Building New Plants or Entering by Acquisition? Firm Heterogeneity and Entry Barriers in the U.S. Cement Industry Hector Perez-Saizy October 23, 2014
Abstract I estimate a model of entry for the cement industry that considers two options of expansion into new markets: building a new plant (green…eld entry) or acquiring an incumbent. The model takes into account that there is a transfer of the buyer …rm-level characteristics to the acquired plants, which a¤ects pro…ts from the acquisition. Estimates show that a less-permissive Reagan-Bush administration’s merger policy would decrease the number of acquired plants by 71%, green…eld entry would increase by 9.2% and consumer surplus would decrease by 23.5%. Results suggest that regulators should be particularly concerned about policies that negatively a¤ect the e¢ cient reallocation of assets between incumbents and entrants.
This is a revised version of my job market paper entitled "Building New Plants or Entering by Acquisition? Estimation of an Entry Model for the U.S. Cement Industry." I am grateful to my advisors Jeremy Fox, Ali Hortaçsu, Chad Syverson and Dennis Carlton for guidance and support in my research. I also wish to thank Jason Allen for detailed comments to various versions of the paper, to three referees for very useful comments, and to Victor Aguirregabiria, Gary Becker, Gustaf Bruze, Allan Collard-Wexler, Pedro Gete, Günter Hitsch, Kim Huynh, Ken Judd, Priscilla Man, Miguel Molico, Philipp Schmidt-Dengler, Matt Shum, Matias Tapia, Ben Tomlin, and participants of numerous seminars for interesting conversations about this topic. I am also especially grateful to Glen Keenleyside, who provided excellent editorial assistance. Support for this research at the Chicago RDC from NSF (ITR-0427889) is also gratefully acknowledged. I am also grateful for the …nancial support of the Fulbright Commission, the Fundacion Caja Madrid, the Henry Morgenthau Jr. Memorial Fund and the Margaret G. Reid Memorial Fund. The research in this article was conducted while the author was Special Sworn Status researcher of the U.S. Census Bureau at the Chicago Census Research Data Center. Any opinions and conclusions expressed herein are those of the author and do not necessarily represent the views of the U.S. Census Bureau or the Bank of Canada. All results have been reviewed to ensure that no con…dential information is disclosed. y Bank of Canada, Financial Stability Department, 234 Laurier Avenue West, Ottawa, Ontario, K1A 0G9. Contact email:
[email protected].
1
Introduction
In many industries, …rms can enter into new markets either by building a new plant (green…eld entry) or by acquiring an incumbent facility. Factors such as …rm heterogeneity among entrants and incumbents, barriers to green…eld entry and to entry by acquisition, and the level of competition can in‡uence the entry decision. The mode of entry may have di¤erent e¤ects on an industry. Entry by acquisition may increase overall e¢ ciency as less-e¢ cient incumbents are acquired by more-e¢ cient entrants. Total output can increase without any change in the total number of plants. Conversely, green…eld entry increases competition and total production. This article studies the factors that in‡uence the mode of entry chosen by …rms expanding into new markets. I propose an empirically tractable model that endogenizes the mode of entry in a concentrated industry. The model takes into account that, after an acquisition, there is a transfer of the buyer …rm-level characteristics to the acquired plants, a¤ecting the pro…ts that can be extracted from the acquired assets. I use the estimates of the model to evaluate the e¤ects of a permissive merger policy during the Reagan-Bush administration on the mode of entry and on key variables such as production, consumer surplus, pro…ts and total factor productivity (TFP). The model extends equilibrium entry models estimated by Bresnahan and Reiss (1991) and Berry (1992), among others, by explicitly accounting for the two modes of entry. The model is a static perfect information entry game with three stages. First, potential entrants decide the mode of entry. Second, there is a perfect information acquisition game that determines which incumbents are acquired by which entrants. In the …nal stage, all plants compete à la Cournot. In the primitives of the model, I introduce relevant plant-level characteristics that a¤ect the plants’pro…ts, such as age and capital. I also include variables that characterize the entrant …rms, such as …rm-level TFP and size. When an entrant buys a plant, the plant has a new owner with di¤erent …rm-level characteristics, a¤ecting the pro…ts. Since entrants compete to acquire the incumbents, the acquisition cost is endogenous and depends on the relative e¢ ciency of entrants and incumbents. This transfer of characteristics represents a novel way of using …rm heterogeneity that has not yet been considered in the entry literature. I estimate the model using a database from the U.S. Census of Manufactures (CM) for the cement industry in the period 1963-2002. This industry is particularly interesting given there is signi…cant variation across years of the two modes of entry. Acquisitions of plants, for example, occurred at more than twice the
2
rate of construction of new plants in this period. Second, the high transportation costs restrict the size of the market, which favors empirical analysis. Third, since cement is a homogeneous product, cost heterogeneity by …rms, and thus productivity, are important determinants of competition and …rm expansion. Finally, changes in environmental regulations have created barriers to the construction of new plants, and changes in antitrust regulations have created barriers to plant acquisition. I estimate demand, cost and investment primitives for this industry using a recent estimator for discrete games of complete information from Bajari et al. (2010). This estimator requires the computation of all equilibria and uses an equilibrium selection rule that is estimated with the rest of the primitives of the model. The estimates of the inverse demand function show that green…eld plants have a signi…cant lower demand for cement compared to incumbent plants. This e¤ect is equal to $9.28 per million short tons of cement produced by the plant, and it is economically more important than the e¤ect of competitors’ production. Also, TFP and energy prices have a signi…cant e¤ect on the variable costs of production. In addition, my estimates show that sunk entry costs for green…eld plants increased by 50% after the 1990 Clean Air Act (CAA) Amendments. The estimates are used to measure the e¤ect of the permissive merger policy during the Reagan-Bush administration (1982-1992). I …nd that barriers to entry by acquisition were 63% lower during this period. My simulations show that this policy increased the number of acquired plants from 35.9 to 124.1 and decreased the number of green…eld plants from 27.3 to 24.9. In addition, TFP increased by 3%, production rose from 321 to 374 million short tons, pro…ts increased by 79% and total consumer surplus increased by 30.1%. I also compare the e¤ects of policies that a¤ect entry by acquisition and green…eld entry. I …nd that the impact of barriers to entry by acquisition more negatively a¤ect consumer surplus, production, …rms’ pro…ts and TFP than equivalent barriers to green…eld entry. This result suggests that policies that favor e¢ cient reallocation of assets between incumbents and entrants are particularly relevant for regulators. The mode-of-entry decision by …rms is a relatively old question in economics.1 In recent years, some researchers have used game theory tools to study the strategic decisions of …rms when choosing their mode of entry.2 Also, the increasing availability of manufacturing databases and other …rm-level databases has led to improved empirical analysis of …rm entry in general, and the mode of entry in particular. Caves and Mehra (1986) and Baldwin and Gorecki (1987) use a cross-industries panel to study the mode of entry 1
Beginning with Coase (1937), economists have been interested in understanding …rm expansion and how this expansion is achieved. For instance, Hines (1957) discusses the lower barriers of entry of established …rms with respect to new …rms. 2 See, for example, Gilbert and Newbery (1992), who examine the importance of competition and complementarities in the mode of entry. Other related research is McCardle and Viswanathan (1994) and Jovanovic and Braguinsky (2004).
3
and …nd that entry by acquisition is more likely in industries that are more concentrated or are more pro…table. Maksimovic and Phillips (2001) and Schoar (2002) use plant-level data from the CM to show that TFP increases signi…cantly after manufacturing plants change ownership. These results suggest that …rms that acquire plants are able to increase the productivity of the acquired assets by adding a number of positive characteristics that improve their performance. My model considers a transfer of the buyer …rm-level characteristics to the acquired plants as a way of modelling these observed facts.3 This article is related to research that has extended the basic static entry framework of Bresnahan and Reiss (1991) or Berry (1992) to study other issues. For example, Mazzeo (2002) and Seim (2006) endogenize …rms’product choices upon entry. In the dynamic entry literature, Gowrisankaran (1999) is the …rst article that extends the Ericson and Pakes (1995) framework to consider green…eld entry and acquisitions jointly. Gowrisankaran numerically solves the dynamic model and characterizes the set of equilibria. In a closely related article to mine, Ryan (2012) uses a dynamic model to study green…eld entry into the U.S. cement industry and estimates the increases in sunk entry costs due to the 1990 CAA Amendments. The remainder of this article is organized as follows. In the next section I discuss the data sources I use. Section 3 describes the industry and the patterns of …rm expansion. Section 4 describes the entry model and Section 5 the empirical methodology. Section 6 describes the estimated primitives and Section 7 the e¤ect of policies that favor acquisition. Section 8 concludes.
2
Data
The primary source of information is the CM database, which contains information on every plant’s production activities in the manufacturing sector for every census year. The database includes …rm and plant-level indicators that can be used to identify acquisitions and green…eld entry. There is plant-level information such as revenues by type of product, input and output quantities, or costs by input that can be used to measure prices and variable costs. Also, the book value of assets adjusted by capital de‡ators can be used to obtain a measure of the stock of capital. I use plants with a primary Standard Industrial Classi…cation code equal to 3241.4 See Appendix A for more details about the CM database. To measure construction activity, I use data on earnings at the state level (wages and proprietors’ 3
Additionally, the international trade literature has extensively studied di¤erent modes of expansion of multinational …rms (see, for example, Nocke and Yeaple, 2007). 4 Cement plants are basically single-product plants. The specialization ratio of manufacturing plants that produce cement (as the primary product) was 99% in 1992 and 1987, and 98% in 1982 (see 1992 CM, 3241 Industry Series).
4
income) for the construction sector from the Regional Economic Information System of the U.S. Bureau of Economic Analysis. Since …rms take into account the future ‡ows of revenues when making their entry decision, I use the average construction activity over the 10 years following the year of entry. Energy prices by state and year for di¤erent energy sources are obtained from the Energy Information Administration. All nominal variables in my model are de‡ated using value of shipments of the U.S. cement industry obtained from the NBER-CES Manufacturing Industry Database, using 1987 as the base year. In the entry game, the geographic unit of a market is a U.S. state, with some exceptions. I divide some large states and aggregate some small contiguous states on the east coast.5 This leads to a total of 450 market-census year observations, similar to Ryan (2012) and consistent with the average shipping distance for cement. According to the Commodity Flow Survey, the average transportation distance for cement was 64 miles in 1992, and 82 miles in 1997. The entry game uses three …rm-level variables: …rm size, …rm-level TFP and an indicator variable for …rms that were present in the U.S. cement industry in a previous census year (insider …rms). To generate …rm size, I aggregate all the revenues in all manufacturing sectors for every …rm. There is substantial variation in …rm size, given that some …rms have few manufacturing plants, while others are large conglomerates with interests in many industrial sectors. This variable proxies for experience or some other comparative advantage. To calculate …rm-level TFP, I use the accounting method of Syverson (2004). I then obtain the weightedaverage TFP level for each …rm by weighting the TFP levels of the plants owned by each …rm with the quantities produced. I …nd the dispersion of plant-level TFP among a …rm’s plants to be relatively small, such that highly productive …rms have highly productive plants.
3
Green…eld entry and entry by acquisition in the U.S. cement industry
3.1
General characteristics of the U.S. cement industry
Cement is a material usually used as an input for other construction materials, such as concrete. The main material used to produce cement is limestone, a ubiquitous material. Cement is usually transported only for short distances, because of high transportation costs relative to cement prices. Transportation costs and the abundance of limestone explain why there are cement plants in many U.S. states. 5
Northern and Southern division for California and Texas; Western and Eastern division for New York and Pennsylvania.
5
Although there are several types of cement produced, most cement is Portland (about 85% of the value of all cement produced in 1992). Because there is limited product di¤erentiation in this industry, …rms mostly compete on price; cost advantages are key in explaining the pro…tability, expansion and survival of …rms.6 I identify three sources of cost advantages in this industry: technological improvements in cement manufacturing, managerial skills and economies of scale. The use of scale economies is restricted by high transportation costs and limited demand in some local markets.7 The production of cement has a high environmental impact. The 1970 Clean Air Act and successive amendments in 1977 and 1990 have increased the costs of operating plants and building new facilities. Many environmentally ine¢ cient cement plants closed because it was not pro…table for them to comply with these regulations.8
3.2
Structure of the U.S. cement industry and patterns of …rm expansion
Table 1 reports summary statistics for the industry over the period 1963-2002. Although the number of active …rms in the industry was relatively stable over this period, the number of active plants decreased. Many plants were closed because they were too small and ine¢ cient to survive or to be renovated or sold to other …rms. Also, the frequency of construction of new plants decreased over the years, and this decline gained momentum after the 1990 CAA Amendments. The U.S. cement industry has a considerable level of concentration in the geographic markets I consider. Table 2 uses public information from the USGS Minerals Yearbooks to generate detailed statistics on concentration levels for the period 1963-2002. The number of plants per market is typically small (on average, 3.07). Interestingly, most …rms are single-plant or own a small number of plants, and the largest …rm in the United States did not own more than 15% of the total number of plants in the industry. In addition, a given …rm rarely operates more than one plant per market (on average, 1.10 plants per …rm in every market). Table 2 also reports statistics about the mode of entry and shows that, on average, there are only 0.12 entrants by acquisition or green…eld in each market year. I use this fact when estimating the model by assuming that there are relatively few potential entrants in a market. 6
Although the product is homogeneous, there is substantial spatial di¤erentiation (see Miller and Osborne, 2014). Other sources of cost advantage, such as multi-plant economies, are hard to identify (FTC, 1966). 8 Interestingly, these regulations are usually asymmetrical because new plants are generally subject to more stringent regulations than existing plants (grandfather vs. new source regulations). 7
6
Table 1: The U.S. cement industry for every census year (1963-2002) Census year 1963 1967 1972 1977 1982 1987 1992 1997 2002
# of plants 181 188 175 168 149 130 121 116 114
# of …rms 46 49 47 49 44 39 43 39 40
# of acquisitions . 6 8 16 56 63 27 13 33
# of green…eld . 22 14 18 15 6 2 0 10
Price 63.3 58.6 49.8 52.3 62.9 49.3 53.7 49.7 49.0
Production 66.6 70.5 79.5 74.8 63.2 76.2 70.1 81.3 85.2
Imports 0.7 1.1 3.2 2.3 2.4 14 4.9 15.9 24.1
Notes: Number of acquisitions and green…eld plants are aggregated in between census years. Production and imports in million short tons. Prices in de‡ated dollars per short ton. Sources: USGS Minerals Yearbook and Census of Manufactures.
Table 2: Statistics per year, and per market-year (1963-2002)
Variable Number plants per market-year Number plants per year Number green…eld entrants per market-year Number green…eld entrants per year Number acquired plants per market-year Number acquired plants per year Number plants owned by …rm (statistics per market-year) Number plants owned by …rm (statistics per year) Number markets where …rms are present (statistics per year)
Mean 3.07 147.45 0.045 2.17 0.115 5.55
Min 0 114 0 0 0 0
25th Pct 1 117.5 0 0 0 2
Median 2 142.5 0 1.5 0 3.5
75th Pct 4 171 0 4 0 8
90th Pct 6.5 182.5 0 5 0 14
Max 18 188 2 7 3 21
1.10
1
1
1
1
1
3
2.81
1
1
1
3
8
18
3.15
1
1
2
4
6
16
Notes: Statistics of key variables per market-year or per year. The statistics need to be "aggregated" for 5-year periods to compare them to the CM database. Source: USGS Minerals Yearbook.
Table 3 uses public information from the USGS Minerals Yearbooks to show detailed statistics about the mode of entry. Most of the acquired plants were bought by …rms not previously present in their respective geographical markets; that is, they were non-horizontal transactions. Also, …rms usually acquire or build plants in markets that are not contiguous to the markets where they are already present. Hence, geographic proximity is unlikely to be relevant in predicting these acquisitions. Finally, …rms that acquire plants are typically present in the industry in previous years. In any case, I do not observe a strong
7
correlation between geographic characteristics, or previous experience of …rms, and mode of entry into the market, perhaps with the exception of the construction of green…eld plants by insiders. Table 3: Mode of entry, contiguous states, insiders and horizontal mergers Mode of entry Acquisitions in non-contiguous states Acquisitions by insiders Acquisitions within states Acquisitions in 1982-1992 Partial acquisitions of multi-plant …rms Green…eld plants in non-contiguous states Green…eld plants by insiders Green…eld plants within states Green…eld plants in 1982-1992
Number 150 146 12 146 83 58 69 6 23
Percent on total 67.5% 65.7% 5.4% 65.8% 86.4% 66.7% 79.3% 6.9% 26.4 %
Notes: Acquisitions and green…eld plants in "non-contiguous states" refer to expansion by …rms that were not present (the previous year) in any state contiguous to the state where there is expansion. "insiders" are …rms that (the year previous to the acquisition) were present in the cement industry. Acquisitions and green…eld plants "within states" refer to expansion by …rms that (the previous year) were present in the same state where the plant is acquired/built. "Partial acquisitions of multi-plant …rms": for all multi-plant …rms that sold at least one plant in a given year, I calculate the percentage of times the …rm did not sell all its plants in the same year. Source: USGS Minerals Yearbook.
Using the stylized facts reported in Tables 2 and 3, I assume that acquisitions in this industry can be modelled as individual decisions made on a plant-level basis by each potential buyer, as opposed to …rms buying other complete …rms. The number of single-plant …rms is signi…cant and there are many partial acquisitions of multi-plant …rms (about 86%).
3.3
Comparative advantage in plant acquisitions in the U.S. cement industry
The importance of a comparative advantage in expansion by acquisition is exempli…ed by the acquisition of plants by foreign …rms between the late 1970s and the early 1990s.9 Decreased barriers to acquisitions and the lack of competitiveness of the industry created incentives for the more e¢ cient and modern foreign …rms to launch massive acquisitions of U.S. plants during this period.10 When comparing the relative e¢ ciency of potential buyers and sellers, I …nd similar qualitative results to Maksimovic and Phillips (2001) (see Tables 8 and 9 in Appendix B). For example, I …nd that the 9
Entry of foreign …rms in U.S. was usually a gradual process. A foreign …rm typically acquired and built additional plants several years after its …rst acquisition. Therefore, these foreigners are classi…ed as "insiders" only the …rst year they entered in the market. 10 See Mabry (1998) for an excellent analysis of the U.S. cement industry in the last century, and Bianchi (1982) to understand the comparative advantages of European cement …rms.
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relative TFP of acquired plants (relative to the average TFP level in the United States for that census year) increases between 1.4% and 2.2% with respect to the relative TFP level of the previous census year. Also, when I regress the increase in a plant’s TFP after an acquisition on the di¤erence in TFP between the buyer …rm and the acquired plant during the census year before the acquisition, I …nd a positive and signi…cant coe¢ cient equal to 0.33. This increase in the productivity of plants when there is a change in ownership suggests that the new plant owner has the ability to add more value to the acquired assets than the previous owners. These results, together with the non-horizontal character of these transactions, imply that acquisitions are driven by e¢ ciency considerations and not by market power issues.
4
Structural model of entry by green…eld or by acquisition
I extend a static perfect information entry game as in Bresnahan and Reiss (1991), Berry (1992), and Ciliberto and Tamer (2009), among others, to consider entry by acquisition. The model has three stages, with perfect information in all stages (see Figure 1):
1. First stage (entry decision): Every potential entrant j 2 E chooses simultaneously action ej to enter green…eld (ej = g), enter by acquisition (ej = a), or not to enter (ej = 0). 2. Second stage (acquisition game): The entrants that entered by acquisition in the …rst stage bid simultaneously for the existing incumbents. The outcome of this stage determines which incumbents are acquired by which entrant, and the price paid. 3. Third stage (Cournot competition): All active plants in the market choose simultaneously the quantities to produce. Variable pro…ts are determined. Active plants are the incumbents not acquired, the entrants that entered green…eld and the entrants that acquired an incumbent.
All the subgame perfect Nash equilibria of this game can be solved by backward-induction. By sequentially solving the last subgames of this perfect information multi-stage game, it is possible to …nd the payo¤ of every potential entrant j for any vector of …rst-stage actions e. Denote by
j (e)
the payo¤ of
every entrant j in the …rst stage after solving sequentially for the second and third stages. Depending on
9
Figure 1: Stages of the entry game.
the value of ej ,
where
j
j
is decomposed as follows:
j (ej
= g; e
j)
=
j (e)
CKj (e);
(1)
j (ej
= a; e
j)
=
j (e)
CAj (e);
(2)
is the variable pro…t equal to revenues minus variable costs (cost of energy, labor and materials)
from Cournot competition. CK is the cost of building a new plant, and CA is the price paid for an incumbent. Note that both costs are endogenous since they depend on the actions by all potential entrants and must be solved in equilibrium. Entrants that choose not to enter in the …rst stage earn zero pro…ts. The static game setting implies that capital levels are optimally set in one period. This is a simpli…cation that neglects any adjustments to capital (see Ryan, 2012). Nevertheless, this static setting can be considered to be reasonable for the following reasons. The basic production element in a cement plant is the kiln, which is a large-scale piece of industrial equipment that requires years of planning to install. Plants are at times subject to major renovations. In some cases, these renovations take several years and are so signi…cant that the plant is considered a new plant for the U.S. Census. In addition, I have calculated the ratio of the standard deviation of the changes of capital over two census periods after the construction of a plant, divided by the initial level of capital and obtained a median ratio of 0.3.11 This is a relatively small 11
The approximate values for the 25% percentile and 75% percentile are, respectively, 0.2 and 0.5.
10
value that implies that changes of capital across years are moderate. Although incumbent plants are part of the game by strategically choosing quantities with the rest of the entrants (third stage), I do not explicitly model the exit of incumbents from the market (which occurs before the …rst stage). Many of the exiting plants were old and small, with obsolete technology, and therefore too ine¢ cient to be worth acquiring by entrants, or to stay and compete in the market. Therefore, exit can be considered, to a certain extent, an exogenous decision.
4.1
Primitives of the model
The CM database has information on prices, quantities, capital, and variable costs, allowing me to separately identify demand, supply and investment primitives. Most articles in the entry literature estimate a reduced-form pro…t function because they do not have this detailed data.12
4.1.1
Production technology
I assume that the variable costs of production for plant j in market m depends linearly on the quantity produced, MC MC MC MC C(Qj ; Xj;m ; "j;m ) = M C(Xj;m ; "j;m ) Qj ;
(3)
M C are observed exogenous variables and "M C is where M C is the constant marginal cost of production, Xj;m j;m
the unobserved error term. The linear assumption is a good approximation for the cement industry, where a number of inputs, such as materials and energy, are used in …xed proportions (Das, 1992). Observed variables can be classi…ed as market-level variables (input prices and a technological year trend), plant-level variables (capital, age and an indicator for green…eld plants) or …rm-level variables C (TFP, size and an indicator for insider …rms). The error term "M j;m has distribution N (0;
2 M C ).
I assume
a multiplicative expression for the marginal cost of plant j in market m: MC
MC MC M C(Xj;m ; "j;m ) = e"j;m e
0
e
1Y
EARm
F IRM SIZEj 2 T F Pj 3 IN SIDERj 4
BIRT Hj 5 CAPj 6 AGEj 7 W AGE m8 F U ELm9 ELECTm10 ; where 12
(4)
is the vector of parameters to be estimated. Note that the possible cost advantages of green…eld
Some exceptions are Berry and Waldfogel (1999), Ellickson and Misra (2012), Nishida (2014).
11
plants not included in the variable T F Pj are present in the variable BIRT Hj . Similarly, an old plant acquired by a …rm may have cost disadvantages (higher maintenance costs, obsolete technology), which are proxied by the variable AGEj .13
4.1.2
Demand function
To model spatial di¤erentiation, I consider a di¤erentiated inverse demand function for every plant, and I assume a linear functional form:
p(Qj ; Q
D P j ; Xj;m ; "j;m )
D = A(Xj;m ; "Pj;m ) +
1
Qj +
2
X Qi ;
(5)
i6=j
D ; "P ) is the intercept that depends on observed variables X D and the unobserved error where A(Xj;m j;m j;m
term "Pj;m ,
1
is the e¤ect of the plant production on the plant price level, and
2
is the e¤ect of the
competitors’production on the price of the plant. The intercept depends on market-level variables (construction activity and a year trend) and a plantlevel variable (a binary variable equal to one if it is a green…eld plant). I assume that the intercept has a linear form equal to: D A(Xj;m ; "Pj;m ) =
0
+
const
CON ST RU CT IONm +
where the error term "Pj;m has distribution N (0;
2 P ).
year
Y EARm +
birth
BIRT Hj + "Pj;m ;
(6)
Counteracting the potential cost advantages of
green…eld plants, new plants may have demand disadvantages (a "demand gap") represented in variable BIRT Hj (assuming
birth
< 0).14
Using these primitives, plant-level variable pro…ts are obtained by subtracting costs from revenues:
(Qj ; Q
D MC P MC j ; Xj;m ; Xj;m ; "j;m ; "j;m )
= p(Qj ; Q
13
D P j ; Xj;m ; "j;m )
Qj
MC MC C(Qj ; Xj;m ; "j;m ):
(7)
Note that the variables F IRM SIZEj , T F Pj and IN SIDERj do not change for any plant j owned by the same …rm. As Foster et al. (2013) show, new manufacturing plants start with a considerable demand de…cit with respect to existing plants. For example, building a customer base or a reputation takes considerable time. 14
12
4.1.3
Cost of building a new plant
The cost of building a new plant consists of a sunk entry cost component ( the 1990 CAA Amendments (
1 ),
and a variable component (
k)
0 ),
an incremental cost due to
that depends on the amount of capital
of the new plant: CKj (e) =
0
+
1
1[Y EARm = 1992; 1997] +
K
CAPj (e);
(8)
where CAPj is the capital of the green…eld plant, which is obtained using an approach fairly similar to Ryan (2012). I assume that green…eld entrants choose the optimum initial level of capital CAP according to an investment function I estimate. This function depends on the …rm-level characteristics of the green…eld entrant and on the total number of plants in the market, which shows a competitive e¤ect on the investment strategies of green…eld entrants. The investment function has the following functional form:
CAPj (e) =
0
+
1
log Im +
X
1[ei = g]
i2E
!
+
size
SIZEj +
TFP
T F Pj + "K j;m ;
(9)
where CAPj is capital expressed in logs, SIZEj is the …rm size expressed in logs, T F Pj is …rm-level TFP, Im is the number of incumbents, "K j;m is an unobserved error term with distribution N (0;
2 K ),
and
are
parameters to be estimated.
4.2
Equilibrium of the game
I summarize next how the equilibria are calculated. In the last stage, for given entry decisions by all potential entrants in the …rst stage, and for given bids in the second stage, the unique Nash equilibrium of the Cournot subgame can be solved. This is the standard solution shown in Appendix C. In the second stage, entrants by acquisition bid for existing incumbents, taking into account the equilibrium Cournot payo¤s. The equilibrium of this perfect information acquisition game is such that every incumbent plant is acquired by the …rm that can obtain the highest variable pro…ts, and the acquisition price is equal to the second-highest variable pro…t that can be obtained from that plant among all …rms in the market. Finally, the …rst-stage payo¤s of entrants in (1) and (2) are constructed using Cournot payo¤s and acquisition/green…eld entry costs, and all the subgame perfect Nash equilibria can be obtained. Appendix D provides more details on the algorithm used to calculate the equilibrium and other aspects of the estimation.
13
4.2.1
Second stage: Acquisition game
In this perfect information acquisition game, every entrant j simultaneously submits a take-it-or-leave-it bid for every incumbent plant i.15 Every incumbent chooses to be acquired by the entrant that submits the highest bid (provided that the bid is greater than the variable pro…ts made by the incumbent in case the o¤er is not accepted). If an entrant by acquisition cannot buy an incumbent, it earns zero variable pro…ts. A key feature of this game is the role played by …rm heterogeneity. The acquisition game is modelled in such a way that after an acquisition of a plant, the …rm-level variables of the seller …rm are substituted by the …rm-level characteristics of the buyer. In contrast, the plant-level variables of the acquired plant remain constant. More speci…cally, if …rm j buys plant i, the …rm-level variables F IRM SIZEi , T F Pi and IN SIDERi of the incumbent plant i are replaced by the corresponding …rm-level variables of the acquiring C …rm j. In addition, there is an unobserved e¤ect of this acquisition (error term "M ij ) that replaces the C of the incumbent plant. This transfer of characteristics a¤ects the variable costs of the error term "M i
acquired plant, and hence the variable pro…ts.16 The following Proposition shows the equilibrium of this game:
Proposition 1 The equilibrium of this acquisition game is such that an incumbent plant i is acquired by the …rm j that can obtain the highest variable pro…ts
from the plant. The winning bid is equal to the
second-highest variable pro…t that can be obtained from the plant among all …rms in the market. Proof. See Appendix C
I also introduce a sunk …xed merger cost (F M > 0) that is constant and paid by all entrants by acquisition; thus, it does not a¤ect the results of Proposition 1. Therefore, the total acquisition cost CAj in equation (2) is equal to the second-highest variable pro…ts among all participants plus F M . The cost F M represents rents dissipated from the acquisition and could be interpreted as barriers to …nancial markets, antitrust costs (such as the obligation to divest part of the assets acquired or litigation costs), or a higher bargaining power for the seller plant. F M is estimated with the other primitives of the model. To better represent the merger waves that occurred during the Reagan-Bush administration, I consider that 15
I allow for multiple acquisition for two reasons: …rst, I observe it in my data (although infrequently), and second, this game is computationally much simpler than other acquisition games where there can be only one acquisition by every entrant. 16 P Similarly, the term "P j in the demand function is replaced after the acquisition by a …rm-plant-speci…c error term "ij .
14
F M changes for census years 1982, 1987 and 1992.17
4.2.2
First stage: Decision of type of entry
A pure-strategy equilibrium of this game, e , must satisfy two inequalities for every potential entrant in every market. For example, an equilibrium where …rm j enters green…eld must satisfy the following two inequalities:
j (ej
= g; e
j)
j (ej
= a; e
j );
(10)
j (ej
= g; e
j)
j (ej
= 0; e
j );
(11)
and similar inequalities for the rest of the potential entrants.
4.3
Elimination of strategies that are not an equilibrium
There are signi…cant number of strategies that cannot be an equilibrium in this game. The crucial assumption that gives this result is the existence of a …xed merger cost F M that is paid by all entrants by acquisition in the …rst stage. With it, all entrants by acquisition that do not acquire an incumbent are better o¤ choosing ej = 0 at the …rst stage, because they can obtain zero pro…ts, rather than
F M < 0.
Note that if F M = 0 there are many equilibria that are not reasonable. For example, if it is an equilibrium for an entrant to enter by acquisition without buying any incumbent (obtaining it may also be optimal for the same entrant not to enter (and also obtaining
= 0), then
= 0). I discard the former
because in practice entering into a bidding game with other entrants should imply some non-negligible costs for entrants. Note that these two equilibria could give the same total pro…ts in some cases,18 and therefore using an equilibrium selection rule that considers the maximization of total pro…ts would not be useful here. Using similar arguments and the existence of sunk entry costs paid by green…eld entrants, it can be shown that any corner solution of the Cournot game can be discarded. The following Proposition summarizes the set of strategies that cannot be an equilibrium in this game: 17
To simplify the computational burden of the estimation, I assume that if one entrant buys more than one incumbent, this entrant does not internalize the e¤ects of the quantities produced in other owned plants when solving the Cournot game. Therefore, the usual Cournot solution is used. This assumption could be justi…ed because multi-plant …rms have managers that independently optimize production in every plant. 18 For example, this is the case of a market with one incumbent that is much more e¢ cient than any of the entrants by acquisition.
15
Proposition 2 The following set of strategies cannot be an equilibrium:
1. There cannot be equilibria where more entrants than incumbents choose to enter by acquisition, 2. there cannot be equilibria where at least one entrant by acquisition does not buy any incumbent, and, 3. all solutions of the Cournot game played in the last stage of the game must be interior.
Proof. See Appendix C
4.4
Main trade-o¤s of the model
I next summarize the main trade-o¤s in the model for every type of entry. First, green…eld entrants create a new competitor in the market when they build a new plant; therefore, they increase competition and pro…ts decrease. This e¤ect is not present when entrants enter by acquisition because the number of competitors remains constant. Also, entrants by acquisition already have an established customer base, which gives potential advantages on the demand side (parameter by acquisition buy old capital that can be obsolete (
5
birth
in equation (6)). On the cost side, entrants
and
7
in equation (4)), and they do not have the
‡exibility to adjust it, whereas green…eld entrants can use state-of-the-art technology for the new plant ( 5 ). Firm characteristics such as TFP or size can a¤ect the costs of production (
2
and
3)
and variable
pro…ts. These variable pro…ts also a¤ect the cost of entering by acquisition. As shown in Proposition 1, entrants by acquisition pay a price for the existing incumbents that depends on the …rm characteristics of incumbents and potential entrants. The more e¢ cient are the incumbents and other potential entrants, the more expensive it is to enter by acquisition, because e¢ cient incumbents are more expensive to acquire in equilibrium. There are also exogenous …xed merger costs (F M ) that may have been lower during the Reagan-Bush administration. On the other hand, green…eld entrants pay a price that depends on the sunk entry cost and on the amount of capital they are willing to build given their …rm characteristics.
5 5.1
Empirical strategy Simulated method of moments estimator
The existence of multiple equilibria is one of the main di¢ culties in the estimation of entry games with heterogeneous entrants. A number of solutions have been proposed. I use the solution proposed by Bajari 16
et al. (2010) for discrete games of complete information. This solution requires the calculation of all equilibria of the game, and an equilibrium selection mechanism is included as part of the primitives of the model. I focus only on pure-stregy equilibria.19 I use a simulated method of moments (SMM) estimator. Given a weighting matrix W and a vector of sample moments m(X; b ) that depend on the vector of all exogenous variables (X) and the vector
of all
parameters to be estimated, the SMM estimator b is obtained by minimizing the following expression: min m b 0 (X; ) W m(X; b ):
(12)
I use two types of moments. As in Bajari et al. (2010), I use moments corresponding to observed equilibrium decisions. At the true values of the parameters, the population moment corresponding to the equilibrium outcome k must be equal to:
mk (X; ) = E [(1(k is observed)
Pr(kjX; )) !(X)] = 0;
(13)
where Pr(kjX; ) is the probability of observing equilibrium k, and !(X) is a function of the exogenous variables. Because I also observe other variables such as prices, quantities, investment or marginal costs, I construct population moments corresponding to some of these observed outcomes (O):
mO (X; ) = E [(O
E[OjX; ]) !(X)] = 0;
(14)
where E[OjX; ] is the expected outcome.
5.1.1
Moments for observed strategies
The moments for the observed strategies are the probability that a plant is built, and that a plant is acquired. Section 5.2 explains with more detail all the moments I use. These moments require the calculation of Pr(kjX; ): To calculate this probability, I solve all the pure-strategy equilibria of the game using equilibrium conditions as in (10) and (11). 19
There is also a literature on partial identi…cation of structural models. Ciliberto and Tamer (2009) provide a good example. Their estimator also requires the calculation of all equilibria of the game.
17
More formally, let (X; "; ; ; ; ) denote the set of all possible equilibria given the observed variables and the unobserved vector of error terms, ". Pr(kjX; ) can be expressed as: Z
Pr(kjX; ) =
2 4
X
e 2 (:)
3
(e ; (X; "; ; ; ; ); )5 dF ("):
1[k 2 e ]
(15)
(e ; ( ); ) denotes the equilibrium selection rule that depends on the equilibrium vector e , the set of equilibria ( ) and the equilibrium selection parameter . ( ) is the probability that the e¢ cient equilibrium (the one with highest total pro…ts) is selected.20 I use a logit speci…cation for ( ), and
is a parameter
to be estimated. The expression of Pr(kjX; ) in (15) does not have an analytical solution and must be estimated by c simulation. Let Pr(kjX; ) denote this simulated probability that can be written as: 2 S X X 1 c 4 Pr(kjX; )= S s=1
e 2 (:)
3
(e ; (X; "s ; ; ; ; ); ) 1[k = e ]5 ;
(16)
where f"s gs=1;:::;S are random draws of the unobserved error terms. Given this expression, the sample expression of the moment mk in (13) is: P
1X 1(ei = k) m b k (X; ) = P i=1
c Pr(kjX i; )
!(Xi );
(17)
where P is the number of plants.
5.1.2
Moments for observed outcomes
Let O(e ; X; "; ; ; ; ) denote the outcome variable generated for one (of the potentially multiple) equilibria e . Then, the expected value of observing some outcome can be constructed in a way similar to that for Pr(kjX; ):
E[O=X; ] = 20
Z
2 4
X
O(e ; X; "; ; ; ; )
e 2 (:)
3
(e ; (X; "; ; ; ; ); )5 dF ("):
(18)
The selection of the e¢ cient equilibrium in an entry game has already been suggested by Berry (1992) and Ciliberto and Tamer (2009).
18
b As in the case of Pr(kjX; ), there is no analytical solution for E[O=X; ]. Let E(OjX; ) denote the
simulated expression. The simulated expected value of the outcome variable can be written as: 2 S X X 1 b 4 O(e ; X; "s ; ; ; ; ) E(OjX; )= S s=1
e 2 (:)
3
(e ; (X; "s ; ; ; ; ); )5 :
(19)
Given this expression, the sample expression of the moment mO in (14) is: P
m b O (X; ) =
1X Oi P i=1
b E(OjX i; )
!(Xi );
(20)
where Oi is the observed outcome in plant i. The vector of moments used in the estimation is formed by all the moments corresponding to the observed outcomes and to the observed strategies: 2
3
b k (X; ) 7 6 m m(X; b )=4 5: m b O (X; )
(21)
I use the e¢ cient optimum SMM estimator, with the identity matrix as the weighting matrix in an initial optimization stage, and then use the inverse of the sample covariance matrix of the moments (calculated at the estimated parameters in the …rst stage) as the weighting matrix in a second optimization stage. McFadden (1989) provides the asymptotic distribution of this estimator, which I use to calculate the standard errors.
5.2
Identi…cation
The estimator uses moments for observed entry strategies (the probability that a plant is built, and that a plant is acquired), and for observed outcomes (variables costs, prices, quantities, and capital of new plants), interacted with other variables. In total, I use 40 moments to identify the 30 parameters of the model (see Appendix D for further details). The equilibrium quantities and prices from the Cournot equilibrium depend both on demand and marginal cost parameters (see Appendix C). Therefore, moments for prices and quantities depend both on demand and marginal costs parameters. Expected prices or quantities in (18) are calculated by solving the equilibrium of the entry game, which takes into account which entrants enter and which incumbents are acquired. Therefore, these moments are also a¤ected by parameters that are more directly related with entry, such as green…eld entry costs parameters or parameters that
19
a¤ect initial capital investment. In summary, the model is nonlinear; all parameters are a¤ected by most moments. To better understand the sensitivity of every parameter to every moment, I follow Gentzkow and Shapiro (2014) to build "scaled sensitivity" measures that demonstrates how changes in moment conditions a¤ect changes in estimated parameters.21 Results from a Monte Carlo experiment are shown in Figure 2 in Appendix D. The larger these measures are, the more sensitive the parameter estimates are to the corresponding moments. The diagram con…rms the wide dependence of parameters on most moments, but also shows that some moments can be more relevant than others. Capital moments and green…eld entry moments in‡uence the estimation of the capital parameters. Capital moments also have a relevant in‡uence on the demand parameters, the green…eld cost parameters, and in the merger cost parameters. Capital moments not only provide information about the cost of building capital, but also about the relative cost of the two modes of entry. Demand parameters are a¤ected by price moments, but also by marginal cost, quantities and capital moments. Marginal cost parameters and the equilibrium selection also have a similar dependence on these moments. The fact that capital moments have a relatively large in‡uence in the majority of parameters is interesting. This suggests that most parameters are sensitive to selection issues derived from entry, and that moments that a¤ect entry have a large e¤ect on the rest of the primitives. The fact that merger moments have a small in‡uence on most parameters is also interesting. Since the cost from entry by acquisition depends on the second-highest variable pro…t among all entrants, most of this information is already provided by the remainder of the moments that in‡uence variable pro…ts.
5.3
Potential entrants
c The main computational di¢ culty of the estimation procedure is the calculation of Pr(kjX; ) in (16),
because the set of all pure-strategy equilibria must be computed a large number of times to …nd the optimum of the SMM objective function in (12). The calculation of all equilibria must be done at every stage of the optimization routine. Based on the large levels of concentration in every market and the relatively small number of entrants, I consider that …ve potential entrants is a sensible number to estimate the model that renders the computations tractable. The potential entrants are selected randomly among all …rms in all other markets for the same census 21
This is equivalent to measuring the coe¢ cients from a regression of the estimated parameters on the moment conditions. These measures are normalized using the standard deviation of parameters and moments.
20
year (I include in the set of potential entrants the actual entrants of that market if there was entry into that market).22 As shown earlier, the geographic location of entrants or previous experience are not highly correlated with entry behavior. Similarly, although I …nd evidence that acquired plants increase TFP, it is certainly not the case that the most productive …rm buys all plants in the United States in a given year. Therefore, I select randomly the potential entrants in every market. I have not obtained signi…cant di¤erences in my estimates when changing the identity of potential entrants in the market, suggesting that this selection procedure is not critical for the results. Similarly, in order to solve the bidding game, I need to make assumptions about the …rm-level variables that an acquired plant in year t would have had if it had not been acquired by the observed buyer in year t. In this case, I assume that these …rm-level variables would correspond to the variables observed in the previous census year. Appendix D provides additional details about the estimation procedure.
6
Empirical results
I …rst analyze the estimates corresponding to the demand function in Table 4. I …nd that the production of one million extra short tons of cement by a plant decreases the price by almost $19, whereas the e¤ect of competitors is much smaller. Given that cement is a homogeneous product, this result could be attributed to a high degree of spatial di¤erentiation. This is consistent with a recent study by Miller and Osborne (2014).23 This relatively small competitive e¤ect implies that the creation of a new competitor does not have a substantial e¤ect on the entry decision of a potential entrant. In contrast, I …nd a demand de…cit of green…eld plants equal to $9.28 per million short tons produced. This estimated parameter is economically signi…cant if compared with the average price of cement (the e¤ect is between 14% and 19% over the average cement prices). This result is comparable with the recent …ndings of Foster et al. (2013) that study the size of the gap between new and established plants due to demand fundamentals. This demand gap found for green…eld plants is economically more relevant than the competition e¤ect. In other words, the estimates suggest that new plants produce less, not because they create more competition in the market, but because they need time to build a new customer base. This result is in contrast to Gilbert and Newbery (1992), who …nd that entrants may prefer to buy an incumbent because green…eld entry has a negative impact of 22 I do not observe the TFP of non-insiders that do not enter in any market in a given year. Therefore, any non-insider that is considered a potential entrant in a market is also an observed entrant in one or more markets in that year. On the contrary, potential entrants that are insiders may have expanded or not in that given year. 23 Additionally, my model does not consider capacity constraints and this could be another factor that a¤ects competition.
21
creating a new competitor in the market. Table 4: Estimates of the model: Demand function Demand parameters: Quantity ( 1 ) Quantity of competitors ( Construction activity ( New plants ( Year trend (
2)
const )
birth ) birth )
Standard deviation of price (
P)
-18.65 (0.94) -1.46 (0.24) 1.33 (0.50) -9.28 (1.26) -3.60 (1.44) 12.87 (2.91)
Notes: Standard errors in parentheses. Prices expressed in dollars per million short tons of cement. Construction activity measured in billions of dollars (measured as personal income), averaged over 10 years after the year of entry.
To conclude the analysis of the demand estimates, I …nd that every extra billion dollars of construction activity increases the price paid by 1.33 dollars (a state such as California had construction activity of 51.6 billion dollars in 2001). There is also a negative coe¢ cient in the year trend, equal to $3.6 dollars per census year. Consumption of cement has been considerably slower than the population growth over the past 100 years, perhaps due to changes in technology and materials used for construction. The estimates of the marginal cost parameters in Table 5 provide valuable information about the importance of …rm-level variables relative to other market-level variables such as input prices. The functional form used leads to an interpretation of the coe¢ cients in terms of elasticities. I …nd that the e¤ect of TFP is the highest among all estimates. A 1% increase in TFP decreases the marginal cost by 1.62%. This elasticity is higher compared to the other two …rm-level variables that are considered: size and the insider dummy variable. This suggests that TFP is the relevant …rm-level variable a¤ecting variable costs. When analyzing the plant-level variables, I …nd intuitive signs. A green…eld plant produces cement less expensively than an existing plant. The newer the plant, and the more capital the plant has, the lower the variable cost. The e¤ect of capital is economically the most relevant among all plant-level variables, but still signi…cantly inferior to the e¤ect of TFP. Finally, analyzing the market-level coe¢ cients, I …nd that the e¤ects of wages and electricity are high, with a value slightly lower than the e¤ect of TFP (in absolute terms). This is consistent with the importance of energy in the production of cement. However, 22
the coe¢ cient for fuel is small compared to electricity and wages, which is surprising. Also, I …nd that the decrease in costs due to technological improvements over the years is high compared to most parameters, with an estimated parameter equal to 0.27. Table 5: Estimates of the model: Cost function Marginal cost parameters: Year trend ( 1 ) Size ( 2 ) TFP ( 3 ) Insider …rm ( 4 ) New plant ( 5 ) Capital ( 6 ) Age of plant ( 7 ) Wages ( 8 ) Fuel price ( 9 ) Electricity price (
10 )
Constant (marginal cost) Standard deviation of error term (
MC)
-0.271 (0.04) -0.00181 (0.0004) -1.621 (0.471) -0.019 (0.006) -0.0052 (0.00258) -0.066 (0.022) 0.00038 (0.00007) 1.104 (0.52) 0.032 (0.009) 1.516 (0.14) 9.25 (0.76) 0.280 (0.074)
Notes: Standard errors in parentheses. Marginal costs expressed in dollars per short ton of cement. Capital expressed in thousands of dollars. Size in millions of dollars.
Table 6 shows the estimates of the rest of the primitives. I …nd that the initial investment of green…eld plants increases with the size of the entrant …rm and decreases with the number of plants in the market. Larger …rms may have better access to …nancial markets, allowing them to invest more. Also, greater competition in the market decreases the quantities produced and hence the investment in new capital. A surprising result that is di¢ cult to interpret is that more-productive …rms actually invest less. I also estimate variable and …xed sunk costs for green…eld entry. I use one-year revenues and costs, as well as the value of the stock of capital observed in that period. This explains why the coe¢ cient for the variable costs of capital is 0.704 dollars for every unit of capital, signi…cantly lower than one. This also 23
explains the relatively small values of sunk entry costs.24 I …nd a …xed sunk cost for green…eld plants of 6.04 million dollars,25 with an additional cost of 4 million dollars for census years 1992 and 1997 due to the CAA Amendments (a 50% increase). Also, I …nd a positive value in the equilibrium selection parameters, which shows that the observed equilibrium in the market is more likely to be the one that maximizes joint pro…ts, suggesting that the equilibrium selected is the e¢ cient one. Analyzing the estimations of the …xed merger costs, I …nd a value equal to 25.9 million dollars with an additional negative value of 16.5 million dollars during the period 1982-1992 (a 63% decrease). Therefore, the net …xed cost of acquisition decreases substantially to 25:9
16:5 = 9:4 million dollars during the
Reagan-Bush administration, helping to explain the merger wave in these years. Table 6: Estimates of the model: Rest of primitives Optimum investment parameters: Log of size ( size ) TFP (
0.343 (0.139) -9.987 (0.61) -0.892 (0.278) 4.88 (8.75)
TFP )
Log of number of plants in market ( 1 ) Standard deviation of error term (
K)
New capital cost parameters: Capital variable term ( K ) Sunk cost 1963-2002 (in millions of dollars) (
0)
Additional sunk cost 1992-1997 (in millions of dollars) ( Fixed merger cost (F M ) (in millions of dollars): Fixed merger cost (1963-2002) Additional …xed merger cost (1982-1992) Equilibrium selection rule: Pro…t-maximizing equilibrium ( )
1)
0.704 (0.15) 6.04 (0.586) 4.00 (0.816) 25.91 (6.24) -16.55 (5.93) 9.43 (3.30)
Notes: Standard errors in parentheses. Capital (cost function) expressed in thousands of dollars. Capital variable term in millions of dollars. Size in millions of dollars.
24 25
Currently, the cost of building a cement plant can reach several hundred million dollars. Using a 6% interest rate, this amount is equivalent to 6:04=0:06 = 100:6 million dollars in net present value.
24
7
E¤ect of policies that favor entry by acquisition
In this section, I measure the e¤ects of government policies that a¤ect entry by acquisition. As Table 1 shows, many plants were acquired in the 1980s and early 1990s, and many of those plants were acquired by foreign …rms that were either present or were new to the U.S. market. Estimates of merger costs show that, controlling for other aspects, there were advantages to entry by acquisition in those years because the cost of acquiring plants was lower. According to previous research (Adams and Brock, 1988; Baldwin, 1990; Krattenmaker and Pitofsky, 1988; Mueller, 1986), the relaxation of antitrust enforcement standards announced in the Department of Justice’s merger guidelines of 1982 and 1984, cuts in the budget and the personnel of enforcement agencies, and a willingness to accept mergers that did not meet previous standards facilitated the acquisitions in these years. Also, additional factors may have come into play, such as tax law changes in the 1980s and better access to …nancial markets by potential buyers. This favorable policy for mergers stopped in the early 1990s; activism against mergers increased during the Clinton administration. To evaluate the e¤ect of the Reagan-Bush years on this industry, I …rst solve for the equilibrium in the market using a high number of random draws of the error terms (S = 150), and calculate averages of key economic variables. Then, I eliminate the estimated bene…ts of entering by acquisition in these years (18.2 million dollars) and recalculate the equilibrium. By comparing the two equilibria, I calculate the e¤ect of this merger policy. Table 7 reports the results of this experiment. The …rst column reports key economic variables using the estimated parameters. The …t of the model is reasonably good. The observed number of green…eld plants and acquisitions (23 and 146, respectively, see Table 3) is relatively close to the simulated values in Table 7 (25 and 124). The observed average price in these years (55.3 dollars, see Table 1) is quite close to the average price of 46.6 dollars, although the total quantity produced is not that close to the observed value (209.5 vs 373.8 million short tons). The second column of the table reports the results of the counterfactual experiment. I …nd that the permissive Reagan-Bush administration’s merger policy increased the number of mergers from 35.9 to 124.1 and decreased the number of green…eld entrants from 27.3 to 24.9. As would be expected, a policy that favors mergers has a signi…cant direct e¤ect on the number of entrants by acquisition and a smaller substitution e¤ect on the number of green…eld entrants. In addition, new investment barely changed. Average maximum TFP increased from 3.58 to 3.69 due to the acquisition of ine¢ cient incumbents by more-e¢ cient entrants. Because the permissive merger policy 25
decreased the number of green…eld entrants, there were fewer plants with state-of-the-art technology. Since the marginal cost of production fell from 29.9 to 28.5 dollars, the e¢ ciency gains from entry by acquisition drive the reduction in marginal costs. Total pro…ts increased from 1.84 to 3.30 billion dollars. Production increased from 320.9 to 373.8 million short tons, because the additional production of the more-e¢ cient …rms compensated for the drop in competition caused by lower green…eld entry. Also, prices increased from 44.3 to 46.6 dollars per short ton of cement, and total consumer surplus increased from 4.09 to 5.35 billion dollars. The simultaneous increase in the average prices and the total production may be explained by the green…eld entry of plants in markets where there is no cement production. Although the number of green…eld entrants does not change much, the large increase of e¢ cient entrants by acquisition could create incentives for green…eld entrants to enter in other markets where there are no cement plants. These green…eld entrants are monopolists in the markets where they enter, setting a high price. On aggregate, the average price increases due to these plants, but total quantity and consumer surplus expands due to the entrants by acquisition. Table 7: Counterfactual policy experiments (1982-1992)
(I) Estimated parameters Average price (in dollars) Production (m. short tons) Net consumer surplus (b. dollars) Pro…ts (b. dollars) Variable cost (b. dollars) Revenues (b. dollars) Average marginal cost Average maximum TFP New capital (b. dollars) Number of green…eld entrants Number of acquisitions
46.6 373.8 5.35 3.30 8.29 17.42 28.56 3.69 0.24 24.97 124.11
Counterfactual experiments (II) (III) (IV) Merger Higher No bene…ts green…eld mergers eliminated costs 44.31 46.78 44.13 320.9 357 289.54 4.09 5.19 3.50 1.84 3.16 0.18 7.20 7.78 6.85 14.22 16.70 12.78 29.95 29.99 28.55 3.58 3.69 3.59 0.24 0.01 0.27 27.26 2.23 28.51 35.89 124.74 0
Notes: Values obtained by solving for all equilibria in every market 150 times and using the estimated equilibrium selection rule to determine the average outcome. Column (I) results are obtained using the estimated parameters from the previous section. Counterfactual experiment (II) results are obtained by eliminating the merger bene…ts estimated for 1982-1992. Counterfactual experiment (III) results are obtained by increasing the green…eld entry costs by the same amount as in experiment (II), but maintaining the estimated bene…ts of entering by acquisition in those years. Counterfactual experiment (IV) is obtained by setting in…nite merger costs. Average price is obtained by dividing total revenues by total quantities produced.
26
In a second experiment (column III in Table 7), I maintain the estimated bene…ts of entering by acquisition in these years but assume that green…eld costs increased by the same amount as in counterfactual (II). A comparison of columns (I) and (III) of Table 7 yields interesting results. As expected, I observe a large decrease in green…eld entry, from 24.97 to 2.23 plants built, and new capital decreases signi…cantly. This decreases production from 373.8 to 357 milion short tons, and prices increase. The number of acquisitions increase, but by a small number. The substitution e¤ect in terms of new plants built is small. Also, productivity does not change, which may be explained by the fact that e¢ cient entrants are still acquiring ine¢ cient incumbents, and do not take into account green…eld entry. As a consequence, variable costs do not change signi…cantly. This implies that variable costs are mainly a¤ected by e¢ ciency e¤ects from mergers. Also, pro…ts do not change signi…cantly, which suggests that pro…ts are mostly made by entrants by acquisition. The comparison between counterfactuals (II) and (III) in Table 7 shows that, in general, an increase in the …xed cost of entry by acquisition has more adverse e¤ects than an identical increase in the …xed cost of green…eld entry. Barriers to entry by acquisition have a larger negative impact on consumer surplus, production, …rms’pro…ts and TFP than equivalent barriers to green…eld entry. This result suggests that regulators should be particularly concerned about policies that negatively a¤ect the e¢ cient reallocation of assets between incumbents and entrants. Removing these barriers may have signi…cant positive e¤ects on the economy. It should be noted that this result depends on the assumption that acquisitions are non-horizontal; that is, they are a mere change of ownership without a¤ecting the number of plants in the market, which could negatively a¤ect the degree of competition. Finally, in column (IV) I consider an in…nite merger cost, which drives the number of acquisitions to 0. In the absence of acquisitions, green…eld entry increases by 14.4%. The results con…rm part of the …ndings in the previous counterfactuals. Average maximum TFP decreased signi…cantly, but marginal costs did not change signi…cantly. Therefore, the new technology of the green…eld plants compensated for the lower e¢ cient reallocation of productivity across the markets. Because of no entry by acquisition and lower production, consumers are heavily penalized. Consumer surplus decreases from 5.35 to 3.5 billion dollars and production decreases from 373.8 to 289.5 million short tons. These are the largest decreases among all three counterfactuals considered. If acquisitions are completely eliminated, the e¤ects are strongly negative. It is also interesting to see that pro…ts dramatically decrease, suggesting that, during the Reagan-Bush administration, entrants by acquisition were obtaining a large share of the pro…ts in the market.
27
In summary, these results are mainly driven by two opposing e¤ects. A policy that makes entry by acquisition more expensive reduces the transfer of assets from less-e¢ cient incumbents to more-e¢ cient entrants. This negatively impacts prices and the costs of production. On the other hand, such a policy encourages green…eld entry of plants with state-of-the-art technology, which increases competition, expands production, reduces marginal costs and decreases prices in the market. The combination of these two e¤ects explains the results obtained.
8
Conclusion
In this article, I propose an empirically tractable model that endogenizes the mode of entry in a concentrated industry. The model takes into account that, after an acquisition, there is a transfer of the buyer …rm-level characteristics to the acquired plants, a¤ecting the pro…ts that can be extracted from the acquired assets. This, in turn, a¤ects the cost of entering by acquisition. The results show signi…cant variation in the entry costs to both modes of entry over the years, an important demand gap by green…eld entrants, and the relevant e¤ect of TFP and energy prices on variable costs. Second, I show that eliminating policies that facilitate entry by acquisition has non-trivial e¤ects on the economy in terms of new investment, productivity, marginal costs, consumer surplus or number of green…eld entrants. More interestingly, I show that policies that favor entry by acquisition can have more-positive e¤ects than equivalent policies that a¤ect green…eld entry. These results show that it is important to consider the di¤erent modes of entry when analyzing …rm expansion. Substitution e¤ects exist, arising from policies that a¤ect a speci…c type of expansion, and this has implications for key economic variables and for the welfare of the economy. Therefore, to understand fully what drives market entry decisions and its consequences, it is necessary to take into account the di¤erent strategic choices that …rms have to expand into new markets, and the factors that a¤ect pro…ts in every mode of entry. Regulators should be particularly concerned about policies that negatively a¤ect the e¢ cient reallocation of assets between incumbents and entrants.
28
References Adams, W. and Brock, J.: 1988, Reaganomics and the transmogri…cation of merger policy, Antitrust Bulletin 33, 309. Bajari, P., Hong, H. and Ryan, S.: 2010, Identi…cation and Estimation of a Discrete Game of Complete Information, Econometrica 78(5), 1529–1568. Baldwin, J. and Gorecki, P.: 1987, Plant creation versus plant acquisition: The entry process in Canadian manufacturing, International Journal of Industrial Organization 5(1), 27–41. Baldwin, W.: 1990, E¢ ciency and competition: The Reagan administration’s legacy in merger policy, Review of Industrial Organization 5(2), 159–174. Berry, S.: 1992, Estimation of a Model of Entry in the Airline Industry, Econometrica 60(4), 889–917. Berry, S. and Waldfogel, J.: 1999, Free Entry and Social Ine¢ ciency in Radio Broadcasting, RAND Journal of Economics 30, 397–420. Bianchi, P.: 1982, Public and private control in mass product industry, Kluwer Academic Pub. Bresnahan, T. and Reiss, P.: 1991, Empirical Models of Discrete Games, Journal of Econometrics 48(12), 57–81. Caves, R. E. and Mehra, S. K.: 1986, Entry of foreign multinationals into US manufacturing industries, in M. E. Porter (ed.), Competition in Global Industries, Harvard Business School Press, pp. 449–481. Ciliberto, F. and Tamer, E.: 2009, Market structure and multiple equilibria in airline markets, Econometrica 77(6), 1791–1828. Coase, R. H.: 1937, The nature of the …rm, Economica 4(16), 386–405. Das, S.: 1992, A micro-econometric model of capital utilization and retirement: the case of the US cement industry, Review of Economic Studies 59(2), 277–297. Ellickson, P. B. and Misra, S.: 2012, Enriching interactions: Incorporating outcome data into static discrete games, Quantitative Marketing and Economics 10(1), 1–26. Ericson, R. and Pakes, A.: 1995, Markov-Perfect Industry Dynamics: A Framework for Empirical Work, Review of Economic Studies 62, 53–53. Foster, L., Haltiwanger, J. and Syverson, C.: 2013, The Slow Growth of New Plants: Learning about Demand, working paper, University of Chicago, Booth School of Business. FTC: 1966, Economic Report on Mergers and Vertical Integration in the Cement Industry, Federal Trade Commission. Gentzkow, M. and Shapiro, J.: 2014, Measuring the sensitivity of parameter estimates to sample statistics, Unpublished Manuscript . Gilbert, R. and Newbery, D.: 1992, Alternative Entry Paths: The Build Or Buy Decision, Journal of Economics & Management Strategy 1(1), 129–150. Gowrisankaran, G.: 1999, A Dynamic Model of Endogenous Horizontal Mergers, RAND Journal of Economics 30, 56–83. Hines, H. H.: 1957, E¤ectiveness of "entry" by already established …rms, Quarterly Journal of Economics 71(1), 132–150. 29
Hortacsu, A. and Syverson, C.: 2007, Cementing Relationships: Vertical Integration, Foreclosure, Productivity, and Prices, Journal of Political Economy 115(2), 250–301. Jovanovic, B. and Braguinsky, S.: 2004, Bidder discounts and target premia in takeovers, American Economic Review 94(1), 46–56. Judd, K.: 1998, Numerical Methods in Economics, MIT Press. Krattenmaker, T. and Pitofsky, R.: 1988, Antitrust merger policy and the Reagan administration, Antitrust Bulletin 33, 211. Mabry, J.: 1998, The U.S. Portland Cement Industry, PhD thesis, Columbia University. Maksimovic, V. and Phillips, G.: 2001, The Market for Corporate Assets: Who Engages in Mergers and Asset Sales and Are There E¢ ciency Gains?, Journal of Finance 56(6), 2019–2065. Mazzeo, M.: 2002, Product Choice and Oligopoly Market Structure, RAND Journal of Economics 33(2), 221–242. McCardle, K. F. and Viswanathan, S.: 1994, The direct entry versus takeover decision and stock price performance around takeovers, Journal of Business 67(1), 1–43. McFadden, D.: 1989, A method of simulated moments for estimation of discrete response models without numerical integration, Econometrica 57(5), 995–1026. McKelvey, R. D. and McLennan, A.: 1997, The maximal number of regular totally mixed Nash equilibria, Journal of Economic Theory 72(2), 411–425. Miller, N. H. and Osborne, M.: 2014, Spatial di¤erentiation and price discrimination in the cement industry: evidence from a structural model, RAND Journal of Economics 45(2), 221–247. Mueller, W.: 1986, A new attack on antitrust: The Chicago case, Antitrust Law and Economics Review 18(1), 29–66. Nishida, M.: 2014, Estimating a model of strategic network choice: the convenience-store industry in Okinawa, working paper, Johns Hopkins Carey Business School. Nocke, V. and Yeaple, S.: 2007, Cross-border mergers and acquisitions vs. green…eld foreign direct investment: The role of …rm heterogeneity, Journal of International Economics 72(2), 336–365. Ryan, S.: 2012, The costs of environmental regulation in a concentrated industry, Econometrica 80(3), 1019–1061. Schoar, A.: 2002, E¤ects of Corporate Diversi…cation on Productivity, Journal of Finance 57(6), 2379– 2403. Seim, K.: 2006, An empirical model of …rm entry with endogenous product-type choices, RAND Journal of Economics 37(3), 619–640. Syverson, C.: 2004, Market Structure and Productivity: A Concrete Example, Journal of Political Economy 112(6), 1181–1222. Train, K.: 2003, Discrete Choice Methods with Simulation, Cambridge University Press.
30
Appendices Appendix A A.1
Some variables used from the CM database
New plants built and acquired plants
To study green…eld entry and closings of plants, I use the Permanent Plant Number (PPN) from the CM database, which is a variable created by the U.S. Census Bureau speci…cally designed to link plants longitudinally and to accurately determine exits and entries of new plants in the market. Unlike other variables, such as the Census File Number, which is a plant identi…er in the CM database that may change from census year to census year, the PPN is supposed to remain constant during the entire life of the plant. Using this variable, I de…ne plant openings and closings as follows:
A new plant is opened in census year T if it has a PPN that did not exist in the CM in census year T
1.26
A plant with a PPN in census year T
1 is closed in census year T if the PPN does not exist any
more in the CM in census year T .
In measuring changes of ownership, I use the variable F IRM ID, which identi…es common ownership of plants. Using this variable, I de…ne changes of plant ownership as follows: a plant changes ownership in census year T if it has a di¤erent F IRM ID in census year T
A.2
1.
Calculation of plant-level productivity values
I use the accounting method of Syverson (2004), also used in Hortacsu and Syverson (2007). They measure productivity using a standard TFP index. Plant-level TFP for every plant census year, T F Pit ; is computed as the log of the physical output minus a weighted sum of the log values of labor, capital, materials and energy inputs: T F Pit = qit
lt lit
kt kit
26
mt mit
et rit ;
There are special cases where plants receive a new PPN even if they are not entirely new constructions. This is the case for plants that undergo a major renovation, typically after being closed for several years. From the CM data, I cannot determine whether a plant is new or fully renovated, but, in many cases, the magnitude of the renovations makes the plant virtually brand new.
31
where the weights
represent input elasticities that are industry-speci…c.
Syverson (2004) uses
industry-speci…c cost shares as the measure of the input elasticities. These cost shares are computed from the industry-level labor, materials and energy expenditures reported in the CM database. The plant-level quantities of the …nal product qit and the corresponding number of production hours are available in the CM database. The quantity of materials and energy used (mit and rit ) are obtained by dividing the reported expenditures on materials and energy by their respective industry-level de‡ators from the NBER Productivity Database. Finally, the most problematic step is the measure of capital. Syverson (2004) uses reported book values of buildings and machinery, and de‡ates them by the book-real value ratio for the corresponding three-digit industry (obtained from published U.S. Bureau of Economic Analysis data).
32
Appendix B
The U.S. cement industry (1963-2002): Patterns of …rm expansion Table 8: Changes in TFP level and in relative TFP level
Change of ownership Year dummies
TFP level (1) (2) 0.150*** 0.044 (0.049) (0.050) No Yes
Market dummies
No
No
Changes in Relative TFP level (1) (2) (3) 0.0141* 0.0213** 0.0228** (0.0081) (0.010) (0.0107) No Yes Yes No
No
Yes
Notes: OLS regression. We consider two cases. In the …rst case we regress changes of plant-level TFP (with respect to the previous census year) on plant changes of ownership. In the second case we regress relative change of plant-level TFP (relative to the average TFP level in the country, change with respect to the previous census year) on plant changes of ownership. Standard errors in parentheses. *, **, and *** denote signi…cance at the 90%, 95%, and 99% con…dence levels, respectively. Source: Census of Manufactures.
Table 9: Changes in TFP level between buyers and sellers Change of TFP Di¤erence TFP buyer-seller Year dummies
(1) 0.3515*** (0.1044) No
(2) 0.3639*** (0.1359) Yes
Notes: OLS regression of changes of TFP levels on TFP di¤erences between buyers and sellers. (1): No dummies. Change of TFP: Change of plant-level TFP of the acquired plant in the year of the acquisition (with respect to the previous census year). Di¤erence TFP buyer-seller: Di¤erence between TFP of buyer …rm and TFP of the acquired plant in the census year before the acquisition. Standard errors in parentheses. *, **, and *** denote signi…cance at the 90%, 95%, and 99% con…dence levels, respectively. Source: Census of Manufactures.
Table 10: Construction of new plants Construction of new plant Construction activity Years 1992-1997
Probit coe¢ cient 0.0284*** (0.0069) -0.372*** (0.135)
Marginal e¤ect 0.00496*** (0.00121) -0.0650*** (0.0244)
Notes: Probit regression. Construction activity in billions of U.S. dollars. Standard errors in parentheses. *, **, and *** denote signi…cance at the 90%, 95%, and 99% con…dence levels, respectively. Source: Census of Manufactures.
33
Appendix C C.1
Proofs
Cournot competition with linear di¤erentiated demand and heterogeneous …rms
I show the interior solution to the Cournot problem with linear di¤erentiated demand and n heterogeneous …rms present in the market. From the …rst-order conditions, using standard algebra, I obtain the optimum prices and quantities:
Pj = Aj
1(
2
1
+ (1
n)
2)
M Cj (
2 )(
1
2
1
+ (1
n)
2)
n P
1 2
n P
Ai
i=1
(
2
and Qj =
(Aj
M Cj )( 2 (
2
1 )(
2
1
+ (1
n)
2)
P + (1 n) 2 ) + 2 ( ni=1 Ai 2 1 )( 2 1 + (1 n) 2 ) 2
Pn
i=1 M Ci )
1
M Ci
i=1
;
:
(22)
(23)
Using (22) and (23), variable pro…ts are:
( j
C.2
(Pj
1 ) (Aj
M Cj )( 2
M Cj )Qj =
(
2
2
1 + (1 2 1) (
n) 2
1
2) +
+ (1
2
n)
n P
Ai
i=1 2
n P
2
M Ci
i=1
2)
:
(24)
Proof of Proposition 1
For every incumbent j, the variable pro…ts of every entrant i when they buy any incumbent can be calculated from the Cournot equilibrium, and ranked. I denote by
j i1
and
j i2
the highest and second-
highest valuation (i.e., variable pro…ts) of incumbent plant j among all …rms in the market. Firms i1 and i2 are the …rms with the highest valuation. Note that incumbent j is also considered, so i1 = j in case incumbent j has the highest valuation among all …rms. I also assume that in the case of ties in bids, the winner is the …rm with the highest valuation. First, I show that bids bi1 ;j =
i j2
j i2
and bi;j
for any i 6= i1 (with equality if i = i2 ) are an equilibrium.
Note that the total payo¤ of the winner …rm (without considering the cost F M ) is
j i1
j i2
> 0 (with
strict inequality because there cannot be identical valuations, since the error terms are random variables drawn from continuous distributions), and the payo¤s of all other entrants are 0. The winner …rm i1 does 0
not increase payo¤s by setting a higher bid bi1 ;j > bi1 ;j because 34
j i1
0
bi1;j <
j i1
bi1;j . And if …rm i1 sets
0
bi1 ;j <
j i2 ,
it does not buy the incumbent and makes 0. Also, …rm i2 does not pro…tably deviate by setting
a lower bid (it still makes 0), or a higher bid (it makes zero or negative pro…ts). Second, I show that this outcome is unique. Considering only …rms i1 and i2 , it is easy to show that there cannot be equilibria where increase pro…ts. Also,
j i2
j i2
< bi2 ;j < bi1 ;j and bi2 ;j <
j i1 ,
because …rm i1 can set bi1 ;j = bi2 ;j and
< bi1 ;j < bi2 ;j cannot be an equilibrium because …rm i2 makes negative pro…ts
and can make 0 by decreasing the bid. Moreover, any situation in which bi1 ;j < bi2 ;j <
j i2
cannot be an
equilibrium, because i1 can pro…tably deviate by setting bi1 ;j = bi2 ;j . Similar arguments apply to equilibria where bi2 ;j
bi1 ;j <
j i2 .
The arguments are easily extended for the case of other …rms apart from i1 and
i2 . Finally, these arguments can be extended to every incumbent acquired. Although the Cournot variablepro…ts equation shows that the acquisitions of other incumbents a¤ect the pro…tability of every entrant that is buying an incumbent, the rank of valuations within entrants bidding for the same incumbent is not a¤ected. Therefore, the same previous arguments can be applied and the same outcome obtained independently for every incumbent. These equilibrium outcomes do not depend on the sunk cost F M paid by all entrants by acquisition before they bid. The total acquisition cost CA is equal to bi1 ;j + F M .
C.3
Proof of Proposition 2
First, if more market entrants than incumbents choose to enter by acquisition, then at least one of the entrants cannot buy an incumbent. The …rm that does not buy an incumbent plant can pro…tably deviate by choosing not to enter the market, thereby making a pro…t of 0 instead of
FM.
Second, using a similar argument, there cannot be equilibria where one of the entrants by acquisition does not buy any incumbent. In that case, that entrant is better o¤ not entering into the market. Finally, if there is a Cournot solution that is not interior, it means that one of the entrants has a marginal cost that is too high to make a pro…t in the market, and so it produces zero. But, in that case, it can pro…tably deviate in the …rst stage by not entering into the market (because it can save either the cost F M or the sunk entry cost from entering by green…eld).
35
Appendix D D.1
Computational details
Algorithm to solve for all the equilibria
Assume a market-census year m with a set of E potential entrants and incumbents with certain observed C ; "K g. The algorithm has the following steps: characteristics X and unobserved characteristics f"Ps ; "M s s
Step 1: Select one entry vector e from the set of all possible actions by entrants; i.e, e 2 f0; a; ggE . Step 2: Obtain optimum capital CAP for every green…eld entrant using equation (9). Step 3: For every incumbent i, use characteristics of green…eld entrants and entrants by acquisition and CAP from the previous step to rank variable pro…ts of every entrant if buying incumbent i using equation (24). Identify the …rms ji;1 and ji;2 with the two highest valuations to buy incumbent i. Step 4: Repeat step 3 for every possible incumbent. Then proceed to step 5. Step 5: Generate total payo¤s j of every potential entrant. Given characteristics of all active plants, variable pro…ts for every plant j, j (e) are given by equation (24). The cost of building a new plant is calculated in (8) and uses optimum capital from step 2. The cost of acquiring an incumbent is obtained from Proposition 1. If a …rm buys more than one incumbent plant, total pro…ts j are the sum of pro…ts of the acquired plants. Step 6: Repeat steps 1-5 for every possible entry vector e: Then proceed to step 7. Step 7: Using payo¤s for every action,
j (e),
solve for all equilibria using equations (10) and (11).
By solving this algorithm for every market-census year m and every random draw s = 1; :::; S, I calculate simulated observed entry probabilities and simulated observed outcomes using (16) and (19) to construct the SMM objective function in (12). The algorithm must be repeated for every s and market-census year at every stage of the optimization routine.
D.2
Details of estimation
The estimation procedure is computationally intensive, because for every iteration step in the optimization routine of the objective function, I must solve for all the pure-strategy equilibria in all markets considered. Furthermore, the calculation of the solution to the acquisition game has to be done for every possible vector of strategies e. Also, the entry game has three possible actions to play, as opposed to the two actions considered in the simpler green…eld-only entry models. Therefore, the number of possible pure-strategy equilibria
36
is signi…cantly higher. With nine potential entrants, for example, there are 39 = 19; 683 possible purestrategy equilibria in my model, but only 29 = 512 in a green…eld-only entry model. If I consider mixed equilibria, these numbers increase exponentially. For example, according to McKelvey and McLennan (1997), the maximum number of totally mixed equilibria in a game with nine agents and two actions is 133; 496, whereas it is 1:6 1012 for nine agents and three actions. Given all these di¢ culties, I have greatly reduced the time required to estimate my model by adopting a number of computational strategies. First, I have constrained the calculation of equilibria to the case of pure strategies. This greatly simpli…es the estimation, because calculating mixed equilibria requires solving a system of polynomial equations (see Judd, 1998), whereas pure-strategy equilibria entails satisfying two inequalities. Second, I try to exploit the structure of the game to eliminate all possible sets of actions that cannot be equilibria because they are strictly dominated by other actions (see Proposition 2). Third, I use a reasonable number of potential entrants (…ve potential entrants in each market). Finally, I use Halton draws for the calculation of the simulated probabilities. Halton draws have probed to achieve a greater accuracy than pseudo-random draws with a relatively small number of draws used (see Train, 2003).
D.3
Moments used in the estimation Moments (1) - (7): Probability that a plant is built (1); interaction of moment (1) with the observed capital; interaction of moment (1) with an indicator for the 1990 CAA Amendments; interaction of moment (1) with an indicator for the Reagan years; interactions of moment (1) with a indicators for years 1982, 1987 and 1997. Moments (8) - (13): Probability that a plant is acquired (8); interaction of moment (8) with an indicator for the 1990 CAA Amendments; interaction of moment (8) with an indicator for the Reagan years; interactions of moment (8) with indicators for years 1982, 1987 and 1997. Moments (14) - (24): Marginal cost of a plant (14); interaction of moment (14) with the age of the plant; interaction of moment (14) with a dummy for plant built; interaction of moment (14) with the capital of the plant; interaction of moment (14) with the price of electricity; interaction of moment (14) with the price of fuel; interaction of moment (14) with the wage; interaction of moment (14) with indicator IN SIDER; interaction of moment (14) with the size of the …rm; interaction of moment (14) with T F P ; interaction of moment (14) with a year trend.
37
Moments (25) - (30): Price of a plant (25); interaction of moment (25) with a dummy for plant built; interaction of moment (25) with the construction activity; interaction of moment (25) with construction activity x indicator for plant built; interaction of moment (25) with construction activity x indicator for year 1987; interaction of moment (25) with the year trend. Moments (31) - (36): Quantity produced by a plant (31); interaction of moment (31) with the construction activity; interaction of moment (31) with the price of electricity; interaction of moment (31) with the price of fuel; interaction of moment (31) with the wage; interaction of moment (31) with the year trend. Moments (37) - (40): New capital built (37); interaction of moment (37) with the total number of plants; interaction of moment (37) with …rm size; interaction of moment (37) with TFP.
D.4
Sensitivity of estimates to moments Figure 2: Sensitivity of estimates to moments
Notes: This diagram shows the results of a Monte Carlo experiment to show how sensitive are the estimates to the moments used in the estimation using the "scaled sensitivity" ( e pj ) from Gentzkow and Shapiro (2014). The 30 parameters and the 40 moments have been grouped by category. The lighter the color, the more sensitive is the set of parameters to the set of moments. Average of e pj across parameters and moments is shown in every cell. The Monte Carlo experiment uses 1000 markets with 3 potential entrants and up to 3 incumbents per market.
38
