New techniques in the measurement of multifactor productivity

The Journal of Productivity Analysis, 1,267-285 (1990) © 1990 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.

New Techniques in the Measurement of Multifactor Productivity*

CATHERINE MORRISON Tufts University, Department of Economics, Medford, MA 02155 and National Bureau of Economic Research, Cambridge, MA.

W. ERWIN DIEWERT University of British Columbia, Department of Economics and National Bureau of Economic Reasearch, Cambridge, MA.

A b s t r a c t

This article outlines procedures for adjustment for characteristics of the production structure which are typically ignored in productivity growth computations but affect the correct valuation of inputs and outputs. There are many such characteristics, including changes in the terms of trade and fixity of factors, but only one appears to have much impact on productivity fluctuations: imperfect competition in output and input markets. To illustrate this, traditional and adjusted productivity growth indexes based on assumed markups are constructed for the U.S., Canadian and Japanese business sectors for comparison with each other and with other adjustments done in previous studies. The methodology is based on finding shadow values of all domestic and traded outputs and inputs to use to evaluate the contribution of each to profits. We find that evidence of markups suggests adjustments in traditional measures that are quite significant and which tend to smooth both cyclical and time trends in productivity growth.

1. Introduct ion

In the past two decades, large product ivi ty f luctuations exper ienced in the U.S. and other

industr ial ized countries have s t imulated substantial research on the factors under ly ing this

turbulence. Numerous studies in the 1970s focused on the impacts of energy prices on

product iv i ty per formance in the U.S., because the f luctuations apparently c o m m e n c e d at

approximate ly the same t ime as the O P E C - i n d u c e d energy price changes. Other researchers

noted that the product iv i ty decl ine recognized in the 1970s had its roots earlier, in the late 1960s, and suggested that other measurement issues might be involved. 1 These measure-

ment approaches, however , have not yet been part icularly fruitful as explanat ions for the

dramatic product ivi ty growth s lowdown seen f rom the vantage of the late 1970s, because

they have tended to have only a modes t impact in expla ining the s lowdown.

By the early 1980s, roughly speaking, the general interest in expla in ing the product ivi ty

s l owdown of the 1970s had been refined in the l ight of additional ev idence and forces. For example , it was recognized that a l though strong product ivi ty declines were evident at

*The refereeing process of this paper was handled through M. Denny.

268 MORRISON AND DIEWERT

certain times in the 1970s, the overall trend was not as strongly downward as alleged in the 1970s, particularly in manufacturing which appears to have regained almost its former growth rate. There were some instances of substantial fluctuations in the U.S. during the late 1960s to early 1980s in manufacturing, however, and certain catastrophic years such as 1970, 1975 and 1980 which did have a strong role in pulling down the overall average growth rate for some time periods. Also, for the total U.S. economy productivity growth remains in a slump which appears to have worsened since 1980.

In addition, due to the internationalization of the U.S. economy, international issues took on new significance during this time. In particular, international comparisons provided the important information that other industrialized countries, including countries with very strong productivity growth rates like Japan, also had experienced similar patterns in productivity growth fluctuations. This provided new stimulus for productivity studies comparing and contrasting production structures and their implications for productivity growth experience among different countries.

Finally, since measurement analysis and adaptations alone did not seem to provide the kind of explanations sought for productivity fluctuations, researchers have become in- creasingly interested in the theory underlying measurement issues. This methodological emphasis has become an important focus of productivity research in the past decade. A number of studies have focused on incorporating structural determinants of productivity into models of production decisions, with the goal of refining existing productivity measures and thereby providing insight into the types of changes in production structure that have affected productivity growth.

Methodological developments in productivity growth studies have taken many forms. Many of these have revolved around theoretical extensions of productivity growth analysis to accomodate characteristics of the production structure which affect correct economic valuation of inputs and outputs but are typically ignored in productivity growth computations. One of the characteristics that has been focused on in this literature is the existence of short run fluctuations in capacity utilization. Adjustments for this are based on evaluating productivity growth rates using shadow values of fixed inputs instead of market prices which may not reflect the true contribution of the input. 2 Another extension based on a similar framework but which has not received as much attention is to adjust for changes in the terms of trade between countries, which requires identifying the values of traded goods independently from those for domestic outputs. 3 Many other adaptations can be dealt with similarly to these, including those for the existence of unproductive pollution abatement capital, which requires reevaluating the valuation of output to reflect the contribution of this capital, 4 and modifications to include the impact of returns to scale.

These methodological developments have provided provocative insights both about the existence and size of different impacts on productivity growth, and also, in come cases, about comparative productivity growth trends in different industrial countries. However, although the theory highlights important deviations between what should be and what is measured for productivity indicators, empirical implementation of these models have resulted in adjustments to traditional productivity growth measures which, while not trivial, have not been large enough to help explain the dramatic productivity growth fluctuations that have been evident in the past two decades.

NEW TECHNIQUES IN THE MEASUREMENT OF MULTIFACTOR PRODUCTIVITY 269

More recently, attempts have been made to incorporate the impact of imperfect competition in output markets. This can similarly be considered to other valuation extensions by explicitly recognizing the difference between price and marginal cost when markups exist, s In addition, other output and input markets (exported goods and labor, for example) might have markups or deviations between average cost (price) and marginal (factor) cost. These adjustments may have more impact on productivity growth fluctuations than has been found for the other types of adaptations of the traditional framework.

In this article, we outline a general index number framework in which many adaptations to traditional productivity growth measures can be specified and interpreted. We use this methodology to motivate adjustments to productivity growth measures which can be thought of as adapting the valuations attached to inputs and outputs to reflect their true economic valuation. We show how this has been used to adapt measures to include terms of trade changes and capacity utilization, and then address how it may be used to incorporate the existence of market power. We then postulate different markup scenarios, and use these to evaluate the relative explanatory power of markups for observed productivity growth fluctuations.

Our conclusions are that a general framework for productivity measurement facilitates motivation and interpretion of different types of adaptations to productivity growth measures, including those for market power. We also find that the adjustments to productivity indexes for imperfect competition are larger than most adjustments for other characteristics of the production structure. In particular, the results suggest that markup behavior is important for the U.S., Canada and Japan in domestic and exported output markets and possibly also in labor markets through a backward bending supply curve. These tendencies are quite robust across countries. The combined result of the market power impacts is that traditional productivity growth estimates have tended to be downward biased, and fluctuations and downward time trends have been exacerbated.

2. An index number methodology for productivity growth measurement

Since the work by Tinbergen [1942], Solow [1958] and Jorgenson and Griliches [1967] it has become traditional to measure productivity growth from the primal or output perspec- tive as din Y/dt-dln v/dt = ~z/Y-Z~ Sk (f'Jvk) = e~, where Y represents output and v a vector of inputs, e~ is standard notation for this measure assuming a production function Y = f(v), and Sk is the share of input k in terms of the value of total output. Ohta [1975] later identified the equivalence of the primal with the cost-side measure, - (din c/dt-dln w/d O = (d /c--ZkSk'(r~Jwk) = ect (given constant returns to scale), where c is unit costs, Ect is standard notation assuming a cost function C(w,}7) = Y.c(w) and w is a vector of input prices wk. These indexes can also be measured using absolute rather than logarthmic changes as ( y t/y t-1)/(V t/V t-l) and (c t/c t-1)/(Wt/W t-~) where V and W represent share-weighted indexes of the vk and w~ quantities and prices.

An analogous exact index number approach to productivity growth measurement deals with problems resulting from the necessity of approximating time derivatives such as Y/Y


by finite differences. 6 This method can be motivated by defining a productivity function g' for each period t:

g ' ( p , v ) =-- m a x y { p "y : ( y , v ) e r ' }, ( 1 )

where y is a vector of net outputs, p is the corresponding price vector, v represents the available domestic inputs with price vector w, and F t is the technology set for period t. Using Equation (1), productivity growth is defined as:

R t ( p , v ) =- g ' ( p , v ) / g t - l ( p , v ) . ( 2 )

This measures the percentage increase in output that can be produced by the period t technology set as compared to the period t-1 technology set given p and v. If we assume that g has a translog functional form, and we choose t and v appropriately, R t can be calculated as an implicit translog index of outputs divided by a translog index of inputs, 7 Rt=a/bc, where

a =- p t . y t / p , - ~ .y~- 1, (3 a)

In b =- YN,= 1 ( 1 / 2 ) [ ( p ~ y ~ / p t . y ') + ( p t , - l y ~ - l / p t - l . y t - 1 ) ] l n ( p ~ / p ~ - l ) , ( b )

and

t t t t - 1 t - 1 / w t - 1 . v t - 1 t t - 1 l n c = - Z ~ = l ( 1 / 2 ) [ ( w i v j w "v t ) + ( w j vj ) ] l n ( v j / v j ) . ( c )

Thus the standard measure eft can be thought of as a logarithmic approximation to this measure; In R' = In a- ln b-ln c ~- e~.

Many recent developments in productivity growth measurement have focused on the relevance of these measures and the equivalence of the primal and cost measures when valuation of inputs differs from that assumed in the traditional framework. This difference could be a result of dissimilarities among components of an aggregated output or input vector (like that for a net output vector distinguishing domestic from traded goods), deviations of shadow prices from market prices (such as with fixed factors), or disparities between cost and output shares (from imperfect competition or fixity of inputs). Adapta- tions for these differences are similar conceptually; they consist of changes in one of the three component indexes of Equation (3) to take away (add) changes that should not (should) be considered part of the productivity growth measure given the interpretation desired. Developing this common framework allows a decomposition of economic performance measures based on productivity growth into the different impacts resulting from changes in the terms of trade, utilization, market power, or other technological or market forces.


3. Adaptation of productivity growth measures for valuation discrepancies

One valuation adaptation to productivity growth measures outlined by Diewert and Mor- rison [1986] distinguishes between domestic and internationally traded outputs and inputs, which allows one to measure the effects of changes in the terms of trade. This adaptation is different than most; it adds a component to the measure of economic performance that augments the impact of productivity change on welfare rather than decomposing or refining the traditional productivity growth measure. That is, terms of trade changes not measured in R t may be thought of similarly to a productivity increase; a favorable change in a country's terms of trade (the ratio of export prices to import prices) has a similar impact on domestic production. Either an increase in technology or an increase (decrease) in the price of an exported (imported) good cause an exogenous change in the value of output which is potentially available based on the same levels of inputs and domestic prices. Therefore, a combined measure of welfare change, based on the standard productivity change plus these changes, may be informative.

To consider this extension of productivity measurement more formally, it must explicitly be recognized that the net output vector y includes traded as well as domestic goods; Y=(Y*,--Ym,Yd) is a vector of net output quantities with corresponding strictly positive prices P=(Px,Pm,Pcl), where x, m, and d denote vectors of export goods, import goods and domestic output, respectively. The total value change between periods t and t-1 is the change in the entire vector, pdYd+p/yx--p,,ym, measured by Equation (3a). To isolate the change only in the output level for productivity growth measurement, the effect of price changes is generally purged by dividing by Equation (3b), which includes the prices of all the domestic and traded net outputs. However, including the terms of trade impact implies that changes in the terms of trade are not purged from the index; traded goods are not included in the summation in Equation (3b). This results in a measure including both the terms of trade effects and productivity change as in Diewert and Morrison [1986]:

W ' ( p e , v ) ~ g ' ( p a , p t , p t , v ) / g ' - l ( p d , P ' x - a , p tm-~,V ) = R , A t (4 )

In d -~ ZiX=l(1/2)[(pxt~ y , , t i / p t ' y t ) + ( p t x F l y t c l / p t - ~ ' y t - 1 ) ] l n (p,:ti/pJFa ) , ( 5 a )

t-1 t-1 t - 1 . t- ) ] l n ( p m f f p , , . ) , ( 5 b ) l n e E y ~ t = l ( 1 / 2 ) [ ( P t ~ c v ~ t j p t ' y t ) + ( P m i Ymi /P y ~ t t-~

where At= d/e, X indexes exported commodities, and M denotes imported goods. The effect of the terms of trade adjustment can be thought of as a bias in In b from

Equation (3b), where the new measure from including rather than purging terms of trade changes is In b* = In b - I n d+ln e = In b - l n A t. The bias or adjustment factor In d - l n e = In A t o r d / e = A t may be interpreted as the welfare change resulting only from changes in the terms of trade.

These traditional productivity growth and adjusted welfare measures were computed by Morrison and Diewert [1985] for the U.S. and Japanese total business sectors. The bias l n A t is not large, peaking at almost 2% lower welfare than productivity growth in 1980 for


the U.S. and and over 3% lower for Japan in 1974. The adjustment smooths productivity growth fluctuations somewhat for the U.S., although the reverse occurs for Japan.

Another adaptation to traditional productivity measurement methodology involving the deviation between shadow and market values due to fixity of factors has been pursued by Bemdt and Fuss [1986], Hulten [1986] Morrison [1986] and Schankerman and Nadiri [1986]. This problem arises because construction of Equation (2) implicitly assumes full equilibrium in both periods; the indexes are computed assuming that the long run equilibrium condition wk=r k holds, where r k represents the shadow value of the k-th quasi-fixed input vk and wk is its observed ex-ante rental price. Thus the shares used for aggregration of the input indexes (or price indexes for the cost case), computed using actual observed values of the inputs rather than the true marginal products, are mis-measured if short run fixity exists. Adjustment of the productivity growth measure in this case involves correcting for this problem, allowing decomposition of the standard measure into a technological effect and the impact of utilization changes, s

Adjustment to reflect the deviation between the observed value of an input and its actual contribution to production is not straightforward to implement because the shadow value must be identified 9 and the method used for adjustment of the traditional productivity growth index must be determined. However, the conceptual distinction between using observed as compared to shadow values can easily be motivated; computation of the adjusted productivity growth index simply requires valuation of the inputs at rk rather than wk for the inputs which are fixed.

Using our framework this requires that the measure of productivity growth Rt=a/bc, or In R t= In a-In b - In c must be adjusted to obtain Et=a/bc *, or In Et=ln a- ln b-In c*, where In c*= In c-In g+ln h,

F t t t t - I l n g ~ Y j = l ( 1 / 2 ) [ ( w f j v q / w t ' v t ) + ( w ~ j v ~ j / w t - l ' v t - 1 ) ] l n ( v q / v f j ) , ( 6 a )

___ F t t t-1. ) ] l n ( v ~ j / v t f ~ ) , ( 6 b ) In h Z j = l ( 1 / 2 ) [ ( r ~ j v ~ j / r t ' v t) + ( r q v f J r v t-1

and F represents the fixed inputs in the overall input vector. The difference between the traditionally measured index using the rental prices wk and

the adjusted measure using the shadow prices r k captured by U t = g/h represents the bias due to fixity and the resulting deviations in capacity utilization from optimal levels. Thus, E t can be written as E t = R t U t, where E t is the true or corrected productivity index purged of utilization changes. This can be interpreted as a decomposition of the traditional measure R t by writing this as R t = E t /U' , or In R t = In Et-ln U 1.

This type of bias, as documented in Morrison [1986], Berndt and Fuss [1986] and Hulten [1986], appears to be fairly small but not negligible. The measures suggest that post 1950 productivity growth in the U.S. adjusted for capacity utilization was lower overall than traditionally measured and tends to show a larger bias downward in the earlier than later years. Therefore, the productivity slowdown found in traditional measures is somewhat attenuated.

Other adaptations to the standard framework either adding to the traditional productivity growth measure or decomposing it to refine the measure and its interpretation are analo-


gous to these two adjustment approaches. These adaptations can include any type of reevaluation of value that causes a deviation between output values and costs or the correct valuation of net outputs. An example similar to the terms of trade refinement is the adjustment for pollution abatement regulation by Conrad and Morrison [1989]. This can be thought of as an adaptation to the measure of the marginal cost of output to reflect only those costs that should correctly be attributed to producing output, not producing a better environment. The Ohta [1975] adjustment for returns to scale is accomplished analogously to that above for utilization, where residually measured returns to the fixed factors is recognized to include scale economies or diseconomies. This has been empirically considered in Morrison [1986] in a slightly different context. Neither of these adaptations are numerically very large; fluctuations in productivity growth are not well explained by these characteristics of the production structure, although they do provide more correct measures which tend to have slightly less secular and cyclical trend.

4. Incorporating market power into traditional measures

One such modification of productivity growth measures which may be dealt with in this framework was addressed by Robert Hall [1988]. He noted that if price differs from marginal cost because of market power, traditional measurement of the marginal contribution of an extra unit of output to cost by the observed price is not correct for indicators such as productivity. Thus, if a measure of marginal cost can independently be determined, this should be used to value output in productivity growth measures. If the implied bias in the standard measure is significant, markups for domestic output may help explain observed cyclical fluctuations in productivity. This notion further implies that if other output or input markets such as those for exported output or labor are subject to market power this should be taken into account. Formally this requires revaluing any noncompetitive net output in Equation (3) at its marginal cost (marginal factor cost), 1° although this may be difficult because constructing valid measures for these marginal costs is problematic. 11

To develop a model which may be used to incorporate market power impacts on firm behavior, consider a production structure where the firm determines the supply of domestic output and exported goods, and the demand for domestic inputs and imported goods, and has market power in the domestic output market and possibly other net output markets. The firm's decisions can be represented by maximization of profits subject to a production function for a competitively supplied (demanded) good, where profits are the value of this good plus the value of all other net outputs (measured as negative values for inputs). If the firm faces demand functions for its outputs (supply functions for inputs), this can be incorporated by recognizing that the prices of these products are not fixed but are a function of the quantity supplied (demanded). The resulting system of equations representing the behavior of the imperfectly competitive firm can be used to motivate computations of marginal valuations of these net outputs for computation of productivity growth indexes.

More formally, let us denote the quantity of the one competitive good by x0>0 and its corresponding price by P0. We assume p0>0 if x0 is an output and p0<0 if x 0 is an input. We


also assume that there is one input Zo > 0 that is fixed in the short run and that z --- [zl,...Zm] is a non-negative vector of other outputs and inputs that are utilized by the economy in the period under consideration. If the m-th variable good is an output (input), then its price, w,,, is positive (negative). We allow each w~ to depend on the corresponding quantity z m, so in period t we have Wm= d~(Zm,t), m = 1,. . .M.

Period t technology of the economy is represented by the production function (factor requirements function if the competitive good Xo is an input ) fwhere xo ---f(zo,z,t). 12 Thus, neglecting aggregation problems, 13 the private economy's monopolistic profit-maximization problem may be written as:

M m a x z { p o f ( Z o , Z , t ) + ~ d m ( z m , t ) z m } , ( 7 )

m=l

with first order conditions

Of Odin (Zm, t ) z m = O , m=l ,M. (8) P0 ~ (Zo,Z1 . . . . . z M , t ) -}" Wm-[" OZ m , . . .

In order to allow for market power, we assume the inverse demand or supply function dm 14 has the functional form:

d m ( z m , t ) = c t t - ~ m P t l n z m , m = l . . . . , M . ( 9 )

where pt is an index representing the general price level. 15 If variable good m is an output, then dm is an inverse demand function and P~ represents a relevant price index on the other side of the market. If the inverse demand curve is downward sloping, then ~m>0. If instead the inverse demand curve is horizontal, so the economy faces a fixed selling price for good my ~m = 0 for all periods. If good m is an input into the economy, then by our sign convention, wm= dm(z,,,t) is negative. In this case, the usual upward sloping inverse supply curve gets transformed into a negative downward sloping inverse supply curve, so again we would expect [3,. to be positive. On the other hand, if the economy faces a fixed supply price for good m in all periods, ~m = 0.

If we divide Equation (9) through by P0, use the functions defined by Equation (10) to evaluate the derivative Odin/Oz~, substitute period t data into the resulting equations, and rearrange we obtain the system of M equations:

_ t _ [ ] O f ( z ~ , z ~ t ) Wm ~rn --ptm + ' , m = l . . . . M. ( 1 0 ) p t p~ Oz~

From Equation (10), we see that to adjust traditional index number techniques for measuring total factor productivity growth to take market power into account, we simply replace the observed period t price for variable good m, w~, by the appropriate marginal (shadow) price

r t -= Wm t -- [3m p t --= w t -- ~m', m = l . . . . . M ; t = l , ... , T . ( 1 1 )

NEW TECHNIQUES IN THE MEASUREMENT OF MULTIFACTOR PRODUCT1VIT~ 275

The term ~,, P t = ~ m ' thus represents the period t markup (markdown or monopsonistic exploitation impact) for good m if it is an output (input).

In addition, once net inputs are evaluated at their marginal values, it must be recognized that the period t shadow price for the fixed factor, rt0, must be redefined using the identity:

M M r~ = [p~ x~ + ~ r tmz t ] / z~ = w~ + ~ ~m' / Z~ = W~ -- ~O' ( 1 2 )

rn=l m=l

where the rtm a r e defined byEquation (11). Note that these adjustments are analogous to the replacement by shadow values dis-

cussed in the previous section, although the motivation differs. Thus, corresponding biases B t = q can be constructed, so M t = R t n t, where M ~ is productivity growth evaluated at marginal prices and B t adjusts for market power. More specifically, instead of In R t =

In a - ln b- ln c (where c includes all noncompetitive outputs and inputs now) the adjusted measure is In M t = In a- In b-In c' = In a - I n b - ln c+ln q, where In c' = In c-In q, and

M l n q ~ ( 1 / 2 ) [ ,t t ,t t ) ] l n ( z m j = ~ m j Z f j / ~ ' t . z t ) . l . ( ~ m j Z m j / l ~ t t - l . z t - 1 t / Z m j t t - 1 ) . ( 1 3 )

j=0

Thus, the bias can explicitly be shown to be dependent on the [3'mS , although it is also analogous to Equations (6a,b) in terms of the difference between r m and Wm.

In order to obtain econometric estimates for the markup factors [3,~ we must specify a functional form for the production function f. In Diewert and Morrison [1987], we chose a normalized quadratic functional form which is a primal counterpart to dual functional forms defined by Fuss [1977], Diewert [1986] and Diewert and Wales [1987]:

M M

Xo = f ( z o , z , t ) =-z0[a 0 +Y~ am(Zm/ZO) + bot +~ b m t ( Z m / Z o ) m=l m=l

M N + (1/2) ~ ~amn(ZmZn/Z2)] ( 1 4 )

m=l n=l

where am, = a.m. This function exhibits constant returns to scale in %, z. If one uses Equation (14) to form the derivatives Of/OZm which occurs in Equation (10), picks appropriate indexes P tin, divides both sides of Equation (14) by Zo, and appends error terms to Equations (10) and (14), the resulting system of M+I equations can be used for estimation to obtain values of the ~m terms for adjustment of productivity growth measures.

5. Empirical implementation overview

Once the set of relevant outputs and inputs are specified and markups determined, the marginal valuation of domestic output may be measured and used for productivity growth computations. We assume that the factors that determine a firm's production process include domestic and exported good outputs, and capital, labor, and imported good inputs. 16 The vectors of imported and exported goods are somewhat disaggregated for the U.S. and Japan, although the Canadian data were not sufficient for disaggregation. The U.S. disaggregation was into two imports, fuel and other imports and two exports, nondurable


and durable exports. The Japanese disaggregation was into three imports, food, fuel and other, and two exports, metal products and machinery and other.

To determine the values for [3 m to use to compute the markup-adjusted productivity index, evidence from empirical implementation based on the quadratic profit function was used. From a series of estimations, it appeared that domestic output markets for all three countries are subject to a substantial degree of market power. In particular, although the estimates were not as large as those found by Hall (63% markup on average for U.S. manufacturing) the estimated markups ranged between 25% and 70% (13m'S of approxi- mately .2 to .4). 17 This information, and additional estimates for U.S. and Japanese manufacturing from Morrison [1988] which suggest markups in the 10--40% range, provided the basis for the three [~r (Y denotes domestic output) markup assumptions used for comparison, .1, .2, and .4.18

In addition, the export market appears to be subject to imperfect competition to about the same degree as domestic output, particularly in Canada. Thus, a fourth scenario used for comparison is based on the assumption that 15y and [3 x both are .2, where X denotes exports. Finally, both labor and imported inputs appear to have downward sloping supply curves. However, only for labor was the elasticity significantly different from zero. This suggests that import markets are competitive and that, rather than being subject to monopsony power, a backward-bending labor supply curve exists for the labor market in these countries. 19 Thus, the fifth scenario for comparison is based on assuming [5r=.2 and 13L=-.2, where L denotes labor.

Possibly the most significant finding from the estimations used for setting this range of assumed markups is that the experience of all three countries was very similar. Although the estimated domestic markups tended to be larger in Japan and export good markups higher in Canada, the implied demand curve slopes for domestic and exported output were reasonable for all estimations and the findings for imported goods and labor were very robust.

6. Productivity growth estimates for the U.S.

The pattern of productivity growth for the U.S. as traditionally measured is reported as lrt R t in Table la. Note that a downturn has been experienced over time, as well as cyclical slumps around the late 1960s, 1975 and 1980. The most severe downturn was in 1979- 1984. These trends are highlighted by the averages presented at the bottom of the Table. The most dramatic result is the negative annual growth rate for the 1968--84 period, driven by the very large negative values in 1981-82. The post-1973 numbers are also somewhat surprising; for the U.S. the average from 1973 to 1977 is .99%/year, larger than the 1968-73 average of .59% and much higher than post-1977. This arises largely because of the good years in 1973 and 1977. 20

When adjustments are carried out for market power in the domestic output market productivity growth appears better than with the traditional measures, and productivity changes are smoothed to some degree. However, the adjustments are not large compared to productivity growth fluctuations themselves. The downward bias in traditionally


Table la. Traditional and Adjusted Productivity Growth and Biases (Annual %), U.S.

In R t In M t In B t

~ r = .1 ~y = .2 fir = .4 ~y = .2 ~y = .2 fir =" 2 fir = .2

f ix= .2 ~L = - .2 ~L = - .2

1968 2.5000 2.529 2.618 2.904 2.601 2.290 .118 -.210 1969 -1.113 -1.065 -.983 -.729 -1.016 -1.145 .130 -.032 1970 -2.428 -2.082 -1.567 .857 -1.615 -2.433 .861 -.005

1971 .331 .466 .665 1.271 .717 .166 .334 -.165 1972 1.058 1.024 .980 .848 .938 1.012 -.078 -.046 1973 3.166 3.237 3.327 3.616 3.174 3.424 .161 .258 1974 .129 .739 1.624 5.676 1.519 .618 1.495 .489 1975 -1.302 -.414 .904 7.130 1.051 -.846 2.206 .456 1976 -.165 -.578 -1.178 -3.700 -1.158 -.742 -1.013 -.577 1977 3.109 2.794 2.326 .514 2.418 2.779 -.783 -.330 1978 .545 .392 .156 -.742 .737 .598 -.389 .053 1979 -.610 -.504 -.357 .223 -.486 -.277 .253 .333 1980 -1.968 -1.248 -.210 3.995 -.301 -1.150 1.758 .818 1981 -2.461 -2.349 -2.188 -1.561 -2.021 -2.646 .273 -.185

1982 -6.143 -5.667 -5.044 -2.826 -4.904 -6.358 1.099 -.215 1983 2.493 2.372 2.223 1.736 2.305 2.050 -.270 -.443 1984 2.536 2.176 1.668 .373 1.626 2.101 -.868 -.435 1985 -.973 -.912 -.802 -.456 -.824 -1.066 .171 -.093

Averages 1968-80 .250 .407 .639 1.682 .660 .330 .389 .080

1968-84 -.019 .107 .292 1.152 .329 .137 .311 -.014 1968-73 .586 .685 .840 1.461 .800 .552 .254 -.033 1973-77 .987 1.156 1.401 2.647 1.401 1.047 .413 0.59 1977-80 .269 .358 .479 1.368 .592 .488 .210 .218 1980-84 -1.109 -.943 -.710 1.261 -.660 -1.201 .398 -.092

measured indexes suggests that capital investment has been large relative to labor accumulation since monopoly returns previously attributed to capital are now purged from the shadow value of capital. 21 The relative expansion of the capital stock is also apparent in the smoothing of the indexes over time. In booms, the upward adjustment is small because capital investment is less dominant and in recessions this adjustment is larger from extra- proportional labor declines.

More specifically, in the U.S. indexes the years 1970-71, 1973-75, and 1980 are adjusted upward most significantly over the period. In fact, for the ~r = .4 scenario, the adjusted productivity growth figures become large and positive in years generally thought of as problem years; productivity growth in 1976 is low relative to that for 1974 and 1975 when market power is taken into account. In addition, although the measures for 1969-70, 1976 and 1981-82 still reflect slow growth, much of the differentiation in performance is smoothed with the adjustment. The same tendencies are evident but not as dramatic for lower and possibly more reasonable markup assumptions.


Including the export market markups, (the ~r = .2, ~x = .2 case) smooths the cyclical and time trends of productivity growth further. The averages highlight the time trend adjustment; the 1968-73 annual productivity growth average is worse than for the base case, 1973-77 is the same and the next two categories are slightly better. The differences are, however, not large. Incorporating instead market power for labor, so ~r = .2 and [3 t = -.2, the smoothing process is reversed. As compared to either the 13 r = 0 (traditional) or 13 v = .2 case, the 1981-85 productivity growth estimates, as well as those for 1976-77 and 1969-71, decline. Other poor economic performance years such as 1979-80 are not affected quite as much by the labor market adjustment. The overall implication of the negative [3 L estimate is that if a recession causes decreases in labor demand the price must increase to compensate at least in part, causing traditional productivity growth estimates to be upward biased.

The biases (In B') are reported for the first and last adjustment scenario. The numbers emphasize the large number of years that the U.S. has experienced negative biases even for the [3L=0 case, particularly for 1976-78 and 1983-84, indicating that productivity growth in these years was worse than traditionally estimated. Large and positive biases occur also, however, especially in 1970, 1974-75, 1980 and 1982; in these years traditional productivity growth measures have been understated. The average biases indicate that over time the bias has not varied very much.

7. Canada

The Canadian R t, M t and B t measures are presented in Table lb. Overall, productivity growth in Canada was better than for the U.S., although the downward tendency is still evident toward the end of the sample. Cyclical fluctuations are even stronger, however; 1967, 1970, 1980 and particularly 1974-77 (except 1976) were years of negative productivity growth. The averages highlight the trends. Although on average to 1980, Cana- dian productivity growth is better than the U.S., the decline over time is more dramatic; productivity growth drops from 2.1% per year from 1968-73 to .72% for 1973 to 1977 and finally to .19% for 1977-80.

When market power in the domestic output market is taken into account, productivity growth appears stronger and some smoothing occurs, similarly to the U.S. However, the upward tendency in productivity growth estimates resulting from the markup adjustment is more dramatic, and also occurs in years of both good and bad performance, so the smoothing effect is not as pronounced. In particular, although productivity growth measures for low growth years like 1970, 1975 and 1980 improve when adjusted for imperfect competition, strong growth years such as 1966-69, 1972-73 and 1976 also appear better when adjusted. Growth for most years in the OPEC-shock period improves, although for 1974, which already was negative, it worsens. The main smoothing tendency is over time; greater productivity growth is evident for 1976 to 1980 with the adjustment. The averages emphasize these trends.

When imperfect competition in the export market is also incorporated into the productivity growth indexes, a more definite tilt to productivity growth adjustments occur, resulting from a lower bias at the beginning and higher bias at the end of the sample for


Table lb. Traditional and Adjusted Productivity Growth and Biases (Annual %), Canada


~r = .1 ~ y = .2 ~ y = .4 ~y = .2 ~y =. 2 ~y =. 2 ~y = .2

~x = .2 ~L = -.2 ~L = -.2

1965 2.120 2.034 1.927 1.621 2.125 1.872 -.193 -.248 1966 1.914 2.202 2.557 3.585 2.331 2.011 .643 .097 1967 -.566 --.123 .415 1.935 .354 -.472 .981 .094 1968 3.788 4.297 4.910 6.611 4.614 4.064 1.122 .276 1969 2.194 2.307 2.444 2.828 2.484 2.061 .250 -.133 1970 -.536 .196 .645 2.407 .457 -.141 1.181 .395 1971 1.071 1.048 1.021 .949 1.089 .556 -.050 -.515 1972 2.618 2.727 2.858 3.222 2.890 2.594 .240 -.024 1973 3.549 3.696 3.879 4.416 3.667 3.816 .330 .267 1974 -.677 -.690 -.707 -.759 -.314 -.993 -.030 -.326 1975 -2.206 -1.946 -1.619 -.609 -.544 -2.632 .587 -.426 1976 2.963 3.385 3.908 5.442 3.991 3.226 .945 .263 1977 -.017 .469 1.057 2.715 1.033 .406 1.074 .423 1978 .106 .404 .766 1.781 .641 .422 .660 .316 1979 .965 1.123 1.320 1.904 1.403 1.040 .355 .075 1980 -.284 .220 .849 2.720 .979 .335 1.133 .619

Averages 1968-80 1.041 1.326 1.641 2.587 1.731 1.135 .600 .093 1968-73 2.114 2.378 2.626 3.406 2.552 2.158 .512 .044 1973-77 .722 .983 1.304 2.190 1.567 .765 .581 .040 1977-80 .192 .554 .998 2.280 1.014 .551 .806 .358

the h ighes t g r o w t h years. T he cycl ica l t rend also adapts no t i ceab ly w i th the add i t iona l

ad jus tmen t ; the poores t p roduc t iv i ty g r o w t h years such as 1974, 1975 and 1980 improve ,

a l t h o u g h o ther qui te low g r o w t h y e a r s - - 1 9 6 7 , 1970, 1 9 7 8 - - r e g r e s s as c o m p a r e d to the

base 13 r = .2 scenar io . T h e ave rages s h o w tha t annua l g r o w t h in the 1 9 6 8 - 7 3 and 1 9 6 8 - 8 0

per iods dec l ines as c o m p a r e d to the base case, e m p h a s i z i n g the tilt. The b ias is la rger than

in the U.S. bu t is still qui te smal l ; in par t icular , in 1 9 6 8 - 7 3 the decl ine , and in the o ther

pe r iods the inc rease f rom the ba se case, is on ly in the r ange of abou t .1 to .3%.

Final ly , w h e n the d o w n w a r d s lop ing supply cu rve for l abor is t aken in to accoun t the

impac t s are s imi la r to the U.S. and a lmos t as s t rong. For example , for years whe re

t rad i t iona l p roduc t iv i ty g r o w t h indexes ind ica te the wors t pe r fo rmance , such as 1970 and

1 9 7 4 - 7 5 , the m e a s u r e s appea r ac tual ly to b e u p w a r d biased. 1 9 7 7 - 8 0 , also years of poor

p roduc t iv i ty g r o w t h in t e rms o f t rad i t ional measures , do not appear as b a d once ad jus ted

for [ ~ 0 , [~L~0.

The B t measu re s h igh l i gh t the t rends out l ined. T h e s e b iases are la rge and pos i t ive for the

[5 r = .2, [5 L = 0 case a r o u n d the late 1960s, 1977 and 1980. O the rwise they are genera l ly

pos i t ive bu t no t ve ry large and w i t hou t a s t rong t rend or cycl ica l c o m p o n e n t . Note ,


however , that the largest upward biases are in 1970, 1980 and to some extent 1975, years

o f general ly bad economic per formance , w h i c h indicates an overal l smooth ing tendency.

In addit ion, the negat ive 1974 bias indicates worse p o s t - 1 9 7 3 product ivi ty g rowth than

usually measured, in contrast to the U.S. f indings. The average annual bias is also quite

constant , but at a s l ightly h igher level than for the U.S. For [~t ~ 0 Canada does not exhibi t

a part icularly s t rong cycl ical t rend but a t ime trend is evident; the adjus tment appears to

have the largest (posi t ive) effect at the end and the wors t in 1970 and 1975, two recess ion

years.

8. Japan

Product ivi ty g rowth measures for Japan are repor ted in Table lc . As expected , Japan ' s

tradit ionally measured product iv i ty g rowth rate has been much larger throughout the

sample per iod than that for the U.S. or Canada, a l though even for Japan a downturn has

been exper ienced over time. By contras t to the U.S. and Canada, before the decl ine

Table lc. Traditional and Adjusted Productivity Growth and Biases (Annual %), Japan


~y = .1 ~y = .2 ~y = .4 ~g = .2 ~y = .2 ~y = .2 ~y = .2 ~x = .2 ~L = -.2 ~L = -.2

1968 7.865 8.096 8.535 9.950 8.535 7.700 .670 -.165 1969 7.261 7.819 8.351 10.021 8.360 7.061 1.090 -.200 1970 6.736 7.222 7.756 9.426 7.842 6.363 1.020 -.373 1971 -.667 -.129 .862 3.906 .843 -.650 1.529 .017 1972 4.770 5.541 6.128 7.821 6.223 4.915 1.358 .145 1973 6.404 7.355 7.651 8.514 7.815 6.874 1.245 .468 1974 .803 1.729 2.876 6.446 2.941 1.659 2.073 .756 1975 2.941 3.112 3.971 6.723 4.011 3.132 1.030 .191 1976 6.153 6.763 7.376 9.294 7.412 6.885 1.223 .732 1977 4.063 4.221 4.615 5.805 4.620 4.263 .552 .200 1978 3.889 4.278 4.495 5.130 4.536 4.179 .606 .290 1979 4.850 5.196 5.360 5.848 5.436 5.018 .510 .168 1980 4.565 4.998 5.741 8.015 5.768 5.358 1.176 .793 1981 2.052 2.861 3.541 5.658 3.555 3.196 1.489 1.144 1982 .366 1.498 1.803 2.808 1.847 1.466 1.437 1.100 1983 -.304 .807 .583 2.358 .555 .319 .887 .623 1984 1.680 2.155 2.740 4.734 2.747 2.441 1.060 .761

Averages 1968-80 4.587 5.092 5.671 7.458 5.719 4.828 1.083 .232 1968-84 3.731 4.325 4.846 6.618 4.885 4.128 1.115 .391 1968-73 5.395 5.984 6.547 8.281 6.603 5.377 1.152 -.018 1973-77 3.073 4.636 5.298 7.356 5.360 4.563 1.225 .469 1977-80 4.342 4.673 5.053 6.200 5.090 4.704 .7 11 .363 1980-84 1.672 2.464 2.882 4.715 2.894 2.556 1.210 .884


commencing in the 1980s, only one year of declining productivity is found in Japan, 1971, and only one dramatic drop in productivity growth, 1974. The stronger productivity growth found in 1984 indicates a productivity growth upturn after a short term fall.

The reported average annual growth rates provide additional insights. On average to 1980, although Canadian productivity growth exceeds that for the U.S., Japanese growth is by far the strongest. When the years to 1984 are included for Japan and the U.S., although the averages for both countries drop, the drop in Japan is very slight; for Japan the average is 3.73%, down from 4.59%, as compared to the U.S. average of -.019 (.250).

With markup behavior incorporated for Japan the overall increase in productivity growth indexes is significant. The positive bias B t in the last columns causes the adjusted productivity growth terms to be larger, and increases toward the end, smoothing the apparent downturn. A cyclical smoothing effect is also evident to some extent because low productivity growth years like 1971 and 1974 become substantially better, although not as good as the best years, with the adjustment.

Including export markups has a negligible impact on the cyclical time trend of productivity growth for Japan, and overall augments the growth rate slightly over the 13y=.2 case except in the worst years such as 1971 and 1983. This slightly reverses the smoothing process but the impact is insubstantial; the upward boost in the index is only about .05% on average.

Finally, the worst productivity growth years improve as compared to the traditional measures with the ~r=.2, 15L=-.2 adjustment compared to R t, as is evident particularly for 1971 and 1983. The adjustment again is larger at the end, partially counterracting the downward time trend in R t. This results from the dominance of the 15r~0 over the 13L~0 assumption; productivity growth in this case is generally higher than for 13y=0 but lower than for [3y=.2, ~L=0.

The averages highlight these tendencies. The adjusted measures indicate lower productivity growth than the traditional model for 1968-73, but the rates for 1973-77 and 1977-80 are higher on average by about .5% per year and for 1980-84 increase by about .9%/year. Comparing this to the [3r=.2 case suggests that the bias from ~L~0 is quite strongly negative, and more so in the later years.

9. Conclusions

In this article we have outlined some methodological developments in productivity growth measurement from the 1980s. These developments, which focus on the evaluation of inputs and outputs at their correct values provide important insights concerning impacts on productivity growth and interpretation of productivity growth measures. Evidence reported here suggests that market power adjustments especially may provide some explanation of fluctuations since they tend to smooth traditional productivity growth indexes more than other adjustments. These results suggest that further research in this area would be fruitful.

In particular, we have assumed markups for domestic and exported output and labor based on econometric estimates to adjust productivity growth indexes for the impacts of imperfect competition. We found that traditional productivity growth measures which


ignore market power appear to have underestimated productivity growth. This tendency, which arises from markups in output markets, may be partially attenuated by the impact of a backward-bending labor supply function. The estimates also suggest larger differences between countries than traditionally measured because in Japan capital growth, and thus the underestimation of productivity growth, has been relatively high. Cyclical variation has been overstated in traditional measures, however, since capital growth seems to fall less severely than growth of other inputs in downturns (and conversely in upturns), at least partially smoothing productivity growth measures. The alleged slowdown in productivity growth over time in industrial countries thus appears to be at least partly a result of markup behavior; the underestimation of productivity growth is particularly acute late in the sample periods under consideration when economic performance overall was relatively poor. The slowdown, however, still remains.

It is worth emphasizing again that the methodological developments expounded in this study have not attempted to provide an exhaustive overview of the many developments in the 1980s. For example, other important recent methodological research in the 1980s which have been neglected, include contributions dealing with:

(i) obsolescence of captital, recognized as a measurement issue by Baily [1981] and Berndt and Wood [1984];

(ii) output measurement issues, dealt with by Lichtenberg and Griliches [1986]; (iii) the impact of environmental regulations, discussed by Denison [1979] and pursued

by researchers including Norsworthy et al. [1979], Crandall [1980] and Conrad- Morrison [1989];

(iv) nonconstant returns to scale (Hall [1988], Fuss and Waverman [1986], and Morrison [1986c], among others);

(v) R&D, patents and innovations (see for example Griliches [1980,1986]); and (vi) the increasing importance of the service sectors and poor productivity performance

of the non-manufacturing sectors.

Many of these can either be thought of in our framework as determining biases, as mentioned in the text for two of them, or are simple refinements of data measurement techniques. Other important aspects of production may also cause biases but have yet to be explicitly incorporated into empirical productivity modeling, such as inventory behavior.

Overall, since 1980, much progress has been made in terms of the methodology of dealing with productivity measurement. A real explanation for productivity growth fluctuations remains elusive since the methodological developments have not provided adjustments sufficient to account for these fluctuations, although those found here for markup behavior are encouraging. However, the large body of literature now existing on methodological developments for productivity growth measurement provides a fruitful basis for further studies on the determinants of productivity fluctuations, and particularly on the productivity growth puzzle of the 1970s and 1980s.


Acknowledgments

B o t h a u t h o r s a c k n o w l e d g e s u p p o r t f r o m the N a t i o n a l S c i e n c e F o u n d a t i o n , G r a n t # S E S

8611683 .

Notes

1. See the papers from a Symposium on The Slowdown in Productivity Growth in the Journal of Economic Perspectives, Fall 1988, and the references cited for an excellent survey of the problem and associated research.

2. See, for example, Berndt and Fuss [1986], Morrison [1986a], and Hulten [1986]. 3. See Diewert and Morrison [1986] and Morrison and Diewert [1985]. 4. See Conrad and Morrison [1989] for further discussion of this. 5. This was, for example, the focus of the work by Hall [1988]. 6. There are many ways of doing this, and no clear way to distinguish between the various methods. 7. See Diewert [1980] or Diewert and Morrison [1986]. 8. The equivalence of fixity and capacity utilization here arises because the restriction on fixed factors causes

available inputs to be nonoptimal for the given output level. Thus capacity output is defined as the output that reproduces the steady state given these inputs. This does not depend on utilization costs, but simply a restriction on input adjustment that may stem from adjustment costs of any type.

9. This may be accomplished, for example, as in Morrison [1986] using an econometric model and measuring OG/Ovk=r k where G is the variable cost function. Alternative methods are used in Berndt and Fuss [1986] and Hulten [1986].

10. This general index number technique of replacing observed prices by appropriate marginal prices was first suggested by Frisch [1936]. See also Diewert [1974].

11. Constmction of marginal cost measures for domestic output using production theory has been attempted recently by researchers by including Appelbaum and Kohli [1979] and Morrison [1988].

12. If the competitive good is an output (input), then fwill be non~tecreasing (non-increasing) in z 0 and the components of z that correspond to inputs and non-increasing (non~zlecreasing) in the components of z that correspond to outputs.

13. It is clear that aggregation problems exists when specifying a monopolistic model for an economy. This will, however, allow us to determine whether significant market power does exist, because if all firms set price and marginal cost equal this will also be found for the economy. Therefore, although clear interpretation of the markup is difficult, adjustment by these numbers for total productivity growth is reasonably justifiable as a first approximation.

14. This function was chosen over others which may appear to be useful but pose implementation difficulties. For example, with a linear function the markup is not invariant to changes in inflation, for an exponential model one would have to use nonlinear or two stage estimators, and a log-log model results in a constant relative markup. The log-linear framework, therefore, appears the most useful.

15. This is based on the assumption of a constant markup, which is maintained for implementation reasons, and has been rationalized by Hall [1988]. It is also based on finding a relevant normalization index, which might be problematic.

16. The data used for this study has been discussed in two other studies. The Canadian data (1961-1980) is from Cas, Diewert and Ostensoe [1986] and the U.S. (1967--82) and Japanese (1965--82) data is from Morrison and Diewert [1986]. The data is for the entire business sectors of these countries. The Canadian data is based on input-output information from Statistics Canada for 37 Canadian industries for 1961-1980. The U.S. and Japanese data were instead based primarily on national accounts information, using additional information on capital and labor from the Michael Harper at the Bureau of Labor Statistics and from Dale Jorgenson and Barbara Fraumeni. For this study the U.S. data were updated to 1985 and the Japanese data to 1984.

17. These assumptions are equivalent to making assumptions about the elasticity of demand (supply) facing the firm for their outputs (inputs). In particular, the inverse price elasticity from Equation (9) is 01n Wm/Oln z m =


[~mpo/w m. Thus at the point of normalization (which for these estimates was 1972) the demand (supply) elasticity is simply -[5 m for an output and [~m for an input since outputs are measured as negative and inputs as positive values. Thus, given an assumption of .2 for 13r the small (.2%) price decrease required for an (1%) output change indicates a fairly elastic demand curve.

18. A perplexing problem with markups in the highest range is that, as Hall found, the implied returns to capital in some cases become small or even negative. This is particularly true for the U.S. for the highest markup estimates. This result is not intuitively plausible, although Hall has proposed an interpretation in terms of monopolistic competition and division between production and marketing profits. The assumptions used, however, span an intuitively and computationally reasonable range.

19. The perverse labor supply elasticity here may help to explain the evidence of small or negative returns to capital found when only market power in the domestic output market is assumed. A markup resulting from a downward sloping supply curve for labor will have the reverse effect of the markup from domestic output. Note also that results found by Bengt Hansson [1988] for Sweden are consistent with this finding.

20. These are averages of the growth rates for the specified periods, so actually this reflects growth from 1972 on.

21. See Morrison [1988] for more discussion of the importance of the relative growth rates of capital and other inputs.

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