Technological Progress, “Money” in the Utility Function, and the “User Cost of Money”

Technological Progress,“Money” in the Utility Function,and the “User Cost of Money”

Susanto Basu and J. Christina Wang

Second World Congress on National AccountsWashington DC, May 2008

User Cost of "Money" 2

Financial output measurement

• Financial services’ share in GDP large & growing• U.S. 2006: Manuf. 12% of GDP

FIRE 21%

• How do we measure output in financial industries?• What is the real (or even nominal) output of a bank

or an insurance company?

• Especially, how to measure the output of services that are implicitly charged for?


Real output measures in banking

• Everyone agrees: objective is to measure bank services, not amount of funds lent or managed• Most difficult: services supplied without explicit fees

• Option 1: count bank services directly• BLS: Index of (transactions) activities counts

(4 types of loan services, 2 depositor services)• Quality adjustment important but difficult

• Option 2: count real balances of loans and deposits • Assumes services in fixed proportion to balances• A lot easier to observe balances than services

• Question for theory:Under what conditions are actual services performed by banks in fixed proportion to real balances?


Long tradition of assuming services ~ balances: Sidrauski (1967)

• Real balances m, like consumption, directly create utility• Services of m (a flow) proportional to real stock• Relative price of m proportional to r – r m

• For currency, r – r m r – (-π) = i

0

,tt tt

V c m

1 1 1

,

, 1

c t t t

mm t t t t t t

V c m

V c m r r r

Maximize:

FOCs:

1 11 1 mt t t t t t t tc a m y r a r m

subject to:


How to justify V(c,m)?

0

ttt

U c

A. Max:

1 1, 1 1 mt t t t tt t tt tc a m y r ac r mm

s.t.:

Feenstra (1986): Problem A is functionally equivalent to

B. Max:

s.t.:

0

,ttt tV mx

,t t t tx c c m where:

1 11 1 mt t t t t tt tx a m y r a r m


Our Q: What’s ? Implications for V(x,m)?

(c,m) = Transaction costs incurred in consuming c if one has real balances m

c > 0, m < 0 is a reduced-form representation of transaction

technology• Will be stable over time if there’s a change in

technology for making transactions?• If not, will V(c+ , m) be stable?• If V becomes unstable, can services associated with

m still be measured as proportional to its balance?


Model microfoundations of

• Derive from financial institutions & their technology: A general-equilibrium Baumol-Tobin model

• Banking sector produces payment services necessary for consumption

• Need 1 unit of bank service (S) to consume 1 unit of C

• Need deposits D ≥ C in bank account

• S produced using primary inputs that bank must pay for

• No explicit fees for services; Bank recoups cost by paying r D < r

• Non-“money” assets = capital, held in mutual funds


Microfoundations of (cont’d)

• Fixed cost of each transfer from mutual fund to bank

• Explicit specifications of technology for both banks and mutual funds

Intuition for optimal solution: Consumers balance cost of making transfers versus interest foregone by holding bank deposits

• Interest foregone = implicit payment for bank services,not a “loss”


What we show: (Limited) good news

• Suppose all the following are constant 1) MF’s technology for making transfers,2) bank’s technology for producing payment services,3) factor prices

• Then there is a stable function … and thus a stable V(X,D) function• Can measure flow of payment services (S) using

real stock of bank deposits Price index of S = “user cost of money”

• Proportional to (r – r D)

• “Nominal” output of bank services is (r – r D)D


What we show: The bad news

• Suppose either mutual fund technology or bank technology changes• Certainly what we think we observe

• Then flow of payment services, S, is not in fixed proportion to real stock of bank deposits, D

Price index of S not equal to “user cost of money”• Implication: D invalid as a measure of real bank

output for computing banking TFP• Valid only if TFP never changes

• “Nominal” output of bank services is still (r – r D)D


What theory implies about measurement (1)

• Only robust way to measure S … is to measure S• Even though it’s so much easier to measure D!

• S must be index of what banks actually do—a la BLS industry output measure• Examples: clear checks, screen loan applications

• A significant advantage of this direct measure of S:Consistent aggregates of services implicitly and explicitly charged for• …and whether or not the service is associated with an

asset balance

• Nominal output and real output index imply a deflator for S


What theory implies (2)

• User-cost insight completely correct, and key for measuring nominal financial output:If consumers are giving up (r – r D)D, they must be getting services worth that much

• In real world with risk, need to compare apples to apples — r and r D must carry the same risk


Borrower services

• Wang-Basu-Fernald (2005) show same conclusion applies to loans: Bank services need not be in fixed proportion to real loan balances

• Especially true with securitization• Banks originate & service loans that they do not hold

on their balance sheets

• Risk adjustment especially important for imputing nominal borrower services• Ensures consistent measurement of borrowing firms’

output


Applied measurement

• Real bank output: indices of transaction counts (BLS)• Each associated with a category of loans or deposits

• Prices: deflator implied by this real output index and nominal output based on risk-adjusted reference rate

• Components in BLS aggregate real output index should be weighted by nominal output shares• Shares: risk-adjusted implicit nominal output + fees

• BLS currently uses employment shares

• Weights matter little, but real output series differ a lot• Figures from joint papers with Robert Inklaar


BLS output components: BLS vs. BIW weights

Weighting real growth of imputed U.S. bank output: BLS vs. risk-adjusted output, 1987-2003

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Risk-adjusted output shares BLS employment shares

Correlation: 0.88

Both series based on BLS activity indices

Mean growth rates: Emp wts: 0.9%; Risk-adj. nom. wts: 0.8%


BLS-IW real output vs. CPI-deflated balances

Real growth of imputed U.S. bank output: BLS activity vs. CPI-deflated balances, 1987-2003

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

BLS activity indices CPI-deflated balances

Correlation: -0.08

Both series weighted using risk-adjusted output

Mean growth rates: BLS—0.8%, Balances—1.4%


Conclusion

• Real output: activities counts always a correct measure• Quality adjustment crucial but difficult

• Should collect activities data on more and finer categories of services, in addition to current BLS series

• Aggregate using nominal-output shares as weights

• Real balances of loans or deposits not generally valid measure of real financial service output, albeit easier• Unless willing to assume, eg, no TFP in financial services

• Current output should not include risk premium• Removal of premium most sensible theoretically

• Implementation practical

Technological Progress, “Money” in the Utility Function, and the “User Cost of Money”

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