Prices, Markups and Trade Reform*
Jan De Loecker†

Pinelopi K. Goldberg ‡Amit K. Khandelwal§

Nina Pavcnik¶

First Dra : February 2012
This Dra : August 2012

Abstract
This paper examines how prices, markups and marginal costs respond to trade liberaliza on. We develop a framework to es mate markups from produc on data with mul -product ﬁrms. This approach
does not require assump ons on the market structure or demand curves faced by ﬁrms, nor assumpons on how ﬁrms allocate their inputs across products. We exploit quan ty and price informa on
to disentangle markups from quan ty-based produc vity, and then compute marginal costs by dividing observed prices by the es mated markups. We use India’s trade liberaliza on episode to examine
how ﬁrms adjust these performance measures. Not surprisingly, we ﬁnd that trade liberaliza on lowers
factory-gate prices and that output tariﬀ declines have the expected pro-compe ve eﬀects. However,the price declines are small rela ve to the declines in marginal costs, which fall predominantly becauseof the input tariﬀ liberaliza on. The reason is that ﬁrms oﬀset their reduc ons in marginal costs byraising markups. Our results demonstrate substan al heterogeneity and variability in markups acrossﬁrms and me and suggest that producers beneﬁted rela ve to consumers, at least immediately a er
the reforms. Long-term gains to consumers may be higher to the extent that higher ﬁrm proﬁts leadto new product introduc ons and growth. Indeed, ﬁrms with larger increases in markups had a higher
propensity to introduce new products during this period.

Keywords: Markups, Produc vity, Pass-through, Input Tariﬀs, Trade Liberaliza on*

The work for this project was carried out while Goldberg was a Fellow of the Guggenheim Founda on, De Loecker was a visitorof the Cowles Founda on at Yale University and a visi ng Professor at Stanford University, and Khandelwal was a Kenen Fellow at
the Interna onal Economics Sec on at Princeton University. The authors thank the respec ve ins tu ons for their support. We
also wish to thank Steve Berry, Elhanan Helpman, Ariel Pakes, Andres Rodriguez-Clare and Frank Wolak for useful discussions at
early stages of this project and seminar par cipants at several ins tu ons and conferences.
†
Princeton University, Fisher Hall, Prospect Ave, Princeton, NJ 08540, email: jdeloeck@princeton.edu‡
Yale University, 37 Hillhouse, New Haven, CT 06520, email: penny.goldberg@yale.edu§
Columbia Business School, Uris Hall, 3022 Broadway, New York, NY 10027 email: ak2796@columbia.edu¶
Dartmouth College, 301 Rockefeller Hall, Hanover, NH 03755, email: nina.pavcnik@dartmouth.edu

11Introduc on

Trade reforms have the poten al to deliver substan al beneﬁts to economies by forcing a more eﬃcient
alloca on of resources. A large body of theore cal and empirical literature has analyzed the mechanisms
behind this process. When trade barriers fall, aggregate produc vity rises as less produc ve ﬁrms exit
and the remaining ﬁrms expand (e.g., Melitz (2003) and Pavcnik (2002)) and take advantage of cheaperor previously unavailable imported inputs (e.g., Goldberg et al. (2010a) and Halpern et al. (2011)). Tradereforms have also been shown to reduce markups (e.g., Levinsohn (1993) and Harrison (1994)). Based on
this evidence, we should expect trade reforms to exert downward pressure on ﬁrm prices. However, wehave li le direct evidence on how prices respond to liberaliza on because they are rarely observed during
trade reforms. We ﬁll this gap by developing a uniﬁed framework to es mate jointly markups and marginal
costs from produc on data, and examine how prices, and their underlying markup and cost components,
adjust during India’s comprehensive trade liberaliza on.
Our paper makes three main contribu ons. The ﬁrst contribu on is towards measurement. In order toinfer markups, one requires es mates of produc on func ons. Typically, these es mates have well-known
biases if researchers use revenue data rather than quan ty data to es mate produc on func ons. Es matesof “true” produc vity (or marginal costs) are confounded by demand shocks and markups, and these biases
may be severe (see Foster et al. (2008)). De Loecker (2011) demonstrates that controlling for demand
shocks substan ally a enuates the produc vity increases in response to trade reforms in the European
Union tex le industry. As a result, approaches to infer markups from produc on data may be problema c
if one uses revenue informa on. We alleviate this concern by inferring markups from a quan ty-based
produc on func on using data that contain the prices and quanes of ﬁrms’ products over me.

Second, we develop a uniﬁed framework to es mate markups, marginal costs and produc vity of mul product ﬁrms across a broad set of manufacturing industries. Since these performance measures are unobserved, we must impose some structure on the data. However, our approach requires substan ally fewer
assump ons than is typically required in industrial organiza on studies. Crucially, our approach does not
require assump ons on consumer demand, market structure or the nature of compeon. This ﬂexibility

enables us to infer the full distribu on of markups across ﬁrms and products over me in diﬀerent manufacturing sectors. Moreover, since prices are observed, we can directly recover marginal costs from ourmarkup es mates. Our approach is quite general and since data containing this level of detail are becoming increasingly available, this methodology is useful to researchers studying other countries and industries.
The drawback of this approach is that we are unable to perform counterfactual simula ons since we do not
explicitly model consumer demand and ﬁrm pricing behavior.
Third, exis ng studies that have analyzed the impact of trade reforms on markups have focused exclusively on the compeve eﬀects from declines in output tariﬀs (e.g., Levinsohn (1993) and Harrison(1994)). Comprehensive reforms also lower tariﬀs on imported inputs and previous work, par cularly on
India, has emphasized this aspect of trade reforms (e.g., see Goldberg et al. (2009)). These two tariﬀ reducons represent dis nct shocks to domes c ﬁrms. Lower output tariﬀs increase compeon by changing

the residual demand that ﬁrms face. Conversely, ﬁrms beneﬁt from lower costs of produc on when input
tariﬀs decline. It is important to account for both channels of liberaliza on to understand the overall impact
2

of trade reforms on prices and markups. In par cular, declines in markups depend on the extent to whichﬁrms pass these cost savings to consumers, the pass-through being inﬂuenced by both the market structureand nature of demand. For example, in models with monopolis c compeon and CES demand, markups

are constant and so by assump on, pass-through of tariﬀs on prices is complete. Arkolakis et al. (2012)
demonstrate that several of the inﬂuen al trade models assume constant markups and by doing so, abstract away from the markup channel as a poten al source of gains from trade. This is the case in Ricardianmodels that assume perfect compecompe

on, such as Eaton and Kortum (2002), and models with monopolis con such as Krugman (1980) and its heterogeneous ﬁrm extensions like Melitz (2003). There aremodels that can account for variable markups by imposing some structure on demand and market structure (e.g., Bernard et al. (2003), Melitz and O aviano (2008), Mayer et al. (2011), Feenstra and Weinstein(2010), Arkolakis et al. (2012) and Edmonds et al. (2011)). While these studies allow for richer pa erns ofmarkup adjustment, the empirical results on markups and pass-through ul mately depend on the underlying parametric assump ons. Ideally, we want to understand how trade reforms aﬀect markups without
having to rely on explicit parametric assump ons of the demand systems and/or market structures, whichthemselves may change with trade liberaliza on.
The structure of our analysis is as follows. We use produc on data to infer markups by exploi ng theop mality of ﬁrms’ variable input choices. Our approach is based on De Loecker and Warzynski (2012), but
we extend their methodology to account for mul -product ﬁrms and to take advantage of observable pricedata. The key assump on we need to infer markups is simply that ﬁrms minimize cost; then, markups are
the devia on between the elas city of output with respect to a variable input and that input’s share of total
revenue.1 We obtain this output elas city from es mates of produc on func ons across many industries. In
contrast to many studies, we u lize physical quan ty data rather than revenues to es mate the produc onfunc ons.2 This alleviates the concern that the produc on func on es ma on is contaminated by prices,
yet presents diﬀerent challenges that we discuss in detail in Sec on 4. Most importantly, using physicalquan ty data forces us to conduct the analysis at the product level since without a demand system toaggregate across products, prices and physical quanes are only deﬁned at the product level. We also

confront the poten al concern that (unobserved) input prices vary across ﬁrms. This concern is usuallyignored in earlier work, but we show how to deal with this issue by exploi ng varia on in observable ﬁrm
and market characteris cs.
This approach calls for an explicit treatment of mul -product ﬁrms. We show how to exploit data on
single-product ﬁrms along with a sample selec on correc on to obtain consistent es mates of the produc on func ons. The beneﬁt of using single-product ﬁrms in the produc on func on es ma on stage isthat we do not require assump ons on how ﬁrms allocate inputs across products, something we do not
observe in our data.3 While this approach may seem strong, it simply assumes that the physical rela on1
Our framework explicitly accounts for produc on that relies on ﬁxed factors that may be costly to adjust over me. These
include machinery and capital goods, and poten ally also labor. This is par cularly important in a country like India that hasrela vely strong labor regula ons (Besley and Burgess (2004)) as well as capital market distor ons. Our approach requires at least
one ﬂexible input that is adjustable in the short run; in our case, this variable input is materials.
2
Foster et al. (2008) also use quan ty data in their analysis of produc on func ons, but they focus on a set of homogeneous
products.
3
Suppose a ﬁrm manufactures three products using raw materials, labor and capital. To our knowledge, no dataset covering

3

ship between inputs and outputs is the same for single- and mul -product ﬁrms that manufacture thesame product. That is, a single-product ﬁrm uses the same technology to produce a rickshaw as a mul product ﬁrm. This assump on is already implicitly employed in all previous work that pools data acrosssingle- and mul -product ﬁrms (e.g., Olley and Pakes (1996) or Levinsohn and Petrin (2003)). Moreover,this assump on of the same physical produc on structure does not rule out economies of scope, which
can operate through lower input prices for mul -product ﬁrms (for example, due to their size), or higher(factor-neutral) produc vity of mul -product ﬁrms. Once we es mate the produc on func ons from thesingle-product ﬁrms, we show how to back out the produc vity of mul -product ﬁrms and their alloca onof inputs across their products. We obtain the markups for each product manufactured by ﬁrms by dividing
the output elas city of materials by the materials share of total revenue.4 Finally, we divide prices by themarkups to obtain marginal costs.
Our es ma on of the output elas ci es of the produc on func on provides reasonable results. Notably, many ﬁrms exhibit economies of scale, a ﬁnding consistent with Kle e and Griliches (1996) and De
Loecker (2011) who show that es ma on based on revenue data leads to a downward bias in the es matedreturns to scale.
The performance measures are correlated in intui ve ways and are consistent with recent heterogeneous models of mul -product ﬁrms. Markups (marginal costs) are posi vely (nega vely) correlated witha ﬁrm’s underlying produc vity. More produc ve ﬁrms manufacture more products, but ﬁrms have lower
markups (higher marginal costs) on products that are farther from their core competency. Foreshadowing
the impact of the trade liberaliza ons, we ﬁnd that changes in marginal costs are not perfectly reﬂected inchanges in prices because of variable markups (i.e., incomplete pass-through).
We then analyze how prices, marginal costs, and markups adjust during India’s trade liberaliza on. As
has been discussed extensively in earlier work, the nature of India’s reform provides an iden ﬁca on strategy that alleviates the standard endogeneity concerns associated with trade liberaliza on. The combina onof an important trade reform that has sta s cal beneﬁts and the ability to observe prices and their underlying components is a unique contribu on of our analysis. Perhaps not surprisingly, we observe price declines
during the reform period, but these declines appear modest rela ve to the size of the reform. On average,
prices fall 16.8 percent despite average tariﬀ declines of 62 percentage points. Marginal costs, however,decline on average by 40.3 percent due primarily to input tariﬀ liberaliza on; this ﬁnding is consistent withearlier work demonstra ng the importance of imported inputs in India’s trade reform. Output tariﬀs have
only a small and sta s cally insigniﬁcant eﬀect on costs, sugges ng that reduc ons of X-ineﬃciencies aremodest in comparison to reduc ons due to imported inputs.5 Since our prices decompose exactly into
manufacturing ﬁrms reports informa on on how much of each input is used for each product. One way around this problem is to
assume input propor onality. For example, Foster et al. (2008) allocate inputs based on products’ revenue shares. Their approachis valid under perfect compe on or the assump on of constant markups across all products produced by a ﬁrm. While theseassump ons are appropriate for the par cular homogenous good industries they study, we study a broad class of diﬀeren ated
products where these assump ons may not apply. Moreover, our study aims to es mate markups without imposing such implicit
assump ons.
4
For mul -product ﬁrms, we use the es mated input alloca ons in the markup calcula on.
5
The rela ve importance of input and output tariﬀs is consistent with Ami and Konings (2007) and Topalova and Khandelwal(2011) who ﬁnd that ﬁrm-level produc vity changes in Indonesia and India, respec vely, were predominantly driven by input tariﬀ
declines.

4their underlying cost and markup components, we can show that the reason the rela vely large decline
in marginal costs did not translate to equally large price declines was because markups increased: on average, the trade reform raised rela ve markups by 23.4 percent. The results imply that ﬁrms oﬀset thecost declines from input tariﬀ reduc ons by raising markups, and the net eﬀect is that the reform has ana enuated impact on prices. The increases in markups do not imply that the trade reforms caused ﬁrms tocollude or engage in less compeve behavior. Rather, the results simply show that prices do not respondfully to cost, a ﬁnding that has been studied extensively in the exchange rate literature and is consistent
with any model with variable markups. Finally, we observe that ﬁrms’ ability to raise markups even further
is mi gated by the pro-compeve impact of output tariﬀ declines, par cularly for those ﬁrms with very

high ini al markups.
Our results suggest that the most likely beneﬁciaries of the trade liberaliza on in the short-run are
domes c Indian ﬁrms who beneﬁt from lower produc on costs while simultaneously raising markups. The
short-run gains to consumers appear small, especially considering that we observe factory-gate prices rather
than retail prices. However, the addi onal short-run proﬁts accrued to ﬁrms may have spurred innova onin Indian manufacturing, par cularly in the introduc on of many new products, that beneﬁt consumers
in the long run. These new products accounted for about a quarter of overall manufacturing growth (seeGoldberg et al. (2010b)). In earlier work, we showed that the new product introduc ons were concentrated
in sectors with dispropor onally large input tariﬀ declines that allowed ﬁrms access to new, previously
unavailable imported materials (see Goldberg et al. (2010a)). In the present paper, we ﬁnd that ﬁrms withlarger increases in average markups were more likely to introduce new products. This evidence suggeststhat the higher proﬁts may have ﬁnanced the development of new products that contributed to long run
gains to consumers. A more detailed inves ga on of this channel is beyond the scope of the present paper.
In addi on to the papers discussed earlier, our work is related to a wave of recent papers that focus on
produc vity in developing countries, such as Bloom and Van Reenen (2007) and Hsieh and Klenow (2009).
The low produc vity in the developing world is o en a ributed to lack of compeon (Bloom and Van

Reenen (2007)) or the presence of policy distor ons that result in a misalloca on of resources across ﬁrms
(Hsieh and Klenow (2009)). Against this background, it is natural to ask whether there is any evidence thatan increase in compeon or a removal of distor ons increases produc vity. India’s reforms are an excellent

context to study these ques ons because of the nature of the reform and the availability of detailed data.
Trade protec on is a policy distor on that distorts resource alloca on. Limited compeon beneﬁts someﬁrms rela ve to others, and the high input tariﬀs are akin to the capital distor ons examined by Hsieh andKlenow (2009). Our results suggest that the removal of barriers on inputs lowered produc on costs, so thereforms did indeed deliver produc vity gains. However, the overall picture is more nuanced as ﬁrms do
not appear to pass the en rety of the cost savings to consumers in the form of lower prices. Our ﬁndings
highlight the importance of jointly studying changes in prices, markups and costs to understand the full
distribu onal consequences of trade liberaliza on.
The remainder of the paper is organized as follows. In the next sec on, we provide a brief overview
of India’s trade reform and the data used in the analysis. In Sec on 3, we lay out the general empiricalframework that allows us to es mate markups, produc vity and marginal costs. In Sec on 4, we explain5the es ma on and iden ﬁca on strategy employed in our analysis, paying par cular a en on to issues
that arise speciﬁcally in the context of mul -product ﬁrms. Sec on 5 presents the results and Sec on 6
concludes.

2

Data and Trade Policy BackgroundWe ﬁrst describe the Indian data since it dictates our empirical methodology. We also describe key elements of India’s trade liberaliza on that are important for our iden ﬁca on strategy. Given that the Indian
trade liberaliza on has been described in a number of papers (including several by a subset of the present
authors), we keep the discussion of the reforms brief.

2.1

Produc on and Price data

We use the Prowess data that is collected by the Centre for Monitoring the Indian Economy (CMIE). Prowess
includes the usual set of variables typically found in ﬁrm-level produc on data, but has important advantages over the Annual Survey of Industries (ASI), India’s manufacturing census. First, unlike the repeatedcross sec on in the ASI, Prowess is a panel that tracks ﬁrm performance over me. Second, the data span
India’s trade liberaliza on from 1989-2003. Third, Prowess records detailed product-level informa on foreach ﬁrm. This enables us to dis nguish between single-product and mul -product ﬁrms, and track changes
in ﬁrm scope over the sample period. Fourth, Prowess collects informa on on quan ty and sales for eachreported product, so we can construct the prices of each product a ﬁrm manufactures. These advantages
make Prowess par cularly well-suited for understanding the mechanisms of ﬁrm-level adjustments in response to trade liberaliza ons that are typically hidden in other data sources, and deal with measurement
issues that arise in most studies that es mate produc on func ons.
Prowess enables us to track ﬁrms’ product mix over me because Indian ﬁrms are required by the 1956
Companies Act to disclose product-level informa on on capaci es, produc on and sales in their annual
reports. As discussed extensively in Goldberg et al. (2010b), several features of the database give us conﬁdence in its quality. Product-level informa on is available for 85 percent of the manufacturing ﬁrms, whichcollec vely account for more than 90 percent of Prowess’ manufacturing output and exports. Since productlevel informa on and overall output are reported in separate modules, we can cross check the consistencyof the data. Product-level sales comprise 99 percent of the (independently) reported manufacturing sales.6
We refer the reader to Goldberg et al. (2010a,b) for a more detailed discussion of the data.
The deﬁni on of a product is based on the CMIE’s internal product classiﬁca on. There are a total of
1,501 products in the sample for es ma on.7 Table 1 reports basic summary sta s cs by two-digit NIC (India’s industrial classiﬁca on system) sector. As a comparison, the U.S. data used by Bernard et al. (2010),
contain approximately 1,500 products, deﬁned as ﬁve-digit SIC codes across 455 four-digit SIC industries.
6

We deﬂate all nominal values for our analysis. Materials are deﬂated by the wholesale price index of primary ar cles. Wages
are deﬂated by the overall wholesale price index for manufacturing. Capital stock is ﬁxed assets deﬂated by sector-speciﬁc wholesale price indexes. Unit values are also deﬂated by sector-speciﬁc wholesale price indexes.
7
We have fewer products than in Goldberg et al. (2010b) because we require non-missing values for quan es and revenues
rather than just a count of products.

6Thus, our deﬁni on of a product is similar to earlier work that has focused on the U.S. Table 2 provides a
few examples of products available in our data set. In our terminology, we will dis nguish between “sectors” (which correspond to two-digit NIC aggregates), “industries” (which correspond to four-digit NIC aggregates) and “products” (the ﬁnest disaggrega on we observe); we emphasize that since the “product”
deﬁni on is available at a highly disaggregated level, unit values are plausibly interpreted as “prices” in ourapplica on.
The data also have some disadvantages. Unlike Census data, the CMIE database is not well suited forunderstanding ﬁrm entry and exit. However, Prowess contains mainly medium large Indian ﬁrms, so entry
and exit is not necessarily an important margin for understanding the process of adjustment to increased
openness within this subset of the manufacturing sector.8
We complement the produc on data with tariﬀ rates from 1987 to 2001. The tariﬀ data are reported at
the six-digit Harmonized System (HS) level and were combined by Topalova (2010). We pass the tariﬀ data
through India’s input-output matrix for 1993-94 to construct input tariﬀs. We concord the tariﬀs to India’s
na onal industrial classiﬁca on (NIC) schedule developed by Debroy and Santhanam (1993). Formally, in∑put tariﬀs are deﬁned as τ input= k aki τ output, where τ output
is the tariﬀ on industry k at me t, and aki
itktkt
is the share of industry k in the value of industry i.

2.2 India’s Trade Liberaliza on
A key advantage of our approach is that we examine the impact of openness by relying on changes in trade
costs induced by a large-scale trade liberaliza on. India’s post-independence development strategy was
one of na onal self-suﬃciency and heavy government regula on of the economy. India’s trade regime
was amongst the most restric ve in Asia, with high nominal tariﬀs and non-tariﬀ barriers. In response to abalance-of-payments crisis, India launched a drama c liberaliza on of the economy as part of an IMF structural adjustment program in August 1991. An important part of this reform was to abandon the extremely
restric ve trade policies it had pursued since independence.
Several features of the trade reform are crucial to our study. First, the external crisis of 1991, whichcame as a surprise, opened the way for market oriented reforms (Hasan et al. (2007)).9 The liberaliza on of
the trade policy was therefore unan cipated by ﬁrms in India and not foreseen in their decisions prior to thereform. Moreover, reforms were passed quickly as sort of a “shock therapy” with li le debate or analysis
to avoid the inevitable poli cal opposi on (see Goyal (1996)). Industries with the highest tariﬀs received
the largest tariﬀ cuts implying that both the average and standard devia on of tariﬀs across industries fell.
While there was signiﬁcant varia on in the tariﬀ changes across industries, Topalova and Khandelwal(2011) show that tariﬀ changes through 1997 were uncorrelated with pre-reform ﬁrm and industry characteris cs such as produc vity, size, output growth during the 1980s and capital intensity. The tariﬀ lib8

Firms in Prowess account for 60 to 70 percent of the economic ac vity in the organized industrial sector and comprise 75
percent of corporate taxes and 95 percent of excise duty collected by the Government of India (CMIE).
9Some commentators (e.g., Panagariya (2008)) noted that once the balance of payments crisis ensued, market-based reforms
were inevitable. While the general direc on of the reforms may have been an cipated, the precise changes in tariﬀs were not.
Our empirical strategy accounts for this shi in broad an cipa on of the reforms, but exploits varia on in the sizes of the tariﬀ
cuts across industries.

7

eraliza on does not appear to have been targeted towards speciﬁc industries and appears rela vely freeof usual poli cal economy pressures un l 1997 (which coincides with an elec on that changed poli cal
power). We es mate the produc on func on and markups on the full sample, but restrict our analysis of
the trade reform to the 1989-1997 period when trade policy did not respond to pre-exis ng industry- or
ﬁrm-level trends. We again refer the reader to previous publica ons that have used this trade reform fora detailed discussion (Topalova and Khandelwal (2011); Topalova (2010); Sivadasan (2009); Goldberg et al.
(2010a,b)).

3

Produc on Technology, Markups and Costs

This sec on describes the framework to es mate markups and marginal costs from ﬁrm-level produc on
data. Our approach to recovering markups follows De Loecker and Warzynski (2012).10 The main diﬀerence
from their empirical se ng is that we use product-level quan ty and price informa on, rather than ﬁrmlevel deﬂated sales. This enables us to iden fy markups for each ﬁrm-product-year triplet observa on.
We are forced to confront a number of new issues in order to implement our approach. Once we obtainmarkups, we compute marginal costs by simply dividing the observed prices by the es mated markups.
Consider the following produc on func on for ﬁrm f that manufactures a product:
Qf t = Ft (Xf t ) exp(ω f t )(1)

where Q is physical output and X is a vector of inputs. To simplify the exposi on, we assume for now that
this producer is a single-product ﬁrm. In Sec on 4, we explicitly deal with the empirical challenges that arise
with mul -product ﬁrms. The produc on func on in (1) is general; we can consider alterna ve func onal
forms for F and allow the produc on technology to vary over me. There are only two assump ons that are
essen al for the subsequent analysis. First, produc vity ω enters in log-addi ve form and is Hicks-neutral.
Second, we assume that produc vity is ﬁrm-speciﬁc. This second assump on follows a tradi on in the trade
literature that models produc vity along these lines (e.g., Bernard et al. (2011)). For single-product ﬁrms,
this assump on is of course redundant.
Although this produc on func on is en rely standard, the advantage of our se ng is that we directly
observe output (Q) at the product level. This dis nguishes our approach of es ma ng a produc on func on
from the tradi onal literature where researchers rely on deﬂated sales data. We discuss the es ma on andthe iden ﬁca on issues in Sec on 4.
We assume that producers minimize costs. Let Vf t denote the vector of variable inputs used by the ﬁrm.
We use the vector Kf t to denote dynamic inputs of produc on. Any input that faces adjustment costs will
fall into this category; capital is an obvious one, and our framework will include labor as well. We consider
10This approach to infer markups from produc on data began with Hall (1986). An alterna ve approach to es ma ng markups
would be to assume a par cular market structure, ﬁrm behavior and u lity func on of consumers, which jointly determine markups(e.g., Berry et al. (1995) or Goldberg (1995)). However, we explicitly want to avoid making the many func onal form assump ons
required to implement this approach. This approach is also less feasible when inferring markups across the en re manufacturingsector. We therefore believe that inferring markups from produc on data is the appropriate path in this se ng, and one that canbe easily implemented in a variety of contexts.

8

the ﬁrm’s condi onal cost func on where we condi on on the set of dynamic inputs Kf t . The associatedLagrangian func on is:
L(Vf t , Kf t , λf t ) =V∑

Pfvt V vf t +

v=1

D
∑

rfdt Kfdt + λf t [Qf t − Qf t (Vf t , Kf t , ω f t )]

(2)

d=1

where Pfvt and rfdt denote the ﬁrm’s input prices for the variable inputs v = 1, . . . , V and the prices of dynamic inputs d = 1, . . . , D, respec vely. The ﬁrst order condi on for any variable input free of adjustment
costs is

∂Lf t
∂Qf t (.)
= Pfvt − λf t
=0
v
∂Vf t
∂Vfvt

(3)
∂L

where the marginal cost of produc on at a given level of output is λf t since ∂Qfftt = λf t . Rearranging terms
Vand mul plying both sides by Qfftt , provides the following expression:v
v v∂Qf t (.) Vf t
1 Pf t Vf t=
∂Vfvt Qf t
λf t Qf t(4)

The le -hand side of the above equa on represents the elas city of output with respect to variable input
Vfvt (the “output elas city”). The approach simply requires one freely adjustable input into produc on. This
becomes important in se ngs, such as ours, where there are fric ons in adjus ng capital and labor. DeﬁneP

the markup µf t as µf t ≡ λff tt . As De Loecker and Warzynski (2012) show, the cost-minimiza on condi on
can be rearranged to write the markup as:µf t = θvf t (αvf t )−1(5)
Pv V v

where θvf t denotes the output elas city on variable input V v and αvf t = PffttQfftt is its expenditure share ofrevenue. This expression forms the basis for our approach. To compute the markup, we need the output
elas city and the share of the input’s expenditure in total sales. We obtain the output elas city by es mating the produc on func on in (1). We compute the input’s revenue share for single-product ﬁrms directlyfrom the data.
Markups for mul -product ﬁrms are obtained using the exact same expression; the markup is computedfor each product j produced by ﬁrm f at me t using:µf jt = θvf jt (αvf jt )−1(6)

The only diﬀerence between expressions (5) and (6) is the presence of the product-speciﬁc subscript
j. This seemingly small diﬀerence complicates the analysis considerably. In contrast to the single productse ng, αvf jt is not directly observed in the data because ﬁrms do not report input expenditures by product.11 Moreover, we require an es mate of the output elas city for each product manufactured by eachmul -product ﬁrm. In the next sec on, we discuss the iden ﬁca on strategy we employ in order to obtain11

To our knowledge, no dataset reports this informa on for all inputs.

9the output elas ci es for both single- and mul -product ﬁrms, and recover the ﬁrm-product speciﬁc input
expenditures (the αvf jt ) for the mul -product ﬁrms.
This approach provides markups that vary at the ﬁrm-product-year level. Since prices are observed at
this same level of disaggrega on, we can simply calculate the marginal costs from the observed price data:
mcf jt =

Pf jt
.
µf jt

(7)

We believe that this approach to recover markups is quite ﬂexible and suitable for a se ng where one
wants to es mate markups for many industries. The approach requires the presence of at least one inputthat can be freely adjusted, but allows for fric ons in the adjustment of capital and labor. This is importantin a country like India that has had heavily regulated labor markets and is o en associated with labor andcapital market distor ons. It does not impose assump ons on the returns to scale nor assump ons on the
demand and market structure for each industry. Moreover, we do not require knowledge of the user cost ofcapital, a factor price that is diﬃcult to measure in a country like India with distorted capital markets. This
ﬂexible approach allows us to be a priori agnos c about how prices, markups and marginal costs changewith trade liberaliza on.

4

Empirical Framework

This sec on discusses our empirical framework. We ﬁrst discuss the iden ﬁca on strategy and then describe the es ma on rou ne.
Consider the log version of the general produc on func on given in equa on (1):qf jt = f j (xf jt ; β) + ω f t + ϵf jt(8)where lower case le ers denote logs. We introduce the subscript j since many ﬁrms in our sample manufacture more than one product. The quan ty of product j in ﬁrm f at me t, qf jt , is produced using a set ofﬁrm-product-year speciﬁc inputs, xf jt . The error term ϵf jt captures measurement error in recorded output
as well unan cipated shocks to output. As noted earlier, the produc vity term ω f t is assumed to vary at
the ﬁrm level. Our goal is to es mate the parameters of the produc on func on – the output elas ci es β
– for each product.
In the subsequent subsec ons, we discuss the restric ons we impose on equa on (8) given the natureof our data and how we iden fy the output elas ci es. The key challenge is that the data do not record
how inputs are allocated across outputs within a ﬁrm. For single-product ﬁrms, this concern is of course
not an issue. The challenge is how to deal with the unobserved input alloca on among mul -product ﬁrms
while also controlling for unobserved produc vity shocks.

10

4.1

Iden ﬁca on Strategy: The Use of Single-Product Firms

By wri ng the produc on func on in equa on (8) in terms of physical output rather than revenue, we
exploit our ability to observe separate informa on on quanes and prices for each product manufactured

by ﬁrms. This advantage eliminates the concern about a “price bias” that arises when one must deﬂate sales
by an industry-level price index to obtain ﬁrm output (for a detailed discussion, see De Loecker (2011)). For
single-product ﬁrms, the inputs are allocated to the only product these ﬁrms manufacture and so we are notconcerned about how to allocate inputs across products. The typical concern that arises in the produc vity
es ma on is correla on between the unobserved produc vity shock and inputs. Removing this bias has
been the predominant focus of the produc on func on es ma on literature and following the insights of
Olley and Pakes (1996), Levinsohn and Petrin (2003), and Ackerberg et al. (2006), we use proxy es mators
to deal with this correla on.12
For mul -product ﬁrms, a new iden ﬁca on problem arises since the data do not record how the inputs
are allocated across the products within a ﬁrm. To understand this, denote the log of the share of input X
in the produc on of product j as ρX
f jt = xf jt − xf t , for any input X = {L, M, K}, where L is labor, M
is materials and K is capital. We only observe ﬁrm-level inputs Xf t and not how each of them is allocatedacross products. Subs tu ng this expression into equa on (8) yields:
qf jt = f j (xf t ; β) + ω f t + Af jt (ρXf jt , xf t , β) + ϵf jt(9)where xf t denotes the log of inputs Xf t . For mul -product ﬁrms, the produc on func on contains an
addi onal component in the error term, A(.), that will generally be a func on of the unobserved input
shares (ρXf jt ), the ﬁrm level inputs (xf t ) and the produc on func on coeﬃcients, β. The expression (9)clearly demonstrates that A(.) is correlated - by construc on - with the inputs on the right-hand-side of the
produc on func on which results in biased es mates of β.13 We could deal with this bias by taking a standon the underlying demand func on for each product and model how ﬁrms compete in that market, but as
discussed earlier, we wish to avoid these assump ons in this paper.14
We propose an iden ﬁca on strategy that does not require assump ons on the input alloca on acrossproducts. The strategy is to obtain es mates of the produc on func on using a sample of single-productﬁrms, since as discussed above, the input alloca on problem does not exist for these ﬁrms. This sample
12

Unobserved input prices might s ll bias es mates of the produc on func on. We discuss this issue in detail in Sec on 4.3.2.
To illustrate the bias, consider a translog produc on func on with a single factor of produc on, labor. The produc on func onin equa on (9) would be: qf jt = β l lf jt + β ll lf2 jt + ω f t + ϵf jt . We observe labor at the ﬁrm level, lf t . The labor allocated forthe produc on of j can be wri en as: lf jt = ρf jt + lf t . Subs tu on yields:
13()2
qf jt = β l lf t + β ll lf2 t + β l ρf jt + β ll ρf jt + 2β ll (ρf jt lf t ) +ω f t + ϵf jt
|
{z
}

(10)

=Af jt (ρf jt ,xf t ,β)Clearly, the component Af jt (ρf jt , xf t , β) is unobserved and would be subsumed in the produc vity term, ω f t . This would resultin biased es mates of β l since lf t would be correlated with this composite error.
14
The few produc vity studies that have explicitly dealt with mul -product ﬁrms had to make assump ons on how inputs areallocated. For example, De Loecker (2011) allocates inputs equally across products and Foster et al. (2008) allocate inputs according
to revenue share. These approaches rest on implicit assump ons about markups, i.e., markups are the same across the products
manufactured by a ﬁrm. These assump ons are innocuous in the above studies since the authors are not interested in recovering
markups, but they would be inappropriate in our se ng since es ma on of markups is the primary objec ve of this paper.

11

consists of those ﬁrms that produce a single product at a given point in me; it includes ﬁrms that may
eventually add addi onal products later in the sample period. This feature of the sample is important since
many ﬁrms start oﬀ as single product ﬁrms and add products during our sample. Our analysis uses theseﬁrms in conjunc on with ﬁrms that always manufacture a sole product.
This approach implies that we use an unbalanced panel of ﬁrms for es ma on; the imbalance occurs byremoving ﬁrms from the es ma on if they add a product over the sample period. The unbalanced panel isimportant because it allows for the non-random event that a ﬁrm becomes a mul -product producer basedon produc vity shocks. This non-random event results in a sample selec on issue analogous to the nonrandom exit of ﬁrms discussed in Olley and Pakes (1996). In their context, Olley and Pakes are concerned
about the le tail of the produc vity distribu on; here, a balanced panel of single-product ﬁrms would
censor the right tail of the produc vity distribu on. The use of the unbalanced panel of single-productﬁrms improves upon this selec on problem. In addi on, we use a sample selec on correc on procedure toaccount for the possibility that the produc vity threshold determining the transi on of a ﬁrm from single- tomul -product status is correlated with the right-hand side variables of the produc on func on (in par cular,
capital). We describe the sample selec on correc on procedure in 4.3.3.15

4.2

Economies of Scope and Rela onship to Cost Func on Es ma on

In this subsec on, we discuss the assump ons underlying the iden ﬁca on strategy laid out in the previous
subsec on. We explain that despite relying on single-product ﬁrms in our es ma on, our strategy does not
rule out economies of scope and relate our approach to cost func on es ma on.
Our iden ﬁca on strategy assumes that the produc on technology is product-speciﬁc rather than speciﬁc to the ﬁrm. Once we obtain the coeﬃcients of the produc on func on from the sample of singleproduct ﬁrms, we use those on the mul -product ﬁrms that produce the same product. This iden ﬁca on
strategy rules out physical synergies across products. For example, imagine a single-product ﬁrm produces
a t-shirt using a par cular technology, and another single-product ﬁrm produces carpets using a diﬀerent
combina on of inputs. We assume that a mul -product ﬁrm that manufactures both products will use
each technology on its respec ve product, rather than some third technology. This assump on is not unusual. In fact, it is implicitly used in all produc vity studies when researchers pool single- and mul -productﬁrms in the same industry and es mate an industry-level produc on func on. We feel that this restric on is
mild, especially given the current prac ce within the produc on func on es ma on literature and weighedagainst the costs of assuming a market structure/demand system that would dictate how to allocate inputs
across products.
This approach does not rule out economies of scope, which may be important for mul -product ﬁrms.
To be precise, Baumol et al. (1983) speak of economies of scope in produc on, if the cost func on is subaddi ve: cf t (q1 , q2 ) ≤ cf t (q1 ) + cf t (q2 ) where cf t () is a ﬁrm’s cost curve. While our framework rules out
produc on synergies, it allows for economies of scope through cost synergies. For example, economies of15

Firms in our sample very rarely drop products, so we do not observe the reverse transi on from mul - to single-product status.
We refer the reader to Goldberg et al. (2010b) for a detailed analysis of product adding and dropping in our data. Unlike Olley andPakes (1996), we are also not concerned with ﬁrm exit. Firm exit is rare in our data, since Prowess covers the medium and large
ﬁrms in India which are rela vely stable.

12scope can emerge if mul -product ﬁrms face lower input prices than single-product ﬁrms due to their sizeor the nego a on of be er deals with their suppliers. Furthermore, we allow for poten al diﬀerences in
produc vity between the two types of ﬁrms that might be caused by diﬀerences in management prac cesor organiza onal structures.
An alterna ve way of explaining the assump ons underlying our approach is to express them in termsof the cost func on rather than the produc on func on. A mul -product ﬁrm faces the short-run cost
func on, wri en in a general form as:
C(Q) = Φ(Ω)C(Q, W, β) + F (ι(Q))
where C denotes the total costs for a ﬁrm producing a vector of outputs Q, Φ(Ω) denotes the impact offactor-neutral produc vity on costs, W denotes a vector of input prices, F are the ﬁxed costs (which would
be zero in long-run cost func on), and ι(.) is an indicator that takes the value of 1 if a ﬁrm produces apar cular product in the vector Q and is zero otherwise. The assump on we impose is that the func onC(Q, W, β)is the same across single- and mul -product ﬁrms. However, costs between the two types ofﬁrms can s ll diﬀer because of: 1) factor-neutral produc vity diﬀerences reﬂected in Φ(Ω); 2) diﬀerencesin factor prices reﬂected by W; and 3) (in the short run) the amor za on of ﬁxed costs F across moreproducts for mul -product ﬁrms.
The above representa on raises the natural ques on of why we do not exploit the duality between
produc on and cost func on and es mate a mul -product cost func on as done in an earlier literature.
The main reason for focusing on the produc on func on is that we do not have informa on on wages andthe ﬁrm-speciﬁc user cost of capital, which we would need in order to es mate a cost func on. Further, amul -product cost func on es ma on would require addi onal iden ﬁca on assump ons in order to deal
with the endogeneity of mul ple product outputs on the right-hand side. Finally, even if one could comeup with such iden ﬁca on assump ons, the product por olios during our sample period are not stable.
While Indian ﬁrms very rarely drop products, they o en add products during this period (see Goldberg
et al. (2010b)). These frequent addi ons require explicitly modeling a ﬁrm’s decision to add a par cular
product (in contrast, our approach requires us to model only the change from single- to mul -productstatus). Given these challenges, our approach to es mate produc on func ons from single-product ﬁrms
while accoun ng for the poten al selec on bias is an appealing alterna ve.

4.3 Es ma on
This sec on discusses the produc on func on es ma on on the sub-sample of single-product ﬁrms.
4.3.1 The Basic Setup
Since we focus on a subsample of single-product ﬁrms for the es ma on rou ne, we drop the subscript j tosimplify nota on.16 Since we have a physical measure of output, we control for diﬀerences in units across16
To be clear, we observe many ﬁrms manufacturing the same product j, but we subsume the subscript j when describing ﬁrms
that only manufacture one product.

13

products by using unit ﬁxed eﬀects throughout the es ma on procedure.
The produc on func on we es mate is of the form:17
qf t = f (xf t ; β) + ω f t + ϵf t

(12)where we subsume the constant term in produc vity, collect all inputs in xf t and β is the vector of coefﬁcients describing the transforma on of inputs into output. In the case of a translog produc on func on,
the vector of log inputs xf t are labor, material and capital, their squares, and their interac on terms; thevector of coeﬃcients is β = (β l , β m , β k , β ll , β mm , β kk , β lm , β lk , β mk , β lmk ).
We deal with the poten al correla on between unobserved produc vity shock and input choices by
relying on the approach taken by Ackerberg et al. (2006), who modify Olley and Pakes (1996) and Levinsohn
and Petrin (2003).18
The law of mo on for produc vity is:
inputxω f t = gt−1 (ω f t−1 , τ output
it−b , τ it−b , If t−1 ) + ξ f t(13)

where b = {0, 1} and Ixft−1 is a dummy indica ng whether the ﬁrm is expor ng. Output tariﬀs enter thelaw of mo on for produc vity because we expect the compe
import compeve pressure associated with an increase in

on to induce ﬁrms to undertake changes (e.g., reorganiza on; reduc on of X-ineﬃciencies)that increase produc vity. Input tariﬀs enter because they lead ﬁrms to use new imported input varie esthat aﬀect measured produc vity (see Halpern et al. (2011) and Goldberg et al. (2010a)). The nota on
implies that we allow trade liberaliza on to impact a ﬁrm’s produc vity instantaneously or with a lag.19
We assume that the dynamic inputs–labor and capital–are chosen prior to observing ξ f t . Materials
mf t are chosen when the ﬁrm learns its produc vity. These ming assump ons treat labor, in addi on tocapital, as an input that faces adjustment costs, which we feel is appropriate in a country like India wherelabor markets are not ﬂexible (see Besley and Burgess (2004)).
We proxy for produc vity by inver ng the materials demand func on:
mf t = mt (lf t , kf t , ω f t , zf t ).

(14)

The vector zf t contains all addi onal variables that aﬀect a ﬁrm’s demand for materials. It includes output
outputprices, product dummies, product market shares, and the input (τ input) that theit ) and output tariﬀs (τ itﬁrm faces on the product. The subscript i on the tariﬀ variables denotes an industry to indicate that tariﬀs
17

Our main speciﬁca on is the translog and is given by

qf t = β l lf t +β ll lf2 t +β k kf t +β kk kf2 t +β m mf t +β mm m2f t +β lk lf t kf t +β lm lf t mf t +β mk mf t kf t +β lmk lf t mf t kf t +ω f t (11)18
By using a sta c control to proxy for produc vity, we do not have to revisit the underlying dynamic model and prove inver bility
when modifying Olley and Pakes (1996) for our se ng to include addi onal state variables (e.g., tariﬀs). See De Loecker (2011)
and Ackerberg et al. (2006) for an extensive discussion. In developing countries, many ﬁrms report zero investment, which further
complicates the use of investment as a proxy.
19
De Loecker (2010) discusses the importance of including all variables which may aﬀect produc vity in the law of mo on gt ().

14vary at a higher level of aggrega on than products.20 The vector also includes product ﬁxed eﬀects and theprice of the product.21 These variables capture demand shocks that aﬀect a ﬁrm’s output, which in turnaﬀects a ﬁrm’s demand for materials. For example, the product’s price aﬀects the quan ty produced which
in turn aﬀects a ﬁrm’s input expenditure. As discussed in Olley and Pakes (1996), the proxy approach does
not require knowledge of the market structure for the input markets; it simply states that input demanddepends on the ﬁrm’s state variables, capital and labor, produc vity and the aforemen oned variables.
As is usual in the proxy approach, our es ma on proceeds in two steps.22 We begin by inver ng equaon (14) to obtain the proxy for ﬁrm produc vity, ω f t = ht (mf t , lf t , kf t , zf t ). Following Ackerberg et al.
(2006), in the ﬁrst stage, we run:qf t = ϕt (lf t , kf t , mf t , zf t ) + ϵf t

(15)b ) and an es mate for the residual ϵf t .23
to obtain es mates of expected output (ϕftThe ﬁrst stage separates the eﬀect of ω f t on output from the eﬀects of unan cipated shocks ϵf t onb − f (xf t ; β) for any vector of β. The
output. A er the ﬁrst stage, we compute produc vity as ω
bf t = ϕftsecond stage provides es mates of all produc on func on coeﬃcients by relying on the law of mo on for
produc vity. By non-parametrically regressing ωb f t (β) on its lag ωb f t−1 (β), the set of tariﬀ variables (τ it ),and the ﬁrm export indicator Ixft−1 , we recover the innova on to produc vity ξ f t (β) for a given β.
To es mate the parameter vector β, we use moments that are now standard in this literature basedon degree of variability of a given input. In our context, we assume that ﬁrms freely adjust materials andtreat capital and labor as dynamic inputs that face adjustment costs. In other se ngs, one may choose totreat labor as a ﬂexible input. Since material expenditure is the ﬂexible input, we construct its moments
using lagged materials.24 For labor and capital, we construct moments using current and lagged values.
The moments are:)(E ξf t (β)Yf t = 0(16)where Yf t contains lag materials, the one-year lag labor, current capital, and their higher order terms25 :Yf t = {lf t−1 , lf2 t−1 , mf t−1 , m2f t−1 , kf t , kf2 t , lf t−1 mf t−1 , lf t−1 kf t , mf t−1 kf t , lf t−1 mf t−1 kf t }(17)This method iden ﬁes the produc on func on coeﬃcients by exploi ng the fact that current shocks to
produc vity will immediately aﬀect a ﬁrm’s materials choice while labor and capital do not immediately
20

For example, all tea products (industry 1549) face the same output and input tariﬀs.
As we discuss below, we es mate the produc on func ons at the two-digit sector level; the product ﬁxed eﬀects are iden ﬁed
since there are many products within each sector.
22
In principle, we could es mate both stages jointly using a system GMM es mator, but in prac ce this is diﬃcult to implement
because the ﬁrst stage contains many parameters including product ﬁxed eﬀects (see De Loecker (2011) for more details). We
therefore adopt a two-stage approach.
23
The set of es mated unit ﬁxed eﬀects are included in our measure of ϵf t .
24
In our se ng, input tariﬀs are serially correlated and since they aﬀect input prices, input prices are serially correlated overme.
25
We have also experimented with including current labor and the one-year lag in capital in Yf t and the results were virtuallyunchanged.
21

15

respond to these shocks; moreover, the degree of adjustment can vary across ﬁrms and me.
We es mate the model using a GMM procedure on a sample of ﬁrms that manufacture a single productfor at least three consecu ve years. We choose three years since the moment condi ons require at least two
years of data because of the lagged values; we add an extra year to allow for poten al measurement error
in the precise ming of a new product introduc on. In principle, one could run the es ma on separately
for each product. In prac ce, our sample size is such that we es mate (12) at the two-digit sector level.
4.3.2

Input Price Varia on Across Firms

Although we observe quanes and prices for ﬁrm outputs, we do not have this informa on for ﬁrm in-puts and so we follow the standard prac ce of deﬂa ng input expenditures using price indexes. If input
prices vary across ﬁrms, this prac ce results in unobserved input price varia on across ﬁrms genera ng ananalogous concern that arises if output revenue is deﬂated by a common deﬂator. This concern is present
even when data on worker wages are available, as researchers typically do not have informa on on ﬁrmspeciﬁc materials prices, and never observe the ﬁrm-speciﬁc user cost of capital. But while this issue always
arises when researchers do not observe input-level prices and quanes, the problem is exacerbated in our

se ng because we use physical quan ty data rather than deﬂated revenues.
To understand this concern, suppose we want to es mate the produc vity of two shirt producers. Imagine that the only diﬀerence between the ﬁrms is that one ﬁrm manufactures shirts made from expensive
silk while the other manufactures shirts made from cheaper co on. Otherwise, the two ﬁrms have iden cal produc vity: they u lize the same quan ty of inputs (balls of yarn, number of workers and number ofsewing machines) to produce the same quan ty of shirts. In our data, we would not observe the price ofthe materials (or workers or capital) and so we would deﬂate the ﬁrms’ input expenditures by a common
deﬂator. Since we do not account for varia on in input prices, we will es mate a lower produc vity forthe silk shirt manufacturer because it sells the same quan ty as its co on producer counterpart, but has
higher (deﬂated) input expenditures. Our es ma on procedure would yield downward biased es mates ofthe produc on func on coeﬃcients and ﬁnd produc vity diﬀerences between the two ﬁrms, even though
they are exactly iden cal. Ul mately, the bias in the produc on func on coeﬃcients would lead to biased
markup es mates.26
We propose an approach to control for unobserved input price varia on across ﬁrms using informa on
on observables, par cularly (but not exclusively) output prices. The intui on is that output prices contain
informa on about input prices. For example, using data from Colombia that uniquely record price informa on for both inputs and outputs, ? document that producers of more expensive products also use more
expensive inputs. Formally, we begin by modifying our nota on to account for the fact that we observe deﬂated input expenditures, rather than input quanes. We use x̃f t to denote the ﬁrm’s vector of deﬂated

input expenditures and re-write the produc on func on in (12) as:
qf t = f (x̃f t ; β) + ω f t + B(Wf t ; Wf t × x̃f t ; β) + ϵf t .
26

See also the related discussion in Katayama et al. (2009).

16

(18)

Let Bf t ≡ B(Wf t ; Wf t ×x̃f t ; β). The term Bf t appears because the input deﬂators are sector-, rather thanﬁrm-speciﬁc. In our translog speciﬁca on, this term captures devia ons of the ﬁrm input prices from thesector deﬂators, Wf t , their interac ons with the deﬂated expenditures, Wf t ×x̃f t and the parameter vector
β. It is clear from (18) that Bf t is correlated with the deﬂated inputs and will generate biased es mates ofthe produc on func on.27
The presence of Bf t is not a concern for the ﬁrst stage of the es ma on since it is not correlated withrandom unan cipated shocks to produc on ϵf t . The purpose of the ﬁrst stage is simply to es mate expectedb , net of unan cipated shocks ϵf t .
output ϕft

However, in the second stage of es ma on, we need to recover an es mate of the true innova on to
produc vity ξ f t in order to form moments in equa on (17). The presence of Bf t in (18) violates theseorthogonality condi ons. To see this problem, deﬁne ω̃ f t as the composite term:ω̃ f t = ω f t + Bf t .

(19)

The expected output from the ﬁrst stage will yield a second-stage es mate of produc vity ω̃ f t that contains
the unobserved varia on in input prices. Using the law of mo on for produc vity in equa on (13), let the
input xmeasured innova on to produc vity be ξ̃ f t = ω̃ f t − gt−1 (ω̃ f t−1 , τ output
it−b , τ it−b , If t−1 ) where b = {0, 1}.

Using (19) and the law of mo on for produc vity (13), we can express the measured innova on to producvity ξ̃ f t as a func on of true innova on in produc vity ξ f t :input xξ̃ f t = ξ f t + Bf t − e(Bf t−1 , τ output
it−b , τ it−b , If t−1 )(20)

input xoutput input x
output input x
where e(Bf t−1 , τ output
it−b , τ it−b , If t−1 ) = gt−1 (ω̃ f t−1 , τ it−b , τ it−b , If t−1 )−gt−1 (ω f t−1 , τ it−b , τ it−b , If t−1 ).

Equa on (20) illustrates that ξ̃ f t is a func on of current and lagged input prices, which are obviously correinput x
lated with the current and lagged input expenditures. The term Bf t −e(Bf t−1 , τ output
it−b , τ it−b , If t−1 ) createsa correla on between the measured innova on ξ̃ f t and measured input use, so the moment condi ons are
violated.
Our approach for dealing with this bias is to explicitly control for the Bf t term in the second-stage. To
implement this approach, we need to take a stand on the factors that drive input price varia on acrossﬁrms. Our premise is that, condi onal on observable variables, the only reason input prices vary acrossﬁrms manufacturing the same product is due to quality diﬀerences. If two ﬁrms produce the same quality,
they face the same input prices. If they produce diﬀerent quali es, their input prices will diﬀer. While there
27

To illustrate this bias, consider again the translog produc on func on with a single factor of produc on, labor, that we speciﬁed
in Footnote 13. Here, we focus on the bias that arises on single product ﬁrms due to unobserved input price varia on. We observe
the total wage bill of the ﬁrm which we deﬂate with a sector-speciﬁc index to obtain the ﬁrm’s deﬂated (log) labor expenditure,˜
lf t . Let ˜
lf t = lf t + wfLt , where wfLt is the (log) ﬁrm-speciﬁc devia on of the price of labor (e.g., the ﬁrm’s wage) from the sectoral
average. Since we do not observe wfLt , we would es mate:()2
qf t = β l ˜
lf t + β ll ˜
lf2 t − β l wfLt + β ll wfLt − 2β ll (wfLt ˜
lf t ) +ω f t .
{z}|=Bf t (Wf t ;Wf t ×x̃f t ;β)Clearly, the component Bf t (Wf t ; Wf t × x̃f t ; β) is unobserved and would be subsumed in the produc vity term, ω f t . This would
result in biased es mates of β l since ˜
lf t would be correlated with this composite error.

17

may be other factors that cause input prices to vary across ﬁrms, we believe that quality diﬀerences are theﬁrst-order concern in our se ng and the primary factor genera ng input price varia on.28
We provide a formal model that ra onalizes our approach in the Appendix. Here, we sketch the mainargument and provide the economic intui on underlying our empirical strategy. Our main premise is that
manufacturing high quality products requires high quality inputs, and high quality inputs are expensive. We
further assume complementarity in input quality: manufacturing high quality products requires combining
high quality materials with high quality labor and capital. This is a common assump on in the literature andunderlies ‘O-Ring’-type theories of produc on (e.g., Kremer (1993), Verhoogen (2008) and ?). This complementarity is important in our framework because it allows us to express the prices of all inputs facing a ﬁrm
as a func on of a single index of product quality.29 The appendix shows that input prices are an increasing
func on of product quality in this se ng. Accordingly, we can control for input price varia on across ﬁrms
using diﬀerences in output quality across ﬁrms. Before we explain how to control for output quality, it isimportant to note that our approach does not assume that products are only ver cally diﬀeren ated. It canallow for costless horizontal diﬀeren a on, but diﬀeren a on along the ver cal dimension requires higher
quality inputs that have higher input prices. This assump on is common in trade models (e.g., Verhoogen(2008) and Khandelwal (2010)).
Our control for quality is a ﬂexible func on of output prices, market share and product dummies. This
speciﬁca on does not force us to commit to a par cular demand func on since it encompasses a large
class of demand models used in the literature. For example, in a purely ver cal diﬀeren a on model,
there is a one-to-one mapping between product quality and product prices, so output prices perfectly proxyfor quality; in this case, one would not require controls for market share or product characteris cs. In a
simple logit model, quality will be a func on of output prices and market shares (see Khandelwal (2010)
for a detailed exposi on). In more general models, such as a nested logit or random coeﬃcients model,
quality will be a func on of addi onal variables, such as product characteris cs, condi onal market shares,
etc. While we do not observe product characteris cs, product dummies accommodate these more generaldemand speciﬁca ons. We also note that using output prices as a proxy for quality does not imply that weassume complete pass-through of input to output prices; the degree of pass-through will be dictated bythe (unspeciﬁed) underlying demand and market structures and behavioral assump ons. Accordingly, our
speciﬁca on is consistent with any degree of pass-through between input and output prices. The empiricalstrategy uses a ﬂexible func on of output price, market share and product dummies to control for output
quality, which reﬂects input quality and in turn, input prices.
Formally, let vf t denote output quality. We can re-write the produc on func on as
qf t (vf t ) = f (x̃f t (vf t ); β) + ω f t + B(Wf t (vf t ); Wf t (vf t ) × x̃f t (vf t ); β) + ϵf t .
28

(21)

Note that this approach allows for input prices to vary across geographic loca ons; the crucial assump on is that condi onal
on loca on, which is observed, the only reason that input prices vary across two ﬁrms producing the same product is that thequali es of their products are diﬀerent.
29
We maintain the assump on of perfectly compe ve input markets throughout the analysis. We assume that condi onal ona par cular input quality, all ﬁrms face the same input price. In principle, we could allow input prices to vary across regions (while
maintaining the assump on that ﬁrms within a region producing the same quality face the same input prices), but in prac ce we
do not have reliable informa on on loca on of produc on in the data.

18

The speciﬁca on makes explicit that both the deﬂated ﬁrm input expenditures x̃f t and the (unobserved)
ﬁrm input prices Wf t are func ons of product quality vf t . Product quality is expressed as a ﬂexible func onof output price, market share, and product dummies: vf t = υ t (pf t , msf t , If t ). Since input prices are
an increasing func on of output quality, input prices are also a func on of these variables, i.e., Wf t =wt (pf t , msf t , If t ). We can then write the term Bf t as a ﬂexible polynomial in output price, market share,product dummies, and interac on of these variables with the deﬂated input expenditures. That is, we
specify Bf t as a polynomial dt , so that: Bf t ≡ dt [pf t , msf t , If t , (pf t , msf t , If t ) × x̃f t ]. The produc onfunc on that we take to the data becomes:
qf t = f (x̃f t ; β) + ω f t + dt [pf t , msf t , If t , (pf t , msf t , If t ) × x̃f t ] + ϵf t

(22)

In the ﬁrst stage, we es mate:
qf t = ϕt (x̃f t , zf t ) + ϵf t(23)

where zf t includes pf t , msf t and If t . Produc vity is given by ω f t = ϕf t − f (x̃f t ; β) − dt (.) = φf t −f (x̃f t ; β) − bf t δ, where bf t contains the price, market share, their interac ons with input expenditures,and product dummies.30 The coeﬃcients on the variables in bf t are themselves not of direct interest since
we compute markups using the es mates of β. Next, we obtain the innova on in produc vity, ξ f t (β, δ),in the usual way as the diﬀerence between realized and expected produc vity. The moments that iden fy
the parameters become:)(E ξ f t (β, δ)Y∗f t = 0(24)where Y∗f t now contains in addi on to the variables men oned in the previous subsec on, lagged output
prices, lagged market shares, (double) lagged input tariﬀs, and their appropriate interac ons with the input
terms.31 The reason we use these variables to form addi onal moment condi ons, is that we jointly iden fy
the produc on func on coeﬃcients and the coeﬃcients capturing the input price varia on, δ, which describe the rela onship between the elements of dt (.) and input prices (although the la er coeﬃcients are
not of direct interest). For example, the parameter related to the output price is iden ﬁed oﬀ the moment
E(ξ t pt−1 ) = 0; this moment condi on is based on the insight that current prices do react to produc vity
shocks, so we need to use lagged output prices which exploit the serial correla on of prices.
4.3.3 The Sample Selec on Correc on
In this subsec on, we discuss the correc on procedure we employ to account for the poten al sample
selec on bias arising from using only single-product ﬁrms in the es ma on.
As noted earlier, rather than relying on ﬁrms that remain single-product producers for the en re sam30

We do not interact the product dummies with the other elements of bf t to reduce the dimensionality of the es ma on.
We form moments using the actual innova on ξ f t since we use dt (.) to proxy for the unobserved input price varia on. We
therefore recover physical produc vity shocks (ω f t ) given parameters (β, δ). If input prices or quality do not vary across ﬁrms,
the es mates from this approach would be iden cal to those obtained when using the method described in the Sec on 4.3.1.
31

19

ple, our es ma on uses an unbalanced panel of single-product ﬁrms. As in Olley and Pakes (1996), theunbalanced panel improves on the selec on problem since it includes ﬁrms that may eventually become
mul -product producers in response to produc vity shocks. Even with an unbalanced panel, a selec onbias may s ll arise if the produc vity threshold determining a ﬁrm’s decision to become mul -product iscorrelated with the inputs (in par cular, capital). We address this bias by introducing a correc on for sample selec on and modifying the law of mo on for produc vity following a similar approach to Olley andPakes (1996).
The underlying model behind our sample selec on correc on is one where the number of products
manufactured by ﬁrms increases with produc vity. There are several mul -product ﬁrm models that generate this correla on and the one that matches our setup most closely is Mayer et al. (2011). In that model,
the number of products a ﬁrm produces is an increasing step func on of the ﬁrms’ produc vity. Firms havea produc vity draw which determines their core product. Condi onal on entry, the ﬁrm produces this coreproduct and incurs an increasingly higher marginal cost of produc on for each addi onal product it manufactures. This structure generates a “competence ladder” that is characterized by a set of cutoﬀ points,
each associated with the introduc on of an addi onal product.32
The cutoﬀ point that is relevant to our sample selec on procedure is the one associated with the introduc on of a second product. We denote this cutoﬀ by ω̄f t . Firms with produc vity that exceeds ω̄f t
are mul -product ﬁrms that produce two (or more) products while ﬁrms below ω̄f t remain single-productproducers and are included in the es ma on sample.
If the threshold ω̄f t is independent of the right-hand side variables in the produc on func on, there
is no selec on bias and we obtain consistent es mates of produc on func on coeﬃcients (as long as we
use the unbalanced panel). A bias arises when the threshold is a func on of capital and/or labor. For
example, it is possible that even condi onal on produc vity, a ﬁrm with more capital ﬁnds it easier toﬁnance the introduc on of an addi onal product; or, a ﬁrm that employs more workers may have an easierme expanding into new product lines. In these cases, ﬁrms with more capital and/or labor are less likely to
be single-product ﬁrms, even condi onal on produc vity, and this generates a nega ve bias in the capitaland labor coeﬃcients.
To address the selec on bias, we allow the threshold ω̄f t to be a func on of the state variables andthe ﬁrm’s informa on set at me t − 1 (we assume the decision to add a product is made in the previous
period). The state variables in our se ng include capital, labor, produc vity and all variables in zf t that areserially correlated (i.e., input and output tariﬀs, output prices and product dummies).33 The selec on rule
requires that the ﬁrm make its decision to add a product based on a forecast of these variables in the future.
Deﬁne an indicator func on χf t to be equal to 1 if the ﬁrm remains single-product (S) and 0 otherwise, andlet ω̄f t be the produc vity threshold a ﬁrm has to clear in order to produce more than one product.
32

Alterna ve models of mul -product ﬁrms, such as Bernard et al. (2010), introduce ﬁrm-product-speciﬁc demand shocks thatgenerate product switching (e.g., product addi on and dropping) in each period. We avoid this addi onal complexity in our setup
since product dropping is not a prominent feature of our data (Goldberg et al. (2010b)). Moreover, in the empirical sec on we ﬁndstrong support that ﬁrms’ marginal costs are lower on their core competent products (products that have higher sales shares).
33
If we modeled the behavior of mul -product ﬁrms that shed products to become single-product producers, the number of
products would be a natural state variable to include in z. So while we abstract away from product dele ons since they are rare inour data, our approach can accommodate this case as well.

20

The selec on rule can be rewri en as:
Pr(χf t = 1) = Pr [ωf t ≤ ω̄f t (lf t , kf t , zf t )|ω̄f t (lf t , kf t , zf t ), ωf t−1 ](25)= κt−1 (ω̄f t (lf t , kf t , zf t ), ωf t−1 )= κt−1 (lf t−1 , kf t−1 , if t−1 , zf t−1 , ωf t−1 )= κt−1 (lf t−1 , kf t−1 , if t−1 , zf t−1 , mf t−1 ) ≡ Sf t−1
We use the fact that the threshold at t is predicted using the ﬁrm’s state variables at t − 1, the accumula on equa on for capital34 , and ωf t−1 = ht (lf t−1 , kf t−1 , zf t−1 , mf t−1 ) to arrive at the last equa on.35
The law of mo on for produc vity now becomes:
output x′
ωf t = gt−1
(ωf t−1 , τ input
it−b , τ it−b , If t−1 , ω̄f t ) + ξf t

(26)

where b = {0, 1} .
As in Olley and Pakes (1996), we have two diﬀerent indexes of ﬁrm heterogeneity, the produc vity andthe produc vity cutoﬀ point. Note that Sf t−1 = κt−1 (ωf t−1 , ω̄f t ) and therefore ω̄f t = κ−1
t−1 (ωf t−1 , Sf t−1 ).
Plugging this last expression into the modiﬁed law of produc vity gives:
output x′
ω f t = gt−1
(ω f t−1 , τ input
it−b , τ it−b , If t−1 , Sf t−1 ) + ξ f t(27)

This is the law of mo on we use to form the moments in the second stage of the es ma on. To obtain
Sf t−1 , we es mate by industry, a probit that regresses a ﬁrm’s single-product status on materials, capital,
labor, the tariﬀ variables, the output price of the product the ﬁrm currently produces, product and me
dummies. Once the probit is es mated, we construct the propensity score Ŝf t−1 –the predicted probability
that the ﬁrm remains single-product at me t given the ﬁrm’s informa on set at me t − 1–and insert it in
the modiﬁed law of mo on for produc vity.

4.4 Markups and Marginal Costs
4.4.1 Single-Product Firms
We can now apply our framework from Sec on 3 to compute markups and marginal costs using the esMmates of the produc on func on. Using equa on (5), we compute markups µb =b
θ (αM )−1 , where
ft

ft

ft

M
the es mated output elas ci es b
θf t on materials are computed using the es mated coeﬃcients of the

produc on func on36 and αM
f t , the revenue share of materials, is data. We then use the markup deﬁnion in conjunc on with the price data to recover the ﬁrm’s marginal cost, mcf t , at each point in me as
The accumula on equa on for capital is: kf t = (1 − δ)kf t−1 +if t−1 ,where δ is the deprecia on rate of capital.
This speciﬁca on takes into account that ﬁrms hire and/or ﬁre workers based on their labor force at me t − 1 and theirforecast of future demand and costs captured by z and ω. So all variables entering the non-parametric func on κt−1 (.) help
predict the ﬁrm’s employment at me t.
M
36
The expression for the materials output elas city is: b
θf t = β̂ + 2β̂
mf t + β̂ lf t + β̂ kf t + β̂
lf t kf t .
34

35

m

21

mm

lm

mk

lmk

P

mc
c f t = µbf t .37
ft

4.4.2

Mul -Product Firms

We now discuss how we obtain markups and marginal costs for the mul -product ﬁrms.
As shown in equa ons (6) and (7), compu ng markups and marginal costs requires the product-speciﬁc
output elas city on materials and product-speciﬁc revenue shares for materials. We obtain the output
elas city from the single-product ﬁrms, but we do not know the product-speciﬁc revenue shares of inputs
for mul -product ﬁrms. Here, we show how to compute the input alloca ons across products of a mul product ﬁrm in order to construct αM
f jt .
()
X̃f jtLet ρf jt = ln X̃
be product j’s input cost share, where X̃f t denotes total deﬂated expendituresft

on each input by ﬁrm f at me t. We assume that this share does not vary across inputs. We solve forρf jt as follows. We ﬁrst eliminate unan cipated shocks and measurement error from the output data byfollowing the same procedure as in the ﬁrst stage of our es ma on rou ne in Sec on 4.3.1 for the singleproduct ﬁrms. We project output quan ty, qf jt , on interac ons of all inputs, output and input tariﬀs, theoutput price, product dummies and me dummies and obtain the predicted values. We next compute aﬁrm-product-speciﬁc term ωb f jt : ωb f jt ≡ E(qf jt ) − f (x̃f t ; β̂).38 From (9), this becomes:
ωb f jt = ω f t + Af jt (ρf jt , xf t , β̂)= ω f t + âf t ρf jt + b̂f t ρ2f jt + ĉf t ρ3f jt

(28)
(29)

where the second equa on follows from applying our translog func onal form. The terms âf t , b̂f t , and ĉf t
are func ons of the es mated parameter vector β̂.39
With an es mate of E(qf jt ), we can construct ωb f jt for each mul -product ﬁrm observa on (ﬁrm-yearproduct triplet). For each year, we obtain the ﬁrm’s produc vity and input alloca ons, the J + 1 unknowns
37
Output elas ci es will vary across sectors because we es mate β separately for each sector. Moreover, given our translog
speciﬁca on, even single-product ﬁrms within a sector will have diﬀerent output elas ci es.
38
The es mated parameter vectorβ̂ is already purged of the bias arising from input price varia on discussed in Sec on 4.3.2.
39
For the translog produc on func on:

âf t

=

(
)
β̂ l + β̂ m + β̂ k + 2 β̂ ll lf t + β̂ mm mf t + β̂ kk kf t + β̂ lm (lf t + mf t )+β̂ lk (lf t + kf t ) + β̂ mk (mf t + kf t ) + β̂ lmk (lf t mf t + lf t kf t + mf t kf t )

b̂f t

=

β̂ ll + β̂ mm + β̂ kk + β̂ lm + β̂ lk + β̂ mk + β̂ lmk (lf t + mf t + kf t )

ĉf t

=

β̂ lmk22

()ω f t , ρf 1t , . . . , ρf Jt , by solving a system of J + 1 equa ons:ωb 1f t=

ω f t + âf t ρf 1t + b̂f t ρ2f 1t + ĉf t ρ3f 1t(31)... . . .
J
∑

(30)

ω
b f Jt=

ω f t + âf t ρf Jt + b̂f t ρ2f Jt + ĉf t ρ3f Jt

exp (ρf jt )=1,

exp(ρf jt ) ≤ 1∀j

(32)
(33)

j=1

This system imposes the economic restric on that each input share can never exceed one and they must
together sum up to one across products in a ﬁrm. We numerically solve this system for each ﬁrm in eachyear.40
We now have all the ingredients to calculate markups and the implied marginal costs for the mul product ﬁrms according to equa on (6):Mµ̂f jt = θ̂f jt

Pf jt Qf jt
exp (ρ̂f jt )PfMt VfM
t

(34)

M

The product-speciﬁc output elas city for materials θ̂f jt is a func on of the produc on func on coeﬃcients,
the product-speciﬁc output (which is data) and the materials allocated to product j. Hence, it can be easily computed once the alloca on of inputs across products has been recovered.41 Marginal costs for the
products made by mul -product ﬁrms are then recovered by dividing prices by the markup according toequa on (7).

5 Results
5.1 Output Elas ci es
In this subsec on, we present the output elas ci es recovered from the es ma on procedure outlined in
Sec on 4. We also describe how failing to correct for input price varia on or account for the selec on bias
aﬀects the parameters.
The output elas ci es for the single-product ﬁrms used in the es ma on are reported in Table 3.42 A
nice feature of the translog is that unlike in a Cobb-Douglas produc on func on, output elas ci es canvary across ﬁrms (and across products within ﬁrms). We report both the average and standard devia on of40

We ﬁnd that the input alloca ons across products are highly correlated with, but not iden cal to, alloca ng inputs according
to product revenue shares. We experiment with various star ng values for the unknowns and ﬁnd that condi onal on converging
to an inside solu on (e.g., all the product’s input shares are between 0 and 1, non-inclusive), the solu on is unique. Out of thetotal 13,394 mul -product ﬁrm-year pairs, we hit a corner solu on in 894 cases. We exclude these observa ons from from theanalysis in Sec on 5.
[]
M
41
The expression for the materials output elas city for product j at me t is: b
θf jt = β̂ m + 2β̂ mm ρ̂f jt + mf t +
[
]
[
]
[
][
]
β̂ lm ρ̂f jt + lf t + β̂ mk ρ̂f jt + kf t + β̂ lmk ρ̂f jt + lf t ρ̂f jt + kf t . For single product ﬁrms, exp(ρf jt ) = 1 and the output
elas city becomes the one reported in Footnote 36.
L42
The output elas city for materials is reported in Footnote 36. The output elas ci es for labor and capital are b
θf t = β̂ +K
2β̂ ll lf t + β̂ lm mf t + β̂ lk kf t + β̂ lmk mf t kf t and b
θf t = β̂ k + 2β̂ kk kf t + β̂ lk lf t + β̂ mk mf t + β̂ lmk lf t kf t .

23lthe elas ci es across sectors. The last column in the table reports the returns to scale. The main messageof the table is that there is a distribu on around the average and returns to scale exceed one in mul ple
industries. In each sector, approximately 25 percent of the ﬁrms produce under increasing returns to scale.
These ﬁndings on increasing returns to scale are consistent with Kle e and Griliches (1996) and De Loecker(2011) who showed that unobserved ﬁrm-level price varia on can lead to a downward bias of the returns
to scale.
The le panel of Table 4 re-runs the es ma on without implemen ng the correc on for the unobserved
input price varia on discussed in Sec on 4.3.2. It is clear that the uncorrected procedure yields nonsensical es mates of the produc on func on. For example, the labor output elas ci es are o en nega ve andrange from -3.01 to 3.17 across sectors, while the returns to scale are either very low or extremely high. As
we discussed earlier, these results are not surprising given that we es mate a quan ty-based produc onfunc on using deﬂated input expenditures. It is clear that failing to account for input price varia on yields
distorted es mates. For example, a nega ve labor elas city stems from the fact that there are ﬁrms that
produce similar quanes of output using more expensive labor, resul ng in a downward biased labor elas-city. In general, it is diﬃcult to sign this bias because there are three inputs which interact in complicatedways in the translog, but it is clear that one needs to correct for input price varia on across ﬁrms using theprocedure described above.
The right panel of Table 4 presents the output elas ci es from es ma on of the produc on func on
on a balanced panel of single-product ﬁrms. This es ma on does not incorporate the sample selec oncorrec on described in Sec on 4.3.3. As discussed earlier, we expect the output elas city for capital, andto a lesser extent for labor, to change if we use a balanced panel. In several instances, the output elas ci esof capital and labor change. The output elas city of materials does not change as dras cally, which isconsistent with our premise that it is the correla on between the produc vity threshold and capital andlabor that may generate a selec on bias.

5.2

Prices, Markups and Marginal Costs Pa erns

Our data and methodology deliver measures of ﬁrm performance–prices, markups, marginal costs, and produc vity, which are usually not simultaneously considered in the exis ng literature. This sec on describes
the rela onship between prices, markups, marginal costs, and produc vity.
The markup es mates are reported in Table 5. The mean and median markups are 2.13 and 1.10,
respec vely, but there is considerable varia on across sectors.
The methodology provides measures of markups and marginal costs without a priori assump ons on the
returns to scale. The es mates show that many ﬁrms are characterized by increasing returns to scale. We
would therefore expect to observe an inverse rela onship between a product’s marginal cost and quan ty
produced.43 In Appendix Figure A.1 we plot marginal costs against produc on quanes (we de-mean eachvariable by product-year ﬁxed eﬀects in order to facilitate comparisons across ﬁrms). The ﬁgure shows43

It is important to note here that we do not derive marginal cost based on the duality of produc on and cost func ons. Instead,we bring in addi onal informa on on prices and derive marginal cost based on its deﬁni on as the ra o of price to markup. Thisimplies that even though we ﬁnd returns to scale in the produc on func on es ma on, it does not follow automa cally that oures mated marginal costs will be declining in quan ty.

24

indeed that marginal costs vary inversely with produc on quanthat quanes. The le panel of the ﬁgure showses and markups are posi vely related indica ng that ﬁrms producing more output also enjoy

higher markups (due to their lower marginal costs).
We next examine the rela onships between the performance measures. Table 6 reports the raw pairwise correla on matrix across prices, markups, marginal costs and ﬁrm-level produc vity. As we expect,
prices are posi vely correlated with marginal costs and markups, but nega vely correlated with ﬁrm produc vity. Marginal costs are nega vely correlated with markups and produc vity, and there is a posi ve
correla on between markups and produc vity.
Figure A.2 in the Appendix presents an alterna ve way to see the inter-relatedness of the ﬁrm performance measures by plo ng ﬁrms’ produc vity against the marginal costs and markups of their products.
In order to compare these variables across ﬁrms, we regress the ﬁrm-level produc vity measures on the
ﬁrm’s main industry-year pair ﬁxed eﬀects and recover the residuals. This allows us to compare produc vity
across ﬁrms within industries. We compare the markups and marginal costs across products by de-meaningeach by product-year ﬁxed eﬀects. The ﬁgure plots the de-meaned markups and marginal costs against thede-meaned produc vi es, and removes outliers above and below the 97th and 3rd percen les. Again, thevariables are correlated in ways that one would expect: produc vity is posi vely correlated with markups
and strongly nega vely correlated with marginal costs.
The previous tables and ﬁgures demonstrate correla on pa erns that arise across ﬁrms. We also examine how markups and marginal costs vary across products within a ﬁrm. Our analysis here is guided by the
recent literature on mul -product ﬁrms. Our correla ons are remarkably consistent with the predic onsof this literature, especially with those of the mul -product ﬁrm extension of Melitz and O aviano (2008)
developed by Mayer et al. (2011). A key assump on in that model is that mul -product ﬁrms each have a“core competency”. The “core” product has the lowest (within a ﬁrm) marginal cost. For the other products, marginal costs rise with a product’s distance from the “core competency”. A ﬁrm’s product scope isdetermined by the point at which the marginal revenue of a product is equal to the marginal cost of manufacturing that product. This structure on the produc on technology is also shared by the mul -product ﬁrm
models of Eckel and Neary (2010) and Arkolakis and Muendler (2010). In all three models, more produc ve
ﬁrms manufacture more products, a pa ern clearly conﬁrmed by Figure A.3.
Mayer et al. (2011) also assume a linear demand system which implies that ﬁrms have non-constantmarkups across products. Further, ﬁrms have their highest markups on their “core” products with markups
declining as they move away from their main product. Figures A.4 and A.5 in the Appendix provide evidence
suppor ng both implica ons. In these two ﬁgures, markups and marginal costs are de-meaned by productyear and ﬁrm-year ﬁxed eﬀects in order to make these variables comparable across products within ﬁrms.
Figure A.5 plots the de-meaned markups and marginal costs against the sales share of the product withineach ﬁrm, and A.4 plots the same variables against the product’s rank. We observe that the marginal costs
rise as a ﬁrm moves away from its core competency while the markups fall. In other words, the ﬁrm’s most
proﬁtable product (excluding any product-speciﬁc ﬁxed costs) is its core product. Despite not imposing
any assump ons on the market structure and demand system in our es ma on, these correla ons are
remarkably consistent with Mayer et al. (2011).

25

Foreshadowing the results in the next subsec on, we also ﬁnd evidence of imperfect pass-through ofcosts on prices because of variable markups. In column 1 of Table 7, we regress prices on ﬁrm-product ﬁxed
eﬀects and marginal costs and ﬁnd a pass-through coeﬃcient of 0.29. Since marginal costs are es mated,
they are measured with error. We instrument marginal costs with ﬁrm-level produc vity and input tariﬀs incolumn 2. These are valid instruments since they aﬀect prices only through their eﬀect on marginal costs.
That is, neither produc vity nor input prices have a direct eﬀect on prices; they only aﬀect prices throughtheir eﬀects on marginal costs. The coeﬃcients in the ﬁrst stage have the expected signs: produc vity (input
tariﬀs) is nega vely (posi vely) correlated with costs and the ﬁrst stage F-sta s c is large. The pass-throughcoeﬃcient increases to 0.60 in the IV speciﬁca on, which is in line with long-run pass-through es matesin the exchange rate literature. This imperfect pass-through means that any shocks to marginal costs, forexample shocks from trade liberaliza on, do not lead to propor onal changes in factory-gate prices becauseof changes in markups. We examine this markup adjustment in detail in the subsequent sec on.

5.3

Prices, Markups and Trade Liberaliza on

We now examine how prices, markups and marginal costs adjusted as India liberalized its economy. As
discussed in Sec on 2, we restrict the analysis to 1989-1997 since tariﬀ movements a er this period appear
correlated with industry characteris cs.
We begin by plo ng the distribu on of prices in 1989 and 1997 in Figure 1. Here, we include only ﬁrmproduct pairs that are present in both years, and we compare the prices over me by regressing them onﬁrm-product pair ﬁxed eﬀects and plo ng the residuals. As before, we remove outliers in the bo om andtop 3rd percen les.44 This comparison of the same ﬁrm-product pairs over me exploits the same varia on
as our regression analysis below. The ﬁgure shows that the distribu on of (real) prices is virtually unchanged
between 1989 and 1997. This is a surprising result given nature of India’s economic reforms during thisperiod that were designed to reduce entry barriers and increase compeon in the manufacturing sector.

As a ﬁrst pass, the ﬁgure suggests that prices did not move much despite the reforms.
Of course, the ﬁgure includes only ﬁrm-product pairs that are present at the beginning and end of
the sample, and does not control for macroeconomic factors that could inﬂuence prices beyond the tradereforms. We use the en re sample and control for macroeconomic trends in the following speciﬁca on:45
pf jt = δ f j + δ st + δ 1 τ output+ η f jt .
it

(35)

We exploit varia on in prices and output tariﬀs within a ﬁrm-product over me through the ﬁrm-productﬁxed eﬀects (δ f j ) and control for macroeconomic ﬂuctua ons through sector-year ﬁxed eﬀects δ st . Since
the trade policy measure varies at the industry level, we cluster our standard errors at this level. We report
the price regression with just year ﬁxed eﬀects in column 1 of Table 8. The coeﬃcient on the output tariﬀ
44
We trim to ensure that the results are not driven by outliers. Our results are robust to alterna ve trims (e..g, the top andbo om 1st or 2nd percen les) and to not trimming at all. These results are available upon request.
45
One could try to capture the net impact of tariﬀ reforms using the eﬀec ve rate of protec on measure proposed by Corden(1966). However, this measure is derived in a se ng with perfect compe on and an inﬁnite export-demand and import-supply
elas ci es which imply perfect pass-through. As we show below, these assump ons are not sa sﬁed in our se ng, so that theconcept of the “eﬀec ve rate of protec on” is not well deﬁned in our case.

26

is posi ve implying that a 10 percentage point decline is associated with a very small–0.94 percent–decline
in prices.46 Between 1989 and 1997, output tariﬀs fall on average by 62 percentage points; this results ina precisely es mated average price decline of 5.9 percent (=62*0.094). This is a small eﬀect of the tradereform on prices and it is consistent with the raw distribu ons plo ed in Figure 1. The basic message
remains the same if we control more ﬂexibly for trends with sector-year ﬁxed eﬀects in column 2. The
results imply that the average decline in output tariﬀs led to a 8.0 (=62*.128) percent rela ve drop in prices.
These results show that although the trade liberaliza on led to lower factory-gate prices, the decline ismore modest than we would have expected given the magnitude of the tariﬀ declines. Since earlier studies(Goldberg et al. (2010a), Topalova and Khandelwal (2011)) have emphasized the importance of declines in
input tariﬀs in shaping ﬁrm performance, we separate the eﬀects of output tariﬀs and input tariﬀs on prices.
Output tariﬀ liberaliza on reﬂects primarily an increase in compeon, while the input tariﬀ liberaliza on

should provide access to lower cost (and more variety of) inputs. We run the analog of the regression in(35), but separately include input and output tariﬀs:
pf jt = δ f j + δ st + δ 1 τ output+ δ 2 τ input+ η f jt .
it
it

(36)

We refer the reader to the weighted regression in column 4 of Table 9 (the reason for weighing the regressions is discussed below). There are two interes ng ﬁndings that are important for understanding how
trade aﬀects prices in this liberaliza on episode. First, there is a posi ve and sta s cally signiﬁcant coefﬁcient on output tariﬀs. This result is consistent with the common intui on that increases in compevepressures through lower output tariﬀs will lead to price declines. The eﬀect is tradi onally a ributed toreduc ons in markups and/or reduc ons in X-ineﬃciencies within the ﬁrm. The point es mates imply thata 10 percentage point decline in output tariﬀs results in a 1.36 percent decline in prices. On the other hand,the coeﬃcient on input tariﬀs is small and very noisy. In a counterfactual analysis that holds input tariﬀs
ﬁxed and reduces output tariﬀs, we would observe a fairly precisely es mated decline in prices. However,
the overall changes of prices taking into account both types of tariﬀ declines is less precise (although s ll
sta s cally signiﬁcant at the 10 percent level). Output tariﬀs and input tariﬀs fall by 62 and 24 percentage
points, respec vely, and using the point es mates in column 1, this implies that prices fall on average by
16.8 percent.
We use the es mates of markup and costs to examine the mechanisms behind these moderate changes
in factory-gate prices. We begin by plo ng the distribu on of markups and costs in Figure 2. Like Figure
1, this ﬁgure considers only ﬁrm-product pairs that appear in both 1989 and 1997 and de-means the observa ons by their me average. The ﬁgure demonstrates that between 1989 and 1997, the marginal cost
distribu on shi ed le indica ng an eﬃciency gain. However, this marginal cost decline is almost exactly
oﬀset by a corresponding rightward shi in the markup distribu on. Since (log) marginal costs and (log)markups exactly sum to (log) prices, the net eﬀect is virtually no change on prices.
We re-run speciﬁca on (36) using marginal costs and markups as the dependent variables. Since marginal
costs and markups are es mated variables, we weigh the regressions by the number of observa ons in each46

Our result is consistent with Topalova (2010) who ﬁnds that a 10 percentage point decline in output tariﬀs results in a 0.96
percent decline in wholesale prices in India during this period.

27

sector’s produc on func on es ma on reported in Table 3. Some sectors recover the produc on func onusing more observa ons than others (for example, Table 3 reports that the produc on func on es ma on
for the apparel sector has 301 observa ons compared with 1,681 observa ons for the food products sector). We are more conﬁdent in our es mates of the output elas ci es, and consequently the es mates ofmarkups and marginal costs, for sectors where we have more data. This weigh ng procedure should reducenoise. Since prices decompose exactly to the sum of marginal costs and markups, the coeﬃcients in columns
5 and 6 sum to their respec ve coeﬃcients in column 4. We ﬁrst focus on marginal costs regressions reported in column 5. The coeﬃcient on output tariﬀs is posi ve, sugges ng that marginal costs decline with
output tariﬀ liberaliza on but the decline is small and sta s cally insigniﬁcant. However, the coeﬃcient on
input tariﬀs is both posi ve and large in magnitude, indica ng that improved access to cheaper and morevariety of imported inputs results in large cost declines; this coeﬃcient is signiﬁcant at the 11% level. The
ﬁnal row of Table 9 reports the average eﬀect on marginal costs using the average declines in input andoutput tariﬀs. On average, marginal costs fell 40.3 percent.
This magnitude of the marginal costs decline is fairly sizable and would translate to larger prices declines
if markups are constant. However, Figure 2 suggests that markups rose during this period, and in column
6 of Table 9, we directly examine how input and output tariﬀs aﬀected markups. The coeﬃcient on input
tariﬀs is large and nega ve implying that input tariﬀ liberaliza on resulted in higher markups. The results
suggest that ﬁrms oﬀset the beneﬁcial cost reduc ons from improved access to imported inputs by raisingmarkups. The overall eﬀect, taking into account the average declines in input and output tariﬀs between
1989 and 1997, is that markups, on average, increased by 23.4 percent. This increase oﬀsets about halfof the average decline in marginal costs, and as a result, the overall eﬀect of the trade reform on prices ismoderated. We obtain a qualita vely similar pa ern of results in the unweighted regressions in columns
1-3, but not surprisingly, the coeﬃcients are slightly less precisely es mated.
Although temp ng, it is misleading to draw conclusions about the pro-compeve eﬀects (or lackthereof) of the trade reform using the markup regressions in column 6 of Table 9. The reason is that output tariﬀ liberaliza on can aﬀect marginal costs through changes in X-ineﬃciencies and scale. As we haveshown, ﬁrms raise markups when costs fall and this imperfect pass-through a enuates the coeﬃcient on
output tariﬀs in the markup regressions. In order to isolate pro-compeve eﬀects, we need to control forany simultaneous shocks to marginal costs. We do this by re-running the markup regression but controlling
ﬂexibly for marginal costs. Condi oning on marginal costs, the output tariﬀ coeﬃcient isolates the direct
pro-compe

ve eﬀect of the trade liberaliza on on markups. We report the weighted results in the rightpanel of Table 10 (the unweighted results are reported in the le panel).47 Indeed, the coeﬃcient on output
tariﬀs in column 4 is posi ve and signiﬁcant; this provides direct evidence that output tariﬀ liberaliza on
exerted pro-compeve eﬀects on markups. The way to interpret the results in column 4 is to consider themarkups on two products in diﬀerent industries. Condi onal on any (poten ally diﬀeren al) impact of the
trade reforms on their respec ve costs, the product in the industry that experiences a 10 percentage point
larger decline in output tariﬀs will have a 1.30 percent rela ve decline in markups. Column 5 adds input
47

To control for marginal costs as ﬂexibly as possible, we use a third-order polynomial for marginal costs and suppress these
coeﬃcients in Table 10. We ﬁnd very similar results if we simply include marginal costs as the only control. These results areavailable upon request.

28

tariﬀs to the regression. As discussed earlier, input tariﬀs should aﬀect markups only through the imperfect transmission of their impact on costs through improved access to imported inputs. Once we control
for marginal costs, input tariﬀs should have no eﬀect on markups and that is what we ﬁnd. In contrast tocolumn 5 of Table 9, the coeﬃcient on input tariﬀ falls basically to zero. We observe a similar pa ern ofresults with the unweighted results in the le panel of Table 10. Our analysis demonstrate that India’s tradereform led to large cost reduc ons leading ﬁrms to respond by raising markups. But once we control forthese cost eﬀects, output tariﬀ reduc ons do exert pro-compeve eﬀects by pu ng downward pressure

on markups as we would expect.
The pro-compeve eﬀects might diﬀer across products. For example, output tariﬀs may exert morepressure on products with high markups prior to the reform. We explore this heterogeneity by crea ng a
me-invariant indicator for ﬁrm-product pairs in the top decile of their industry’s markup distribu on in
the ﬁrst year that a product-pair is observed in the data. We interact output tariﬀs with this indicator toallow for diﬀeren al eﬀects of output tariﬀs on markups for these high markup products. The results arereported in columns 3 and 6 of Table 10. We remind the reader that the speciﬁca on includes sector-year
ﬁxed eﬀects to allow for changes in market condi ons over me. The table shows a very strong eﬀect of
output tariﬀs on these high markup products. Using the numbers in the weighted speciﬁca on in column
6, a 10 percentage point decline in output tariﬀs leads to a 1.18 percent fall in markups for products ini ally
below the 90th percen le in the markup distribu on. For high markup products, the same policy reform
results in a 4.27 percent decline a markups. In short, once we control for the incomplete pass-through ofcosts, output tariﬀs reduce markups and these reduc ons are substan ally more pronounced on productswith ini ally high markups.
In sum, our results call for a nuanced evalua on of the eﬀects of the Indian trade liberaliza on on
markups. While we do ﬁnd evidence that the tariﬀ reduc ons have pro-compeve eﬀects, especially at

the right tail of the markup distribu on, our results suggest that the most signiﬁcant eﬀect of the reforms is
to reduce costs to producers. Due to variable markups, cost reduc ons are not passed through completely
to consumers. This suggests that the trade reforms beneﬁted producers rela vely more than consumers, atleast in the short run. However, this does not imply that the reform lowered consumer welfare, especiallyin the long run. In Goldberg et al. (2010a), we show that ﬁrms introduced many new products–accoun ng
for about a quarter of output growth–during this period. If the cost reduc ons (and associated markup
increases) induced by the trade reform spurred this product growth, the beneﬁts to consumers are potenally substan ally larger. In Table 11, we report results that relate a ﬁrm’s product addi ons to changes
in its average markup across its products. In column 1, we regress an indicator if a ﬁrm adds a product inperiod t on the change in (log) average markups between t − 1 and t, while controlling for ﬁrm and year
ﬁxed eﬀects. In column 2, we use the change in the (log) number of products as the dependent variable. In
both cases, increases in markups are strongly correlated with new product introduc ons.48 This suggeststhat ﬁrms used the input tariﬀ reduc ons and associated proﬁt increases to ﬁnance the development of
48

These ﬁndings are consistent with Peters (2012) who develops a model with imperfect compe on that generates heterogeneous markups which determine innova on incen ves. We note however that we did not obtain these results by commi ng toa par cular structure (demand, market structure and compe on) - our ﬁndings could also be consistent with alterna ve mechanisms.

29

new products, implying poten al long-term gains to consumers. A complete analysis of this mechanism
and the impact on welfare lies beyond the scope of this current paper.

6

Conclusion

This paper examines the adjustment of prices, markups and marginal costs in response to trade liberalizaon. We take advantage of detailed price and quan ty informa on to es mate markups from quan tybased produc on func ons. Our approach does not require any assump ons on the market structure or
demand curves that ﬁrms face. This feature of our approach is important in our context since we want toanalyze how markups adjust to trade reforms without imposing ex ante restric ons on their behavior. An
added advantage of our approach is that since we observe ﬁrm-level prices in the data, we can directlycompute ﬁrms’ marginal costs once we have es mates of the markups.
Es ma ng quan ty-based produc on func ons for a broad range of diﬀeren ated products introduces
new methodological issues that we must confront. We propose an iden ﬁca on strategy to es mate produc on func ons on single-product ﬁrms. The advantage of this approach is that we do not need to takea stand on how inputs are allocated across products within mul -product ﬁrms. We also demonstrate how
to correct for a bias that arises when researchers do not observe input price varia on across ﬁrms, an issue
that becomes par cularly important when es ma ng quan ty-based produc on func ons.
The large varia on in markups suggests that trade models that assume constant markups may be missing an important channel when quan fying the gains from trade. Furthermore, our results highlight theimportance of analyzing the eﬀects of both output and input tariﬀ liberaliza on. We observe large declines
in marginal costs, par cularly due to input tariﬀ liberaliza on. However, prices do not fall by as much.
This imperfect pass-through occurs because ﬁrms oﬀset the cost declines by raising markups. Condi onal
on marginal costs, we ﬁnd pro-compeve eﬀects of output tariﬀs on markups. Our results suggest that

trade liberaliza on can have large, yet nuanced eﬀects, on marginal costs and markups. Understanding thewelfare consequences of these results using models with variable markups is an important topic for future
research.
Our results have broader implica ons for thinking about the trade and produc vity across ﬁrms in developing countries. The methodology produces quan ty-based produc vity measures that can be comparedwith revenue-based produc vity measures. Hsieh and Klenow (2009) discuss how diﬀerences between
these two measures can inform us about distor ons and the magnitude of misalloca on within an economy. Importantly, our quan ty-based produc vity measure is purged of substan al varia on in markups
across ﬁrms which poten ally improves upon our understanding of the impact of misalloca on on producvity dispersion. We leave the analysis of the role of misalloca on on the distribu on of these performancemeasures for future research.

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Melitz, M. J. and G. I. P. O aviano (2008). Market size, trade, and produc vity. Review of Economic Studies 75(1), 295–316.
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Sivadasan, J. (2009). Barriers to compe
Economic Analysis & Policy 9(1), 42.

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The Quarterly Journal of Economics 123(2), 489–530.

33

Tables and Figures
Table 1: Summary Sta s cs^ŚĂƌĞŽĨ^ĂŵƉůĞ^ŝŶŐůĞͲWƌŽĚƵĐƚKƵƚƉƵƚ
ůů&ŝƌŵƐ
&ŝƌŵƐWƌŽĚƵĐƚƐ
^ĞĐƚŽƌ
;ϭͿ
;ϮͿ
;ϯͿ
;ϰͿ
ϭϱ&ŽŽĚƉƌŽĚƵĐƚƐĂŶĚďĞǀĞƌĂŐĞƐ
ϴй
Ϯϴϴ
ϭϯϳ
ϭϯϰ
ϭϳdĞǆƚŝůĞƐ
ϳй
ϯϮϯ
ϭϵϲ
ϳϴ
ϭϴtĞĂƌŝŶŐĂƉƉĂƌĞů
Ϭй
ϮϮ
ϮϬ
ϭϰ
ϮϭWĂƉĞƌĂŶĚƉĂƉĞƌƉƌŽĚƵĐƚƐ
Ϯй
ϳϱ
ϱϵ
ϯϬ
ϮϯŽŬĞ͕ƌĞĨŝŶĞĚƉĞƚƌŽůĞƵŵƉƌŽĚƵĐƚƐ
Ϯϰй
Ϯϲ
ϭϭ
ϮϮ
ϮϰŚĞŵŝĐĂůƐ
ϭϵй
ϰϯϲ
Ϯϭϲ
ϰϳϵ
ϮϱZƵďďĞƌĂŶĚWůĂƐƚŝĐ
ϰй
ϭϰϰ
ϭϬϮ
ϴϮ
ϮϲEŽŶͲŵĞƚĂůůŝĐŵŝŶĞƌĂůƉƌŽĚƵĐƚƐ
ϱй
ϭϭϮ
ϴϴ
ϱϵ
ϮϳĂƐŝĐDĞƚĂů
ϭϭй
Ϯϭϯ
ϭϰϯ
ϵϵ
Ϯϴ&ĂďƌŝĐĂƚĞĚŵĞƚĂůƉƌŽĚƵĐƚƐ
ϭй
ϳϯ
ϱϱ
ϰϱ
ϮϵDĂĐŚŝŶĞƌǇĂŶĚĞƋƵŝƉŵĞŶƚ
ϱй
ϭϱϬ
ϴϰ
ϭϴϮ
ϯϭůĞĐƚƌŝĐĂůŵĂĐŚŝŶĞƌǇĂŶĚĂƉƉĂƌĂƚƵƐ
ϯй
ϴϭ
ϱϱ
ϵϳ
ϯϮZĂĚŝŽ͕dsĂŶĚĐŽŵŵƵŶŝĐĂƚŝŽŶ
Ϯй
ϰϲ
ϯϵ
ϴϲ
ϯϰDŽƚŽƌǀĞŚŝĐůĞƐ͕ƚƌĂŝůĞƌƐ
ϳй
ϱϳ
ϰϬ
ϵϰ
dŽƚĂů
ϭϬϬй
Ϯ͕Ϭϰϲ
ϭ͕Ϯϰϱ
ϭ͕ϱϬϭ
EŽƚĞƐ͗dĂďůĞƌĞƉŽƌƚƐƐƵŵŵĂƌǇƐƚĂƚŝƐƚŝĐƐĨŽƌƚŚĞƐĂŵƉůĞ͘dŚĞĨŝƌƐƚĐŽůƵŵŶƌĞƉŽƌƚƐƚŚĞƐŚĂƌĞŽĨŽƵƚƉƵƚďǇƐĞĐƚŽƌŝŶϭϵϵϱ͘ŽůƵŵŶƐϮĂŶĚϯƌĞƉŽƌƚƚŚĞŶƵŵďĞƌŽĨĨŝƌŵƐĂŶĚŶƵŵďĞƌŽĨƐŝŶŐůĞͲƉƌŽĚƵĐƚĨŝƌŵƐŵĂŶƵĨĂĐƚƵƌŝŶŐƉƌŽĚƵĐƚƐŝŶƚŚĞƐĞĐƚŽƌŝŶϭϵϵϱ͘ŽůƵŵŶϰƌĞƉŽƌƚƐƚŚĞŶƵŵďĞƌŽĨƉƌŽĚƵĐƚƐŽǀĞƌƚŚĞĨƵůůƐĂŵƉůĞ͕ϭϵϴϵͲϮϬϬϯ͘34

Table 2: Example of Sector, Industry and Product Classiﬁca ons

E/ŽĚĞ
ϮϳǆĂŵƉůĞƐŽĨ/ŶĚƵƐƚƌŝĞƐ͕^ĞĐƚŽƌƐĂŶĚWƌŽĚƵĐƚƐ
ĞƐĐƌŝƉƚŝŽŶ
ĂƐŝĐDĞƚĂů/ŶĚƵƐƚƌŝĞƐ;^ĞĐƚŽƌƐͿϮϳϭϬϭϯϬϭϬϭϬϭϬϬϬϬ
ϭϯϬϭϬϭϬϮϬϬϬϬ
ϭϯϬϭϬϭϬϯϬϬϬϬ
ϭϯϬϭϬϲϬϰϬϴϬϬ
ϭϯϬϭϬϲϬϰϬϵϬϬ
ϭϯϬϭϬϲϬϱϬϬϬϬ
ϭϯϬϭϬϲϭϬϬϬϬϬ
ϭϯϬϭϬϲϭϬϬϯϬϬ

DĂŶƵĨĂĐƚƵƌĞŽĨĂƐŝĐ/ƌŽŶΘ^ƚĞĞů;/ŶĚƵƐƚƌǇŝͿWŝŐŝƌŽŶ
^ƉŽŶŐĞŝƌŽŶͿũ &ĞƌƌŽĂůůŽǇƐ
;ƐƚĐtĞůĚĞĚƐƚĞĞůƚƵďƵůĂƌƉŽůĞƐ
ƵĚ^ƚĞĞůƚƵďƵůĂƌƐƚƌƵĐƚƵƌĂůƉŽůĞƐ
ŽƌWdƵďĞΘƉŝƉĞĨŝƚƚŝŶŐƐ
tŝƌĞƐΘƌŽƉĞƐŽĨŝƌŽŶΘƐƚĞĞů
^ƚƌĂŶĚĞĚǁŝƌĞϭϯϬϭϬϲϬϯϬϬϬϬ
ϭϯϬϭϬϲϬϯϬϭϬϬ
ϭϯϬϭϬϲϬϯϬϭϬϭ
ϭϯϬϭϬϲϬϯϬϭϬϮ
ϭϯϬϭϬϲϬϯϬϭϬϯ
ϭϯϬϭϬϲϬϯϬϭϬϰ
ϭϯϬϭϬϲϬϯϬϭϵϵ

ĂƐƚŝŶŐŽĨŝƌŽŶĂŶĚƐƚĞĞů;/ŶĚƵƐƚƌǇŝͿĂƐƚŝŶŐƐΘĨŽƌŐŝŶŐƐ
ĂƐƚŝŶŐƐͿũ;Ɛƚ ^ƚĞĞůĐĂƐƚŝŶŐƐ
ĐĂƐƚŝƌŽŶĐĂƐƚŝŶŐƐƵĚŽƌ DĂůĞĂďůĞŝƌŽŶĐĂƐƚŝŶŐƐ
W^͘'͘ŝƌŽŶĐĂƐƚŝŶŐƐ
ĂƐƚŝŶŐƐ͕ŶĞĐϮϳϯϭEŽƚĞƐ͗dŚŝƐƚĂďůĞŝƐƌĞƉůŝĐĂƚĞĚĨƌŽŵ'ŽůĚďĞƌŐĞƚĂů͘;ϮϬϭϬďͿ͘&ŽƌE/ϮϳϭϬ͕ƚŚĞƌĞĂƌĞĂƚŽƚĂůŽĨϭϭϭƉƌŽĚƵĐƚƐ͕ďƵƚŽŶůǇĂƐƵďƐĞƚĂƌĞůŝƐƚĞĚŝŶƚŚĞƚĂďůĞ͘&ŽƌE/Ϯϳϯϭ͕ĂůůƉƌŽĚƵĐƚƐĂƌĞůŝƐƚĞĚŝŶƚŚĞƚĂďůĞ͘35

Table 3: Output Elas ci es of Translog Produc on Func on, by Sector^ĞĐƚŽƌ
ϭϱ&ŽŽĚƉƌŽĚƵĐƚƐĂŶĚďĞǀĞƌĂŐĞƐ
ϭϳdĞǆƚŝůĞƐ
ϭϴtĞĂƌŝŶŐĂƉƉĂƌĞů
ϮϭWĂƉĞƌĂŶĚƉĂƉĞƌƉƌŽĚƵĐƚƐ
ϮϯŽŬĞ͕ƌĞĨŝŶĞĚƉĞƚƌŽůĞƵŵƉƌŽĚƵĐƚƐ
ϮϰŚĞŵŝĐĂůƐ
ϮϱZƵďďĞƌĂŶĚWůĂƐƚŝĐ
ϮϲEŽŶͲŵĞƚĂůůŝĐŵŝŶĞƌĂůƉƌŽĚƵĐƚƐ
ϮϳĂƐŝĐDĞƚĂů
Ϯϴ&ĂďƌŝĐĂƚĞĚŵĞƚĂůƉƌŽĚƵĐƚƐ( / 3   4     / 3     # *5         / #  KďƐĞƌǀĂƚŝŽŶƐŝŶWƌŽĚƵĐƚŝŽŶ&ƵŶĐƚŝŽŶƐƚŝŵĂƚŝŽŶ
;ϭͿ
ϭ͕ϲϴϭ
Ϯ͕Ϭϱϰ
ϯϬϭ
ϳϲϭ
ϭϳϮ
Ϯ͕ϯϲϳ
ϭ͕ϬϳϮ
ϵϳϴ
ϭ͕ϯϵϮ
ϲϯϳ
($
$&
)
!(%

>ĂďŽƌ
;ϮͿ
Ϭ͘Ϯϵ

DĂƚĞƌŝĂůƐ
;ϯͿϬ͘ϲϬĂƉŝƚĂů
;ϰͿϬ͘ϬϴZĞƚƵƌŶƐƚŽ
^ĐĂůĞ
;ϱͿ
Ϭ͘ϵϴ

΀Ϭ͘ϬϮ΁

΀Ϭ͘Ϭϯ΁

΀Ϭ͘Ϭϯ΁

΀Ϭ͘Ϭϰ΁

Ϭ͘ϯϭ

Ϭ͘ϱϳ

Ϭ͘ϭϭ

Ϭ͘ϵϴ

΀Ϭ͘Ϭϭ΁

΀Ϭ͘ϬϮ΁

΀Ϭ͘Ϭϯ΁

΀Ϭ͘Ϭϰ΁

Ϭ͘ϯϵ

Ϭ͘ϲϮ

Ϭ͘Ϭϵ

ϭ͘ϭϬ

΀Ϭ͘Ϭϵ΁

΀Ϭ͘Ϭϵ΁

΀Ϭ͘Ϭϳ΁

΀Ϭ͘ϮϬ΁

Ϭ͘Ϯϵ

Ϭ͘ϱϵ

Ϭ͘ϭϬ

Ϭ͘ϵϳ

΀Ϭ͘ϬϮ΁

΀Ϭ͘ϬϮ΁

΀Ϭ͘ϬϮ΁

΀Ϭ͘Ϭϱ΁

Ϭ͘ϯϬ

Ϭ͘ϲϬ

Ϭ͘ϭϬ

ϭ͘ϬϬ

΀Ϭ͘ϬϬ΁

΀Ϭ͘ϬϬ΁

΀Ϭ͘ϬϬ΁

΀Ϭ͘ϬϬ΁

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΀Ϭ͘Ϭϰ΁

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΀Ϭ͘Ϭϴ΁

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΀Ϭ͘ϮϮ΁

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Ϭ͘Ϭϱ

ϭ͘Ϭϳ

΀Ϭ͘Ϭϵ΁

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΀Ϭ͘ϭϵ΁

΀Ϭ͘ϭϳ΁

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΀Ϭ͘ϱϮ΁

Ϭ͘Ϯϵ

Ϭ͘ϱϳ

Ϭ͘ϭϬ

Ϭ͘ϵϳ

΀Ϭ͘Ϭϯ΁

΀Ϭ͘Ϭϲ΁

΀Ϭ͘Ϭϭ΁

΀Ϭ͘Ϭϵ΁

&'!

&'$

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&'(

 

 

 

 

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&'%(

 

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 



&'

&'$

&'&!

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 



 



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&'&

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 



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

0 6 *   /      .  /   .  ' */ .      / .   .  /   .    '    1   / "  
   3 7 /   / .  .   .  /   "   .  .   .  "1      . '      . /        -   7
/  ' */ !/     / "    # 7/ /  /  . /  .  /  " /   '

36

Table 4: Output Elas ci es, Input Price Varia on and Sample Selec onƐƚŝŵĂƚĞƐǁŝƚŚŽƵƚŽƌƌĞĐƚŝŶŐĨŽƌ ƐƚŝŵĂƚĞƐŽŶĂĂůĂŶĐĞĚWĂŶĞů/ŶƉƵƚWƌŝĐĞsĂƌŝĂƚŝŽŶ
ŽĨ^ŝŶŐůĞͲWƌŽĚƵĐƚ&ŝƌŵƐ>ĂďŽƌ DĂƚĞƌŝĂůƐ ĂƉŝƚĂů
>ĂďŽƌ DĂƚĞƌŝĂůƐ ĂƉŝƚĂů
^ĞĐƚŽƌ
;ϭͿ
;ϮͿ
;ϯͿ
;ϰͿ
;ϱͿ
;ϲͿ
ϭϱ&ŽŽĚƉƌŽĚƵĐƚƐĂŶĚďĞǀĞƌĂŐĞƐ
ϭ͘ϮϮ
Ϭ͘ϱϬ
Ϭ͘ϯϲ
Ϭ͘ϯϲ
Ϭ͘ϲϭ
Ϭ͘ϭϬ
ϭϳdĞǆƚŝůĞƐ
ϯ͘ϭϳ
ͲϬ͘Ϯϰ
ͲϮ͘ϱϬ
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ϭϴtĞĂƌŝŶŐĂƉƉĂƌĞů
Ϭ͘ϳϰ
Ϭ͘ϭϰ
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Ϭ͘Ϯϳ
Ϭ͘ϲϯ
Ϭ͘ϭϮ
ϮϭWĂƉĞƌĂŶĚƉĂƉĞƌƉƌŽĚƵĐƚƐ
Ϭ͘ϬϬ
ϭ͘ϯϬ
ϭ͘ϭϵ
Ϭ͘ϯϭ
Ϭ͘ϱϳ
Ϭ͘ϭϬ
ϮϯŽŬĞ͕ƌĞĨŝŶĞĚƉĞƚƌŽůĞƵŵƉƌŽĚƵĐƚƐ
Ϭ͘ϱϯ
Ϭ͘ϭϬ
ͲϬ͘Ϭϰ
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ϮϰŚĞŵŝĐĂůƐ
Ϭ͘ϬϬ
ϭ͘ϯϲ
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ϮϱZƵďďĞƌĂŶĚWůĂƐƚŝĐ
Ͳϭ͘ϭϮ
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ϮϲEŽŶͲŵĞƚĂůůŝĐŵŝŶĞƌĂůƉƌŽĚƵĐƚƐ
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ϮϳĂƐŝĐDĞƚĂů
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Ϯϴ&ĂďƌŝĐĂƚĞĚŵĞƚĂůƉƌŽĚƵĐƚƐ
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ϯϭůĞĐƚƌŝĐĂůŵĂĐŚŝŶĞƌǇĂŶĚĂƉƉĂƌĂƚƵƐ
ͲϬ͘ϳϭ
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ͲϬ͘ϳϬ
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ϯϮZĂĚŝŽ͕dsĂŶĚĐŽŵŵƵŶŝĐĂƚŝŽŶ
Ͳϯ͘Ϭϭ
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ϯϰDŽƚŽƌǀĞŚŝĐůĞƐ͕ƚƌĂŝůĞƌƐ
Ϭ͘ϰϯ
Ϭ͘ϰϳ
Ϭ͘Ϯϱ
Ϭ͘Ϯϳ
Ϭ͘ϲϮ
Ϭ͘ϭϮ
EŽƚĞƐ͗dŚĞƚĂďůĞƌĞƉŽƌƚƐƚŚĞŽƵƚƉƵƚĞůĂƐƚŝĐŝƚŝĞƐĨƌŽŵƉƌŽĚƵĐƚŝŽŶĨƵŶĐƚŝŽŶĞƐƚŝŵĂƚŝŽŶƐƚŚĂƚĚŽŶŽƚĂĐĐŽƵŶƚĨŽƌŝŶƉƵƚƉƌŝĐĞǀĂƌŝĂƚŝŽŶŽƌƐĂŵƉůĞƐĞůĞĐƚŝŽŶ͘dŚĞĨŝƌƐƚƉĂŶĞůƌĞƉŽƌƚƐƚŚĞĞůĂƐƚŝĐŝƚŝĞƐĨƌŽŵƚŚĞĞƐƚŝŵĂƚŝŽŶƚŚĂƚĚŽĞƐŶŽƚĂĐĐŽƵŶƚĨŽƌŝŶƉƵƚƉƌŝĐĞǀĂƌŝĂƚŝŽŶ͘dŚĞƐĞĐŽŶĚƉĂŶĞůƌĞƉŽƌƚƐƚŚĞŽƵƚƉƵƚĞůĂƐƚŝĐŝƚŝĞƐĨƌŽŵƚŚĞĞƐƚŝŵĂƚŝŽŶƚŚĂƚƵƐĞƐŽŶůǇĂďĂůĂŶĐĞĚƐĞƚŽĨƐŝŶŐůĞͲƉƌŽĚƵĐƚĨŝƌŵƐĨƌŽŵϭϵϴϵͲϮϬϬϯ͘dŽƐĂǀĞƐƉĂĐĞ͕ƚŚĞƐƚĂŶĚĂƌĚĚĞǀŝĂƚŝŽŶƐŽĨƚŚĞĞůĂƐƚŝĐŝƚŝĞƐĂƌĞŶŽƚƌĞƉŽƌƚĞĚ͘37

Table 5: Markups, by SectorDĂƌŬƵƉƐ
^ĞĐƚŽƌ
DĞĂŶ DĞĚŝĂŶ
ϭϱ&ŽŽĚƉƌŽĚƵĐƚƐĂŶĚďĞǀĞƌĂŐĞƐ
Ϯ͘ϬϮ
Ϭ͘ϵϳ
ϭϳdĞǆƚŝůĞƐ
ϭ͘ϰϱ
ϭ͘ϭϭ
ϭϴtĞĂƌŝŶŐĂƉƉĂƌĞů
ϭ͘ϭϱ
ϭ͘ϭϬ
ϮϭWĂƉĞƌĂŶĚƉĂƉĞƌƉƌŽĚƵĐƚƐ
ϭ͘Ϭϱ
Ϭ͘ϵϴ
ϮϯŽŬĞ͕ƌĞĨŝŶĞĚƉĞƚƌŽůĞƵŵƉƌŽĚƵĐƚƐ
ϰ͘ϭϳ
Ϭ͘ϵϯ
ϮϰŚĞŵŝĐĂůƐ
Ϯ͘ϭϭ
ϭ͘ϬϬ
ϮϱZƵďďĞƌĂŶĚWůĂƐƚŝĐ
ϭ͘ϵϲ
ϭ͘Ϯϴ
ϮϲEŽŶͲŵĞƚĂůůŝĐŵŝŶĞƌĂůƉƌŽĚƵĐƚƐ
ϰ͘ϰϬ
Ϯ͘Ϭϱ
ϮϳĂƐŝĐDĞƚĂů
ϭ͘ϴϲ
Ϭ͘ϵϭ
Ϯϴ&ĂďƌŝĐĂƚĞĚŵĞƚĂůƉƌŽĚƵĐƚƐ
ϯ͘ϯϱ
ϭ͘Ϭϳ
ϮϵDĂĐŚŝŶĞƌǇĂŶĚĞƋƵŝƉŵĞŶƚ
Ϯ͘ϯϰ
ϭ͘Ϯϳ
ϯϭůĞĐƚƌŝĐĂůŵĂĐŚŝŶĞƌǇ
Ϯ͘ϰϮ
ϭ͘Ϭϰ
ϯϮZĂĚŝŽ͕dsĂŶĚĐŽŵŵƵŶŝĐĂƚŝŽŶ
ϭ͘ϳϴ
ϭ͘ϯϭ
ϯϰDŽƚŽƌǀĞŚŝĐůĞƐ
Ϯ͘ϭϲ
ϭ͘ϴϭ
ǀĞƌĂŐĞϮ͘ϭϯϭ͘ϭϬEŽƚĞƐ͗dĂďůĞĚŝƐƉůĂǇƐƚŚĞŵĞĂŶĂŶĚŵĞĚŝĂŶŵĂƌŬƵƉďǇƐĞĐƚŽƌĨŽƌƚŚĞƐĂŵƉůĞϭϵϴϵͲϮϬϬϯ͘dŚĞƚĂďůĞƚƌŝŵƐŽďƐĞƌǀĂƚŝŽŶƐǁŝƚŚŵĂƌŬƵƉƐƚŚĂƚĂƌĞĂďŽǀĞĂŶĚďĞůŽǁƚŚĞϯƌĚĂŶĚϵϳƚŚƉĞƌĐĞŶƚŝůĞƐǁŝƚŚŝŶĞĂĐŚƐĞĐƚŽƌ͘
Table 6: Pairwise Correla on Matrix between Prices, Markups, Marginal Costs and Produc vityWƌŝĐĞƐ
DĂƌŬƵƉƐ
DĂƌŐŝŶĂůŽƐƚƐ WƌŽĚƵĐƚŝǀŝƚǇ
WƌŝĐĞƐ
ϭ͘ϬϬDĂƌŬƵƉƐϬ͘ϭϲϭ͘ϬϬDĂƌŐŝŶĂůŽƐƚƐ
Ϭ͘ϵϰ
ͲϬ͘ϭϵ
ϭ͘ϬϬ
WƌŽĚƵĐƚŝǀŝƚǇ
ͲϬ͘ϯϵ
Ϭ͘Ϭϰ
ͲϬ͘ϰϬ
ϭ͘ϬϬ
EŽƚĞƐ͗dĂďůĞƌĞƉŽƌƚƐƚŚĞƉĂŝƌǁŝƐĞ ĐŽƌƌĞůĂƚŝŽŶŵĂƚƌŝǆĂĐƌŽƐƐĨŽƵƌƉĞƌĨŽƌŵĂŶĐĞǀĂƌŝĂďůĞƐ͗ƉƌŝĐĞƐ͕ŵĂƌŬƵƉƐ͕ŵĂƌŐŝŶĂůĐŽƐƚƐĂŶĚƉƌŽĚƵĐƚŝǀŝƚǇ͘ůůǀĂƌŝĂďůĞƐĂƌĞĞǆƉƌĞƐƐĞĚŝŶůŽŐƐ͘WƌŝĐĞƐ͕ŵĂƌŬƵƉƐĂŶĚŵĂƌŐŝŶĂůĐŽƐƚƐǀĂƌǇĂƚƚŚĞĨŝƌŵͲƉƌŽĚƵĐƚůĞǀĞůǁŚŝůĞƉƌŽĚƵĐƚŝǀŝƚǇǀĂƌŝĞƐĂƚƚŚĞĨŝƌŵůĞǀĞů͘dŚĞƚĂďůĞƚƌŝŵƐŽďƐĞƌǀĂƚŝŽŶƐǁŝƚŚŵĂƌŬƵƉƐƚŚĂƚĂƌĞĂďŽǀĞĂŶĚďĞůŽǁƚŚĞϯƌĚĂŶĚϵϳƚŚƉĞƌĐĞŶƚŝůĞƐǁŝƚŚŝŶĞĂĐŚƐĞĐƚŽƌ͘38

Table 7: Pass-Through of Costs to Prices>ŽŐWƌŝĐĞĨũƚ
;ϭͿϬ͘ϮϵϯΎΎΎ
Ϭ͘Ϭϯϳ>ŽŐDĂƌŐŝŶĂůŽƐƚĨũƚ

;ϮͿϬ͘ϲϬϯΎΎΎ
Ϭ͘ϬϱϮϮϬ͕ϲϯϭ
ϮϬ͕ϲϯϭ
ǇĞƐǇĞƐEŽƚĞƐ͗dŚĞĚĞƉĞŶĚĞŶƚǀĂƌŝĂďůĞŝƐ;ůŽŐͿƉƌŝĐĞ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĞǆĐůƵĚĞŽƵƚůŝĞƌƐŝŶƚŚĞƚŽƉĂŶĚďŽƚƚŽŵϯƌĚƉĞƌĐĞŶƚŽĨƚŚĞŵĂƌŬƵƉĚŝƐƚƌŝďƵƚŝŽŶ͘ůůƌĞŐƌĞƐƐŝŽŶƐŝŶĐůƵĚĞĨŝƌŵͲƉƌŽĚƵĐƚĨŝǆĞĚĞĨĨĞĐƚƐ͘ŽůƵŵŶϭŝƐĂK>^ƌĞŐƌĞƐƐŝŽŶŽŶůŽŐŵĂƌŐŝŶĂůĐŽƐƚƐ͘ŽůƵŵŶϮŝŶƐƚƌƵŵĞŶƚƐŵĂƌŐŝŶĂůĐŽƐƚƐǁŝƚŚĨŝƌŵͲůĞǀĞůƉƌŽĚƵĐƚŝǀŝƚǇĂŶĚŝŶƉƵƚƚĂƌŝĨĨƐ͘dŚĞĐŽĞĨĨŝĐŝĞŶƚƐŽŶƉƌŽĚƵĐƚŝǀŝƚǇĂŶĚŝŶƉƵƚƚĂƌŝĨĨƐŝŶƚŚĞĨŝƌƐƚƐƚĂŐĞĂƌĞͲϬ͘ϳϬĂŶĚϬ͘ϱϮ͕ƌĞƐƉĞĐƚŝǀĞůǇ͕ĂŶĚĂƌĞďŽƚŚƐƚĂƚŝƐƚŝĐĂůůǇƐŝŐŶŝĨŝĐĂŶƚĂƚƚŚĞϭͲƉĞƌĐĞŶƚůĞǀĞů͘dŚĞƐĞĂƌĞƚŚĞĞǆƉĞĐƚĞĚƐŝŐŶƐĂŶĚƚŚĞũŽŝŶƚ&ͲƐƚĂƚŝƐƚŝĐŝƐϭϯϳ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĂƌĞƌƵŶĨƌŽŵƵƐŝŶŐĚĂƚĂĨƌŽŵϭϵϴϵͲϭϵϵϳĂŶĚƚŚĞƐƚĂŶĚĂƌĚĞƌƌŽƌƐĂƌĞĐůƵƐƚĞƌĞĚĂƚƚŚĞŝŶĚƵƐƚƌǇůĞǀĞů͘^ŝŐŶŝĨŝĐĂŶĐĞ͗ΎϭϬƉĞƌĐĞŶƚ͕ΎΎϱƉĞƌĐĞŶƚ͕ΎΎΎϭƉĞƌĐĞŶƚ͘KďƐĞƌǀĂƚŝŽŶƐ
&ŝƌŵͲWƌŽĚƵĐƚ&Ɛ

39

Table 8: Prices and Output Tariﬀs, Annual Regressions>ŽŐWƌŝĐĞƐĨũƚ

>ŽŐWƌŝĐĞƐĨũƚ

;ϭͿ

;ϮͿ

KƵƚƉƵƚdĂƌŝĨĨŝƚ

Ϭ͘ϬϵϰΎϬ͘ϬϱϲϬ͘ϭϮϴΎΎΎ
Ϭ͘Ϭϰϯ

ZͲƐƋƵĂƌĞĚ

Ϭ͘ϬϬ

Ϭ͘ϬϮ

KďƐĞƌǀĂƚŝŽŶƐ

ϮϬ͕ϲϯϭ

ϮϬ͕ϲϯϭ

&ŝƌŵͲWƌŽĚƵĐƚ&Ɛ

ǇĞƐ

ǇĞƐ

zĞĂƌ&ƐǇĞƐŶŽ^ĞĐƚŽƌͲzĞĂƌ&Ɛ

ŶŽ

ǇĞƐ

Ͳϱ͘ϵΎ
ϯ͘ϱ

Ͳϴ͘ϬΎΎΎ
Ϯ͘ϳKǀĞƌĂůů/ŵƉĂĐƚŽĨdƌĂĚĞ>ŝďĞƌĂůŝǌĂƚŝŽŶ

EŽƚĞƐ͗dŚĞĚĞƉĞŶĚĞŶƚǀĂƌŝĂďůĞŝƐĂĨŝƌŵͲƉƌŽĚƵĐƚΖƐ;ůŽŐͿƉƌŝĐĞ͘dŚĞůĞĨƚĐŽůƵŵŶŝŶĐůƵĚĞƐǇĞĂƌĨŝǆĞĚĞĨĨĞĐƚƐĂŶĚƚŚĞƌŝŐŚƚĐŽůƵŵŶŝŶĐůƵĚĞƐƐĞĐƚŽƌͲǇĞĂƌĨŝǆĞĚĞĨĨĞĐƚƐ͖ĂůůƐƉĞĐŝĨŝĐĂƚŝŽŶƐŚĂǀĞĨŝƌŵͲƉƌŽĚƵĐƚĨŝǆĞĚĞĨĨĞĐƚƐ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĞǆĐůƵĚĞŽƵƚůŝĞƌƐŝŶƚŚĞƚŽƉĂŶĚďŽƚƚŽŵϯƌĚƉĞƌĐĞŶƚŽĨƚŚĞŵĂƌŬƵƉĚŝƐƚƌŝďƵƚŝŽŶ͘ůůƌĞŐƌĞƐƐŝŽŶƐŝŶĐůƵĚĞĨŝƌŵͲƉƌŽĚƵĐƚĨŝǆĞĚĞĨĨĞĐƚƐĂŶĚĂƌĞƌƵŶĨƌŽŵϭϵϴϵͲϭϵϵϳ͘^ƚĂŶĚĂƌĚĞƌƌŽƌƐĂƌĞĐůƵƐƚĞƌĞĚĂƚƚŚĞŝŶĚƵƐƚƌǇůĞǀĞů͘dŚĞĨŝŶĂůƌŽǁƵƐĞƐƚŚĞĂǀĞƌĂŐĞϲϮйĚĞĐůŝŶĞŝŶŽƵƚƉƵƚƚĂƌŝĨĨƐĨƌŽŵϭϵϴϵͲϭϵϵϳƚŽĐŽŵƉƵƚĞƚŚĞŵĞĂŶĂŶĚƐƚĂŶĚĂƌĚĞƌƌŽƌŽĨƚŚĞŝŵƉĂĐƚŽĨƚƌĂĚĞůŝďĞƌĂůŝǌĂƚŝŽŶŽŶƉƌŝĐĞƐ͘dŚĂƚŝƐ͕ĨŽƌĞĂĐŚĐŽůƵŵŶƚŚĞŵĞĂŶŝŵƉĂĐƚŝƐĞƋƵĂůƚŽƚŚĞͲϬ͘ϲϮΎϭϬϬΎ΂ĐŽĞĨĨŝĐŝĞŶƚŽŶŽƵƚƉƵƚƚĂƌŝĨĨƐ΃͘^ŝŐŶŝĨŝĐĂŶĐĞ͗ΎϭϬƉĞƌĐĞŶƚ͕ΎΎϱƉĞƌĐĞŶƚ͕ΎΎΎϭƉĞƌĐĞŶƚ͘40

Table 9: Prices and Tariﬀs, Annual Regressions>ŽŐDĂƌŐŝŶĂůŽƐƚĨũƚ
;ϮͿ

>ŽŐWƌŝĐĞƐĨũƚ
;ϭͿ

>ŽŐDĂƌŬƵƉĨũƚ
;ϯͿ

>ŽŐWƌŝĐĞƐĨũƚ
;ϰͿ

>ŽŐDĂƌŐŝŶĂůŽƐƚĨũƚ
;ϱͿ

>ŽŐDĂƌŬƵƉĨũƚ
;ϲͿKƵƚƉƵƚdĂƌŝĨĨŝƚ

Ϭ͘ϭϭϴΎΎ
Ϭ͘Ϭϰϴ

Ϭ͘ϬϱϬ
Ϭ͘Ϭϵϵ

Ϭ͘Ϭϲϴ
Ϭ͘Ϭϳϯ

Ϭ͘ϭϯϲΎΎ
Ϭ͘Ϭϱϯ

Ϭ͘Ϭϴϱ
Ϭ͘ϭϭϱ

Ϭ͘Ϭϱϭ
Ϭ͘ϬϴϮ

/ŶƉƵƚdĂƌŝĨĨŝƚ

Ϭ͘ϯϭϯ
Ϭ͘ϰϬϴ

ϭ͘Ϭϱϰ
Ϭ͘ϳϱϭ

ͲϬ͘ϳϰϭ
Ϭ͘ϰϵϯ

Ϭ͘ϯϰϲ
Ϭ͘ϰϰϵ

ϭ͘ϰϰϰ
Ϭ͘ϴϴϴ

Ͳϭ͘ϬϵϴΎΎϬ͘ϱϰϵZͲƐƋƵĂƌĞĚ
KďƐĞƌǀĂƚŝŽŶƐ
&ŝƌŵͲWƌŽĚƵĐƚ&Ɛ^ĞĐƚŽƌͲzĞĂƌ&ƐtĞŝŐŚƚƐ;ƐĞĞĨŽŽƚŶŽƚĞͿϬ͘ϬϮϮϬ͕ϲϯϭ
ǇĞƐ
ǇĞƐ
ŶŽ

Ϭ͘Ϭϯ
ϮϬ͕ϲϯϭ
ǇĞƐ
ǇĞƐ
ŶŽ

Ϭ͘Ϭϯ
ϮϬ͕ϲϯϭ
ǇĞƐ
ǇĞƐ
ŶŽ

Ϭ͘ϬϮ
ϮϬ͕ϲϯϭ
ǇĞƐ
ǇĞƐ
ǇĞƐ

Ϭ͘Ϭϯ
ϮϬ͕ϲϯϭ
ǇĞƐ
ǇĞƐ
ǇĞƐ

Ϭ͘ϬϮ
ϮϬ͕ϲϯϭǇĞƐǇĞƐǇĞƐͲϭϱ͘ϬΎ
ϴ͘ϱ

ͲϮϴ͘ϳ
ϭϵ͘ϰ

ϭϯ͘ϳ
ϭϯ͘ϵ

Ͳϭϲ͘ϴΎϵ͘ϭͲϰϬ͘ϯΎϮϮ͘ϭϮϯ͘ϰKǀĞƌĂůů/ŵƉĂĐƚŽĨdƌĂĚĞ>ŝďĞƌĂůŝǌĂƚŝŽŶ

ϭϱ͘ϮEŽƚĞƐ͗dŚĞĚĞƉĞŶĚĞŶƚǀĂƌŝĂďůĞŝƐŶŽƚĞĚŝŶƚŚĞĐŽůƵŵŶƐ͘tŝƚŚŝŶĞĂĐŚƉĂŶĞů͕ƚŚĞƐƵŵŽĨƚŚĞĐŽĞĨĨŝĐŝĞŶƚƐĨƌŽŵƚŚĞŵĂƌŬƵƉĂŶĚŵĂƌŐŝŶĂůĐŽƐƚƐƌĞŐƌĞƐƐŝŽŶĞƋƵĂůƐƚŚĞŝƌƌĞƐƉĞĐƚŝǀĞĐŽĞĨĨŝĐŝĞŶƚŝŶƚŚĞƉƌŝĐĞƌĞŐƌĞƐƐŝŽŶ͘dŚĞůĞĨƚƉĂŶĞůƌĞƉŽƌƚƐƚŚĞƵŶǁĞŝŐŚƚĞĚ ƌĞŐƌĞƐƐŝŽŶƐ͘dŚĞƌŝŐŚƚƉĂŶĞůƵƐĞƐƚŚĞŶƵŵďĞƌŽĨŽďƐĞƌǀĂƚŝŽŶƐĨƌŽŵƚŚĞƉƌŽĚƵĐƚŝŽŶĨƵŶĐƚŝŽŶĞƐƚŝŵĂƚŝŽŶ;ƐĞĞĐŽůƵŵŶϭŽĨdĂďůĞϯͿĂƐǁĞŝŐŚƚƐĨŽƌĞĂĐŚƐĞĐƚŽƌ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĞǆĐůƵĚĞŽƵƚůŝĞƌƐŝŶƚŚĞƚŽƉĂŶĚďŽƚƚŽŵϯƌĚƉĞƌĐĞŶƚŽĨƚŚĞŵĂƌŬƵƉĚŝƐƚƌŝďƵƚŝŽŶ͕ĂŶĚŝŶĐůƵĚĞĨŝƌŵͲƉƌŽĚƵĐƚĨŝǆĞĚĞĨĨĞĐƚƐĂŶĚƐĞĐƚŽƌͲǇĞĂƌĨŝǆĞĚĞĨĨĞĐƚƐ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĂƌĞƌƵŶĨƌŽŵϭϵϴϵͲϭϵϵϳĂŶĚƐƚĂŶĚĂƌĚĞƌƌŽƌƐĂƌĞĐůƵƐƚĞƌĞĚĂƚƚŚĞŝŶĚƵƐƚƌǇůĞǀĞů͘dŚĞĨŝŶĂůƌŽǁƵƐĞƐƚŚĞĂǀĞƌĂŐĞϲϮйĂŶĚϮϰйĚĞĐůŝŶĞƐŝŶŽƵƚƉƵƚĂŶĚŝŶƉƵƚƚĂƌŝĨĨƐĨƌŽŵϭϵϴϵͲϭϵϵϳ͕ƌĞƐƉĞĐƚŝǀĞůǇ͕ƚŽĐŽŵƉƵƚĞƚŚĞŵĞĂŶĂŶĚƐƚĂŶĚĂƌĚĞƌƌŽƌŽĨƚŚĞŝŵƉĂĐƚŽĨƚƌĂĚĞůŝďĞƌĂůŝǌĂƚŝŽŶŽŶĞĂĐŚƉĞƌĨŽƌŵĂŶĐĞŵĞĂƐƵƌĞ͘dŚĂƚŝƐ͕ĨŽƌĞĂĐŚĐŽůƵŵŶƚŚĞŵĞĂŶŝŵƉĂĐƚŝƐĞƋƵĂůƚŽƚŚĞͲϬ͘ϲϮΎϭϬϬΎ΂ĐŽĞĨĨŝĐŝĞŶƚŽŶŽƵƚƉƵƚƚĂƌŝĨĨ΃нͲϬ͘ϮϰΎϭϬϬΎ΂ĐŽĞĨĨŝĐŝĞŶƚŽŶŝŶƉƵƚƚĂƌŝĨĨ΃͘^ŝŐŶŝĨŝĐĂŶĐĞ͗ΎϭϬƉĞƌĐĞŶƚ͕ΎΎϱƉĞƌĐĞŶƚ͕ΎΎΎϭƉĞƌĐĞŶƚ͘

Table 10: Pro-Compeve Eﬀects of Output Tariﬀs>ŽŐDĂƌŬƵƉĨũƚ
KƵƚƉƵƚdĂƌŝĨĨŝƚ

>ŽŐDĂƌŬƵƉĨũƚ

;ϭͿ

;ϮͿ

;ϯͿ

;ϰͿ

;ϱͿ

;ϲͿ

Ϭ͘ϭϭϵΎΎΎ
Ϭ͘ϬϮϵϬ͘ϭϭϴΎΎΎ
Ϭ͘ϬϯϰϬ͘ϭϬϵΎΎΎ
Ϭ͘ϬϯϭϬ͘ϭϯϬΎΎΎ
Ϭ͘ϬϮϵϬ͘ϭϮϵΎΎΎ
Ϭ͘ϬϯϳϬ͘ϭϭϴΎΎΎ
Ϭ͘ϬϯϮ/ŶƉƵƚdĂƌŝĨĨŝƚ

Ϭ͘Ϭϯϰ
Ϭ͘Ϯϳϯ

KƵƚƉƵƚdĂƌŝĨĨŝƚ ǆdŽƉĨƉ

Ϭ͘ϬϮϯ
Ϭ͘Ϯϵϲ
Ϭ͘ϯϭϳΎΎΎ
Ϭ͘ϬϴϬϬ͘ϯϬϵΎΎΎ
Ϭ͘ϬϳϮ

ZͲƐƋƵĂƌĞĚ

Ϭ͘ϱϵϰ

Ϭ͘ϱϵϰ

Ϭ͘ϱϵϳ

Ϭ͘ϲϮϮ

Ϭ͘ϲϮϮ

Ϭ͘ϲϮϰ

KďƐĞƌǀĂƚŝŽŶƐ

ϮϬ͕ϲϯϭϮϬ͕ϲϯϭϮϬ͕ϲϯϭϮϬ͕ϲϯϭϮϬ͕ϲϯϭϮϬ͕ϲϯϭDĂƌŐŝŶĂůĐŽƐƚĐŽŶƚƌŽůƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

&ŝƌŵͲWƌŽĚƵĐƚ&Ɛ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

^ĞĐƚŽƌͲzĞĂƌ&Ɛ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

ǇĞƐ

tĞŝŐŚƚƐ;ƐĞĞĨŽŽƚŶŽƚĞͿ
ŶŽ
ŶŽ
ŶŽ
ǇĞƐ
ǇĞƐ
ǇĞƐ
EŽƚĞƐ͗dŚĞĚĞƉĞŶĚĞŶƚǀĂƌŝĂďůĞŝƐ;ůŽŐͿŵĂƌŬƵƉ͘dŚĞůĞĨƚƉĂŶĞůƌĞƉŽƌƚƐƚŚĞƵŶǁĞŝŐŚƚĞĚ ƌĞŐƌĞƐƐŝŽŶƐ͘dŚĞƌŝŐŚƚƉĂŶĞůƵƐĞƐƚŚĞŶƵŵďĞƌŽĨŽďƐĞƌǀĂƚŝŽŶƐĨƌŽŵƚŚĞƉƌŽĚƵĐƚŝŽŶĨƵŶĐƚŝŽŶĞƐƚŝŵĂƚŝŽŶ;ƐĞĞĐŽůƵŵŶϭŽĨdĂďůĞϯͿĂƐǁĞŝŐŚƚƐĨŽƌĞĂĐŚƐĞĐƚŽƌ͘ŽůƵŵŶƐϯĂŶĚϲŝŶƚĞƌĂĐƚŽƵƚƉƵƚƚĂƌŝĨĨƐĂŶĚƚŚĞƚŚŝƌĚͲŽƌĚĞƌŵĂƌŐŝŶĂůĐŽƐƚƉŽůǇŶŽŵŝĂůǁŝƚŚĂŶŝŶĚŝĐĂƚŽƌŝĨĂĨŝƌŵͲƉƌŽĚƵĐƚŽďƐĞƌǀĂƚŝŽŶǁĂƐŝŶƚŚĞƚŽƉϭϬƉĞƌĐĞŶƚŽĨŝƚƐƐĞĐƚŽƌΖƐŵĂƌŬƵƉĚŝƐƚƌŝďƵƚŝŽŶǁŚĞŶŝƚĨŝƌƐƚĂƉƉĞĂƌƐŝŶƚŚĞƐĂŵƉůĞ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĞǆĐůƵĚĞŽƵƚůŝĞƌƐŝŶƚŚĞƚŽƉĂŶĚďŽƚƚŽŵϯƌĚƉĞƌĐĞŶƚŽĨƚŚĞŵĂƌŬƵƉĚŝƐƚƌŝďƵƚŝŽŶ͘ůůƌĞŐƌĞƐƐŝŽŶƐŝŶĐůƵĚĞĨŝƌŵͲƉƌŽĚƵĐƚĨŝǆĞĚĞĨĨĞĐƚƐ͕ƐĞĐƚŽƌͲǇĞĂƌĨŝǆĞĚĞĨĨĞĐƚƐĂŶĚ ĂƚŚŝƌĚͲŽƌĚĞƌƉŽůǇŶŽŵŝĂůŽĨŵĂƌŐŝŶĂůĐŽƐƚƐ;ƚŚĞƐĞĐŽĞĨĨŝĐŝĞŶƚƐĂƌĞƐƵƉƉƌĞƐƐĞĚĂŶĚĂǀĂŝůĂďůĞƵƉŽŶƌĞƋƵĞƐƚͿ͘dŚĞƌĞŐƌĞƐƐŝŽŶƐĂƌĞƌƵŶĨƌŽŵϭϵϴϵͲϭϵϵϳĂŶĚƐƚĂŶĚĂƌĚĞƌƌŽƌƐĂƌĞĐůƵƐƚĞƌĞĚĂƚƚŚĞŝŶĚƵƐƚƌǇůĞǀĞů͘^ŝŐŶŝĨŝĐĂŶĐĞ͗ΎϭϬƉĞƌĐĞŶƚ͕ΎΎϱƉĞƌĐĞŶƚ͕ΎΎΎϭƉĞƌĐĞŶƚ͘

41

Table 11: Markups and Product ScopeŚĂŶŐĞŝŶ>ŽŐĚĚƵŵŵǇ
WƌŽĚƵĐƚƐ
;ϭͿ
;ϮͿ
Ϭ͘ϬϱϱΎΎΎ
Ϭ͘ϬϰϱΎΎΎ
Ϭ͘ϬϬϲ
Ϭ͘ϬϬϰ

ŚĂŶŐĞŝŶ>ŽŐǀĞƌĂŐĞDĂƌŬƵƉ

Ĩƚ&ŝƌŵ&ƐǇĞƐǇĞƐzĞĂƌ&ƐǇĞƐǇĞƐZͲƐƋƵĂƌĞĚϬ͘ϯϬϬ͘ϮϯKďƐĞƌĂƚŝŽŶƐ
ϵ͕ϯϱϯ
ϵ͕ϯϱϯ
EŽƚĞƐ͗dŚĞƌŝŐŚƚͲŚĂŶĚͲƐŝĚĞǀĂƌŝĂďůĞŝƐƚŚĞĐŚĂŶŐĞďĞƚǁĞĞŶƚͲϭ ĂŶĚƚ ŽĨĂ
ĨŝƌŵΖƐĂǀĞƌĂŐĞ;ƵŶǁĞŝŐŚƚĞĚͿůŽŐŵĂƌŬƵƉ͘dŚĞĂǀĞƌĂŐĞŝƐĐŽŶƐƚƌƵĐƚĞĚďǇĨŝƌƐƚĚƌŽƉƉŝŶŐŽƵƚůŝĞƌŵĂƌŬƵƉƐďĞůŽǁĂŶĚĂďŽǀĞƚŚĞϯƌĚĂŶĚϵϳƚŚƉĞƌĐĞŶƚŝůĞ͕ƌĞƐƉĞĐƚŝǀĞůǇ͕ĂŶĚƚŚĞŶĐŽŵƉƵƚŝŶŐƚŚĞ;ƵŶǁĞŝŐŚƚĞĚͿĂǀĞƌĂŐĞŵĂƌŬƵƉĂĐƌŽƐƐƉƌŽĚƵĐƚƐĨŽƌĞĂĐŚĨŝƌŵĂŶĚƚŚĞŶƚĂŬŝŶŐĨŝƌƐƚĚŝĨĨĞƌĞŶĐĞƐ͘dŚĞĚĞƉĞŶĚĞŶƚǀĂƌŝĂďůĞŝŶĐŽůƵŵŶϭŝƐĂŶŝŶĚŝĐĂƚŽƌŝĨƚŚĞĨŝƌŵĂĚĚƐĂƉƌŽĚƵĐƚďĞƚǁĞĞŶƚͲϭ ĂŶĚƚ͘dŚĞĚĞƉĞŶĚĞŶƚǀĂƌŝĂďůĞŝŶĐŽůƵŵŶϮŝƐƚŚĞĐŚĂŶŐĞŝŶƚŚĞ
ĨŝƌŵΖƐůŽŐŶƵŵďĞƌŽĨƉƌŽĚƵĐƚƐ͘ůůƌĞŐƌĞƐƐŝŽŶƐŝŶĐůƵĚĞĨŝƌŵĂŶĚǇĞĂƌĨŝǆĞĚĞĨĨĞĐƚƐ͘^ŝŐŶŝĨŝĐĂŶĐĞ͗ΎϭϬƉĞƌĐĞŶƚ͕ΎΎϱƉĞƌĐĞŶƚ͕ΎΎΎϭƉĞƌĐĞŶƚ͘42

Figure 1: Distribu on of Prices in 1989 and 1997

0.5

Density
1
1.5

2

2.5

Distribution of Prices−.50
Log Prices
1989

.5
1997

Sample only includes firm−product pairs present in 1989 and 1997.
Observations are demeaned by their time average, and outliers above and below the 3rd and 97th percentiles are trimmed.

43

Figure 2: Distribu on of Markups and Marginal Costs in 1989 and 1997

0.5

Density1

1.5

Distribution of Marginal Costs

-2

-1

0
Log Marginal Costs

1

2

Distribution of Markups
1.5

1989

1997

0

.5

Density1

Sample only includes firm-product pairs present in 1989 and 1997.
Observations are demeaned by their time average, and outliers above and below the 3rd and 97th percentiles are trimmed.

-2

-1

0
Log Markups
1989

1
1997

Sample only includes firm-product pairs present in 1989 and 1997.
Observations are demeaned by their time average, and outliers above and below the 3rd and 97th percentiles are trimmed.

442