P.1 

OAR Box 1669 

Prepped by Charmelle Mathews 

Document Number: 

Docket Number: 

A-98-13 

Printed 9/23/2008 9:36:49 AM Sheet 97 of 110 
I?. 

•*• • 

* " • 

P.2 

7 "J 

> 

COWLES FOUNDATION FOR RESEARCH IN ECONOMICS 

AT YALE UNIVERSITY 

Box 2125, Yale Station 

New Haven, Connecticut 06520 

COWLES FOUNDATION DISCUSSION PAPER NO. 828 

Note: Cowles Foundation Discussion Papers are preliminary 

materials circulated to stimulate discussion and 

critical comment. Requests for single copies of a 

Paper will befilled by the Cowles Foundation within 

the limits of the supply. References in publications 

to Discussion Papers (other than acknowledgment that 

a writer had access to such unpublished material) 

should be cleared with the author to protect the tentative character of these papers. 

MEASURING MARKET POWER IN U.S. INDUSTRY 

Matthew D. Shapiro 

April 1987 

/ 
P.3 

MEASURING MARKET POWER IN U.S. INDUSTRY 

&" 

Matthew D. Shapiro 

Yale University and National Bureau of Economic Research 

October 1986 

Revised March 1987 

I am grateful for helpful discussion with Ernst Berndt, Timothy 

Bresnahan, Zvi Griliches, R. Glenn Hubbard, N. Gregory Mankiw, Whitney Newey 

and participants in seminars at MIT, NBER, Northwestern, NYU, Princeton, and 

Yale; for financial support from the NSF and NBER-Olin Fellowship; and for 

research assistance by Mico Loretan. 
P.4 

Measuring Market Power in U.S. Industry 

ABSTRACT 

?;, 

Non-competitive conduct can be assessed by estimating the size of the 

markup or Lerner index achieved in a market. The markup implies a price 

elasticity of demand faced by the representative firm. For a given markup, 

non-competitive conduct is greater the more elastic is the market elasticity 

of demand. The ratio of the firm's to the market elasticity is a measure of 

non-competitive conduct that is insensitive to the value of the monopoly. 

To implement this measure, both the firm's and the market elasticities of 

demand must be estimated. Hall shows how to estimate the markup, and hence 

the elasticity faced by the firm, from the cyclical behavior of 

productivity. To estimate the market elasticity, an instrumental variables 

procedure exploiting a covariance restriction between productivity shocks 

and demand shocks is used. Results for broad sectors of private industry 

and for non-durable manufacturing industries display a wide range of 

monopoly power. 

Matthew D. Shapiro 

Cowles Foundation for Research in Economics 

Yale University 

Box 2125 Yale Station 

New Haven, CT 06520-2125 

tel. 203 432-3716 
P.5 

"• r-),-

•••.?m. fit 

1. Introduction 

This paper presents some new estimates of the degree of market power in 

U.S. industry. Non-competitive outcomes can be assessed by comparing price 

and marginal cost. Using price-cost margins alone to assess market power is 

problematic because they fail to take into account the value of the 

monopoly. A monopoly will command a greater margin the more inelastic is 

the demand for the good. Differences in elasticity of demand should be 

taken into account in comparing conduct across markets. The measure in this 

paper does so by normalizing the estimated markup by the elasticity of 

demand. 

In a recent series of papers, Robert Hall suggests that many U.S. 

industries are not competitive. This result is based on a simple and 

elegant reinterpretation of the well-known fact that productivity varies 

pro-cyclically. The reasoning is as follows: As output expands in the 

trough of a recession, labor increases less than is warranted by a standard 

production function. Hence, price exceeds marginal cost. Put differently, 

when output is low, price does not fall enough to allow the sale of goods 

that can be produced at very low marginal cost. Hall reasons that this 

finding is only consistent with a high degree of monopoly power. There is 

little evidence of substantial profits in U.S. industry; he reasons that 

the monopoly profits are dissipated by chronic excess capacity. 

h, all (1986a, b, c) 

M 
P.6 

In this paper, I extend Hall's framework to yield an independent 

measure of the degree of monopoly power in an Industry. Hall takes perfect 

competition as his null hypothesis and then measures departures from pure 

competition. In the formulation in this paper, the polar hypothesis of pure 

monopoly can be studied. More importantly, if the industry is neither 

perfectly competitive nor perfectly monopolistic, a measure of the degree of 

market power can be calculated. The markup implies an elasticity of demand 

faced by the representative firm in the industry. The ratio of the market 

elasticity of demand to that implied by the markup is a measure of market 

power. In the polar case of perfect competition, it equals zero. In the 

opposite polar case of perfect monopoly, it equals one. In the intermediate 

range between zero and one, it measures non-competitive conduct. 

To implement this measure it is necessary to estimate both the market 

elasticity of demand and the implied by the markup ratio. I follow Hall in 

estimating the latter from the cyclicality of productivity. To estimate the 

market elasticity of demand, I exploit the covariance restriction between 

the productivity shock and the disturbance in the demand equation. By 

definition, an industry productivity shock is uncorrelated with the demand 

disturbance. The restriction serves to identify the price elasticity of 

demand. This covariance restriction has an instrumental variables 

interpretation. The productivity shock is a valid instrument for the price 

variable in the demand equation. This approach to estimating the elasticity 

of demand should have wide application beyond its use here in measuring 

market power. 

6~, 
_JL2_ 

ie 

"Mi. 

V. 

• \ 11 

« • 

3 -

2. Theoretical Framework for Measuring Market Power 

In this section of the paper, I review Hall's measure of noncompetitive behavior and develop a further measure of the degree of monopoly 

power. 

Under assumptions of constant returns to scale and competition Solow 

(1957) shows that the total factor productivity residual (the "Solow 

residual") will measure technological change in a production function. This 

residual is defined as 

(1) Ac t -Ay t - Akt - «t (Ant - Akt) 

where Ay , Ak , $nd An equal the percent change in output, capital, and 

labor, and a equals the share of labor income in nominal output. The share 

is measured as a - W N /P Y where W , N , P , and Y are the levels of the 

nominal wage, labor, the nominal price level, and real output. Equation (1) 

applies equally well to the aggregate economy or to a nars»wly defined 

2 industry. Solow's derivation requires that the technology be constant 

returns to scale and that technological change be disembodied. Solow's 

derivation also requires that markets are competitive and labor is variable 

Variables and parameters should all be thought of as subscripted by i 

for industry. This subscript is suppressed except where it is needed in a 

particular context. Productivity has a drift so Act is not mean zero. 

Hence the equations in Ac. have constants that are suppressed for notational 

convenience. In the estimates, a constant is included in all the 

regressions so the estimated Ac are mean zero in the sample. 

(* 
P.8 

- 4 

within the period, so labor is paid its marginal product. Capital need not 

be paid its marginal product so it can be fixed in advance. 

A similar relationship holds under imperfect competition. Define X to 

be marginal cost. Solow's derivation holds if price does not equal marginal 

cost, but in equation (1) labor's share in output should be replaced by 

labor's share in cost. Denote labor's share in cost as a - W N /X Y and 

denote the true productivity shock as Ac . Then the true productivity shock 

is given by 

(!') Ac * - Ayt - Akt - «° (Ant - Akt) 

Marginal cost is, however, unobservable, Hall suggests assuming that 

H - P^/X is a constant. Then (1) and (1') can be combined to yield 

(2) Act - (/i-l)at(Ant - Akt) + Act 

where Ac is the measured Solow residual, where Ac is the true 

productivity shock, and where n is an unknown parameter to be estimated. 

Hall's strategy is then to estimate the markup ratio /x and to test the 

hypothesis that it equals one. For a wide range of industries he is able to 

reject the null of perfect competition. The markup does not provide a 

natural metric for the degree of monopoly power in an industry. For 

example, a monopoly facing relatively inelastic demand will have a larger 

markup than a monopoly facing more elastic demand. Moreover, it may be 

desireable to rank industries according to their degree of non-competitive 

7 
P.9 

- 5 -

conduct rather than simply to categorize them as competitive or not 

competitive. I consider a measure of monopoly power that takes into account 

the elasticity of demand in the industry. The measure nests the special 

cases of perfect competition and perfect monopoly. 

The markup can be expressed in terms of the elasticity of demand faced 

by the representative firm in the industry. Hence, 

(3) 

* 

A -

if the representative firm acts as if it faces an elasticity of demand equal 

* 3 * 

to 0 . The value -1//3 is the Lerner index of market power. Denote the 

market elasticity of demand as 0. If the industry is monopolized, or if its 

firms collude effectively to duplicate the monopoly outcome, then 0 will 

equal 0. Given estimates of both parameters, it is possible to test the 

natural null hypotheses of monopoly (0 - 0 ) as well as that of perfect 

competition (0 - -« or, equivalently, y. - 1). 

Attention need not be confined, however, to these polar cases. The 

ratio of the market to the firm's elasticities is a natural measure of 

This formula is a simple rearrangement of the first order condition 

for the one-period profit maximization problem. It will also arise from a 

discounted present value maximization problem as long as sales today do not 

affect demand in the future. 
monopoly power. Define this ratio as 

P.10 

(4) 6-0/0 . 

The coefficient has a natural interpretation. Under competition 8 equals 

zero; under monopoly it equals one. If the industry functions as a Cournot 

oligopoly, the reciprocal of 8 measures the number of equally-sized firms. 

Bresnahan (1987) argues persuasively that the ratio 6 is an interesting 

measure of conduct for models where Cournot behavior is not maintained. It 

normalizes the departure of price from marginal cost by the elasticity of 

demand. The interpretation as the reciprocal of the number of firms in a 

Cournot oligopoly provides a useful metric for market outcomes even under 

different models of firm behavior. 

3. Identification and Estimation 

The strategy is to estimate the markup ratio n and the price elasticity 

of demand 0 and then to compute the index of market power 8. In this 

section, I consider instrumental variables procedures for estimating these 

parameters. 

To estimate the markup ratio, j». Hall makes the crucial identifying 

if 

assumption that the true productivity shock Ac has no aggregative 

4 * 

The distinction between 0 and 0 has been discussed at least since 

Chamberlain. It is developed by Bresnahan (1982) and analyzed in detail by 

Bresnahan (1987). 

°l 
P.11 

•ty 

? 

r 

8$. 

If 

t 

- 7 -

component. This assumption is specifically at variance with some theories 

of the business cycle. Specifically, Kydland and Prescott (1982) rely on an 

aggregate productivity shock as the only driving variable in the business 

cycle. (It is important to note, however, that some implementations of real 

business cycle theories, notably that of Long and Plosser (1983), generate 

cycles with shocks that are independent across sectors.) Hence, Hall's 

formulation, as he is careful to acknowledge, can shed no light on theories 

that require an aggregative productivity shock as an essential ingredient in 

aggregative fluctuations. 

Under Hall's assumption, aggregate GNP growth is a valid instrument for 

a (An - Ak ) in equation (1) on industry data. Some recent work of my own 

calls into question Hall's assumption in this data. In particular, for many 

industries it is difficult to reject that marginal cost moves consistently 

with observed productivity under the hypothesis that observed productivity 

is true productivity (Shapiro, 1987). In this case, Hall's procedure is 

invalid. On the other hand, In about half the non-durable manufacturing 

industries--results for which I will highlight here--my earlier test rejects 

the null that observed productivity is true productivity. Moreover, it is 

common practice in industrial organization to assume that year-to-year 

changes in aggregate output come from demand. Hence, it seems best to 

remain agnostic; I present results based on Hall's elegant solution of using 

aggregate GNP growth as an instrument in the markup equation. 

by 

Usually identification is not achieved by disaggregation alone. In 

this case, at least approximately, disaggregation does lead to 

identification because of the role of the aggregate demand shock. See the 

Appendix for details. 

to 
P.12 

This agnosticism need not be nihilism. It there are truly exogenous 

variables that are correlated with movements in labor input, these can be 

used as instruments. Valid estimates can be offered without taking a stand 

on whether or not there is a macroeconomic component to true productivity 

growth. Oil prices and government purchases (especially military purchases) 

are candidates for instruments. Estimates that use these will also be 

6 

presented. 

Although one only needs to estimate the elasticity of demand to 

estimate 8, it is helpful to write down the entire demand equation. 

Consider the following demand equation in percent change form for a given 

industry: 

(5) Ayt - /?Apt + Zt7 + A»t 

Here, Ay is the growth rate of output, Ap is the growth rate of the 

relative price, the Z are demand shift variables, and tAv is a taste shock. 

To estimate the elasticity of demand, it is necessary to overcome a 

difficult simultaneity problem. The often intractable identification 

problem has a straightforward solution in this context. Consider the 

Hall (1987) takes the agnostic position and uses similar instrument 

lists. But see Hall (1986a, b, c). 

/ / 
4

r

-.r: 

9 -

following identifying assumptions: 

• The productivity shock Ac is uncorrelated with aggregate demand 

or other aggregate demand shifters such as military expenditure or 

oil prices. 

ie 

• The productivity shock Ac is uncorrelated with the taste shock 

At/ and with other variables that shift demand. 

The first of these assumptions has already been discussed. It is used by 

Hall to identify p. in equation (2). For aggregate demand to be a valid 

instrument for <* An then aggregate demand must be one of the demand 

shifters Z . For an instrument to be valid it must both be uncorrelated 

with the disturbance and correlated with the endogenous variable. 

The second assumption follows virtually by definition of a productivity 

shock. Independent movements in technology should be uncorrelated with 

changes in taste. The identifying assumption Is a covariance restriction 

rather than the more conventional exclusion restriction. ^.Such a covariance 

restriction has an instrumental variables interpretation (Hausman and 

Taylor, 1983). The estimated disturbance Ac is a valid instrument for 

price in the demand equation (5). It is certainly correlated with price 

movements, it is by construction uncorrelated with the aggregate demand 

component of Z , and it is, by assumption, uncorrelated with the taste 

shocks Ai/ . Implicit is the assumption that the productivity shock is 

%. 

.2-
P.14 

10 

uncorrelated with the other excluded variables, which are thrown into the 

error term. 

The two-step estimator where the residuals from (2) are used as 

instruments for (5) is consistent asymptotic normal and is efficient (see 

Hausman, Newey and Taylor (1987)). Indeed, since the demand equation Is 

just-identified, the instrumental variables estimator is numerically 

identical to maximum likelihood. Yet, the covariance matrix printed out by 

standard computer packages is incorrect. The true covariance matrix is a 

function of nuisance parameters. I compute and report the correct 

estimates. See the Appendix for details of the computation. 

One possible excluded variable, future price changes, could defeat 

identification. If goods are durable, this variable is relevant for demand 

and could well be correlated with the productivity shock. The results for 

the durables are suspect in any case because the flow demand curve is 

completely inadequate for them. Developing a complete theory of supply and 

demand for durables under imperfect competition is well beyond the scope of 

this paper. The results for durables are included only for completeness. 

Before presenting the estimates, further consideration of the 

parameterization of the demand equation is in order. As noted above, only 

the parameter of the relative price will be estimated. The omitted 

variables are orthogonal to the instrument, so this procedure yields 

consistent estimates. Nonetheless, it is worthwhile thinking about the 

Under the identifying assumptions, instrumental variables estimation 

of /3.is consistent even if all the Z are omitted.. Efficiency could be 

gained, however, by including some it they are observable. Of course, if 

they are endogenous, one would need instruments for them. 

A 
P.15 

- 11 -

omitted variables. In particular, aggregate demand is omitted. Note the 

instrument is orthogonal to this omitted variable not just in theory but by 

construction as long as aggregate GNP is used an instrument in the markup 

equation. Yet, omitting this crucial demand shifter leads to an 

inefficiency. One way to include it without having to estimate another 

parameter is to estimate a homogenous demand system. In this case, the left 

hand side of (5) becomes industry output growth minus aggregate output 

growth. Hence, the demand equation becomes 

(5') Ayt - Aqt - /JAP(; + Z ^ + A ^ 

where Ay , Ap , and Ai/ are, as before, the industry output growth, relative 

price growth, and demand shock; where Aq is aggregate output growth; and 

where Z. are demand shifters excluding aggregate output growth. All the 

elements of Z.. except the constant are subsumed into the error term so only 

0 and the intercept are estimated. Note that the orthogonality of aggregate 

output growth to the instruments implies that the estimate of 0 will be 

numerically the same whether (5) or (5') is estimated. The standard errors 

will, however, be affected. The demand equation actually estimated is (5') 

where all of the demand shifters (except the constant) are subsumed into the 

disturbance. 

Gross output versus value added 

The data used to estimate both the markup and the demand equation will 

be on a value-added rather than a gross price basis. Hence, the estimated 

M 
P.16 

12 

parameters are not comparable to conventionally estimated ones. Hall 

(1986a) gives the formula to convert the value-added markup to the ratio of 

gross price to marginal cost (ji). If 7 is the share of materials in gross 

output and materials are used in fixed proportions with gross output, then 

Jt. - p/(l+(/i-l)7). Hubbard (1986) and Domowitz, Hubbard, and Petersen 

(1987) stress how Hall's empirical results on the value-added markups are 

substantially larger than the gross-output markups. 

* 

The firm's and the market elasticities of demand (0 and 0) also are 

estimated on a value-added basis. Again under the assumption that materials 

are used in fixed proportions with gross output, it is possible to calculate 

the elasticities on a gross price/gross output basis. Specifically, the 

gross price/gross output elasticities are 0- 0 /(I-7) and 0 - 0/(l-i). 

Note that the correction for both the firm's and the market elasticities are 

g 

Using the value-added deflator rather than the gross output price 

index in the demand function also adds a multiple of the growth in real 

materials prices to the disturbance of the demand function. This component 

of the disturbance is orthogonal to the productivity shock instrument. 

Changes in materials prices will not bias the measure of total factor 

productivity as long as materials are used in fixed proportions (the 

assumption made here) or value-added is measured as a Divisia index (Bruno, 

1978, Theorem 2). The GNP data are double-deflated, not Divisia indexes. 

(The U.S. national income and product accounts are rebased every ten years, 

not continually.) The bias in using the double-deflated data instead of a 

Divisia calculation is very small even in the face of materials price 

changes of the size seen in the 1970s. (Bruno and Sachs, 1985, p. 58). 

Finally, in the estimates where oil price changes are included as 

instruments for the markup equation, the instrument in the demand equation 

is orthogonal by construction to this major component of materials price 

changes. 

ys' 
P.17 

re 

ffi 

*..-• 

•:& • 

- 13 

the same. Hence the measure 8 need not be corrected for the materials 

share. 

Data are available for materials share is manufacturing. Results on a 

gross output basis can hence be reported. 

4. Data and Results 

The markup equation (2) and the demand equation (5') are estimated on a 

panel of all U.S. private industries. Estimates are presented for both 

t 

broad sectors and for two digit industries. The two digit industries have 

the narrowest definitions provided in published National Income and Product 

Accounts (NIPA) data. The data reflect the comprehensive revisions of the 

NIPA that were published in December 1985 and are revised as of July 1986. 

Details are provided in the Appendix. The data are available from 1947 to 

1985 except for the labor data, which begin in 1948. The sample period in 

thus 1949 to 1985 to allow for computing the changes. These data are at a 

higher level of aggregation than is often used in studies <£f market power. 

Consequently, the estimates will be averages of sometimes disparate markets. 

The advantage of these data over accounting data is that, at least in 

theory, the NIPA measures the appropriate economic concepts. 

The markups equation (2) and the demand equation (5') are estimated by 

the instrumental variables procedures discussed in the previous section. 

The elasticity faced by the firm, 0 , and the ratio of the market to firm's 

elasticity, 8, are computed from the estimated p. and 0. The standard errors 

* 

of the estimated 0 and 8 are computed using the first-order Taylor series 

i 

/ * 
14 -

approximation, which Is valid asymptotically. The covariance between the 

* 

estimated p and 0 is zero in the sample because of the covariance 

restriction on the disturbances of the equation. 

Basic Results 

Table 1 presents results for broad sectors. The estimates are based on 

pooled rather than the data for the total sector. Data for the two digit 

industries are pooled under the corresponding sector. The two digit 

industries are given in the Appendix. Construction, Wholesale Trade, and 

Retail Trade have no two-digit sub-industries in these data. The pooling 

procedure is as follows. The markup equation (2) is estimated by 

instrumental variables on each sectoral panel of industries. Within the 

panels, each two digit industry has a different intercept but the same slope 

coefficient (p-1). The residuals from these equations are used as 

9 

instruments for price in the demand equation (5'). Again, each demand 

equation has a different intercept but a common slope coefficient. For both 

equations, I report the system two stage least squares standard errors. 

The reported Durbin-Watson statistics are the average for those of the two 

The residuals from the unrestricted estimates of equation (2) where p 

varies across industries are used as the instruments. This procedure 

assures that the covariance restriction holds in the sample for each 

industry. 

The standard errors thus are consistently estimated in light of the 

clear heteroskedasticity across the two digit industries. 

'7 
P.19 

* 5-

1 

- 15 

digit equations. The pooling has two advantages over estimates carried 

out on the total data for each sector. First, the estimates are more 

efficient. Second, it is possible to remove a fixed effect for each 

industry. 

12 The results of the pooled estimates are presented in Table 1. The 

first three columns give the estimated markup coefficients, the standard 

errors of estimates, and the Durbin-Watson statistics for Hall's markup 

equation (2). The standard errors of the coefficient estimates are given in 

parentheses. The markups are essentially zero in agriculture, construction, 

and services. In durable and non-durable manufacturing and in finance, the 

markups are moderately sized but strongly significant. In mining, 

transportation, communications and utilities, and trade, the markups are 

very large. All the markups are estimates with a moderate to very fine 

degree of precision. 

The next three columns give the estimates for the demand equation. The 

results of the instrumental variables estimation is highly satisfactory. 

Except for mining, all the estimated elasticities are negative. Except for 

mining and finance, the elasticities are precisely estimated to be values 

bounded away from zero. 

The distribution across industries of the Durbin-Watson statistics 

for non-durables are given in the next table. The distribution of the 

statistics across the industries is consistent with the hypothesis of no 

serial correlation. Results for other sectors are similar. 

12 

For completeness, Table 1 reports results for durable goods. These 

should be discounted because, as noted above, the form of the demand 

function is inappropriate for them. 

/ « 
- 16 

w 

The next two columns give the values of the implied elasticity 

* * 

0 - p/(l ' p) and of the measure of market power 8 - 0/0 . There is a one-

* 

to-one relationship between p and 0 . Industries with high markups have low 

implied elasticities. The measure of market power 8 gives a somewhat 

different ranking of the competitive than do the markups alone. Mining and 

finance have estimated market elasticities that are essentially zero. 

Consequently, they appear to be competitive based on the 8 measure 

regardless of the markup. Industries with non-degenerate estimates of the 

markup also display interesting differences in ranking. For example, 

transportation and retail trade have similar estimated markups. The 

industries face different elasticities of demand and hence can be ranked in 

terms of degree of market power. 

The assumption that the slope coefficients in each of the subindustries are equal underlies the pooling of equations (2) and (5'). For 

all industries except for durables, one cannot reject these hypotheses using 

conventionally-sized tests. 

, Estimates for the individual non-durable manufacturing industries are 

presented in Table 2. The estimation procedure is the same as for the 

results in Table 1 except there is no pooling. In several of the industries 

(food, textiles, apparel, and printing and publishing), the estimated 

markups are insignificantly different from zero. These industries also have 

small markups. Other markups are significantly different from zero. Rubber 

and leather have relatively small markups; paper, chemicals, and petroleum 

have intermediate markups; tobacco has a very large markup. 
P.21 

« 

ve 

er 

- 17 

The estimated market elasticities all lie between -1.0 and -1.8. Most 

are estimated very precisely. Using the innovation in industries 

productivity as an instrumental variable is' a promising approach for 

estimating elasticities of demand. 

* 

The last two columns of Table 2 give the implied estimates of 0 and 8. 

The estimates of 8 display interesting dispersion and yield rankings as to 

market power that are different from those implies by the markup alone. As 

in Table 1, all of the point estimates of 8 fall within the admissible range 

between zero and one. Tobacco, paper, and chemicals all have values of 8 

insignificantly different from the monopoly outcome and at least three 

standard deviations different from the competitive outcome. All three 

industries can be characterized as monopolized despite their very different 

estimated markups. Apparel and leather have values of 8 of 0.3 and 0.5 

respectively. Moreover, each estimate has standard error such that both the 

competitive and monopolized outcomes can be rejected. Food and textiles 

have small estimated 8. These industries appear to be competitive, although 

the point estimates are imprecise. Finally, the standard errors for 

printing and publishing, petroleum, and rubber are large enough to make it 

difficult to reject any hypothesis. 

Alternative Instruments 

The previous results are based on the perhaps incorrect assumption that 

year to year changes in aggregate output are unrelated to productivity 

shocks. To provide estimates that are robust to failure of this assumption, 

I present estimates based on alternative instruments. These instruments 

20 
18 

should be strictly exogenous. The instruments used are growth in oil prices 

13 

and military employment. Oil prices have been determined largely by 

forces independent of the U.S. business cycle. These include the Suez 

crisis, the OPEC price increases after the Yom Kippur war and after the fall 

of the Shah of Iran, import quotas, and domestic price regulations. Changes 

in military employment are largely determined by wars, which again are not 

caused by U.S. business cycles. On the other hand, oil price changes and 

wars effect the business cycle. Therefore, they are likely to be adequate 

instruments. 

The results for the pooled manufacturing data with the alternative 

instrument lists are presented in Table 3. The first line repeats the 

results from Table 1 for ease of reference. The next three lines show the 

results for the combinations of the alternative instruments. The final line 

shows the result with all three instruments. With either oil price or 

military employment growth alone or jointly as instruments, 8 is estimated 

to be 0.1 or 0.2. With any of these combinations of instruments, the 

estimates of p. and hence of 8 are very imprecise. By comparing the 

estimates of the last two lines, it is potentially possible to judge whether 

the use of aggregate GNP growth as an instrument is a valid over-Identifying 

14 restriction. The point estimates of market power with the alternative 

instruments are smaller than with aggregate GNP growth as an instrument. 

13 

See the Appendix for sources of these data. 

14 

A formal Hausman specification test computed on the last two 

estimates of the markup and demand equations in Table 3 does not reject the 

overidentifying restriction. 
19 

Yet, those estimates are so imprecise that it is impossible to reject the 

hypothesis that use of aggregate GNP growth is an instrument is a valid 

overidentifying restriction. 

5. Discussion 

alternative Estimates of the Markup 

It is interesting to compare these estimates of market power with those 

obtained by other techniques. The markup can be estimated from a cost 

function rather than from the cyclicality of productivity. Appelbaum 

(1982), for example, estimates 8 using the markup from the derivative of an 

estimated, parametric cost function. He examines three non-durable 

manufacturing industries: textiles, rubber, and tobacco. His findings for 

textiles and tobacco agree qualitatively with mine. Textiles are 

essentially competitive and tobacco has strong market power. He finds 

rubber is essentially competitive whereas I find that industry to be close 

to the monopoly outcome, albeit with an imprecise point estimate. 

Appelbaum estimates less monopoly power than do I because he finds 

smaller markups. It is fairly straightforward to explain why Appelbaum's 

implementation of the cost function yields systematically lower markups than 

does Hall's non-parametric approach that I follow in this paper. Appelbaum 

uses a constant returns to cost function where labor, materials, and capital 

The underlying estimates for most of the individual industries using 

only oil and military employment growth have large standard errors. 

Note that rubber is a very concentrated industry (see below). 

P2-
- 20 

are all free to vary within the period. Thus, he constrains marginal cost 

to equal average cost. If an industry shows little profit in excess of the 

required rate of return on capital, as do most industries, this approach 

will yield a small markup. Hall's procedure admits the possibility of 

higher markups in such industries because Solow's formulation allows 

marginal cost to be below average cost. In the Solow calculation, capital 

can be quasi-fixed (as it surely is), so the marginal cost curve can have 

upward slope. 

Measures of Market Power Compared 

It is useful to compare the measures of market power presented in this 

paper with other measures. Before doing so, it is necessary to put the 

measures on an equal basis. As discussed above, p, 0 , and 0 are on a 

value-added basis. Table 4 presents the estimates from Table 2 converted to 

18 

a gross output basis. As Hubbard (1986) and Domowitz, Hubbard, and 

Petersen (1987) stress, the gross output based markup is substantially lower 

than the value-added based ones. Moreover, the ranking^of the markups 

changes depending on the materials intensity of the industries. 

U.S. manufacturing industries have low price-cost margins. Domowitz, 

Hubbard, and Petersen (1986, Table 1) find that profits per output is only 

about 35 percent in the most concentrated industries and 26 percent overall. 

Since their calculation of profit includes normal return to capital, their 

figures imply, lower markups than those included in this paper. Any 

calculation that is based on average cost must similarly yield low markups. 

18 The gross output elasticities should be interpreted with caution 

because the share of materials may have shift over time. 

r 

i 

< 
21 -

Table 5 compares a number of measures for the non-durable manufacturing 

industries. They are the markup coefficient as estimated in Table 2 (p); 

the markup Adjusted to a gross output basis (£); the implied elasticity of 

demand from Table 2 (0 ); the implied elasticity on a gross output basis 

(0 ); the index of market power from Table 2 {8); and a measure of average 

19 concentration (CR,). The cross-sectional standard deviation and simple 

and rank correlations of these measures are given in Table 5. The simple 

correlations among all the variables are quite high. Particularly striking 

Is the fairly strong correlation of the concentration ratio with the other 

measures. Concentration ratios might be very misleading as to market power 

in cases where the other measures may not. This is especially true if 

market power arises because of monopolization of local markets. The rank 

correlations of the measures with concentration are substantially weaker. 

Much of the leverage for the correlations comes from the extreme observation 

of tobacco. Excluding tobacco, the correlation of Ji and the concentration 

measure falls to 0.40 and that of 8 and the concentration measure falls to 

0.49. Figures 1 and 2 give a scatter of the observations for Ji and 8 versus 

concentration. The important correlation between the measures clearly 

emerges from the Figures. Aside from petroleum, the scatter diagrams are 

qualitatively quite similar. The estimates of market power in this paper 

give a similar picture of the degree of monopolization of U.S. non-durable 

manufacturing industries than do the concentration ratios. 

I^JY 

19 

The measure is the sales ratio average of four firm concentration 

ratios based on the four digit data in Rotemberg and Saloner (1986). 

3H 
22 

. $ . 

Conclusion 

In this paper, I discuss estimation of demand elasticities by 

exploiting the restriction that demand shocks and technological shocks are 

independent. Although this technique may have broad implications, it is 

used here to compare market demand elasticities with those implied by price -

marginal cost margins. The price-marginal cost ratio is not, per se. a 

measure of monopoly power. If an industry has a price-marginal cost ratio 

that differs significantly from unity, one can reject the hypothesis of pure 

competition, but one can say nothing else about the degree of monopolization 

in the industry. A given price-marginal cost ratio will imply more monopoly 

power the more elastic is demand. Monopoly power must be strong in order to 

extract high prices in an industry with elastic demand. 

The estimated measures of market power correspond to a wide range of 

conduct. The point estimate for tobacco and chemicals is that they achieve 

the monopoly outcome. Paper is also close to the monopoly outcome. On the 

other hand, for apparel and leather, both the monopoly and competitive 

outcomes can be decisively rejected. 

Finally, this paper shows how to estimate the price elasticity of 

demand by exploiting the covariance restriction between productivity shocks 

and demand shocks. This covariance restriction is an important step in 

overcoming the difficulty in identifying the demand curve because of the 

lack of valid instruments. This technique for estimating the elasticity of 

demand should have important applications beyond the measurement of market 

power. 
ere 

on 

iy 

to 

23 

APPENDIX 

1. Data 

The data used in this paper are described in this Appendix. 

Except for the data on the capital stock, they are from the National 

Income and Product Accounts (NIPA). The data are annual and are available 

at the two digit level of disaggregation. The NIPA were rebenchmarked in 

December 1985. At the same time, the base year for the constant dollar 

calculations was changed to 1982. The data incorporate the July 1986 

revisions and were extracted from BEA computer tapes. The industry 

* 

definitions are based on the 1972 standard industrial classification. 

In detail, the NIPA data are as follows. Table number refer to those in the 

NIPA as published in the July Survey of Current Business. 

output (y ): Real value-added in 1982 dollars (Table 6.2). 

deflator (p ): Value-added deflator (Tables 6.1, 6.2). In the demand 

equation estimates, the relative price is calculated as the ratio of the 

industry value-added deflator to the aggregate GNP deflator. 

manhours (n ): Hours of full-time and part-time employees (Table 

6.11). The industry level manhours data are only available at the sectoral 

level. To construct hours for the two digit industries, the hours for the 

sectoral total are divided among the appropriate two digit industries in 

proportion to the two digit industry's share in full-time equivalent 

employment (Table 6.7) in the sector. 

compensation: Compensation (Table 6.4) is used in the calculation of 

the labor's share, a . It includes wages and salaries, employers' 

contributions to social insurance, and other labor income, but not 

96? 
24 

proprietors' income. The share a is calculated as a Divisia index, that 

is, it is a moving average of the share at time t and time t-1. 

The capital stock data are also based on the rebenchmarked NIPA data. 

They are published in the Survey of Current Business (August 1986, for 

example) were obtained for this study from computer tape. The capital stock 

is constant dollar net capital stock of equipment plus structures. 

The data for the instruments is as follows: aggregate GNP is from the 

NIPA Table 6.2 and is measured in constant 1982 dollars. Oil prices are 

measured as the ratio of the producer price index for crude oil (PPI561) to 

the GNP deflator. Military employment is full time equivalent Federal 

military employment (NIPA Table 6.6). All instruments are annual and log 

differenced. 

The two digit industries pooled in the estimates in Table 1 for the 

respective sectors are as follows. The number of two digit industries is 

given in parentheses. 

Agriculture (2): Farms; Agricultural services, forestry, and 

fisheries. Mining (4): Metal mining; Coal mining; OlT and gas 

extraction; Non-metallic minerals, except fuels. Construction (1). 

Durable manufacturing (11): Lumber and wood products; Furniture and 

fixtures; Stone, clay, and glass; Primary metal industries; Fabricated 

metal products; Machinery, except electrical; Electric and electronic 

equipment; Motor vehicles and equipment; Other transportation 

equipment; Instruments and related products; Miscellaneous 

manufacturing industries. Non-durable manufacturing (10): Food and 

kindred products; Tobacco manufactures; Textile mill products; Apparel 

17 
P.29 

- 25 

and other textile products; Paper and allied products; Petroleum and 

coal products; Rubber and miscellaneous plastic products; Leather and 

leather products. Transportation (7): Railroad transportation; Local 

and interurban passenger transit; Trucking and warehousing; Water 

transportation; Transportation by air; Pipelines, except natural gas; 

Transportation services. Communications and Utilities (3): Telephone 

and telegraph; Radio and television broadcasting; Electric, gas, and 

sanitary services. Wholesale trade (1). Retail trade (1). Finance. 

insurance, and real estate (6): Banking; Credit agencies other than 

« 

banks; Security and commodity brokers, and services; Insurance 

carriers; Insurance agents and brokers, and services; Real estate. 

Services (10): Hotels and other lodging places; Personal services; 

Business services; Auto repair, services, and garages; Miscellaneous 

repair services; Motion pictures; Amusement and recreation services; 

Health services; Legal services; Educational Services 

2. Econometric Issues „ 

Disaggregation and Identification 

Aggregate output growth will not in general be a valid instrument for 

estimating the markup equation (2) on disaggregate data. Disaggregation 

alone typically does not yield identification. If there is an Important 

aggregate demand shock, equation (2) will be approximately identified. Say 

aggregate GNP growth (denoted Aq ) evolves as 

Aq - Av + Zjfa^Ac 

* 

i-i-'it 

2Z 
- 26 

where Av is an aggregate demand shock and w. is the share of industry i in 

the aggregate. (The shares are constant only for notational convenience.) 

The inconsistency in estimating p. that arises because the aggregate is the 

some of the industries is 

(Al) plim T"1(Mi - PL) - u>± Var(Acit) / Cov(ait(Anlt-Aklt) , Aqt) 

The usual problem with identification by disaggregation is that as Var(Av ) 

vanishes, the inconsistency is of order one. On the other hand, if the 

variance of the demand shock is not small, the inconsistency is on the order 

of w., which is small. 

Instrumental Variables Estimator and Covariance Restrictions 

Consider estimation of two equations analogous to the markup equation 

and the demand equation. Data are available on a panel of industries. 

Denote them — 

(A2) 7kr -*,J. + V it "it 1 it 

where k - 1,2 indexes equations, where i - 1,M indexes indvistrles, and where 

t - 1,T indexes time. In matrix notation we have 

(A3) yk - Xk «

k + vk 
P.31 

ce 

- 27 -

k k where the y and v are stacked vectors of observations and disturbances and 

k k 

X - diag(X.). First consider identification of the parameters. Suppose 

that the first equation (k-1) is at least just-identified as is the case of 

markup equation. It can be estimated by standard instrumental variables 

techniques. Suppose that the second equation has two right hand side 

variables. (In the demand equation they the constant and the price term.) 

The equation Is under-identified by conventional means. That is, no 

instrument is available. Suppose that the disturbances of the two equations 

1 2 

are independent Indus try-by-industry. That is, E(v v.) - 0. This 

* 

restriction is sufficient to just-identify the parameters of the' second 

equation. Moreover, it has an instrumental variables interpretation. The 

residual from the first equation can be used as an instrument for the second 

equation. This procedure yields consistent, asymptotic normal estimates 

and, because the second equation is just identified, is equivalent to 

maximum likelihood (see Hausman, Newey, and Taylor (1987)). 

The covariance matrix printed by the computer for the second equation 

will not be correct. The correct one depends on the estimated parameters 

and the data from the first equation because the fitted value rather than 

the true value of v is used as the instrument. Let Z, be the instruments 

for the second equation for the i equation and where Z - diag(Z.). (In 

this paper, Z, has two columns, the constant and the residuals from the 

A2 first equation.) The instrumental variables estimator of 5. is such that 

(A4) "2 2 2-1 2 S\ - S\ + (Z.'X^) \>v\ 

m&. 

BO 
- 28 -

Note that the second term of the right hand side of (A4) will have an 

2 1A1 element involving the correlation of v and X S because Z is dependent on 

the estimated value of S . This term will add to the covariance of the 

estimate 6 Define a matrix Q that has elements 

A2 1 Al Al 1A2 (A5) Wi j - v£'xJ'cov(Sj,«j)XjV^ 

This term is the covariance between the residual from the second equation 

1

A1 

and X 6 . Let £ be the MxM covariance matrix of the disturbances of the 

2 2 

second equations (Indus try -by- industry) . That is, E(v v ') - 2381. Let 

-[i°x] 

be a matrix that selects elements of Z. corresponding to the fitted 

instrument. The correct variance-covariance matrix of the system 

2 instrumental variables estimator of S is then 

(A6) V(*2) - (Z'X2)"1Z'(2»I)Z(X2'Z)"1 + (Z2'X)"1Z'(0®S)Z(X2'Z)"1 

The first term is the standard system instrumental variables covariance 

matrix. The second is the correction term. The resulting standard errors 

are strictly greater than the ones printed by the standard computer program. 

In this application, the correction adds ten to twenty percent to the 

standard errors. 

St. 
j^f*4**

s

i'^"' 

i^^tt^gtmmmm 

C/J 

n 

3 t * 

o (D V) 

"1 

H 3 

B 3 

o 

» 

rt 

P H

-

H 

H H 0> o. (P 

? 

O 

H (P 01 

H » (V 

H 

H 

P 0

-

(V 

P> 

3 P. c j rt HH 

H 

rt 

H 

rt> 

W 

^ 

o 

O 

1 

§ p» 

o to 

rt H 

o 3 

u 

* * 

K 3 

u "d 

o H 

rt 

m rt 

H 

• o 3 

'f- Y S3 

o 

2C 3 

(a • 3 a Me c i H to CO o o* rt H C CD 

K H

-

3 00 

* <! 

? 

CC H 

(_ p. 3 cr C H M> » Pl 

O rt 

C 

M M* 

3 

$-.* • 

a 

o 

3 Ul 

rt 

2 

o rt H 

o 3 

EC 

H 3 

H 

3 

W 

> 

H 

H 

O 

C 

H 

rt C 

M R> 

3

 ?t#^ 

o o H O 6.6 ) 1.5 

^-\ i 

O H OJ to to to 

H 

H 00 

O t o 

• -0.N 1 

o t o 5.5 1.1 0.1 1 t o 

CT> 

JP* 

H 

•«J 

O H P- t o 2.3 ) 2.4 

/-» i O H IO t o t o U l 

H 00 

o o\ •0.^ 5 H »J 3.4 1.6 1.1 5 u> 

b 

H 

•«j 

o 

• v j 

•"0.N 4 

H u> 24.2 1.5 1.• 2 H 

*»l 00 VO 

H 00 

o t o 

x -0.s 1 

H 

H 11.4 1.7 1.1 0 av 

'*• 

H 00 

O 

H 

/•0.x 1 

O 

•p» 5.0 1.9 1.1 3 av VO 

H VO 

o 

o 

^-0.v 2 

o • o 5.1 2.2 1.1 4 t o ~ j U l 

H ^J 

o t o 

• -0.x 2 

o t o 3.9 0.7 1.1 0 t o VO 

H U l 

O U> 

••»0.* 1 

o vO 9.3 1.4 0.1 vO Ov t o 

b 

o 

•*> 

s -1.^ 0 

o 

o 6.4 1.7 1.• 8 H 

•P" U l t o U> 

t 

H see g" 

"CO CO a> 9* 

< 

3: rkup Equation (man 0 d 

w 4 3 

0 ati 

o 3 

Pooled, Se ctox pi 

H Estl B ates 

PI 

H P> ticlties L 3 

H 

H and 

m stimate 

a 

ro vO 

' u» 

^N i ro i 

\ji to ^\ I S~* I ^N I /^ • x^ • *-\ • •"•* i ^s l >-N • VO VO 

^JCTV UIUI OH OH OH OH O Ul O Ul U>UI OtO -P" Ov 

vo*> HUI u> oo io gi p- oo i-»vo a» *- u»ui to to PH rou> 

* .§ 

OO OO OO OO oo oo oo oo o o 

I1 O oo ro ^i Ul VO U» VI HUI H -P- H-P- Hr o 

o o av o 

CD 

CA) 

co co 
IT 

pi 

rt 

3* 

to 

H 

2? 

c 

o* 

cr CD 

H 

*a 

a 

rr 

n 

o H eum 

o. 

3* (0 

S H> 

o als 

*a 

H 

*0 H 

£O. a 

* ft 

H Hn- g and 

Ishing 

m 

P> 

•o ft 

ri 

> 

•o 

•d 

PI 

n 

n> H 

H 

(ft 

X 

rt 

H 

H 

CD 

u 

H 

O 

V 

pi 

o 

o 

o 

*n 

o 

o Q. 

o o o o O H or o O O O H O O O O HP - o o 

4>oo ro«»j vj u si o ui *> p»ui rou i u> u> oo o »«J Puiuiuiovtouiroovovu i 

VOIOVOIOVOUIOOOUIU I 

P-Ovp»00>4vlvO-^IUlU > 

^ N I /*V I ^ v • S*< I X-\ • /-S • ^ • •"* I /- * I *-^ I 

O H t-1 f-* H H O H O H O H O H O H O H O H 

ui to rooo o ui p- ui ov oo tout UI H UI UI UJ U> U> 0 

CO 

CD 

CD 

8-

Ov 

VJ 

ro 

00 

•vl 

p> 

Ov 

Ul 

u> 

t o H 

H 00 

u> 

•vl 

Ov 

Ul 

Ul 

IO 

u> 

b 

0 0 

Ov 

ro 

b 

00 

ro U l 

H ro 

oo ro 

CO 

CD 

ID 

8" 

pi 

M 

P l 

X I 

c 

pi 

rt 

H 

O 

3 

o 

CD 

5 

Pi 

3 

OPl 

o 

3 

58 

o 3 

i 

& 

i-t 

8-

to H 

CD PC CO 

Pl 

8 

Ml 

P> 

O 

rt 

C 

H3 

W 

3 

e 

10 

rt 

M 

g £• 

p i 

H 

P> 

CO 

rt !-•• 

O 

•8 

(D 

§ 

0. 

H 

6-

ro 

u> 

o 

H P l 

CO 

rt 

H 

B 

Pl 

rt 

CD 

o. 

% 

o r o or o O H O H rou> O H H* - •P*P* O H UIU J 

OVU I u>ui *-> J roui «sj ro ro »J UI H O »>I HU > rooo 

"Co H 

o o o o o o O H O O O O O O O O O H O O 

roui uioo ov vo co o UIUI tovo H UJ UJ ui to o P~u> 

CD 

a 

j^rrmr^t\(%rim''-'irmmm^^ ij-fiTTiritJi 

OP 

co 
P.35 

- 31 

Table 3 

Elasticities Implied and Estimated 

Pooled Non-durable Manufacturing Industries 

Alternative Instruments for Markup Equation 

w 

Instruments Markup Equation Demand Equation Implied 

w 

& ' 

ft 

f.l 

growth in: 

GNP 

oil prices 

military employment 

oil prices and 

military employment 

GNP, oil prices, and 

military employment 

0.4 

(0.1) 

0.1 

(0.3) 

0.2 

(0.3) 

0.2 

(0.3) 

0.3 

(0.1) 

see 

5.0 

14.4 

97.3 

6.0 

4.9 

dw 

1.9 

1.8 

1.7 

1.9 

1.9 

P 

-1.3 

(0.1) 

-1.2 

(0.2) 

-1.2 

(0.2) 

-1.2 

(0.2) 

-1.3 

(0.1) 

see 

6.9 

6.7 

22.5 

10.6 

7.4 

dw 

1.9 

1.8 

1.9 

1.9 

1.9 

0 

-3.4 

(0.6) 

-8.6 

(17.3) 

-5.9 

(7.1) 

-7.6 

(U.3 ) 

-3.9 

(0.9) 

8 

0.4 

(0.1) 

0.1 

(0.3) 

0.2 

(0.2) 

0.2 

(0.2) 

0.3 

(0.1) 

3*. 
32 -

Table 4 

Value-Added and Gross Output Parameter Estimates 

Food 

Tobacco 

Textiles 

Apparel 

Paper 

Printing 

Chemicals 

Petroleum 

Rubber 

Leather 

P-l 

0.4 

4.0 

0.3 

0.3 

1.5 

0.4 

2.0 

1.3 

0.7 

0.8 

value added 

* 

-3.8 

-1.3 

-4.7 

-4.1 

-1.7 

-3.2 

-1.5 

-1.7 

-2.3 

-2.3 

A 

-1.0 

-1.3 

-1.5 

-1.1 

-1.5 

-1.8 

-1.5 

-1.5 

-1.8 

-1.2 

£-1 

0.2 

0.5 

0.1 

0.1 

0.4 

0.3 

0.6 

0.2 

0.3 

0.3 

gross output 

"* 

-7.1 

-2.9 

-11.2 

-8.4 

-3.5 

-4.7 

-2.8 

-5.3 

-4.4 

-4.8 

fi 

-2.0 

-2.9 

-3.6 

-2.3 

-3.1 

-2.6 

-2.8 

-4.6 

-3.4 

-2.5 

7 

0.466 

0.566 

0.582 

0.510 

0.522 

0.314 

0.455 

0.671 

0.462 

0.519 

Note: The estimated fi, 0 , and 0 are from Table 2. The gross output based 

estimates are derived according to the formulas Ji - /i/(l+(p-l)7) (Hall, 1986a), 

"* * * 

0 - 0 /(1-7). and 0 - 0/(l-i). The materials shares (7) are from Hubbard 

(1986). 

5S", 
P.37 

33 

Table 5 

Alternative Measures of Market Power 

Non-durable Manufacturing Industries 

|||| standard 

deviation 1.14 0.16 

fi 

1.21 2.7 0.30 

CR, 

0.19 

§g; simple 

correlation 

with: 

IT':-* 

13." 

fi 

CR, 

1.00 0.83 

1.00 

0.76 

0.85 

1.00 

0.65 

0.87 

0.92 

1.00 

0.80 

0.88 

0.94 

0.84 

1.00 

0.68 

0.59 

0.51 

0.44 

0.62 

1.00 

m 

rank ' 

correlation 

with: 

A* 

P 

f 

Y 

8 

CR, 

1.00 0.77 

1.00 

1.00 

0.77 

1.00 

0.77 

1.00 

0.77 

1.00 

0.86 

0.77 

0.86 

0.77 

1.00 

0.17 

0.17 

0.17 

0.86 

0.25 

1.00 

3b 
P.38 

Figure 1 

c 

o 

_ 

• 

o 

c 

6 

o 

u.o -

0.7 -

0.6 -

0.5 -

0.4 -

0.3 -

0.2 -

•»«Kttl«_ -»ood 

•apparel 

•rubber 

.pqp«r 

•tooHtar 

•printing and publishing 

•ahamtoolft 

0.1 - 1 — 

0.2 

—T— 

0.4 

-~r— 

o.e 

Markup (gross prfoa/marglnal aosr) 

Figure 2 

• 

o 

c 

o U 

u.o -

0.7 -

0.6 -

0.5 -

0.4 -

0 J -

0_2-

/ 

•foodr«tl|«_ 

•opporti 

i i 

• rubber 

•leather 

• printing and publishing 

III I 

-

• petroleum 

• paper 

i 

•taboooc 

•ahamlac 

T 1 

*:>." 

I 

0.2 0.4 0.6 0.6 

Theto 

-34-
35 

REFERENCES 

I Appelbaum, Elie, "The Estimation of the Degree of Oligopoly Power," Journal 

of Econometrics 19 (1982) 287-299. 

Bresnahan, Timothy F., "The Oligopoly Solution Concept is Identified," 

Economics Letters 10 (1982) 87-92. 

Bresnahan, Timothy F., "Empirical Studies of Industries with Market Power," 

Handbook of Industrial Organization. Richard Schmalensee and Robert 

Willig, eds., forthcoming (1987). 

J s, 

V 

\ & 

Bruno, Michael, "Duality, Intermediate Inputs and Value-Added," in 

Production Economics: A Dual Approach to Theory and Applications. vol. 

2, Melvyn Fuss and Daniel McFadden, eds. Amsterdam: North-Holland, 

1978. 

Bruno, Michael and Jeffrey D. Sachs, Economics of Worldwide Stagflation. 

Cambridge, Mass.: Harvard University Press, 1985. 

Domowitz, Ian, R. Glenn Hubbard, and Bruce C. Petersen, "Business Cycles and 

the Relationship between Concentration and Price-cost«Margins," Rand 

Journal of Economics 17 (1986) 1-17. 

Domowitz, Ian, R. Glenn Hubbard, and Bruce C. Petersen, "Market Structure 

and Cyclical Fluctuations," unpublished paper, Northwestern University 

(1987). 

Hall, Robert E., "The Relation Between Price and Marginal Cost in U.S. 

Industry," unpublished paper, Hoover Institution (1986a). 

I* I 

Hall, Robert E., "Chronic Excess Capacity in U.S. Industry," National Bureau 

of Economic Research Working Paper No. 1973, Cambridge, MA (1986b). 

3& 
- 36 

Hall, Robert E., "Market Structure and Macro Fluctuation," Brookings Papers 

on Economic Activity (2:1986) 285-322 (c). 

Hall, Robert E., "Productivity and the Business Cycle," Carnegie-Rochester 

Conference on Public Policy, forthcoming (1987). 

Hausman, Jerry A. and William Taylor, "Identification in Linear Simultaneous 

Equations Models with Covariance Restrictions: An Instrumental 

Variables Interpretation," Econometrica 51 (1983) 1527-49. 

Hausman, Jerry A., Whitney Newey, and William Taylor, "Efficient Estimation 

and Identification of Simultaneous Equations with Covariance 

Restrictions," Econometrica (1987), forthcoming. 

Hubbard, R. Glenn, "Discussion," Brookings Papers on Economic Activity 

(2:1986) 238-336. 

Kydland, Finn E. and Edward C. Prescott, "Time to Build and Aggregate 

Fluctuations," Econometrica 50 (1982) 1345-1370. 

Long, John B., Jr. and Charles I. Plosser, "Real Business Cycles," Journal 

of Political Economy 91 (1983) 39-69. 

Rotemberg, Julio J. and Garth Saloner, "A Supergame-Theoretic Model of Price 

Wars during Booms," American Economic Review 76 (1986) 390-407. 

Shapiro, Matthew D., "Are Cyclical Fluctuations in Productivity Due More to 

I! 

Supply Shocks or Demand Shocks?" American Economic Review Proceedings 

77 (1987) 118-124. 

Solow, Robert M., "Technical Change and the Aggregate Production. Function," 

Review of Economics and Statistics 39 (1957) 312-320. 

•37 j