On the Estimation of Returns to Scale, Technical Progress and Monopolistic

Markupsby Erwin Diewert and Kevin Fox

Discussion by Susanto Basu

Comments on

SSHRC Conference, Vancouver, July 3, 2004

Returns to Scale SSHRC Conference, July 3, 2004 2

Reactions

• Theory developed is very nice

• Returns to scale/markup estimates seem too high

Returns to Scale SSHRC Conference, July 3, 2004 3

Comments on the theory

• Bring index-number theory into the estimation of returns to scale

• Generalize literature to multiple outputs and inputs

• Using previous results (esp. Diewert, 1976), extend existing work on estimating returns to scale using first-order approximations

• Show that the nice result of being able to get a second-order approximation by time-averaging shares (a Törnqvist index) extends to imperfect competition and increasing returns

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This is a nice achievement

• A result of large practical importance: MANY fewer parameters to estimate than standard translog, but maintain the same degree of flexibility

• Confirms the intuition of applied researchers (e.g., me!) that it shouldn’t be necessary to estimate all the translog parameters. Since share equations cannot give information on scale, why use up degrees of freedom?

• But addresses critiques (e.g., Nadiri and Prucha, 2001) that restricting elasticities of substitution to one (as in the first-order/Cobb-Douglas approximation) can lead to large biases

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Why Zvi would be skeptical (1)

• …but only about the empirical results• Zvi emphasized large range of firm sizes, even in

narrowly-defined industries• Employment ratios of 100:1 not uncommon• But then (Zvi said) RTS have to be close to constant,

or bigger firms would have an overwhelming efficiency advantage

• Ex: D-F estimate manufacturing RTS about 1.5.Implies a firm 100 times larger should have average cost that is 1/10th that of the smaller firm

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Why Zvi would be skeptical (2)

• Not consistent with most firm- and establishment-level studies

• One of the earliest: Griliches and Ringstad (1971)• Later ones—numerous, but an early example is

Baily, Hulten and Campbell (1992)• Establishment-level data. Missing the “headquarters,”

which might be the source of overhead costs and RTS

• Erwin and Kevin suggest that industry-level production function might be different

• Few reasons for industry RTS to exceed firm RTS• If due to externalities, give examples of large, high-frequency external effects

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An aside: Short- and Long-Run RTS

• For an industry production function, have to worry about time horizon over which RTS estimate applies

• Ex: Suppose an industry with identical firms, each with increasing returns. Short run: Number of firms constant, output per firm varies. Long run: Output per firm constant, number of firms varies

• Then short-run industry PF will have the same RTS as each firm. But the long-run industry PF will have CRS, regardless of the RTS at the firm level

• Important for conclusions about TFP growth. Paper takes short-run RTS estimates (based on one-year differences), and applies to long-run trend growth

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One final reason

• Domar (1961) and Hulten (1978) showed industry contribution to aggregate TFP is

• With markups, this becomes

• Need k-1sM < 1 to avoid infinite contributions!

• The highest-RTS industries violate this condition(for Paper, Table 2 has k-1sM = 2.06 x 0.60 = 1.24)

1

i

Mi

t

s

11 1i i

i Mi i Mi

t t

M s k s

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Conjectures about the cause

• To avoid too-large RTS estimates, costs have to be more procyclical than they appear in the data

• Variations in labor hours may be much larger than measured, especially for white-collar workers

• Real wage may be more procyclical than in data• Marginal versus average wage (overtime) [Bils, 1987]• Maybe short-term nominal wage stickiness, that firms

know they will have to “make up” in a later contract (Card, 198?)

• Changes in utilization, especially for capital• Try longer differences to align ΔCost and ΔY• Worry about endogeneity as reason for high RTS

• Explains lower estimates from reverse regressions

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Conclusion

Really nice and useful theory; need to think more about the empirics