Changes in the Opportunity Cost of Cash: A Solution to the Corporate Cash Hoarding Puzzle∗ Jos´e Azar

Jean-Fran¸cois Kagy

Princeton University

Princeton University

November 6, 2011

Abstract We document a strong negative correlation between the aggregate corporate cashto-assets ratio and short-term nominal interest rates between 1951 and 2010. Most of the variation in the cash ratio, especially at lower frequencies, can be understood as movements along a relatively stable money demand relationship. A variance decomposition shows that more than 75% of the long-run variation, and roughly 50% of the medium-run variation, can be explained by shocks to interest rates. Most of the increase in the cash ratio between 1982 and 2010 can be explained by the large decrease in nominal interest rates over that period.

∗

We are grateful to Chris Sims for invaluable feedback.

1

1

Introduction

In recent years, there has been considerable interest in the cash hoarding behavior of corporations–both from academic economists and the financial world more generally. The fact that US corporations have roughly doubled their cash-to-assets ratio since the early 1980s, as documented by Bates, Kahle, and Stulz (2009), is widely considered a puzzle. Bates, Kahle, and Stulz (2009) show that the precautionary motive is important to explain variations in the cash ratio at the firm level. However, their results also suggest that only around 20% of the increase in the cash ratio between the 1980s and 2006 can be explained by the increase in cash flow volatility over that period. In this paper, we provide an alternative explanation for the observed trend in aggregate cash holdings. We examine aggregate data for the US nonfinancial corporate sector between 1951 and 2010, and find a remarkable negative correlation between the cash-to-assets ratio of corporations and the short-term nominal interest rate. We find that the current level of the corporate cash ratio is in line with historical patterns given the low levels of nominal interest rates that have been observed in recent years. The decline in the corporate cash-to-assets ratio between the 1950s and the 1980s can also be explained by changes in the nominal interest rate, which had an upward trend over that period. Historically, the main determinant of the long-run pattern of nominal interest rates was inflation, which increased between the 1950s and the 1980s, then declined until the present. Thus, our analysis suggests that the fundamental force behind the observed trends in the cash ratio was the change in the inflationary environment over time. Today’s higher corporate cash ratio relative to the early 1980s should not be too surprising, given the dramatic reduction in inflation since that period. The negative correlation between the cash ratio and the nominal interest rate suggests that the corporate cash ratio has been moving over the past 60 years along a relatively

2

stable demand function for broad money. Because the nominal interest rate is a proxy for the opportunity cost of holding cash, corporations choose to hold less cash when rates are higher. However, the nominal interest rate is a rough measure of opportunity cost, because some liquid instruments that are included in our measure of cash holdings, such as money market mutual fund shares, pay positive interest. Thus, we construct an alternative measure of the opportunity cost of holding cash, namely the difference between the short term interest rate and a weighted average of the rates of return on the components of cash. We estimate money demand equations for the nonfinancial corporate sector, and find that either measure of opportunity cost has a negative and statistically significant effect on the cash ratio. To test our interpretation of the correlation between cash and interest rates as a money demand relation, we estimate a Bayesian vector autoregression model of these variables. We find that the cash ratio responds significantly and negatively to shocks to either measure of the opportunity cost. In contrast, the response of either measure of opportunity cost to shocks to the cash ratio is relatively small and not statistically significant. We test for Granger causal priority, and find a Granger causal ordering with interest rates causing cash, but not the other way around. Using a variance decomposition, we show that more than 75% of the long-run variation in the cash ratio can be explained by shocks to the interest rate. At business-cycle frequencies, interest rate shocks can explain roughly 50% of the variation in the cash ratio. A historical decomposition also confirms that most of the medium and long-run variation in the cash ratio can be explained by movements in interest rates. Our paper is related to the literature on money demand for broad measures of money. Hetzel and Mehra (1989), Mehra (1993), Mehra (1997) and Carpenter and Lange (2003) estimate models of money demand that focus on M2. Barnett, Fisher, and Serletis (1992) estimates a model of the demand for the various components of broad money. A notable feature of the work of Barnett, Fisher, and Serletis (1992) is that they obtain estimates for 3

the demand for each component of broad money, whereas the other studies do so only for overall M2. While these studies focus on the relationship between broad measures of cash and its opportunity cost for the economy as a whole, we are specifically concerned with the money demand of the nonfinancial corporate sector. This paper is organized as follows. In Section 2, we describe the data. Section 3 describes the results from our regression analysis of the cash ratio and our measures of opportunity cost. Section 4 presents the vector autoregression analysis and the results. In Section 5, we discuss our findings. In Section 6, we conclude.

2

Data Description

We construct a quarterly series of the aggregate cash-to-assets ratio for US corporations between 1951 and 2010. Following Greenwood (2005), we use data from the Federal Reserve Flow of Funds, and calculate cash as the sum of currency and checking deposits, time and savings deposits, money market mutual fund shares and commercial paper held by the nonfarm nonfinancial corporate sector. We obtain the cash-to-assets ratio by dividing cash by the total assets held in the sector. Although they can be considered as cash-like assets, we omit short-term loans in our measure of cash because quarterly data is available only since 1992 and they represent a relatively small fraction of cash. As a first measure of the opportunity cost of holding cash, we use the nominal interest rate on 3-month T-Bills (I3M ). This is only an approximation to the true opportunity cost of holding cash for corporations, since most components of our measure of cash earn positive interest. As an alternative measure of the opportunity cost of holding cash, we use the difference between the 3-month T-Bill rate and a weighted average of the interest rates on the components of the cash ratio. We assume that currency and checking deposits pay zero

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interest. Data on rates of return on commercial paper and certificates of deposit is available from FRED. For commercial paper, between 1971Q2 and 1997Q1, we use the 3-month AA commercial paper rate. After 1997Q1, we use the average of the 3-month AA nonfinancial commercial paper rate and the 3-month AA financial commercial paper rate. For time deposits, we use the 3-month certificate of deposit secondary market rate, which has data starting in 1964Q2. We do not have data on rates of return on savings deposits, or on the relative proportion of savings and time deposits held by corporations. We thus apply the rate of return on time deposits to savings deposits. There are many types of money market mutual funds, and we do not have an index of rates of return for these funds as an asset class. As a proxy, we use the rate of return on commercial paper for this asset category. For periods in which data on the rate of return on a given component of the cash measure is not available, we proxy using the 3-month T-bill rate. We refer to the alternative measure of opportunity cost as I3M-RC. Figure 1 shows the evolution of the cash ratio over time, along with the I3M and the alternative measure I3M-RC. The scale for the cash ratio is shown on the right axis, and the scale for the other two variables is shown on the left axis. The cash ratio declined between 1951Q4 and 1982Q2, and then rose until 2010Q4 to levels similar to where it stood in the early 1950s. The long-run pattern of the measures of opportunity cost mirrored the pattern of the cash ratio. The short-term rate I3M increased until 1981Q3, then declined until 2010; since 2008Q4, it has been very close to zero. Similarly, the alternative measure I3M-RC increased until the 1980s, reaching its peak in 1980Q1, then declined until 2010, approaching near-zero levels as well. [Figure 1 goes here] To depict the relationship between the cash ratio and the measures of opportunity cost, 5

Figure 2 shows scatter plots of the cash ratio and I3M, and of the cash ratio and I3M-RC. Both measures of opportunity cost are strongly negatively correlated with the cash ratio: the correlation between the cash ratio and I3M is -0.79, and the correlation between the cash ratio and I3M-RC is -0.61. [Figure 2 goes here]

3

Regression Analysis

The negative correlation between the cash ratio and short-term interest rates can be interpreted as a money demand relation. A commonly used model for aggregate money demand is M = T · L(i), P where

M P

denotes real cash balances, T is the level of real transactions, and L(i) is a decreasing

function of the nominal interest rate i, which represents the opportunity cost of holding cash. In the case of the corporate sector, it is reasonable to assume that the level of transactions is proportional to the size of the sector, which can be proxied by the sector’s total real assets. Thus, we can express the money demand for the corporate sector as M ∝ A · L(i), P where A refers to total real assets of the sector. We can rewrite this equation in terms of the corporate cash ratio: M ∝ L(i). · A} |P {z cash ratio

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A standard functional form for money demand sets L(i) = exp (α + βi). This leads to the following regression specification:  log

Mt Pt · At

 = α + βit + t .

Table 1 summarizes the regression results. We perform the analysis using both I3M and I3M-RC. In some specifications, we include squared terms of the opportunity cost measures to test for possible nonlinearities in the money demand relationship. Both measures of opportunity cost are statistically significantly related to the cash ratio. These relations are also economically significant. In the case of I3M, an increase of 100 basis points (bp) in the interest rate is associated with a decline of approximately 6.1% in the cash ratio. In the case of the I3M-RC, an increase of 100 bp is associated with a decrease of approximately 8.5% in the cash ratio. Adding quadratic terms improves the fit in the model that uses I3M , but not in the model with I3M − RC. We note that the fit is better in the regressions that use I3M as the measure of opportunity cost compared to those that use I3M-RC. [Table 1 goes here]

4

Vector Autoregression Analysis

Before we can interpret the relationships estimated in the previous section as the response of corporate cash holdings to changes in the opportunity cost, we need to consider that changes in cash holdings can simultaneously affect the macroeconomy, thereby driving interest rates. In this section, we study the joint dynamics of the cash ratio and the measure of opportunity cost, and find that the latter does not respond to movements in the cash ratio. Figure 3 shows confidence bands for the impulse responses from a bivariate Bayesian vector autoregression (BVAR) of the log cash ratio and I3M with a flat prior and three 7

lags. The methodology to estimate the Bayesian vector autoregressions models used in this paper is described in detail in Sims and Zha (1998). We also include seasonal dummies as exogenous variables. We calculate error bands for the impulse responses following the methodology described in Sims and Zha (1999). On each graph, the darkest pair of bands represent 5% error bands; the next pair, 10% error bands; and so on, with the lightest pair being 95% error bands. We use a triangular identification scheme, where we restrict the contemporaneous response of the cash ratio to shocks to the interest rate to be zero. This is a conservative assumption for our purposes, since this ordering of the variables gives the cash ratio a better chance to explain interest rates. [Figure 3 goes here] We find that shocks to the T-Bill rate are quite persistent: a one standard deviation shock to I3M does not die out even after 6 years. Shocks to the T-Bill rate also have a negative, significant and highly persistent effect on the cash ratio. The magnitude of the effect is similar to that of a typical shock to the cash ratio equation, with a one standard deviation shock to the T-Bill rate lowering the cash ratio by almost 3.5 percent after 17 quarters. From the impulse responses, we also see that the effect of a typical shock to the cash ratio dies out almost completely after 6 years. While the effect of a shock to the cash ratio on I3M is negative, the magnitude is relatively small in comparison to the size of a typical shock to I3M, and the effect is not statistically significant. A Granger causality Wald test confirms that there is a Granger causal ordering, with the interest rate explaining the cash ratio and not the reverse. The results of the test are shown in Table 2. We obtain similar impulse responses and Granger causality test results when using I3M-RC as measure of opportunity cost. [Table 2 goes here] 8

Figure 4 shows posterior densities for a variance decomposition analysis of the bivariate BVAR up to an 80-quarter-ahead horizon. Shocks to I3M explain a significant fraction of the variance of the cash ratio: at horizons longer than 5 years, the median fraction of the variance of the cash ratio explained by I3M is more than 50 percent, and exceeds 75 percent at very long horizons (20 years). At shorter horizons, the fraction explained is smaller but still significant. In contrast, shocks to the cash ratio do not explain a significant portion of the variation in interest rates. Our impulse response and variance decomposition analyses thus confirm the results from the Granger causality tests: while the interest rate has substantial forecasting power for predicting movements in the cash ratio, the cash ratio does not explain movements in the interest rate. [Figure 4 goes here] Figure 5 shows historical decompositions of the log cash ratio. To calculate the historical decomposition, we take as given the initial conditions of the system (the first three quarters of our sample) and simulate the path of the BVAR using the posterior mean of the BVAR parameters under different scenarios for the shocks. Panel (a) shows what the path of the cash ratio would have been from 1951 to 2010 if shocks to the cash ratio and I3M equations had been zero in all periods. We find that, without any shocks, the cash ratio would have reverted to its long-run mean by the late 1970s and would have been approximately constant from then on. Panel (b) shows what the path of the cash ratio would have been if shocks to the I3M equation had been equal to the estimated residuals, while shocks to the cash ratio equation had been zero in all periods. In this scenario, the cash ratio would have declined from the 1950s until 1982, and then it would have started to trend upwards, in a remarkably similar way to the actual pattern of the cash ratio over our sample period. Our bivariate BVAR analysis thus shows that both the decrease in the cash ratio between the 1950s and 9

the early 1980s, and its subsequent increase between 1982 and 2010, can largely be explained by the movements in the nominal interest rate that occurred over these periods. [Figure 5 goes here] To control for potential cyclical effects, we also estimate the VAR model with the log of real GDP as an additional endogenous variable. Figure 6 shows impulse responses for this specification. As before, we use a triangular identification scheme and impose zero restrictions on the contemporaneous response of the cash ratio to shocks to I3M and shocks to GDP, and on the contemporaneous response of GDP to shocks to I3M. We find that shocks to GDP have a significant negative effect on the cash ratio, and a significant and positive effect on the interest rate. Shocks to I3M have a negative and significant effect on GDP. The effect of I3M on the cash ratio remains essentially unchanged. Shocks to the cash ratio do not have a significant effect on GDP or I3M. [Figure 6 goes here] Figure 7 shows the corresponding variance decomposition. Shocks to the interest rate equation account for more than 50% of the long-run variation in the cash ratio, and around a third of the variation at business-cycle frequencies. Shocks to GDP account for roughly 25% of the variation in interest rates at both long and short horizons. They also account for approximately 20% of the variation in the cash ratio. Since GDP affects both the interest rate and the cash ratio, it is not clear whether GDP has an independent effect on the cash ratio beyond its effect through the interest rate. In fact, the evidence suggests that it does not. As shown in Table 3, lags of GDP are not jointly significant in the cash ratio equation of the VAR. On the other hand, they do have a significant effect in the interest rate equation. As before, lagged interest rates are highly significant in the cash ratio equation. Thus, the 10

evidence suggests that shocks to GDP affect the cash ratio mostly through their effect on interest rates.1 [Figure 7 goes here] [Table 3 goes here] In all cases, using I3M-RC instead of I3M produces similar results. An interesting difference is that the fraction of the long-run variance of the cash ratio that is explained when using I3M-RC is somewhat higher than when using I3M, while the fraction of the short-term and medium-term variance (horizons of 38 quarters or lower) explained by I3MRC is somewhat lower than the fraction explained by I3M, as shown in Figure 8. This figure shows, at different horizons, the posterior median of the fraction of the variation in the cash ratio that can be explained by I3M or I3M-RC in bivariate BVARs. The specifications are identical–same number of lags, ordering, and prior as described above–except for the different measure of opportunity cost. [Figure 8 goes here]

5

Discussion

As we noted in the previous section, I3M performs relatively better at explaining the shorthorizon variations in the cash ratio, while I3M-RC performs relatively better at explaining the long-horizon variations. Part of the explanation could be that, at business cycle frequencies, the corporate cash ratio are driven mainly by movements in the currency and checking deposits component, so the true opportunity cost of holding cash should be close to the cost of holding currency and checking deposits, which equals the short-term nominal rate. 1

Note that the results still imply a Granger causal ordering, where the interest rate and log GDP are Granger causally prior to the cash ratio.

11

[Figure 9 goes here] To verify our hypothesis, we measure the cyclical comovement between the cash ratio and its various components using a Baxter-King filter to select frequencies between 6 and 32 quarters (see Baxter and King, 1999). Figure 9 shows the filtered series for the log cash ratio along with the filtered series for each component. We find that the correlation between the currency and checking deposits component and the cash ratio is positive and strong (0.73). The time and savings deposits component has a positive correlation with the cash ratio (0.60), but the relation is not as strong as for the currency and checking deposits component. The money market mutual funds component has a weak negative correlation with the cash ratio (-0.25), while the correlation is weakly positive for commercial paper (0.27). At longer horizons, however, the high correlation between the cash ratio and the currency and checking component does not hold. This can be seen in Figure 10, which shows an area graph of the evolution of the each component of the cash ratio. In recent decades, corporations have been rebalancing the composition of their portfolio of liquid assets by substituting away from currency and checking deposits towards interest-bearing cash-like assets. Thus, to explain variations in the cash ratio at longer horizons, it seems reasonable that the relevant measure of the opportunity cost of cash is closer to I3M-RC, which does not assume that cash pays zero interest. [Figure 10 goes here]

6

Conclusion

Our empirical analysis shows that there is a significant negative relation between corporate cash holdings and measures of the opportunity cost of holding cash between 1951 and 2010.

12

This pattern can be interpreted as a relatively stable demand for broad money for the nonfinancial corporate sector. In particular, the increase in corporate cash holdings between the early 1980s and 2010 can largely be explained by the large decrease in the opportunity cost of holding cash over the same period. In addition, between the 1950s and the early 1980s, the cash ratio decreased substantially, a trend that can also be explained by changes in interest rates, which had an upward trend over that period. Thus, we show evidence in favor of a simple money demand explanation for the corporate cash hoarding puzzle. Corporations have roughly doubled their cash holdings in the past 30 years as a response to the large decrease in the opportunity cost of holding cash over that period. While we show that the behavior of aggregate corporate cash can be described by a standard money demand relationship, it would be also interesting to understand the determinants of the composition of the corporate cash holdings. For instance, the extent to which corporations substitute between currency and non-M1 components of broad money can be useful for the conduct of monetary policy. To this end, we could develop a structural model similar to Barnett, Fisher, and Serletis (1992) and apply it to data on the composition of the aggregate cash portfolio.

References Barnett, William A., Douglas Fisher, and Apostolos Serletis, 1992, Consumer theory and the demand for money, Journal of Economic Literature 30, 2086–2086. Bates, Thomas W., Kathleen M. Kahle, and Ren´e M. Stulz, 2009, Why do us firms hold so much more cash than they used to?, The Journal of Finance 64, 1985–2021. Baxter, Marianne, and Robert G. King, 1999, Measuring business cycles: Approximate bandpass filters for economic time series, Review of Economics and Statistics 81, 575–593. 13

Carpenter, Seth B., and Joe Lange, 2003, Money demand and equity markets (Divisions of Research & Statistics and Monetary Affairs, Federal Reserve Board). Greenwood, Robin, 2005, Aggregate corporate liquidity and stock returns (Division of Research, Harvard Business School). Hetzel, Robert L., and Yash P. Mehra, 1989, The behavior of money demand in the 1980s, Journal of Money, Credit and Banking 21, 455–463. Mehra, Yash P., 1993, The stability of the m2 demand function: evidence from an errorcorrection model, Journal of Money, Credit and Banking 25, 455–460. , 1997, A review of the recent behavior of m2 demand, Federal Reserve Bank of Richmond Economic Quarterly 83, 27. Sims, Christopher A., and Tao Zha, 1998, Bayesian methods for dynamic multivariate models, International Economic Review 39, 949–68. , 1999, Error bands for impulse responses, Econometrica 67, 1113–1156.

14

Dependent Variable: Log Cash Ratio Variables I3M

(1)

(2)

-6.087***

-9.853***

(0.294)

(0.818)

I3M 2

(3)

(4)

-8.529***

-8.419***

(0.706)

(1.743)

30.58*** (6.237)

I3M-RC

(I3M-RC )2

-2.129 (30.85)

Constant

-3.014***

-2.928***

-3.097***

-3.098***

(0.0222)

(0.0275)

(0.0286)

(0.0315)

Seasonal Dummies

Yes

Yes

Yes

Yes

Observations

237

237

237

237

0.654

0.686

0.394

0.394

R-squared

*** p<0.01, ** p<0.05, * p<0.1 Standard errors in parentheses

Table 1: Regression of the Logarithm of the Cash Ratio on I3M, I3M-RC, and Seasonal Dummies. This table shows results of the regression of the log cash ratio on (1) the 3-month T-Bill rate (I3M ), (2) the 3-month T-Bill rate and its square, (3) the difference between the 3-month T-Bill rate and the return on cash holdings (I3M-RC ), (4) the difference between the 3-month T-Bill rate and the return on cash holdings and the square of this difference. Each regression includes a constant and seasonal dummies. The cash ratio is calculated as aggregate cash holdings for the US nonfarm nonfinancial corporate sector (currency an checking deposits, savings and time deposits, money market mutual fund shares, and commercial paper) divided by total assets held by the sector. The return on cash holdings is measured as a weighted average of the returns on the components of cash.

15

Equation

Excluded

χ2

df

p-value

I3M

Log Cash Ratio

2.9323

3

0.402

I3M

All

2.9323

3

0.402

Log Cash Ratio

I3M

36.268

3

0.000

Log Cash Ratio

All

36.268

3

0.000

Table 2: VAR of Log Cash Ratio and I3M : Granger Causality Wald Tests This table shows the results of Granger causality Wald tests for a bivariate VAR with the short-term interest rate (I3M ) and the log cash ratio as endogenous variables. The VAR also includes seasonal dummies as exogenous variables. Variables are defined in Table 1.

16

Equation

Excluded

χ2

df

p-value

I3M

Log GDP

15.95

3

0.001

I3M

Log Cash Ratio

3.4042

3

0.333

I3M

All

19.083

6

0.004

Log GDP

I3M

17.147

3

0.001

Log GDP

Log Cash Ratio

6.1938

3

0.103

Log GDP

All

24.495

6

0.000

Log Cash Ratio

I3M

31.964

3

0.000

Log Cash Ratio

Log GDP

1.6309

3

0.652

Log Cash Ratio

All

38.152

6

0.000

Table 3: VAR of Log Cash Ratio, Log GDP, and I3M : Granger Causality Wald Tests This table shows the results of Granger causality Wald tests for a VAR with the short-term interest rate (I3M ), the log of real GDP, and the log cash ratio as endogenous variables. The VAR also includes seasonal dummies as exogenous variables. Variables are defined in Table 1.

17

0.16  

0.06  

0.14   0.05   0.12  

0.1   0.04   0.08  

0.06  

0.03  

0.04   0.02   0.02  

0   0.01  

T-­‐Bill  Rate:  3-­‐month  (Le>  Axis)  

T-­‐Bill  Rate  minus  Return  on  Cash  (Le>  Axis)  

2008Q4  

2005Q4  

2002Q4  

1999Q4  

1996Q4  

1993Q4  

1990Q4  

1987Q4  

1984Q4  

1981Q4  

1978Q4  

1975Q4  

1972Q4  

1969Q4  

1966Q4  

1963Q4  

1960Q4  

1957Q4  

1954Q4  

-­‐0.04  

1951Q4  

-­‐0.02  

0  

Cash  /  Assets  (Right  Axis)  

Figure 1: Cash ratio, I3M, and I3M-RC. This figure shows the evolution over time of the aggregate corporate cash ratio, the 3-month T-Bill rate, and the difference between the 3-month T-Bill rate and the return on cash holdings for the period 1951Q4:2010Q4. The cash ratio is calculated as aggregate cash holdings for the US nonfarm nonfinancial corporate sector (currency an checking deposits, savings and time deposits, money market mutual fund shares, and commercial paper) divided by total assets held by the sector. The return on cash holdings is measured as a weighted average of the returns on the components of cash.

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0.055 0.040 0.025

0.030

0.035

Cash Ratio

0.045

0.050

0.055 0.050 0.045 0.040

Cash Ratio

0.035 0.030 0.025 0.00

0.05

0.10

0.15

-0.02

I3M

0.00

0.02

0.04

0.06

I3M-RC

(a) Cash ratio and I3M

(b) Cash ratio and I3M-RC

Figure 2: Scatter plots of the cash ratio and I3M, and the cash ratio and I3M-RC This figure shows scatter plots of the cash ratio and I3M, and the cash ratio and I3M-RC for the period 1951Q4:2010Q4. Variables are defined in Figure 1.

19

Log Cash Ratio

Shock to Log Cash Ratio

Shock to 3−Month T−Bill Rate

0.04

0.04

0.02

0.02

0

0

−0.02

−0.02

−0.04

−0.04

−0.06

0

5

10

15

−0.06

20

−3

3−Month T−Bill Rate

15

5

10

15

20

5

10

15

20

−3

x 10

15

10

10

5

5

0

0

0

0

5

10

15

20

x 10

0

Figure 3: Impulse responses of a BVAR of the cash ratio and I3M This figure shows the posterior density of the impulse responses of a 3-lag BVAR of the cash ratio and I3M as endogenous variables, and seasonal dummies as exogenous variables. In each case, the x-axis indicates quarters after the shock. The first column shows the response of each variable to a shock to the cash ratio, and the second column shows the responses to a shock to the 3-month interest rate. Variables are defined in Figure 1.

20

Log Cash Ratio

Shocks to Log Cash Ratio 1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

3−Month T−Bill Rate

Shocks to 3−Month T−Bill Rate

20

40

60

0

80

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

20

40

60

0

80

20

40

60

80

20

40

60

80

Figure 4: Variance decomposition of a BVAR of the cash ratio and I3M This figure shows the posterior density of the variance decomposition of a 3-lag BVAR of the cash ratio and I3M as endogenous variables, and seasonal dummies as exogenous variables. In each case, the x-axis indicates the number of steps ahead in the forecast. The first column shows the fraction of the variance of each variable explained by shocks to the cash ratio, and the second column shows the fraction of the variance of each variable explained by shocks to the 3-month interest rate. Variables are defined in Figure 1.

21

Log Cash Ratio

−2.8 −3 −3.2 −3.4 −3.6 −3.8 −4 1952

Actual Simulated 1957

1962

1967

1972

1977

1982

1987

1992

1997

2002

2007

1992

1997

2002

2007

(a) No shocks Log Cash Ratio

−2.8 −3 −3.2 −3.4 −3.6 −3.8 −4 1952

Actual Simulated 1957

1962

1967

1972

1977

1982

1987

(b) Only shocks to I3M

Figure 5: Historical decompositions of the cash ratio: no shocks and only shocks to I3M. This figure shows historical decompositions of the log cash ratio, using a 3-lag BVAR with the cash ratio and I3M as endogenous variables, and seasonal dummies as exogenous variables. Panel (a) shows what the path of the cash ratio would have been from 1951 to 2010 if shocks to the cash ratio and I3M equations had been zero in all periods. Panel (b) shows what the path of the cash ratio would have been if shocks to the I3M equation had been equal to the estimated residuals, while shocks to the cash ratio equation had been zero in all periods. Variables are defined in Figure 1.

22

Log Cash Ratio

Shock to Log Cash Ratio

Shock to GDP

Shock to 3−Month T−Bill Rate

0.02

0.02

0.02

0

0

0

−0.02

−0.02

−0.02

−0.04

−0.04

−0.04

−0.06

0

10

20

−0.06

0

10

20

−0.06

0.02

0.02

0.01

0.01

0.01

0

0

0

−0.01

−0.01

−0.01

GDP

0.02

−0.02

0

10

20

−0.02

−3

3−Month T−Bill Rate

10

0

10

20

−0.02

−3

x 10

10

10

5

5

0

0

0

10

20

0

10

20

0

10

20

10

20

−3

x 10

5

0

0

10

20

x 10

0

Figure 6: Impulse responses of a BVAR of the cash ratio, I3M, and the log of real GDP This figure shows the posterior density of the impulse responses of a 3-lag BVAR of the cash ratio, I3M, and the log of real GDP as endogenous variables, and seasonal dummies as exogenous variables. In each case, the x-axis indicates quarters after the shock. The first column shows the response of each variable to a shock to the cash ratio, the second column shows the responses to a shock to GDP, and the third column shows the responses to a shock to the 3-month interest rate. Variables are defined in Figure 1.

23

Log Cash Ratio

Shocks to Log Cash Ratio

GDP

Shocks to 3−Month T−Bill Rate

1

1

1

0.5

0.5

0.5

0

20

40

60

80

0

20

40

60

80

0

1

1

1

0.5

0.5

0.5

0

3−Month T−Bill Rate

Shocks to GDP

20

40

60

80

0

20

40

60

80

0

1

1

1

0.5

0.5

0.5

0

20

40

60

80

0

20

40

60

80

0

20

40

60

80

20

40

60

80

20

40

60

80

Figure 7: Variance decomposition of a BVAR of the cash ratio, I3M, and the log of real GDP This figure shows the posterior density of the variance decomposition of a 3-lag BVAR of the cash ratio, I3M, and the log of real GDP as endogenous variables, and seasonal dummies as exogenous variables. In each case, the x-axis indicates the number of steps ahead in the forecast. The first column shows the fraction of the variance of each variable explained by shocks to the cash ratio, the second column shows the fraction explained by shocks to GDP, and the third column shows the fraction explained by shocks to the 3-month interest rate. Variables are defined in Figure 1.

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0.8

Fraction of Variance of the Log Cash Ratio Explained

0.7

0.6

0.5

0.4

0.3

0.2

0.1 I3M I3M−RC 0

0

10

20

30

40 Steps

50

60

70

80

Figure 8: Posterior median of the fraction of the variance of the cash ratio explained by I3M and by I3M-RC This figure shows the posterior median of the fraction of the variance of the cash ratio explained by I3M and by I3M-RC. Each calculation is done with separate bivariate BVARs with three lags and seasonal dummies as exogenous variables. The x-axis indicates the number of steps ahead in the forecast. Variables are defined in Figure 1.

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−3

4

x 10

2 0 −2 −4 1952

1957

1962

1967

1972

1977

1982

1987

1992

1997

2002

2007

1997

2002

2007

1997

2002

2007

2002

2007

(a) Currency and checking deposits −3

4

x 10

2 0 −2 −4 1952

1957

1962

1967

1972

1977

1982

1987

1992

(b) Time and savings deposits −3

6

x 10

4 2 0 −2 −4 1952

1957

1962

1967

1972

1977

1982

1987

1992

(c) Money market mutual fund shares −3

4

x 10

2 0 −2 −4 1952

1957

1962

1967

1972

1977

1982

1987

1992

1997

(d) Commercial paper

Figure 9: Filtered series of the cash ratio and its components This figure shows the filtered series of the cash ratio and its components. In each panel, the cash ratio is represented by the solid line, and the respective component is represented by the dashed line. The series are filtered using a Baxter-King filter to select frequencies between 6 and 32 quarters. The cash ratio is defined in Figure 1.

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0.06  

0.05  

0.04  

0.03  

0.02  

0  

1951Q4   1953Q2   1954Q4   1956Q2   1957Q4   1959Q2   1960Q4   1962Q2   1963Q4   1965Q2   1966Q4   1968Q2   1969Q4   1971Q2   1972Q4   1974Q2   1975Q4   1977Q2   1978Q4   1980Q2   1981Q4   1983Q2   1984Q4   1986Q2   1987Q4   1989Q2   1990Q4   1992Q2   1993Q4   1995Q2   1996Q4   1998Q2   1999Q4   2001Q2   2002Q4   2004Q2   2005Q4   2007Q2   2008Q4   2010Q2  

0.01  

Checkable  Deposits  and  Currency  /  Assets  

Time  and  Savings  DeposHs  /  Assets  

Money  Market  Mutual  Fund  Shares  /  Assets   Commercial  Paper  /  Assets  

Figure 10: Nonfinancial corporate cash holdings by type: 1951-2010 This figure shows an area graph of the evolution of the each component of the cash ratio over time, for the period 1951Q4:2010:Q4. The cash ratio is defined in Figure 1.

27