DBJ Discussion Paper Series, No.1306

On the Function of Gold Standard in Idealism and in Reality

Masayuki Otaki(Institute of Social Science, University of Tokyo)

January

2014

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors in orderto protect the tentative characters of these papers. Any opinions, findings, conclusions or
recommendations expressed in these papers are those of the authors and do not reflect the viewsof the Institute.

On the Function of Gold Standard in Idealism and in Reality
Masayuki Otaki
Institute of Social Sciences, University of Tokyo
ohtaki@iss.u-tokyo.ac.jp
7-3-1 Hongo Bunkyo
Tokyo 113-0033, Japan
Abstract
The gold standard system did not function as was expected between the mid-1920s andthe early 1930s. This study explores why the system brings about such devastatingconsequence as the deep worldwide depression. Two main reasons are identified asfollows.
First, the income effect caused by product differentiation, which is entirely excluded in
the purchasing power parity theory, plays a key role. A depression in overseas
territories cannot be canceled out simply by the adjustment of international commodity
prices.
Second, people are confident of the intrinsic value of gold in the sense that people
rationally expect that gold is always convertible to commodities at some fixed ratio. Thisimplies that gold or fiducial money is non-neutral and that the outflow of gold
substantially contracts financial conditions, and thus, economic activities.
These important factors are completely neglected in the traditional ``specie flow’’
theory, which originated from Hume (1752-b)

1. Introduction
The gold standard was believed to be an ideal cohesive international financial system
until the early 1930s. The following adjustment process, which is called the specie flow,
works at least in the long run, and affiliated countries are isolated, and thus, protectedfrom international diffusion of business cycle.
The ``specie flow’’ is a theory which combines the quantity theory of money with thepurchasing power parity of money. That is, domestic price levels are assumed toincrease proportionately with the quantity of fiducial currency. In other words, the totalpurchasing power of gold is kept constant. Simultaneously, by arbitrage, the ratio of acountry’s domestic price level to a foreign country’s price level is equal to the nominal
exchange rate, which is fixed by the parities of both fiducial currencies.
Consequently, if the home country is a small country in the sense that it cannot affectthe economic activities of the foreign country, from the purchasing power parity theory,
domestic price level is fixed by the foreign country’s price level. By interpreting thequantity theory of money conversely, this implies that permissible amounts of gold or
fiducial currency are also endogenously fixed.1
Once the hoarding of gold exceeds such amounts, the domestic price level becomes
relatively high to that of the foreign country, and thus, the home country temporarily
experiences deficits in its balance of payments. This implies that a part of gold
stockpiles flows overseas, and thus, the excess gold or fiducial currency are entirely
dissolved.
In the opposite case, when business within the foreign country turns up and its goods
become expensive, the home country experiences surpluses in the balance of payments
and corresponding amounts of gold flow in. Nevertheless, domestic prices also become
expensive by such gold inflows. Consequently, the foreign business upturn is entirely
absorbed by inflation in the home country, and there is no substantial change in outputs.
This is the employment isolation mechanism assumed in the specie flow theory. Such an
idealistic function was advanced by advocates of the gold standard during the 1920s.
Hume (1752-b) is the pioneer of the specie flow theory. He asserts, ``Suppose
four-fifths of all the money in GREAT BRITAIN to be annihilated, and the nation
reduces to the same condition, with regard to specie, as in the reign of the HARRYS andEDWARDS, what would be the consequence? Must not the price of all labour andcommodities sink in proportion, and everything be sold as cheap as they were in thoseages? What nation could then dispute with us in any foreign market, or pretend tonavigate or to sell manufactures at the same price, which to us would afford sufficientprofit? In how little time, therefore, must bring back the money which we had lost, andraise us to the level of all the neighboring nations? Where, after we have arrived, we
immediately lose the advantage of the cheapness of labour and commodities; and thefarther flowing in of money is stopped by our fullness and repletion. ’’
11However, around the time of the Great Depression in the 1930s, the inherent cruelty of
the gold standard was revealed. The synchronization of business cycle under the gold
standard all over the world became prominent. Every advanced country fell into a
serious slump that originated from the United States. By the middle of the 1930s, mostadvanced countries had abandoned the gold standard and moved to a flexible exchange
rate regime.
This study analyzes why the actual workings of the gold standard were so different to
its hypothetical prospect. There are two points of departure between the ideal andactual. First, goods produced by various countries are differentiated, and perfectcompetition, which the specie flow theory presumes, is never upheld. In such a case, theincome effect within reciprocal demand functions cannot be igonored. Thus, thepurchasing power parity is violated.
Second, and more important is whether individuals are confident of the value of gold.
The specie flow theory assumes that the value of gold decreases proportionately with its
quantity. This implies that people disbelieve in the intrinsic value of gold, which isdefined by the exchange ratio to goods (i.e., the inverse of the price level), and the value
varies with the existing quantity within the country.
However, under the regime of the gold standard, people were confident of the value ofgold. That is, people are confident that gold could be converted to goods at the same rate
at that time in the future and independent of the existing quantity2.
This fact suggests that there is an internal inconsistency in the specie flow theory.
That is, the specie flow theory assumes that although the value of gold is disbelieved
within the domestic economy, there is confidence internationally and this serves as areliable store of value. It is natural to assume that people’s confidence of or disbelief inthe value of gold should not depend on where gold is transacted.3
Keynes (1924) was quite anxious about the collapse of confidence in gold owing to its
imbalanced distribution. According to Keynes, ``I hold that gold flows to America
because America offers in return for it a greater value in commodities than the gold isworth to the rest of the world. As none know better than Sir Henry Strakosch, gold isfreely offered for sale in London every week; America is open to buy unlimited
quantities of it at an almost fixed price in terms of goods;……It is not true, therefore,that she ``has secured a free option to acquire goods, services, and securities inexchange for the gold whenever it happens to suit her’ , if it means `getting as much as
goods for the gold as she originally gave for it’.’’Mundell (1997) argues that people are more confident about gold than the US dollar,
which is the present key currency. He is also anxious about the inflation caused by thedisbelief in the worldwide glut of dollars. Hence, he recommends that gold should play
more important role as a foreign reserve to discipline monetary policy, especially in the
United States.
3 Although Hume (1752-a) admits that money stimulates economic activities at least in2

2

To summarize, in reality, the gold standard rests on two economic conditions: (i) the
dominance of the income effect relative to the substitution effect caused by a change inthe real exchange rate, and (ii) absolute confidence in the value of gold.
The second makes the real exchange rate stable, because the relative prices of goods
remain in some narrow ranges and each nominal exchange rate is fixed by parities.
Thus, adjustment by price levels is relatively difficult when the balance of payments isin disequilibrium.
The facts (i) and (ii), imply that the imbalance in the balance of payments is adjusted
mainly by the flow of gold under some stable price level, once a country experiences achange of business environment. This also implies that, in reality, serious international
diffusion of business cycles is unavoidable under the gold standard, because an
imbalance in the balance of payments immediately links to a change in the purchasing
power of gold within a country. Thus, in contrast to the idealism, the gold standard
system is actually an acute transmitter of the international business cycle. This
assertion is endorsed by world economic history between the 1920s-1930s.
This paper is organized as follows. In Section 2, we formulate the ``specie flow’’ modeland ascertain the isolation effect from foreign business cycles. Section 3 deals with themodel of the gold standard in reality based on Otaki (2007, 2012). In addition, we showthat deepened confidence in gold overseas, which brings about deflation, diffuses to thehome country, and mitigates the depressive effects of the outflow of gold. In other words,
in contrast to the historical conjecture, the imported deflation adjoining the outflow ofgold contributes to eliminating the depressive effect of monetary contraction, because itheightens the purchasing power of gold. Section 4 is concluding remarks.
2. The gold standard in idealism: Disbelief in gold
2.1 A model of the specie flow theory and the isolation effectAs depicted in the Introduction, the specie flow theory can be regarded as a
combination of the quantity theory of money and the purchasing power parity theory of
the short run, he asserts ``And no other satisfactory reason can be given, why all prices
have not risen to a much more commodities exorbitant height, except that which isderived from a change of customs and manners. Besides that more commodities areproduced by additional industry, the same commodities some more to market, after men
depart from their ancient simplicity of manners. And though this increase has not beenequal to that of money, it has, however been considerable, and has preserved the
proportion between coin and commodities nearer the ancient standard.’’ That is, Humewas skeptical about the role of money in the real economy in the long run. However, we
regard the stable proportion between money and commodities acutely as indicating thatpeople are confident about money (gold), and suggesting that money is non-neutral evenin the long run.
3

nominal exchange rates. We capture these characteristics in a two period
overlapping-generations model in a production economy with an infinite time horizon.
We assume that only one good exists in the world and that the home country is too
small to be able to affect economic conditions in the rest of the world. Perfectcompetition prevails in the good market. That is, the home country behaves as a pricetaker in the integrated good market.
We assume that the utility function of each individual U is identical to and additively
separable between the lifetime consumption stream and the labor supply. That is,U  u  c1t , c2t 1    t   ,(1)where cit i 1 is the consumption level of an individual who is born at the beginning of
period t and located at the i-th stage of life;  denotes the disutility of labor; and  t is adefinition function, which takes the value unity when the individual is employed andzero when he is unemployed. We also assume that u   is a well-behaved concave andlinear homogenous function. Finally, let us assume that labor productivity is unity.
The lifetime budget constraint is

pt c1t  pt 1c2t 1  wt   t ,(2)

where  pt , pt 1  is the price vector of the good; and wt and  t denote the nominal wage
and the nominal profits, respectively.
An elementary calculus leads us to the following indirect utility function h  concerning lifetime consumption. That is,h  pt , pt 1 , wt  

wt   t,  pt , pt 1 

(3)

where    is a linear homogenous function.
Based on Equation (3), the nominal reservation wage can be calculated by thefollowing procedure. The nominal reservation wage is the wage at which an individual
is indifferent to whether to work or not, and thus,

4

h

 p 
   wt     pt , pt 1   wt    pt  1, t 1 
  pt , pt 1  pt 

t(4)

holds.
As long as private firms are sustainable, they must be able to earn non-negative profits.
Accordingly, the following inequality must hold.

 pt 1 0, pt 

 t   pt  wt  Lt  0  1    1,(5)

where Lt is the employment level. Since prices are unchanged in equilibrium where thespecie flow ceases, the inflation rate becomes unity, and thus, the non-negative profit
condition (5) is transformed into

1    1,1  0 .

(6)Whenever  is sufficiently small, Inequality (6) is satisfied. We must note that as longas Equation (6) is upheld as strict inequality, all firms are incentivized to expand theirproduction as much as possible, and hence the economy attains full-employment
equilibrium.
Since we have finished describing the economic decisions of individuals and firms andequilibrium condition of the labor market, we turn to equilibrium conditions of the goodmarket. Ahead of the analysis, we make the following assumption of the value of gold or
fiducial money. That is,
Assumption 1

People disbelieve in the intrinsic value of money in the sense that the value decreases
proportionately with its quantity. That is,

M t    pt

(7)

holds. M t is the stock of fiducial money during period t , and  is some positive
constant, which is determined endogenously.
Since the utility function u   is linear homogenous, the aggregate consumptionfunction of young individuals Ct becomes5p 
Ct  c  t 1   yt  c 1  yt , pt 

(8)

where yt is the real GDP in terms of the current goods.
Then, we obtain the following equilibrium condition for the goods market. That is,y f  c 1  y f 

M t 1  M t M t 1 


,
pt
pt 
 pt

(9)

where y is GDP in full employment. The second term of the right-hand side off

Equation (9)Third term

M t 1denotes the aggregate consumption demand of old individuals, thept

M t M t 1
corresponds to the surplus of the balance of payment.
pt
pt

Rearranging the terms and substituting Equation (7) into Equation (9),we obtain

yf 



1  c 1.

(10)

If  is determined to satisfy Equation (10), the macroeconomic equilibrium is a rational
expectation equilibrium (REE) under the expectation (7). 4
Thus, it is clear that the imbalance in the balance of payment never affects thedomestic economy and unemployment prevails as long as  is sufficiently small. That is,
we obtain the following theorem.
Theorem 1

A disturbance of business overseas never diffuses to the home country under theidealistic gold standard.
2.2 The specie flow
In conjunction with this theorem, we consider how the imbalance in the balance of
payments is adjusted: the mechanism of specie flow. First, by measuring the unit ofgood properly, we can set the nominal exchange rate at unity. Second, since purchasing
power parity is assumed to be upheld, we obtain the following equation.

The procedure for determining REE is essentially the same with as that of Lucas(1972).
46

p*  pt .

(11)

When business turns up overseas and p rises, ceteris paribus, goods are exported*

from the home country because the home good is cheaper relative to the good overseas.
Thus, gold or fiducial money is imported to the home country. As such, the domestic
price rises because people are in disbelief about the value of money as expressed in
Equation (7).
The total imported amounts of gold are calculated by differentiating Equations (7) and(11). That is,

dp* dp dM t


.
p*
p
Mt
Thus, the total increase rate of money
overseas

(12)

dM t
is equal to the temporary inflation rate
Mt

dp*
around the vicinity of the equilibrium.
p*

3. Gold standard in reality: Confidence in gold
3.1 Confidence in the intrinsic value of gold
Whenever the intrinsic value of gold is in disbelief and Equation (7) holds, the gold
standard functions as a cohesive international financial settlement system. Nonetheless,there is an internal inconsistency within the specie flow theory. That is, although there
is disbelief in gold domestically, the theory also assumes that all affiliate countries are

confident of that intrinsic value internationally.
In other words, people in every affiliate country, that experiences a surpluses in its
balance of payments, are ready to receive gold, despite the fact that the inflows of gold
never benefits that country’s economy and only serves to cause inflation. It is natural toassume that gold should be either in confidence or disbelief, independently of where it isexchanged.
Hence, we hereafter assume that every individual is confident of the intrinsic value ofgold independent of where it is exchanged. That is, instead of Assumption 1, we
presume that
Assumption 2

Every individual is confident of the intrinsic value of gold and rationally expects that7

gold is exchanged for goods independently of its quantity. That is,

dpt
0
dM t

(13)

holds.
3.2 The gold standard in reality: Business cycles diffuse internationally
As touched on the Introduction, it is natural to regard goods that are tradedinternationally as being differentiated. This implies that the income effect to tradable
goods cannot be neglected, and we shall reformat the model along this line.
Let us assume that there are two kinds of goods; a and b. The home country specializes
in the production of good a and the rest of the world produces good b. The consumption
bundle in the utility function (1) cit i 1 becomescit i 1   ait i 1   bit i 1 
1 

,0    1 ,(14)

where ait i 1 and bit i 1 are the consumption levels of good a and b by those who are bornin period t during the i-th stage of their lives, respectively.
Since u   is linear homogenous, we obtain the following indirect utility function h :
1

h1 

where



wt   ta 1   pt   ptb 



1 

,  pta1   ptb 



,

(15)

 p , p  are the prices of good a and b during period t  j , respectively. In
a
t j

b
t j

addition, we take the value of the nominal exchange rate unity without loss of generality.
Because we have assumed that people have confidence in the intrinsic value of gold andEquation (13) holds, the equilibrium price level is constant over time except for the casein which the price level of goods produced overseas, ptb , changes.
Thus, by the linear homogeneity of   , Equation (15) can be transformed intoh1 

wt   t 1   p a 1 pta  e ,  t a1  e  pt 8

wt   t

pta  e1  1,1

,

(16)



where e  



ptb 
 is the real exchange rate. From Equations (1) and (16), we canpta calculate the nominal reservation wage as

wt   pta e1  1,1 .

(17)

Henceforth, we make the following assumption.
Assumption 3

The economy of the home country is always located at an interior equilibrium. That is,there are some individuals who are unemployed in equilibrium.
As will be clarified later, if the stockpile fiducial money is small enough, such
equilibrium surely exists.
By Assumption 3, the nominal reservation wage corresponds to the nominal
equilibrium wage. Furthermore, the zero-profit condition of firms also requires t  pta 1   e1  1,1  0  e*  1 

1  1,1

.

(18)

Thus, the equilibrium real exchange rate, e , takes a constant value independent of the*balance of payments. So does the domestic equilibrium price level p a* .
Since the utility function u   is assumed to be linear homogenous, the aggregate
consumption function of young individuals Ct is

Ct  c 1  yt .
Then, similar to Equation (9), we obtain the equilibrium condition of the good a marketasyt  c 1  yt 

Mt
.
p a*

(19)

Besides the equilibrium condition of the good market, we must consider the specie flowin conjunction with the imbalance in the balance of payments. Since incomes areconcentrated within the young generation, financial transactions are unfeasible
between the same generations. Hence, the supply of fiducial money is limited to the sum
9

of the imports of the members of the old generation who reside overseas. This amounts
to  1  c 1 e  y , where y is the real GDP of the rest of the world. The demand isbbsavings of the fiducial money of the young generation in the home country to prepare for
consumption after their retirement. This amounts to 1    1  c 1 yt . The difference
between these two values is the total amount of inflows of the fiducial money, and thus,
we obtain

M t  M t 1
 1  c 1   e* y b  1    yt  .
p a*

(20)

Equations (19) and (20) describe the dynamics of this model under REE. Solving (19) on

yt , we obtain

yt 

M
1
 a*t ,
1  c 1 p(21)

Substituting (21) into (20), we find the following dynamics of the stock of the fiducial
money. That is,

Mt
1 M t 1 1  c 1 * b
e y .
a*p
2   p a*
2

(22)

Figure 1 illustrates the adjustment process. It is clear the long-run equilibrium (PointE), where the flow of the fiducial money equilibrates, is unique and stable. If the initialstock exceeds the long-run equilibrium, imports are boosted since the business in thehome country turns up. However, the circulated fiducial money gradually decreases
because the country experiences deficits on the balance of payments. Thus, thetemporarily boosted economy converges to the long-run equilibrium.
Figure 2 illustrates how the business cycle diffuses internationally. Whenever theworld economy stagnates and the value of y decreases, the line which representsbEquation (22) shifts downward from ll to l’l’. The long-run equilibrium moves from E1 to

E2. Since exports from the home country are curtailed, there is deficit in the balance of
payments and circulated money decreases. This triggers a financial contraction, andthus, the home country cannot be immune from the business downturn. Thus, we havethe following theorem.
Theorem 2
10

As long as people are confident of the intrinsic value of gold, the isolation effect becomes
imperfect and business cycles diffuse among countries.
3.3 Perturbation in the confidence of the intrinsic value of gold
In reality, business downturns under the gold standard often deepen confidence in thevalue of gold. This might be due to a psychological propensity that everyone heavily
relies on gold for precautionary savings for their unforeseeable future. We analyze how
the deepened confidence in gold worldwide affects the home country’s economy.
By differentiating Equation (18), we obtain



dp a*
dp b*
.


p a*
pb*

(23)

This implies that the deepened confidence overseas entirely diffuses into the homecountry. In other words, temporary deflation overseas is transmitted to the homecountry under the gold standard.
Since this increases the real value of the existing fiducial money

M t 1, the transmitted
p a*

deflation mitigates the contractionary pressure caused by the stagnation overseas. Moreformally,
Theorem 3

The sequences of the equilibrium real GDP with and without deflation are

y 
*
t j


j 0

 y  and
*

t j



j 0

, respectively. Then,*yt* j  y t  j , j(24)holds.
Proof
Assume that the initial nominal stock of the fiducial money M t 1 is the same in bothcases. Then, by the difference equation (22), the real cash balance

M t jp a*with deflationis larger than that without deflation for all j. Since it is apparent from Equation (21)that real GDP increases proportionately with the real cash balance, Equation (24) holds.

11Thus, deflation in conjunction with severe recession overseas discussed in 3.2
mitigates damage from the recession. This is because the imported deflation raises thereal cash balance, and thus contributes to moderating the financial contraction owing tooutflows of gold.
4. Conclusions
The function of the gold standard was analyzed in reality, in which people areconfident of the intrinsic value of gold. Results obtained are as follows.
First, the gold standard in idealism, which is called the specie flow theory andoriginated from Hume (1752-b), can be regarded as the combination of the quantity
theory of money and purchasing power parity concerning the nominal exchange rate.
There is no economic factor other than commodity prices that would transmit thebusiness cycle between countries. We have found that full-employment equilibrium isalways achieved and changes in the overseas economic environment never affect thedomestic economy. That is, the employment-isolation effect is perfect under theidealistic gold standard, although this runs counter to the historical evidence.
Second, although the specie flow theory presumes disbelief in the intrinsic value ofgold, people were confident of that value in the sense that they rationally expected that
unit of gold would always be convertible to commodities at some fixed ratio. Based onsuch a reality, we have revealed that a downturn of business overseas reduces exports of
the home country, and hence gold/fiducial money flows out. This triggers a financial
contraction and makes the domestic economy slump. As such, the gold standard inreality is a transmitter of international business cycle diffusion.
Finally, the coexistence of deflation with stagnation overseas mitigates the depressive
effect. This is because deflation raises the existing real cash balance and partly
moderates the financial contraction owing to deficits in the balance of payments.

12References
D. Hume (1752-a). Of money, in Political Discourses, 2nd edition, Oxford University,
Oxford, U.K., pp.41-59.
http://books.google.co.uk/books?id=m0gVAAAAQAAJ&hl=ja&source=gbs_navlinks_sD. Hume (1752-b). Of the balance of trade, in Political Discourses, 2nd edition, Oxford
University, Oxford, U.K., pp.79-114.
http://books.google.co.uk/books?id=m0gVAAAAQAAJ&hl=ja&source=gbs_navlinks_s
J. M. Keynes (1924). The prospects of gold, in The Collected Writings of John Maynard
Keynes XIX: Activities 1922-1929: The Return to Gold and Industrial Policy, Cambridge
University Press, Cambridge, U.K., pp.177-182.
R. E. Lucas, Jr. (1972). Expectations and the neutrality of money, Journal of Economic
Theory 4, pp. 103-124.
R. A. Mundell (1997). The international system in the 21st century: could gold make acomeback? Lecture delivered at St. Vincent College, Letrobe, Pennsylvania.
http://robertmundell.net/ebooks/free-downloads/#56
M. Otaki (2007). The dynamically extended Keynesian cross and the welfare-improving
fiscal policy, Economics Letters 96, pp. 23-29.
M. Otaki (2012). A Keynesian model of a small open economy under a flexible exchange
rate, Theoretical Economics Letters 2, pp.278-282.

13

Mt

1−c(1)
1 Mt−1∗ b
Mt = 2−βpa∗ + 2−β βe y

E

45◦
Mt−1

O
Figure 1: The Adjustment Process

1

Mt
l
E1

l′

l

E2
l′

45◦
Mt−1

O
Figure 2: Diﬀusion of Business Cycle

2