Show Me the Money: Retained Earnings and the Real Effects of Monetary Shocks

Show Me the Money: Retained Earnings
and the Real Effects of Monetary Shocks?
Matthias Doepke
UCLA
November 2003
Abstract
The empirical literature on monetary policy shocks documents that contrac-
tionary shocks are followed by a persistent rise in interest rates and a persis-
tent fall in output. Standard monetary business cycle models can account for the
initial effects of monetary shocks, but have dif?culty generating persistence. In
this paper, I examine whether frictions that affect the asset allocation decisions
of households can lead to persistent effects. In the model economy, households
hold two assets, one used for transactions (the checking account) and one used
for investment (the savings account). There is a small transaction cost for moving
funds between the accounts. Another key feature of the economy is that the busi-
ness sector accumulates retained earnings and credits pro?ts to the consumers
only with a delay. I show that in this environment monetary shocks have persis-
tent effects even when the adjustment cost is very small.
?I thank two anonymous referees and seminar participants at the University of Chicago and Uni-
versit¨at Hamburg for helpful discussions and comments. Financial support by the National Science
Foundation and the UCLA Academic Senate is gratefully acknowledged. Address: Department of
Economics, UCLA, 405 Hilgard Ave, Los Angeles, CA 90095. E-mail: doepke@econ.ucla.edu.

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1
Introduction
In recent years a large number of studies have used the identi?ed-VAR methodology
to assess the effects of monetary shocks. This literature documents that contractionary
monetary shocks have a persistent negative effect on output and employment, and
a persistent positive effect on interest rates. For example, Christiano, Eichenbaum,
and Evans (1999) review a number of different approaches for identifying monetary
shocks, and ?nd that interest rates rise for at least six month after a contractionary
monetary shock, whereas the negative effect on output lasts for well over a year.
These conclusions are robust across most identi?cation schemes for monetary shocks
used in the literature.1
Explaining these ?ndings is a challenge for economic theory. Frictionless models do
not generate any real effects of monetary disturbances. In the recent theoretical lit-
erature there are two main classes of models which generate real effects of monetary
shocks, the “liquidity” model and the “sticky-price” model (see Cole and Ohanian
2002 for a recent comparison of the two frameworks). Even though both models give
rise to real effects of monetary shocks, they have trouble generating persistence. In
the “liquidity” or “limited participation” model, households are unable to adjust their
asset holdings immediately when a monetary shock hits (see Lucas Jr. 1990 and Chris-
tiano and Eichenbaum 1992). Firms and banks can react to monetary disturbances at
once, whereas households react only with a delay of one period. The liquidity model
generates real effects of monetary shocks. However, the effects are short-lived. Once
households are able to adjust their asset position in the period following the shock, all
real effects disappear. The friction at the heart of the “sticky price” model are nom-
inal rigidities generated by staggered price-setting (see Taylor 1980 and Blanchard
1991). While in a sticky-price models real effects can last longer than one period,
Chari, Kehoe, and McGrattan (2000) show that in a calibrated model with staggered
price setting there is very little persistence unless the frequency of price adjustments
is assumed to be unrealistically low.
This paper explores whether a model with a different friction, namely small ad-
justment costs for household asset transactions, can account for persistent effects of
1An exception is Uhlig (2000). Uhlig uses a Bayesian approach to identify monetary shocks, and
does not ?nd that contractionary monetary shocks lower output.
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monetary shocks. I develop an otherwise standard cash-in-advance model in which
households have checking and saving accounts and face a small adjustment cost for
transfers between their accounts. This cost can be interpreted as banking fees, as well
as the opportunity cost of the time which is used for carrying out the transactions (the
“shoe-leather” cost of the Baumol-Tobin model). Notice that this setup is very similar
to the liquidity model in spirit. In particular, the liquidity model can be interpreted
as an adjustment-cost model where the cost for immediate transactions is in?nite, but
the cost for scheduled future transactions is zero.
I use a calibrated version of the adjustment-cost model to ask two questions. First,
does the model generate real effects of monetary shocks that are similar to what is
observed in the data? Second, how large do the adjustment costs have to be to for the
real effects to be sizable and persistent? The answer to the ?rst question is a quali?ed
“yes.” The adjustment-cost model can generate real effects of monetary shocks, but
only if the model is extended to allow a realistic representation of the ?ow of funds
between ?rms and households. Speci?cally, it is necessary to allow for retained earn-
ings in the business sector. Retained earnings serve to isolate the households from
the direct impact of monetary disturbances. If we do not allow for retained earnings,
persistence does not arise. This is a surprising outcome, in the sense that in existing
models the speci?cs of the ?ow of funds between ?rms and households are not im-
portant for the transmission of monetary shocks. The answer to the second question
is that once we allow for retained earnings, very small adjustment costs are suf?cient
to lead to sizable and persistent real effects of monetary policy. The adjustment cost
is modeled as a time cost, and it can be quanti?ed by comparing it to working time.
In the baseline calibration, the realized adjustment cost never exceeds three seconds
per quarter per person.
Our results stand in marked contrast to a number of existing papers that also intro-
duce adjustment costs within the liquidity-constraint framework, and ?nd that ad-
justment costs lead to persistent effects even without requiring the accumulation of
retained earnings (see, for example, Christiano and Eichenbaum 1992, Chari, Chris-
tiano, and Eichenbaum 1995, or Evans and Marshall 1998). The reason for the dif-
ferent ?ndings is that the authors rely on a speci?c asymmetric formulation for the
adjustment cost. In particular, while adjusting savings is assumed to be costless, ad-
justing the amount of cash used for consumption expenditures is costly. As pointed
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out by Rotemberg (1995), this asymmetry is hard to justify from a microeconomic
perspective. In the existing models, an asymmetric adjustment cost is essential to
generate persistence, since the models require that savings react much more strongly
to a monetary shock that cash holdings. If the adjustment cost also applied to savings
or to transfers between cash and savings, monetary shocks would no longer have per-
sistent real effects. This paper shows that if adjustment cost are introduced in a more
realistic form, the presence of retained earnings is necessary for monetary shocks to
have persistent effects.
Retained earnings matter for the transmission of monetary policy because they affect
the overall balance between different uses of funds in the economy. In the model,
funds can be used either for consumption expenditures or for savings. Since prices
are ?exible, the overall amount of funds that is initially available in the economy
does not affect real variables. In this sense, money is neutral. On the other hand,
the balance of the use of funds between consumption and savings does have real
consequences.
In the model economy, households own funds in two different ways. First, they hold
funds directly in their own checking and savings accounts. Second, households hold
funds indirectly through the ?rms in the economy, which they own. It is through
these indirect holdings that retained earnings matter. When a monetary shock hits,
initially only the asset holdings of ?rms are affected. For example, an expansionary
monetary shock increases the amount of funds held by the business sector. Since
funds held by the business sector are not used for consumption, the economywide
ratio of funds used for consumption and savings changes after such a shock. Without
adjustment costs, households would then lower their own savings to re-establish the
preferred ratio of consumption to savings. With adjustment costs, consumers adjust
their asset holdings to a lesser degree, and the resulting imbalance affects real vari-
ables such as output and employment. If earnings in the business sector are retained,
the imbalance and therefore the real effects of the monetary shock will persist.
The implications of the model with retained earnings for the ?ow of funds between
households and the business sector are in line with empirical ?ndings. In the next
Section, we present evidence that shows that corporate pro?ts react quickly to a mon-
etary shock, whereas dividend payments adjust only after a considerable delay. Con-
sistent with this ?nding, Christiano, Eichenbaum, and Evans (1996) report that the
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household sector does not adjust its ?nancial assets and liabilities for several quarters
after a monetary shock, while there is an immediate impact on the business sector.
In summary, our results suggest that portfolio adjustment costs are a promising av-
enue for explaining persistent real effects of monetary shocks. A key ?nding is that a
better account of the ?ow of funds between the household and business sectors may
be central for understanding the monetary transmission mechanism. This conclu-
sion puts the adjustment-cost model in marked contrast to existing monetary models,
which do not assign a major role to the ?ow of funds.
The paper is organized as follows. The next section provides an empirical analysis of
the relationship between monetary shocks and corporate pro?ts and dividends. The
model is introduced in Section 3. Section 4 discusses some theoretical results on the
effects of monetary shocks, and shows how the decision problem of the household is
modi?ed in different versions of the model. In Section 5 the model is calibrated, and
numerical experiments are carried out to assess the effects of monetary shocks in the
adjustment-cost model. Section 6 concludes.
2
Empirical Evidence
This section examines the effects of monetary shocks on corporate pro?ts and divi-
dend payments. A central conjecture of this paper is that pro?ts or losses in the corpo-
rate sector which arise from monetary shocks are transferred to households only with
a delay. If this conjecture is true, the asset position of the household sector is insulated
temporarily form the effects of monetary disturbances. The theoretical analysis in the
remainder of the paper will show that this insulation has important implications for
the real effects of monetary shocks.
Following the major part of the empirical literature on monetary shocks, we rely on
the identi?ed-VAR methodology to assess the reactions of aggregate economic vari-
ables to monetary disturbances. In particular, our speci?cation is close to Christiano,
Eichenbaum, and Evans (1996). The data set contains quarterly observations on U.S.
economic and monetary aggregates from the ?rst quarter of 1959 until the third quar-
ter of 2002. The following variables were included in the analysis: Real GDP (Y), the
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GDP de?ator (P), an index of commodity prices (PCOM), total reserves (TR), non-
borrowed reserves (NBR), the federal funds rate (FF), real corporate pro?ts (PR),
and real corporate dividends (DIV). With the exception of the federal funds rate,
all variables are in logs. Pro?ts and dividends were de?ated using the GDP de?a-
tor.2 The commodity price index was included to avoid the well known price puzzle.
Without this measure, contractionary monetary policy shocks (de?ned as orthogo-
nalized innovations to FF or NBR) lead to a prolonged rise in the price level (see
Sims). As discussed in Christiano, Eichenbaum, and Evans (1996), this anomalous
response disappears if a measure of commodity prices is included in the VAR. The
usual interpretation is that commodity prices matter, because they contain informa-
tion about future in?ation that is available to the policy maker, but not contained in
the remaining variables in the VAR.
Monetary shocks were identi?ed by by imposing a triangular structure on the variance-
covariance matrix of the error term. In other words, the variables were ordered such
that each variable can have an instantaneous effect only on variables lower in the or-
der. The following ordering was employed: Y, P, PCOM, FF, NBR, TR, RPR, RDIV.
This is the same ordering as in Christiano and Eichenbaum (1995), with new the vari-
ables speci?c to this analysis (RPR and RDIV) ordered last. It appears plausible to
order dividends after pro?ts, since pro?ts ?rst have to exist before they can be dis-
tributed. Of course, the impulse response functions presented below depend to some
degree on the speci?c ordering employed. In terms of the overall effect of monetary
shock, what appears to matter most is that Y is ordered ?rst. Our basic conclusions re-
garding the relationship between monetary shocks, corporate pro?ts, and dividends
are surprisingly robust with respect to the ordering of the Cholesky decomposition.
In particular, the effects are virtually unchanged if dividends are ordered before prof-
its.
I use orthogonalized shocks to FF as the de?nition of a monetary policy shock. Us-
ing a shock to non-borrowed reserves as an alternative measure yields similar re-
sults. Figure 1 shows the impulse response of the main variables we are interested
in to a one-standard-deviation contractionary shock to FF. The dashed lines are two-
standard error bands. Output starts to decline with a delay of two quarters after the
2All data were extracted from the FRED data base at the Federal Reserve Bank of St. Louis. The
identi?cation codes for the series are: GDPC1, GDPDEF, PPICRM, TRARR, BOGNONBR, FEDFUNDS,
CPROFIT, and DIVIDEND.
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Quarter
0
1
2
3
4
5
6
7
8
9
10
11
Response
-1.6
0.2
8.7
15.8
18.8
18.9
15.8
10.4
6.2
3.3
1.5
1.0
Accumulated
-1.6
-1.3
7.3
23.2
42.0
60.9
76.6
87.1
93.2
96.5
98.0
99.0
Table 1: Reaction of Dividends to Pro?t Shock (Percent of Total Impact)
shock, with the largest impact occurring after about two years. The reaction of pro?ts
has a similar shape as the reaction of output. Notice, however, that the reaction of
pro?ts is much stronger than the reaction of output in magnitude. A contractionary
monetary policy shock therefore has a sizable negative impact on the pro?ts of the
corporate sector. Corporate dividends re?ect these lower pro?ts, but only with a de-
lay. The impulse response function of dividends shows almost no reaction for the
?rst ?ve quarters after the monetary shock, and turns negative thereafter. The reac-
tions of pro?ts and dividends have a similar magnitude, but the reaction of dividends
is delayed relative to pro?ts. The results are consistent with the conjecture that the
corporate sector transfers pro?ts or losses to households only with a delay. Figure 2
repeats the same exercise with nominal pro?ts and dividends, instead of in?ation-
adjusted ?gures. The results are very similar to Figure 1.
Figure 3 displays impulse response functions for shocks to GDP, real pro?ts, and real
dividends. Of particular interest here is the reaction of dividends to a change in prof-
its. Notice that our ordering assumption allows dividends to adjust immediately after
a shock to pro?ts. The graph shows, however, that this does not happen. Instead, the
reaction of dividends to a change in pro?ts is hump-shaped, with almost no immedi-
ate reaction, and the maximum impact being reached only after ?ve to six quarters.
Thus, once again the results back up our assumption that the corporate sector retains
earnings. This result is entirely plausible if we take into account how decisions on
dividend payments are made in practice. While dividends are often paid quarterly,
the vast majority of ?rms adjusts dividends at most once a year, based on pro?ts in
the preceding year. Additional delays arise because of?cial pro?t ?gures are generally
available only a few months after the end of a ?scal year, and shareholder meetings
are held even later.
For the purposes of calibrating the theoretical model described below, it will be useful
to look at the relationship of dividends and pro?ts in more detail. Table 1 shows how
the reaction of dividends to a shock to pro?ts is spread out over time. The largest
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impact occurs ?ve quarters after impact. Half of the total accumulated impact is
reached between four and ?ve quarters after impact, and the reaction fades out about
three years after the innovation to pro?ts.
In summary, the empirical evidence supports the conjecture that contractionary mon-
etary shock lower corporate pro?ts, and that this change affects households in the
form of lower dividend payments only with a delay. Consistent with these ?ndings,
Christiano, Eichenbaum, and Evans (1996) report that the household sector does not
adjust its ?nancial assets and liabilities for several quarters after a monetary shock.
The next section develops a model that demonstrates why these ?ndings may be im-
portant for the transmission of monetary shocks.
3
The Model
The model is based on the standard cash-in-advance framework. The economy is
populated by the monetary authority and a continuum of three types of competitive
agents: households, ?rms, and banks. There is measure one of each type of agent, so
that the model can be formulated in terms of a representative household, ?rm, and
bank. Apart from the cash-in-advance constraint, there are two additional frictions
present in the baseline model: a liquidity constraint and an adjustment cost. The
liquidity constraint forces consumers to make saving decisions before the monetary
shock is revealed, while the adjustment cost penalizes changes in the stock of sav-
ings. The liquidity constraint can be interpreted as an in?nite adjustment cost for
immediate changes in savings. The baseline model incorporates the liquidity con-
straint to facilitate comparisons to earlier literature. Speci?cally, if adjustment costs
are set to zero, the economy reduces to the baseline model in Christiano and Eichen-
baum (1995). I also consider a version of the model without the liquidity constraint. If
adjustment costs are set to zero in this version, the economy reduces to the stochastic
cash-in-advance model considered by Cooley and Hansen (1989).
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Assets and the Monetary Authority
In the model economy, consumers have access to two different assets, checking ac-
counts and saving accounts. All transactions are settled using the checking account.
Banks are subject to a 100 percent reserve requirement on checking accounts, which
implies that these accounts carry no interest in equilibrium.3
There is a central bank which supplies currency to the economy. The money stock
at the beginning of period t is denoted by Mt. Since households and ?rms do not
hold any cash (the only assets are checking and savings accounts), all the money is
in hands of the banks. The central bank carries out monetary policy by giving a cash
injection Xt to the bank at the beginning of period t. Xt is a random variable, and
monetary policy is the only source of uncertainty in the model. The money stock Mt
evolves according to:
Mt+1 = Mt + Xt.
(1)
Banks
There is a competitive banking industry which accepts deposits from ?rms and house-
holds and makes loans to ?rms. Banks are owned by the households. At the begin-
ning of the period, the assets of the bank consist of the money stock Mt (recall that the
entire money stock is held by the bank). The liabilities consist of the checking deposit
Dt and the saving deposit St of the household. We will see later that the bank makes
pro?ts and transfers pro?ts to the households (who own the bank) only with a delay.
Consequently, there is an amount ?t of retained earnings that was carried over from
earlier periods. Since assets have to equal liabilities, we have:
Mt = Dt + St + ?t.
(2)
The ?rst event within the period is the realization of the monetary policy shock. The
central bank hands out Xt dollars to the bank. After the arrival of the monetary injec-
3Even though cash is not used for transactions in the economy, results are the same as in an other-
wise identical economy that uses only cash and no checking accounts at all. In other words, checking
accounts could equivalently be labeled as cash. I prefer the checking-account terminology since most
of M1 is made up of deposits. The important distinction is between non-interest-bearing assets that
can be used for transactions, and interest-bearing assets such as saving accounts.
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tion Xt, the bank gives a loan Bt to the ?rm, where the loan takes a form of a demand
deposit make available to the ?rm. The bank has to observe the 100 percent reserve
requirement on checking accounts, that is, the demand deposits have to be backed by
cash:
Dt + Bt ? Mt + Xt.
(3)
The banking industry is competitive, so that the interest rate rt is taken as given by
the bank. The optimization problem of the bank is to maximize pro?ts from giving
the loan to the ?rm, subject to the reserve requirement. The bank therefore solves:
max {rt(Bt ? St)}
Bt
subject to (3). As long as the interest rate is non-negative (as will be assumed later),
the problem of the bank has a trivial solution: the loan Bt will be the maximum possi-
ble given the reserve requirement, so that the reserve requirement holds with equality.
All transactions during the period are transfers between the demand deposits of the
?rm and the household. At the end of the period, after the ?rm pays back the loan,
the bank credits fraction ? of retained earnings ?t to the consumer’s checking ac-
count. Here ? is an institutional parameter that represents the rate at which retained
earnings ?ow from the business sector to households. Typically ? will be smaller
than one, which re?ects that businesses usually do not pay dividends whenever a
cash ?ow occurs, but only in larger intervals. Since the consumers own the banks, in
a frictionless model they would consider retained earnings as equivalent to their own
savings, and the choice of ? would be irrelevant. In the adjustment-cost economy, in
contrast, the value of ? is a key determinant of the effects of monetary shocks.
The current pro?ts of the bank in period t are given by the sum of the monetary
injection Xt and net interest income rt(Bt ? St). The law of motion for the retained
earnings of the bank is therefore:
?t+1 = Xt + rt(Bt ? St) + (1 ? ?)?t.
Using the accounting identity (2), the reserve requirement can be written as Bt ?
St + ?t + Xt. Since the reserve requirement holds with equality in equilibrium, the
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