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Measuring the nominal value of financial services in the national income accounts.



The treatment of financial services in national income accounting has been a sometimes controversial subject for over thirty years. For economies which specializes in financial services, such as Switzerland and Luxembourg, the treatment of these services has always been critical to an accurate assessment of their domestic product and foreign trade status. With the recent growth in the financial services sector in the United States, this controversy and its resolution are again topical. In the United States, between 1977 and 1985, the commercial banking share of GNP increased by 34.7 percent while its share in national employment increased by 23.3 percent. Furthermore, the internationalization of capital markets has significantly increased the importance of financial services in the U.S. trade accounts.

In this paper we examine both current and proposed treatments of financial services in the national income accounts. Specifically, we briefly review the concepts and methods currently used by the United Nations (U.N.) and the United States (U.S.) Commerce Department to determine the nominal value of financial services, with particular emphasis on their treatment of uncharged-for services. Many financial services are provided without an explicit charge these uncharged-for financial services can be viewed as implicit payments to depositors for their funds or simply as payments-in-kind. The issue in the national accounting literature is whether the net interest earned by financial firms should be treated as the value of these uncharged-for services and whether it should be included in the nominal value of output in the national accounts. (1)

We then evaluate a variety of possible methods for inferring the nominal value of financial services from existing sources of information. These methods are called imputation methods. We base our evaluation of alternative imputation methods on their consistency with a microeconomic theory of financial firms grounded in a user cost of money concept developed by Donovan [1978! and Barnett [1980!, and applied to financial firms by Hancock [1985!. We show that several of these imputation methods are inconsistent with or not closely related to this microeconomic foundation. We then derive a general imputation formula within the financial firm framework and demonstrate how the two leading imputation methods (those of the U.S. Department of Commerce and the U.N. Statistical Office) are specializations of this formula. Our framework thus provides a heretofore absent economic rationalization for the imputation methods commonly used. We then briefly introduce a conceptual framework for the construction of a financial firm output price index this index yields a measure of real output consistent with the accounting approaches. We summarize our points in the concluding section.



The revenues of financial firms consist largely of net interest, the difference between interest received (primarily from loans) and interest paid (primarily on deposit accounts), and explicit service charges. Service charges are typically only a minor part of the total revenue received by banks, and fall short of covering the non-interest cost of operations. By implication, financial firms provide services for which there is not an explicit charge, and the cost of these services must be partly or wholly offset by net interest. Controversy, however, exists over how to value the implicit financial services provided because of long-held differences about the way in which interest is viewed: as a transfer payment between borrowers and lenders or as a payment for services rendered.

Interest as a Transfer Payment

In this view financial firms merely serve as conduits for the interest payment flows between borrowers and lenders (depositors). The intermediary services provided by the financial firm are not considered productive. By implication, interest received by enterprises cannot be regarded as income, nor can the interest paid by households be regarded as an expense. (2) All government interest is taken as a transfer from taxpayers to holders of government securities. Thus the interest receipts of financial enterprises are not counted in their sales to business, households, government, and foreigners. the transfer view of interest derives from the belief that interest is "pure" in the sense that it is a reward to depositors, the "ultimate lenders," for foregone consumption.

Interest as a Payment for Service

Under this view, interest is a payment for financial services which Arndt [1984! characterizes as:

a) Community services: the provision of payments services and the creation of money

b) Depositor services: the holding of deposits, recordkeeping, safekeeping, and the payment of interest as a result of intermediation (securing for depositors a use for their idle cash) and

c) Borrower services: funding projects, providing signals of creditworthiness.

There are two variants of this view. Gross interest receipts may be taken as payment for services, or net interest receipts viewed as the price of services for which there are no explicit charges.



The current treatments of financial services by the U.N. System of National Accounts and the U.S. Commerce Department are founded ont he proposition that interest is part financial service charge and part "pure interest." However, each implements this view in a different way.

U.N. System of National Accounts

Under the U.N. accounting system, the value of financial services is defined as the sum of net interest and property income earned by financial enterprises. (3) However, because it may be contaminated by "pure interest," this sum is removed from value added of the financial sector via the creation of a fictitious bank whose purchases of financial services are of equal value. By implication, the value of final sales of the financial services sector is equal to non-interest earnings (explicit service charges) received from final consumers.

U.S. Commerce Department and U.N.

Statistical Office Proposal

The U.S. Commerce Department defines the aggregate value of financial services as the net interest earnings of the financial sector plus explicit service charges. Since the Commerce Department's method is used in our discussion of the microeconomic foundations of imputation methods below, we will treat it in some detail here.

The Commerce acountants' purpose is to value the uncharged-for services sold by financial business to each consuming sector of the economy. Let the net interest received by the financial business sector be given by [F.sub.r!-[F.sup.p! where the subscripts respectively denote receipts and payments. Let the other sectors be: the nonfinancial business sector, NF, the household sector, C, the government sector G, and the foreign sector, X. Thus the imputed interest receipts to all sectors are

(1) [Mathematical Expressions Omitted!

where the "hat" denotes imputed variables. The term [Mathematical Expression Omitted! denotes the imputed value of the financial services provided within the financial sector. Commerce computes the net interest paid term entered on the income side of the national income accounts (value added) as

(2) ([NF.sub.p! - [NF.sub.r!) + (F.sub.p.! - [F.sub.r!) +

(imputed interest receipts to C, X and G). (4)

FRom equation (1) we have

(3) [Mathematical Expression Omitted!

Substituting the right-hand side of this expression for the parenthetical imputed interest term in equation (2) yields the following expression for the Commerce definition of net interest paid:

(3') [Mathematical Expression Omitted!

Expression (3') is the net interest paid by nonfinancial business net of imputed sales of services to nonfinancial and financial business. Observe that the imputed receipts of the nonfinancial business sector are a further adjustment to the interest receipts of that sector. The values [Mathematical Expression Omitted! and, [Mathematical Expression Omitted! are counterentries on the final demand (product) side of the ledger. (5)

The imputed value of financial services allocated to each sector is found by multiplying [F.sub.r! - [F.sub.p! by the sectoral share of total deposits. Thus, if business (financial and nonfinancial) deposits are a given by a fraction [d.sup.b! of all deposits, the imputed value [Mathemathical Expression Omitted! would be given by [d.sup.b!([F.sub.r! - [F.sub.p!). In other words, the imputed sales of financial services are allocated between intermediate sales and final demand in proportion to business versus household and foreign deposits rather than by actual net interest flows. By using the volume of deposits as the rule for cross-sectoral allocation, the allocation rule does not take into account how credit (loan) services affect the flow of financial services across sectors.

Recognizing that the current U.N. accounting system fails to properly capture the role of financial services in a nation's economy, the U.N. Statistical Office has recently proposed that net interest be allocated to sectors according to the sum of loans and deposits. This is effectively a variation on the U.S. Commerce method, which is designed to recognize borrower services as well as depositor services.

Proposed Alternative Accounting Systems

The current methods of measuring the value of output of the financial sector are compromises between the view that interest is a transfer payment and a payment for services rendered. Not suprisingly, critics of current methods have tended to group according to their views of interest payments. Some of the major protagonists for alternative treatments of financial services are cited below.

Speagle and Silverman [1953!, Ruggles and Ruggles [1982!, Sunga [1967 1984!. For this group of analysts, interest received by banks is the payment for financial services. According to these writers, interest receipts should be allocated across sectors as payments for services. Thus there is no need to impute the value of services or for an attending allocation mechanism. One of the important implications of adopting this approach is that interest payments by government would be included in final sales of the financial sector.

Rymes [1985 1986!. In a world without regulation or market imperfections, the aggregate net interest earnings of financial enterprises (and "pure" net interest) would be zero, and all financial services would be explicitly paid for. Recognizing that in the real world interest is not entirely "pure" interest, Rymes argues, nevertheless, that financial services should be conservatively valued only by explicit service charges. By implication, there should be no imputation of the value of services, and (measured) interest should be treated as a transfer.

Haig [(1973 1986!. Haig argues that the approach of Brown [1949! should be followed wherein financial enterprises are treated the same as government and their services valued using traditional factor cost methods. The Haig approach estimates implicit service charges as the difference between estimated value added and explicit service charges, where estimated value added is the sum of labor costs and capital consumption allowances. In addition, there is a special final demand category called expenditures of financial intermediaries that balances final sales plus intermediate financial sales (measured by explicit service charges received from business) with intermediate purchases plus estimated value added.


A Fundamental Accounting Identity for Banks

We now present a context within which the major approaches to accounting for the value of banking services can be assessed and compared. We begin with a fundamental accounting identity for a simple banking enterprise that takes homogeneous deposits and uses them to make homogeneous loans:

(4) [r.sub.d'[z.sub.d! + w'[y.sup.F! = [r.sub.l![z.sub.l! + [s.sub.d![z.sub.d!,


[r.sub.d! = the deposit interest rate,

[s.sub.d! = the service charge rate,

[z.sub.d! = the level of deposits in monetary units (dollars),

[z.sub.l! = the level of loans in monetary units (dollars),

w = an m-vector of prices of nonfinancial inputs into bank operations,

[y.sub.f! = an m-vector of quantities of nonfinancial inputs into bank operations, and

[r.sub.l! = the interest rate earned on loans.

The vector w includes the remittance of profit to the owners of the banking firm. Thus equation (4) sets payments on the left-hand side equal to receipts on the right-hand side. We decompose the quantity [w'y.sup.F! as

(5) [w'y.sup.F! = [w.sub.v.'v.sup.F! + [w.sub.L.'L.sup.F! + [w.sub.k.k.sup.F!

where for the [! consuming sector

[v.sup.i! = intermediate materials inputs,

[L.sup.i! = labor services, [K.sup.i! = services from equity capital, i = NF, F, C, G, X, and [w.sub.j,J! = v, L, K, are the input prices.

The expression [w.sub.k.K.sup.f! is the profit paid to the owners of the banking enterprise, determined from equation (4) ast eh residual

(6) [Mathematical Expression Omitted!


[Mathematical Expression Omitted!

The Direct Methods of Measuring the

Value of Bank Output

We will call accounting methods that measure all values by transacted money flows direct methods. Equation (4) represents the variant of the direct accounting approach for gross output favored by writers, such as Ruggles and Ruggles [1982! and Sunga [1984!, who advocate the payment for services approach. We will call their approach the gross direct method.

The net direct method subtracts the cost of deposits from both sides of equation (4), so that

(7) [w'y.sup.F! = [r.sub.l.Z.sub.l.! - ([r.sub.d! - [s.sub.d!)[Z.sub.d.!

Identity (7) reflects the view that services

91 not covered by direct charges are covered implicitly in the interest "spread" between loans and deposits. The right-hand side of (7) constitutes the value of sales under the direct approach, and is identically equal to the costs of production on the left-hand side. We use the net direct method to relate the theory of the financial firm to methods of national income accounting.

Value added is defined as the excess of gross sales over purchases from other enterprises. Under the gross direct approach favored by Sunga [1984!, labor compensation is added to both sides of (6), yielding (6)

(8) [Mathematical Expression Omitted!

We now introduce a net direct approach

91 in which the value added for the banking sector is calculated by subtracting intrasectoral net interest and service charge payments from gross output:

(8') [Mathematical Expression Omitted!

Under the gross direct method, the value of sales to business consumers and final consumers--households, government, and foreigners--is calculated as the sum of service charges and interest received by banks from these customers (foreign interest only being net and representing net financial exports). The net direct method subtracts the interest paid on the deposits of intermediate and final consumers from these entries. Under either method, the gross value of bank output is allocated as paid between intermediate and final consumption, and among final consumers. Thus, on this score, both are consistent with the payment for services view of interest.

The Imputation Methods

The imputation methods for computing the value of gross output begin with an alternative to the accounting identity in (7),

(9) [Mathematical Expression Omitted!

The left-hand side of this equation represents gross costs of production for financial services, and the right represents the gross value of output. The term [mathematical Expression Omitted! is the rate at which in-kind (not explicitly charged for) services are provided to depositors, and [Mathematical Expression omitted! is the rate at which in-kind services are provided to borrowers. The expression [Mathematical Expression Omitted! adjusts accounting profit on the left-hand side to reflect the imputations of payments-in-kind on the right-hand side. These flows represent what the bank would have received had it explicitly charged for in-kind depositor and borrower services. The quantity [Mathematical Expression Omitted! would thus be the return on equity received by the owners of banks had they explicitly charged for financial services. (7)

Among advocates of a bank imputation approach there are two schools: factor cost and net interest. In defining gross output the Haig-Brown factor cost school specifies the price of owned capital as

(10) [Mathematical Expression Omitted!

where [pi! is the profit rate and [sigma! is the owned capital depreciation rate. In Haig's view, banks provide only community services, as in Arndt's taxonomy of financial services, and therefore bank services should be valued at factor cost, the traditional method of valuing the output of public enterprises. Consistent with accounting methods for nonprofit, public enterprises, Haig counts only depreciation, [Mathematical Expression Omitted!, in the cost of owned capital and sets [Mathematical Expression Omitted!. Imputed gross output of financial services [Mathematical Expression Omitted! is then determined residually from (9).

Value added is obtained by simply subtracting [pi!K from both sides of (8). This follows from the practice of only counting depreciation for nonprofit public enterprises.

To compute final sales, the factor cost school creates an additional final transactor to purchase the entire direct and imputed value of financial service production. This sector is labeled sales to financial intermediaries.

The net interest school is represented by the U.S. Department of Commerce, which takes the view that the difference between the interest received on loans and paid on deposits must cover the cost of in-kind services. Hence, Commerce sets [Mathematical Expression Omitted!. Thus Commerce's computation of the gross output of banks is equivalent to the net direct method. The United Nations computes gross output in the same way.

In its calculation of value added, the net interest school includes imputed service charges less net interest received less imputed intraindustry consumption of services. Thus, expression (8) is adjusted by adding

[Mathematical Expression Omitted!

to both sides of the equality. The first bracketed term accounts for the difference between the imputed and direct valuation of bank gross output, and the second bracketed term accounts for the difference between paid and imputed intraindustry consumption of financial services. The total adjustment reduces to the bank intraindustry consumption adjustment.

[Mathematical Expression Omitted!,

because, by definition, the net interest imputation is [Mathematical Expression Omitted!. To compute value added for the nonfinancial business sector, the quantity [mathematical Expression Omitted! is added to capital compensation. This adjustment accounts for the difference between the paid and imputed value of financial services consumed by nonfinancial business. The adjustment to aggregate value added (Gross National Income) computed by direct accounting is the sum of the two business sector adjustments:

(11) [Mathematical Expression Omitted!

which is an alternative way of writing the Commerce net interest item (3') in the income accounts using the notation of this section. (8)

To calculate final sales, the net interest school allocates the imputed gross output for the banking sector according to deposits held by intermediate and final consumers of financial services. Underlying this procedure is the arguable assumption that the rate of provision of in-kind services to borrowers is zero, that all services are provided to depositors as the ultimate lenders. Thus [Mathematical Expression Omitted! in equation (9). The United Nations Statistical Office proposes to allocate the same gross output measure according to the sum of deposits and loans, recognizing that services are provided to borrowers as well as depositors by banking enterprises. The underlying assumption is that the rates of implicit services provision on deposits and loans are the same, which is also arguable. It would follow that [Mathematical Expression Omitted! in equation (9). Finally, the current U.N. accounting system takes final sales of banking services as given by explicit service charges only, [Mathematical Expression Omitted!.

Placement of the Central Bank

A simple and clear treatment of central bank institutions would be to place them in the financial sector and net all of their activity from gross output as intermediate consumption. This treatment would be appropriate in the sense that these institutions almost exclusively deal with commercial banks or other financial firms. Sunga [1984! argues that central banks should be considered as part of the government specifically, as a government business enterprise whose purpose is to create money to meet budget shortfalls. Currently, the Canadian central bank is treated as an enterprise and its "trading" profit is included in GNP. Since the majority of the trading profit results from transactions in government securities, at least in the case of Canada, Sunga argues that expenses of the central bank should be considered as government expenditures and these should be offset by revenues from interest receipts and other sources of revenue. In the United States the central bank has considerable independence from the government, and thus it is appropriate to treat it as part of the financial sector.


We have reviewed four methods for measuring the nominal output of banking services: the gross direct method, the net direct method, the factor cost imputation method, and the net interest imputation method. Of the direct valuation techniques, the net direct method has been introduced here as a new and, we will argue, preferable method. In measuring gross output, the net direct method and the Commerce, current U.N. System of National Accounts, and proposed U.N. Statistical Office imputation methods would yield the same result. The factor cost method is lower by the amount of bank profit, and the gross direct methods higher by the amount of interest paid on deposits. In computing value added for banks, the gross method favored by Sunga [1984! and the net direct method are identical, both exceeding the factor cost method by the amount of bank profit. (9) The Sunga gross direct and the net direct value added lie below that estimated by the Commerce method by the amount of interest on borrowed capital less imputed services consumed

by financial business. The U.N. System of National Accounts has relatively high nonfinancial and relatively low financial value added compared with the other methods.

Finally, the four methods generate different allocations of gross output to intermediate and final consuming sectors. The gross direct method takes measured gross interest plus service charges as the flow determining the nominal allocation of gross output acrss the consuming sectors, while the net direct method takes measured net interest plus service charges. In their favor, the direct methods use a straightforward and easily understood technique, allocation as paid, for distributing the sales of financial services across the consuming sectors. (10) The imputation methods use intuitive but arbitrary allocation rules. The greatest weakness of all the imputation methods is their lack of an economic calculus for allocating the value of gross bank output between intermediate and final sales.




Light can be shed on the merits of the various positions on measuring the nominal value of financial services by examining their microeconomic foundations. We use a microeconomic theory of financial firms based on the Donovan [1978! and Barnet [1980! concept of the user cost of money and its application to financial firms by Hancock [1985!. We develop a general formula from the financial firm model for imputing the value of sales of financial services to the consuming sectors of the economy. We will show that all of the imputation methods reviewed above require strong and in some cases counter-intuitive assumptions. We will also recommend the net direct method of accounting for financial services over the gross direct method because of its consistency with the underlying microeconomics of the industry. As in the foregoing sections, our point of reference is the commercial bank, though the general framework applies to the financial operations of any enterprise.

The literature on banking offers no consensus on how one ought to iew the production of financial services. Part of the difficulty in measuring these services derives from the inability to classify the products of a bank as inputs to or outputs of its financial operations. For example, it might be argued that because demand deposits are an input to the production of loans they ought to be classified as bank inputs. It would follow that the payment of deposit interest and any "free" services attached to the deposit account should be treated as payments to an input. The problem with this argument is that it is possible that demand deposit products can in fact be an output of a bank. Individuals acquire demand deposit accounts for the services of recordkeeping and safekeeping, and if there are service charges, minimum balance requirements and the like, there is no reason to believe that the net income earned on these accounts cannot be positive. In such an event there would be no question that services to deposit holders should be treated as outputs.

Under the theory of financial firms banks produce financial products to which bundles of services attach. The quality of the financial services is determined by a bundle of characteristics that describe the product e.g., the quality of demand deposit services is determined by the allowed checks per month and the minimum balance requirements. The quatity of financial services produced can be measured in two ways. A nominal measure of financial service output is obtained by viewing the bundle of financial services as being attached to each dollar in a financial product. Thus, the demand deposit financial services would be measured by the volume of deposits in al of the demand deposit products. A transaction measure of financial service output is obtained by viewing the financial service bundle as attaching to the financial instruments associated with the financial product. Accordingly, the financial services associated with a loan of a particular type would be measured by the quantity of the corresponding loan notes.

The assignment of financial products to input and output categories is an unavoidable aspect of the measurement of bank output. The financial firm approach handles the assignment problem by permitting the user cost of money in each financial product to endogenously assign input-output status to financial products. Furthermore, the financial firm approach includes the financial services attached to a product regardless of its financial input/output status.

The user cost measures the economic return to the financial firm for providing a financial product. The economic return is the difference between the financial firm's opportunity cost of money and the holding revenue in the case of an asset or the holding cost in the case of a liability. The holding revenue (cost) is the difference between receipts and expenditures where expenditures include such items as loan loss reserves, deposit insurance premia, and reserve requirements. Thus, a positive user cost denotes an input and a negative user cost an output. Using the notation of identity (4) for a simple bank, ignoring, for simplicity, capital gains and assuming a continuous time flow, the point-in-time user cost of a deposit (liability) is [u.sub.d! = [([r.sub.d! - [s.sub.d!) - (1 - k)p[, while the point-in-time user cost of a loan (asset), is [u.sub.1! = (p - [r.sub.1!), where k is the reserve requirement and p is the firm's opportunity cost of money. We will show below that the determination of p plays a pivotal role in comparing the various accounting methods.

The user cost focuses on the economic rather than the accounting cost to the financial firm of a unit of money in a financial product. (11) The (negative of the) accounting price of deposits is given by [[alpha!.sub.d! = -[r.sub.d! + [s.sub.d' while the accounting price for loan is [[alpha!.sub.d! = [r.sub.1!. The negative of the user cost and the accounting price (with the above sign conventions) will thus in general be different, possibly even in sign. Hence the nominal interest flows used by accountants represent only indirectly the prices that determine the bank's allocation of its portfolio into the array of financial products it offers. This discrepancy between accounting and economic prices can be viewed as either a price measurement or deflation problem that can be empirically handled in a straightforward manner, or as an accounting imputation problem. Either way, the real output of banks should be the same whether nominal direct sales are deflated by the appropriate direct output price index or nominal imputed sales are deflated by the appropriate imputed, economic price index, as we will call it.

Generalizing from our simple two-product, one-deposit--one-loan bank, we now specify sector specific deposit and loan products. We can characterize the financial firm's optimization problem as

(12) [Mathematical Expression Omitted!


where x' = [[x.sup.i.sub.d!, [x.sup.i.sub.1!!, i = NF,F,C,G,X, is the vector of quantities of money in deposit or loan products in each consuming sector, y is the m-dimensional vector of fixed inputs, T is the production possibility set and p is the financial product price vector, defined as the absolute value of the user cost vector. The maximization problem in (12) is the economic underpinning for a fixed input-output prce index, which is the conventional form of output price indexes. For a given bundle of inputs (labor, physical capital, etc.) the financial firm choose the optimal qunatity of funds that each product should contain. If, according to the sign of its user cost, product i is an
output, then [x.sup.i.sub.k! 0 and if it is an input,
then [x.sup.i.sub.k! 0.




We shall now show how the financial firm model encompasses certain of the current and proposed methods of accounting for financial services. We examine the measure of gross output and then go to the allocation of the imputed values, which forms the heart of the currently used and proposed alternative imputation techniques.

We begin with the observation that if the user costs vary in sign across products, the problem (12) defines an economic variable profit function,

(13) [pie!(p, y) = p![x.sup.*!

where [x.sup.*! is the solution to (5.1) for some input vector y. In this context we identify variable profits as economic portfolio profits, the analog for banking to gross revenue for nonfinancial enterprises. The corresponding accounting measure, accounting portfolio profits, is [alpha!z, where the star superscript has been dropped, all z's being assumed optimal for problem (12). The relationship between economic and accounting portfolio profits is best elucidated by detailing equation (13) as

(14) [Mathematical Expression Omitted!

Accounting portfolio profit can be written as

(15) [Mathematical Expression Ommited!

and we have from equation (14)

(16) [Mathematical Expression Omitted!

The second expression in (16) is the value at the opportunity cost rate p of the difference between aggregate loanable deposit funds [[Summation!.sub.1!(1 - [k.sup.i!)[z.sup.i.sub.d!, i = NF,F,C,G,X and aggregate loans [[Summation!sub.i.z.sup.i.sub.d!,i = NF,F,C,G,X,. While not generally zero, this can be expected to be small because aggregate loanable deposit funds should be close to aggregate loans. (12) The quantity \[alpha!\'x is the gross output of banks as measured by the net direct, U.S. Commerce, and United Nation's methods. Thus, all of these methods will generate a gross output figure close to the economic portfolio profit when all interest payment flows through banks are considered. If the objective of the imputation methods is to reflect economic revenue, then according to (16) they will be in error by a small amount when the opportunity cost term is excluded.

Ruggles and Rugges [1982! and Sunga [1984! propose a view of interest that is entirely consistent with the financial firm approach in the sense that the economic prices of financial products are functions of measured interest rates. However, the gross direct method preferred by them does not naturally arie from the financial firm model. As noted above, there are major differences in the calculation of gross output, value added, and final sales between the gross and net direct accounting methods. Implicit in the gross direct method is the identification of liabilities as inputs and assets as outputs of the financial firms. This input/output assignment may not correspond to the user-cost-based assignment in the financial firm model. The two approaches thus differ in their characterizations of the price of financial services and of bank equilibrium. The gross interest approach assumes that banks adjust their output of financial services until marginal cost rates equal interest and explicit service fee rates. The financial firm model characterizes the equilibrium service output by an equality between financial product marginal cost rates and the negative of the user cost of money in the product, which is closely related to the net interest-plus-service-charges characterization of accounting revenue. The other imputation methods also do not closely relate to the financial firm model. (13)

Recall that the Commerce and both of the United Nation's imputation approaches must allocate their calculated net interest across sectors to separate final and intermediate sales of financial services. We now show that the financial firm approach subsumes these approaches in its calculation of the sectoral allotments.

Economic revenue for the [! consuming sector is

(17) [Mathematical Expression Omitted!

The first term after the second equality in (17) is sectoral net interest, the measure of nominal sectoral financial services under the net direct method. The second term is the value, at the opportunity cost rate, of the difference between sectoral loanable reserves and sectoral loans. In contrast to the economy-wide case, this term can be potentially large for individual sectors because lending activity may be concentrated in different sectors than deposit activity.

The second term arises from the difference between the accounting prices of deposits and loans, respectively, ([r.sup.i.sub.'! - [s.sup.i.sub.d!) and [r.sup.i.sub.l!, and their respective economic prices \[u.sup.i.sub.d!\ and \[u.sup.i.sub.l!\. The difference between accounting and economic prices can be accommodated entirely in the price deflator under net direct accounting for financial services. We deal with this aspect of the deflation problem below.

(2) [Mathematical Expression Omitted!

(3) [Mathematical Expression Omitted!

(4) [Mathematical Expression Omitted!

Conditions (1)-(3) are identical with the above conditions for the allocation by deposits, while (4) sets [rho! as a weighted average between the "break even" rate on loanable deposit funds, [Mathematical Expression Omitted!, and the loan rate [Mathematical Equation! with respective weight (1-k/[1+(1-k)! and 1/[1 + (1-k)!. Again, although (1)-(3) are important, (4) is the crucial assumption.

To summarize, we have used the economic theory of financial firms to derive a general sectoral bank imputation formula that subsumes the U.S. Commerce and U.N. Statistical Office imputation methods. These methods are shown to be special cases of the general imputation formula, and the distinguishing feature of each case is the assumed value of [rho!, the bank's opportunity cost of money. The assumed value of [rho! has potentially major implications for the sectoral distribution of imputed financial service sales when the distribution of deposits between intermediate and final consumption sectors is markedly different from the distribution of loans. The implicit choices made by U.S. Commerce and U.N. Statistical Office are reasonable but still arbitrary. Further light might be shed on [rho! by viewing it as a shadow price and determining it econometrically using an assumed form for the bank's technology T. (16)




The output price index is defined conventionally as a ratio of maximal revenues for the reference and comparison price vectors given fixed technology and inputs as in Fisher and Shell [1972! and Archibald [1977!. The economic portfolio profit function is the banking analog to the revenue function, hence following Fixler [1988! the economic output price index for a bank is (17)

(18) [Mathematical Expression Omitted!

It is possible to develop from this conceptual framework an index formula for a "Fisher Ideal" version of (7.1) that depends only on observed prices and quantities.

[Mathematical Expression Omitted!

Specifically, if [Mathematical Expression! is a translog function, then by applying the methods of Caves, Christensen, and Diewert (1982), we have

(18') [Mathematical Expression Omitted!

where [w.sup.i.sub.k! denotes the share of variable profit of the kth financial product (k=d, l) in the ith sector in some period that is,

[Mathematical Expression Omitted!


From results in Reece and zieschang [1987!, the deflator for bank portfolio profit in accounting prices is simply

The term [Mathematical Expression Omitted! can also be interpreted as an imputed adjustment to (net direct) sectoral accounting revenue such an adjustment enables us to construct sectoral economic revenue in the financial firm model. Accordingly, an accurate evaluation of this term is the goal of any sectoral imputation.

In principle, data for all of the variables in (17) could be obtained through bank surveys, with the exception of [rho!, the opportunity cost of bank funds. If we view [rho! as a parameter in the economic shadow price vector for financial products, p, we could determine it econometrically using an assumed form for the technology T. It remains to be seen whether this technique holds promise in light of the practical need to produce timely national accounts statistics. Meanwhile, it turns out that other methods for determining the value of economic revenue are effectively in use at U.S. Commerce or have been proposed by the U.N. Statistical Office.

We first evaluate the U.S. Commerce Department's methodology by stating conditions under which sectoral economic revenue is proportional to sectoral deposits. These conditions are

(1) [Mathematical Expression Omitted!

(2) [Mathematical Expression Omitted!

(3) [Mathematical Expression Omitted!

(4) [Mathematical Expression Omitted!

where the bar indicates a fixed value. According to the first three conditions, an allocation by deposits requires that reserve requirements, deposit rates, and loan rates be the same across sectors. While arguable, these conditions may be "close enough" to being empirically satisfied in certain cases. (15) The most important condition is (4), which determines the opportunity cost rate [rho! as the economy-wide loan rate [Mathematical Expression Omitted!, eliminating sectoral loans [Z.sup.i.sub.l! from expression (17).

The current U.N. System of National Accounts is rather schizophrenic in first calculating the value of net interest for gross output, but then lumping the entire amount into intermediate consumption of the banking sector so that none of it escapes to final sales. The U.N. Statistical Office proposal is designed to rationalize this state of affairs by allocating the aggregate imputed value to consuming sectors according to the sum of sectoral deposits and loans. We will thus deal only with the U.N. Statistical Office's proposal. From equation (17), sectoral economic revenue will be proportional to the sum of sectoral deposits and loans if and only if the sectoral deposit user cost equals the sectoral loan user and and both do not vary across sectors. We thus have [Mathematical Expression Omitted! so that by our definition of asset and liability user costs [Mathematical Expression Omitted!. Our sufficient conditions for the consistency of the U.N. Statistical Office model with the financial firm model are thus

(1) [Mathematical Expression Omitted!

(19) [Mathematical Expression Omitted!

where [Mathematical Expression! is the ratio of accounting to economic portfolio profit in period t. (For a detailed derivation of the indexes in (18) and (19) see Fixler [1988[.)

If we are speaking of the banking industry and i indexes the consuming sectors of the economy, the sectoral economic price indexes will deflate the sectoral economic revenue developed in the text as

(20) [Mathematical Expression Omitted!

where [Mathematical Expression Omitted!

By approximate consistency in aggregation of the Tornqvist index, a Tornqvist aggregate of these sectoral indexes will be close to P when price and qualities are not too different between the compared situations. If fixed weight Laspeyres or Paasche approximations were used instead of the Tornqvist formula, the sectoral indexes would exactly aggregate to gross output under the same formula used for the sectors because these fixed weight formulate are exactly consistent in aggregation. (18)

The price index (19) would deflate the accounting gross output computed by the net direct method as given in equation (7). Similar versions of (19) (conditional sub-indexes) applying to sectoral sales of financial services (computed as net interest plus service charges) to business, households, government, and foreigners would have to be constructed. The price index (18) would deflate the general imputed nominal gross bank output given in equation (16). Sectoral versions of index (18) would apply to sectoral imputed nominal sales given by equation (17). The economic index (18) would apply approximately to the nominal output imputed by the U.S. Commerce and U.N. Statistical Office methods, provided, among other things, that prices p are constructed with the value of [rho! assumed by the imputation. (19) Moreover, under the assumptions required for these imputations the single gross output price index (18) applies to every sector, eliminating the need for sector specific price indexes.


We have revisited the controversy over methods of accounting for the nominal value of financial services in national income and product accounts and the underlying debate over whether interest should be treated as a transfer payment or as payment for services. We believe that our conceptual approach provides for an economically meaningful valuation for an services. Based on a theory of financial firms, we find ourselves concurring in principle with the interest as payment for services school, though we advocate a net rather than gross interest approach. Moreover, we show that the financial firm approach to output valuation also subsumes the imputation approaches currently used. The financial firm approach not only provides the proper characterization of the imputed value for financial services but also provides the proper deflator for that imputation. We show that the economic foundations of the accounting methods in use are predicted on assumptions about the opportunity cost of funds that deserve further examination.

Our characterization of the value of financial services could be included in the national income accounts via net direct accounting without resorting to the currently available methods of imputation. Adoption of the net direct method would relegate to deflation the problem of measuring [rho! and coping with sectoral variation in interest rates and reserve requirements. These problems would be added to the usual laundry list of problems in price measurement, including the impact of regulation, market imperfections, and quality variation on the real level of financial services provided. The financial firm approach to interpreting either the direct or imputation approaches to accounting revenue removes the problem of determining and deciding what to do with pure interest. The user cost approach advocated here characterizes the gross output of banks in a way that closely resembles the calculation used by the Department of Commerce or that proposed by the U.N. Statistical Office. Thus, our approach would not require extensive rearrangement of the proposed U.N. System of National Accounts or the system used by the U.S. Department of Commerce. In fact, the financial firm approach can generate the deflators for the imputed values derived by either of these methods.

Our main comments on current U.S. and U.N. practice are that (1) net direct accounting should be considered as a straighforward alternative to the imputation of values, and (2) if the decision is made in favor of imputation, the particular assumptions underlying the imputed value of financial services and its allocation to consuming sectors of the economy by sectoral deposits or deposits and loans should be empirically evaluated. The way these matters are addressed has direct implications for construction of the price index that will be needed to obtain measures of real financial output, and the degree of coordination required between national income accountants and price statisticians.

(*1) U.S. Department of Labor, Bureau of Labor Statistics. The views expressed herein are those of the authors and do not reflect the Bureau of Labor Statistics or Department of Labor policy or the views of other staff members of those agencies. We would like to thank two anonymous referees for their valuable comments on an earlier version of the paper. This paper is substantially revised from a version presented at the Second Annual Meetings on Problems in the Compilation of Input Output Tables, in Baden, Austria, March 1988.

(1.) In this paper the discussion is limited to financial services involving payments to or from domestic or foreign financial business establishments. Financial services involving direct payments by the final consumption transactors, households, government, and foreigners, either among themselves or with nonfinancial domestic or foreign business are excluded. Our analytical approach can be extended to cover these excluded flows as well, particularly interindustry and final consumption transactions involving the secondary financial service production of nonfinancial business, but we felt the additional detail might obfuscate the main points.

(2.) Under standard national income accounting procedures interest paid by a firm which employs physical capital is viewed as a distribution of surplus to the holders of the firm's debt. To avoid double counting, the interest received by lenders must be excluded from value added. Interest on consumer debt (except mortgage debt) is treated as transfer (not a distribution of surplus) because the household sector is not a producing sector, except for home ownership.

(3.) Property income is defined as the income earned on all deposits from all sources.

(4.) The interest received by business includes that received from foreigners and the interest paid by business includes that paid to foreigners.

(5.) The imputation can also be justified by the fact that the term [F.sub.r! - [F.sub.p! is negative the financial sector receives more interest than it pays out. Since the imputation is given by [F.sub.r! - [F.sub.p'! the negative entry is offset by the positive imputation. Consequently, the quantitative impact of the imputation is to increase the value added of the financial sector.

(6.) Under the gross direct approach advocated by Ruggles and Ruggles [1982!, labor compensation and gross interest paid to households and government would be added to both sides of (6), as

[Mathematical Expression Omitted!

The quantity [Mathematical Expression Omitted! is Ruggles and Ruggles' [1982, 15! "interest income of persons." Interest received from the financial sector by households and government are included in labor compensation or as separate "appropriation account" items in value added. The Sunga approach creates an additional production sector for households and government, so that their interest receipts are not mixed with those of banks.

(7.) The income-side adjustment for the imputation of bank services sold to final consumers has been the source of some discussion among national income accountants. The issue is whether payments for the owned capital input and payments to the borrowed capital input should be treated interchangeably as entries in bank value added. See for example Rymes [1986!. Owned capital is not interchangeable with borrowed capital because the two are contractually distinct. The imputation for bank services correctly preserves this distinction.

(8.) The notation we introduce here relates in the context of this paper (see note 1) to our discussion above of the U.S. Commerce imputation method as follows:

[Mathematical Expression Omitted!

(9.) As mentioned above, the gross direct method favored by Ruggles and Ruggles [1982! differs from the other direct methods by the addition of interest paid to households and government. Sunga [1984! prefers to treat the interest earned by households and government as payment for nonbusiness production of financial services. The final sales entries of this production sector would be zero, since all services are sold as intermediate input to the financial business sector. Its value added would equal interest earnings, since no intermediate purchases would be made from either the business or the new nonbusiness production sectors. This approach generates the same aggregate value added as the Ruggles and Ruggles [1982! approach, but has the advantage that the interest earnings of households and government are not assigned to banks, which is consistent with the way banking establishments themselves would view deposit interest, as a cost and not a revenue. Under the net direct approach, household and government deposit interest would be an offset to bank final sales, netted against the loan interest and other property income banks earn from those sectors.

(10.) The flow of services treatment of owner occupied housing used by the U.S. Commerce Department in the national accounts and the U.S. Labor Department in the Consumer Price Index results in a household real estate production sector. Because mortgage interest would be an intermediate purchase of financial services for this industry in the U.S. accounts, it would not be included in the interest paid by households in computing the final sales of financial business under the direct approaches.

(11.) The economic input/output status of a financial product is distinct from its asset/liability or accounting input/output status, which is determined by the attending property right.

(12.) Banks have other liabilities besides deposits (loans payable, [z.sup.F.sub.1!, and stockholders' equity) and thus other sources of funds with which to make loans. However, deposits are the dominant liability category.

(13.) The Haig method would not generate gross outputs close to aggregate economic portfolio profit. The method proposed by Rymes would require

[Mathematical Expression Omitted!

implying that

[Mathematical Expression Omitted!

Rymes argues that net interest, the first term, is a net transfer payment and should not be considered in the production accounts, but within the financial firm model this equation implies potentially strange values of [rho!, particularly if the second term is positive. We will not deal further with the Ruggles/Ruggles/Sunga gross direct, the Haig, or the Rymes proposals in this section.

(14.) If we permit the opportunity cost of capital [rho! to vary across sectors, it is only necessary that [rho.sup.i! be equal to the sectoral loan rate [r.sup.i.sub.1!, and that the "spread" between the effective interest rate on deposit funds loaned (1 - [k.sup.i!)[r.sup.i.sub.1! and the sectoral deposit rate [r.sup.i.sub.d! be invariant across sectors. Given the differences in risk and the levels of in-kind services provided that are likely to be present across sectors, this is only a slight relaxation of conditions (1)-(4).

(15.) Conditions (1)-(3) might be satisfied to some extent by first dividing the banking industry into specialized sub-strata such as commercial banks, savings banks, credit unions, and so on, in the hope that the within-stratum variance in the [k.sup.i!, [r.sup.1.sub.d!, and [r.sup.i.sub.1! across sectors would be lower than the between-stratum variance. The allocation of aggregate net interest would then be done according to the sectoral deposits for each banking establishment stratum. This is in fact the way the allocation is done by the U.S. Commerce Department (response to query by the authors, Bureau of Economic Analysis, 1988). However, we are not aware of any empirical evidence that a stratification of this type results in strata that have lower sectoral dispersion in these variables than the aggregate banking sector. We thus reserve judgment as to whether Commerce procedures effectively result in the satisfaction of (1)-(3).

(16.) See Fare and Zieschang [1988! for methods of obtaining shadow prices using production duality theory.

(17.) The standard theory of output price indexes assumes that a firm maximizes a restricted revenue function. In the case of banks a restricted profit function is used instead in order to allow financial products, especially deposit-based products, to be classified at a point in time as financial inputs or outputs according to the sign of the product's user cost. For the most part, the properties of the index are the same as those of an index based on a restricted revenue function. A detailed description of the properties of the bank output price index is provided in Fixler [1988!.

(18.) See Diewert [1978! for results on exact and approximate consistency in aggregation.

(19.) The index would apply only approximately because the numerator of the right-hand side of (16) would not be equal to aggregate net interest plus service charges unless loanable reserves were equal to loans or the opportunity cost [rho! were zero. In the latter case, there would be no difference between the gross output or sectoral sales entries for the net direct or economic imputation accounting approaches.
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Author:Fixler, Dennis; Zieschang, Kimberly D.
Publication:Economic Inquiry
Date:Jan 1, 1991
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