Interest Rates and Corporate Cash:

An Inverted-U Relationship

Xiaodan Gao and Na Zhang ∗†

Abstract

We present an empirical finding on the lack of a significant negative relationship between

nominal interest rates and firms’ cash holdings that contradicts conventional wisdom. We de-

velop a theoretical framework to rationalize the observed finding and reexamine this relationship.

The model captures the benefit of holding cash by introducing external financing costs that are

endogenously determined by interest rates. In the model, interest rates affect firms’ cash poli-

cies through two channels: (i) forgone interest earnings, and (ii) saved borrowing costs on loans.

The first is the cost of carrying cash, and the latter is the benefit. The net effect of interest

rates on cash holdings relies on which force—cost or benefit—dominates. The calibrated model

quantitatively reproduces key empirical features and suggests an inverted-U relationship between

corporate cash and interest rates, which is strongly supported by data. The derived corporate

money demand schedule has important implications for monetary policy.

JEL Classification: E41, E43, G12, G32.

Keywords: Corporate cash holdings; interest rates; cost of debt; financial frictions.

∗This draft: June 2016.†Corresponding author: Xiaodan Gao, Department of Strategy and Policy, NUS Business School, Singapore, E-

mail: gao.xiaodan@nus.edu.sg. Na Zhang is from the Department of Finance, Fudan University, China, E-mail:nazhang@fudan.edu.cn. We would like to thank Laura Xiaolei Liu, Pablo Moron, and the audiences at the 2014 CEAmeeting and Peking University (Guanghua School of Management) for insightful comments and suggestions. Na Zhangis sponsored by Shanghai Pujiang Program.

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1 Introduction

The steady increase in cash reserves by U.S. businesses has inspired a resurgence of interest

in firms’ cash holdings. As shown in Figure 1, U.S. nonfinancial businesses held around 40%

of the aggregate money stock (M1) in the 2000s, which accounted for a significant share.

Despite this, a disproportionate amount of attention has been paid to household money

demand behavior with respect to interest rates and its implications for the welfare cost of

inflation (Mulligan and Sala-i Martin, 2000), while much less attention has been paid to

firms’ money demand. In this paper, we focus on the latter and explore its implications

for monetary policy.

[Figure 1 about here.]

Conventional wisdom suggests a negative association between firms’ cash holdings and

nominal interest rates (Baumol, 1952; Tobin, 1956; Meltzer, 1963). In response to a drop in

interest rates, firms tend to accumulate larger cash reserves as a result of lower opportunity

costs. Although at first glance this negative correlation appears to be supported by the

data, as shown in Figure 2, this result is not robust.1 Bates et al. (2009) and Graham

and Leary (2015) find that corporate cash and T-bill rates were uncorrelated from the

1980s to 2000s. Stone and Gup (2013) examine this relationship over the period 1970-

2011, controlling for firm characteristics, and uncover an insignificant relationship in the

1990s. In this paper, we reexamine this relationship by proposing a theory to rationalize

the empirical observations and providing supportive evidence.

[Figure 2 about here.]

We start by empirically reconsidering the relationship between firms’ money demand

and interest rates. Following Bates et al. (2009) and Stone and Gup (2013) and controlling

1Figure 2 plots the times series of average cash ratios and three-month T-bill rates from 1970 to 2013 in a sample ofnonfinancial nonutility firms constructed from Compustat. The graph, on average, exhibits an unconditional negativecorrelation between cash holdings and interest rates.

2

for other macroeconomic factors besides interest rates, we find a positive yet statistically

insignificant relationship over the sample period. Although surprising, this result is robust

to various measures of interest rates and regression specifications, and naturally raises

the question: How are interest rates and firms’ cash policies related, in addition to the

conventional opportunity-cost channel?

To address this question, we build a theoretical model. In the model, firms face demand

and productivity shocks and financial frictions. They combine labor and capital to produce

output and pay fixed operating costs in advance of production. To finance operating

expenses, firms can use internal cash reserves and/or external funds. External borrowing

takes the form of risky inter-period debt and costly equity issuance. Interest rates in the

model affect firms’ cash policies through two channels: (i) forgone interest earnings, and

(ii) saved borrowing costs on loans. The first is the cost of carrying cash, and the latter is

the benefit. The net effect of interest rates on cash holdings relies on which force—cost or

benefit—dominates. Deriving the shape of money demand, therefore, requires quantitative

analysis.

We calibrate the model carefully. It successfully explains the data and offers a reliable

platform to derive the relationship between firms’ money demand and interest rates. Com-

parative statics results suggest an inverted-U relationship, which is generated by financial

frictions and fixed operating costs. Specifically, fixed operating costs consume debt capac-

ity that would otherwise be available to service old debt and finance capital investments,

and push leverage up. This drives up firms’ default risk and cost of debt. In response,

firms accumulate internal cash to save expensive external borrowing costs. As interest rates

increases, firm value tends to fall, and default probability and cost of debt rise. Fixed op-

erating costs tighten firms’ budget constraints and further push up default risk and cost of

debt. The benefit of holding cash to preserve financial flexibility for facilitating operation,

lower default probability, and reduce borrowing costs becomes stronger. Firms, therefore,

demand more cash. However, as interest rates become high, firms that survive tend to

3

disinvest when facing tightened budget constraints and worsened credit markets caused by

fixed operating costs. Weak capital investment needs lower the demand for cash, leading

to a drop in cash holdings. The inverted-U relationship provides an explanation for the

documented insignificant monotonic relationship between interest rates and corporate cash

ratios. Results remain when we perform sensitivity analyses.

This key model result, when tested in a sample of nonfinancial nonutility U.S. firms

constructed from Compustat Industrial Annual files for the period 1970-2013, is strongly

supported by data. Specifically, firms, on average, tend to raise their cash-to-assets ratios

as the interest rate increases but stays below 5.4%, indicating a positive relationship. Firms

start reducing their cash ratios in response to an increase in interest rates when the rate is

higher than 5.4%. Estimation results are robust to different regression models, measures

of interest rates, and country samples.

Lastly, we use our result to revisit several important questions of money demand: the

welfare cost of inflation, monetary policy and its transmission channels, and the U.S.

corporate cash puzzle. First, the inverted-U relationship between cash and interest rates

implies the existence of a satiation level of firms’ money demand at zero interest rates,

which in turn suggests a moderate welfare cost of the Federal Reserve’s low inflation policy.

Second, it suggests that an interest-rate targeting should be favored over a monetary-

aggregates targeting, because the latter may produce multiple equilibria in the money

market. In addition, the existence of corporate cash reserves makes capital investment

insensitive to interest-rate changes when interest rates are low, and dampens the importance

of the interest-rate channel and balance-sheet channel in the transmission of monetary

policy to the real economy. Lastly, it challenges the role of interest rates in resolving the

corporate cash puzzle. During the 1990s and 2000s when interest rates were relatively low,

a decline in interest rates is expected to be associated with a decline in cash ratios.

In this paper, we abstract from the allocation choice between cash and short-term

marketable securities. Under business sweep programs during the 1960s and 1970s and

4

retail sweep programs in a later period, the cost of holding cash relative to short-term

marketable securities is small, because firms earn interest overnight on the cash sitting

idle in their checking accounts. In addition, short-term marketable securities account

for a relatively constant and low share of firms’ total assets, regardless of interest-rate

movements over time. As shown in Figure 3, the short-term financial investment to assets

ratio, measured as the distance between the two plotted lines, has stayed constant at

approximately 5% since the late 1980s. In light of these two facts, we abstract from

decisions about whether and how much to invest in short-term financial assets. Why firms

allocate a small and constant share of total assets to short-term interest-bearing securities

is an interesting question that we plan to address in future.

[Figure 3 about here.]

Our paper contributes to the literature in several ways. First, it focuses on firms’ money

demand, which constitutes a large fraction of M1 monetary aggregate in the economy. De-

spite its nonnegligible share, the literature on monetary economics has been relatively silent

on corporate cash holdings. Examining the effect of interest rates on corporate cash bal-

ances in great detail offers a more complete picture of the money demand schedule. Meltzer

(1963) highlights the importance of interest rates in determining firms’ cash balances, and

acknowledges the complexity of the problem. Mulligan (1997) and Bover and Watson

(2005) empirically estimate the interest elasticity of firms’ money demand using firm-level

data. They use a regression specification without controlling for several important firm-

specific characteristics, and find a negative relationship. Stone and Gup (2013) document

an insignificant negative correlation between interest rates and firms’ money demand in the

1990s. Our findings are in line with those of Stone and Gup. Moreover, we find that this

insignificant correlation holds for the entire sample period when we take into account other

aggregate macroeconomic conditions proxied by real GDP and its growth rate. We further

develop a model to understand these empirical observations. Our paper is also related to

Azar et al. (2016), who examine a similar question. Unlike their work, we focus on the

5

narrowly defined money held by firms and emphasize both benefits and costs of holding

money in response to changes in interest rates.

Second, this paper provides insights into the shape of the money demand schedule and

the welfare cost of inflation. Lucas (2000) and Ireland (2009) suggest two different money

demand specifications. Their conflicting findings center on money demand behavior at

low interest rates, which has significantly different implications for the welfare cost of the

Federal Reserve’s monetary policy of a low but positive inflation. Our result suggests an

inverted U-shaped money demand function. This result supports the existence of a satia-

tion level of money demand under the Friedman rule, and suggests a modest welfare cost of

the Fed’s low-inflation policy. Moreover, the derived nonmonotonic money demand func-

tion has important implications for monetary policy and provides a rationale for targeting

interest rates instead of money supply.

Lastly, this paper helps to understand firms’ cash policies. There is a growing literature

on this topic. Several main holding motives have been identified and modeled, including

the transaction motive (Baumol, 1952), precautionary motive (Riddick and Whited, 2009),

tax motive (Armenter and Hnatkovska, 2014), and agency motive (Nikolov and Whited,

2014). Our paper complements these by introducing another reason for accumulating cash:

Keeping cash on hand makes firms look stronger to external lenders and lowers interest

rates on loans. This motive is widely recognized in practice but absent in the literature

(Lins et al., 2010). In this paper, we capture this idea by allowing firms to pledge cash as

collateral and endogenizing interest rates on debt.

The paper is organized as follows. The next section presents stylized facts on the

relationship between interest rates and corporate cash holdings. Section 3 lays out the

model to rationalize the empirical observation and characterizes optimal cash policies.

Section 4 performs quantitative analyses, provides empirical evidence, and discusses the

model’s implications for monetary policy. Section 5 concludes.

6

2 Interest Rates and Corporate Cash Holdings

To reexamine the empirical relationship between corporate cash and nominal interest rates,

we adopt a regression specification similar to those used by Bates et al. (2009) and Stone

and Gup (2013), but isolate interest rates from other macroeconomic factors that affect

firms’ cash decisions.2

2.1 Regression Specification

The regression model is specified below:

cashi,t = α0 + α1 interest ratet + α2 GDP growtht + α3 GDPt + α4 market to booki,t

+ α5 cash flowi,t + α6 net working capitali,t + α7 capital expenditurei,t + α8 leveragei,t

+ α9 R&Di,t + α10 dividendi,t + α11 firm sizei,t + α12 acquisitioni,t + α13 investment

gradeit + α14 industry riskj,t + α15 lagged cashi,t + industryj + decaden + εi,t.

(1)

Here, subscript i refers to firm, t is time, j refers to the industry in which firms operate,

and n denotes the decade to which year t belongs.

The dependent variable is the cash-to-assets ratio, where cash is measured by the item

ch in Compustat. This variable corresponds to M1 monetary aggregate, which excludes

short-term interest-bearing investments. The independent variable of particular interest in

this regression is the nominal interest rate. To isolate the effects of other macroeconomic

factors on firms’ cash decisions from interest rates, we include the logged real GDP, real

GDP growth rate, and decade dummy variables.

Note that in the regression model, we use the level of cash ratio as the dependent

variable instead of its log transformation. The reason for not using the logged cash ratio

2Graham and Leary (2015) find that macroeconomic variables, such as GDP growth, are important for understandingcorporate cash decisions.

7

is that 1% of firm-year observations in our sample have zero cash ratios, and roughly 14%

of the observations have cash ratios lower than 1%. The logarithm moves small values

farther apart. Taking logs, therefore, generates outliers at the low end, which tends to

drive estimation results.3

Other covariates are commonly used in previous empirical cash studies, including market-

to-book ratio, cash flow, net working capital, capital investment, leverage, R&D expen-

ditures, a dividend dummy, firm size, acquisition expenses, investment grade dummy,

industry-level risk, and lagged cash ratio. Appendix A provides detailed descriptions of

variable definitions and constructions.

2.2 Data and Summary Statistics

The sample is constructed from Compustat files, covering annual observations from 1970 to

2013. Following previous studies, we exclude financial firms (SIC 6000-6999) and utilities

(SIC 4900-4999), as cash is held for regulatory purposes and business practices in these

sectors. These selection criteria yield an unbalanced panel of 5,773 U.S. firms with 81,139

firm-year observations. We impose outlier rules on variables by winsorizing them at the 1st

and 99th percentiles. Macroeconomic data are collected from databases maintained by the

Federal Reserve System, Bureau of Labor Statistics, and Bureau of Economic Analysis.

[Table 1 about here.]

Descriptive statistics are given in Table 1. On average, cash holdings account for 14.5%

of total assets, with the lowest being zero and the highest being greater than 90%. We use

six measures of interest rates: three-month and one-year T-bill rates, one-year, five-year,

and ten-year treasury constant maturity rates, and federal funds effective rate.4,5 Over

3When using the log of 1 plus cash ratio as the dependent variable, we have findings quantitatively similar to thosereported in Tables 2, 3, 6, and 7. Results are available upon request.

4Note that data are unavailable between 2002 and 2007 for one-year T-bill rates.5Following Nagel (2016), we also use federal funds rates as an interest-rate measure, because the T-bill rate is an

imperfect although good proxy for cash-holding costs.

8

the time period, the average annualized three-month T-bill rate is 3.4%, and the average

one-year treasury constant maturity rate is 3.7%. The average federal funds effective rate

is 3.8%. In addition, more than 10% of the firm-year observations in this sample have

investment-grade debt securities.6 Other covariates have characteristics similar to those in

previous studies.

2.3 Results

Table 2 summarizes estimation results for the baseline model with three-month T-bill rates.

Column (1) reports the results without controlling for industry fixed effects. Columns

(2)-(4) present results estimated by exploiting different variations, in which we include

2-digit SIC industry fixed effects, 3-digit SIC industry fixed effects, and firm fixed effects,

respectively.

[Table 2 about here.]

We find a positive relationship between interest rates and firms’ cash ratios, which is

contrary to the traditional view of monetary economics—i.e., a drop in interest rates reduces

the carrying costs of cash and induces firms to raise their cash holdings. Results remain

unchanged when we include industry fixed effects and firm fixed effects. Our finding is

slightly different from Stone and Gup’s (2013), who find a statistically significant negative

relationship during 1970-2011 except for the 1990s. We conjecture that this discrepancy

arises from the inclusion of real GDP and real GDP growth rate, which are strongly related

to firms’ cash decisions and are added to capture other non-interest macroeconomic factors.

The signs of the coefficients on other explanatory variables are broadly consistent with

previous studies. Firms’ cash holdings increase with the market-to-book ratio, cash flow

ratio, and risks, and decrease with net working capital and various expenditures, including

capital investment, dividend payment, and acquisition expenses. Leverage has a negative

6A firm is considered investment grade if it has a bond grade of BBB- or higher by Standard & Poor’s. Firms withunrated bonds or bond ratings below BBB- are considered non-investment grade.

9

relationship with cash holdings, because it acts as a financing alternative to cash. A

similar argument applies to investment grade. Firms that have bond ratings above the

investment-grade threshold of BBB hold less cash, as they have easier access to external

funds compared to firms with poorer ratings. Lastly, cash holdings are persistent, reflected

by the positive coefficient on lagged cash ratios.

We next perform robustness tests using alternative measures of interest rates. Results

are presented in Table 3. Panel A uses one-year T-bill rates, Panels B, C, and D show

results with one-year, five-year, and ten-year treasury constant maturity rates, respectively,

and Panel E uses the federal funds effective rates. As shown in Table 3, statistically

insignificant results are found in all cases. The lack of a significant negative correlation

between corporate cash and interest rates, therefore, is robust to different interest rate

measures.

[Table 3 about here.]

Overall, the estimation results presented in this section suggest that corporate cash

balances do not decrease with interest rates, as traditional theories predict. Stone and

Gup (2013) also uncover a nonnegative relationship between interest rates and firms’ cash

balances during the 1990s. They examine the explanations associated with taxes, cash

flows, and pension fund contributions, but find that none explains the nonnegative relation.

To understand the observed facts, we next build a model and describe it below.

3 Model

We examine a firm’s problem in a partial equilibrium setting to analyze its cash decision

with respect to nominal interest rates. In the model, the firm faces frictions in capital

markets and uncertainty from demand and productivity. At each period, after observing the

shock, the firm makes decisions about capital investment, debt borrowing, cash holdings,

and dividend payment/equity issuance.

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We first specify the firm’s production technology, capital accumulation process, and

financing options, then present the firm’s problem.

3.1 Technology

The firm combines labor l and predetermined capital stock k to produce output and faces

a combination of idiosyncratic demand and productivity shocks z. Its revenue is given by

the following function:

y = zν(l1−αkα)θ.

The parameter α ∈ (0, 1) represents the capital share, and θ ∈ (0, 1) captures a decreasing

returns-to-scale technology and/or the firm’s market power. The parameter ν is normalized

to be 1 − (1 − α)θ, such that the firm’s revenue function π(z, k) is linear in shocks after

optimizing over the variable production factor labor. The shock z is governed by persistence

parameter ρ and the volatility of the innovation σ2z , which follows a normal distribution,

ln z′ = ρ ln z + ε′z, where εz ∼ N(0, σ2z),

where prime denotes a variable in the subsequent period.

3.2 Labor Hiring and Capital Investment

The firm hires labor to produce output and faces an upward-sloping labor supply curve,

which is specified as

ls = wγ,

where w denotes the prevailing wage rate in the labor market. The labor supply curve

exhibits a constant elasticity γ > 0.

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In addition, the firm augments its capital stock by capital investment, I, given as

I = k′ − (1− δ)k.

The parameter δ ∈ (0, 1) is the capital depreciation rate. Adjusting capital by purchasing

or selling it incurs adjustment costs, which are defined by

A(k, I) = γ0k1I 6=0 +γ12

(I

k)2k + (1− γ2)|I|1I<0.

This specification includes nonconvex adjustment costs γ0 > 0, convex adjustment costs

γ1 > 0, and partial irreversibility of capital γ2 ∈ (0, 1).

3.3 Financing

The firm has four sources of funds to finance its expenditures: current-period cash inflows

from sales, internal cash balance, inter-period risky debt, and equity issuance.

Cash balance, c, earns no interest. The cost of holding cash, therefore, is the nominal

interest rate i.7 The firm has access to credit markets. It can raise funds with an inter-

period risky debt, b, and repay it in the subsequent period when the debt matures. The

price of the debt, q, depends on the uncertainty facing the firm and the firm’s current-period

decisions, namely, debt borrowing, cash holdings, and capital stock.

In addition to debt financing, the firm can issue equity. Following Hennessy and Whited

(2007), we denote d ≤ 0 as equity issuance and d > 0 as dividend payment, and assume

that issuing equity incurs both fixed costs λ0 > 0 and linear costs λ1 > 0.

7Because firms earn interest on their cash balances under business sweep programs, we will relax this restriction inSection 4.1.4.2 to check the robustness of the model’s main result.

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3.4 The Firm’s Problem

3.4.1 Timing

At the beginning of period t, after observing the shock realization, zt, the firm decides

whether or not to default on its existing debt obligations bt. Default leads to liquidation

of the firm’s assets. The firm’s internal resources are then distributed to creditors and

the remaining unpaid debt is discharged. If the firm decides to continue, it pays off debt,

pays fixed production costs cf , and produces output. Upon receiving the current-period

revenue, the firm makes its capital investment and financial decisions.

3.4.2 Set-up

The firm is risk neutral. Its objective is to maximize its value that is discounted at the

risk-free nominal interest rate. Each period, after observing the shock realization and given

the debt price schedule, the firm decides whether to default. If the firm is economically or

financially distressed—that is, either the firm value drops below zero or there is no way to

roll over the maturing debt—the firm defaults. We let the firm value in the case of default

equal zero, and the firm’s problem is

V (zt, kt, ct, bt) = max{0, V c(zt, kt, ct, bt)},

where V c(zt, kt, ct, bt) denotes the continuation value.

If the firm decides to continue to operate, its problem can be viewed in two stages:

the pre-production stage and the post-production stage. In the pre-production stage, the

firm repays debt and pays fixed operating costs in advance of production. It can issue new

debt and roll over existing debt. If funds remain insufficient to cover expenses, the firm

can issue equity. Unused funds at this stage will be carried forward to the post-production

stage. In the post-production stage, the firm produces output and makes capital invest-

ment and financial decisions. If current-period revenue is insufficient to meet investment

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expenditures, the firm again issues equity; otherwise, the firm distributes dividends. The

firm’s continuation problem can be summarized by

V c(zt, kt, ct, bt) = maxIt,bt+1,ct+1

{φd1,t [d1,t + φd1,t(−λ0 + λ1d1,t)] + [d2,t + φd2,t(−λ0 + λ1d2,t)]

+1

1 + iEV (zt+1, kt+1, ct+1, bt+1)

}subject to budget constraints:

d1,t = ct + qtbt+1 − bt − cf ,

d2,t = π(zt, kt) + (1− φd1,t)d1,t − It − A(kt, It)− ct+1,

bt+1 ≥ 0,

ct+1 ≥ 0,

φdj,t =

1 if dj,t ≤ 0

0 otherwise,

at all dates t ≥ 0. Here, dj,t represents the net equity flow in stage j ∈ {1, 2} at period t,

φdj,t is an indicator function, and qt is the debt price, which we will discuss below.

3.4.3 Debt Pricing

Lastly, we consider the debt pricing schedule required to solve the firm’s problem. We

assume that the firm borrows from a competitive and risk-neutral lender. The lender

provides a state-contingent contract that compensates for the loss in case of default.

More specifically, the firm will completely pay off the debt bt+1 if it continues to operate

at t + 1, and pay ct+1 + χ(1 − δ)kt+1 in case of default. The parameter χ ∈ (0, 1) is the

recovery rate and governs the magnitude of bankruptcy costs. The zero profit, therefore,

14

implies the following pricing expression:

qtbt+1 = (1

1 + i)E{1Vt+1>0bt+1 + 1Vt+1≤0[ct+1 + χ(1− δ)kt+1]},

where 1Vt+1>0 is an indicator function that equals one if the condition specified by the

subscripts is satisfied and zero otherwise. It can be rewritten as

qt = (1

1 + i)E{1Vt+1>0 + 1Vt+1≤0

ct+1 + χ(1− δ)kt+1

bt+1

}.

Note that we abstract from strategic default in the model. That is, the firm defaults only

if it has negative firm value, or, more importantly, it fails to roll over maturing debt.

3.5 Nominal Interest Rates and Cash Holdings

In this subsection, we characterize the firm’s optimal cash policy and develop the intuition

behind the equation that links cash holdings with nominal interest rates.

Solving the firm’s problem, we derive the optimal condition for cash holdings shown

below:

1 + φd2λ1 =1

1 + iE{1Vt+1>0Λ

′}+ Λqc′b′ + µ, (2)

where Λ = φd1(1 + φd1λ1) + (1 − φd1)(1 + φd2λ1). The prime denotes a variable in the

subsequent period, and qc′ is the first derivative of the bond price with respect to cash

balances.

The left side of equation (2) gives the marginal cost of carrying one additional dollar of

cash into the subsequent period, which is the shadow value of dividends—forgone dividends

or the sum of external equity financing and corresponding costs in the case of issuing equity

to save cash during the current period.

The right side represents the marginal benefit and has three components. The first is the

expected present value of an additional dollar of cash to avoid defaults and relax financial

15

constraints in the future, 11+i

E[1Vt+1>0Λ]. In other words, firms hold cash to save equity

financing costs in case there are liquidity shortages, and therefore need to issue equity at

either of the two stages in the subsequent period. This motive for accumulating cash is the

same as that in previous structural cash models (Riddick and Whited, 2009).

The second component on the right side of equation (2) reflects the beneficial effect of

increased internal liquidity on cost of debt, qc′ , and in turn the increased debt borrowing,

qc′b′, that can be used to relax the financing constraints at either of the two stages in

the current period and avoid expensive equity issuances. This extra motive for holding

cash is missing in previous cash studies, yet is consistent with reality. According to Lins

et al. (2010), CFOs indeed view the “ability to issue debt at a ‘fair’ price when funds are

needed” as one of the key factors that drive their cash decisions. The last component is

the Lagrange multiplier of the nonnegativity constraint on cash holdings, µ.

Multiplying both sides of equation (2) by the gross nominal interest rate 1 + i, we can

rewrite the optimal condition in a form easier for interpretation. In the case of an interior

solution with positive cash balances (i.e., µ = 0), equation (2) becomes

(1 + i)(1 + φdλ1) = E[1Vt+1>0Λ′] + Λ

∂E{1Vt+1>0 + 1Vt+1≤0c′+χ(1−δ)k′

b′}

∂c′b′.(3)

Evidently, nominal interest rates affect firms’ cash holdings in a nontrivial way. The

conventional wisdom highlights the nominal interest rate as a cost of holding cash, which

is captured by the left side of equation (3) and implies a negative relationship. That is, as

the nominal interest rate increases, the cost of holding cash rises and therefore firms have

weaker incentives to accumulate cash. Nevertheless, the terms on the right side of equation

(3) suggest that nominal interest rates also affect the benefit of holding cash. Interest

rates affect discount rates. As the nominal interest rate increases, firm value Vt+1, which

is the discounted value of expected future dividends, falls. This in turn affects the default

probability (E1Vt+1≤0) and the cost of debt. Firms, therefore, can benefit from holding cash

16

by reducing the likelihood of default, lowering borrowing costs on loans, and raising more

cheap debt to save equity-financing costs in both the current period and the subsequent

period if they decide to continue operating.

The discussion above suggests that the nominal interest rate has impacts on both the

costs and benefits of holding cash, and its net effect on firms’ cash policies depends on which

channel dominates. Examining the relationship between interest rates and corporate cash

reserves, therefore, requires careful quantitative analysis which we perform and discuss

below.

4 Empirical Results

In this section, we apply the model described in Section 3 to data. We start by parame-

terizing the model and examine the relationship between interest rates and corporate cash

holdings. We then perform a number of sensitivity analyses to gauge the robustness of

the model’s key result and provide empirical evidence to support it. Lastly, we study our

finding’s implications for the welfare cost of inflation, monetary policy, and corporate cash

hoarding puzzle.

4.1 Quantitative Analysis

To explore the interest-cash relationship, we calibrate the model with a sample of non-

financial nonutility firms from 1970 to 2013 constructed from Compustat, then examine

firms’ money demand behavior with respect to interest rates.

4.1.1 Calibration

We solve the model at an annual frequency and set the nominal interest rate i equal to

4%. This implies that the discount factor is 0.96.

To calibrate the revenue function π(z, k) and the process for the idiosyncratic revenue

17

shock z, we estimate the regression model specified below:

Yi,t = β0 + β1ki,t + firmi + yeart + εi,t. (4)

The dependent variable Yi,t is the logarithm of real sales for firm i during period t. The

independent variables include a constant term, the logarithm of capital stock, firm dummies

and time dummies. The error term εi,t corresponds to the logarithm of the idiosyncratic

revenue shock zi,t in the model. The coefficient of capital stock corresponds to the curvature

of the revenue function π(z, k), β1 = αθ1−θ+αθ . Estimating equation (4) yields β̂1 = 0.6. We

set the capital share α to be 0.3, which implies θ = 0.83. We then collect the fitted residuals

and estimate the following AR(1) model to calibrate the persistence ρ and volatility σz that

govern the shock process,

ε̂i,t = β3ε̂i,t−1 + εi,t.

Estimation results yield ρ = 0.64 and σz = 0.34.

We set fixed capital adjustment costs γ0 to be 0.039 and convex adjustment costs γ1

to be 0.7, following Cooper and Haltiwanger (2006) and Nikolov and Whited (2014); set

the resale price of capital γ2 to be 0.5, following Gilchrist et al. (2014); and choose the

capital depreciation rate δ at the value commonly used in the literature, 0.12. Labor

supply elasticity is set to be 7, a value between those used by Clementi and Palazzo (2016)

and Khan and Thomas (2008).

Parameters related to financial frictions are chosen as follows. We set the debt recovery

rate χ to be 0.5, within the range [0.37, 0.9] suggested by previous studies (Khan et al.,

2014; Hennessy and Whited, 2007; Gilchrist et al., 2014). Estimates for equity issuance

costs vary widely in the literature (Gomes, 2001; Cooley and Quadrini, 2001; Hennessy

and Whited, 2007; Nikolov and Whited, 2014). We choose conservative values by setting

the nonconvex equity-issuance cost λ0 = 0.2 and linear cost λ1 = 0.05.

Lastly, we set the fixed operating costs cf to be 0.068 to match the average cash-to-assets

18

ratio 0.145 in the data. Table 4 summarizes the parameter choices.

[Table 4 about here.]

4.1.2 Model Validation

Table 5 reports the model predictions along with the corresponding data moments, in-

cluding the first and second moments of cash holdings, inter-period debt financing, capital

investment, and equity issuance.

We construct data moments using a sample of nonfinancial nonutility U.S. firms in

Compustat from 1970 to 2013. We define cash in the model as M1 money stock and

accordingly measure it by cash (item ch). The inter-period debt is defined as the total

debt and measured as the sum of short-term debt (item dlc) and long-term debt (item

dltt). Capital investment and equity issuance are measured by the items capx and sstk,

respectively. To minimize the effect of outliers, we winsorize all variables at the bottom

and top 1% level. To obtain model moments, we solve the model numerically.

[Table 5 about here.]

As shown in Table 5, model performance in explaining data moments is good. The

targeted moment used for calibration—the average cash ratio—matches its data counter-

part closely. We also assess model performance by reporting the nontargeted moments of

variables of particular interest. Although the model-implied volatility of inter-period debt

is smaller than the data, other nontargeted model moments are quantitatively similar to

their corresponding data moments.

Overall, the model is able to reproduce key features of the data. This strengthens the

reliability of using the parameterization in Table 4 to examine the relationship between

interest rates and firms’ money demand.

19

4.1.3 The Relationship between Interest Rates and Corporate Cash

In this subsection, we use the calibrated model to examine how firms’ cash-holding decision

responds to changes in interest rates. We let interest rates take the values of equally

spaced points in the interval [0.01,0.09] and keep other parameters the same as those in

the benchmark model. The comparative statics result is plotted in the upper left panel

of Figure 4. To facilitate the interpretation, we also plot the response of firms’ capital

investment decisions to interest rates in the upper right panel, and the responses of cash

and capital investments to interest rates in the case of zero fixed operating costs (cf = 0)

in the lower two panels.

[Figure 4 about here.]

As shown in the upper left panel of Figure 4, the interest-cash relationship exhibits an

inverted-U shape. This result is generated by the interaction among interest rates, financial

frictions and fixed operating costs: The presence of financial frictions and fixed operating

costs creates a wedge between the cost of borrowing and risk-free interest rates, which

in turn generates strong transaction demand for cash holdings. More specifically, fixed

operating costs consume the debt capacity that would otherwise be available to service old

debt and finance capital investments, and thus push leverage up. This drives up firms’

default risk and cost of debt. In response, firms accumulate internal cash for two purposes:

(i) to reduce default risk, increase debt capacity, and utilize the raised cheap debt to

facilitate operation in the current period without resorting to expensive equity financing,

and (ii) to save equity-financing costs in the subsequent period if firms have to borrow

externally to finance debt payment, operating costs and/or capital investments.

Interest rates affect discount rates. As interest rates increase, firm value Vt+1 (present

value of expected future dividends) falls and default probability (E1Vt+1≤0) rises. Fixed

operating costs tighten firms’ budget constraints and further push up default risk and cost

of debt, which result in stronger demand for cash. As a result, cash holdings increase with

20

interest rates, when we assume no impacts of interest rates on firms’ capital investment

decisions.

Next, we consider the response of investment to changes in interest rates. When interest

rates and thus cost of debt are low, firms raise leverage to loosen budget constraints. Having

adequate resources on hand, firms choose the first best level of capital investment. As

interest rates go up and become high, tightened budget constraints and high borrowing costs

caused by fixed operating costs discourage investment spending. Weak capital investment

needs significantly lower the demand for cash, resulting in a negative relationship between

firms’ cash holdings and interest rates at high interest rates. Putting these pieces together

produces an inverted-U relationship between cash ratios and interest rates—that is, cash

ratios first increase and then fall with interest rates.

There are three points to note here. First, the reason for the negative relationship

between interest rates and cash ratios when interest rates are high differs from the common

view. That is, the negative relationship is mainly driven by the weak investment that

results from high fixed operating costs and financial frictions, rather than the higher forgone

interest earnings, as conventional wisdom maintains.

Second, our benchmark model’s prediction on the sensitivity of firms’ capital invest-

ments to interest rates is consistent with the survey evidence provided by Sharpe and

Suarez (2015), which lends further support to the validity of our model. That is, firms do

not adjust their capital investment in response to interest rates changes when interest rates

are low, either because of low cost of debt or because of adequate cash on hand; and firms

tend to cut back their capital spending when they face high interest rates.

Lastly, considering the cash-holding benefit that is generated by financial frictions in

the model overturns the traditional monetary theory’s prediction on the monotonically

negative relationship between cash and interest rates. This is true even if we remove fixed

operating costs, as shown in the lower two panels of Figure 4. In the absence of transaction

motive for cash demand induced by fixed operating costs (cf = 0), budget constraints are

21

occasionally binding. Firms, therefore, keep a low and constant level of cash holdings for

precautionary considerations and invest at the first-best level regardless of interest rate

changes.

4.1.4 Sensitivity Analysis

Next we consider the robustness of the key result obtained above with respect to several

debatable parameters—convex capital adjustment costs (γ1), resale price for disinvestment

(γ2), and debt recovery rate (χ)—and the model assumption about the interest income

earned on cash holdings. We make one modification at a time and present results in Figure

5.

[Figure 5 about here.]

4.1.4.1 Parameterization

The effect of convex capital adjustment costs γ1 on interest-cash relationship is plotted in

the upper left panel. As shown, the relationship remains inverted U-shaped. Changes in

convex capital adjustment costs mainly affect the level of cash ratios by shifting the whole

money demand schedule upward. When γ1 falls to 0.049, firms have weaker incentives

to smooth out investment compared to the benchmark case. As such, firms have less

predictable investment needs, and therefore a stronger precautionary motive for holding

cash.

The response of the money demand curve to resale price for disinvestment γ2 is plotted in

the upper right panel. The overall shape of the curve is unchanged, yet a lower resale price

of capital affects firms’ cash policy at different interest rates in different ways. When the

interest rate is low, capital investment is on average positive, because of cheap borrowing

costs. A lower resale price then implies a lower benefit of investing in capital, leading

to a weaker need for holding cash to fund capital investment relative to the benchmark

model. When the interest rate is high, firms tend to disinvest. A lower resale price of

22

capital indicates a smaller internal liquidity buffer. Facing financial frictions, firms choose

to accumulate more cash to remain active on the market and fund fixed operating costs.

Changes in the debt recovery rate χ also have no effects on the shape of the money

demand curve but affect the cash level, as shown in the bottom left panel. A lower recovery

rate of physical capital implies that a larger loss would arise in the event of default, and

thus raises the value of cash in reducing the cost of debt when default risk is high. The

average cash ratio, therefore, decreases with debt recovery rate χ.

4.1.4.2 Business Sweep Programs

In the benchmark model, we assume zero interest income on cash holdings. However, in

reality firms earn interest on their cash reserves under business sweep programs.8 Taking

into account this fact, we next relax the model restriction. To ensure the existence of an

upper bound on optimal cash holdings, interest income is taxed at a rate of 35%.

Overall, allowing firms to earn interest i on their cash balances has no impacts on the

shape of corporate money demand, as shown in the bottom right panel. This is because

the inverted-U shape is driven by two factors: (i) a rise in the default risk and thus the

spread between external borrowing costs and cash-holding costs as interest rates increase,

and (ii) weak external borrowing needs caused by low capital investment at high interest

rates. Paying interest on cash balances lowers cash-holding costs and strengthens the role

of the first factor. However, it affects the optimal levels of cash holdings. When interest

rates are low, firms are less likely to be financially distressed. Lower holding costs translate

into more resources available in future and lead firms to accumulate less cash relative to

the benchmark model. When interest rates are high, cost of debt becomes expensive and

firms are more likely to be financially constrained. Lower holding costs make cash more

valuable and result in higher cash ratios relative to the benchmark case.

8Business sweep programs, similar to NOW accounts, were initiated by commercial banks during the 1960s and1970s. In these programs, money in business checking accounts were swept overnight into interest-earning assets. Theprimary intention was to allow firms to earn interest overnight on demand deposits, which was prohibited under theBanking Acts of 1933 and 1935.

23

Overall, although changes in parameters and cash-holding costs have significant effects

on the level of cash ratios, they have only a slight influence on the inverted-U shape of

firms’ money demand, and therefore do not alter the model’s central result.

4.2 Empirical Evidence

The model implies that the nominal interest rate affects corporate cash holdings through

two channels: changes in holding costs and changes in external borrowing costs. These two

channels move against one another. On average, the response of corporate cash to changes

in interest rates exhibits an inverted-U shape. In this subsection, we test this prediction.

4.2.1 Regression Model

We use the baseline cash regression model (1) in Section 2 and include a quadratic term of

nominal interest rates:

cashi,t = α0 + α1 interest ratet + α2 interest rate2t + α3 GDP growtht + α4 GDPt

+ α5 market to booki,t + α6 cash flowi,t + α7 net working capitali,t + α8 capital

expenditurei,t + α9 leveragei,t + α10 R&Di,t + α11 dividendi,t + α12 firm sizei,t

+ α13 acquisitioni,t + +α14 investment gradei,t + α15 industry riskj,t + α16 lagged

cashi,t + industryj + decaden + εi,t. (5)

Our model predicts an inverted-U relationship between nominal interest rates and firms’

cash ratios. We therefore expect that the coefficient of interest rates α1 to be positive, and

the coefficient of the quadratic term of interest rates α2 to be negative.

4.2.2 Estimation Results

Estimation results are reported in Table 6. The estimated coefficients of the three-month

T-bill rate and its squared term are consistent with our model’s prediction. The former is

24

positive, and the latter is negative. Both are statistically significant at the 1% level.

[Table 6 about here.]

Estimation results indicate that firms’ cash ratios, on average, increase with nominal

interest rates when the rate is lower than 5.41% and decline with nominal interest rates

when the rate is higher than that level. Adding industry fixed effects and firm fixed effects

hardly changes the estimation results. The cut-off points suggested in Columns (2)-(4)

range from 5.07% to 5.3%.

We estimate the regression model (5) using alternative measures of nominal interest

rates and report results in Table 7. Estimates confirm the findings in Table 6—that is,

firms’ cash ratios first increase and then fall with nominal interest rates—although the

implied cut-off point changes slightly, and moves within the range [3.85%, 6.82%].

[Table 7 about here.]

In summary, Tables 6 and 7 provide strong evidence in support of the model’s prediction

of an inverted-U relationship between interest rates and firms’ cash holdings. The turning

point is approximately at an interest rate of 5-6%. Figure 6 provides a graphic depiction of

the estimated interest-cash relationship derived from the firm fixed-effects specification.9

[Figure 6 about here.]

4.2.3 International Evidence

In addition, we test whether our model’s prediction of the inverted U-shaped money demand

also holds in other major developed countries, including UK, Germany, France, Italy, Spain,

and Japan.

9To plot the estimated conditional relationship between cash and interest rates, we fix other covariates at theirsample means and compute the cash ratio at each interest-rate level with the estimated coefficients reported in Tables6 and 7.

25

The sample for each country is constructed from Compustat Global files, covering annual

observations from 1987 to 2011 for all countries except for Germany. We use the post-

reunification period (1991-2011) for the latter so as to remove possible effects of structural

breaks. As in the U.S. analysis, We exclude financial firms and utilities, and impose outlier

rules on variables by winsorizing them at the 1st and 99th percentiles. Macroeconomic data

are collected from the International Data Section of the Federal Reserve Systems.

Since only a small number of firms have a full set of firm-level characteristics available

in the Compustat Global files, we follow the specification used by Azar et al. (2016) to

conserve data. We use firm size as the only observed firm-specific control and include cubic

time trend and firm fixed effects in addition to interest rates, GDP and GDP growth rate.

The regression model is specified below:

cashi,t = α0 + α1 interest ratet + α2 interest rate2t + α3 GDP growtht + α4 GDPt

+ α5 firm sizei,t + α6 t+ α7 t2 + α8 t

3 + firmi + εi,t. (6)

We use three-month T-Bill rates as our interest-rate measure for UK, France, Italy, Spain,

and Japan, and use 90-day interbank rates for Germany, because the three-month T-Bill

rates are unavailable for the latter after 2007.

Table 8 summarizes the estimation results. Panel A shows the results when only the

linear term of interest rates is included. Like in the U.S., we find no evidence of a sig-

nificantly negative correlation between corporate cash and interest rates in any of the six

countries. A significantly positive relationship, instead, is found in France, Italy, Spain,

and Japan. Panel B reports the results of regression model (6) when the quadratic term of

interest rates is added. The estimated coefficients of interest rates α1 and squared interest

rates α2 are found to be positive and negative, respectively, in all countries. Moreover,

the estimated coefficients are statistically significant in most cases. These results provide

international evidence for the inverted-U relationship between interest rates and firms’ cash

26

holdings predicted by our model.

[Table 8 about here.]

4.3 Implications of the Inverted-U Cash-Interest Relationship

In this subsection, we revisit three important questions of money demand: the welfare cost

of inflation, monetary policy and its transmission channels, and the U.S. corporate cash

puzzle.

4.3.1 Welfare Cost of Inflation

A classic question concerning money demand is the welfare cost of inflation. Bailey (1956)

treats real money balances as a consumption good and inflation as the tax imposed on

them, and measures the welfare cost of inflation by calculating the area under the inverse

money demand curve over a given segment of real money balances. Different money demand

curves, therefore, imply different estimates for the welfare cost.

In spite of a long line of research on this question, no clear consensus has been reached

on the magnitude of the cost. One source of the discrepancy for the estimates arises from

the money demand behavior at low interest rates. Lucas (2000) shows that U.S. historical

real balances from 1900 to 1994 are well predicted by a log-log function. This demand

specification implies an arbitrarily large money demand, and thus a sizeable welfare cost of

inflation as the nominal interest rate approaches zero. Ireland (2009) extends the analysis

and considers more recent data. He finds that a semi-log curve better fits U.S. money

demand behavior. This suggests a finite level of real balances when the interest rate is

close to zero, which in turn implies a moderate level for the welfare cost of inflation.

Our estimation result speaks to the question of whether a satiation level in money

demand exists at zero interest rates, and sheds light on the magnitude of the welfare cost.

It suggests an inverted U-shaped money demand function. When interest rates go low, the

low cost of holding cash in terms of forgone interest earnings is offset by its low benefit

27

from reducing borrowing costs, which leads to weak demand for cash. This implies a

modest welfare cost of the low and stable inflation policy pursued by the Federal Reserve,

supporting the view put forward by Mulligan and Sala-i Martin (2000) and Ireland (2009).

4.3.2 Monetary Policy

Two of the central questions in monetary economics are the effectiveness of monetary

policy and its transmission mechanisms. The responses of corporate cash and investment

to interest rates derived in Subsection 4.1.3 have important implications for them.

The inverted-U relationship between corporate cash and interest rates suggests that an

interest-rate target should be preferred to a money-supply target. The latter can generate

multiple equilibria in the money market, move interest rates toward an unintended level,

and cause undesirable economic consequences.

Moreover, our model suggests that, as a result of low borrowing costs and/or sufficient

cash on hand, firms invest at the first-best level and do not respond to interest rate changes

when interest rates are low. This result challenges two often-discussed channels through

which monetary policy stimulates the real economy: the interest rate channel and the

balance sheet channel.10 Both channels boost output by increasing lending and raising

investment. However, the existence of corporate cash reserves reduces the likelihood of

financial distress and underinvestment in capital and, therefore, dampens the importance

of both transmission mechanisms.

4.3.3 U.S. Corporate Cash Puzzle

The last few decades have witnessed substantial cash accumulation in the economy. As

shown in Figure 2, the average cash-to-assets ratio for the U.S. corporate sector has in-

creased steadily from 4.1% in 1984 to 21.1% in 2013. Puzzled by the trend and concerned

about potential resource misallocation within firms from high-productivity assets to cash,

10Mishkin (1996) provides a summary of the channels of monetary transmission.

28

there is a rapidly growing number of studies that aim to understand this phenomenon.

Azar et al. (2016) argue that corporate cash hoarding phenomenon can be rationalized

by the reduction in interest rates since the 1980s. More specifically, nominal interest rates

are positively associated with the cost of holding cash. A fall in interest rates implies a

drop in the carrying cost of cash and therefore can explain the secular trend in corporate

cash balances.

We in this paper emphasize cash-holding benefit, which co-moves with interest rates.

Our result obtained in previous subsections challenges the cost-based explanation proposed

by Azar et al. (2016). The increase in cash holdings from 1984-1991 can be attributed to

a drop in interest rates, yet for a different reason. Interest rates fell significantly from

9.5% to 5.4% during that period. Lower borrowing costs encourage investment spending

and then generate strong demand for cash. Moreover, the drop in interest rates from 5.4%

to 0.06% during 1991-2013 hardly contributes to the secular increase in corporate cash

reserves during that period; instead, the interest-rate cuts would reduce borrowing costs

and cash-holding benefit, and lead to a decline in cash ratios.

5 Conclusion

This paper investigates the relationship between interest rates and corporate cash holdings.

We first demonstrate that the nominal interest rate is, on average, insignificantly positively

associated with firms’ cash-to-assets ratios. This finding is at odds with the literature on

monetary economics, which suggests a negative relationship. We then develop a structural

model to rationalize the observed finding and carefully study the interest-cash relationship.

We show that the response of corporate cash holdings to interest rates displays an

interesting nonmonotonic pattern: an inverted-U shape. Initially, the benefit of holding

cash by reducing default risk and cost of debt and saving equity-issuance costs outpaces

the cash-holding costs in terms of forgone interest, which generates the upward-sloping

29

part of the schedule. As interest rates continue to rise and become high, worsened credit

conditions and tightened firms’ budgets result in capital investment cuts. Lower capital

investment needs contribute to a lower demand for cash, and the cash ratio, accordingly,

declines with interest rates. This result is strongly supported by data, and offers a plausible

explanation for the insignificant interest-cash relationship highlighted in Section 2.

We then explore the policy implications of the implied inverted-U relationship between

interest rates and corporate cash holdings. First, the inverted-U shape implies a satiation

level of cash holdings at zero interest rates, which in turn suggests that low inflation—a

modest departure from the Friedman rule—generates moderate welfare losses. Second,

the shape suggests that the Federal Reserve should choose interest-rate targeting over

monetary targeting. The latter may result in undesirable economic consequences due to

multiple equilibria in the money market. Third, the U.S. corporate cash puzzle cannot be

attributed to a drop in the cost of cash holdings over time. The benefit of cash holdings

also co-moves with nominal interest rates.

In this paper, we take as given that firms allocate a constant and low share of their total

assets to short-term interest-bearing securities and abstract from the trade-off between

cash and interest-bearing assets. Although this data feature per se is interesting and

worth exploring, disregarding it has little impact on our conclusion about the interest-cash

relationship. We plan to return to this in future work.

30

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33

Appendix

A. Variable Definitions

Following Bates et al. (2009), we construct the sample from Compustat and define the

variables used in the cash regressions as follows:

Cash is defined as the ratio of cash over total assets.

Firm size is the natural logarithm of a firm’s total assets divided by GDP deflator in the

corresponding year.

Industry risk is measured by the volatility of cash flow to assets within two-digit or

three-digit SIC groups. As in Bates et al. (2009), we calculate the standard deviation of

cash flow to assets for the previous 10 years for each firm within that group. We exclude

firms that have fewer than three observations. Industry risk for each group is the average

of the standard deviation of cash flow to assets in that group.

Cash flow is the ratio of earnings after interest and dividend to total assets.

Market-to-book ratio is measured as the market value of the firm divided by total book

asset value. Market value is proxied by book value of assets plus market value of equity,

less book value of common equity and deferred tax.

Net working capital is defined as net working capital less cash to total assets.

Capital investment is measured as capital expenditure divided by total assets.

Leverage is defined as current debt plus long-term debt over total assets.

R&D investment is measured as R&D expenses over sales. We set R&D expenses to zero

if they are missing.

Dividend is set to one if a firm pays a common dividend or preferred dividend in a given

year and zero otherwise.

Acquisition is defined as acquisitions divided by total assets.

Investment grade dummy is set to one if a firm has a bond grade of BBB- and above;

otherwise, the dummy is zero.

34

Interest rate is measured as three-month T-bill rate in our baseline specification. We

also consider one-year, five-year, ten-year Treasury Constant Maturity Rates, and federal

funds effective rate in the robustness analysis.

GDP is the natural logarithm of annual real GDP in billions of chained 2009 dollars.

35

.2.3

.4.5

sh

are

of

ca

sh

ho

ldin

gs in

no

nfin

an

cia

l b

usin

esse

s

1960 1970 1980 1990 2000 2010year

Figure 1: Share of Aggregate Money Stock Held by Nonfinancial Businesses in the U.S. The figure plotsthe share of aggregate money stock M1 (i.e., checkable deposits and currency) held by nonfinancial businesses in theU.S. from 1959 to 2013. Data are collected from FRED and the Flow of Funds accounts maintained by the FederalReserve Bank of St. Louis and the Federal Reserve Board.

36

0.0

5.1

.15

.2fr

action

1970 1980 1990 2000 2010year

3−month T−bill Rate Average Cash Ratio

Figure 2: Average Cash Ratio and Nominal Interest Rates. The figure plots the average cash-to-assets ratio andnominal interest rates in the U.S. from 1970 to 2013. The average cash ratio is calculated with a sample of nonfinancialnonutility publicly traded U.S. firms in Compustat, with cash measured by item ch (corresponding to M1 monetaryaggregate). The nominal interest rate is the annualized three-month T-bill rate in the economy.

37

.05

.1.1

5.2

.25

fraction

1970 1980 1990 2000 2010year

Cash and Short−term Assets Ratio Cash Ratio

Figure 3: Average Short-term Investment Ratio. The figure plots the average cash and average cash plus short-term investment ratios in the U.S. from 1970 to 2013. Ratios are calculated with a sample of nonfinancial nonutilitypublicly traded U.S. firms in Compustat. Cash is measured by the item ch, and cash and short-term investment aremeasured by the item che. The short-term investment-to-assets ratio is the distance between the two plotted ratios.

38

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

0.05

0.1

0.15

0.2

0.25

ca

sh r

atio

r

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

investm

ent ra

tio

r

benchmark benchmark

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090

0.05

0.1

0.15

0.2

0.25

cash

ratio

r

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

investm

ent ra

tio

r

cf=0 c

f=0

Figure 4: Corporate Money Demand: Channel Exploration. The figure plots the responses of firms’ cash andinvestment ratios with respect to interest rates under different parameterizations to illustrate the mechanisms of theinverted-U relationship between coporate cash demand and interest rates. The upper two panels plot the responses inthe benchmark model, and the lower two panels show the responses in the case of zero fixed operating costs cf = 0.

39

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.1

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Sweep programs

Figure 5: Corporate Money Demand: Sensitivity Analysis. The figure plots the responses of firms’ cash ratioswith respect to interest rates under different parameterizations (γ1, γ2, and χ) and model assumptions.

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0 .02 .04 .06 .08 .1interest rate

3−month T−bill 1−year T−bill

1−year TCMR 5−year TCMR

10−year TCMR

Figure 6: Average Cash Ratio and Nominal Interest Rates: Quadratic Specification. The figure plots theestimated relationship between cash ratio and nominal interest rates using regression model (5). Estimates are obtainedfrom the firm fixed-effects specification, reported in the last columns of Tables 6 and 7.

41

Table 1: Summary Statistics

Table 1 presents descriptive statistics for each variable used in regression equation (1)and reports the mean, standard deviation, minimum value, maximum value, and numberof observations. The sample is constructed from Compustat Annual files from 1970 to2013. A detailed definition of variables is provided in Appendix A.

Mean Std. Min Max Number of Obs.Cash holdings 0.1453 0.1974 0 0.9610 81139Three-month T-bill 0.0345 0.0293 0.0005 0.1403 84345One-year T-bill 0.0383 0.0318 0.0013 0.1314 64595One-year TCMR 0.0385 0.0313 0.0013 0.1478 84345Five-year TCMR 0.0473 0.0283 0.0076 0.1425 84345Ten-year TCMR 0.0530 0.0249 0.018 0.1392 84345Federal Funds Rate 0.0380 0.0328 0.001 0.1639 84345GDP 9.3691 0.3027 8.4591 9.6653 84345GDP growth rate 0.0250 0.0189 -0.028 0.073 84345Market-to-book ratio 4.8550 17.0697 0.5047 149.8135 72643Cash flow -0.2835 1.7388 -14.2821 0.3764 78728Net working capital -0.2321 1.8187 -15.4524 0.5539 81899Capital expenditure 0.0625 0.0730 0 0.4137 83215Leverage 0.3384 0.7395 0 6.1842 84028R&D 0.3284 1.7940 0 15.8444 81990Dividend dummy 0.4400 0.4964 0 1 83542Firm size 5.3435 2.9093 -6.9715 11.8244 84345Industry risk (2-digit) 0.1905 0.1937 0.0029 1.3177 83932Industry risk (3-digit) 0.2080 0.2997 0.0029 7.1635 81829Acquisition 0.0181 0.0532 -0.0052 0.3330 79648Investment grade dummy 0.1166 0.3209 0 1 84345

42

Table 2: Cash Holdings and Interest Rates: Baseline Model

Table 2 reports estimation results of the baseline cash regression on interestrates, firms’ characteristics, industry risk, and real GDP and its growth.Industry and decade fixed effects are also included in the regressions. Theheteroskedasticity-consistent standard errors reported in parentheses accountfor possible correlation within a firm cluster. Significance levels are indicatedby *, **, and *** for 10%, 5%, and 1%, respectively.

(1) (2) (3) (4)Three-month T-bill 0.0463∗ 0.0339 0.0311 0.0223

(0.0266) (0.0267) (0.0274) (0.0292)GDP growth -0.0009∗∗∗ -0.0010∗∗∗ -0.0012∗∗∗ -0.0011∗∗∗

(0.0003) (0.0003) (0.0003) (0.0003)GDP 0.0407∗∗∗ 0.0461∗∗∗ 0.0513∗∗∗ 0.0529∗∗∗

(0.0057) (0.0057) (0.0058) (0.0066)Market-to-book 0.0011∗∗∗ 0.0011∗∗∗ 0.0011∗∗∗ 0.0018∗∗∗

(0.0002) (0.0002) (0.0002) (0.0002)Cash flow 0.0063∗∗∗ 0.0058∗∗∗ 0.0053∗∗∗ 0.0074∗∗∗

(0.0015) (0.0015) (0.0015) (0.0019)Net working capital -0.0086∗∗∗ -0.0078∗∗∗ -0.0073∗∗∗ -0.0058∗

(0.0016) (0.0016) (0.0016) (0.0020)Capital expenditure -0.2200∗∗∗ -0.2222∗∗∗ -0.2275∗∗∗ -0.2436∗∗∗

(0.0093) (0.0116) (0.0126) (0.0140)Leverage -0.0302∗∗∗ -0.0295∗∗∗ -0.0288∗∗∗ -0.0323∗∗∗

(0.0028) (0.0028) (0.0028) (0.0039)R&D 0.0064∗∗∗ 0.0061∗∗∗ 0.0054∗∗∗ 0.0024∗∗∗

(0.0006) (0.0007) (0.0007) (0.0010)Dividend -0.0067∗∗∗ -0.0046∗∗∗ -0.0011 0.0066∗∗∗

(0.0012) (0.0012) (0.0012) (0.0018)Size -0.0038∗∗∗ -0.0037∗∗∗ -0.0039∗∗∗ -0.0118∗∗∗

(0.0003) (0.0004) (0.0004) (0.0013)Acquisition -0.2752∗∗∗ -0.2759∗∗∗ -0.2730∗∗∗ -0.2037∗∗∗

(0.0092) (0.0094) (0.0097) (0.0096)Investment grade -0.0052∗∗∗ -0.0057∗∗∗ -0.0055∗∗∗ -0.0025

(0.0013) (0.0014) (0.0014) (0.0017)Industry risk (2-digit) 0.0485∗∗∗ 0.0290∗∗∗ 0.0268∗∗∗

(0.0048) (0.0057) (0.0083)Industry risk (3-digit) 0.0151∗∗∗

(0.0038)Lagged Cash 0.6268∗∗∗ 0.6179∗∗∗ 0.6064∗∗∗ 0.3820∗∗∗

(0.0077) (0.0079) (0.0081) (0.0098)Decade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5703 0.5731 0.5773 0.5321No. of Obs. 56595 56595 55352 56595

43

Table 3: Cash Holdings and Interest Rates: Robustness

Table 3 reports robustness checks on the main results presented in Table2. Panel A summarizes results when regression model (1) is estimatedusing one-year T-bill rates. Panels B, C, and D consider one-year,five-year, and ten-year treasury constant maturity rates, respectively.Panel E uses the federal funds effective rates. The heteroskedasticity-consistent standard errors reported in parentheses account for possiblecorrelation within a firm cluster. Significance levels are indicated by *,**, and *** for 10%, 5%, and 1%, respectively.

Panel A (1) (2) (3) (4)One-year T-bill 0.0564∗ 0.0381 0.0262 -0.0433

(0.0334) (0.0334) (0.0347) (0.0375)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5757 0.5783 0.5827 0.5405No. of Obs. 42139 42139 41051 42139Panel B (1) (2) (3) (4)One-year TCMR 0.0381 0.0249 0.0222 0.0139

(0.0266) (0.0267) (0.0274) (0.0294)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5703 0.5731 0.5773 0.5321No. of Obs. 56595 56595 55352 56595Panel C (1) (2) (3) (4)Five-year TCMR 0.0585 0.0358 0.0334 0.0200

(0.0376) (0.0376) (0.0388) (0.0420)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5703 0.5731 0.5773 0.5321No. of Obs. 56595 56595 55352 56595Panel D (1) (2) (3) (4)Ten-year TCMR 0.0392 0.0117 0.0177 -0.0011

(0.0454) (0.0455) (0.0474) (0.0496)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5703 0.5731 0.5773 0.5321No. of Obs. 56595 56595 55352 56595Panel E (1) (2) (3) (4)Federal Funds Rate 0.0408∗ 0.0302 0.0283 0.0206

(0.0229) (0.0230) (0.0236) (0.0250)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5703 0.5731 0.5773 0.5321No. of Obs. 56595 56595 55352 56595

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Table 4: Model Parameterizations

Table 4 summarizes the parameter values used to solve the model at anannual frequency. Parameters include those specifying revenue func-tion, shocks, a firm’s external financing conditions, interest rates, andfixed production costs.

Parameter Valuerisk-free rate (r) 0.04capital share (α) 0.30curvature of revenue function (θ) 0.83persistency of idiosyncratic revenue shock (ρ) 0.64standard deviation of idiosyncratic revenue shock (σz) 0.34nonconvex capital adjustment costs (γ0) 0.039convex capital adjustment costs (γ1) 0.7resale price for disinvestment (γ2) 0.50capital depreciation rate (δ) 0.12labor supply elasticity (γ) 7debt recovery rate (χ) 0.50fixed equity issuance costs (λ0) 0.20linear equity issuance costs (λ1) 0.05fixed production costs (cf ) 0.068

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Table 5: Model Moments

Table 5 presents moments of particular interest. Data moments are calculatedbased on a sample of nonfinancial and nonutility firms over the period from1970 to 2013.

Moments data model(i) cash to assets (ct+1/(kt+1 + ct+1))mean 0.145 0.142standard deviation 0.193 0.192(ii) inter-period debt to assets (bt/(kt+1 + ct+1))mean 0.338 0.352standard deviation 0.677 0.373(iii) capital investment to assets (It/(kt+1 + ct+1))mean 0.063 0.100standard deviation 0.073 0.116(iv) equity issuance to assets (et/(kt+1 + ct+1) when et < 0)mean 0.108 0.128standard deviation 0.312 0.313

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Table 6: Cash Holdings and Interest Rates: Quadratic Specification

Table 6 reports estimation results of the cash regression on interest rates,quadratic term of interest rates, firms’ characteristics, industry risk, and realGDP and its growth. Industry and decade fixed effects are also included in theregressions. Heteroskedasticity-consistent standard errors reported in paren-theses account for possible correlation within a firm cluster. Significance levelsare indicated by *, **, and *** for 10%, 5%, and 1%, respectively.

(1) (2) (3) (4)Three-month T-Bill 0.2067∗∗∗ 0.1765∗∗∗ 0.1430∗∗∗ 0.1496∗∗∗

(0.0481) (0.0480) (0.0487) (0.0550)Three-month T-Bill2 -1.9110∗∗∗ -1.6912∗∗∗ -1.3480∗∗∗ -1.4751∗∗∗

(0.3542) (0.3512) (0.3597) (0.4007)GDP growth -0.0012∗∗∗ -0.0013∗∗∗ -0.0014∗∗∗ -0.0013∗∗∗

(0.0003) (0.0003) (0.0003) (0.0003)GDP 0.0413∗∗∗ 0.0463∗∗∗ 0.0517∗∗∗ 0.0525∗∗∗

(0.0057) (0.0057) (0.0058) (0.0066)Market-to-book 0.0011∗∗∗ 0.0011∗∗∗ 0.0011∗∗∗ 0.0018∗∗∗

(0.0002) (0.0002) (0.0002) (0.0002)Cash flow 0.0062∗∗∗ 0.0058∗∗∗ 0.0053∗∗∗ 0.0074∗∗∗

(0.0015) (0.0015) (0.0015) (0.0019)Net working capital -0.0086∗∗∗ -0.0079∗∗∗ -0.0073∗∗∗ -0.0059∗∗∗

(0.0016) (0.0016) (0.0016) (0.0020)Capital expenditure -0.2198∗∗∗ -0.2221∗∗∗ -0.2273∗∗∗ -0.2438∗∗∗

(0.0093) (0.0116) (0.0126) (0.0140)Leverage -0.0302∗∗∗ -0.0295∗∗∗ -0.0288∗∗∗ -0.0323∗∗∗

(0.0028) (0.0028) (0.0028) (0.0039)R&D 0.0064∗∗∗ 0.0061∗∗∗ 0.0054∗∗∗ 0.0023∗∗

(0.0006) (0.0007) (0.0007) (0.0010)Acquisition -0.2764∗∗∗ -0.2770∗∗∗ -0.2739∗∗∗ -0.2049∗∗∗

(0.0093) (0.0094) (0.0097) (0.0097)Dividend -0.0066∗∗∗ -0.0045∗∗∗ -0.0010 0.0068∗∗∗

(0.0012) (0.0012) (0.0012) (0.0018)Investment grade -0.0057∗∗∗ -0.0062∗∗∗ -0.0058∗∗∗ -0.0033∗∗

(0.0013) (0.0014) (0.0014) (0.0017)Size -0.0037∗∗∗ -0.0037∗∗∗ -0.0038∗∗∗ -0.0117∗∗∗

(0.0003) (0.0004) (0.0004) (0.0013)Industry risk (2-digit) 0.0467∗∗∗ 0.0307∗∗∗ 0.0284∗∗∗

(0.0048) (0.0057) (0.0084)Industry risk (3-digit) 0.0158∗∗∗

(0.0038)Lagged Cash 0.6269∗∗∗ 0.6181∗∗∗ 0.6066∗∗∗ 0.3822∗∗∗

(0.0077) (0.0079) (0.0081) (0.0098)Decade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5704 0.5732 0.5773 0.5325No. of Obs. 56595 56595 59352 56595

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Table 7: Cash Holdings and Interest Rates: Robustness

Table 7 reports robustness checks on the results presented in Table 6.Panel A summarizes the results when regression model (5) is estimatedusing one-year T-bill rates. Panels B, C, and D consider one-year, five-year and ten-year treasury constant maturity rates, respectively. Panel Euses the federal funds effective rate. Heteroskedasticity-consistent stan-dard errors reported in parentheses account for possible correlation withina firm cluster. Significance levels are indicated by *, **, and *** for 10%,5%, and 1%, respectively. Note that to conserve space, we do not reportnumber of observations which are the same as those in Table 3.

Panel A (1) (2) (3) (4)One-year T-bill 0.3171∗∗∗ 0.2799∗∗∗ 0.2111∗∗∗ 0.1320∗

(0.0691) (0.0689) (0.0702) (0.0804)One-year T-bill2 -2.6651∗∗∗ -2.4486∗∗∗ -1.9044∗∗∗ -1.7141∗∗∗

(0.4767) (0.4744) (0.4831) (0.5409)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5758 0.5785 0.5828 0.5410Panel B (1) (2) (3) (4)One-year TCMR 0.2033∗∗∗ 0.1729∗∗∗ 0.1383∗∗∗ 0.1538∗∗∗

(0.0476) (0.0474) (0.0482) (0.0550)One-year TCMR2 -1.8323∗∗∗ -1.6337∗∗∗ -1.3026∗∗∗ -1.5047∗∗∗

(0.3253) (0.3227) (0.3301) (0.3721)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5704 0.5732 0.5773 0.5326Panel C (1) (2) (3) (4)Five-year TCMR 0.3402∗∗∗ 0.2934∗∗∗ 0.2408∗∗∗ 0.2892∗∗∗

(0.0671) (0.0667) (0.0679) (0.0790)Five-year TCMR2 -2.7802∗∗∗ -2.5247∗∗∗ -2.0686∗∗∗ -2.5381∗∗∗

(0.4164) (0.4124) (0.4212) (0.4804)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5704 0.5733 0.5774 0.5329Panel D (1) (2) (3) (4)Ten-year TCMR 0.5096∗∗∗ 0.4406∗∗∗ 0.3688∗∗∗ 0.4519∗∗∗

(0.0979) (0.0973) (0.0993) (0.1130)Ten-year TCMR2 -3.7381∗∗∗ -3.3893∗∗∗ -2.8114∗∗∗ -3.4760∗∗∗

(0.5504) (0.5452) (0.5553) (0.6328)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5705 0.5733 0.5774 0.5329Panel E (1) (2) (3) (4)Federal Funds Rate 0.1750∗∗∗ 0.1487∗∗∗ 0.1206∗∗∗ 0.1246∗∗∗

(0.0420) (0.0419) (0.0426) (0.0477)Federal Funds Rate2 -1.3547∗∗∗ -1.1908∗∗∗ -0.9437∗∗∗ -1.0208∗∗∗

(0.2592) (0.2571) (0.2630) (0.2912)Other covariates Yes Yes Yes YesDecade fixed effect Yes Yes Yes YesIndustry fixed effect No Two-digit Three-digit FirmR-squared 0.5704 0.5732 0.5773 0.5324

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Table 8: Cash Holdings and Interest Rates: International Evidence

Table 8 reports the estimation results of the cash regression on interest rates, firm size, realGDP and its growth for six major developed countries. Firm fixed effects and cubic time trendare also included in the regressions. Panel A summrizes the results when only the linear termof interest rates is included. Panel B reports the results when the quadratic term of interestrates is added. Heteroskedasticity-consistent standard errors reported in parentheses accountfor possible correlation within a firm cluster. Significance levels are indicated by *, **, and ***for 10%, 5%, and 1%, respectively.

Panel A (1) (2) (3) (4) (5) (6)UK Germany France Italy Spain Japan

Interest Rate 0.1669 0.2018 0.4118∗∗ 1.6108∗∗∗ 0.3315∗∗∗ 0.6403∗∗∗

(0.1703) (0.4193) (0.1914) (0.2397) (0.1029) (0.0714)Macro Controls Yes Yes Yes Yes Yes YesFirm Size Control Yes Yes Yes Yes Yes YesFirm fixed effect Yes Yes Yes Yes Yes YesCubic Time Trend Yes Yes Yes Yes Yes YesR-squared 0.1513 0.1021 0.0653 0.1640 0.1222 0.0332No. of Obs. 12236 6570 6051 2145 1294 44373Panel B (1) (2) (3) (4) (5) (6)

UK Germany France Italy Spain JapanInterest Rate 1.0568∗∗∗ 1.1758∗∗ 0.7098∗∗ 3.2889∗∗∗ 0.5514∗∗ 0.8468∗∗∗

(0.2817) (0.5019) (0.2928) (0.5535) (0.2253) (0.1787)Interest Rate2 -5.5687∗∗∗ -11.5108∗∗∗ -3.7997∗∗ -10.7731∗∗∗ -2.3915 -2.8974

(1.3231) (4.2701) (1.8776) (2.5095) (1.9552) (2.1778)Macro Controls Yes Yes Yes Yes Yes YesFirm Size Control Yes Yes Yes Yes Yes YesFirm fixed effect Yes Yes Yes Yes Yes YesCubic Time Trend Yes Yes Yes Yes Yes YesR-squared 0.1521 0.0989 0.0700 0.1723 0.1246 0.0338No. of Obs. 12236 6570 6051 2145 1294 44373

49