The Phillips Curve and Orthodox Keynesian Economics
The Phillips curve is concerned with the controversy over the relationship
between inflation and unemployment and is one of the most famous relationships
in macroeconomics (see Smithin, 2002). It should be noted that the first
statistical study investigating the relationship between unemployment and
inflation was carried out by Irving Fisher in 1926 (see Fisher, 1973). However,
the curve that bears A.W. Phillips’s name was derived from a statistical
investigation published in 1958 into the relationship between unemployment
(U) and the rate of change of money wages (W˙ ) in the UK over the period
1861–1957. As depicted in Figure 3.14, the estimated average relationship
was found to be non-linear and inverse. For example, at an unemployment
level of approximately 5.5 per cent, the rate of change of money wages was
zero per cent, while at an unemployment level of approximately 2.5 per cent
the rate of change of money wages was 2.0 per cent.
Remarkably, Phillips found that the data for the period 1948–57 fitted very
closely to the curve fitted for the earlier period, 1861–1913, given by equation
(3.6).
W˙ = −0.9 + 9.638(U)−1.394 (3.6)
To some, this finding suggested the possible existence of a stable long-run
negative relationship between wage inflation and unemployment.
Although the original Phillips paper (1958) was an empirical investigation
into the relationship between money wage inflation and unemployment, Phillips
opens his paper with an outline sketch of the underlying theoretical reasoning
that could be used to explain why we might expect to observe a negative
relationship between these two variables. He opens with these words:
When the demand for a commodity or service is high relative to the supply of it
we expect the price to rise, the rate of rise being greater the greater the excess
demand. Conversely, when the demand is low relative to the supply we expect the
price to fall, the rate of fall being greater the greater the deficiency of demand. It
seems plausible that this principle should operate as one of the factors determining
the rate of change of money wage rates.
Following Phillips’s pioneering work, there developed two strands to the
literature, one theoretical, the other empirical. On the empirical front, economists
were interested to establish whether a stable relationship between
inflation and unemployment prevailed in other market economies (for a discussion
of the empirical literature, see Santomero and Seater, 1978). As far as
the simultaneous achievement of low inflation and low unemployment was
concerned, the discovery of a possible stable trade-off between these two
objectives implied a policy dilemma, one which might be overcome if the
curve could be shifted to the left by appropriate economic policies. However,
the design of effective policies to achieve this objective would first necessitate
a coherent theoretical explanation of the economic forces which lay
behind the relationship.
The first major attempt to provide a robust theoretical underpinning to the
curve was provided by Lipsey (1960) through the combination of two postulated
relationships: (i) a positive linear relationship between the rate of increase
in money wages and the excess demand for labour (XL), and (ii) a negative
non-linear relationship between excess demand and unemployment. These
postulated relationships are given in equations (3.7) and (3.8).
W˙ (X ) [(D S )/S ] = α L = α L − L L (3.7)
XL = β(U) (3.8)
where DL is the demand for labour, SL is the supply of labour, α is a positive
coefficient of wage flexibility, and β is a variable negative parameter such
that when XL → 0, U = U* and U* > 0; and when XL → ∞, U → 0. By
combining these two postulated relationships, Lipsey was able to provide an
economic rationale for Phillips’s observed non-linear inverse relationship
between the rate of change of money wages and unemployment shown in
Figure 3.14.
The relationship between wage change and excess demand for labour is
illustrated in Figure 3.15. Panel (a) shows that at any wage rate below We ,
wages will rise as a result of excess demand in the labour market. Panel (b)
shows that the rate of increase in money wage rates will be greater the larger
the excess demand for labour. For example, at a wage rate W1 in panel (a)
there is an excess demand for labour of aa. This excess demand is equal to 0a
in panel (b) and results in a rate of increase in money wage rates of W˙1. The
relationship between excess demand for labour and unemployment is illustrated
in Figure 3.16. Even when the labour market clears (that is to say, there
is neither excess demand nor excess supply) there will be some positive
amount of unemployment due to frictions in the labour market as people
change jobs and search for new employment, that is, 0e in Figure 3.16.
Lipsey argued that, although unemployment would fall in response to positive
excess demand (for example, jobs become easier to find as vacancies
increase), unemployment would only asymptotically approach zero. In other
words, steadily increasing excess demand would be accompanied by increasingly
smaller reductions in unemployment.
In summary, Lipsey’s rationale suggests that, in its simplest form, the rate
of change of money wages depends on the degree of excess demand (or
supply) in the labour market as proxied by the level of unemployment. This
can be expressed by the equation:
W˙ = f (U) (3.9)
Referring back to Phillips’s opening statement in his 1958 paper, it is clear
that he viewed the high correlation between money wage inflation and unemployment
as strong evidence in favour of the ‘demand pull’ explanation of
inflation.
In Lipsey’s model, due to labour market frictions, equilibrium in the labour
market occurs when U = U* > 0 (see Lipsey, 1960, pp. 470–71). When U = U*,
the number of job vacancies (V) is equal to the number of unemployed who
are actively seeking work. Since SL equals the total number employed (E) and
unemployed (E + U), and DL equals the total number of vacancies (V) plus
the number employed (V + E), we can express the proportional excess
demand for labour as follows:
XL = [(DL − SL )/SL ] = [(V −U) /(E +U)] (3.10)
Letting v = V/SL and u = U/SL, we can express the excess demand for labour
in terms of variables that can be measured, that is the vacancy rate (v) and the
unemployment rate (u).
140 Modern macroeconomics
XL = v − u (3.11)
Over the business cycle the vacancy rate will be positively related to XL and
unemployment will be negatively related to XL, assuming the quit rate does
not exceed the hiring rate as XL increases.
Later, Hansen (1970) refined Lipsey’s analysis by assuming that vacancy
and unemployment rates are related in a hyperbolic form, that is, h = vu
where h = coefficient of friction in the labour market (with no friction in the
labour market h = 0 and either v or u = 0). The relationship between XL, u
and v when there are frictions present in the labour market is shown in Figure
3.17.
In panel (a) we can see that even when excess demand for labour is zero,
both the unemployment and vacancy rates are positive, reflecting friction in
the labour market. In a frictionless labour market the relationship between XL,
v and u will be a 45° line, as shown by AB. Panel (b) of Figure 3.17 shows all
the combinations of vu tracing out a hyperbolic curve. Anywhere along the
45° line indicates equilibrium in the labour market since with XL = 0, we also
have v = u. The existing degree of friction illustrated in Figure 3.17, panel
(b), is indicated by the position of the hyperbolic curve at F. With increasing
friction in the labour market this curve will shift out. In turn this will cause
the Phillips curve to shift to the right since the level of unemployment
consistent with XL = 0 increases as labour market friction increases. There is
strong evidence, for example, that such a shift occurred in the UK economy
in the late 1960s and early 1970s (Gujarati, 1972; see also Taylor, 1972).
Given Hansen’s refinements, the Phillips relationship can now be expressed
in the following form:
W˙ = α(h/u − u) + w* = αh/u − αu + w* (3.12)
where w* is exogenously determined wage inflation (for example, brought
about by trade union power). In (3.12) we can see that the slope of the
Phillips curve is dependent on the coefficient of wage flexibility, α, and the
position of the Phillips curve will be influenced by w* and also the degree of
friction in the labour market, h. The more inflexible the labour market the
higher the degree of friction, and the higher will wage inflation be for any
given level of unemployment (see Rothschild, 1971; Frisch, 1977; Lipsey,
1978).
During the 1960s the Phillips (1958) curve was quickly taken on board as
an integral part of the then-dominant orthodox Keynesian paradigm, not least
because it was interpreted by many orthodox Keynesians as implying a stable
long-run trade-off which provided the authorities a menu of possible inflation–
unemployment combinations for policy choice. Within academia the
textbook interpretation of the Phillips curve came to be presented as a proposition
that permanently low levels of unemployment could be realistically
achieved by tolerating permanently high levels of inflation. As James Galbraith
(1997) points out, in 1968 mainstream American Keynesians were ‘committed
to Samuelson and Solow’s (1960) version of the Phillips curve’. According
to Robert Leeson (1994a, 1997a, 1999), this is not how Bill Phillips himself
ever viewed the relationship he had discovered. In Leeson’s view, Phillips’s
1958 paper was an attempt to locate the level of unemployment consistent
with price stability. Richard Lipsey has confirmed that Phillips had ‘no tolerance
for accepting inflation as the price of reducing unemployment’ (Leeson,
1997a). However, up to at least the late 1960s the prevailing Keynesian
economic orthodoxy used the Phillips curve to predict the rate of inflation
which would result from different target levels of unemployment being attained
by activist aggregate demand policies, with particular emphasis on
fiscal instruments. As DeLong (1998) points out, once those target rates of
unemployment kept falling, the inflationary outcome of this approach to
macroeconomic policy was inevitable and duly arrived with a vengeance with
the ‘Great Peacetime Inflation’ of the 1970s.
One of the main reasons why the Phillips curve was quickly adopted by
orthodox Keynesians was that it seemed to provide an explanation of inflation
which was missing in the then-prevailing macroeconomic model. The
reader will recall from the discussion contained in section 3.3 that within the
IS–LM model the price level is assumed to be fixed at less than full employment,
with the result that up to full employment, changes in aggregate demand
affect the level of real income and employment. Up to full employment
money wages are assumed to be fixed and unresponsive to changes in aggregate
demand. Only when full employment is reached will changes in aggregate
demand affect the price level. The Phillips curve allowed the orthodox
Keynesian theory of output and employment determination to be linked to a
theory of wage and price inflation. Following Lipsey (1978), this is illustrated
in Figure 3.18. The top panel of Figure 3.18 depicts the standard IS–LM
model, while the bottom panel shows the Phillips curve with the modified
axes of price inflation (P˙ ) and output/income (Y). Panel (b) is derived by
assuming (i) that the level of output depends on the level of employment and
that the level of unemployment is inversely related to the level of employment,
and (ii) a hypothesis that prices are set by a mark-up to unit costs of
production, the main component of which is wages. Put in its simplest form,
the mark-up pricing hypothesis suggests that price inflation depends on money
wage inflation minus productivity growth. In this context it is interesting to
note that the estimated Phillips curve (Figure 3.14) showed that an unemployment
level of approximately 2.5 per cent was compatible with stable
prices because at this level of unemployment the rate of change of money
The orthodox Keynesian school 143
Figure 3.18 The link between the Keynesian model and wage and price
inflation
wages was approximately equal to the then average growth of productivity of
2 per cent. Suppose the economy is initially operating at a full employment
level of income (YFE), that is, the intersection of IS0 and LM0 in panel (a) of
Figure 3.18. Reference to panel (b) reveals that the full employment level of
income is compatible with stable prices; that is, ˙P = 0. Following a onceand-
for-all expansionary real impulse, the IS curve shifts outwards to the
right, from IS0 to IS1, and real income rises above its full employment level of
YFE to Y1. Reference to panel (b) reveals that as income rises above its full
employment level, price inflation increases to P˙1. As prices increase, the real
value of the money supply is reduced, causing the LM curve to shift to the
left, from LM0 to LM1, and the economy returns to full employment, that is,
the intersection of IS1 and LM1 in panel (a). At full employment stable prices
prevail, that is, ˙P = 0 in panel (b).
Following the influential contribution from Samuelson and Solow (1960),
the Phillips curve was interpreted by many orthodox Keynesians as implying
a stable long-run trade-off which offered the authorities a menu of possible
inflation–unemployment combinations for policy choice (see Leeson, 1994b,
1997a, 1997b, 1997c). Following the Samuelson–Solow paper the trade-off
has generally been expressed in terms of price inflation rather than wage
inflation. However, by the late 1960s/early 1970s, both inflation and unemployment
had begun to increase, as is evident from Tables 1.4 and 1.5. As we
will discuss in the next chapter, the notion of a stable relationship between
inflation and unemployment was challenged independently by Milton Friedman
(1968a) and Edmund Phelps (1967), who both denied the existence of a
permanent (long-run) trade-off between inflation and unemployment.
The Phillips curve is concerned with the controversy over the relationship
between inflation and unemployment and is one of the most famous relationships
in macroeconomics (see Smithin, 2002). It should be noted that the first
statistical study investigating the relationship between unemployment and
inflation was carried out by Irving Fisher in 1926 (see Fisher, 1973). However,
the curve that bears A.W. Phillips’s name was derived from a statistical
investigation published in 1958 into the relationship between unemployment
(U) and the rate of change of money wages (W˙ ) in the UK over the period
1861–1957. As depicted in Figure 3.14, the estimated average relationship
was found to be non-linear and inverse. For example, at an unemployment
level of approximately 5.5 per cent, the rate of change of money wages was
zero per cent, while at an unemployment level of approximately 2.5 per cent
the rate of change of money wages was 2.0 per cent.
Remarkably, Phillips found that the data for the period 1948–57 fitted very
closely to the curve fitted for the earlier period, 1861–1913, given by equation
(3.6).
W˙ = −0.9 + 9.638(U)−1.394 (3.6)
To some, this finding suggested the possible existence of a stable long-run
negative relationship between wage inflation and unemployment.
Although the original Phillips paper (1958) was an empirical investigation
into the relationship between money wage inflation and unemployment, Phillips
opens his paper with an outline sketch of the underlying theoretical reasoning
that could be used to explain why we might expect to observe a negative
relationship between these two variables. He opens with these words:
When the demand for a commodity or service is high relative to the supply of it
we expect the price to rise, the rate of rise being greater the greater the excess
demand. Conversely, when the demand is low relative to the supply we expect the
price to fall, the rate of fall being greater the greater the deficiency of demand. It
seems plausible that this principle should operate as one of the factors determining
the rate of change of money wage rates.
Following Phillips’s pioneering work, there developed two strands to the
literature, one theoretical, the other empirical. On the empirical front, economists
were interested to establish whether a stable relationship between
inflation and unemployment prevailed in other market economies (for a discussion
of the empirical literature, see Santomero and Seater, 1978). As far as
the simultaneous achievement of low inflation and low unemployment was
concerned, the discovery of a possible stable trade-off between these two
objectives implied a policy dilemma, one which might be overcome if the
curve could be shifted to the left by appropriate economic policies. However,
the design of effective policies to achieve this objective would first necessitate
a coherent theoretical explanation of the economic forces which lay
behind the relationship.
The first major attempt to provide a robust theoretical underpinning to the
curve was provided by Lipsey (1960) through the combination of two postulated
relationships: (i) a positive linear relationship between the rate of increase
in money wages and the excess demand for labour (XL), and (ii) a negative
non-linear relationship between excess demand and unemployment. These
postulated relationships are given in equations (3.7) and (3.8).
W˙ (X ) [(D S )/S ] = α L = α L − L L (3.7)
XL = β(U) (3.8)
where DL is the demand for labour, SL is the supply of labour, α is a positive
coefficient of wage flexibility, and β is a variable negative parameter such
that when XL → 0, U = U* and U* > 0; and when XL → ∞, U → 0. By
combining these two postulated relationships, Lipsey was able to provide an
economic rationale for Phillips’s observed non-linear inverse relationship
between the rate of change of money wages and unemployment shown in
Figure 3.14.
The relationship between wage change and excess demand for labour is
illustrated in Figure 3.15. Panel (a) shows that at any wage rate below We ,
wages will rise as a result of excess demand in the labour market. Panel (b)
shows that the rate of increase in money wage rates will be greater the larger
the excess demand for labour. For example, at a wage rate W1 in panel (a)
there is an excess demand for labour of aa. This excess demand is equal to 0a
in panel (b) and results in a rate of increase in money wage rates of W˙1. The
relationship between excess demand for labour and unemployment is illustrated
in Figure 3.16. Even when the labour market clears (that is to say, there
is neither excess demand nor excess supply) there will be some positive
amount of unemployment due to frictions in the labour market as people
change jobs and search for new employment, that is, 0e in Figure 3.16.
Lipsey argued that, although unemployment would fall in response to positive
excess demand (for example, jobs become easier to find as vacancies
increase), unemployment would only asymptotically approach zero. In other
words, steadily increasing excess demand would be accompanied by increasingly
smaller reductions in unemployment.
In summary, Lipsey’s rationale suggests that, in its simplest form, the rate
of change of money wages depends on the degree of excess demand (or
supply) in the labour market as proxied by the level of unemployment. This
can be expressed by the equation:
W˙ = f (U) (3.9)
Referring back to Phillips’s opening statement in his 1958 paper, it is clear
that he viewed the high correlation between money wage inflation and unemployment
as strong evidence in favour of the ‘demand pull’ explanation of
inflation.
In Lipsey’s model, due to labour market frictions, equilibrium in the labour
market occurs when U = U* > 0 (see Lipsey, 1960, pp. 470–71). When U = U*,
the number of job vacancies (V) is equal to the number of unemployed who
are actively seeking work. Since SL equals the total number employed (E) and
unemployed (E + U), and DL equals the total number of vacancies (V) plus
the number employed (V + E), we can express the proportional excess
demand for labour as follows:
XL = [(DL − SL )/SL ] = [(V −U) /(E +U)] (3.10)
Letting v = V/SL and u = U/SL, we can express the excess demand for labour
in terms of variables that can be measured, that is the vacancy rate (v) and the
unemployment rate (u).
140 Modern macroeconomics
XL = v − u (3.11)
Over the business cycle the vacancy rate will be positively related to XL and
unemployment will be negatively related to XL, assuming the quit rate does
not exceed the hiring rate as XL increases.
Later, Hansen (1970) refined Lipsey’s analysis by assuming that vacancy
and unemployment rates are related in a hyperbolic form, that is, h = vu
where h = coefficient of friction in the labour market (with no friction in the
labour market h = 0 and either v or u = 0). The relationship between XL, u
and v when there are frictions present in the labour market is shown in Figure
3.17.
In panel (a) we can see that even when excess demand for labour is zero,
both the unemployment and vacancy rates are positive, reflecting friction in
the labour market. In a frictionless labour market the relationship between XL,
v and u will be a 45° line, as shown by AB. Panel (b) of Figure 3.17 shows all
the combinations of vu tracing out a hyperbolic curve. Anywhere along the
45° line indicates equilibrium in the labour market since with XL = 0, we also
have v = u. The existing degree of friction illustrated in Figure 3.17, panel
(b), is indicated by the position of the hyperbolic curve at F. With increasing
friction in the labour market this curve will shift out. In turn this will cause
the Phillips curve to shift to the right since the level of unemployment
consistent with XL = 0 increases as labour market friction increases. There is
strong evidence, for example, that such a shift occurred in the UK economy
in the late 1960s and early 1970s (Gujarati, 1972; see also Taylor, 1972).
Given Hansen’s refinements, the Phillips relationship can now be expressed
in the following form:
W˙ = α(h/u − u) + w* = αh/u − αu + w* (3.12)
where w* is exogenously determined wage inflation (for example, brought
about by trade union power). In (3.12) we can see that the slope of the
Phillips curve is dependent on the coefficient of wage flexibility, α, and the
position of the Phillips curve will be influenced by w* and also the degree of
friction in the labour market, h. The more inflexible the labour market the
higher the degree of friction, and the higher will wage inflation be for any
given level of unemployment (see Rothschild, 1971; Frisch, 1977; Lipsey,
1978).
During the 1960s the Phillips (1958) curve was quickly taken on board as
an integral part of the then-dominant orthodox Keynesian paradigm, not least
because it was interpreted by many orthodox Keynesians as implying a stable
long-run trade-off which provided the authorities a menu of possible inflation–
unemployment combinations for policy choice. Within academia the
textbook interpretation of the Phillips curve came to be presented as a proposition
that permanently low levels of unemployment could be realistically
achieved by tolerating permanently high levels of inflation. As James Galbraith
(1997) points out, in 1968 mainstream American Keynesians were ‘committed
to Samuelson and Solow’s (1960) version of the Phillips curve’. According
to Robert Leeson (1994a, 1997a, 1999), this is not how Bill Phillips himself
ever viewed the relationship he had discovered. In Leeson’s view, Phillips’s
1958 paper was an attempt to locate the level of unemployment consistent
with price stability. Richard Lipsey has confirmed that Phillips had ‘no tolerance
for accepting inflation as the price of reducing unemployment’ (Leeson,
1997a). However, up to at least the late 1960s the prevailing Keynesian
economic orthodoxy used the Phillips curve to predict the rate of inflation
which would result from different target levels of unemployment being attained
by activist aggregate demand policies, with particular emphasis on
fiscal instruments. As DeLong (1998) points out, once those target rates of
unemployment kept falling, the inflationary outcome of this approach to
macroeconomic policy was inevitable and duly arrived with a vengeance with
the ‘Great Peacetime Inflation’ of the 1970s.
One of the main reasons why the Phillips curve was quickly adopted by
orthodox Keynesians was that it seemed to provide an explanation of inflation
which was missing in the then-prevailing macroeconomic model. The
reader will recall from the discussion contained in section 3.3 that within the
IS–LM model the price level is assumed to be fixed at less than full employment,
with the result that up to full employment, changes in aggregate demand
affect the level of real income and employment. Up to full employment
money wages are assumed to be fixed and unresponsive to changes in aggregate
demand. Only when full employment is reached will changes in aggregate
demand affect the price level. The Phillips curve allowed the orthodox
Keynesian theory of output and employment determination to be linked to a
theory of wage and price inflation. Following Lipsey (1978), this is illustrated
in Figure 3.18. The top panel of Figure 3.18 depicts the standard IS–LM
model, while the bottom panel shows the Phillips curve with the modified
axes of price inflation (P˙ ) and output/income (Y). Panel (b) is derived by
assuming (i) that the level of output depends on the level of employment and
that the level of unemployment is inversely related to the level of employment,
and (ii) a hypothesis that prices are set by a mark-up to unit costs of
production, the main component of which is wages. Put in its simplest form,
the mark-up pricing hypothesis suggests that price inflation depends on money
wage inflation minus productivity growth. In this context it is interesting to
note that the estimated Phillips curve (Figure 3.14) showed that an unemployment
level of approximately 2.5 per cent was compatible with stable
prices because at this level of unemployment the rate of change of money
The orthodox Keynesian school 143
Figure 3.18 The link between the Keynesian model and wage and price
inflation
wages was approximately equal to the then average growth of productivity of
2 per cent. Suppose the economy is initially operating at a full employment
level of income (YFE), that is, the intersection of IS0 and LM0 in panel (a) of
Figure 3.18. Reference to panel (b) reveals that the full employment level of
income is compatible with stable prices; that is, ˙P = 0. Following a onceand-
for-all expansionary real impulse, the IS curve shifts outwards to the
right, from IS0 to IS1, and real income rises above its full employment level of
YFE to Y1. Reference to panel (b) reveals that as income rises above its full
employment level, price inflation increases to P˙1. As prices increase, the real
value of the money supply is reduced, causing the LM curve to shift to the
left, from LM0 to LM1, and the economy returns to full employment, that is,
the intersection of IS1 and LM1 in panel (a). At full employment stable prices
prevail, that is, ˙P = 0 in panel (b).
Following the influential contribution from Samuelson and Solow (1960),
the Phillips curve was interpreted by many orthodox Keynesians as implying
a stable long-run trade-off which offered the authorities a menu of possible
inflation–unemployment combinations for policy choice (see Leeson, 1994b,
1997a, 1997b, 1997c). Following the Samuelson–Solow paper the trade-off
has generally been expressed in terms of price inflation rather than wage
inflation. However, by the late 1960s/early 1970s, both inflation and unemployment
had begun to increase, as is evident from Tables 1.4 and 1.5. As we
will discuss in the next chapter, the notion of a stable relationship between
inflation and unemployment was challenged independently by Milton Friedman
(1968a) and Edmund Phelps (1967), who both denied the existence of a
permanent (long-run) trade-off between inflation and unemployment.
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