Comment

Thomas Mitchell �

Department of Economics, Southern Illinois University Carbondale, Carbondale, IL 62901-4515, USA

Received 9 December 2004; received in revised form 20 December 2004; accepted 20 December 2004

1. Introduction

The preceding article (Sato and Fujii, 2006) is a follow-up to Sato (2004), which was the

first paper to consider the notion of a ‘‘conservation law’’ at the microeconomic level.

Samuelson (1970) was the first to show that conservation laws might apply to an economic

environment when he derived the constancy of the capital-output ratio in a neoclassical von

Neumann economy in which all output is saved (i.e., there is no consumption) thereby

maximizing economic growth. Weitzman (1976) identified the income-to-wealth conserva-

tion law in a neo-classical growth model. Sato (2004) is the first empirical investigation of a

possible conservation law using industry-level data. Sato and Fujii (2004) refines that work by

testing the Sato (2004) conservation law using firm-level data. Since studies using firm-level

data are more likely to turn up a positive result, for obvious reasons related at the very least to

issues of aggregation, that is the primary contribution of the present paper.

2. The Conservation Law

The key equation is their Eq. (5),

r ¼G½xðtÞ; xðtÞ� þ

Pnj¼1p

jx jðtÞR1t exp �r ðs� tÞG½xðtÞ; xðtÞ�f g ds

: (1)

The authors interpret the numerator of the right-hand side fraction as the current value of

profit plus changes in the value of the firm; they interpret the denominator as the present

value of the firm. Thus, Eq. (1) indicates that the right-hand side ratio is equal to the

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discount rate on the left-hand side, presumed to be constant while the firm is attempting to

maximize long-run profit. Not surprisingly, this conservation law—applied at the level of a

firm or industry—is quite similar to Samuelson’s (1970) conservation law. It is also the

microeconomic conservation law the authors wish to subject to empirical tests.

3. The regression

There is certainly more than one approach to test the conservation law. The present

authors look upon the discount rate, r, as being a constant, so that its sample standard

deviation should be close to zero. Therefore, the regression equation the authors fit takes its

dependent variable as the standard deviation of the calculated discount rate, sri. The

regression equation they fit is

sri¼ b1PIi þ b2

L

V

� �i

þb3DIi þ ei: (2)

The statistical method is ordinary least squares.

Before we review the data employed for the variables, we observe that the regression

equation possesses no intercept term. Given that the variable on the left-hand side is a

standard deviation, a right-hand side intercept term would account for any ‘‘permanent’’ or

systematic variance or volatility. In a perfect world (or if economics were a laboratory

science) sriand sri

(sriwithout the ‘‘hat’’ over the subscripted r) would both be zero. Then

we would hope that a regression equation, sri¼ b0 þ b1PIi þ b2ðL=VÞi þ b3DIi þ ei,

would reveal that all of the estimated coefficients— b0, b1, b2 and b3—would be statistically

indistinguishable from zero. That is, any and all changes in the right-hand side variables

would have no effect upon the value of srior ri (or ri).

In reality, however, allowing for a lag would be essential for at least some exogenous

changes; the managers may require some amount of time:

� to perceive a disruption of their long-run-profit maximization plan;

� additional time to react;

� additional time for the managers’ reaction and the resulting restoration of their long-run

plan to become evident in the data again.

The variables in the regression are: ri, PIi, ðL=VÞi, and DIi. The subscript i distinguishes

between firms with firm-level data, and an additional subscript (t) is added when a time

series is added for each variable.

4. The data

4.1. Discount rate, ri, and standard deviation, sri

The authors use a 3-year moving average to compute the value of ri, given in their

Eq. (6):

T. Mitchell / Japan and the World Economy 19 (2007) 133–137134

ri ¼1

3

Xt

j¼t�2

Ri j þ DVi j

Vi j

¼ 1

3

Xt

j¼t�2

profit in period jþ change in market value of firm i from period j� 1

to period j

market value of firm i in period j:

(3)

If a firm has no outstanding debt, then the value of the firm in period t is computed as the

market capitalization of the firm in period t. In practice, however, most firms have debt.

Therefore, the authors calculate the value of firm i in period t as

Vit¼Eit þ Bit¼market value of equity in period tþbook value of debt in period t:

The left-hand side variable, sri, is merely the sample standard deviation of the computed

discount rate in Eq. (3) above.

The authors state in Section 3.2: ‘‘If a mean value of calculated ri is negative, the firm is

excluded because a negative discount rate is hard to reconcile with theory’’. We do not

propose to push the idea of a negative discount rate in equilibrium. However, we should

acknowledge that long-run-profit maximizing plans are disrupted by exogenous shocks.

The short-run consequences of a particular shock may be unpredictable, even extreme. The

question may be quirky, but how are the results different when we include those firms with

a transitory calculated discount rate that is negative?

4.2. A dummy variable, DIi

The variable DIi is a dummy variable to pick up anything that may be unique to a

particular industry. This is probably wise. For example, the production and planning

decisions in different industries may be extremely different. In particular, firms in one

industry may be able to react to exogenous shocks much more quickly than firms in other

industries and this can affect the lag structure embodied in the ‘‘perceive-react-and-

restore’’ process suggested in the bulleted list above. Heavy manufacturing comes to mind

as industries with extremely long planning periods.

As an aside, we call attention to the fact that the authors do not include financial-sector

corporations. Given the lack of a ‘‘manufactured’’ output, these are the kinds of firms

that may have the shortest ‘‘perceive-react-and-restore’’ processes. These are firms that

may be able to react most quickly to exogenous shocks; if so, then these firms may offer us

the best chance of revealing a conservation law in their financial and other public

statements.

4.3. Performance indicator, PIi

The authors use three different performance indicators:

1. The Nikkei Performance Index (NPI) is a composite index with unequal weights for its

components: firm profitability, firm size, firm stability and growth potential.

T. Mitchell / Japan and the World Economy 19 (2007) 133–137 135

2. The firm’s return on assets

return on assetsit ¼Rit

Vit¼ current profit of firm i in period t

value of firm i in period t:

3. Growth of total assets, GRit: the average growth of assets in the first 3 years of the

sample period is calculated; the average growth of assets in the last 3 years of the sample

period is calculated; GRit is the interpolated constant growth rate between the average

growth rates of the first-three and last-three years of the sample period.

4.4. ‘‘Leverage’’ indicator, ðL=VÞi

Finally, the authors include a ratio to account for possible effects due to differing

degrees of ‘‘leverage’’ across firms

L

V

� �i

¼ total of interest-bearing liabilities

value of the firm:

5. Results

Eq. (2) above contains the regression model in symbolic form; a descriptive form is

ri ¼ b1ðperformance indicatorÞi þ b2

total of interest-bearing liabilities

value of the firm

� �i

þ b3ðindustry dummy variableÞi þ ei:

The authors have refined the initial investigation in Sato (2004) by obtaining firm-level

data; we probably stand a much better chance of observing a possible conservation law at

the level of the single firm than we do at the level of an entire industry.

As the authors write, their regression results are tentative and inconclusive. With the

present paper as a starting point, however, there are additional tests and strategies with

which we could attack the problem with the same data.

Economists in several fields have been concerned about issues of ‘‘volatility’’ with such

quantities as money supply measures, interest rates, exchange rates and share prices to

name a few. Volatility is the essential issue here: if there is a conservation law at work, then

in theory and in the absence of shocks, the volatility of the ‘‘conserved’’ variable is zero.

Under non-laboratory conditions, the measured value will vary and it will have some

degree of volatility. To test hypotheses about volatility, there are several approaches one

might take. Depending on the model and the data, ‘‘White’s test’’ or Engle’s ‘‘ARCH test’’

may be the best approach. See White (1980) for the introduction of White’s test; Engle

(1982) initiated the interest in auto-regressive conditional heteroscedasticity (ARCH)

models, but see also Engle (2001).

In summary, the study of possible ‘‘conservation laws’’ at the microeconomic level is

still in its infancy. Much work remains to be done at both the theoretical and the empirical

level. Perhaps we will find nothing; perhaps the optimizing processes of firms and their

T. Mitchell / Japan and the World Economy 19 (2007) 133–137136

managers do not lead to any invariant or ‘‘conserved’’ quantities or economic measures. On

the other hand, who knows now what we may find. Sato and Fujii have pushed us. Now it is

up to us to join them: can we and will we conserve the energy or momentum they have

expended on us and move forward?

Acknowledgement

I have benefited significantly from discussions with Scott Gilbert, but any errors in fact

are my own.

References

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Kingdom inflation. Econometrica 50 (4), 987–1007.

Engle, R.F., 2001. GARCH 101: the use of ARCH/GARCH models in applied econometrics. The Journal of

Economic Perspectives 15 (4), 157–168.

Samuelson, P.A., 1970. Law of conservation of the capital-output ratio. Proceedings of the National Academy of

Sciencesunknown:issue, Applied Mathematical Science 67, 1477–1479.

Sato, R., 2004. Economic conservation law as indices of corporate performance. Japan and the World Economy

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T. Mitchell / Japan and the World Economy 19 (2007) 133–137 137