Advanced Lecture Notes for Hall and Taylor, Chapter 4

Course Instructor: Professor Leigh Tesfatsion
Last Updated: 29 January 1996


Basic References:  Hall and Taylor, Chapter 4;
                   Study Guide, Chapter 4.


     In this chapter, HT first review the determinants of the
aggregate supply of goods and services in an economy in any
given period T:

    (a) the labor force [quantity and quality];

    (b) the stock of productive capital [quantity and quality];

    (c) and technology.

     They then provide an extended discussion of the notion of
"potential real GDP," previously introduced in brief terms in
Chapter 3.  Specifically, HT interpret "potential real GDP" as
potential (i.e., full employment) aggregate supply.  Thus,
potential GDP in any period T measures an economy's
#capabilities# for producing goods and services during period T,
conditional on the given labor force, capital stock, and state
of technology.  For concreteness, HT generally take T = one

     The remaining portions of chapter 4 discuss various factors
affecting the growth of potential GDP over time.


     The #real wage# is the nominal wage divided by the cost of
living as measured by some appropriate price index--e.g., the
CPI or the GDP implicit price deflator P.  In this chapter HT
take the latter index P as the price index and define:

(4.1)      W(T)  =  nominal wage during period T

                        Total labor earnings during T
                 =   ----------------------------------
                    Total number of hours worked during T

                 =      Average hourly wage during T.

(4.2)     ------  =   real wage during period T.

     The #potential employment for period T# is defined to be
the volume of employment N*(T) that would obtain in period T,
given existing incentives such as fringe benefits, unemployment
insurance, etc., if real wages were fully flexible and
responsive to demand and suply pressures.

(4.3)     N*(T)  =  the potential (or "natural") level of
                    employment for period T

                 =  amount of employment which would obtain in
                    period T, given existing incentives such as
                    fringe benefits, unemployment insurance,
                    etc., if real wages were fully flexible and
                    responsive to demand and supply pressures.

     Suppose the maximum amount Y of real GDP which can be
produced from any given amount (N,K) of labor and capital used
in production, given the current technology A, is described by
an #aggregate production function#

(4.4)      Y  =  F(N,K,A)  .

It is assumed that the production function F(N,K,A) is an
increasing function of N, K, and A---that is, the partial
derivatives of F(N,K,A) with respect to N, K, and A, denoted by
F_N, F_K, and F_A, are assumed to be strictly positive.  Thus,
for any given K and A, F(N',K,A) is strictly greater than
F(N'',K,A) if and only if N' > N'', and similarly for changes in
K (holding N and A fixed) and A (holding N and K fixed).

     The level of real GDP, Y*(T), which would result in period
T if employment N were equal to potential employment N*(T), and
the existing capital stock K(T) were fully in use, is called the
#potential (or "natural") level of real GDP#.

(4.5)      Y*(T)  =  the potential (or "natural") level of real
                     GDP for period T

                  =  F(N*(T),K(T),A), where

           N*(T)  = potential employment for period T

           K(T)   = existing stock of capital for period T

     The unemployment rate U*(T) which prevails when real GDP
coincides with potential real GDP is called #the natural rate of
unemployment#.  Currently, U*(T) seems to be about 6 percent in
the U.S.

     The reason the natural rate of unemployment is not zero is
that there is always #frictional unemployment#---e.g., people in
the process of changing jobs, or engaging in job search,
acquiring new training, etc.  Some economists thus refer to
U*(T) as the period T rate of #voluntary# unemployment.


     We will now undertake a more detailed understanding of the
market equilibrium interpretation for N*(T) and Y*(T) which HT
and other macroeconomists ascribe to.


     The #labor demand curve# shows the maximum amount of labor
which profit-maximizing firms would be willing to hire at each
possible different real wage, taking as given the existing
capital stock.  Profit maximization requires that this demand
for labor be such that the marginal product of labor is just
equal to the real wage.  Recall that the marginal product of
labor is the incremental change in produced output due to an
incremental change in labor input.  Thus, letting N^D denote the
labor demand of firms, the requirement that the marginal product
of labor be equal to the real wage can be expressed in the form

(4.6)           F_N(N^D,K(T),A)   =   W/P,

where the left-hand-term in (4.6) denotes the derivative of the
aggregate production function F(N,K,A) with respect to N,
evaluated at (N^D, K(T), A).  Under normal production
circumstances, one would expect to see a downward sloping labor
demand curve in the N-W/P plane.

               -----------------------------  N

         Fig. 4.1: Downward Sloping Labor Demand Curve


     The #labor supply curve# shows the maximum amount of labor
which households would be willing to supply at each different
real wage.  Letting N^S denote household labor supply, it will
be supposed that the labor supply curve takes the form

                       N^S = h(W/P).

     Note that W/P measures the "price" (opportunity cost) of an
hour of leisure.  Consequently, in analogy to other goods, one
might expect to see the demand for leisure #fall# (and hence the
supply of labor #rise#) as the real wage W/P increases, implying
an upward sloping labor supply curve.  Call this the "price
effect" of an increase in W/P.

     Nevertheless, an increase in W/P also represents a direct
increase in #income# (or wealth = accumulated income); and this
increase in income is more substantial the longer the increase
in W/P is expected to last.  If leisure is a "normal good" in
the sense that demand for leisure increases with increases in
income, then an #increase# in W/P, viewed as an increase in
income, would tend to #increase# the demand for leisure and
hence to #decrease# the supply of labor.  Call this the "wealth

     The wealth effect and price effect thus tend to move the
supply of labor in opposite directions, implying that the #net#
change in labor supply following upon a wage increase is
theoretically ambiguous.  Labor supply might increase in
response to an increase in the real wage, resulting in an upward
sloping labor supply curve (price effect outweighs wealth
effect), or it might decrease, resulting in a backward bending
labor supply curve (wealth effect outweighs price effect).  In
Fig. 4.2, for example, the labor supply curve becomes backward
bending (wealth effect outweighs price effect) for real wages
higher than (W/P)'.

              |              .
              |              .
               -----------------------------  N
              0              N'

         Fig. 4.2: Backward Bending Labor Supply Curve

     This theoretical ambiguity about the slope of the labor
supply curve is reflected in empirical estimates showing that
estimated labor supply curves tend to be fairly steeply sloped.
Actual labor supply thus seems to be fairly insensitive overall
to changes in the real wage, suggesting that the wealth and
price effects are offsetting one another.

#DETERMINATION OF N*(T), (W/P)*(T), and Y*(T)

     N*(T) and (W/P)*(T) are then jointly and simultaneously
determined as the point of intersection of the demand and supply
curves for labor.  Given this derivation, N*(T) and (W/P)*(T)
are also referred to as the period T #full employment# levels
for employment N and the real wage rate W/P.

 (W/P)*(T) |...................... LE
           |                     .
           |                     .
           |                     .
            -------------------------------------------------    N
           0                   N*(T)

             Fig. 4.3: Labor Market Equilibrium at Point LE

     Once N*(T) is determined, Y*(T)---the potential real GDP
for period T---is determined as the maximum amount of output
which can be produced using N*, taking as given the existing
capital stock K(T).  Given this derivation, Y*(T) is also
referred to as the #full employment# level of real GDP.

  Y*(T) |
         ---------------------------------------------------   N
        0                  N*(T)

   Fig. 4.4: Determination of potential (full employment) GDP

HT define the "potential output line" for period T to be the
vertical line at Y = Y*(T).  Increasingly, macroeconomists now
use the more accurate term "full employment line" for the
vertical line through the full employment level of output Y*(T).
We will follow this latter usage.

             P                 FE Line
             |                    |
             |                    |
             |                    |
             |                    |
             |                    |
             |                    |
             |                    |
              ---------------------------------------  Y
             0                  Y*(T)

     Fig. 4.5: The Full Employment (Potential Output) Line


     N*(T)  =  "potential" or "natural" or "full employment"
                level of employment for period T; hereafter we
                will use the latter term.

     Y*(T)  =  "potential" or "natural" or "full employment"
                level of real GDP for period T; hereafter we
                will use the latter term.

 (W/P)*(T)  =  "potential" or "natural" or "full employment"
                level of real wage in period T; hereafter we
                will use the latter term.

#Key Points to Note#

     (a)  The period T full employment levels N*(T), (W/P)*(T),
and Y*(T) depend #only# on the period T supply and demand curves
for labor, and on the period T capital-conditioned production
function F(N,K(T),A).  Unless there is some change either in the
labor supply schedule h(W/P), the production function F(N,K,A),
or the capital stock K(T), these full employment levels will be
#unchanged# over time.  Note in particular that Y*(T) does not
vary in response to changes in the period T market price P(T).

     (b) #Unanticipated# disturbances to the economy in period T
which affect the period T production function, and hence change
the period T full employment levels Y*(T), N*(T), and (W/P)*(T),
are referred to as period T #supply shocks#.  For example---as
will be discussed below---the 1973 and 1979 sharp increases in
the price of oil are viewed as prime examples of supply shocks.

    (c) But note that a variety other types of factors, both
anticipated and unanticipated in period T, can affect these full
employment levels over time, such as: (a) changes in the capital
stock K(T) as the result of ongoing investment; (b) changes in
household tastes for labor vs. leisure, which affect the labor
supply function h(z); and (c) gradual changes in technology
which affect the production function F(N,K,A), e.g., upward
shifts in A reflecting technological improvements that permit a
higher level of output for each given level of N and K.

     QUESTION:  How would a change in the period T price of oil
be reflected in our diagrams for the determination of Y*(T),
N*(T), and (W/P)*(T)?

     First note that oil is an intermediate good and not a final
good, hence its price does #not# enter into the implicit GDP
deflator, P(T).  In our simplified model of production, oil
enters as a capital input to production.  An increase in the
price of oil increases the #costs# of production to each
oil-using firm, and hence would result in firms cutting back on
their oil usage.  This cutback in the use of oil in turn implies
that less output can be produced for any given quantity of other
inputs to production.  In particular, then, the period T
production function F(N,K(T),A) shifts down for each level of N
as K(T) shifts down in response to the decrease in oil usage.

     The downward shift in the production function F(N,K(T),A)
due to the downward shift in K(T) implies less capital input is
available per worker at each level of N.  This in turn will
generally imply a decrease in the #productivity# of labor for
each given level of N, and hence a downward shift in the period
T labor demand curve.  Assuming the period T labor supply curve
is unaffected, this implies a drop in the full employment level
of employment N*(T), and hence also in potential output Y*(T).

     For example, it has been estimated that the increase in the
relative price of energy resulting from the 1979-1989 oil price
shock resulted in a 5.7% drop in output in the U.S.  Indeed, the
U.S. went into a recession following both the 1973 and 1979-1980
oil price shocks, with negative real GDP growth in each case,
combined with a drop in the real wage rate.

#Keynesian vs. Real Business Cycle Interpretation
of Employment Fluctuations#

     In Keynesian-type macro models, fluctuations in observed
employment N(T) over time are generally interpreted as
fluctuations #around# the trend line defined by the graph of the
full employment level of employment, N*(T).  In particular,
Keynesians believe that "involuntary unemployment", as measured
by the difference between supply and demand at any given real
wage, is a major recurring problem in the downward
(recessionary) phase of the business cycle.

     In contrast, during the past ten years an alternative
school of thought has arisen, referred to as the "real business
cycle school."  This school argues that employment N(T) in each
period T is #always# at the intersection of the labor supply and
demand curves, and hence #always# equal to its full employment
level N*(T).  According to this view, changes in employment over
time #represent fluctuations in N*(T) itself.# It is argued that
these fluctuations in N*(T) are due entirely to various types of
supply shocks---in particular, to direct shocks to the production
function ("productivity shocks").

     If the latter school of thought is right, it would have
tremendous implications for government policy.  Traditionally,
Keynesians have viewed the proper role of government as
minimizing "involuntary unemployment" in each period T.  In
contrast, the real business cycle interpretation implies that
fluctuations in employment represent the natural and desirable
responses of private optimizing agents to various productivity
shocks, hence government should not attempt to offset these

     Although the real business cycle theory has generated quite
a research industry, many economists argue that the empirical
support for this theory to date is not compelling.  They argue
that adverse "productivity shocks" in practice are not large
enough to explain, in and of themselves, the timing and
magnitudes of the recessions experienced by the U.S.; and that
shocks to aggregate demand (particularly money shocks) are
equally, if not more, important in understanding the business

     To test the real business cycle theory and other theories
of the business cycle, it is essential to have a way of
measuring the magnitude and sign of productivity shocks.  One
approach to this measurement is through the "Solow growth
formula."  This formula is developed in the next section.



     In most years, potential real GDP grows relative to its
previous magnitude.  Focusing on the supply side of the economy,
three factors contribute to the growth of potential real GDP:

(1) growth in the quantity and/or quality of the labor force;

(2) growth in the quantity and/or quality of the capital stock;

(3) changes in "total factor productivity" stemming from
    technological improvements in the efficiency with which
    labor and capital inputs are transformed into output.

     Growth in the #quantity# of labor and capital inputs, and
to some extent the #quality# of labor and capital inputs, is in
principle measurable; but changes in total factor productivity
are more problematic.  Many researchers attempt to measure
changes in total factor productivity---or "productivity change"
for short---by defining productivity change as a residual change
in actual #measured# real GDP after changes in the quantity and
quality of labor and capital inputs have been accounted for.

[Change in Productivity] = [Total change in real GDP]

             - [Change in real GDP due to change in N usage]

             - [Change in real GDP due to change in K usage],

where labor and capital input measures have been adjusted to
account for changes in quality.  For example, N might be
measured in hours of "unskilled labor."  An hour of skilled
labor would then be counted as more than one hour of "unskilled

     This was the approach taken by Robert Solow, a 1987 Nobel
prize winner in economics.  The "Solow growth formula" is now so
well known, and so extensively used in empirical and policy
research, that it is important we take a bit of time to
understand its derivation, and its potential uses and


     Suppose the production function F(N,K,A) for period T takes
the particular form

(4.7)          Y  =  Af(N,K),

so that the technology factor A multiplies some function f(N,K)
of N and K.  The technology factor A is then an index of #total
(or overall)# factor productivity in period T.  If A grows by
one percent during period T, it means that, by the end of period
T, the economy can produce one percent more output (real GDP)
from each given amount of labor N and capital K than it was
capable of producing at the beginning of period T.

     More generally, the representation (4.7) for the aggregate
production function implies that any growth in Y from one period
to the next must be attributable either to a change in total
factor productivity, A, or to a change in labor usage, N, or to
a change in capital usage, K.

     Robert Solow used representation (4.7) to derive a formula
connecting the percentage rate of change in Y with the
percentage rates of change in A, N, and K.  The derivation of
this formula is discussed in the appendix to Chapter 4 of Hall
and Taylor.  Hall and Taylor use discrete time changes
[Y(T+1)-Y(T)] in place of derivatives dY(T)/dT, so that their
derivation is heuristic rather than rigorous.  Derivatives will
be used in the following discussion so that the relations
obtained are exact rather than approximate.

     The basic math fact used to derive this formula is as
follows:  If V is a time-dependent variable which is expressable
as a #product# of two other time-dependent variables X and Z,
i.e., if

(4.8)           V(T)   =    X(T) x Z(T),

then the percentage time-rate of change of V at T is given by
the #sum# of the percentage time-rates of change of X and Z,

            DV(T)            DX(T)             DZ(T)
(4.9)      -------    =      -----    +       -------  ,
             V(T)             X(T)              Z(T)

where DV(T) = dV(T)/dT, the derivative of V respect to time T,
and similarly for X and Z.

     For the case at hand, Y plays the role of V, A plays the
role of X, and f(N,K) plays the role of Z.  Thus, recalling that
period T real GDP is given by Y(T) = A(T) x f(N(T),K(T)),

            DY(T)         DA(T)          Df(N(T),K(T))
(4.10)     -------   =    ------   +     ------------- .
             Y(T)          A(T)           f(N(T),K(T))

Recalling the standard formula for total differentiation of a
function of two variables---i.e., Dh(u,v) = h_uDu + h_vDv for
any differentiable function h(u,v)---the far right term in
(4.10) can be further broken down as follows.

         Df(N(T),K(T))            DN(T)            DK(T)
(4.11)   -------------  =  M_N(T) -----  +  M_K(T) -----  ,
          f(N(T),K(T))             Y(T)             Y(T)

where M_N(T) = A(T)f_N(N(T),K(T)) denotes the period T marginal
product of labor and M_N(T) = A(T)f_K(N(T),K(T)) denotes the
period T marginal product of capital.

     Suppose firms face "competitive" labor and capital input
markets, and hence take prices as given.  Profit-maximization by
firms then requires that labor and capital inputs N and K are
used up to the point where their marginal products M_N and M_K
are equal to their real rates of return.  The real rate of
return on capital K is defined to be

(4.12a)  R^K
        ----   =  the real rate of return on capital K  (rent,
         P       interest, dividend payments, economic profits)

whereas the real rate of return on labor N is defined to be

(4.12b)   W
         ---    =   the real wage rate  .

Consequently, profit-maximization requires

(4.13a)                       Df(N(T),K(T))         W(T)
          M_N(T)   =    A(T)  -------------   =    ------ ;
                                  DN(T)             P(T)

(4.13b)                        Df(N(T),K(T))        R^K(T)
          M_K(T)   =    A(T)  ---------------  =   -------- .
                                  DK(T)              P(T)

Dividing through by A(T), one obtains

(4.14a)           W(T)               Df(N(T),K(T))
               ---------     =     -----------------     ;
                P(T)A(T)                 DN(T)

(4.14b)          R^K(T)               Df(N(T),K(T))
               ----------    =     ----------------    .
                P(T)A(T)                 DK(T)

Combining (4.10), (4.11), and (4.14), recalling Y = Af(N,K), and
dropping time subscripts for ease of presentation,

          DY        DA          W   DN           R^K   DK
(4.15)   ----   =  ----   +    --- ----    +    ---- ----
           Y         A          P    Y            P    Y

         DY         DA          WN   DN          R^KK    DK
        ----   =   ----   +    ---- ----   +    ------ ----  .
          Y          A          PY    N           PY     K

                             "labor            "capital
                              share"             share"

     The ratio WN/PY is the fraction of nominal GDP (i.e., the
fraction of PY) that is paid out to labor, and the ratio R^KK/PY
is the fraction of nominal GDP paid out to capital.  These
ratios have been remarkably stable over time, equalling
approximately .7 and .3, respectively.  Substituting these
empirical share estimates into (4.15), we finally arrive at
Solow's famous formula expressing growth in national income as
the sum of time-rates of change in productivity, labor, and
capital inputs:


          DY             DA              DN              DK
(4.16)   ----     =     ----    +    .7 ----    +    .3 ----  .
           Y              A               N               K

[Compare Hall and Taylor, equation (4-7).] Re-arranging terms in
(4.16), one then obtains

          DA            DY               DN               DK
(4.17)   ----    =     ----    -    .7  ----    -    .3  ----  .
           A             Y                N                K

Since all terms on the right-side of (4.17) are measurable in
principle, (4.17) gives an empirically operational way to
measure "productivity growth" DA/A.


     According to the Solow growth formula (4.16), a 1% increase
in the growth rate of real GDP requires nearly a 3.3% increase
in the growth rate of physical capital.  That is:

(4.18)  1% increase in DK/K   --->   .3% increase in DY/Y  ;


(4.19)  (1/.3)% = 3.3% increase in DK/K --> 1% increase in DY/Y.

     However, also according to (4.16), employment growth has
over twice the leverage of capital growth.  Specifically:

(4.20)  1% increase in DN/N   ---->   .7% increase in DY/Y


(4.21)  (1/.7)% = 1.43% increase in DN/N --> 1% increase in DY/Y.

Finally, the most leverage of all is obtained from a change in
productivity growth.  Specifically,

(4.22)   1% increase in DA/A   ------->    1% increase in DY/Y  .


     In Figure 4-7, Hall and Taylor give estimates for the
factor contributions DN/N, DK/K and DA/A to real GDP growth,
DY/Y, for the U.S. from 1961 to 1990.  In order to smooth out
business cycle fluctations, the estimated factor contributions
are averaged over ten-year periods.  The data reveal a
relatively increasing contribution to GDP growth from both
capital investment, DK/K, and labor growth, DN/N, over this time
period.  However, there appears to have been a marked decrease
in the relative contribution from total factor productivity
growth, DA/A.

     A more dramatic presentation of similar empirical findings
can be found in the work of E. Denison, an economist at the
Brookings Institution.  According to Denison, the annual real
GDP growth rate DY/Y over 1929-1982 averaged about 2.92%.  The
breakdown by source, averaged over this period, is as follows:


          DY             DA              DN              DK
(4.23)   ----     =     ----    +    .7 ----    +    .3 ----  .
           Y              A               N               K

         2.92%         1.02%            1.34%              0.56%

On the other hand, the breakdown by source of average real GDP
over the shorter more recent period 1973-1982 is strikingly


          DY             DA              DN              DK
(4.24)   ----     =     ----    +    .7 ----    +    .3 ----  .
           Y              A               N               K

         1.55%         -0.27%            1.13%              0.69%

     In other words, Denison estimated that any given
combination of labor and capital inputs would have produced
#less# output in 1982 than in 1973.  This is yet another
manifestation of the "productivity puzzle" mentioned in the
first class lecture.  The main message of Denison's findings is
that the slowdown in output growth is #not# due to a slowdown in
the growth of labor or capital inputs.  Rather, the slowdown is
due largely to a slowdown in productivity growth.


     Various explanations have been offered for the productivity
slowdown, but no compelling single explanation has been found.
Some economists have argued that it simply reflects a
measurement problem---the underestimation of face-paced
#quality# changes in both labor and capital inputs, resulting in
an underestimation of productivity growth.  Other economists
have pointed to increased regulations in the workplace, the
lingering impact of the 1973 and 1979-1980 oil price shocks, and
a slower rate of technological innovation.

     But recently a consensus seems to be forming across all
sectors of the U.S. economy that a large part of the slowdown
must be attributed to a decine in educational quality, leading
to a sharp decline in the human capital embodied in the labor
force.  One very important form of human capital in decline
seems to be entrepreneurial skill.

See:  John H. Bishop, "Is the Test Score Decline Responsible for
      the Productivity Slowdown?," American Economic Review,
      (March 1989), pp. 178-197.

      W. J. Baumol, "Entrepreneurship: Productive, Unproductive,
      and Destructive," Journal of Political Economy (October
      1990), Part 1, pp. 893-921.

     Moreover, there now seems to be widespread agreement that
the deteriorating nature of the U.S. economy's infrastructure
(i.e., its highways, bridges, dams, airports, and other publicly
owned capital) is also a significant factor in the productivity
slowdown.  Over the past twenty years, U.S. government
investment in infrastructure has taken place at a low rate,
relative both to American experience and to rates of
infrastructure investment in other developed countries.

      The primary way to stimulate output growth through
increased labor #quality# is increased expenditures on human
capital, e.g., education, training, health and safety measures,
etc.  An increase in labor #usage# might be encouraged by
increasing labor supply at each real wage by lowering marginal
tax rates on wage income, and/or by increasing labor demand at
each real wage by reducing private firm sector responsibility
for provision of key worker benefits, e.g., health insurance.

     The primary way to stimulate output growth through
increased capital #quality# is through increased expenditure on
research and development (R&D).  An increase in capital #usage#
(as opposed to capital quality) might be stimulated by various
types of tax credits or deductions (e.g., an investment tax

     Finally, output growth might be stimulated through
increased productivity growth (increases in DA/A) by encouraging
more efficient exploitation of economies of scale, better
organization of the workplace, better product distribution
systems, better allocation of resources (e.g., job availability
services), an improved work ethic, etc.

     Government itself might increase its expenditures on these
items, or it might encourage the private sector to increase
expenditures on these items by some type of tax and/or transfer
policy.  The success of past and current government attempts to
implement such policies will explored at a later point in the
course after the complete HT model has been assembled.

     One aggressive approach which has been proposed for
increasing productivity growth is an industrial policy---a
growth strategy in which the government attempts to influence
the nation's pattern of industrial development through taxes,
subsidies, or regulation.  Critics argue that there is no good
reason to expect that the government will be better than the
private sector at picking the most promising technologies and
oversee their development.

    See:  Gene Grossman, "Promoting New Industrial Activities:
          A Survey of Recent Arguments and Evidence," OECD
          Economic Studies, Spring 1990, pp. 87-125.


     The real business school has one important fact on its
side.  When changes in productivity growth are measured by
changes in DA/A, in accordance with the Solow growth formula,
the changes are large.  Moreover, empirical estimates for DA/A
increase at the same time that growth rates for Y and employment
N rise---namely, during boom times---and decline sharply in a
recession.  The real business cycle view is that these changes
in the empirical estimates for DA/A represent exogenous changes
in productivity growth which #cause# the ups and downs in real
GDP growth.

     Critics of the real business cycle theory give another
interpretation for these measured changes in DA/A.   They argue
that these measured changes in DA/A are #caused by# changes in
DY/Y and DN/N rather than vice versa.  Specifically, they argue
that three factors make measured changes in productivity growth
move with changes in output and employment growth:

    (a) #Labor hoarding#:  Firms find it costly to lay off
skilled workers when production declines and rehire them when
production increases.  Hence DN/N remains fairly steady even
during downturns and upturns.  Thus, productivity #per worker#
tends to drop in times of low production (excess workers are
still kept on the payroll) and rise during times of high
production (excess workers now become more productive).

    (b) #Market power#:  Firms with market power are able to pay
a real wage #lower# than the marginal product of labor.
Productivity measurement methods which presume workers are paid
real wages equal to their marginal product are biased because
they give workers too little credit.

    (c) #Increasing returns#: With increasing returns to scale,
an across-the-board 1% increase in inputs results #more# than a
1% change in output.  Standard productivity growth measurements
attribute this difference to productivity growth rather than to
increasing returns.  Consequently, every general expansion in
inputs is bound to result in a concurrently measured increase in
"productivity growth" and vice versa.