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work in^ Paver 9210
DEBT, COLLATERAL, AND U.S.
MANUFACTURING INVESTMENT: 1954-1980
#
by William P. Osterberg
William P, Osterberg is an economist at the
Federal Reserve Bank of Cleveland. The author
is grateful to Paul Bauer, Chris Flinn, Mark
Gertler, Donald Hester, Kim Kowalewski, and
James Thomson for helpful comments and
suggestions.
Working papers of the Federal Reserve Bank of
Cleveland are preliminary materials circulated
to stimulate discussion and critical comment.
The views stated herein are those of the author
and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors
of the Federal Reserve System.
September 1992
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ABSTRACT
I perform an empirical analysis of Euler equations for the firm's choices of
capital, labor, hours, and debt. Financial structure has real effects , since
taxes favor debt. However, the cost of debt increases with the debt-to-collateral
ratio, and capital is part of collateral. The data, for U.S. manufacturing
investment from 1954 to 1980, show that the debt-to-collateral ratio moves
opposite to the direction suggested by tax rates. However, excluding the Euler
equation for debt implies the correct sign for the relation between investment
and the debt-to-collateral ratio. I also find structural instability in the Euler
equations for debt and capital.
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I. Introduction
A growing body of literature examines the empirical impact of financial
factors on fixed investment. Although cash-flow measures have long been known
to have predictive power for investment (see Meyer and Kuh [1957]), until
recently, neither the finance nor macroeconomics literature left any significant
role for capital structure to influence fixed investment. In an early treatment
of the subject, Modigliani and Miller (1958) provide a theoretical rationale for
the view in finance that capital structure is irrelevant to investment.
In
macroeconomics, q came to be regarded as completely summarizing the relevance of
financial markets for investment. q theory usually allows no role for capital
'
structure to influence investment.
A broad literature stimulated by the Modigliani and Miller paper has
explored what Myers (1984) terms "the capital structure puzzle"; that is, how
firms choose their financial structure. Harris and Raviv (1991) survey recent
theories and evidence on the relevance of agency costs, asymmetric information,
product/input market interactions, and corporate control considerations in the
determination of capital structure. Perhaps the most familiar theory of optimal
financial structure emphasizes a "static trade-off" (Myers [1984]) between tax
advantages to debt and various debt-related costs. The empirical relevance of
tax-based theories is widely a~knowledged.~
In this paper, I assume a trade-off
between a tax advantage to debt and a cost of debt that is related to the ratio
of debt to collateral, which I proxy with the book value of tangible assets.
l~or three efforts to embed financial structure in q frameworks, see
Chirinko (1987b), Hayashi (1985), and Osterberg (1989).
2 ~ e eBradley, Jarrell, and Kim (1984) and Haugen and Senbet (1986).
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Scott (1977), Myers and Majluf (1984), and others have suggested that asset
type influences the cost of debt.3 In Scott, the claims of secured creditors
have priority; thus, issuance of secured debt reduces the probability that costs
such as legal damages will be paid in the event of bankruptcy.
In Myers and
Majluf, it may be costly to issue securities implicitly backed by assets whose
value is more easily measured by insiders than outsiders.
In both cases, the
availability of assets that can serve as collateral enhances the value of equity.
This is similar to arguments made by Myers (1977) that reliance on "assets in
place" rather than on growth opportunities increases equity value, since the
former are less dependent on discretionary investment. One influence of
collateral on debt cost is suggested by Barro (1976), who shows how the
equilibrium interest rate can vary with the loan-to-collateral ratio.
Smith
and Warner (1979) and Stulz and Johnson (1985) analyze the case relevant to my
paper, where the assets of the borrower serve as collateral.
Stiglitz and Weiss's (1981) theory of credit rationing was one of the first
asymmetric-information models of investment and finance to show how financial
factors may influence investment decisions. Related work by Bernanke and Gertler
(1989), Gertler and Hubbard (1988), Calomiris and Hubbard (1990), and Hubbard and
Kashyap (1990) points to a role for internal net worth in influencing loan
contracts for investment. Fazzari, Hubbard, and Peterson (1990) describe two
types of tests that have been used to search for the influence of financial
factors. Some have tested for a role for cash flow as a proxy for availability
3~ee
Boot, Thakor, and Udell (1991) for a recent review of the theoretical
and empirical efforts to analyze the role of secured debt.
4~ role for collateral in asymmetric information models of investment has
been suggested by Bernanke and Gertler (1989).
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3
of internal f i n a n ~ e . ~This factor is relevant if informational asymmetries
imply that certain types of firms could have difficulty in raising external
funds. Other studies have estimated Euler equations for the firm's investment
decision in the presence of a binding debt ~onstraint.~Overall, the results
support a role for financial factors in the investment decision.
Unlike recent empirical analyses of the role of asymmetric information,
this paper utilizes aggregate rather than cross-sectional data. However, I
improve on the cited studies by allowing for corporate and personal taxes to
influence the investment decision and by analyzing a simultaneous system in which
the Euler equations for both debt and capital are forced to hold simultaneously.
An interest in examining aggregate production relations is provided by Cochrane
(1991), who demonstrates the ability of aggregate investment data to explain
stock returns. Ferson and Merrick (1987) point to a role for nonstationarity in
explaining aggregate-consumption-based asset pricing relations. In this paper,
the debt-to-collateral ratio has a significant influence on investment, although
of the "wrong" sign. I show that nonstationarity is partly responsible for this
result.
The focus in this paper is on the influence of the debt-to-collateral ratio
on investment in physical capital. I assume a trade-off between tax advantages
to debt and a cost of debt that, as in Barro (1976), varies with the debt-tocollateral ratio. Because taxes may influence the firm's choices of all
productive inputs, I estimate Euler equations for the levels of investment,
employment, and hours. There are potential internal adjustment costs associated
Fazzari and Athey (1987), Fazzari, Hubbard, and Petersen (1988),
Gertler and Hubbard (1988), and Hoshi, Kashyap, and Scharfstein (1991).
'See Gertler, Hubbard, and Kashyap (1990) and Whited (1990).
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4
with all inputs. My specifications of the production function and wage equation
are similar those of Shapiro (1986), who finds that empirical tests of q theories
in which adjustment costs were associated only with capital stock implied
unreasonably high adjustment costs. Here, the estimated total cost of investment
is also influenced by its impact on the debt cost.
I analyze quarterly data for the U.S. manufacturing sector from 1954 to
1980. The estimated parameters in the system describing the optimal choices of
capital, production labor, production hours, nonproduction labor, and debt are
reasonable other than for the incorrect sign on the debt-to-collateral ratio.
However, I find structural instability in the Euler equations for both debt and
capital. In addition, omitting the Euler equation for debt implies the correct
influence for the debt-to-collateral ratio.
11. The Model
I analyze a partial-equilibrium model of a firm that maximizes the expected
market value of its equity through its choices of capital, labor inputs, and
debt. Shareholders discount future dividends at the required after-tax rate of
return on equity. The firm's financial and investment decisions thus affect the
debt cost by influencing the ratio of debt to collateral. since my measure of
collateral is the book value of tangible assets, investment in capital stock
influences the debt cost, and investment and financial structure become
intertwined. In appendix A, I present the equations describing the underlying
behavioral relationships, and in appendix B, I discuss the conditions under which
tax rates favor debt over retained earnings.
In order to understand the important aspects of the firm's decision
problem, I briefly present three key relations. The first is that the before-tax
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5
cost of debt varies with the ratio of the book value of debt to ~ollateral.~
Stulz and Johnson (1985) show how such a relationship can arise when the
assets of the borrower serve as collateral.
The theory implies that
v
is
positive. I assume that 1) all debt is rolled over at the end of each period,
with interest paid on the entire stock of debt, and 2) the book value of physical
capital, <(Kt), is a function of the net stock of physical capital, Kt. <(&)
and K, may differ simply because book depreciation is not necessarily equal to
physical depreciation. Although At
- <(Kt)/Kt
varies through time, it is known
to the firm; thus, by choosing &, the firm indirectly chooses <(Kt).
Another key relation is that of the production function, the form of which
follows Shapiro (1986) and is given by equation 2.
log yt = a,
+
a,log Kt + aLlog L,
+
aalog Ht + aNlog Nt
(2
-
- 5 [ gm(&+l-dt~t>~ + ~ L (L-qt-1Lt-1)
L
+ gHH(~t-~t-1)
2+ gWN(~t-~t-l) I
+
alt + et
Gross adjustments in the levels of factors utilize productive resources.
The assumption of adjustment costs for capital, Kt, production labor, Lt, weekly
hours, H,, and nonproduction labor, N,, implies that current choices will be
influenced by expected future choices.
However, adjustment costs are not
interrelated; the adjustment of an input does not affect the cost of adjusting
another input. Neither Shapiro (1986) nor Kokklenberg (1984) finds strong
evidence in favor of such interrelatedness. Equation 2 also incorporates a
7~efinitionsof all variables are given in the glossary.
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6
multiplicative productivity shock.
The wage bill implies that the variation in hours will be influenced by the
- Wt&[Ht
response of the wage rate as overtime rises: Wt*&Ht
+ oo + ol(Ht-H*,)].
Total labor expenditures also include fixed costs for both production and
nonproduction employees:
w;&H,
+
f,L&
+
(3)
f
k
.
The discrete-time version of the market value of equity at time 0 is
a
t
with
e* =(p+p)/(l-?,,),
t=O j=O
and an expression for the dividend, DV,, is given in appendix A.
111. Optimal Factor Demands and Optimal Financial Structure
At the beginning of period t=0,1,2,..,the firm maximizes the expected
value of V, conditional on information available at the start of period t and
initial conditions:
- &,
-
Nt-l
- Nt-l,Ht-l- Ht-l,and B, - 13.
B,
and K, are stocks given at the start of period t, while &, N,, and H, are
averages over period t. The firm thus chooses Bt+land
Ht
The following first-order conditions hold for all t:
as well as &, N,, and
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+
(- p t + l l + l / t + l 1
1I
+
[ r p t + l ~ t + l - l + ~ ~ ~ t + l l ~-tdt+)}ll.
(
(9)
The transversality conditions are of the form
where
a
is replaced by L, H, N, K, and B.
In equations 5 and 6 , the choices of
production labor and hours for period t each affect period t+l adjustment costs.
The choices of Lt and Ht also influence the wage bill.
Equation 8 states that
the expected cost of funds is equalized between retained earnings and debt issue.
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8
The choices of debt and physical capital are linked through their joint impact
on the cost of debt. An increase in
implies adjustment costs, but raises
period t cash flow via depreciation deductions (D,) and investment tax credits
(ITC,).
While an increase in Kt+1raises period t+l output, its overall impact on
period t+l cash flow is linked to the future choice of &+,.
solution path, I assume that 0 < 1/(1+8*)
To ensure a unique
< 1 and that the production function
is concave and twice continuously differentiable in K, L, N, and H.
IV. Estimation
Since 8* varies over time, I cannot solve for the firm's decision rules
and instead utilize the Euler equations and expression for the employment cost
directly.
The decision rule method, however, would use more information by
imposing the cross-equation restrictions between the stochastic processes
generating the forcing variables and the decision rules. While it appears that
the Euler equation method avoids the need to specify the stochastic processes
generating the forcing variables, Garber and King (1983) point out that Euler
equation methodology does not negate the need to specify the details of the
general equilibrium.
In the analysis developed here, if there are shocks to
preferences but not to production, I will be estimating preference parameters
rather than production parameters.
As discussed by Shapiro (1986, p. 527),
however, utilization of actual production data through substitution of y for the
production function given by equation 2 makes the production shock observable.
In addition, to aid identification, I assume that the shock is additive in logs.
The form of the stochastic Euler equations suggests use of the generalized
instrumental variables estimator of Hansen and Singleton (1982).
They derive a
weighting matrix that minimizes asymptotic standard errors even under conditional
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9
heteroscedasticity. Andrews (1991) discusses the issues involved in computing
covariance matrices under autocorrelation and heteroscedasticity. I utilize the
generalized method of moments (GMM) routine in Time Series Processor Version 4.2
(1991).
I consider the variables listed at the top of table 1 as instruments. This
includes all variables dated t-1, B,, and &. Other than Bt and &, all variables
dated t are realized average values over period t. Values of future endogenous
variables are not known at time t, but will be chosen at the beginning of the
next period, after new information has been received by the firm. If the et's
contain a serially correlated specification error component, instruments dated
t are not valid. Besides contemporaneous instruments, I consider instruments
lagged three and eight quarters, an approach supported by examination of
residuals fromestimates assuming no serial correlation. Autocorrelationof order
three could be due to use of annual data in constructing quarterly observations
for variables such as fNt. The data are described in appendix C.
V.
Results
I first consider the choice of instruments. Shapiro uses 21 variables,
raising the possibility of multicollinearity among the
instrument^.^ In
addition, if all instruments are used in each equation, there are 126
orthogonality conditions
(#
instruments x
#
equations).
A greater number of
these conditions increases the likelihood of numerical inaccuracy.
A
second consideration is
the
treatment of
autocorrelation and
heteroscedasticity. If the model is correctly specified and agents in fact
Rotemberg (1984) suggests focusing on the range over which parameter
estimates of interest vary with use of different instrument lists. This is the
approach adopted in this paper.
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possess information about the variables in the information sets used by the
econometrician, there will be no serial correlation among the residuals.
However, since some quarterly items are calculated from annual data and other
items are constructed from ex post information (for example, the effective taxrate series) it is not clear which forecast horizon is appropriate.
Both
considerations are important given the relatively small sample size.
In the actual estimation, I consider variation in 1) instruments, 2)
forecast horizon, and 3) treatment of serial correlation andheteroscedasticity.
An analysis of the full instrument list, following the suggestions of Belsley,
Kuh, and Welsch (1980), revealed harmful collinearity, so I reduce the list to
seven and consider the seven subsets of six of the seven
instrument^.^ Later,
I split the sample in half and need fewer instruments for the J statistic to have
sufficient degrees of freedom. Thus, I again follow the suggestions of Belsley,
Kuh, and Welsch, reducing the number of instruments to four and then using
subsets of three of the four.
To determine if my results are sensitive to the choice of forecast horizon,
I alternately consider that both the agents and econometrician know 1) current
values, 2) values lagged one quarter, and 3) values lagged four quarters .lo
Variables included in the "large" and "small" instrument lists are indicated in
table 1. The subsets are labeled as 6a
- 6g and 3a - 3d. I report the results
9 ~ o rcomparability with the results of Shapiro, I estimated the full sixequation system, but I do not report those results here. Belsley, Kuh, and Welsch
(1980) suggest examination of the condition indexes and variance decomposition
matrix in order to deal with collinearity. I deemed a condition index over 30
as too high. To reduce the condition number to under 30, only seven of 21
instruments could be retained.
Examination of the decomposition matrix
determined which seven.
1°1 also considered a lag of eight quarters.
qualitatively similar to those reported.
These results are
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11
for each choice of instruments with each choice of forecast horizon and estimate
the model with the assumption of either homoscedasticity or heteroscedasticity
when the full sets of seven or four instruments are used.
I examine the
sensitivity of the results to moving-average corrections of one, three, and seven
for the full sets of seven and four instruments as well.
In order to evaluate the overall adequacy of the model, I utilize the J
statistic suggested by Hansen and Singleton (1982).
It is calculated as NOBS x
the value of the objective function and is distributed as a chi-squared with r-1
degrees of freedom, where r is the number of orthogonality conditions and 1 is
the number of parameters estimated. I use the same instruments for each equation.
A comparison of columns 1 and 2 in tables 2A, 2C, 2D, 2F, 2G, and 21 shows
that a correction forheteroscedasticity reduces the J statistic, indicating that
heteroscedasticity is present. The GMM routine in Time Series Processor Version
4.2 (1991) utilizes a White (1980) correction, a technique I maintain in the
subsequent runs. Tables 2A, 2C, 2D, 2F, 2G, and 21 show that correcting for a
moving-average process reduces the J statistic monotonically with the order of
the process.
Although with higher-order corrections the J statistic does not
imply rejection of the overidentifying restrictions, the presence of serial
correlation may imply misspecification. On the other hand, the sensitivity of
the J statistic to the order of the moving-average correction may reflect a small
sample problem.
In tables 2A
- 21, almost all of the parameters are significant and of the
correct sign and reasonable magnitude.
However, gkk, the adjustment cost
parameter for the capital stock, is consistently negative, while ghh is also
negative for some runs. More important, the estimate of v l is significant but
of the wrong sign. Tables 2D, 2E, and 2F consider the same variations, but with
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12
instruments lagged one period. J statistics are generally lower than with the
current instruments, but the restrictions are still rejected unless I correct for
serial correlation. Tables 2G, 2H, and 21 were obtained when instruments lagged
four periods were employed. The range of values for vl from tables 2A
-
21 is
-0.331 to -0.189.
In the subsequent tables, I consider two explanations for my findings that
1) the overidentifying restrictions are rejected, and 2) while significant, my
estimates of vl are of the wrong sign. I test to see if these results are due
to either temporal instability or rejection of a particular subset of the sixequation model.
In tables 3A to 3D, I present the results of estimating the model when the
sample is split in half.
I consider instrument subsets 3a
- 3d with forecast
horizons of one and four quarters. These smaller instrument sets are chosen to
account for the smaller sample size. The J statistics still imply rejection of
the overidentifying restrictions for each subsample, and the estimate of vl still
tends to be negative and significant.l1
In tables 4A to 4G, I investigate the possibility that subsets of equations
perform better than the full system. My choice of subsets is motivated by several
considerations. First, there are no cross-equation parameter restrictions from
the subset of the W, L, H, and N Euler equations to the K and B Euler equation
subset, although 1) all instrumental variables are used with each equation and
2)
covariances between residuals from different equations are allowed to be
nonzero. Second, my primary focus is on the interaction between the choices of
debt and physical capital. Consequently, I estimate the full system without the
llThe split point is varied with the forecast horizon in order to divide the
sample exactly in half.
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equation for debt, the equations for debt and capital together, and the equations
for debt and capital alone.
I use six instrumental variables with forecast
horizons of one and four quarters.12
Tables 4A and 4E show the coefficient estimates for the five-equation
system that excludes the Euler equation for debt. Although the overidentifying
restrictions are still rejected at the .10 level, the vl coefficient estimate is
positive and significant in 11 of 14 cases.
Next, I see if the restrictions
imposed by the Euler equation for debt are responsible for the sign of vl in the
full system. Tables 4B and 4F show the results from splitting off the equations
for K and B. In all cases, the restrictions are rejected and estimated values
for vl are significant and negative, ranging from -0.210 to -0.306.
I then
estimate the K and B equations individually to see if the restrictions imposed
by the B equation on the K equation are in fact responsible for the negative sign
on ul. Tables 4C, 4D, 4F, and 4G show that while the Euler equation for debt
clearly implies a negative sign for ul (ranging from -0.230 to -0.300), the sign
implied by the single equation for K is ambiguous, ranging from 0.208 to -4.3E-3.
Having determined that 1) temporal instability does not explain the
rejection of the overidentifying restrictions for the full model or the sign of
ul, and 2) subsets of equations still imply rejection, I now further refine my
focus on the main equation of interest, the Euler equation for K. In tables 5A
through 5D, I present the results of estimating equation 11 when the sample is
split in half.
Again, the split point changes with the choice of forecast
horizon. Whereas for the entire sample period the estimate of ul was negative,
now it is more likely to be significantly positive than significantly negative.
121 also estimated this system with all 21 instruments and with the subsets
of three instruments. In each case, I obtained results qualitatively similar to
those reported in this paper.
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In addition, the restrictions on this equation were clearly rejected before, but
here they are generally not rejected for the second half of the sample.13
Tables 6A to 6D present the estimates of vl from the Euler equation for
debt when the sample is split. I find that the restrictions for this equation
are generally not rejected for the first subperiod, although vl is usually
negative. In addition, the magnitude of vl is generally lower for the first half
of the sample than for the second.
V. Conclusions
This paper analyzes a partial equilibrium model of a representative firm
maximizing the expected value of its equity via its choice of production labor,
nonproduction labor, hours of production labor, capital stock, and debt issue.
Financial structure affects investment, since the cost of debt is influenced by
the amount of collateral and the capital stock is included in collateral. I
utilize a generalizedmethod-of-moments procedure to estimate Euler equations for
the inputs and an equation for the wage bill. This differs from previous
empirical investigations by incorporating a role for taxes in the debt-investment
relation and by restricting the movement of the debt variable to satisfy the
Euler equation for debt as well as that for capital,
For a wide variety of instruments, choices of forecast horizons, and
treatments of serial correlation and heteroscedasticity, the overidentifying
restrictions are rejected.
In addition, the estimated coefficient for the
13since it is hard to disentangle the effects of the chosen switch point
from the choice of forecast horizon, I tried the opposite combinations from those
used in tables 5 and 6: instruments lagged four periods with 67:2/67:3 and
instruments lagged one period with 68:1/68:2. With the first combination, four
of eight runs implied nonrejection. With the latter, all eight implied
nonrejection.
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15
response of the cost of debt to the debt-to-collateral ratio is negative and
significant, rather than positive, as implied by my model.
However, the
estimates of the elasticities are significant and reasonable, although some of
the estimated adjustment cost parameters were negative.
Temporal instability does not seem to explain these results for the full
six-equation system. However, omitting the Euler equation for debt implies the
theoretically correct sign for the response of the debt cost to the debt-tocollateral ratio. In addition, a close examination of the Euler equation for
capital shows that there is a temporal instability implying that, for both halves
of the sample, the correct sign for u l obtains. Similarly, a close examination
of the Euler equation for debt indicates that, while the sign of u l is negative
for both subsamples, the estimate is of a much higher magnitude for the second
half.
Overall, then, the evidence in favor of my modeling approach in this paper
is mixed. While there is clearly a significant relationship between capital and
the debt-to-collateral ratio, the mechanism is not the one postulated here, since
the debt-to-collateral ratio moves in the opposite direction from that suggested
by a trade-off between a tax advantage to debt and a debt cost that is increasing
in the debt-to-collateral ratio. Given the substantial evidence that taxes
influence financial structure, this may be surprising. Perhaps of equal interest
is the finding of temporal instability in the single-equation estimates for debt
and capital.
One possible explanation for the instability may be that the complex
interaction between inflation, the tax code, and financial structure needs to be
more carefully handled. The importance of this interaction for investment in the
1970s is suggested by the work of Modigliani and Cohn (1979), among others.
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Harris, Milton, and Artur Raviv. "The Theory of Capital Structure," Journal
of Finance 46 (1991): 297-355.
Haugen, Robert A., and Lemma W. Senbet. "Corporate Finance and Taxes: A
Review," Financial Management (1986): 5-21.
Hayashi, Fumio. "Corporate Finance Side of the Q Theory of Investment,"
Journal of Public Economics 27 (1985): 261-280.
Hoshi, Takeo, Anil Kashyap, and David Scharfstein. "Corporate Structure and
Investment: Evidence from Japanese Panel Data," Quarterly Journal of
Economics 106 (1991): 33-60.
Hubbard, R. Glenn, and Anil Kashyap. "Internal Net Worth and the Investment
Process: An Application to U.S. Agriculture," manuscript, Columbia
University, 1990.
clevelandfed.org/research/workpaper/index.cfm
Ibbotson, R., and R. Sinquefeld. Stocks, Bonds, Bills, and Inflation: The
Past and the Future, Financial Analyst Research Foundation, 1982.
Jorgenson, D., and J. Stephenson. "The Time Structure of Investment and
Behavior in U.S. Manufacturing, 1947-1960," Review of Economics and
Statistics 49 (February 1967): 16-27.
, and M. Sullivan. "Inflation and Corporate Capital Recovery," In
Depreciation, Inflation, and the Taxation of Income from Capital,
Charles R. Hulten, ed., Urban Institute Press, Washington, D.C., 1981.
Kokklenberg, E. "The Specification and Estimation of Interrelated Factor
Demands Under Uncertainty," Journal of Economic Dynamics and Control 7'
(1984): 181-207.
Meyer, John, and Edwin Kuh. The Investment Decision, Cambridge,
Massachusetts: Harvard University Press, 1957.
Modigliani, Franco, and Richard A. Cohn. "Inflation, Rational Valuation and
the Market," Financial Analysts Journal (March/April 1979): 24-44.
, and Merton H. Miller. "The Cost of Capital, Corporation Finance,
and the Theory of Investment," American Economic Review 48 (1958):
261-297.
Myers, Stewart C. "Determinants of Corporate Borrowing," Journal of
Financial Economics 5 (1977): 147-75.
. "The Capital Structure Puzzle," Journal of Finance 39 (1984):
575-592.
, and N.S. Majluf. "Corporate Financing and Investment Decisions when
Firms Have Information that Investors Do Not Have," Journal of
Financial Economics 13 (1984): 187-221.
Osterberg, William P. "Tobin's q , Investment, and the Endogenous Adjustment of
Financial Structure," Journal of Public Economics 40 (1989): 293-318.
Pechman, J. Federal Tax Policy, Washington, D.C.: Brookings Institution,
1983.
Rotemberg, Julio J. "Interpreting the Statistical Failures of Some Rational
Expectations Macroeconomic Models," American Economic Review 74 (May
1984): 188-193.
Scott, J. "Bankruptcy, Secured Debt, and Optimal Capital Structure," Journal
of Finance 32 (March 1977): 1-19.
Shapiro, M. "The Dynamic Demand for Capital and Labor," Quarterly Journal of
Economics 101 (August 1986): 513-42.
clevelandfed.org/research/workpaper/index.cfm
Smith, Clifford W., and James B. Warner. "Bankruptcy, Secured Debt, and
Optimal Capital Structure: Comment," Journal of Finance 34 (1979): 247251.
Stiglitz, Joseph E., and Andrew Weiss. "Credit Rationing in Markets with
Imperfect Information," American Economic Review 71 (1981): 393-410.
Stulz, Rene M., and H. Johnson. "An Analysis of Secured Debt," Journal of
Financial Economics 14 (December 1985): 501-522.
Summers, L. "Inflation, Taxation, and Corporate Investment: A q theory
Approach," National Bureau of Economic Research Working Paper No. 604,
December 1980.
Time Series Processor Version 4.2, Reference Manual, TSP International, Palo
Alto, California, 1991.
White, Halbert. "A Heteroskedasticity-Consistent Covariance Matrix and a
Direct Test for Heteroskedasticity," Econometrica 48 (1980): 721-746.
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from Panel Data," Finance and Economics Discussion Series, No. 114,
Board of Governors of the Federal Reserve System, March 1990.
clevelandfed.org/research/workpaper/index.cfm
20
Glossary of Terms
B*
p
pt
rCt
- the "discount rate" applicable to quarter t cash flow
- fixed real rate of return required by stockholders
- rate of commodity price inflation
=
marginal personal rate of capital gains taxation
- marginal personal rate of dividend income taxation
rpt - corporate profits tax rate
DVt - the dividend
ryt
rt
=
yt
- real output of manufacturing
Kt
Lt
Ht
Nt
d
qt
- physical capital stock at the start of period t
- level of production employment in period t
- weekly hours per production worker
- level of nonproduction employment
- one minus the rate of physical depreciation of capital
- one minus the quit rate
((Kt)=
Bt
H*t
W*t
Wt
fLt
cash flow
book value of the stock of tangible assets
=
- collateral
book value of debt
- level of weekly hours per employee at which overtime starts
- hourly wage rate inclusive of overtime payments
- hourly wage rate exclusive of overtime payments
=
the fixed cost of a production worker
- the fixed cost of a nonproduction worker
at - manufacturing output price index
ISt - investment goods price index
Dt, ITCt - present value of depreciation deductions; investment tax credit
fNt
clevelandfed.org/research/workpaper/index.cfm
Table 1
Instrument Lists
Full List (21 instruments):
ryt-l rpt-l
ITCt-l,
rct-1 qt-1, Ht-leH*t-l Ht-1, Nt-1, 4 - 1 9
Bt
time (trend) , constant, Wt-1, yt-1, fNt-1, and fLt-1
e*t-l
"Largen List (7) :
6a:
6b:
6 ~
6d:
6e:
6f:
6g:
.
9
(Kt)
Dt-1,
8*t-1, rct-1, Ht-l-H*t-l, Kt, ITCt, at-1, Wt-1.
8*t-1, rct-1, Ht-l-H*t-l, Kt, ITCt, at-1.
8*,-i, rct-l, Ht-l-H*t-l, Kt, ITCt, Wt-1:
e*t-l, rct-~,H ~ - ~ - H * ~ -~~t, at-l,
,
w,-I.
B*t-l, ~ ~ t - 1Ht-i-Hft-i,
,
ITCt
Wt-iB*t-l, rct-~,Kt, ITCt, Bt-l, Wt-~.
8*,-1, Ht-l-H*t-l, Kt , ITCt , at-1 , Wt-1
Ht-l-H*t-l, Kt, ITCt,
Wt-i.
"Small" List (4): B*t-l, 7ct-1,ITCt, Ht-l-H*t-l.
3a: B*t-l, rct-l, ITCt.
3b :
rct-l, Ht-l-H*t-l.
3c : e*t-l, ITC, , H,-~-H*,-~.
3d:
ITCt, Ht-l-H*t,l
Notes for Tables 2
-
6
IVs:
The choice of instrumental variable list from those given in table 1.
MA:
The order of the moving-average process used to correct for serial
correlation. No entry implies that no correction was employed.
HC:
A correction for heteroscedasticity was employed.
NOBS:
The number of observations.
J(df): The value of the Hansen-Singleton J statistic, which is distributed as a
chi-squared with df degrees of freedom.
*
:
The coefficient is significant at the 10 percent level for a two-tailed
test.
clevelandfed.org/research/workpaper/index.cfm
Table 2A: Estimates of Equations 11-15 with Current "Large" IV Sets
IVs
7
7
MA
Yes
HC
@o
@I
a1
gll
ah
ghh
%
gm
ak
gkk
ul
a,
NOBS
J(df)
7
7
7
1
3
7
Yes
Yes
Yes
0.113*
0.122*
0.127*
0.125*
0.122*
0.059
0.046
0.041
0.030
0.023
0.470*
0.466*
0.465*
0.466*
0.467*
0.018
0.014
0.013
9.23-3
7.23-3
0.141*
0.144*
0.143*
0.142*
0.141*
0.002
1.23-3
1.43-3
1.33-3
9.03-4
1.53-4
1.23-3*
1.13-3*
8 .53-4*
7 .33-4*
5.53-4
3.53-4
3.13-4
2.43-4
1.83-4
0.173*
0.177*
0.175*
0.173*
0.173*
3.43-3
2.83-3
2.63-3
2.13-3
1.53-3
-1.03-5
-3.03-4
-3.33-4
-4.63-4*
-5.03-4*
4.23-4
2.63-4
2.43-4
1.83-4
1.23-4
0.205*
0.209*
0.208*
0.207*
0.206*
2.93-3
1.93-3
2.13-3
2.03-3
1.43-3
0.048*
0.095*
0.090*
0.085*
0.082*
0.022
0.017
0.014
9.73-3
7.83-3
0.093*
0.096*
0.097*
0.097*
0.097*
6.63-3
2.93-3
3.03-3
2.43-3
1.93-3
-4.93-4*
-4.33-4*
-4.43-4*
-4.OE-4*
-3.83-3*
9.83-5
7.13-5
6.83-5
5.53-5
4.13-5
-0.240*
-0.243*
-0.250*
-0.251*
-0.251*
0.017
0.012
0.012
9.63-3
7.OE-3
0.019*
0.023*
0.269*
0.027*
0.027*
0.010
6.53-3
6.53-3
5.13-3
3.73-3
105
105
105
105
105
174.99(30)
89.87(30)
47.80(30)
25.67(30)
13.64(30)
-
clevelandfed.org/research/workpaper/index.cfm
Table 2B: Estimates of Equations 11-15 with Current "Largen IV Sets
IVs
HC
Wo
W1
a1
gll
ah
,g
a,
gm
ak
gkk
"1
a,
6a
6b
6c
Yes
Yes
Yes
~(df)
6e
6f
6g
Yes
Yes
Yes
Yes
0.133*
0.099*
0.232*
0.140*
0.114*
0.064
0.050
0.052
0.071
0.044
0.048
0.517*
0.531'
0.463*
0.474*
0.432*
0.461*
0.469*
0.020
0.020
0.106
0.016
0.022
0.014
0.105
0.144*
0.144*
0.144*
0.144*
0.144*
0.144*
0.144*
1.4E-3
1.43-3
1.3E-3
1.4E-3
1.6E-3
1.33-3
1.33-3
1.13-3*
1.53-3*
1.9E-3*
2.1E-3*
2.93-3*
9.93-4*
5.03-4
6.43-4
5.73-4
4.43-3
6.9E-4
6.13-4
3.63-4
4.83-4
0.185*
0.187*
0.177*
0.178*
0.172*
0.177*
0.177*
5.OE-3
4.23-3
2.9E-3
4.63-3
3.83-3
2.83-3
3.13-3
-2.2E-3*
-9.83-4*
6.73-5
-3.23-3*
-1.43-3
-1.63-4
-5.7E-4*
1.13-3
5.43-4
3.63-4
1.13-3
1.4E-3
2.23-4
3.73-4
0.209*
0.210*
0.212*
0.210*
0.210*
0.210*
0.209*
2.1E-3
2.13-3
2.33-3
2.13-3
2.43-3
2.13-3
2.03-3
0.094*
0.107*
0.199*
0.085*
0.109
0.103*
0.089
0.020
0.021
0.055
0.021
0.021
0.021
0.020
0.094*
0.093*
0.093*
0.106*
0. loo*
0.092*
0.093*
3.23-3
3.63-3
3.33-3
4.23-3
4.53-3
3.13-3
3.13-3
-4.63-3*
-4.93-4*
-4.6E-4*
-2.73-4*
-3.33-4*
-5.4E-5*
7.83-5
8.23-5
8.3E-5
8.2E-5
1.13-4
8.73-4
7.93-5
-0.229*
-0.229
-0.236*
-0.269*
-0.254*
-0.246*
-0.239
0.014
0.015
0.013
0.103
0.013
0.013
0.014
0.103*
0.011
0.020*
0.038*
0.031*
0.029
0.019*
7.03-3
7.OE-3
6.83-3
105
105
105
-0.041
-0.087
0.064
7.73-3
NOBS
6d
105
86.1(24)
8.13-3
105
86.2(24)
6.93-3
105
88.6(24)
87.5(24)
84.2(24)
89.2(24)
-4.53-4
7.43-3
105
86.2(24)
clevelandfed.org/research/workpaper/index.cfm
Table 2C: Estimates of Equations 11-15 with Current "Small" IV Sets
IVs
4
4
MA
HC
No
Yes
4
4
4
1
3
7
Yes
Yes
Yes
3-a
3-b
3-c
3-d
Yes
Yes
Yes
Yes
-0.132*
-0.138*
-0.121
-0.089
-0.066*
-0.144*
0.120
-0.134*
0.082
0.070
0.075
0.077
0.067
0.108
0.084
0.201
0.084
-0.305*
-0.285*
-0.297*
-0.306*
-0.305*
-0.240*
-0.331*
-0.289*
-0.271*
0.023
0.021
0.026
0.028
0.029
0.025
0.027
0.023
0.025
0.058*
0.048*
0.055*
0.060*
0.059*
0.022
0.076*
0.051*
0.039*
0.014
0.012
0.014
0.016
0.016
0.015
0.016
0.013
0.014
NOES
105
105
105
105
105
105
105
105
J(df)
100 ( 1 2 )
72 (12)
40 (12)
2 2 (12)
13 (12)
Wo
"1
a,
-0.090
53 ( 6 )
105
23 ( 6 )
61 (6)
25 ( 6 )
clevelandfed.org/research/workpaper/index.cfm
Table 2D: Estimates of Equations 11-15: "Large1'IV Sets Lagged One Period
IVs
7
7
MA
Yes
HC
Wo
W1
a1
a 1
ah
ghh
%
&ur
ak
ul
au
NOBS
J(df)
7
7
1
3
7
Yes
Yes
Yes
0.087
0.103*
0.107*
0.113*
0.110*
0.064
0.050
0.045
0.036
0.028
0.478*
0.474*
0.472*
0.471*
0.471*
0.020
0.016
0.014
0.011
8.83-3
0.143*
0.145*
0.144*
0.143*
0.143*
2.03-3
1.43-3
1.43-3
1.23-3
8.73-4
2 .43-4*
3.63-3*
3.53-3*
3.43-3*
3.33-3*
1.33-4
8.83-4
8.63-4
6.73-4
5.13-4
0.176*
0.182*
0.179*
0.175*
0.174*
0.019
0.012
9.63-3
6.53-3
4.83-3
-0.027
-0.013
-0. Oll*
-0. Oll*
-0.010
0.017
8.93-3
7.23-4
5.43-3
3.53-3
0.205*
0.210*
0.208*
0.207*
0.206*
2.83-3
1.93-3
2.03-3
1.73-3
1.33-3
0.040*
0.068*
0.066*
0.061*
0.059*
0.020
0.013
0.013
0,010
8.43-3
0.103*
0.102*
0.103*
0.104*
0.104*
5.93-3
3.53-3
3.63-3
3.33-3
2.63-3
-1.43-4*
-1.63-4*
-1.63-4*
-1.53-4*
8.63-5
6.23-5
6.23-5
5.33-5
3.53-5
-0.218*
-0.225*
-0.229*
-0.235*
-0.237*
0.017
0.011
0.010
8.73-3
5.93-3
5.23-3
0.013*
0.014*
0.017*
0.018*
0.010
5.83-3
5.73-3
4.73-3
3.23-3
104
104
104
104
104
-1.13-4
gkk
7
169.5(30)
,
85.9(30)
47.6(30)
25.7 (30)
13.6(30)
clevelandfed.org/research/workpaper/index.cfm
Table 2E: Estimates of Equations 11-15: "Largen IV Sets Lagged One Period
IVs
6-a
6-b
6-c
6-d
6-e
6-f
6%
HC
Yes
Yes .
Yes
Yes
Yes
Yes
Yes
@o
-1.5E-3
-0.076
0.066
0.066
0.loo*
0.loo*
0.316*
0.110*
0.127*
0.051
0.053
0.068
0.051
0.054
clevelandfed.org/research/workpaper/index.cfm
clevelandfed.org/research/workpaper/index.cfm
Table 2G: Estimates of Equations 11-15:
IVs
7
7
MA
HC
("0
("1
a1
gll
ah
ghh
a,
gnn
ak
gkk
"1
a,
NOBS
J(df)
Yes
"Large" I V S e t s Lagged 4 Periods
7
7
7
1
3
7
Yes
Yes
Yes
0.147*
0.142*
0.170*
0.175*
0.178*
0.070
0.047
0.040
0.031
0.020
0.461*
0.462*
0.453*
0.452*
0.451*
0.021
0.015
0.012
9.5E-3
6.4E-3
0.149*
0.152*
0.151'
0.149*
0.149*
5.93-3
3.53-3
3.43-3
2.51-3
1.7E-3
0.019
0. Oll*
0.109
0.015*
0.015*
6.9E-3
5.1E-3
4.6E-3
2.9E-3
2.OE-3
0.173*
0.176*
0.172*
0.171*
0.171*
6.73-3
4.6E-3
3.33-3
2.71-3
1.8E-3
-4.OE-3
-5.1E-3*
-3.7E-3*
-3.3E-3*
-3.2E-3*
2.6E-3
1.4E-3
1.OE-3
7.63-4
5.3E-4
0.209*
0.212*
0.210*
0.208*
0.208*
3.41-3
1.BE-3
2.1E-3
1.7E-3
1.2E-3
0.117*
0.099*
0.109*
0. Ill*
0.112*
0.033
0.024
0.019
0.013
0.010
0.104*
0.103*
0.109
0.107*
0.106*
5.81-3
3.8E-3
4.1E-3
3.43-3
2.51-3
-5.73-5
-5.43-5
-5.41-5
-6.8E-5*
-7.4E-5*
7.OE-5
4.6E-5
4.73-5
3.93-5
3.OE-5
-0.216*
-0.221*
-0.224*
-0.232*
-0.231*
0.017
0.013
0.103
0.010
9.OE-3
5.OE-3
0.010
0.011
0.019
0.019
0.010
6.9E-3
7.21-3
5.73-3
4.83-3
101
101
101
101
101
131.3
(30)
81.3
(30)
45.8
(30)
24.8
(30)
13.0
(30)
clevelandfed.org/research/workpaper/index.cfm
Table 2H: Estimates of Equations 11-15: "Largen IV Sets Lagged 4 Periods
IVs
6-a
6-b
6-c
6-d
6-9
6-f
6-8
HC
Yes
Yes
Yes
Yes
Yes
Yes
Yes
"'0
"'1
a1
gll
ah
ghh
a,
gm
ak
gkk
v1
a,
NOBS
J(df
0.156*
0. Ill*
0.107*
0.181*
0.138*
0.138*
0.142*
0.075
0.057
0.057
0.050
0.051
0.056
0.047
0.458*
0.471*
0.472*
0.449*
0.463*
0.463*
0.462*
0.023
0.108
0.018
0.015
0.016
0.018
0.015
0.152*
0.155*
0.157*
0.155*
0.152*
0.166*
0.152*
3.93-3
4.43-3
4.53-3
4.1E-3
3.83-3
9.0E-3
3.53-3
0.012*
0.015*
0.014*
0.013*
0.014*
0.023
0.Oll*
5.83-3
6.43-3
6.OE-3
6.43-3
5.83-3
0.023
5.13-3
0.176*
0.177*
0.178*
0.177*
0.176*
0.177*
0.176*
4.73-3
5.33-3
5.43-3
5.13-3
4.33-3
4.73-3
4.63-3
-4.13-3*
-5.43-3*
-5.73-3*
-5.5E-3*
-4.23-3*
-4.23-3*
-5.13-3*
1.BE-3
1.5E-3
1.6E-3
1.73-3
1.13-3
1.33-3
1.43-3
0.212*
0.212*
0.214*
0.214*
0.210*
0.213*
0.212*
2.13-3
2.OE-3
2.23-3
2.1E-3
2.OE-3
2.33-3
1.93-3
0.106*
0.116*
0.115*
0.102*
0.098*
0.163*
0.099*
0.027
0.027
0.028
0.028
0.025
0.056
0.024
0.101*
0.099*
0.099*
0.106*
0.107*
0.105*
0.103*
3.93-3
3.83-3
4.OE-3
4.33-3
4.OE-3
3.83-3
3.83-3
-1.63-4*
-8.43-5
-6.63-5
-2.63-5
-1.23-4*
-1.4E-4*
-5.43-5
7.43-5
5.13-5
4.73-5
5.43-5
6.03-5
5.73-5
4.63-5
-0.231*
-0. ZOO*
-0.198*
-0.220*
-0.244*
-0.237*
-0.221*
0.104
0.013
0.014
0.013
0.014
0.014
0.013
0.106*
-4.63-3
-5.9E-3
9.1E-3
0.023*
0.021*
0.010
7.43-3
7.23-3
7.33-3
7.43-3
7.73-3
7.5E-3
6.93-3
101
101
101
101
101
101
101
y0.5 (24)
78.1 (24)
76.0 (24)
74.6 (24)
80.7 (24)
72.4 (24)
81.3 (24)
clevelandfed.org/research/workpaper/index.cfm
Table 21: Estimates of Equations 11-15: "Small" IV Sets Lagged 4 Periods
IVs
4
4
4
1
3
7
Yes
Yes
Yes
Yes
-0.013
-0.021
-0.032
-0.020
0.010
0.072
-0.321*
0.047
-0.134
0.077
0.072
0.073
0.072
0.050
0.079
0.152
0.078
0.100
0.511*
0.513*
0.516*
0.513*
0.503*
0.486*
0.609*
0.492*
0.549*
0.024
0.022
0.023
0.022
0.016
0.025
0.048
0.025
0.031
0.148*
0.155*
0.154*
0.152+
0.150*
0.161*
0.156*
0.149*
0.148*
6.93-3
4.73-3
4.73-3
4.5E-3
4.OE-3
0.012
4.43-3
0.039
3.53-3
0.014
0.016*
0.019*
0.Ole*
0.017*
0.040*
0.012
0.010
2.33-3
0.011
6.73-3
6.53-3
6.OE-3
5.63-3
0.028
8.53-3
0.076
4.73-3
0.180*
0.190*
0.187*
0.185*
0.180*
0.193*
0.199*
0.195*
0.186*
7.OE-3
6.63-3
6.63-3
6.43-3
5.43-3
6.23-3
0.025
6.OE-3
0.102
-5.OE-3*
-3.9E-3*
-3.5E-3*
-3.3E-3
-4.2E-3*
-9.9E-3
-2.5E-3
-0.034
2.63-3
1.7E-3
1.4E-3
1.2E-3
9.9E-4
1.5E-3
9.8E-3
1.7E-3
0.108
0.208*
0.216*
0.214*
0.211*
0.209*
0.219*
0.220*
0.233*
0.213*
3.2E-3
2.9E-3
3.6E-3
4.1E-3
4.33-3
3.1E-3
3.33-3
0.015
3.4E-3
0.088*
0.104*
0.108*
0.097*
0.087*
0.153*
0.110*
0.621
0,010
0.037
0.031
0.029
0.027
0.022
0.038
0.038
0.495
0.051
0.104*
0.104
0.106*
0.106*
0.107*
0. loo*
0.104*
0. loo*
0.130*
6.3E-3
5.4E-3
5.9E-3
5.6E-3
5.33-3
5.9E-3
5.53-3
7.5E-3
0.013
-1.1E-4
-9.OE-5
-9.1E-5
-1.1E-4*
-1.2E-4*
-4.7E-5
-8.2E-5
-4.1E-4*
4.1E-4
7.53-5
6.OE-5
6.5E-5
6.43-5
5.83-5
6.33-5
8.1E-5
1.4E-4
2.9E-4
-0.229*
-0.237*
-0.242*
-0.184*
-0.232*
-0.260*
-0.250*
4
4
MA
HC
oo
01
a1
gll
ah
ghh
a
gm
a,
gkk
"1
-3.8E-3
-0.226*
-0.219
3-a
3-b
3-c
3-d
Yes
Yes
Yes
Yes
0.023
0.021
0.025
0.026
0.027
0.023
0.028
0.023
0.025
9.8E-3
7.93-3
0.013
0.017
0.020
-0.011
0.014
0.034*
0.028*
0.014
0.012
0.014
0,015
0.015
0.014
0.016
0.013
0.015
NOBS
101
101
101
101
101
101
101
101
101
J(df)
74 (12)
69 (12)
39 (12)
22 (12)
48 (6)
61 (6)
av
12
(12)
36 (6)
41
(6)
clevelandfed.org/research/workpaper/index.cfm
Table 3A: Split Sample, 5 4 : 3
IVs
'"0
'"1
4
3-a
- 67:2,
One-Quarter Lag, "Small" IV Sets
3-b
3-c
3-d
0.198*
0.145
0.196*
0.221*
0.113
0.051
0.097
0.068
0.083
0.077
0.467*
0.488*
0.467*
0.463*
0.496*
0.016
0.032
0.022
0.029
0.025
clevelandfed.org/research/workpaper/index.cfm
Table 3B: Split Sample, 67:3
IVs
"0
"1
-
80:2, One-Quarter Lag, "Smalln IV Sets
4
3-a
3-b
3-c
-0.171*
-0.675
-0.193*
-0.083
-0.260*
0.088
0.539
0.095
0.177
0.109
0.551*
0.705*
0.558
0.525*
0.578*
0.027
0.164
0.029
0.053
0.033
clevelandfed.org/research/workpaper/index.cfm
Table 3C: Split Sample, 55:2
IVs
Wo
W1
a1
gll
ah
ghh
a,
grm
ak
gkk
Yl
a,
NOBS
J(df)
3-a
4
-
68:1, Four-Quarter Lag, "Small" IV Sets
3-b
3-c
3-d
0.181*
0.136
0.208*
0.095
0.206*
0.072
0.088
0.085
0.085
0.075
0.475*
0.493*
0.464*
0.504*
0.469*
0.022
0.028
0.028
0.027
0.023
0.173*
0.175*
0.175*
0.172*
0.174*
7.63-4
0.011
1.63-3
2.53-3
9.73-4
-1.23-3
-0.030
3.23-3
-0.013*
-5.93-3*
1.13-3
0.071
3.73-3
4.53-3
3.33-3
0.226*
0.234*
0.243*
0.272*
0.228*
3.93-3
4.73-3
0.019
0.093
4.23-3
-1.13-3
3.03-3*
-0.018*
0.121
9.93-4
7.63-4
1.33-3
0.016
0.103
9.33-4
0.250*
0.251*
0.253*
0.249*
0.251*
1.03-3
1.3E-3
1.63-3
2.23-3
1.33-3
0.027*
-0.096*
0.123*
-0.151*
-2.93-3
0.015
0.054
0.048
0.066
0.023
0.078*
0.074*
0.076*
0.050*
0.082*
4.03-3
6.73-3
4.53-3
9.53-3
4.43-3
-3.83-4*
-2.33-4*
-3.43-4*
-3.53-4*
5.53-5
9.93-5
1.43-4
2.33-4
7.33-5
-0.190*
-0.099*
-0.115*
0.035
0.050
0.029
0.082
2.13-3
-0.043*
-0.036*
0.139*
-0.016
0.017
0.024
0.014
0.038
0.016
52
52
52
52
52
12 (6)
38 (6)
40 (12)
34 (6)
-1.53-4
20
(6)
-0.097
-0.220*
0.034
clevelandfed.org/research/workpaper/index.cfm
T a b l e 3D: S p l i t Sample, 6 8 : 2
IVs
Wo
a1
a1
3-a
4
ah
&hh
a,
gm
ak
gkk
"1
a,
NOBS
J(df)
8 0 : 2 , Four-Quarter Lag, "Small" I V S e t s
3-c
3-b
3-d
0.043
-0.176*
0.145
0.045
-0.543*
0.073
0.102
0.096
0.080
0.255
0.487*
0.447*
0.455*
0.487*
0.663*
0.023
0.031
0.029
0.025
0.077
0.141*
0.142*
0.139*
0.138*
0.138*
1.83-3
3.23-3
2.73-3
3.33-3
-
gll
-
6.33-3*
7.93-3
-1.63-3
-3.83-4
4.23-4
2.73-3
5.33-3
1. 93-3
4.33-3
1.83-3
0.170*
0.169*
0.169*
0.174*
0.191*
6.73-3
5.1E-3
5.93-3
6.93-3
0.012
-3.63-3*
-1.83-3*
2.13-3
-1.13-3
-5.73-4
1.53-3
9.33-4
1.53-3
2.03-3
5.83-3
0.197*
0.198*
0.197*
0.206*
0.196*
2.53-3
2.83-3
3.03-3
6.83-3
3.03-3
0.060*
0.035
-0.033
0.252*
9.83-3
0.024
0.024
0.025
0.129
0.029
0.066*
0.082*
0.148*
0.059*
-0.024
0.022
0.053
0.021
0.021
0.040
1.23-4*
2.43-4*
7.23-5
-2.03-4
5.33-4
6.43-5
8.33-5
6.73-5
1.33-4
3.73-4
0.080
0.499*
0.041
-0.091
0.108
0.257
0.103
0.116
0.129
-0.213*
-0.505*
-0.186*
0.091
0.021
0.077
0.181
0.073
0.082
0.091
52
52
52
52
52
29 (6)
27 (6)
30 (12)
204 (6)
18
(6)
-0.248*
clevelandfed.org/research/workpaper/index.cfm
Table 4A: Non-Debt Equations, One-Quarter Lag, "Large" IV Sets
IVs
6-a
6-b
wo
-0.011
-0.086
0.067
w1
a1
gll
ah
ghh
a,
gm
ak
gkk
"1
NOBS
J(df)
6-d
6-f
6-9
6 3
0.133*
0.129*
0.352*
0.132*
0.142*
0.069
0.055
0.056
0.071
0.055
0.057
0.509*
0.531*
0.463*
0.465*
0.396*
0.464*
0.462*
0.021
0.021
0.017
0.018
0.022
0.017
0.018
0.147*
0.147*
0.147*
0.147*
0.145*
0.146*
0.146*
1.9E-3
2.OE-3
1.7E-3
1.8E-3
2.OE-3
1.7E-3
1.9E-3
4.6E-3*
4.OE-3*
3.5E-3*
4.4E-3*
4.1E-3*
2.4E-3*
3.7E-3*
1.6E-3
1.8E-3
1.3E-3
1.5E-3
1.6E-3
1.3E-3
1.5E-3
0.200*
0.199*
0.181*
0.184*
0.171*
0.181*
0.181*
0.028
0.019
8.83-3
0.031
4.23-3
6.93-3
8.2E-3
-0.023
-0.015
-0.014*
-0.038*
-2.OE-3
-5.43-3
-0.014*
0.018
0.014
7.8E-3
0.023
2.2E-3
4.6E-3
6.9E-3
0.212*
0.213*
0.212*
0.210*
0.209*
0.211*
0.212*
2.63-3
2.53-3
2.33-3
2.1E-3
2.53-3
2.53-3
--
6-c
-
-
-
-
2.63-3
-
-
0.073*
0.070*
0.067*
0.066*
0.045*
0.053*
0.102*
0.022
0.022
0.019
0.022
0.017
0.018
0.033
0.040*
0.033*
0.033*
0.045*
0.045*
0.040*
0.051*
9.1E-3
0.010
9.8E-3
0.010
9.4E-3
8.7E-3
8.1E-3
8.83-5
1.4E-4
2.43-4
l.lE-4
1.6E-4
1.5E-4
-1.8E-4
1.OE-4
l.lE-4
1.OE-4
9.4E-5
1.OE-4
1.OE-4
l.lE-4
0.176*
-0.233*
-0.263*
0.157*
0.174*
0.192*
0.058
0.068
0.075
0.076
0.070
0.065
0.066
0.066
104
104
104
104
104
104
104
77.3 (19)
74.0 (19)
76.2 (19)
81.2 (19)
74.8 (19)
79.3 (19)
76.1 (19)
clevelandfed.org/research/workpaper/index.cfm
Table 4B: Capital and Debt Equations, One-Quarter Lag, "Large" IV Sets
IVs
ak
gkk
Y1
a,
NOBS
J(df)
6-a
6-b
6-c
6-d
ak
gkk
Y1
NOBS
J(df)
6-f
6-g
0.092*
0.092*
0.090*
0.108*
0.103*
0.092*
0.087*
4.1E-3
4.23-3
4.33-3
5.2E-3
6.1E-3
4.1E-3
3.83-3
-1.3E-4*
-1.3E-4*
-1.9E-4*
-9.OE-5
4.1E-5
-1.9E-4*
-3.4E-4*
7.63-5
7.83-5
9.9E-5
7.93-5
9.3E-5
9.1E-5
l.lE-4
-0.221*
-0.218*
-0.229*
-0.270*
-0.232*
-0.236*
-0.237*
0.017
0.017
0.016
0.018
0.018
0.016
0.016
9.83-3
8.1E-3
0.017*
0.038*
0.019*
-0.020*
0.021*
8.73-3
8.OE-3
8.73-3
0.010
8.63-3
8.53-3
8.63-3
104
104
104
104
104
104
104
40.7 (8)
41.9 (8)
45.7 (8)
25.2 (8)
39.1 (8)
35.1 (8)
Table 4C: Capital Equation, One-uarter
IVs
6-0
6-a
6-b
6-c
6-d
43.9 (8)
Lag, "Large" IV Sets
6-0
6-f
6-8
0.049
0.038*
0.048*
0.066*
0.062*
0.051*
0.060*
9.6E-3
0.011
0.010
0.011
9.83-3
9.1E-3
8. BE-3
1.2E-4
1.7E-4
5.1E-5
3.73-5
1.6E-4
4.73-5
-2.23-4
l.lE-4
1.2E-4
l.lE-4
8.83-5
l.lE-4
1.2E-4
1.3E-4
0.152*
0.208*
0.131*
0.022
0.063
0.112
-4.31-3
0.072
0.081
0.082
0.075
0.070
0.071
0.074
104
104
104
104
104
104
104
7.5 (3)
6.1 (3)
11.3 (3)
6.5 (3)
4.1 (3)
11.5 (3)
4.3 (3)
clevelandfed.org/research/workpaper/index.cfm
Table 4D: Debt Equation, One-Quarter Lag, "Large" IV Sets
IVs
6-a
a,
0.019*
6-b
6-c
6-d
6-9
6-f
6-8
0.014*
0.031*
0.055*
0.041*
0.032*
0.027*
9.3E-3
9.7E-3
9.83-3
0.011
9.9E-3
0.83-3
9.8E-3
-0.239*
-0.230*
-0.253*
-0.300*
-0.276*
-0.259*
-0.248*
0.017
0.028
0.019
0.020
0.018
0.018
0.018
NOBS
104
104
104
104
104
104
104
J (df
13.8 (3)
21.4 ( 3 )
25.5 (3)
26.4 (3)
23.4 (3)
30.8 (3)
"1
6.4 (3)
clevelandfed.org/research/workpaper/index.cfm
Table 4E: Non-Debt Equations, Four-Quarter Lag, "Large" IV Sets
IVs
'"0
'"1
a1
gll
ah
ghh
a,
gm
ak
gkk
Yl
NOBS
J(df)
6-a
6-b
6-c
6-d
6-9
6-f
6-8
0.130*
0.101*
0.243*
0.179*
0.195*
0.181*
0.133*
0.059
0.060
0.058
0.057
0.063
0.057
0.077
0.466*
0.474*
0.430*
0.451*
0.446*
0.449*
0.464*
0.018
0.019
0.018
0.018
0.020
0.018
0.024
0.153*
0.152*
0.155*
0.153*
0.169*
0.151*
0.152*
4.33-3
4.13-3
4.03-3
3.93-3
9.03-3
3.63-3
4.03-3
0.014*
0. Oll*
0.015*
0.015*
0.034
9.83-3*
0.012*
5.53-3
5.33-3
5.4E-3
5.63-3
0.021
5.13-3
5.63-3
0.177*
0.178*
0.176*
0.176*
0.176*
0.175*
0.179*
5.63-3
5.73-3
5.33-3
4.53-3
4.93-3
4.93-3
5.43-3
-5.23-3*
-5.63-3*
-4.93-3*
-3.83-3*
-4.43-3*
-4.83-3*
1.63-3
1.83-3
1.93-3
1.33-3
1.43-3
1.63-3
2.23-3
0.212*
0.211*
0.214*
0.211*
0.214*
0.211*
0.212*
2.63-3
2.73-3
2.73-3
2.53-3
3.03-3
2.83-3
2.73-3
0.107*
0.106*
0.105*
0.103*
0.179*
0.092*
0. OgO*
0.030
0.031
0.032
0.028
0.047
0.033
0.032
0.040*
0.029*
0.044*
0.055*
0.050*
0.042*
0.042*
9.53-3
0.011
9.2E-3
9.43-3
8.53-3
9.41-3
8.71-3
-4.83-3
7.13-5
9.03-5
1.23-4
4.23-5
6.13-5
1.43-4*
6.63-5
6.63-5
7.31-5
7.63-5
6.53-5
7.83-5
8.03-5
0.175*
0.234*
0.165*
0.087*
0.121*
0.172*
0.138*
0.060
0.065
0.058
0.064
0.056
0.061
0.059
101
101
101
101
101
101
101
78.1 (19)
76.5 (19)
70.0 (19)
77.3 (19)
65.1 (19)
75.3 (19)
-4.33-5
75.8 (19)
clevelandfed.org/research/workpaper/index.cfm
gkk
"1
a,
NOBS
J(df)
-1.73-4*
-1.43-4*
-7.13-9
-2.93-4*
-4.03-5*
-2.13-4*
6.53-5
6.23-5
6.73-5
7.93-5
7.33-5
6.23-5
9.5E-4
-0.218*
-0.210*
-0.216*
-0.267*
-0.226*
-0.224*
-0.230*
0.016
0.015
0.016
0.018
0.017
0.016
0.017
8.43-3
3.33-3
9.83-3
0.036*
0.015*
-0.013*
0.017*
8.13-3
8.13-3
8.73-3
9.93-3
9.3E-3
8.43-3
8.73-3
101
101
101
101
101
101
101
39.1 (8)
40.3 (8)
44.3 (8)
23.0 (8)
Table 4G: Capital Equation, Four+arter
IVs
a,
gkk
"1
NOBS
J(df)
6-a
6-b
6-c
6-d
1.83-4*
37.8 (8)
38.9 (8)
45.4 (8)
Lag, "Large" I V Sets
6-0
6-f
6-8
0.054*
0.049*
0.055*
0.068*
0.062*
0.056*
0.055*
9.93-3
0.011
9.93-3
0.011
9.53-3
9.9E-3
9.3E-3
1.03-4
1.23-4
1.33-4
1.93-5
8.23-5
1.73-4
9.63-5
7.53-4
7.73-5
8.33-5
9.03-5
7.63-5
9.13-5
1.13-4
0. Ill*
0.140*
0.114*
0.012
0.055
0.126*
0,100
0.062
0.068
0.062
0.077
0.064
0.066
0.063
101
101
101
101
101
101
101
9.5 (3)
8.6 (3)
6.2 (3)
8.2 (3)
7.9 (3)
8.2 (3)
10.5 (3)
clevelandfed.org/research/workpaper/index.cfm
clevelandfed.org/research/workpaper/index.cfm
Table 5A: Split Sample, Capital Equation, One-Quarter Lag, "Large" IV Sets,
1954:3 - 1967:2
IVs
ak
gkk
"1
NOBS
J(df)
6-a
6-b
6-c
6-d
6-0
6-f
6-8
0.104*
0.082*
0.104*
0.107*
0.098*
0.095*
0.094*
0.022
0.021
0.020
0.024
0.019
0.018
0.019
-3.6E-4*
-3.1E-4
-3.5E-4
-6.8E-4*
-2.83-4
-4.1E-4*
-3.33-4
1.6E-4
1.2E-4
1.2E-4
1.7E-4
1.7E-4
1.2E-4
1.2E-4
-0.485*
0.277*
0.493*
-0.571*
-0.428*
-0.387*
0.243
0.218
0.216
0.266
0.223
0.199
0.204
52
52
52
52
52
52
52
11.9 (3)
7.4 (3)
10.3 (3)
6.6 (3)
-0.414
11.0 (3)
5.3 (3)
9.0
(3)
Table 5B: Split Sample, Capital Equation, One-Quarter Lag, "Large" IV Sets,
1967:3 - 1980:2
IVs
6-a
6-b
6-c
6-d
6-0
6-f
6-8
ak
-0.057
-0.069
-0.061
-0.060
-0.052
-0.037
-7,6E-3*
0.071
0.074
0.078
0.078
0.084
0.068
0.063
1.7E-3
1.6E-4
1.6E-4
l.lE-4
8.73-5
8.83-5
-1.3E-5
1.3E-3
1.3E-4
1.4E-4
l.lE-4
l.lE-4
1.OE-4
1.4E-4
0.667*
0.728*
0.691*
0.672*
0.625
0.553*
-0.380*
0.344
0.359
0.384
0.378
0.409
0.325
0.311
52
52
52
52
52
52
gkk
"1
NOBS
.
J(df)
2.3 (3)
2.4 (3)
3.4 (3)
3.9 (3)
4.3 (3)
4.3 (3)
52
3.5
(3)
clevelandfed.org/research/workpaper/index.cfm
Table 5C: Split Sample, Capital Equation, Four-Quarter Lag, "Large" IV
Sets, 1955:2 - 1968:l
IVa
6-a
ak
gkk
"1
NOBS
J(df)
6-b
6-c
6-d
6-0
6-f
6-g
0.063*
0.065*
0.061*
0.064*
0.065*
0.075*
0.068*
0.022
0.021
0.022
0.021
0.021
0.022
0.022
-3.lE-4*
-3.7E-4*
-2.73-4
-4.OE-4*
-3.33-4
-4.2E-4*
-3.5E-4
1.5E-4
1.5E-4
1.6E-4
1.6E-4
1.5E-4
1.6E-4
1.5E-4
-0.040
-0.076
-6.1E-3
-0.061
-0.060
-0.188
-0.090
0.240
0.240
0.242
0.237
0.239
0.248
0.244
52
52
52
52
52
52
52
10.7 (3)
7.3 (3)
10.2 (3)
9.6 (3)
10.9 (3)
5.7 (3)
9.9
(3)
Table 5D: Split Sample, Capital Equation, Four-Quarter Lag, "Large" IV
Sets, 1968:2 - 1980:2
IVa
ak
gkk
"1
NOBS
J(df)
6-a
6-b
6-c
6-e
6-f
1.5E-3
-2.31-3
-0.019
0.024
6-d
6-g
0.015
0.012
-0.015
0.058
0.058
0.064
0.060
0.060
0.069
0.056
1.2E-4
1.2E-4
1.2E-4
1.2E-4
1.2E-4
1.5E-4
1.6E-4
8.4E-5
8.43-5
8.1E-5
8.5E-5
8.43-5
9.53-5
1.3E-4
0.313
0.323
0.309
0.371
0.386
0.478
0.278
0.278
0.277
0.305
0.283
0.281
0.328
0.262
49
49
49
49
49
6.9 (3)
7.0 (3)
7.0 (3)
6.6 (3)
6.0 (3)
49
5.9 (3)
49
6.7 (3)
clevelandfed.org/research/workpaper/index.cfm
Table 6A: Split Sample, Debt Equation, One-Quarter Lag, "Large" IV Sets,
1954:3 - 1967:2
6-a
6-b
6-c
6-d
6-0
6-f
-0.077*
-0.062*
-0.067*
-0.087*
-0.061*
-0.063*
-0.062*
0.025
0.021
0.022
0.032
0.021
0.022
0.021
Table 6B: Split Sample, Debt ' Equation, One-Quarter Lag, "Large" IV Sets,
1967:3 - 1980:2
6-c
6 4
IVs
6-a
6-b
a,
0.202*
-0.217*
0.216*
-0.224*
0.041
0.038
0.035
-0.505*
0.527*
0.061
52
"1
NOBS
J (df)
16.7 (3)
6-0
6-f
6-45
0.246*
0.214*
0.221*
0.036
0.037
0.035
0.036
0.524*
0.538*
0.571*
-0.524*
-0.533*
0.057
0.053
0.054
0.056
0.053
0.054
52
52
52
52
52
52
16.3 (3)
15.4 (3)
13.9 (3)
11.6 (3)
14.8 (3)
13.5
(3)
clevelandfed.org/research/workpaper/index.cfm
T a b l e 6C: S p l i t Sample, Debt E q u a t i o n , Four-Quarter Lag, "Large" IV S e t s ,
1955:2
1968:l
-
IVs
6-a
6-b
6-c
6-d
6-a
6-f
6-8
a,
-0. OSO*
-0.052*
-0.048*
-0.059*
-0.049*
-0.056*
-0.047*
0.014
0.012
0.011
0.017
0.011
0.013
0.012
T a b l e 6D: S p l i t Sample, Debt E q u a t i o n , Four-Quarter Lag, "Large" IV S e t s ,
1968:2
1980:2
-
IVs
a,
"1
NOBS
J(df)
6-a
6-b
6-c
6-d
6-0
6-f
6-8
0.151*
0.192*
0,237*
0.233*
0.259*
0.231*
0.225*
0.068
0.062
0.049
0.054
0.058
0.051
0.047
-0.431*
-0.489*
-0.554*
-0.548*
-0.585*
-0.544*
-0.536*
0.097
0.090
0.072
0.079
0.085
0.075
0.070
49
49
49
49
49
49
49
14.4 (3)
15.7 (3)
16.5 (3)
16.5 (3)
16.2 (3)
16.3 (3)
4.8 (3)
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45
-Appendix A
Here, I derive an expression for the value of equity, following Summers
(1980). The return on the equity of the firm has two components: after-tax
capital gains, (1-rc)VO
dividends, (1-ry)DV.
(O
denotes time differentiation),
and after-tax
The total equals the return required by stockholders, p,
adjusted for the rate of inflation. This implies
(p+pt)Vt = (l-r,)~to
+
(l-r*)DVt
To prevent the solution to (Al) from exploding, I assume
lim V, e
-~[(p+pu)l(l-rCu)ldu
=
0.
Then, the value of the firm's equity at time t can be written as
and
i
max zoEO= e
-60*(r)dr
r(t)dt,
where
rt =
(1 - ryt)DVt/(1
- rct).
(A61
Next, note that revenues equal the sum of wages, nonwage payments to labor,
taxes, interest, dividends, and retained earnings.
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46
- (a+v~[Bt/<(&) 1 )B,)
+DV,
+
RE,
+
(a+vl[Bt/((Kt)
])B,.
The cost of production and nonproduction employment is expressed as
w,+L~H,
+ f,L&
where W,*
+
f,NN,,
(A8)
is the wage rate for production workers inclusive of overtime, fL, is
the nonwage cost of a production worker, and fN, is the cost of a nonproduction
worker. fN, includes salaries and fringe benefits, while fLt includes only fringe
benefits. I express the wage bill, or variable cost of production employment, as
W,+LtH, = W,& [H, +
where H,* is the level of hours at
@
,
+
@I
(H,-H,+
)I ,
which overtime starts, H,-H,*
(A9)
is overtime
hours per production employee, and Wt is the wage rate for production workers
exclusive of overtime.
Gross investment, I,, is financed through debt issue, retained earnings,
or the decrease in the real debt burden due to inflation.
where 15, is the relative price of investment goods.
The firm receives an investment tax credit, ITC,, on each dollar of
investment expenditure at time t and deducts allowable depreciation expenses.
D, is the present discounted value of all depreciation deductions due to one
dollar of investment at time t.
Total revenue is a,y,,
where at is the relative price of manufacturing
output at time t. Total revenue is the sum of wages, nonwage payments to labor,
taxes, interest, dividends, and retained earnings. All investment is financed
through retained earnings, new debt issue, or the decline in the real burden of
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47
debt due to inflation. The term ptBt is the revenue accruing to the firm because
the bonds are assumed to be denominated in nominal terms. Substituting for RE and
solving yields the following expression for the dividend:
Here, inflation has complex effects on investment, as suggested by previous
investigations (Feldstein [I9871 and Chirinko [1987a]).
First, the investment
tax credit and depreciation deduction are based on historical cost. Second,
inflation erodes the real debt burden.
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48
Appendix B
Tax r a t e s favor debt over retained earnings i f
where sl
-
before-tax
cost of debt issued a t time 0 and paid i n period 1.
The c o s t t o stockholders of one dollar of retained earnings a t time 0 i s
the forgone one d o l l a r of dividends, the present value of which is the l e f t s i d e
-
of equation 4.
The c o s t of one d o l l a r of debt issued a t time 0 i s the reduction
i n dividends paid a t time 1.
The present value of t h i s cost i s the r i g h t s i d e
of equation 4 , which u t i l i z e s the definition of 8* and so and takes account of
the reduction i n the r e a l debt burden due t o i n f l a t i o n .
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49
Appendix C
All data are seasonally adjusted, measured at quarterly rates, and pertain
to all manufacturing, except where noted.
Kt is the stock of physical capital (billions of 1967 dollars) at the start
of period t. It is calculated by the perpetual inventory method:
K, =
-q
- 1
+
It,l/IMPDEFt-l.
(C1)
d is a fixed rate of physical deterioration for structures and equipment
in all manufacturing, as estimated by Jorgenson and Stephenson (1967).
It is
investment on new plant and equipment in manufacturing, published by the Bureau
of Economic Analysis (BEA) , and IMPDEF is the investment price deflator for fixed
nonresidential investment expenditures, published by BEA in the Survey of Current
Business (SCB).
The net additions to the capital stock are expressed in 1967
prices. The starting value for K is the net stock of structures and equipment
in manufacturing at the end of 1953, in 1967 prices as published in SCB.
L, is the average number of production workers (in millions) employed in a
given quarter.
It is obtained by averaging the monthly data published by the
Bureau of Labor Statistics in Employment and Earnings (EE).
For consistency
within the Euler equations, L (and N) must be scaled by 0.001.
Nt is the average number of nonproduction employees (in millions)
over the quarter. The monthly number is calculated as the difference between
total employment and production-worker employment for the manufacturing sector.
The quarterly level is the average of the levels for the three months in the
quarter. The source is EE.
qt is the quit rate for employment, which EE publishes on a monthly,
nonseasonally adjusted basis. I seasonally adjust the arithmetic average of the
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50
three-month data in each quarter using an X-11 seasonal adjustment procedure.
H, is the average number of hours per week for production employment. I use
the average of weekly hours over the quarter. H, which includes overtime hours,
is published in EE. For consistency within the Euler equations, H is scaled by
the average number of weeks in a quarter.
H,
- H*, is the number of overtime hours per production employee per week.
This series is available in EE.
As for H, this series is scaled up by the
average number of weeks per quarter.
W, is the average hourly wage rate for production workers, calculated as the
average of the monthly data over the quarter. The monthly data are published in
EE. W, excludes overtime payments.
W*, is the average hourly wage rate for production workers including
overtime.
The quarterly average is calculated as an average of the monthly
averages. The data, published in EE, are available only from 1956 onward, so I
extrapolate back to 1954 by 1) regressing the available data on a constant and
a trend and 2) using the estimated trend coefficient to extrapolate backwards
from the estimated intercept.
Since this series is available only on an
unadjusted basis, the entire series from 1954 onward was seasonally adjusted
using an X-11 procedure.
fL, is the fixed payment per production employee (billions of dollars per
million employees).
Account data.
This is derived from quarterly National Income and Product
I calculate the total fixed cost to the sum of production and
nonproduction employees as the difference between total compensation and the sum
of wages and salaries and employer contributions to social insurance. This total
is then divided by total employment to yield f,.
fN, is the fixed cost per nonproduction employee (billions of dollars per
clevelandfed.org/research/workpaper/index.cfm
51
million employees). This is calculated as fLt plus a salary component.
The
salary component is computed as wages and salaries minus wages paid to production
employees, and is then divided by the average level of nonproduction employment.
The wage bill for production employment is the product of average hourly wages,
the number of production employees, and the average hours per production employee
per quarter.
p is the quarterly real required rate of return.
It is calculated from
data on common stock returns published by Ibbotson and Sinquefeld (1982) and
represents the difference between the quarterly total rate of return on common
stocks and the quarterly rate of change in the Consumer Price Index (CPI).
quarterly total rate of return is
b, where
(1
The
+ kT)27x4 = the ratio between the
end-of-1980 index on total returns on common stocks and the end-of-1953 index on
total returns.
where (1
+
The quarterly rate of change in the CPI is calculated as kp,
kp)27x4 = the ratio between the end-of-1980 CPI and the end-of-1953
CPI. Thus, p is constant from 1954 to 1980.
pt is the rate of change in the CPI for urban workers over period t,
available in SCB.
7,
is the marginal personal dividend income-tax rate.
This series is
calculated by Estrella and Fuhrer (1983) from annual individual income tax
returns. Thus, 7, is available only on an annual basis. I assume that the rate
for each quarter is equal to the rate for the entire year.
rc is the personal capital gains tax rate.
I follow Summers' (1980) and
Bailey's (1969) treatment of the effect of deferral and the lack of constructive
realization at death on the effective tax rate. Bailey concludes that from 1932
to 1969, each of these factors halvedthe effective rate. Because the statutory
tax rate on capital gains was half that on dividends during this period, I use
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52
12.5 percent of the dividend tax rate from Estrella and Fuhrer as
7,
for 1954 to
1969. I follow Summers and cite the estimate of the NBER TAXSIM model that the
1969 capital gains reform made the rate 50 percent higher or 18.75 percent of the
dividend rate.
rp is the corporate profits tax rate. I use the statutory corporate profits
tax rate as published in Pechman (1983) and assume that quarterly rates are equal
to the annual rate.
y, is the output of the manufacturing sector (billions of dollars). I use
the Federal Reserve Board's index of manufacturing production and inflate the
product of y and a so that its average for 1967 equals actual 1967 manufacturing
output, calculated as equal to the 1967 value of shipments plus the change in
manufacturing inventories over the year. Both the shipments and inventory data
are published by BEA in Business Statistics, with each series unadjusted for
seasonal variation. The inventory data are on a book-value basis. I seasonally
adjust y using an X-11 procedure. The production index is published monthly, and
I use the average level of the index over the quarter.
a is the price of manufacturers' goods. I use the Producer Price Index for
manufacturing, published monthly in Business Statistics, and employ the average
index level for the quarter.
Because this index is available only on an
unadjusted basis, I adjust the quarterly data using an X-11 procedure.
B is the price of investment goods. I use the implicit price deflator for
fixed investment for the nonresidential sector. B is based so that the product
of B and I is measured in 1967 dollars.
I is investment in plant and equipment, measured by BEA.
ITC, is the investment tax credit at time t from one dollar of investment
expenditure at time t.
I use the series calculated by Jorgenson and Sullivan
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53
(1981) for the entire corporate sector. It is published on an annual basis, and
I assume the quarterly rates are equal to the annual rate.
D, is the present value at time t of all current and future depreciation
deductions from one dollar of investment at time t. Jorgenson and Sullivan
publish this series on an annual basis. I assume that the quarterly rates equal
the annual rate.
((&) is the book value of capital at time t (billions of dollars).
I use
the series on the book value of "depreciable and amortizable fixed assets,
including construction in progress," published in the Quarterly Financial Report
(QFR) by the Bureau of the Census. The data were supplied by Data Resources Inc.
Below, I discuss how I compensated for several discontinuities within the series.
After this adjustment, I seasonally adjust the data.
B, is the book value of debt (billions of dollars). I use the series on
short-term debt ("original maturity of one year or less"), "installments due in
one year or less on long-term debt," and "long-term debt" (due in more than one
year) published in the QFR.
I adjust for discontinuities in these series and
then seasonally adjust the total. Thus, B, excludes "trade accounts," "deferred
taxes," and other liabilities.
The QFR series on the book values of debt and the capital stock contain two
breaks in continuity. In 1967, newspapers were added to the sample, and DRI did
not continue the series forward.
In 1974, the entire sampling procedure and
questionnaire were changed. A visual examination of the series suggested that
I make a level adjustment for the 1973:IVQ to 1974:IQ break.
this using the overlap data available for those two quarters.
I accomplished
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