The cost of capital, asset prices, and the effects of monetary policy

Journal of Macroeconomics 42 (2014) 211–228

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Journal of Macroeconomics journal homepage: www.elsevier.com/locate/jmacro

The cost of capital, asset prices, and the effects of monetary policy Edgar A. Ghossoub a,1, Robert R. Reed b,⇑ a b

Department of Economics, University of Texas-San Antonio, One UTSA Circle, San Antonio, TX 78249, United States Department of Economics, Finance, and Legal Studies, University of Alabama, 260 Alston Hall, Tuscaloosa, AL 35487, United States

a r t i c l e

i n f o

Article history: Received 2 April 2014 Accepted 15 August 2014 Available online 16 September 2014 JEL classification: E21 E22 E31 G11 Keywords: Cost of capital Tobin’s Q Asset prices Monetary policy

a b s t r a c t The primary objective of this paper is to study the interaction between monetary policy, asset prices, and the cost of capital. In particular, we explore this issue in a setting where individuals face idiosyncratic risk. Incomplete information also provides a transactions role for money so that monetary policy can be studied. In contrast to standard monetary growth models which focus on the transmission of monetary policy to the demand for capital goods, we incorporate a separate capital goods sector so that the supply response to monetary policy is taken into account. Consequently, in contrast to the standard monetary growth model, monetary policy plays an important role in investment activity through the relative price of capital goods. Moreover, different sources of productivity can affect the degree of risk sharing. Although the optimal money growth rate falls in response to an increase in productivity in either sector of the economy, monetary policy should react more aggressively to the level of productivity in the capital sector. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction One of the primary responsibilities of central banks is to determine the degree of policy intervention necessary to regulate investment activity in the economy. The neoclassical growth model is the building block for understanding the determinants of real economic activity. In order to address the long-run impact of monetary policy on economic activity, a transactions role for money is introduced through a cash-in-advance constraint or as an argument in the utility function. Such models suggest that money growth is either completely unrelated to economic activity (Sidrauski, 1967) or it acts as a tax on investment (Stockman, 1981). Alternatively, monetary policy may affect economic activity through a Tobin asset substitution channel in which an increase in the rate of money growth generates an increase in investment. Regardless of the direction of policy, standard monetary growth models prescribe transmission channels based entirely on one factor – investment demand. However, would the impact of policy depend on the relative price of capital goods? What about the supply response of the capital sector? This transmission channel does not appear to receive attention in the monetary growth literature. Standard neoclassical growth models with money are based upon a fixed price of capital. That is, the standard neoclassical growth model does not

⇑ Corresponding author. Tel.: +1 (205) 348 8667. 1

E-mail addresses: [email protected] (E.A. Ghossoub), [email protected] (R.R. Reed). Tel.: +1 (210) 458 6322.

http://dx.doi.org/10.1016/j.jmacro.2014.08.004 0164-0704/Ó 2014 Elsevier Inc. All rights reserved.

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differentiate between investment and consumption. Alternatively, the neoclassical growth model – resting on the response of a single infinitely-lived representative agent to the direction of monetary policy – cannot address how monetary policy affects the relative price of investment. (See, for example, Stockman (1981) and Abel (1985)) Yet, in evaluating the impact of policy, it is important to consider conditions in the capital sector. For example, Goolsbee (1998) shows that equipment goods prices respond to fiscal policy initiatives designed to promote investment. Consequently, the relative price of capital should also depend on the stance of monetary policy – a policy channel which cannot be studied in standard neoclassical growth models with money or standard adjustment cost models of investment.2 This paper develops a framework to investigate the relationships between monetary policy, asset prices, and the cost of capital. In particular, the paper emphasizes the role of supply behavior from the capital sector. Specifically, the price of capital goods is determined by constructing a two-sector model with adjustment costs in the production of capital goods. In addition, individuals encounter idiosyncratic liquidity risk. Moreover, incomplete information leads to a transactions role for money so that monetary policy can be studied. As in standard models with adjustment costs in investment, the production of capital goods combines consumption goods and the capital stock currently in place. Notably, higher levels of capital accumulation alleviate frictions from adjustment costs. As the rate of money growth affects the relative price of capital goods, the model generates a number of insights into the optimal design of monetary policy. Since the economy includes two sectors of production, the level of productivity in each sector has important implications for asset pricing and risk sharing. In particular, we study the asymmetric impact of productivity from the capital sector compared to neutral technological change. In this manner, interesting connections between monetary policy and the sources of productivity emerge from our framework because money growth affects the degree of risk sharing. We proceed by providing specific details about our modeling framework. We construct a two-period overlapping generations model in which individuals are born in two geographically separated locations. Within each location, agents have complete information regarding others’ asset holdings. If an individual is forced to relocate, there is no public record-keeping device (see, for example, Kocherlakota (1998)) which allows intermediaries to verify an individual’s asset holdings in the home location and authorize a transfer of goods. Thus, individuals do not have the ability to establish claims to assets.3 Moreover, restrictions on asset portability imply that money must be used to overcome these frictions.4 Therefore, the model introduces money into a Diamond and Dybvig (1983) setting, following Schreft and Smith (1997). In addition to two separate locations, there are two different production sectors: consumer goods and capital. In the capital sector, firms face adjustment costs. The equilibrium price of capital reflects decisions by two different groups of participants in the market for capital. On the supply side, capital producers sell capital in order to maximize profits. On the demand side, intermediaries acquire capital on behalf of depositors. From this perspective, our model builds on ideas from ‘‘supply function theory’’ discussed by Mussa (1977). 1.1. Related literature As a benchmark, one might consider adopting a standard Real Business Cycle type model to study the relationships between monetary policy, capital-embodied productivity, and asset pricing. For example, a separate capital goods sector could be introduced in a framework such as Cooley and Hansen (1989) to study how inflation affects economic activity through the relative price of capital goods. Alternatively, one could introduce a cash-in-advance constraint into Christiano and Fisher (2003). There are two primary reasons for adopting our structure as opposed to the other approaches. The first reason is that we wish to study the effects of monetary policy in a framework which has a meaningful transactions role for money. Standard RBC approaches lack microeconomic foundations that provide a medium of exchange role. Therefore, the transmission mechanisms behind the effects of monetary policy are unclear. By comparison, in our framework, some individuals are ‘anonymous’ in trading. Consequently, privately-issued liabilities do not circulate in trade. Thus, only outside money will be accepted as a means of payment. Second, as articulated by Bencivenga and Smith (1991), an active intermediary sector promotes investment and capital accumulation. Yet, standard RBC approaches omit a role for intermediaries as they focus solely on the behavior of an infinitely-lived representative agent. Because all agents are homogeneous in RBC-type models, there is no role for risk-sharing which is an important function of banking firms (Diamond and Dybvig, 1983). As a result, our framework provides some clear contributions to previous research as conditions in the capital sector affect the ability of intermediaries to provide risk-pooling services. Moreover, monetary policy plays an important role in the degree of risk-sharing in the economy. 2 Standard adjustment cost models do not consider a separate capital goods sector. In this manner, standard adjustment cost models are similar to the standard neoclassical growth model – in both approaches, there is a perfectly elastic supply of the investment good. That is, the transmission of monetary policy to capital accumulation primarily works through investment demand. However, standard adjustment cost models differ from neoclassical growth frameworks since firms must incur internal adjustment costs from converting goods into productive capital. In contrast, our framework identifies an interesting transmission channel for monetary policy through the supply of capital goods and external adjustment costs. (See Mussa (1977) and Chirinko (1993) for an extensive survey of the adjustment costs literature.) Moreover, our framework with multiple production sectors features distinct levels of investment-specific productivity and neutral productivity. 3 There are a few examples of random relocation models in which privately-issued liabilities circulate. See, for example, Azariadis et al. (2001). Also, Bullard and Smith (2003a,b). 4 Similar restrictions on asset portability have been exploited in previous work on monetary economies – for example, Kocherlakota (2003).

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Rather than models aimed at short-run fluctuations, our work is closely related to some important contributions to monetary growth models. Notably, the primary emphasis of our work is to posit a transmission channel for policy through supply behavior in the capital sector. Interestingly, Wang and Yip (1992) also elaborate on a transmission channel for policy through a supply response. However, their focus is on the intensive margin of labor supply rather than our analysis of firms in the capital sector. Our paper complements previous research by Chami et al. (2001) and Baier et al. (2003). They also emphasize that activity in the capital goods market is omitted from standard monetary growth models. By introducing a market for capital goods in a cash-in-advance economy, they find that the effects of an inflation tax are much larger in economies with trade in capital. This result echoes our findings. Yet, our work hinges on the transmission channels of policy through the productive capacity of firms in the capital goods sector – investment and consumption goods are homogeneous in Chami et al. and Baier et al. In particular, our model builds on the framework of Abel (2003). Abel (2003) constructs a general equilibrium framework with overlapping generations in which there are adjustment costs in the capital sector and the price of capital is an equilibrium outcome. However, Abel’s focus is on the role of population demographics for stock prices. As money is not an asset in his economy, he does not address the transmission of monetary policy through the relative price of capital. Depending upon the level of risk aversion in Schreft and Smith models, the transmission of monetary policy to investment varies. Recent evidence by Bullard and Keating (1995) and Ahmed and Rogers (2000) indicates that higher inflation rates in the United States promote economic activity. Given this evidence, we choose to focus on economies in which the level of risk aversion is associated with a Tobin asset substitution channel where inflation raises the cost of holding money and increases capital accumulation.5,6 In particular, in our framework where adjustment costs impede capital formation, monetary policy can play an important role. Due to the inclusion of supply-side factors coming from the capital sector, the effects of monetary policy are stronger than a standard neoclassical growth model. The initial shift from money to investment demand promotes capital accumulation. However, the initial increase in capital accumulation alleviates adjustment costs in the capital sector which further promotes capital accumulation. Nevertheless, deviations from efficient risk-sharing are not warranted unless there is sufficient scope for monetary policy to increase the productive capacity of the capital sector. Therefore, compared to the existing literature, our paper highlights that the impact of monetary policy crucially depends on frictions in the supply-side of the capital sector.7 The paper is organized as follows. In Section 2, we describe the important components of our model. The section also analyzes the behavior of the economy in the steady-state, allowing us to determine long-run responses to permanent changes in economic conditions. Section 3 proceeds to study optimal monetary policy which includes numerical exercises. We offer concluding remarks in Section 4. Technical details are available in Appendix A.

2. The model 2.1. The environment The economy consists of two distinct geographic locations. For example, the locations could be viewed as separate islands. Within each location, there is an infinite sequence of two-period lived overlapping generations, plus an initial group of old individuals. On each island, there are three types of agents: workers, firms, and banks. At the beginning of each date a continuum of ex-ante identical young workers are born with unit mass. Since workers will deposit their earnings at banks, the terms workers and depositors are used interchangeably. There are also two types of firms: capital producers and consumer goods producers. c1h t Depositors only derive utility from consumption (ct ) in old-age. Their preferences are expressed by uðct Þ ¼ 1h , where h 2 ð0; 1Þ is the coefficient of relative risk aversion. Each young individual is endowed with one unit of labor. Since there is no disutility of labor effort, an individual’s labor supply is independent of wages. In contrast, individuals are retired when old. As a result, the total labor supply at each date is equal to the total population mass of young individuals. As noted, there are two types of firms on each island. The first type uses labor (Lt ) and capital (K t ) to produce the economy’s consumption good. (These are the consumer goods producers.) Total output per worker produced in period t is given 

1

by a CES production function of the form, yt ¼ A½aky;t þ ð1  aÞ , with an elasticity of substitution, 1=1  , greater than one. While a is the capital share of total output, ky;t is capital per worker employed in the consumer goods sector. A is an exogenous technology parameter. 5 If individuals have log preferences, long-run economic activity is independent of the rate of money growth. However, there would still be an endogenous relative price of capital depending on the level of productivity in the consumption goods sector, capital goods sector, and frictions from adjustment costs. 6 In a model with logarithmic preferences, Ghossoub and Reed (2010) show that multiple steady-state equilibria exist if the reliance on cash balances depends on the economy’s level of development. In a poor economy, a reverse-Tobin effect emerges while a Tobin effect is observed in the advanced steadystate. 7 The primary lesson from our work is that the central bank should factor in the relative price of capital goods in the determination of monetary policy. For example, in an economy with a Tobin effect from monetary policy, the welfare costs of inflation would not be as high as standard analysis would predict since inflation leads to a lower relative price of capital goods. By comparison, in a cash-in-advance economy such as Stockman (1981), the welfare costs of inflation would be even higher because of an increase in the relative price of capital. At higher rates of money growth, the tax on investment would be higher. Consequently, the demand for capital will decline. The decrease in capital formation contributes to additional adjustment costs. In turn, the adverse consequences of inflation for capital formation would be particularly severe.

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In the capital sector, a capital firm uses the consumption good and capital to produce next period’s capital stock through a Cobb–Douglas production technology: q 1q

ktþ1 ¼ ait kk;t

ð1Þ

where it is the level of investment expenditures. In addition, kk;t is the capital stock used by a capital producer. Following Greenwood et al. (1997, 2000), ‘A’ represents the level of ‘neutral’ productivity while ‘a’ is investment-specific productivity. Notably, it is the amount of the economy’s consumption good used in the production of capital. While the neoclassical growth model is based upon linearity from the consumption input to productive capital, the production technology for capital in our model suffers from concavity from the consumption input.8 Concavity captures that there are increasing resource costs involved in the process of generating productive capital from investment expenditures. That is, there are internal adjustment costs in the capital sector. Consequently, q 2 ½0; 1 reflects the degree of convexity of adjustment costs. (Lower values of q indicate there are increasing marginal costs from generating productive capital. It also implies the convexity of adjustment costs is decreasing in q.) The specification of the production technology for capital is the same as Abel (2001, 2003) who studies the impact of population demographics and fiscal policy on the cost of capital goods.9 The production technology in our framework also retains important features from contributions in the adjustment costs literature such as Lucas and Prescott (1971). Notably, the capital goods technology is the same form as many one-sector adjustment cost models of investment. For example, Lucas and Prescott assume that adjustment costs appear in the evolution of a firm’s capital stock. This is equivalent to assuming that all firms have a non-linear technology for converting consumption goods into capital. However, in our setup, consumer goods producers do not have such a technology. As we explain below, adjustment costs in the capital goods technology are responsible for an upward-sloping supply curve of capital. Thus, our model introduces an endogenous relative price of capital while taking a minimal level of departure from the adjustment costs literature. Inclusion of capital in the production technology captures the idea that adjustment costs depend on the ‘‘relative rate of expansion’’ of capital as opposed to the ‘‘level’’ of expansion (see Gould, 1968). That is, it is reasonable to assume that output in the capital sector depends on the investment-capital ratio rather than the level of investment alone.10 Moreover, inclusion of a second factor in the production of capital with constant returns to scale is consistent with zero excess profits in the capital sector. As will become clear throughout the discussion, in our general equilibrium framework with multiple production sectors, adjustment costs are dispersed across industries. Capital-producing firms incur internal adjustment costs. An equilibrium level of external adjustment costs results from a non-trivial relative price of capital, providing interesting transmission channels for monetary policy. There are two types of assets in this economy: money (fiat currency) and capital. The monetary base per worker is given by M t . Assuming that the price level is common across locations, we refer to Pt as the number of units of currency per unit of consumer goods at time t. Thus, in real terms, the supply of money per worker is mt ¼ Mt =Pt . At the initial date 0, the generation of old depositors at each location is endowed with the aggregate stock K 0 and the initial aggregate money stock M0 > 0. Due to private information, depositors face a trading friction. Each island is characterized by complete information about agents’ asset holdings, but communication across islands is not possible. As a result, individuals do not have the ability to issue private liabilities. Moreover, they are also subject to relocation shocks. The probability of relocation, p, is exogenous, publicly known and is the same across locations.11 As in standard random relocation models, fiat money is the only asset that can be carried across locations. Furthermore, currency is universally recognized and cannot be counterfeited – therefore, it is accepted in both locations. In this manner, money facilitates transactions made difficult by spatial separation and limited communication. Since money is the only asset that can cross locations, depositors who learn they will be relocated will liquidate all their asset holdings into currency. Random relocation thus plays the same role that liquidity preference shocks perform in Diamond and Dybvig (1983). As banks provide insurance against the shocks, each young depositor will put all of her income in the bank rather than holding assets directly. In addition to depositors, there is a monetary authority that follows a constant money growth rule. In particular, the money stock evolves according to M tþ1 ¼ rM t , where r > 1 is the gross growth rate in the money supply. Equivalently, in t t in which PPtþ1 is the gross real return to money. In every respect, economic conditions are the same real terms: mtþ1 ¼ rmt PPtþ1 on each island. Consequently, we focus on activity within a representative island. 8 Greenwood et al. (1997, 2000) also study an economy with a separate capital goods sector. Following the neoclassical growth framework, production in the capital sector is linear in the consumption input. However, the position of the perfectly elastic supply of capital depends on investment-specific productivity. 9 See also Basu (1987). 10 Christiano and Fisher (2003) serves as a recent exception. In contrast to the investment-capital ratio, adjustment costs are increasing in the ratio of current investment to previous investment. 11 If relocation is deterministic, asset holdings will be independent of inflation and the return to capital.

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At this juncture, we describe the timing of events at each date. Within each period, activity begins with trade in factor markets and production across firms. Afterwards, the process of intermediation takes place. Additional details are provided immediately below. At the beginning of each date, a new generation of individuals is born. Banks also receive the capital they ordered from the previous period. Workers and banks (from their capital holdings) provide services for production. In turn, workers receive wages and banks obtain their rental earnings. Banks pay returns to non-movers from their capital income. Workers follow by depositing labor earnings at banks. The process of intermediation continues as banks acquire assets on behalf of their depositors. First, old movers show up at banks to exchange their holdings of money for consumption goods. Banks accept these money balances from the old so they can insure depositors against relocation shocks. Thus, intermediaries facilitate intergenerational trade. Banks obtain additional money balances by trading with the central bank. Specifically, the central bank injects additional currency into the banking system based upon its money growth rule. With their remaining deposit income, banks place orders for new capital.12 Finally, depositors learn their location status for the following period. Individuals who will transact in the foreign location liquidate their deposits to obtain cash. The period ends after relocation takes place. 2.2. Trade 2.2.1. The capital sector In the economy, there are two markets for capital goods: a primary market in which banks purchase capital goods from capital producers and a rental market in which banks rent their capital to capital producers and consumer goods producers. In the primary market, supply from capital producers and demand by banks determine the market price of new capital goods, Pk;t . Following the jargon of Tobin’s Q, the equilibrium replacement cost of capital is the equilibrium price in the primary market. In the rental market, supply from banks and demand by firms determine the rental cost, r t . Since there are two markets for capital, equilibrium in each market determines each component of Q.13 Following numerous papers on Q-theory, we interpret that the numerator of Q provides information about stock prices in the economy. Standard analysis treats the behavior of stock prices and the price of capital goods independently – however, as we emphasize below, the price of capital goods will respond to changes in investment behavior. Therefore, asset pricing models should jointly determine stock prices along with the price of capital goods. Production by capital producers determines the supply of capital in the primary market. A typical capital producer solves the following:

Max Pk;t ktþ1  r t kk;t  it kk;t ;it

ð2Þ

q 1q

subject to ktþ1 ¼ ait kk;t . The marginal revenue from renting an additional unit of capital is equal to the increase in revenue tþ1 generated from production of new capital goods, P k;t @k . Marginal cost is simply the rental rate paid to banks. Profit-max@kk;t imization implies:

rt ¼ Pk;t

 q @ktþ1 it ¼ ð1  qÞaPk;t @kk;t kk;t

ð3Þ

From the production technology, the (rental) demand for capital can be expressed in terms of the rental rate, the price of new capital goods, and level of output:

kk;t ¼ ð1  qÞ



rt Pk;t

1

ktþ1

ð4Þ

As the rental cost of capital rises, the demand for capital by a capital producer falls. In turn, the real marginal cost is the rental cost deflated by its purchase price, Prt . Moreover, as ð1  qÞ reflects the ability of capital to lower adjustment costs, the k;t demand for capital will be higher if q is lower (that is, there is more curvature in the adjustment cost technology). Similarly, each capital producer chooses the amount of investment such that the marginal revenue from investment is equal to its marginal cost. Marginal revenue is the value of capital produced with one additional unit of the consumption good, Pk;t @k@itþ1 . However, the marginal cost of investment is equal to one unit of goods. Therefore, t

 1q 1 @ktþ1 kk;t ¼ ¼ aq Pk;t @it it

ð5Þ

12 In overlapping generations models, it is important to limit the redistributive aspects of monetary policy. For example, redistribution of seigniorage revenues alone can lead to suboptimality of the Friedman Rule. To avoid this problem, we follow Huybens and Smith (1999) and Ghossoub and Reed (2010) in which the central bank retains all of its seigniorage revenues. In this manner, monetary policy affects activity through the return to money. 13 In standard Q-theory models of investment, the market value of a firm’s existing capital stock is equal to its discounted flow of revenues. In our general equilibrium overlapping generations framework, capital depreciates completely each period. Hence, total income from capital is equal to rental income. As our focus is on activity in the steady-state, there is little distinction between a firm’s flow of revenue and it’s total discounted flow.

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The level of investment depends on the price of new capital and scale of output:

it ¼ qPk;t ktþ1

ð6Þ

The marginal rate of technical substitution between investment and capital inputs generates the following ‘no-arbitrage’ condition:

Pk;t ¼

q r1 t

ð7Þ

ð1  qÞð1qÞ aqq

When this condition is satisfied, a capital producer is indifferent between renting an additional unit of capital and utilizing the consumption input in the production of new equipment. Notably, this condition reduces to a relationship between the purchase price of capital and its rental cost. As a result, the rental cost of capital is positively related to the replacement cost of capital. In summary, activity among capital producers is important for two reasons. First, capital producers determine supply in the primary market. Second, rental demand for capital by capital producers (along with demand by consumer goods producers) affects the equilibrium rental cost. Thus, it is convenient to express the supply of a capital producer in terms of their rental demand. Capital output (1) and investment decisions (5) yield: 1

S

q

q

q ktþ1 ¼ a1q ðqÞ1q P1 k;t kk;t

ð8Þ

Clearly, the supply of capital is positively related to its price (Pk;t ) – this reflects the profit-maximizing amount of investment expenditures. It is also increasing in the quantity of capital (kk;t ) it seeks to rent. Finally, output is higher if investment-specific productivity is higher. 2.2.2. The consumer goods sector In contrast to the capital sector, the price of consumer goods is normalized to one. The wage rate is given by wt . Profit maximization among consumer goods producers generates factor demands in terms of input costs (without the scale of production):

h i1   wt ¼ Að1  aÞ aky;t þ ð1  aÞ ;

h i1  1  r t ¼ Aaky;t aky;t þ ð1  aÞ

ð9Þ

2.2.3. A representative bank’s problem Banks compete for deposits by offering different interest rate schedules. In turn, a worker will deposit funds with a bank that offers the highest expected utility. As a result of the Bertrand competition over interest rates in the deposit market, banks choose portfolios to maximize the expected utility of each depositor. That is, the deposit market is effectively perfectly competitive. Moreover, since financial intermediaries reduce depositors’ consumption variability, each of them chooses to n deposit all of their income. The bank promises real return rm t if relocation will occur and r t if not. As of period t, a bank determines the amount of capital to acquire. Orders placed in period t are filled in period t þ 1. The bank’s balance sheet is expressed by:

mt þ Pk;t ktþ1 6 wt ;

tP0

ð10Þ

Announced deposit returns must satisfy the following constraints. First, since currency is the only asset that can be transported across locations, relocated agents will choose to liquidate their asset holdings into currency. Depending on the bank’s money holdings and the inflation rate, the return to movers satisfies14:

prmt wt 6 mt

Pt Ptþ1

ð11Þ

In addition, we choose to study equilibria in which money is dominated in rate of return. After individuals learn that they will be relocated in period t þ 1, they liquidate their savings to acquire money balances. Thus, it is the current generation of young movers who hold money balances across time periods. As money is dominated in rate of return by capital, banks do not have any incentive to carry money balances between periods t and t þ 1. Instead, the bank’s total payments to non-movers derive from its capital earnings:

ð1  pÞr nt wt 6 r tþ1 ktþ1

ð12Þ

Thus, each bank solves:

 Max

mt ;ktþ1

p

1h  n 1h rm r wt t wt þ ð1  pÞ t 1h 1h

ð13Þ

14 The returns are based on the deposits provided by the current generation of workers. As the returns are promised at date t, the rates of return are also listed as of date t. However, consumption takes place in the following period.

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subject to (10)–(12). The bank’s demand for capital is: D

ktþ1 ¼

1 Pk;t

1 

1 þ 1pp Q t PPtþ1 t

wt ð1hÞ h

ð14Þ D

where Q t  rPtþ1 . As the return to capital (Q t ) is higher, total spending (Pk;t ktþ1 ) on capital goods by banks will be higher. In k;t turn, the demand for capital will be lower if its purchase price is higher. Moreover, demand will be higher if wages are higher. Due to higher earnings, bank deposits will be higher which contributes to additional capital expenditures. The bank’s money balances are equal to deposit income net of payments for capital:

mt ¼

wt  1h h 1 þ 1pp Q t PPtþ1 t

ð15Þ

t Equivalently, define ct ¼ m to be the fraction of deposits allocated to cash reserves. As in standard models with money, the wt demand for cash reserves declines when its return falls. Finally, the returns to deposits for movers and non-movers are:



rm t







ct Q t ; PPtþ1t Pt 1  ct Q t ; PPtþ1 t ¼ ; r nt ¼ Qt 1p p Ptþ1

ð16Þ

Depositors receive a low amount of insurance against liquidity risk when the return to capital is high. 2.3. Steady-state equilibrium We now combine the results of the preceding section and characterize the steady-state, general equilibrium for the economy. In equilibrium, labor earns its marginal product, (9), and the market clears: L ¼ 1. In the primary market, capital producers choose supply: q

q

1

S

q kF ðP k Þ ¼ a1q ðqÞ1q P1 k kk

ð17Þ

In contrast, the demand for capital by banks is: D

kB ðP k Þ ¼

1 Pk

1 

wðky Þ h1 h

ð18Þ

1 þ 1pp Pr r k



S

D

An equilibrium in the primary market is a pair (P k ; k ) in which kF ðPk Þ ¼ kB ðP k Þ. Consequently, given activity in other sectors  of the economy, k and Pk are pinned down. In the rental market, the supply of capital by banks is: S

kB ðrÞ ¼

1 Pk

1 þ 1pp

1 

r Pk

r

  w ky h1 h

ð19Þ

As the (rental) market value of capital is higher, banks will acquire more capital to take advantage of its returns. The rental demand by consumer goods producers is: 1

ð1  aÞ ky ðr Þ ¼  1  r 1  a Aa

ð20Þ

In contrast to the consumer goods sector, rental demand in the capital sector is written in terms of the scale of output, k:

kk ðr Þ ¼

  ð1  qÞPk k r

ð21Þ

Finally, in addition to rental demand, the behavior of capital producers is reflected by the no-arbitrage condition. It is also used to obtain an expression for Q:

Pk ¼

r 1q ð1  qÞð1qÞ aqq

;

Q¼

r ¼ ð1  qÞð1qÞ aqq r q Pk

ð22Þ

As we will discuss below, our representation of activity in the steady-state allows us to draw a number of insights. Since it involves five endogenous variables (w; P k ; r; kk , ky ), the five variable system renders it difficult to prove existence of steadystate equilibrium. Notably, as our framework provides a general equilibrium perspective on Tobin’s Q and investment, we choose to reduce the system to two variables: Q (the return to capital) and k. This is achieved by reducing the system to the behavior of the primary market for capital in the steady-state. In this manner, the supply of capital by capital goods producers and demand by banks jointly determine the steady-state value of Q and k. We start with the supply of capital.

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2.3.1. The supply of capital We begin with the observation that kk ðrÞ þ ky ðrÞ ¼ k. Substituting Pk and Q (from (9), (20) and (22)) into (17): S

1a1

kF ðQ Þ ¼ 

a

1



Q q1  1 w1 a1

1 1 1  ð1Q qÞ 1

ð23Þ

 q ð1qÞ 1 1 where w ¼ ð1  qÞ q aq qA. Note that if Q exceeds a w and ð1  qÞ, then the supply of capital is positive. Moreover, as Q  Pr , higher relative values of the rental cost imply that capital producing firms will rent less capital from banks. In turn, k the supply of capital will be lower as the real rental cost of capital is higher. 2.3.2. The demand for capital From the no-arbitrage condition in the capital goods sector, labor demand in the consumer goods sector, and portfolio choices by banks, the demand for capital by banks is: D

kB ðQ Þ ¼

 1 1  a  ð1  cðQ; rÞÞQ  1 1  a Q q1  1  1

ð24Þ

w1 a1

 q 1 As in the case of the supply function, the demand for capital will be positive if Q > a w . A change in the rate of return to capital affects its demand in a number of ways. First, for a given amount of bank deposits, a higher return to capital raises the cost of holding cash reserves, which encourages banks to allocate more resources towards capital investment. We refer to this channel as the asset substitution effect of Q. However, Q has an additional effect through its impact on bank deposits. If Q is higher, consumer goods producing firms choose to rent less capital. Due to the complementarity between labor and capital, wages will be lower. This causes deposits to fall, decreasing asset demand by banks. This is the deposit effect of Q. If the asset substitution effect dominates the deposit effect, the bank’s demand for capital is increasing in Q. Interestingly, as we demonstrate in Appendix A, the deposit effect dominates the asset substitution effect. Therefore, if Q is higher, the demand for capital is lower. 0 1  ð1 Þ 1 1 1 @  Proposition 1. Let r0 be such that  þ 1A a wrq0 ¼ 1. A steady-state exists and is unique iff r P r0 . 1 r0 ð1qÞ ð1pÞ

Following the discussion in Appendix A, we show a unique steady-state exists in which money is dominated in rate of return. Specifically, for values of Q in which supply and demand is non-negative, there is a unique value of Q where the primary market clears. We refer to this value as Q  . The only remaining issue is whether or not the market clearing value of Q dominates the return to money. For a given set of parameters, consider a rate of money growth, r0 , in which Q  ¼ r10 . For r P r0 , there is a unique value of Q  which satisfies both requirements for a monetary equilibrium. Hereafter, we denote the steady-state values of all variables with the same superscript as Q  . Though Proposition 1 provides conditions for existence and uniqueness of a steady-state based upon Tobin’s Q, recursive substitution allows us to reduce discussion of existence and uniqueness to simple supply and demand curves. (Details provided in Appendix A.) As one would expect, the demand for capital by financial intermediaries is decreasing in the price of capital. Thus, the demand curve is downward-sloping in its price. The supply curve is upward-sloping. The supply curve of capital producers also depends on the aggregate stock of capital. In economies with a higher overall amount of capital accumulation, adjustment costs in the capital sector will be lower.15 We proceed to determine the effects of monetary policy on Q⁄ and investment behavior. Interestingly, the model produces important transmission channels for monetary policy through the relative price of capital. 



dP







Proposition 2. Under the condition in Proposition 1, di and dk are positive. Moreover, drk ; dr , and dQ are negative. dr dr dr dr Since inflation leads to an increase in investment in the steady-state, our results are consistent with Bullard and Keating (1995) and Ahmed and Rogers (2000) who find evidence of a long-run Tobin effect in the United States. Moreover, as inflation is associated with a lower rental rate, inflation drives down the market value of capital. This coincides with Fama and Schwert (1977) who find that stock returns are negatively related to expected inflation.16 As we explain below, the transmission channel of monetary policy in our framework stands apart from Tobin (1965). To gauge the impact of monetary policy in our framework relative to the existing literature, suppose that an equilibrium in the primary market for capital occurs at a relative price equal to one (the exogenous relative price of capital in the

15 As previously mentioned, the specification of adjustment costs in the capital goods sector is a special case of Lucas and Prescott (1971). Moreover, the specification of the production function is the same as Abel (2001, 2003). Both study the behavior of the capital stock in the long-run. 16 Gultekin (1983) does not find any relationship between nominal stock returns and expected inflation. This also implies that higher expected inflation rates cause real equity returns to decline.

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neoclassical growth model). An increase in the rate of money growth lowers the return to money and triggers an increase in investment demand. Therefore, the increase in capital accumulation that would occur through the conventional Tobin asset substitution story is represented by the horizontal movement of the economy’s demand curve for capital. However, in our framework, the overall impact of monetary policy critically depends on the supply response of the capital sector. As Proposition 2 demonstrates, the relative price of capital goods will, in fact, fall in response to the increased rate of money growth. Thus, inflation has a significant impact on relative prices in the economy – a policy channel which cannot be studied in standard neoclassical growth models with money or standard one-sector adjustment cost models of investment. Despite the increased demand for capital at a higher inflation rate, the lower relative price of capital implies that the supply curve for capital would be sensitive to the increased availability of capital. That is, the outward shift of the supply curve must exceed the outward shift of the demand curve. Consequently, there is room for monetary policy to play an important role in capital formation by reducing the severity of frictions from adjustment costs. Since the shift of the supply curve exceeds the shift of the demand curve, our model demonstrates that the impact of policy through the supply of capital may be much more important than the conventional Tobin asset substitution story would suggest. Obviously, the strength of this transmission channel depends on the level of productivity in the capital sector. Proposition 4 shows that the ability of the central bank to promote the supply of capital plays an important role in the determination of optimal monetary policy. Monetary policy also has an important impact on activity through the degree of risk sharing. By lowering the return to money, individuals who experience liquidity shocks will suffer a consumption loss relative to depositors who derive income from capital earnings. Moreover, the distortion is arguably more severe in our framework compared to standard models with liquidity risk. This occurs since the relative price of capital depends on money growth while it is fixed in neoclassical growth frameworks. As the price of capital goods is lower in higher inflation economies, the return to capital will not fall as much as economies with a fixed price of capital. Thus, the consumption disparity in our model would be higher. We proceed to study how changes in productivity affect asset prices and risk sharing. As previously mentioned, the numerator of Q provides information about the behavior of stock prices in the economy. In particular, stock prices can change over time due to changes in productivity.17 In addition, Greenwood et al. (2000) document that there is significant variation in the price of capital goods over time. They attribute the behavior of equipment prices to supply-side variation in the capital sector – ‘investment-specific’ productivity. However, it seems naive to view that stock prices and capital goods prices are unrelated. Since the behavior of stock prices will not perfectly mimic the behavior of equipment prices, a satisfactory model of asset pricing should be based upon a framework with distinct levels of neutral productivity and capital sector productivity. Our framework provides an important contribution to the asset pricing literature since it is possible to study how both sources of productivity affect the price of capital goods, stock prices, and the extent of risk sharing. The following Proposition characterizes the impact of productivity across sectors on asset prices and the return to capital: Proposition 3. Under the condition in Proposition 1, 

dQ da





dP k dA

and



dr dA

are positive. In contrast,



dPk da

and



dr da

are negative. Moreover,

> dQ if q < Aa. dA The results in Proposition 3 are intuitive. An increase in neutral productivity stimulates deposits and investment in the economy. Therefore, it raises the market value of capital. Since the demand for capital is higher, the rental costs of capital and the price of new capital are also higher. In addition, rental costs increase more than the price of new equipment. In turn, the return to capital will be higher under higher levels of neutral productivity. That is, the demand-induced impact of neutral productivity dominates any indirect effects from increased capital accumulation. Under a higher return to capital, banks allocate a smaller fraction of their deposits to cash reserves. This is another example of the asset substitution effect of Q on investment activity. We obtain analogous predictions for investment-specific technological change. Proposition 3 makes a very important point – failing to consider how the price of capital goods responds to economic conditions would likely over-state the impact of productivity on stock prices.18 Moreover, Cochrane (1991) observes that estimates of (internal) adjustment costs in empirical applications of Q-theory based asset pricing models seem excessive – this highlights the need to incorporate the price of capital goods in models of stock prices and investment.19 Further, inferences regarding risk sharing would be incorrect.20 For example, suppose that there is a permanent change in the level of neutral productivity. Standard models with fixed prices would predict a large surge in investment because they do not take into account that the relative price of capital will

17 In a valuable contribution, Abel and Blanchard (1986) construct a lengthy time series for marginal q. In their analysis, they conclude that there is important variation in marginal profitability over time. 18 Abel (2001, 2003) constructs a general equilibrium overlapping generations model in which the price of capital is an equilibrium outcome. Yet, in his setup, the long-run supply of capital is perfectly elastic, similar to the neoclassical growth tradition. 19 Recent work by Christiano and Fisher (2003) explicitly focuses on the relationship between the price of capital goods and stock prices over the business cycle. In contrast to the standard neoclassical growth model, limited sectoral factor mobility produces a vertical supply curve for capital. By comparison, internal adjustment costs in the capital sector contribute to interesting relative prices in our model. While they study short-run activity, we investigate the long-run behavior of stock prices and capital goods. In addition, we do so in a monetary economy. 20 In Greenwood et al. (1997, 2000), both neutral and capital-embodied productivity shocks occur. However, they study a representative agents, infinitehorizon economy. Consequently, idioyncratic shocks do not take place and there is no role for risk-sharing between groups of individuals.

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increase



dPk dA

 > 0 . As such a model would lead to an upward-bias for capital accumulation, the behavior of stock prices

would exhibit excess sensitivity. Similar arguments apply to investment-specific productivity. The proposition also demonstrates that conditions in the capital sector will be important for the degree of risk sharing. Notably, if adjustment costs are sufficiently convex, investment-specific productivity distorts risk sharing more than neutral productivity. As we demonstrate in the following section, this observation generates a number of insights into the design of optimal monetary policy. 3. Optimal monetary policy In neoclassical growth models with money, it is fairly transparent that the Friedman Rule is the optimal policy. Yet, our framework differs in significant ways. First, there are multiple production sectors with distinct levels of productivity. Moreover, the economy suffers from the friction of adjustment costs. We ask the following: (1) How is the optimality of the Friedman Rule tied to conditions in the capital sector of the economy? (2) How should monetary policy be designed according to the sources of productivity in the economy? We assume that the monetary authority chooses the rate of money growth to maximize the expected utility of a representative generation of depositors:

h

X ¼ pðr m Þ1h þ ð1  pÞðr n Þ1h

i wk 1h y

ð25Þ

1h

Through recursive substitution, the welfare function can be written as:

0

Þ 1hð1 



1 B Q qð1Þ C XðQ Þ ¼ @ ð1 Þ  1A k a1 w 1hÞ where k  ðð1 pÞh



1

a w 1 Að1aÞ 

1h

ðQ  ð1  qÞÞh Q

ð1hÞð1þqÞ

q

ð26Þ

.

In the following Proposition, we provide conditions regarding optimality of the Friedman Rule. In particular, there may be room for a welfare departure from the Friedman Rule if the central bank can aggressively promote the productive capacity of the capital sector: Proposition 4. Suppose h P 1  . Under this condition, the Friedman Rule is optimal. In contrast, suppose h < 1  . Under this condition, the Friedman Rule is optimal if a 6 a0 . By comparison, the Friedman Rule is suboptimal if a > a0 . Although the Friedman Rule provides full insurance against liquidity risk, the Friedman Rule may lead to an excessively high cost of investment.21 Notably, in our model, monetary policy could alleviate frictions from adjustment costs. Consequently, in our framework, the optimal money growth rate balances two important frictions. On the one hand, there is a distortionary impact of inflation from lower risk-sharing. On the other, higher rates of inflation could stimulate capital investment and lower frictions from adjustment costs. These arguments regarding optimal monetary policy are distinct from standard Tobin effect logic in overlapping generations models such as Weiss (1980) – standard Tobin effect arguments do not consider how policy affects the relative price of capital goods. In particular, in our framework, it is critical that policy can promote the productive capacity of the capital sector. Alternatively, as the level of adjustment costs is inversely related to productivity in the capital sector, it is critical that the central bank has the ability to relieve frictions from adjustment costs. If investment-specific productivity is low, the increase in capital formation would not be sufficient to justify deviating from efficient risk-sharing. Yet, if productivity in the capital sector is sufficiently strong, then the Friedman Rule is suboptimal. Therefore, the optimal design of monetary policy crucially depends on conditions in the capital sector of the economy. While Proposition 4 highlights how optimal monetary policy depends on the level of adjustment costs in the capital sector, analysis of a special case provides insight into the role of policy depending on the convexity of adjustment costs. In an economy with a Cobb–Douglas production technology in the consumer goods sector, the resulting degree of tractability allows us to obtain the following:  a q 1a  1a ^ , where q ^ : ð1hÞ Lemma 1. Suppose that yt ¼ Aky;t . The Friedman Rule is optimal if q P q a hð1  qÞð1  pÞ a þ 1 ¼ 1 and q^ < 1 as long as h > 1  1a a. In contrast, the Friedman Rule is suboptimal if q < q^ . Interestingly, Lemma 1 demonstrates that optimal monetary policy focuses exclusively on risk-sharing if there are sufficiently low marginal costs from investment. That is, the Lemma indicates that the monetary authority should follow the Friedman Rule if marginal costs are relatively low. Notably, in the case where q ¼ 1, the production technology is the same 21 Ghossoub and Reed (2010) demonstrate that strategic complementarities occur if the incidence of liquidity risk depends on the economy’s aggregate capital stock. Such coordination failures lead to the possibility of multiple steady-state equilibria in which the effects of monetary policy vary.

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221

as Greenwood et al. (1997) with complete depreciation of physical capital. In such a setting, the Friedman Rule is always the optimal policy. Thus, adjustment costs are important for suboptimality of the Friedman Rule. We proceed to study optimal monetary policy under different degrees of technical change: Proposition 5. Suppose that the conditions in Proposition 3 hold. Also, let a 6 a0 . Then, ddar^ and ddAr^ are both negative. However, dr^  dr^    >  . da dA As previously noted, advances in neutral productivity and investment-specific productivity cause the return to capital to rise. For a given money growth rate, this leads to less risk sharing. Since agents are risk averse, the optimal monetary policy seeks to smooth agents’ consumption across income states. Therefore, in response to either source of productivity growth, monetary policy should provide more insurance against liquidity risk. This occurs by pursuing lower rates of money growth in order to raise the rate of return to money. By Proposition 3, investment-specific productivity generates much higher equity returns. Consequently, capital-embodied productivity further distorts risk-sharing. In this manner, optimal policy should react more aggressively to investment-specific productivity.22 Therefore, monetary policy should be designed according to the sources of productivity in the economy. Inferences based solely on TFP would be misleading. For example, estimates from Greenwood et al. (1997) indicate that TFP continued to decline in the 1980s from its levels in the 1970s. This suggests that inflation rates should have continued to increase in the 1980s. However, inflation rates fell. In comparison to TFP, investment-specific productivity accelerated during the 1980s – at the end of the decade, investment-specific productivity was around twice as high as it was at the beginning. Based upon Proposition 5, inflation should fall in order to promote risk-sharing. This casts doubt on the ability of standard neoclassical growth models to provide insights into the monetary experiences of many countries. 3.1. Numerical analysis The preceding work demonstrates that the convexity of adjustment costs and the level of investment specific productivity should be important factors in the determination of optimal monetary policy. For example, Lemma 1 shows that the optimal policy is the Friedman Rule if adjustment costs in the capital goods sector are not too high. Furthermore, Proposition 4 provides conditions in which the Friedman Rule is suboptimal. However, this only applies if productivity in the capital sector is sufficiently high. If not, the increase in capital formation resulting from higher inflation would not be sufficient to justify deviating from complete risk-sharing. Proposition 5 demonstrates that the optimal money growth rate is lower as investment-specific productivity increases. In order to provide guidance for policymakers, we construct a set of numerical examples which are intended to match recent observations on capital formation and monetary policy in the United States. As a simple benchmark, we assume that the production function in the consumer goods sector is of the Cobb–Douglas form defined in Lemma 1. As is standard, the capital share of total output is set to a ¼ :33. Projections from the Nilson Report (1997) suggested that the dollar volume of payments by consumers in the United States would be around 14% during the past decade. However, other studies indicate that about 27% of purchases are made with cash.23 Thus, as an average, we assume that p ¼ :2. Next, in order for money to be associated with a long-run Tobin effect in the United States as observed by both Bullard and Keating (1995) and Ahmed and Rogers (2000), we require that h < 1. Estimates of the coefficient of relative risk aversion across studies widely vary. Notably, Mehra and Prescott (1985) observe that values anywhere from 0 up to 10 are plausible. In more recent work, Gandelman and Hernandez-Murillo (2014) also cite a wide range of estimates between 0.2 and 10. Again, the coefficient must be less than one in order for the conclusions of the model to line up with Bullard and Keating (1995) and Ahmed and Rogers (2000). Thus, the range of estimates from the literature that line up with the predictions of the model range from 0.2 to 1. Therefore, we consider that h lies in the middle of the range at h ¼ :6. We proceed to explain our choices for the values of q; a, and A. For the parameter values highlighted above, we calibrate the degree of convexity of adjustment costs, q, and different levels of productivity, a and A, to match the average levels of real GDP, capital formation as a percentage of GDP, and the inflation rate in the United States between 1960 and 2011. In particular, the source of data on capital formation comes from the World Bank’s World Development Indicators. During this time period, the average value of capital formation stands at 19.8%.24 In addition, it peaked near 25.1% in 1985 and dropped to about 17.5% in 2009. The average level of real output (in 2005 dollars) was $7.74 trillion and the average inflation rate (as measured by the GDP deflator) was equal to 3.54%. The numerical values for the parameters (q; a, and A) are simultaneously chosen to match the three long-run averages. We impose that the optimal money growth rate was equal to the average inflation rate over the timeframe. The calibrated values are such that q ¼ :65; a ¼ :988, and A ¼ 7:8. Since we begin with the Cobb–Douglas case, Lemma 1 demonstrates that optimal monetary policy only depends on the curvature of adjustment costs. Thus, the first set of numerical exercises focuses solely on the relationship between convexity of adjustment in the capital sector (q) and the optimal money growth rate. Again, the calibrated value of q is equal to 0.65

22 In contrast to this paper, Reed and Waller (2006) study an endowment economy which includes both idiosyncratic and aggregate income risk. It is possible to achieve efficient risk sharing in the low aggregate state, but not the high state. 23 See ‘‘Cash Dying as Credit Card Payments Predicted to Grow in Volume: Report.’’ Catherine New, Huffington Post, June 7, 2012. 24 This variable is only available from 1965 to 2011.

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which indicates that adjustment costs are relatively convex. Table 1 presents numerical calculations for the optimal money growth rate along with other variables under different degrees of adjustment costs (q). Starting from the calibrated value of q, we find that the optimal rate of money growth increases as the convexity of adjustment costs is weaker. In fact, the results in Table 1 indicate that the Friedman Rule is the optimal monetary policy. Moreover, the results suggest that the optimal money growth is positive (and inflationary) as long as Tobin’s Q is lower than 1. As q increases to .75, the price of capital falls and capital as a percentage of GDP just passes its peak of 25% reported in the data from the World Bank. In contrast, as adjustment costs become more convex (q falls), the return to capital increases and the Friedman Rule resorts to its standard deflationary position. Yet, if adjustment costs are sufficiently high (q < :15), capital formation is very low and the price of capital goods is significant at the Friedman Rule. This renders the Friedman Rule to be suboptimal and the monetary authority would respond with significant money growth. However, as can observed from the k=y ratio and the estimated value of real GDP, the level of economic activity would be so low that suboptimality of the Friedman Rule does not appear to be empirically plausible. That is, though there is a theoretical case for departure from the Friedman Rule, the Friedman Rule it is quite robust in practice. This does not imply that optimal monetary policy is invariant to conditions in the capital sector – in order to achieve the Friedman Rule, the monetary authority would need to adjust the money growth rate to the severity of adjustment costs. While the Cobb–Douglas case provides insights regarding the relationship between the convexity of adjustment costs and monetary policy, it cannot shed light on how optimal monetary policy depends on the level of productivity in the capital sector. This is obviously important as Greenwood et al. (1997) document that there have been extended periods where investment-specific productivity surged while TFP declined. Therefore, we proceed by calibrating the production function to empirical studies rather than simply imposing that the production function is Cobb–Douglas. Under a general CES production function,  can vary significantly from zero. Using a panel of 75 countries, Duffy et al. (2004) estimate the degree of substitutability between capital and labor and find that it ranges from 0.2 to 0.8. In this manner, we consider three different examples with different values of ;  ¼ f0:2; 0:5; 0:8g. We recalibrate the other parameters using the previous approach. In Table 2, we illustrate the case where  ¼ :2. Given that h ¼ :6; h < 1  . By Proposition 4, the optimality of the Friedman Rule should depend on the level of productivity in the capital goods sector. To begin, the parametrized values of q; A, and a are respectively, 0:646; 7:814, and 0.99. The values for each endogenous variable corresponding to an optimal rate of money growth of 3.54% are presented in the second column of Table 2. The results in Table 2 confirm our findings in Propositions 4 and 5. First, at low levels of productivity in the capital sector, the Friedman Rule is optimal. As in Table 1, the Friedman Rule may actually be inflationary if Tobin’s Q lies below 1. The relatively low level of capital-embodied productivity contributes to a relatively high cost of capital goods which renders Q to be low. In order to achieve efficient risk-sharing, the optimal rate of money growth is positive. However, as the capital sector becomes more productive, it is optimal to restrict the rate of money growth in order to offset the impact of higher returns to capital (Q) which interrupts risk sharing. If the capital sector becomes too productive, the Friedman Rule is no longer the optimal policy. The Table shows that a departure from the Friedman Rule (at a ¼ 42) to the long-run average inflation rate of 3.54% would lead to an increase in welfare. Nevertheless, as in Table 1, the case for such a departure does not appear to be empirically reasonable. Consequently, policymakers should pay the most attention to our result that the Friedman Rule is optimal and that the rate of money growth to achieve the Friedman Rule depends on the level of investment-specific productivity. In Tables 3 and 4, we consider cases where  ¼ :5 and  ¼ :8, respectively. In this manner, the parameter space is such that h > 1   and the Friedman Rule is the optimal policy by Proposition 4. For both cases, the parametrized values for A and q that correspond to an optimal inflation rate of 3.54% are respectively 7.86, and 0.63. In addition, a ¼ 1:01 when  ¼ :5 compared to a ¼ 1:05, when  ¼ :8. Table 1 Optimal monetary policy and convexity of adjustment costs.

q

0.1

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

r

1.8287 1.4566 1249.2 857.6 2.6637 0.1151 0.0002 0.0001 0.0003 0.0286 0.3708 0.07 5.1186 0.2484 1.5670

0.6598 1.5157 1858.5 1226.2 1.0000 0.2000 0.0001 0.0001 0.0001 0.0409 0.3049 0.04 1.0000 0.2043 1.5641

0.6823 1.4657 231.8 158.1 1.0000 0.2000 0.0017 0.0012 0.0029 0.1139 0.8500 0.34 1.0001 0.5695 2.3257

0.7064 1.4157 73.6 52.0 1.0000 0.2000 0.0087 0.0067 0.0154 0.2004 1.4952 1.03 1.0000 1.0018 2.8750

0.7322 1.3657 34.6 25.3 1.0000 0.2000 0.0252 0.0207 0.0459 0.2907 2.1697 2.12 1.0000 1.4537 3.2890

0.7601 1.3157 19.9 15.1 1.0000 0.2000 0.0538 0.0473 0.1010 0.3818 2.8492 3.55 1.0000 1.9089 3.6134

0.7901 1.2657 12.9 10.2 1.0000 0.2000 0.0953 0.0903 0.1856 0.4726 3.5270 5.26 1.0000 2.3631 3.8749

0.8226 1.2157 9.0 7.4 1.0000 0.2000 0.1498 0.1537 0.3034 0.5633 4.2039 7.22 1.0000 2.8166 4.0903

0.8579 1.1657 6.7 5.7 1.0000 0.2000 0.2162 0.2420 0.4581 0.6544 4.8835 9.38 1.0000 3.2719 4.2706

0.8963 1.1157 5.1 4.6 1.0000 0.2000 0.2928 0.3606 0.6534 0.7465 5.5706 11.73 1.0000 3.7323 4.4233

0.9384 1.0657 4.0 3.8 1.0000 0.2000 0.3774 0.5163 0.8937 0.8403 6.2713 14.25 1.0000 4.2017 4.5537

0.9846 1.0157 3.2 3.2 1.0000 0.2000 0.4665 0.7181 1.1846 0.9370 6.9924 16.94 1.0000 4.6849 4.6658

1.0354 0.9658 2.6 2.7 1.0000 0.2000 0.5556 0.9769 1.5325 1.0372 7.7400 19.80 1.0000 5.1858 4.7624

1.0921 0.9157 2.1 2.3 1.0000 0.2000 0.6391 1.3116 1.9507 1.1431 8.5302 22.87 1.0000 5.7153 4.8467

1.1552 0.8657 1.8 2.0 1.0000 0.2000 0.7077 1.7429 2.4507 1.2555 9.3693 26.16 1.0000 6.2774 4.9203

Q r pk I

c kk ky k m y k=y (%) rn =r m w Welfare

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E.A. Ghossoub, R.R. Reed / Journal of Macroeconomics 42 (2014) 211–228 Table 2 Optimal monetary policy and investment specific productivity, e = .2. a

0.9

0.99

1.1

1.2

1.3

42

42

r

1.0626 0.9411 2.9283 3.1116 1.0000 0.2000 0.4760 0.7904 1.2663 0.9851 7.2398 17.49 1.0000 4.9254 4.6171

1.0354 0.9658 2.6195 2.7123 1.0000 0.2000 0.5613 0.9712 1.5325 1.0392 7.7400 19.80 1.0000 5.1958 4.7660

1.0070 0.9930 2.3327 2.3491 1.0000 0.2000 0.6680 1.2073 1.8752 1.1013 8.3224 22.53 1.0000 5.5063 4.9325

0.9831 1.0172 2.1160 2.0803 1.0000 0.2000 0.7747 1.4531 2.2278 1.1586 8.8679 25.12 1.0000 5.7931 5.0823

0.9613 1.0403 1.9358 1.8608 1.0000 0.2000 0.8886 1.7247 2.6133 1.2157 9.4172 27.75 1.0000 6.0785 5.2278

0.2207 4.5309 0.0871 0.0192 1.0000 0.2000 1217.4351 14376.9946 15594.4298 74.9849 1627.8246 957.99 1.0000 374.9244 48.9769

1.0354 4.3191 0.0809 0.0187 4.4720 0.0843 1942.1992 21773.0738 23715.2730 40.9247 2247.2410 1055.31 12.1387 485.2632 49.1248

Q r pk I

c kk ky k m y k=y (%) rn =rm w Welfare

Table 3 Optimal monetary policy and investment specific productivity, e=.5. a

0.90

1.01

1.10

1.20

1.30

1.40

r

1.1044 0.9055 2.8330 3.1287 1.0000 0.2000 0.5201 0.7725 1.2926 1.0110 7.2436 17.84 1.0000 5.0552 4.5939

1.0354 0.9658 2.6346 2.7278 1.0000 0.2000 0.5781 0.9544 1.5325 1.0451 7.7400 19.80 1.0000 5.2256 4.7769

0.9810 1.0193 2.4892 2.4421 1.0000 0.2000 0.6296 1.1318 1.7613 1.0753 8.1939 21.50 1.0000 5.3766 4.9371

0.9301 1.0752 2.3609 2.1958 1.0000 0.2000 0.6833 1.3331 2.0163 1.1069 8.6815 23.23 1.0000 5.5343 5.1022

0.8846 1.1305 2.2523 1.9924 1.0000 0.2000 0.7364 1.5484 2.2848 1.1381 9.1778 24.89 1.0000 5.6903 5.2637

0.8438 1.1852 2.1592 1.8219 1.0000 0.2000 0.7890 1.7775 2.5665 1.1689 9.6828 26.51 1.0000 5.8447 5.4220

Q r pk I

c kk ky k m y k=y (%) r n =rm w Welfare

Table 4 Optimal monetary policy and investment specific productivity, e = .8. a

0.80

0.90

1.05

1.10

1.20

1.30

1.40

1.50

1.60

r

1.2616 0.7926 2.7657 3.4892 0.2000 1.0000 0.5405 0.6353 1.1758 1.0256 6.8853 17.08 1.0000 5.1282 4.3808

1.1442 0.8740 2.6796 3.0659 0.2000 1.0000 0.5645 0.7896 1.3540 1.0378 7.3049 18.54 1.0000 5.1892 4.5770

1.0354 0.9658 2.6938 2.7891 0.2000 1.0000 0.6427 0.8899 1.5325 1.0686 7.7400 19.80 1.0000 5.3430 4.8196

0.9967 1.0033 2.6641 2.6553 0.2000 1.0000 0.6532 0.9649 1.6180 1.0741 7.9410 20.38 1.0000 5.3704 4.9037

0.9247 1.0814 2.6105 2.4141 0.2000 1.0000 0.6735 1.1247 1.7982 1.0853 8.3624 21.50 1.0000 5.4263 5.0738

0.8625 1.1595 2.5656 2.2127 0.2000 1.0000 0.6921 1.2893 1.9814 1.0961 8.7881 22.55 1.0000 5.4804 5.2380

0.8081 1.2375 2.5272 2.0422 0.2000 1.0000 0.7094 1.4581 2.1675 1.1066 9.2179 23.51 1.0000 5.5330 5.3969

0.7602 1.3155 2.4941 1.8959 0.2000 1.0000 0.7255 1.6309 2.3563 1.1168 9.6516 24.41 1.0000 5.5841 5.5509

0.7176 1.3935 2.4651 1.7690 0.2000 1.0000 0.7405 1.8073 2.5478 1.1268 10.0890 25.25 1.0000 5.6338 5.7004

Q r pk

c I kk ky k m y k=y (%) rn =rm w Welfare

As observed in Table 2, the optimal money growth rate is lower under higher degrees of productivity in the capital sector. Thus, regardless of the elasticity of substitution in the production of consumer goods, optimal policy clearly depends on investment-specific productivity – in order to maximize welfare, the optimal money growth rate is lower if the capital sector is more productive.

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4. Conclusions This paper investigates the relationships between monetary policy, asset prices, and investment. In particular, we contend that it is important to consider the supply response of the capital sector in evaluating the impact of monetary policy. As previously noted, Goolsbee (1998) shows that equipment prices respond to fiscal policy initiatives designed to promote investment. While Goolsbee focuses on the short-run response to fiscal policy, we study the long-run impact of monetary policy. Interestingly, we demonstrate that the supply response to inflation can be stronger than the simple Tobin asset substitution channel would suggest. Yet, this does not imply that central banks should deviate from the Friedman Rule. Notably, productivity in the capital sector must be sufficiently strong in order to justify a departure from the Friedman Rule – otherwise, the increase in capital formation will not warrant deviating from efficient risk sharing. Alternatively, suppose that the central bank is attempting to establish policy to achieve a particular amount of investment activity. Our framework advocates lower average inflation than standard Tobin arguments. If central bankers consider supply behavior in the investment process, inflation does not need to be particularly high – that is, the central bank does not need to be as aggressive as standard Tobin logic would indicate. In our framework, monetary policy can promote the productive capacity of the capital sector by alleviating adjustment costs. Thus, an aggressive position is not necessary. Acknowledgment We thank James Fackler, Todd Keister, and Jenny Minier and an anonymous for their insightful comments. Seminar participants at the University of Alabama, University of Hartford, University of Kentucky, Kansas State University, University of Kansas, Utah State University, University of Texas at San Antonio, the Federal Reserve Bank of Atlanta, and the Board of Governors provided important suggestions. Appendix A

Proof of Proposition 1. Existence and uniqueness. We start by showing that respect to Q and simplifying yields:

D

dkB dQ

< 0. Taking the derivative of (24) with

 1 1 1   1 dc 1 q1  w1 a1 D Q q1 dkB  dQ Q þ ð1  cÞ  ð1  cÞ q Q ¼ 1 1   1    1 wð1  aÞ dQ Q q1  w1 a1 1

ð27Þ

From (15), we have:



ct Q t ; Using (28),

1þ

ptþ1 pt

dkD B dQ

 ¼

1  1h h p 1 þ 1pp Q t ptþ1 t

ð28Þ

< 0 if:

1h 1 cðQ Þ < h q

1 1

ð29Þ

 1 w1 a1 1  q Q 1

Define lðQ Þ ¼ 1 þ 1h cðQ Þ and gðQ Þ ¼ q1 h

1

 1 w1 a1 1  Q q1

1

. It is easily verified that l satisfies: limQ !1 c ! 0 and limQ !1

l ! 1 and

q lð0Þ ¼ 1h > 1, with l0 ðQ Þ < 0. Moreover, g0 ðQ Þ < 0. Next, let Q 1 ¼ a1 w : Then, limQ !Q 1 g ! 1 and limQ !1 g ! q1 > 1. In this manner, g > l for all Q > Q 1 . Therefore,

dkD B dQ



<0.

We proceed to prove existence and uniqueness of a steady-state equilibrium. Using (23) and (24), equilibrium in the capital market requires that: 

Q qð1Þ 1 ð1 Þ  1 ¼ ðQ  ð1  qÞÞð1  cðQ ; rÞÞ 1 a w



ð30Þ

   q  qð1Þ 1 ¼ 0, and limQ !1 GðQ Þ ! 1. Define GðQ Þ ¼  Q1    1 and JðQ Þ ¼ ðQ ð1qÞÞ1ð1cðQ ;rÞÞ. It is clear that G0 ðQ Þ > 0, G Q 1 ¼ a w ð1Þ

a w

Q ;rÞ Furthermore, J 0 ðQ Þ < 0 since @ cð@Q < 0: In addition, limQ !1 JðQ Þ ! 0 since c ! 0 and limQ !Q 0 ¼1q JðQ Þ ! 1. In this manner,

both curves always intersect once in the positive orthant and the polynomial has a unique positive real root, Q  . Specifically,

E.A. Ghossoub, R.R. Reed / Journal of Macroeconomics 42 (2014) 211–228

225

Q  > max ðQ 0 ; Q 1 Þ, which generates a positive equilibrium value of k as discussed in the text. Consequently, a steady state     exists if at Q  money is dominated in rate of return. This is achieved if J r1 P G r1 . This condition is equivalent to 

1

ðr

Þ

1 ð1qÞ

  þ 1 rqð1Þ P  ð1pÞ

1 1

a w

ð1 Þ . It can be verified that there exists a

r0 such that this condition holds with equality.

Moreover, for all r P r0 , Q  P r1 . In the proof of Proposition 4, we also refer to r0 as rFR , the Friedman Rule rate of money growth at which both money and capital yield the same rate of return. This completes the proof of Proposition 1. h Proof of Proposition 3. For a given rate of return to capital, JðQ Þ is increasing in either technology parameter. This occurs ð1qÞ

1

because w ¼ ð1  qÞ q aq qA. Consequently, the steady-state value of Q increases under higher levels of technology in either sector. We proceed to show the impact on capital formation. From the expression for the supply of capital, (23), we have

!1 



1

Q q1 

1 1

w a 1

1a1 

1

a

¼

k

1

1 h i1 1  ð1Q qÞ

Substituting this expression in the capital demand equation, (24), we obtain the following relationship between Q and k, independent of the level of productivity in either sector of the economy:

 k¼

1 1a 

a



1 1 1 ð1  qÞ  ð1  cðQ ; rÞÞ Q  1  Q

ð31Þ

dk dk dk dQ It is clear that dQ > 0 and therefore dA ¼ dQ > 0. A similar proof can be established for the effects of a. dA We next need to show that Q increases more due to investment-specific productivity. This is achieved by holding Q fixed and showing that JðQ Þ shifts more as a rises relative to an increase in A. As we are holding Q fixed, we can ignore constant terms. In this manner, Q rises more due to capital sector productivity if the condition in Proposition 3 holds. Finally, we show the effects of different technology parameters on r and Pk . As discussed previously, the steady-state rate of return to capital is generated by (30). Furthermore, substituting (22) and the expression for w into (30):

V ðPk Þ ¼ Z ðPk Þ;



qð1 q Þ q qÞ where V ðP k Þ ¼ ð1  qÞqð1qÞ P ð1 and Z ðP k Þ ¼ k

h

i

1 1þ ðQ ða;Pk Þð1qÞÞð1cðQ ða;P k Þ;rÞÞ  ð1 Þ ð1 q Þ 1 a ð1qÞ q qA

. Clearly, V 0 ðPk Þ > 0 and Z 0 ðP k Þ < 0. Moreover, under

higher A, Z ðP k Þ increases for a given P k . As a result, the steady-state Pk also rises under higher A. In contrast, under higher levels of a, Z ðP k Þ falls for a given P k . Consequently P k is decreasing in a. As r and P k are positively related by (22), this result also applies for r. This completes the proof of Proposition 3. h Proof of Proposition 4. We start by deriving an expression for (26). Using (11), (12) and (28), the welfare function, (25) can be written as:

ð1  hÞ

ph



X¼

1

r

þ

1h h

1p

p

Q

1h h

h

w1h

ð32Þ

Re-writing the equilibrium condition yielding Q , (30), to obtain:

0 1

r1hh

þ

1p

p

Q

1h h

1  1 1  p 1h C ð1 Þ Q qð1Þ  1AðQ  ð1  qÞÞ p Q h a w

B ¼ @

1

substituting into (32) to get:

0  h ð1  hÞ 1p B X¼ @ h

p

1h

 1 C h 1h    1h w ky ð1 Þ Q qð1Þ  1A ðQ  ð1  qÞÞ Q a w

p

1

  1 1 From (9), the expression for wages can be written as: w ky ¼ Að1  aÞ  1  . Incorporating (22) into the expres 1 sion for wages, we get:  1 1a A1

  1 w ky ¼ Að1  aÞ 

r 1

1 1 w



1  a11 1 Q q1

1 

ð33Þ

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E.A. Ghossoub, R.R. Reed / Journal of Macroeconomics 42 (2014) 211–228

Using (33) into (32) with some simplifying algebra yields:

0

Þ 1hð1 



1B Q C ð1 Þ  1A k 1  aw qð1Þ

XðQ Þ ¼ @

ðQ  ð1  qÞÞh Q

ð1hÞð1þqÞ

q

which is equation (26) using the definition of k in the text. Implicitly, Q  Q ðrÞ and the impact of a change in the rate of money creation on welfare is determined by signing dX dQ dX dX ¼ dQ . Since dQ < 0 by Proposition 2, the Friedman Rule is optimal if dQ > 0. Clearly, dQ > 0 if h  ð1  Þ > 0. Therefore, dr dr < 0 when this condition holds. In contrast, suppose h  ð1  Þ < 0. Under this condition, the impact of Q on the welfare function is ambiguous. dX Differentiating (26) with respect to Q and some simplifying algebra, dQ > 0 if:

dX dr dX dr

 ð1 Þ 1 10 1 w a h ð1  hÞð1 þ qÞAB C ð1  Þ  h @ þ @1  A>  q qð1  Þ Q qð1Þ 1  ð1Q qÞ 0

ð34Þ

Using the polynomial in Q , (30), the condition in (34) can be expressed as:

0

1   h ð1  hÞð1 þ qÞA 1 ð1  Þ  h @ þ > ð1qÞ ðQ  ð1  q q ÞÞ ð 1  c ð Q ; r Þ Þ þ 1 qð1  Þ 1 Q

ð35Þ

where the term on the left is strictly decreasing in Q . Therefore, there exists a Q 2 at which the above expression holds with dX dQ dX equality. For all Q > Q 2 , ddQX > 0, and ddXr ¼ dQ < 0 implying the FR is optimal. In contrast, for all Q < Q 2 , dQ < 0, and dr dX dQ ¼ dQ > 0. dr Due to the high degree of non-linearity in (35), it is hard to find a condition on parameters that guarantees global optimality when h  ð1  Þ < 0. Therefore, we resort to studying the local optimality (or sub-optimality) of the Friedman Rule by evaluating the condition at the Friedman Rule rate of money growth, rFR , where rFR ¼ r0 as indicated in the proof of    dX  > 0, the FR is locally optimal. In contrast, if ddQX < 0, the FR is suboptimal. Specifically, Proposition 1. If dQ  FR r ¼ r r¼rFR   dX > 0 if: dQ  FR dX dr

r¼r

!  h ð1  hÞð1 þ qÞ 1 ð1  Þ  h 1  > þ ð1  ð1  qÞrFR Þ q qð1  Þ rFR  ð1  qÞ ð1  pÞ þ 1



ð36Þ

From (30), the Friedman Rule rate of money creation is such that:



1

 qð1 Þ

rFR

" ð1 Þ ¼ a w 1þ 

1

1  1 rFR  ð1  qÞ ð1  pÞ

# ð37Þ ð1qÞ

1

which has a unique solution for rFR : Note that rFR is decreasing in w and w is such that w ¼ ð1  qÞ q aq qA: Therefore, rFR is also decreasing in a and A. Since the term on the LHS of (36), is strictly increasing in rFR , there exists an a0 such that it holds with equality. For all   dX dX  P 0, implying the FR is optimal. In contrast, for all a > a , < 0, implying the FR is suboptimal. This a 6 a0 , dQ   0 dQ FR FR r¼r

r¼r

completes the proof of Proposition 4. h Proof of Proposition 5. Suppose the Friedman Rule is optimal. Under this condition, welfare is falling with inflation and the optimal monetary policy implies that rFR Q  ¼ 1. Since Q rises under higher levels of technology, then rFR must fall. This must occur as nominal equity returns are rising with inflation. That is, the direct effect of higher money growth on rFR Q  dominates the indirect effect through lower Q . By Proposition 3, the optimal inflation rate under investment specific technological change is lower relative to neutral change. This completes the proof of Proposition 5. Re-writing (23) and (24) as a function of P k and k. From (17) and (18), the supply and demand for capital are such that: S

1

q

q

q kF ¼ a1q ðqÞ1q P 1 k kk

and D

kB ¼

1 Pk

1

Að1  aÞ 1  h1  1   h 1 a1 A1 1 þ 1pp Pr r 1   k r 1

ð38Þ

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E.A. Ghossoub, R.R. Reed / Journal of Macroeconomics 42 (2014) 211–228

  1 where w ky ¼ Að1  aÞ 

1 

1

1  from the work above.

1a1 A1 

r 1

Using (20) and (21) into (17), we get:

1

0 1

q B q 1 ð1  aÞ C S qB C kF ¼ a1q q1q P1 i1 A k @ k  h   r 1 a Aa

ð39Þ

Further, (22) into (39) yields:

1

0 S kF ðP k ; kÞ

1 1q

¼a

q

q 1q

q1q Pk

B B B B Bk  2 B B @ 4

1

ð1  aÞ  1 !1 q 1

ð1qÞa1q q1q P Aa

1q k

C C C C 31 C C C A  a5

which is increasing in P k and k. Furthermore, substituting (22) into (38) to get an expression for the demand for capital by banks as a function of Pk and r: 1

D

kB ¼

1 Að1  aÞ 1 Pk 1 þ 1pp  q 1

q 1q

ð1qÞa1q q1q P k

1h h

r

1

0 B @1  h

q

q 1 1q ð1qÞa1q q1q P k

C i1  A

D D b k : Pk ¼ which behaves in the following manner: limPk !1 kB ! 0 and limPk !P^k kB ! 1 where P

proof of Proposition 1, we have shown that a general equilibrium perspective. Thus,

dkD B dQ

dkD B dPk

ð40Þ

11 

 1 a1 A1



1

a A

q 1 ð1qÞa1q q1q

1qq

. From the

< 0. A similar proof can be provided since Pk and Q are positively related from

< 0. Moreover, a higher rate of money growth raises the demand for capital

goods for a given Pk . h References Abel, A., 1985. Dynamic behavior of capital accumulation in a cash-in-advance model. J. Monet. Econ. 16, 55–71. Abel, A., 2001. Will bequests attenuate the predicted meltdown in stock prices when baby boomers retire? Rev. Econ. Stat. 81, 589–595. Abel, A., 2003. The effects of a baby boom on stock prices and capital accumulation in the presence of social security. Econometrica 71, 551–578. Abel, A., Blanchard, O., 1986. The present value of profits and cyclical movements in investment. Econometrica 54, 249–273. Ahmed, S., Rogers, J.H., 2000. Inflation and the great ratios: long term evidence from the US. J. Monet. Econ. 45, 3–35. Azariadis, C., Bullard, J., Smith, B., 2001. Public and private circulating liabilities. J. Econ. Theory 99, 59–116. Baier, S., Carlstrom, C.T., Chami, R., Cosimano, T.F., Fuerst, T.S., Fullenkamp, C., 2003. Capital trading, stock trading, and the inflation tax on equity: a note. Rev. Econ. Dyn. 6, 987–990. Basu, B., 1987. An adjustment cost model of asset pricing. Int. Econ. Rev. 28, 609–621. Bencivenga, V., Smith, B.D., 1991. Financial intermediation and endogenous growth. Rev. Econ. Stud. 58, 195–209. Bullard, J., Keating, J., 1995. The long-run relationship between inflation and output in postwar economies. J. Monet. Econ. 36, 477–496. Bullard, J., Smith, B., 2003a. Intermediaries and payments instruments. J. Econ. Theory 109, 172–197. Bullard, J., Smith, B., 2003b. The value of inside money. J. Monet. Econ. 50, 389–417. Chami, R., Cosimano, T., Fullenkamp, C., 2001. Capital trading, stock trading, and the inflation tax on equity. Rev. Econ. Dyn. 4, 575–606. Chirinko, R., 1993. Business fixed investment spending: modeling strategies, empirical results, and policy implications. J. Econ. Lit. 31, 1875–1911. Christiano, L., Fisher, J., 2003. Stock Market and Investment Goods Prices: Implications for Macroeconomics. NBER #10031. Cochrane, J., 1991. Production-based asset pricing and the link between stock returns and economic fluctuations. J. Finan. 46, 209–237. Cooley, T.F., Hansen, G.D., 1989. The inflation tax in a real business cycle model. Am. Econ. Rev. 79, 733–748. Diamond, D., Dybvig, P., 1983. Bank runs, deposit insurance, and liquidity. J. Polit. Econ. 91, 401–419. Duffy, J., Papageorgiou, C., Perez-Sebastian, F., 2004. Capital-skill complementarity? Evidence from a panel of countries. Rev. Econ. Stat. 86, 327–344. Fama, E.F., Schwert, G.W., 1977. Asset returns and inflation. J. Finan. Econ. 5, 115–146. Gandelman, N., Hernandez-Murillo, R., 2014. Risk Aversion at the Country Level. Mimeo, Federal Reserve Bank of St. Louis. Ghossoub, E., Reed, R., 2010. Liquidity risk, economic development, and the effects of monetary policy. Eur. Econ. Rev. 54, 252–268. Goolsbee, A., 1998. Investment tax subsidies, prices, and the supply of capital goods. Quart. J. Econ. 113, 121–148. Gould, J.P., 1968. Adjustment costs in the theory of investment of the firm. Rev. Econ. Stud. 35, 47–55. Greenwood, J., Hercowitz, Z., Krusell, P., 1997. Long-run implications of investment-specific technological change. Am. Econ. Rev. 87, 342–362. Greenwood, J., Hercowitz, Z., Krusell, P., 2000. The role of investment-specific technological change in the business cycle. Eur. Econ. Rev. 44, 91–115. Gultekin, N.B., 1983. Stock market returns and inflation: evidence from other countries. J. Finan. 38, 49–65. Huybens, E., Smith, B.D., 1999. Inflation, financial markets and long-run real activity. J. Monet. Econ. 43, 283–315. Kocherlakota, N., 1998. Money is memory. J. Econ. Theory 81, 232–251. Kocherlakota, N., 2003. Societal benefits of illiquid bonds. J. Econ. Theory 108, 179–193. Lucas, R.E., Prescott, E.C., 1971. Investment under uncertainty. Econometrica 39, 659–681. Mehra, R., Prescott, E.C., 1985. The equity premium: a puzzle. J. Monet. Econ. 15, 145–161. Mussa, M., 1977. External and internal adjustment costs and the theory of aggregate and firm investment. Economica 44, 163–178.

228

E.A. Ghossoub, R.R. Reed / Journal of Macroeconomics 42 (2014) 211–228

The Nilson Report, November 1997, p. 6. Reed, R.R., Waller, C.J., 2006. Money and risk sharing. J. Money Credit Banking 38, 1599–1618. Schreft, S., Smith, B.D., 1997. Money, banking, and capital formation. J. Econ. Theory 73, 157–182. Sidrauski, M., 1967. Rational choices and patterns of growth in a monetary economy. Am. Econ. Rev. 57, 534–544. Stockman, A.C., 1981. Anticipated inflation and the capital stock in a cash-in-advance economy. J. Monet. Econ. 8, 387–393. Tobin, J., 1965. Money and economic growth. Econometrica 33, 671–684. Wang, P., Yip, C., 1992. Alternative approaches to money and growth. J. Money Credit Banking 24, 553–562. Weiss, L., 1980. The effects of money supply on economic welfare in the steady state. Econometrica 48, 565–576.