the long-run real-wage rigidity and full employment adjustment in the classical model

The long-run real-wage rigidity and full employment

adjustment in the classical model

Ravi Batra*

Department of Economics, Southern Methodist University, Dallas, TX 75275, USA

Received 18 June 2001; accepted 21 June 2001

Abstract

This paper studies a century of US data to see how real wages behave during unemployment.

Contrary to popular belief, we find that not a single downturn witnessed a general decline in the real

wage. In fact, real earnings usually jumped long before unemployment disappeared. Yet, full

employment returned in every case. The self-correcting mechanism that eliminates unemployment is

not the long-run downward flexibility of real wages as postulated by most economists but a fall in the

real wage relative to labor productivity. This suggests that supply-side policies may be used to

supplement demand-side prescriptions in order to combat short-run unemployment. D 2002 Elsevier

Science Inc. All rights reserved.

JEL classification: E21; E30

Keywords: Wage flexibility; Macroeconomic policy

1. Introduction

Economics, especially macroeconomics, is riddled with controversies. However, if

there is one idea on which most economists find themselves in general agreement, it is

that real wages are flexible, both upward and downward, in the long run. To be sure,

the long run itself is not precisely defined. Its opposite, the short run, could be

anywhere from 1 to 3 or even 5 years, after which the long run takes over. However,

1059-0560/02/$ – see front matter D 2002 Elsevier Science Inc. All rights reserved.

PII: S1059 -0560 (01 )00103 -4

* Tel.: +1-214-768-2707; fax: +1-214-768-1821.

E-mail address: [email protected] (R. Batra).

International Review of Economics and Finance

11 (2002) 117–138

few question the notion that real wages are perfectly flexible once we cross the realm of

the short period.

Broadly speaking, there are two schools of thought in macroeconomics—Keynesians (the

activists) and classicals (the nonactivists). The two differ in their views about the short run,

but as Abel and Bernanke (1995) remark in emphatic italics, Keynesians and classicals both

agree that in the long run prices and wages fully adjust to achieve equilibrium in the markets

for goods, assets, and labor. In other words, ‘‘Complete flexibility of wages and prices in the

long run is not controversial’’ (p. 22).

Wage-price flexibility is also commonly identified as the automatic or self-correcting

mechanism that preserves full employment of labor in an economy. Ruffin and Gregory

(1993) echo the Abel–Bernanke sentiment in their words about activists and nonactivists:

Both believe that the self-correcting mechanism works in the long run (p. 375). Another

confirmation of this viewpoint comes from Landsburg and Feinstone (1997): The most

fundamental source of conflict among macroeconomists is their variety of beliefs about the

stickiness of wages and prices. It is relatively uncontroversial to say that prices are flexible in

the long run and sticky in the short run (p. 535).

The purpose of this paper is to question this long and widely held view. We will show that

over 100 years of US history from 1890 to 1994, there was not a single period, short or long,

when real wages fell systematically to eliminate unemployment. In fact, real wages rose, time

and again, even after unemployment had soared and endured over several years. The paper

does not dispute that prices are fully flexible in asset and goods markets, only that they are

not so in the labor market. Nor do we question the upward flexibility of the real wage in the

wake of excess demand for workers. Only the idea of downward flexibility in the presence of

persistent excess supply of labor is challenged by this paper.

The notion of downward real-wage flexibility underlies much of modern macroeconomics.

In fact, it is at the base of almost all the major branches of economics today, including, macro,

international, growth, public finance, among others. Even the Keynesians adhere to this view in

their long-run studies. However, if real wages are in fact rigid regardless of the time dimension,

how do labor markets clear in the wake of excess supply? There is no doubt that once the time

dimension extends to decades instead of years, the US economy has traveled along the path of

full employment. Recessions and depressions, even when durable, do vanish eventually. How

then has the US economy always returned to the course of full employment in spite of the long-

run rigidity of real wages? In other words, what is the true self-correcting mechanism that

ultimately restores full employment? This is the second question explored by this paper.

We analyze the simple classical model of the labor market because that is where the

entire wage-price debate originated. We also show that under realistic conditions, full

employment equilibrium occurs in this framework even if real wages are inflexible in the

long run.1 Specifically, we demonstrate that it is the ratio of real wage/labor productivity,

1 The classical model has been revived in a variety of ways. Among its latest reincarnations is the theory of the

real business cycle that is standard menu in most macro texts today. See Plosser (1989) for a review of this

literature. Also, see Gordon and Wilcox (1998, pp. 547–548) and Romer (1989).

R. Batra / International Review of Economics and Finance 11 (2002) 117–138118

not the real wage itself, that has fallen time and again to eliminate or mitigate

unemployment in the US economy. In general, when the labor market is tight, real wages

grow faster than labor productivity. In contrast, in the presence of unemployment, real

wages trail labor productivity. However, they seldom fall. This finding suggests that under

certain circumstances, supply-side policy prescriptions may be more effective than

Keynesian remedies to combat cyclical unemployment.

2. The meaning of rigid real wages

Before turning to history, let us give a precise meaning to the notion of real-wage rigidity.

Consider Fig. 1 that describes the well-familiar classical labor market. LD is the downward

sloping labor–demand curve and LS, the upward sloping labor–supply curve, both linked to

the real wage, W. (The position of the two curves depends on the marginal product and

marginal disutility of labor, respectively.) Full employment equilibrium occurs at E, where the

two curves intersect, producing an employment level of Le and a real wage of We. Lerepresents full employment, because it is the product of equality between labor demand and

labor supply at the market-clearing real wage, We.

Now, suppose the economy is hit by an adverse supply shock such as a major rise in the

price of oil or something else that pushes the LD curve down to D*. In the short run, labor

contracts are fixed and assume that the real wage remains constant. Then, labor demand is

Fig. 1. The classical labor market.

R. Batra / International Review of Economics and Finance 11 (2002) 117–138 119

only HWe, labor supply is EWe, the labor market is in disequilibrium, and HE is the level

of unemployment.

At this point, according to classical economists and their adherents, an automatic

mechanism sets in. Competition between the unemployed and the employed drives the

money wage down in new labor contracts and the real wage shrinks until all

unemployment vanishes in the long run. Labor contracts typically last 3 years, suggesting

that after 3–4 years full employment should be restored. Thus, if the real-wage rate is

flexible and sinks to W*, then full employment is preserved in the sense that labor

demand and labor supply are equal again, this time to the level OL*. There is no

involuntary joblessness at this point, although voluntary unemployment has now emerged

by the amount of L * Le. Everyone willing to work at the prevailing market wage of W*

has a job, but those who would work only at the real wage of We are unemployed. Thus,

given the LS curve, a necessary condition for voluntary unemployment to appear is that

the real wage tumbles.

If the LS curve was vertical, even the voluntary component of observed unemployment

would be unchanged, although the real wage will have to fall some more to the point

where the D* curve intersects the line ELe (not shown in the graph). In other words, the

long-run flexibility of the real wage is a self-correcting mechanism that automatically

clears the labor market without any government intervention. Thus, the real-wage

flexibility simply means that once unemployment has appeared for any reason whatsoever,

the real wage declines and keeps declining until all those willing to work at the prevailing

real wage find jobs.2

3. A technical improvement

Suppose, in the interim, even before joblessness fully vanishes, technology improves,

the marginal product of labor rises, and the LD curve shifts from D* to D**. This will

have no impact on the real wage if the labor price is perfectly flexible. All it will do is to

hasten the market-clearing process. The real wage will now have to fall to W** to restore

full employment. This point is important in exploring the historical figures on real wages

and unemployment. The actual data are the product of a host of influences on the money

and real wage, including unemployment, factor productivity, labor supply, and prices of

raw materials. However, if unemployment exists, no positive influence working through

the interplay of labor supply and labor demand should have any impact on the real wage,

because the real wage has to fall as long as there is excess supply of labor.

A formal statement of this process appears in Patinkin’s (1948) work as follows: Let

Ld ¼ hðwÞ, h0 < 0 and Ls ¼ gðwÞ, g0 > 0

2 The general idea is that price falls until the relevant market clears completely (see Abel & Bernanke,

1995, p. 19).


be the respective labor demand and labor supply functions. Then, the labor market is

dynamically stable if

dw=dt ¼ qðLd � LsÞ, q > 0

and

sign dw=dt ¼ sign ðLd � LsÞ:This suggests that if labor demand exceeds labor supply, the real wage should rise and fall in

the opposite case until it approaches its equilibrium value, where

Ld ¼ Ls and dw=dt ¼ 0:

Thus, dw/dt < 0, as long as there is excess labor supply, even if the labor demand and

labor supply functions were to shift before the new equilibrium is reached. Here, dt is the

time derivative.

If technology were to improve when the labor market is in equilibrium, then, of course, the

real wage would rise to eliminate the excess demand for labor. The same would happen if the

LS curve were to shift to the left. However, such influences must be ignored in the presence

of unemployment.

These considerations underscore an important point in analyzing the historical data. The

logical consistency of the classical or any market-clearing model demands that the market

price continues to fall until excess supply completely vanishes even if the demand and supply

curves were to shift in the interregnum. Once unemployment has endured for some time, all

positive influences on the real wage, such as productivity improvements, cease in the classical

model. In other words, to empirically examine the question of long-run real-wage flexibility,

we do not need an econometric analysis that isolates various influences on the real wage.

One of the questions raised by the econometric analysis is: What happens to the real wage

if unemployment rises or falls, keeping productivity and other influences constant? However,

a labor market-clearing model raises a different query: What happens to the real wage when

the observed rate of unemployment rises above a threshold given by, say, the natural rate of

unemployment, regardless of any changes in technology and labor supply? All we need to see

is what happens to the real wage once unemployment has come into being and persisted

above the natural level. An econometric analysis revealing that the real wage declines with a

rise in the jobless rate does not settle the question of the real-wage flexibility, because the

classical model demands that, in the wake of high and persistent joblessness, the real wage

sinks even if the unemployment rate is constant or falls gingerly. In other words, the real

wage must decline as long as the unemployment rate remains above the threshold rate of

natural unemployment, even if improved technology raises the marginal product of labor.

The process of the real-wage decline should start sooner than the expiry of labor contracts,

because a significant portion of workers is not covered by such written agreements. Once

unemployment rises, the real wage should start to fall 1 or 2 years later but certainly after 3

years. The speed of this adjustment will, of course, depend on the severity of the initial rise in

the jobless rate. With all this in mind, let us now turn to a study of history and examine the

behavior of the real wage during each episode of high unemployment.


3.1. 1893–1899

Let us start with the high jobless period of 1893–1899. Reliable figures about unemploy-

ment, or for that matter about most economic variables, are unavailable prior to 1890.

Consider Fig. 2, where the upper part of the chart traces the path of the rate of unemployment

from 1893 to 1899, and the middle part does it for the real-wage rate described by the average

Fig. 2. Unemployment, real wages, and productivity, 1893–1899.


real earnings of nonfarm employees. For the time being, please disregard the lowermost

portion of the graph, to which we will return later.

The 1890s witnessed a long and serious depression. The jobless rate, which was just 3% in

1892 (not shown), shot up in 1893 to 11.7%, peaked at 18.4% the next year, and remained

stubbornly high until 1899. How did the real wage behave during this long period of 6–7

years? The real earnings index stood at 533 in 1893 and indeed fell to 521 the next year but

then started to rise from 1895 and generally kept rising until 1899 when the jobless rate

approached 6%, which may be regarded as the US economy’s natural rate of unemployment.3

(Here, the real-wage index has been computed by dividing money wage with the index of the

cost of living). According to market-clearing models, the real wage should have been

shrinking from 1893 to 1898, because all this time the observed rate of unemployment

towered above the natural rate. However, the real-wage index was at 533 in 1893 and 564 in

1898. Clearly, real earnings were not flexible downward during the long period of high

joblessness of the 1890s (see U.S. Department of Commerce, 1975).

Could the observed rate of unemployment have all been voluntary, as a classical

economist would argue or, mostly involuntary, as a Keynesian would argue? The answer,

for two reasons, is no. First, the jobless rate was only 3% in 1892 and over 18% in 1894,

just 2 years later. It is doubtful that as much as an extra 15% of the labor force had decided

to quit working. However, the real wage fell from 544 in 1892 to 520 in 1894, and this

could have encouraged some workers to withdraw from the labor market, so some

joblessness indeed could have been voluntary. By 1895, the real-wage index reached 557,

surpassing the level of 1892. Therefore, all those who might have quit working voluntarily

should have returned to the labor market by then. However, the jobless rate in 1895 was still

a hefty 14%, far above the 3% level of 1892, which may be regarded as a year of full

employment equilibrium. Thus, from 1895 on unemployment was cyclical, not voluntary.

Yet, full employment returned by 1899. Thus, cyclical unemployment indeed disap-

peared on its own without government intervention but not because of the falling real

wage. In fact, as the middle of the graph displays, the earnings trend during the period

was positive.

It is well known that government intervention to eliminate unemployment did not become

fashionable until after 1930. Thus, a careful study of the depression of the 1890s reveals that

the economy indeed has a self-correcting mechanism that automatically restores full

employment in the long run but not through the medium of a declining real wage. Something

else is at work here.

3 The level of natural unemployment has varied over time. Ruffin and Gregory (1993) among others put it

between 5% and 7%. We have selected 6% as the threshold rate of unemployment that defines a situation of labor-

market disequilibrium. However, our conclusions are not sensitive to this threshold. Gordon and Wilcox (1998)

have provided estimates of the natural rate of unemployment going all the way back to 1890, when it was close to

4%. On the other hand, a lower threshold rate will only reinforce our results that real wages are inflexible both in

the short and the long run. When the real wage fails to fall if unemployment exceeds 6%, it will certainly be rigid

when the jobless rate merely exceeds 4%.


Between 1900 and 1929, the fateful year of the stock market crash and the onset of the

Great Depression, the US economy suffered two recessions that were short lived. Unem-

ployment in 1908 jumped to 8% and generally remained above the natural rate until 1911,

while the real-wage index rose from 567 to 616. Again, real wages went up during a time of

high joblessness. The experience of the early 1920s was much the same. Real wages fell in

1921 with the jobless rate at 11.7% but then resumed their upward march even before cyclical

unemployment vanished.4

3.2. 1930–1941

Let us now turn to a study of the Great Depression, which provides by far the best test of

the classical doctrine of the long-run flexibility of real wages. In 1929, the economy was

clearly at full employment, with unemployment standing at 3.2%. Consider the top and

middle parts of Fig. 3. In 1930, the jobless rate rose to 8.7%, soared as high as 25% in 1933,

and remained above the 14% rate as late as 1940, fully 10 years after the onslaught of the

depression. Surely, a full decade is long enough for the classical automatic mechanism to

reveal itself. However, the real-wage index, which stood at 834 in 1930, actually rose over the

next 2 years and only fell in 1933 and 1934. Thereafter, it generally moved upward and was at

943 at the end of the decade. The unemployment rate fluctuated widely during the 1930s and

remained stubbornly high throughout the decade, while the real wage revealed a remarkable

upward trend. In 1941, the real wage stood at 1018 along with a jobless rate of 9.9%. (Full

employment returned by 1943, but by then, the US was mired in World War II. That is why

we pause at 1941.)

Once again, could all this unemployment be voluntary or involuntary? Note that the

necessary condition for voluntary joblessness to emerge is that the real wage falls and falls

enough to turn some workers against the tedium of work. However, between 1929 and 1930,

there was no change in the real-wage index, which stood at 834 in both years. Yet, millions

more were jobless in 1930. In view of the definition provided by the classical model, this

unemployment had to be involuntary, because it had emerged at the same real wage

prevailing the year before. The real wage did fall in 1933 and 1934 but, in 1936, reached

830, very close to the 1929 level. All this suggests that some unemployment after 1932 could

indeed have been voluntary. However, after 1936, when the real wage nearly reverted to the

1929 level, voluntary unemployment disappeared. Nonfarm employment stood at 31 million

at the end of 1929 and at only 29 million in 1936. Thus, it is interesting that some joblessness

prior to 1936 could indeed have been voluntary.

Real wages were obviously not flexible downward during the decade of the Great

Depression, because real earnings began to rise long before cyclical unemployment vanished.

Yet, a self-correcting mechanism, though excruciatingly sluggish, was at work. Unemploy-

ment peaked in 1933 at 25% but was below 10% by 1941. Millions were still without jobs,

but several millions had also found new jobs, at better wages. This time, the government

4 See U.S. Department of Commerce (1975, Series D 736). This source provides data for all charts until 1941.


intervened heavily but, as many have suggested, erred again and again.5 So, in spite of several

policy errors, unemployment had tumbled in the long run. Clearly, there was some sort of


5 Among the errors that have been widely discussed are (1) a sharp rise in the income tax rate, (2) the Federal

Reserve System ignoring a banking crisis, and (3) a hefty rise in the tariff. The budget deficit also grew manifold,

but many regard that as a positive step. See Gordon and Wilcox (1998, Chap. 7) for an exhaustive analysis of the

economic forces interacting during the Great Depression.


corrective mechanism at work but it was very different from what the classical economists

had envisioned.6

3.3. 1947–1973

The Great Depression, catastrophic as it was, could not but usher a sea change in

economic thinking, policy, and public psychology. Government intervention, even though

error prone during the 1930s, became fashionable; unions became stronger; taxation

shifted from tariffs to income levies and turned highly progressive (Batra, 1996); and

product prices almost never fell. In the past, money wages would fall somewhat during

episodes of high unemployment, but product prices would generally fall even more, so

that real wages climbed. This is what, for instance, transpired during the 1890s and the

1930s. However, after 1933, the consumer price index generally moved up. Did this,

along with other momentous changes, alter the long-run rigidity of real wages? The

answer is no.

Consider Fig. 4. Between 1947 and 1973, there were several years of high unemploy-

ment, which though was never as bad as that in the preceding period. However, the index of

real, nonfarm employee compensation generally moved upward. Unemployment rose

sharply in 1949, 1954, 1958, and 1961, but the real wage never fell. Were real wages

flexible or rigid during this rather long period? It is hard to tell, because joblessness was

fortunately never extraordinarily high or long enough to provide a good test of the classical

thesis. However, we do know that real wages failed to decline whenever joblessness

climbed. It is interesting to note that real wages generally grew faster than productivity in

this era of tight labor markets (U.S. Council of Economic Advisers, various years).

3.4. 1974–1995

After 1973, when the world was hit by a severe supply shock in the form of a quadrupling

of the price of oil, the US economy went through another remarkable change. The most

enduring alteration has been the behavior of the average real wage, which, including

employee benefits, grew tepidly at the rate of 0.3% per year. Unions also grew weaker,

and this has prompted some to conclude that real wages have become more flexible than

before. This may be true, but the classical thesis that real wages fall to eliminate

unemployment still fails.

Consider Fig. 5. From 1974 to 1987, unemployment generally persisted above the

natural rate for 14 years but real wages fell only from 1979 to 1981 and that too by a

minuscule 4% over 3 years. For the classical thesis, the interesting point is that real

wages resumed their upward march in the midst of high unemployment. In 1980, the

jobless rate was 7.2% and the real compensation index stood at 99.4. This was clearly a

6 Bernanke and Parkinson (1989) also argue that some kind of self-correcting mechanism was at work during

the 1930s.


situation of excess supply in the labor market and should have led to a real-wage decline

after 3–4 years, especially when unemployment jumped to 9.6% by 1983. That year, the

wage index stood at 100.8. More recently, unemployment was above the natural rate from

1991 to 1994, during which the wage index went up, not down. Undoubtedly, real wages

have become more flexible than in the past in the sense that they do not now shoot up in

the face of severe joblessness but still do not fall during episodes of high unemployment.

The wage trend is upward in spite of a generally excess supply of labor between 1974

and 1994.



3.5. A recap

To recap, our study of over 100 years of US history reveals two facts:

1. Real wages fail to decline even in the long run in spite of high unemployment.

2. Labor markets have always returned to full employment despite the failure of real wages

to fall. There is clearly a self-correcting mechanism at work, but it is not what the classical

economists had envisioned, for unemployment disappears even in the face of rising real

wages. Real wages are flexible upwards but not downwards.

4. The true self-correcting mechanism

What then is the true adjustment mechanism that in the long run restores full

employment? Let us assume, for the time being, that the real wage is fixed downward

but not upward. A number of theories have appeared to tell us why this may be so. Perhaps

employers find it distasteful to cut wages and hurt employee morale and productivity in the

Fig. 5. Unemployment and real wages, 1974–1995.


process or they pay what are known as ‘‘efficiency wages’’ that are over and above the

market-clearing wage.

Whatever the reason for the downward real-wage rigidity, it is obvious that once a

recession arises and consumer confidence wanes, company profits will fall. The employer

then has two choices: (1) cut the money wage to the remaining employees or offer them a

wage increase below the price increase and risk a loss of employee morale and

productivity or (2) introduce new technology stimulating the marginal and average product

of labor but not raise the real wage.

Both alternatives are available. Because of competition between the unemployed and

the employed, real wages can be trimmed, but that could set off an employee revolt or at

least hurt their efficiency. In the second case, the producer can use its depreciation

account and replace the aging equipment with new and up-to-date machines. The firm

may be unwilling to expand its net investment in a sharp downturn but still may have to

replace the worn out capital stock. Even during the Great Depression, gross investment

was positive, although net investment was negative for a few years. With new

technology, the employer can even offer a slightly higher real wage to reward merit

and still restore company profitability. Caballero and Hammour (1994) view recessions as

times of ‘‘cleansing,’’ when outdated or relatively unprofitable techniques and products

are pruned out of the productive system (p. 1352). The classical economists assumed that

the money wage and hence the real wage is cut during episodes of high joblessness, but

in reality, the real wage does not fall, while labor productivity goes up even

during depressions.

Unemployment usually lasts longer than a recession and may rise for a while even as

the economy and real GDP begin to expand. Investment activity may then pick up to raise

productivity without the end in layoffs. The firm can then easily restore its profitability

without cutting the real wage. All it has to do is to keep the real-wage increase below the

rise in labor’s marginal product. This is how unemployment, though not recessions,

typically end.

Consider Fig. 6 to see how the self-correcting mechanism really works. As in Fig. 1, the

original equilibrium is at E, where the LD and LS curves intersect. Then, the LD curve

shifts down to D* owing to an adverse shock, but the real wage remains fixed at We,

generating involuntary unemployment of HE. In the short run, not much can be done. The

firm has to endure losses and will remain in business as long as the market price covers its

average variable cost. However, in the long run, the producer can introduce new technology.

Suppose this is what is done. Then, the LD curve moves back to D** and unemployment

declines to GE and completely disappears when the technology shift is large enough to

move the LD curve back to LD. Also, if the LD curve shifts up at a fast pace, the firm may

offer a higher real wage of Wn to reward meritorious employees even before unemployment

completely vanishes. In that event, unemployment will fall along with rising real wages, and

at the arrival of the new full employment equilibrium, total employment will be higher than

ever before, as indicated by the heavy line WnEn.

For unemployment to fall, it is not essential that the real wage should decline. What is

needed is that the real wage declines relative to labor’s marginal and average productivity. In


terms of the marginal product of labor, the answer is plain and simple. Suppose for a given

stock of capital

w ¼ FLðL,qÞ,i.e., the real wage equals the marginal product of labor (FL) in a competitive structure, with q

being the engine of technology, so that

FLL < 0 and FLq > 0

Total differentiation yields:

ðdL=dQÞ ¼ ðwq � FLqÞ=FLL

where wq = dw/dq� 0. Thus, as long as wq <FLq, i.e., the rise in the real wage falls short of

the technology-induced rise in labor’s marginal product,

dL=dq > 0,

so that labor demand rises with the introduction of new technology and ultimately catches

up with labor supply. This may explain why frequently real wages rise in spite of

lingering unemployment.

However, the behavior of w relative to the average product of labor, for which the data are

readily available, is somewhat more complex. Suppose the production function (Y) is linearly

homogeneous, so that

Y ¼ FðlK,qLÞ ¼ qLf ðlk=qÞ and k ¼ K=Lð f 0 ¼ df =dk > 0, f 00 < 0Þ,

Fig. 6. Full employment adjustment in the labor market.


is the capital/employment ratio. Here, l and q are the technology parameters initially equal to

1, the average product of labor is qf, the marginal product of capital is f 0, and the marginal

product of labor is qf�lkf 0. Similarly, the real return to capital is given by

r ¼ l f 0 ð1Þand that of labor by (Eq. (2))

w ¼ qf � lk f 0, ð2Þwhereas

v ¼ w=qf ¼ 1� lkf 0=qf ¼ 1� rk=qf ð3Þis the real wage relative to labor’s average product. Total differentiation of Eqs. (1) and (3)

yields the following system of equations:

wrdk þ kf dr ¼ krðkrdl� wdqÞ � f 2dv

ð4Þf 00dk � dr ¼ �rdl� kf 00ðdl� dqÞ

The denominator or the determinant of this system is given by

D ¼ wrð1� sÞ=s ð5Þwhere s is the elasticity of substitution between capital and labor and is defined to be positive

(Eq. (5)). It is the proportionate change in the capital/labor ratio divided by the proportionate

change in the wage/rental ratio. That is,

s ¼ �wr=kff 00 > 0

With diminishing returns to factor proportions, f 00 < 0, so that if s < 1, D is positive.7 The

solution of Eq. (4) gives us

Ddk ¼ f 2dvþ kwr½ð1� sÞ=sdl� kwr½ð1þ sÞ=sdq ð6Þ

Eq. (6) tells us how labor demand behaves over time during episodes of high unemploy-

ment. The sign of dk furnishes how labor hiring changes in response to the parametric

changes listed on the right-hand side of Eq. (6). This is because with capital stock constant, a

change in the capital/labor ratio means an opposite change in employment. Thus, if k rises,

employment falls.

We can now study a variety of cases, noting that D is positive if the elasticity of factor

substitution, as argued later, is less than 1. First, let us note that k moves parallel to v. In other

words, a fall in the real wage relative to the average product of labor alone lowers k or raises

L. This confirms our empirical findings.

As regards to technical progress, if dq= dl, then the new technology raises the marginal

product of capital and labor in the same proportion. This is the case of Hicks neutral technical

7 See Batra (1973) for the expression for s.


improvement. It can also be easily confirmed here that k falls or L rises. In other words, if s is

a fraction, then labor demand rises with the introduction of Hicks neutral technical progress

and eventually restores full employment. The same is true if technical progress is Harrod

neutral where dl = 0, but dq alone is positive, or if it is Solow neutral, where dq= 0 and dlalone is positive. The coefficients of both dl and dq are negative and have similar impact on

the demand for labor, although the impact of Harrod neutral improvement is larger than that

of the Solow type of improvement. In other words, a technology that raises the marginal

product of labor has a larger salutary impact on employment than the one that raises only the

marginal product of capital. The reason why all types of technical improvements, including

Solow neutral advance, enhance employment is that they all raise the average product of labor

or labor productivity.

A positive dl implies that machines of a recent vintage have a higher marginal product

than older machines, a point emphasized by Cooper, Haltiwanger, and Power (1999). It is like

new computers today that are much more productive than the old ones. Improvements in

technology of any kind thus raise employment.

Before concluding this section, a word may be added about the behavior of capital stock

during a downturn. As with most comparative static models of unemployment, we have kept

capital constant until the elimination of unemployment, implying that net investment is zero.

This is not a bad assumption and is generally corroborated by the early years of downturns.

However, if the stock of capital actually rises in the long run, as it did even toward the end of

the Great Depression, the effect will be an even stronger rise in labor productivity and a faster

decline in unemployment. The marginal and average products of labor will then jump apace.

Thus, the effect of a rise in the stock of capital during a long downturn can be easily

accommodated in our model. We have also assumed that the utilization of capital remains

fixed in spite of rising unemployment, but this assumption can be easily relaxed without

modifying our conclusions (see Batra, 2002).

5. Back to history

Time series analyses of the US economy show that s is between 0.3 and 0.5 (Berndt, 1991,

p. 455). The question then is: Does v generally fall during periods of unemployment? For this,

we have to go back to history, calculate v by dividing the real-wage data with average labor

productivity, and plot it against unemployment. Let us go back to Fig. 2 and explore the

lowermost box that plots the wage/productivity ratio from 1893 to 1899. The ratio generally

fell and even moved up slightly in 1896, but its trend was clearly negative. It started off at

20.9 in 1893 and ended below 20.5 in 1899. Let us contrast the behavior of v with that of real

wages, which climbed by over 9% from 1893 to 1899. In other words, the self-correcting

mechanism during the depression of the 1890s was not the long-run flexibility of real wages

but a fall in the wage/productivity ratio in the midst of persistent unemployment.

There were two short recessions before the US economy was hit by another depression.

The recession of 1908 was short lived, and unemployment barely stayed above the natural

rate for 4 years. The record shows that the V-ratio stood at 17.6 in 1908, when the jobless rate


was 8%, and fell to 17.1 the next year. By 1912, full employment returned and so did the

V-ratio, back to 17.7 this time.

The recession of 1920–1921 was worse than before, but our analysis remains much the

same. In 1920, unemployment jumped to 5.2% from just 1.4% the year before. Even though

the jobless rate was then not far from the natural rate, it felt really bad with fast deterioration

in job prospects. The V-ratio was 15.6 in 1920, fell to 14.8 the next year even as joblessness

climbed to 11.7% but reverted to the old figure in 1922, by which time the economy neared

full employment. All this time, the real wage kept rising.

Fig. 7. Unemployment, wages, and productivity, 1974–1978.


As with the classical case, the Great Depression provides a true test of our hypothesis

that the self-correcting mechanism that eliminates or reduces unemployment is not the

falling real wage but the falling V-ratio. Let us now revert to Fig. 3 that plots the v against

unemployment and real wages from 1930 to 1941, when joblessness was down to 9.9%

from 25% in 1933.

The V-ratio remained more or less constant around 16 from 1930 to 1933 even in the midst

of soaring unemployment. As the government committed one error after another, the self-

correcting mechanism did not come into play. However, after 1933, with towering jobless-

ness, the V-ratio generally fell, reached a low of 13.8 in 1936, and was at 15 in 1941. By

then, the jobless rate had plummeted to 9.9%. For the period as a whole, the overall trend in

V is downward, even though the real wage jumped by more than 22%. Thus, the Great



Depression provides by far the clearest evidence that the self-correcting mechanism in the

labor-market downturn is a fall in the real wage relative to labor productivity and not an

absolute fall in the real wage.

Ignoring the war years, let us take a brief look at the relatively stable times of 1947–1973.

For much of this period, joblessness was below 5% and never above 6.7%. The V-ratio was

also then generally stable. However, it fell whenever the jobless rate rose. Thus, the V-index

fell in 1948, 1958, and 1961, all the years of rising unemployment. Only in 1954, another

recession year, the index remained constant. The labor market was roughly in equilibrium



during this long period, and the V-ratio, using a new data base, reflected a similar stability. It

had a slightly upward trend but varied narrowly between 0.97 and 1.03.

After 1973, however, as the specter of joblessness returned, the V-index also became

volatile. The period 1974–1994, being recent and displaying less downward rigidity of

wages, is divided into three episodes to gain a sharper understanding of the true self-

correcting mechanism. Unemployment rose in 1974, peaked in 1975 at 8.5%, but then

reverted to the natural rate by 1978. All this time, the V-index had a negative trend, even

though the real wage, as shown before, grew slightly. See Fig. 7, where the V-ratio is plotted

in the middle box; its trend is strongly negative, even though the real compensation index

kept rising in the midst of high unemployment.

In 1980, joblessness rose again and stayed above the natural rate until 1987. Again, while

the real wage generally increased, the V-index fell steadily to eliminate cyclical unemploy-

ment (see Fig. 8). The narrative of the high unemployment period of 1990–1994 is exactly

the same. While the real wage moved up slightly, the V-index fell until cyclical unemploy-

ment disappeared (see Fig. 9). Thus, our analysis covering more than 100 years clearly shows

that the mechanism that mitigates unemployment is the fall in the wage/productivity ratio and

not a fall in the real wage, which actually goes up even before joblessness vanishes.

6. Policy implications

Our finding that full employment has been historically restored not by the fall in the real

wage but by a decline in the real wage relative to labor productivity yields some interesting

prescriptions. For analytical convenience, let us divide the American unemployment record

into two cases, one where the real wage rises sharply because of deflation and the other

where the real wage is more or less constant or rises only a little. During the 1890s and the

1930s, the real wage soared, whereas during the 1970s and the early 1980s and the 1990s,

the real wage went up a little.

Keynesians offer expansionary fiscal and monetary policies to fight unemployment in the

short run. The idea is that the government should raise aggregate demand either directly

through increased purchases of final goods and services or indirectly by lowering the rate of

interest through expanded money growth. Businesses will then respond by increasing their

output to meet the extra demand, thereby raising the level of employment. However,

increased output may not translate into much new hiring if the real wage rises sharply.

Firms may simply raise their output mainly through increased utilization of idle capacity. This

is what seems to have occurred during the 1930s.

From 1930 to 1933, the supply of money (M1) fell drastically by some 24%. The

unemployment rate also then soared to 25%. However, after 1933, M1 jumped, but the

jobless rate fell reluctantly. In fact, between 1933 and 1939, M1 climbed 70% and real GDP

jumped 50%, but the unemployment rate in 1939 was a hefty 17%. Both money growth and

output soared, but nonfarm employment in 1939 was still below the level in 1929. There are

various explanations for why joblessness stayed stubbornly high during the 1930s, but a

major reason was the sharp rise in the real wage, as displayed in Fig. 3.


What should the authorities have done? Our analysis suggests that in addition to monetary

expansion, the government should have tried some supply-side policies. The true self-

correcting mechanism is that real wages fall relative to labor productivity to alleviate

unemployment. Given the natural reluctance of employers to lower the real wages of their

employees, the government should have introduced supply-side remedies that subsidizes new

technology, especially the one generating new products. Companies should have been offered

tax breaks on new investment either through accelerated depreciation or investment tax credit.

The end result of all such measures would have been to accelerate the introduction of new and

capital-deepening technologies, thereby sharply raising the marginal and average product of

labor. Firms would have then hired more workers in spite of rising real wages.

Expansionary monetary and fiscal policies are likely to lower joblessness significantly in

the short run only if the real wage is restrained. When the real wage soars during periods of

high unemployment, then the monetary and fiscal stimulus must be accompanied with

policies that raise labor productivity. The idea is to accelerate the working of the self-

correcting mechanism that has time and again restored full employment in the US.

Could the supply-side prescription alone do the job of restoring full employment in a

downswing? It possibly could. It may be the only suitable policy, when high joblessness

coexists with a sticky or up-trending real wage and rising prices. Such was the case between

1974 and 1994. Monetary and fiscal stimulus was inappropriate in those times because it

added to inflationary pressures, but supply-side measures designed to raise labor productivity

would have worked by reducing the V-ratio. All we needed to do was to accelerate the fall in

the wage/productivity ratio (V). However, in a dire emergency, such as the Great Depression,

a wide variety of stimulative policies should be tried. Thus, we are led to the conclusion that

the supply-side stimulus should be effective under most circumstances, but the demand-side

policies alone may be sluggish in combating joblessness in the face of rising real wages

caused mainly by the falling price level.

7. Concluding remarks

This paper studied a century of economic data to see how real wages behave during

episodes of high unemployment. Contrary to popular belief, we found that not a single

depression or protracted recession witnessed a general decline in the average real wage. In

fact, real earnings jumped time and again long before unemployment vanished completely

and approached the natural rate. Yet, full employment returned in every case. The self-

correcting mechanism that eliminates cyclical unemployment then is not the long-run

downward flexibility of real wages as postulated by most economists but the long-run

downward flexibility of the wage/productivity ratio. Specifically, the real wage fell relative to

labor productivity in every episode of unemployment in the US. Thus, supply-side policies

may be more effective than demand-side prescriptions to combat unemployment, especially

where the falling price level sharply raises the real wage.

Of course, real wages are always flexible upward during times of excess demand for labor.

This suggests that different processes are at work during periods of labor-market disequilib-


rium, that is, real wages rise in the case of excess demand for labor but fail to decline in the

case of excess supply to restore equilibrium. What repercussions all this has for conventional

theories of aggregate supply is something that needs to be further explored.

Acknowledgments

I am grateful to Nathan Balke, Stuart Fowler, Indro Dasgupta, and Hiranyo Nath for useful

discussions about the subject matter covered in this paper. Thanks are also due to those who

participated in the departmental seminar and provided a lively debate on my work.

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the long-run real-wage rigidity and full employment adjustment in the classical model

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