The Distribution of Seigniorage - Reply

By

Martin Klein and Manfred ,L M. Neumann

I. Introduction

l ' n Klein-Neumann [1990], we presented an accounting framework for the sources and uses of seigniorage and applied it to German

.data for the period 1960-87. We introduced a cash flow measure of seigniorage - fiscal seigniorage - and showed that the seigniorage actually received by the German government according to this mea- sure was significantly lower than the total seigniorage collected by the Bundesbank.

Casper van Ewijk criticizes our results and contrasts them with an alternative concept of seigniorage which is supposed to reflect "the cost . . . to the government if it loses its monetary monopoly". The relevant aspect of his critique is whether his strong negative state- ments about our results are valid. He claims that (0 our accounting framework is inconsistent and (i0 we seriously underestimate fiscal seigniorage by mistakenly subtracting the central bank's revaluation loss.

In what follows, we will demonstrate that Ewijk is wrong on both counts. In particular, we show that (i) our stylized accounting frame- work is consistent (Section II), and (i0 our data on fiscal seigniorage are correct and Ewijk misinterprets the Bundesbank's profit and loss accounts (Section III).

We take the liberty of sticking to our original notation from which Ewijk departs for reasons not known to us.

II. Is the Accounting Framework of Klein-Neumann Inconsistent?

According to Ewijk, our accounting framework is inconsistent. He asserts that we treat revaluation losses on the central bank's net international reserves (V) as "reserved by the central bank" which would lead to a drop in the central bank's net wealth (weB), V = - W cs. His assertion is false. In fact, our accounting system im- plies that, ceteris paribus, the central bank's net wealth is insulated from

Klein/Neumann: Seigniorage 353

revaluation losses. This can be seen from our equation for the central bank's profit (R), 1

R = a A + b B + d D + e f F + N s - V - C. (K-N 2)

The notation is as follows. A, B, D and F denote the levels of credit to government, holdings of government bonds, credit to the private sector and net international reserves, respectively. Lower-case letters denote the respective rates of return. Finally, e denotes the exchange rate, C denotes the central bank's operating costs, and N R denotes all other net revenue. The profit equation (K-N 2) implies that, ceteris paribus, the central bank reduces its profit transfer to the government by the amount of the valuation loss. Obviously, this is the only way for the central bank to protect its net wealth against erosion from valuation losses.

Ewijk misreads our accounting framework because he neglects the residual items N u and N R which function as "catch-all" variables to guarantee consistency between the central bank's flow balance sheet and its profit equation. 2 Generally speaking, an accounting frame- work with two free balancing items cannot possibly be inconsistent.

Why did we not proceed along the lines suggested by Ewijk? The reason for this is that our accounting framework has to be general enough so as to be applicable to actual accounting data of the Deutsche Bundesbank. Neither the assumption V = - d F , which we use in the theoretical part of our paper, nor Ewijk's central bank wealth constraint (E 2) are literally true for the Bundesbank, nor probably for most other real-world central banks. This motivates to write our central bank flow balance identity

_~r= A +/~ + / ) + e ~ ' + N u , (K-N 1)

in which the residual item N u reflects not only the change in the central bank's net wealth but also a host of other items such as, for instance, suspense accounts, whose net balance at the end of the year often exceeds the central bank's net wealth. A similar reasoning ap- plies to the net residual revenue N R . We then take a dual approach with respect to the residual items N u and N R . In the theoretical part, we simply suppress them because they are of no analytical interest for

1 The abbreviation K-N refers to the original equation numbers in our 1990 paper while E refers to the equation numbers in Ewijk's conunent. 2 By the way, our equation (K-N 4) contains a printing error with respect to the net residual N = N R -- N u. The sign of N in this equation should be positive, not negative.

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our cash-oriented seigniorage concept. In the empirical part, on the other hand, we let them arise as residuals from the actual data.

HI. Do Klein-Neumann Underestimate Fiscal Seigniorage?

In Klein-Neumann [1990] we defined fiscal seigniorage (So) by the equation

G - T + bBp - Bp s6 = , (K-N 7)

P

where G denotes primary expenditure, Ttax revenue, Bp government bonds held by the private sector, and p the general price level. This equation shows fiscal seigniorage from the uses side. For empirical estimates it is more convenient to refer to the sources side of fiscal seigniorage, which is derived by combining (K-N 7) with the govern- ment budget constraint

G - T + b B r + a A = B r + JI + R . (K-N 3)

This yields

R +.~ + B - a A - b B s o - (1)

P This represents the actual cash flow from the central bank to the government in a given period. Note that in order to establish (1), we do not even need our equation (K-N 1) which Ewijk mistakenly dis- putes. In the German case, the bulk of fiscal seigniorage is contained in the Bundesbank's profit transfer because direct credit to govern- ment is (with minor exceptions) prohibited. Thus, we can write

R S o .~ - - .

P In our accounting framework, the profit transfer R is given by equa- tion (K-N 2) and could thus be calculated "from scratch" from the central bank's interest income, valuation losses, and operating costs. In practice, however, it is more straightforward to use the true data on profit transfers of the central bank. This is what we do in the case of Germany where the Bundesbank's annual statements on profits and losses are published so that data on profit transfers are easily avail- able) Thus, our data on R represent the actual profit transfer from the Bundesbank to the German government.

3 This is unfortunately not truc for many other cotmtdes.

Klein/Neumann: Seigniorage 355

In order to compile Table 2 in Klein-Neumann [1990] we proceed as follows. From the money supply data we calculate the average annual flow of monetary seigniorage between time t o and tl: 4

s ~ - - - - - d t . t l - - t o p

Similarly we calculate

1 t~ R + A + B - a A - b B

s G - - J P d t t l to to

' ! c = - - C d t t~ -- t o p

for the average annual flows of fiscal seigniorage and operating costs. We then diagnose a gap between measured monetary seigniorage on the one hand and the sum of fiscal seigniorage and operating costs on the other hand. This gap is not an artifice generated by our accounting framework, it is simply a fact of life. During the period from 1960 through 1987, barely 50 percent of the total resources that were gener- ated by issuing base money were received in c a s h by the government and the central bank. This is where valuation losses come into the picture. We show that roughly one half of the gap is explained by valuation losses on the central bank's net international reserves, whose annual average we compute by

v = V dr. t l - to to P

Note that the valuation losses Vare not calculated by us, but reflect the actual losses shown by the Bundesbank in its profit and loss

statement. Ewijk claims that we underestimate fiscal seigniorage because our

profit transfer rule "mistakenly" takes valuation losses into account. This is incorrect. We do not subtract the valuation loss from the profit transfer, it is the B u n d e s b a n k w h i c h r educes i ts p r o f i t t rans f e r to the

G e r m a n g o v e r n m e n t b y the va lua t ion loss. s Ewijk tries to correct for

4 We use integrals for formal consistency with the continuous time setup used in the accounting framework. In the actual data work, the integrals are replaced by sums. 5 The reader is invited to inspect the Bundesbank's Annual Reports. In the appendix of each report it can be seen that the Bank treats valuation losses like operating costs in computing the profit transfer.

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our "mistake" by reclassifying the valuation loss as a component of government revenue. He adds the valuation loss to the profit transfer and claims that, instead of R, the government effectively received the amount R + V. It is easy to see that this measure of seigniorage does not make sense. Undoubtedly, the German government would have been much better off had it received the amounts computed by Ewijk. However, this would have required the exchange rate of the D-mark to remain unchanged since 1960.

References

Ewijk, Casper van, "The Distribution of Seigniorage - A Note on Klein and Neu- mann." Weltwirtschaftliches Archly, Vol. 128, 1992, pp. 158

Klein, Martin, Manfred J. M. Neumaan, "Seigniorage: What Is It and Who Gets It?" Weltwirtschaftliches Archiv, Vol. 126, 1990, pp. 205-221.