econ. J. Macroecon. 5, 1–28. 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