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1、Electronic copy available at: http:/ A Micro-Econometric Model of a Short Run Cost Function with Unobserved Heterogeneity* David Prentice School of Business La Trobe University, Bundoora, VIC, 3083. March 2000 Phone: 0394791482 Fax: 0394791654 email: d.prenticelatrobe.edu.au * This paper is a revise
2、d version of Chapter Three of my Ph.D. dissertation written at Yale University. I would like to thank my supervisors Steven Berry, Moshe Buchinsky and Joel Waldfogel for their advice and support. This paper has also benefited greatly from comments at various stages by Tom Crossley, Iain Fraser, Tue
3、Grgens, John Kennedy, Lisa Magnani, Gylfi Magnusson, Ariel Pakes and Rabee Tourky. Helpful comments were also received from participants in seminars at La Trobe University, Monash University, University of Melbourne, UNSW, University of Sydney, RSSS-ANU and Yale University. I would also like to than
4、k Tony Salvage for assistance with the diagrams. I am most appreciative to Curtis Betts and the FW Dodge Co. for the use of the construction data. All errors remain my own responsibility. Electronic copy available at: http:/ Summary Unobserved plant level heterogeneity and discrete production proces
5、ses can produce problems for estimation. A structural model of discrete production decisions by heterogeneous plants is constructed and, as a case study, estimated for the U.S. Portland cement industry. A new estimator is proposed to handle the discrete production process for which the ordered probi
6、t is a special case. Data on firm survival and exit are used to adjust all input requirement coefficients for unobserved heterogeneity. The structural model is successfully estimated. Differences between many estimated coefficients and independent estimates from external sources are statistically in
7、significant. 1 1. Introduction The short run cost function plays a key role in estimating market power or predicting input and output decisions. Estimation in the new empirical industrial organization, and elsewhere, typically proceeds by assuming that the common short run marginal cost function is
8、both convex and continuous in either all outputs or, as with hedonic cost functions, in product characteristics. However, recent work suggests models based on these assumptions are not always appropriate for empirical work. One set of papers demonstrates productivity and size varies substantially ac
9、ross plants within industries resulting in divergent responses to common shocks (e.g., Davis and Haltiwanger (1992). Furthermore, not controlling for this heterogeneity results in biased estimation (Olley and Pakes (1996). A second set of papers presents evidence that production is sometimes better
10、characterised as a discrete rather than a continuous choice and that cost functions may be non-convex (e.g., Bresnahan and Ramey (1994). If the cost function is severely misspecified then other results could be compromised. In this paper, I specify a structural model of a plant short run marginal co
11、st function in an industry featuring both plant level heterogeneity and discrete production decisions across multiple units. A new estimator is proposed to handle the discrete production decisions. Furthermore, the model is extended to deal with incomplete information about plant output and unobserv
12、ed cost heterogeneity. In particular, plant exit and survival data is used to control for cost differences across operating plants. The structural model is estimated with a new unusually detailed dataset on the U.S. Portland cement industry. Estimates of some parameters of the cost function are foun
13、d to not differ significantly from independent estimates obtained from trade journals and input consumption data. The model estimated in this paper significantly improves on earlier work in three ways. First, the discrete production decision rule for multiple units is estimated more directly and com
14、pletely than in Bertin, Bresnahan and Raff (1996). Second, input requirement coefficients are adjusted directly for unobservable plant level 2 heterogeneity unlike in Olley and Pakes (1996) and Dionne et al (1998) where the effects of unobservable heterogeneity are introduced a more limited way. Fin
15、ally, the methodology and model improves on earlier work by being implementable with datasets typically available to firms or consultants rather than specialized datasets such as census unit record data. Thus the model and technique are more broadly applicable. So, before applying standard technique
16、s in industry analysis, the importance of plant heterogeneity and discrete production decisions should be checked. Where these conditions are important, the techniques presented in this paper can be applied. The structural model is developed explicity for the U.S. Portland cement industry. This is d
17、one, in part, for clarity. It is important to stress, though, that the model and methodology can be applied to a broad set of industries which feature discrete production processes and multiple production units or plants, including steel and electricity generation. However, the cement industry requi
18、res less simplifying assumptions than typical when econometrically analyzing a manufacturing industry for several reasons. First, cement is essentially homogeneous. Second, it is produced by a relatively simple fixed proportions production process. Third, at least some of the most important sources
19、of plant level heterogeneity are observable and they can be systematically included in both the modelling of the production decision and in the estimation of the short run cost function. Finally, the discrete production choice is a direct implication of the combination of the technology and the natu
20、re of competition in the industry. In the next section, the short run cost function for a plant with multiple heterogeneous production units is derived yielding two discrete decision rules for production and retirement. The data are then introduced in Section 3. In Section 4, the model and data are
21、reconciled and integrated producing a structural model for estimation, with a new estimator, of the short run cost function. Section 5 presents the results and in Section 6 some conclusions are presented. 3 2. The Short Run Cost Function Cement is the powder that is mixed with sand, aggregates and w
22、ater to produce concrete. Most cement is a standard grey Portland cement effectively homogeneous across sellers. The primary use of concrete is in construction so cement consumption varies directly with construction activity. Demand is substantially separable across years because construction, in mo
23、st parts of the United States, is concentrated in the summer and fall. In subsequent subsections, the short run cost function for a cement plant is presented. Though such a function could easily be applied to similar industries. Then it is argued that the plant can be modelled as a price taker. This
24、 section concludes with two decision rules for the cement plant for production and retiring capital. The first decision rule provides the foundation for estimating the short run marginal cost function. The second rule is used to control for unobserved heterogeneity in productivity. 2.1. The Short Ru
25、n Cost Function1 Manufacturing cement is a relatively simple process. Limestone, or a substitute, is quarried and ground into a raw mix. The raw mix is baked in a large kiln, producing small pellets known as clinker. Grinding the clinker and mixing it with gypsum produces cement. Once a kiln is inst
26、alled, the input requirements per ton of cement are substantially fixed (e.g., Frsund and Hjalmarsson (1983); Das (1991a). A kiln typically operates for decades and is then scrapped. The raw (material) grinding mills, the finish (clinker) grinding mills, distribution facilities, and other components
27、 of the cement plant are scaled around the kiln, or bank of kilns. The buildings and grinding mills are also usable for decades. The cost function for the nth of N kilns is derived as follows. Denote, I(Qn 0) as an indictator variable that takes the value 1 if the kiln operates and zero otherwise, v
28、n,p as the vector of the input requirement coefficients for the nth kiln which depend on its vintage, v, and process type, p, wf as the vector of fuel prices, n,p the vector of 4 f f p the input requirement coefficients which do not depend on kiln vintage, wo as a vector of other input prices and f*
29、kn as the kiln specific fixed costs. The kiln cost function is Cw,Qn I Qn 0wvn, p Qn wnon,p Qn f * kn (1) Indexing kilns by vintage and type reflects the emphasis placed on these characteristics in both the engineering and economics literature. There are three types of kilns: wet process, dry proces
30、s, and preheater/precalciner process kilns. Both fuel and electricity requirements vary systematically by process. In particular, the wet process features the highest fuel requirements, then the dry process, and then the preheater/precalciner process kilns. Fuel consumption is also believed to incre
31、ase with the age of the kiln because of embodied technological change and depreciation taking the form of increased input requirements (e.g., Das (1992); Rosenbaum (1994). Hence, fuel coefficients increase with age as follows: v1, p v 2, p v3, p (2) Kiln differences lead not only to variation across
32、 plants but within plants as many plants operate multiple kilns of different vintages.2 Denote Q as plant output. Hence, from equations (1) and (2), the short run marginal cost function is as follows: w wp, Q k f v1,p o 1 wmc # v2,p w , o k Q k 1 1 k2 (3) n 1 n w w , k Q k f v3,p o p i 1 i i 1 i Hen
33、ce marginal cost is a step function. For a plant with three kilns with capacities k1, k2 and k3 plant marginal cost is depicted in Figure 1. Fixed costs are composed of two components: start-up and expected shut down costs, and non-sunk capital costs. Expenditure on the plant and equipment is substa
34、ntially sunk after installation because of the size and immobility of the kilns. 2.2. The Decision Variable of the Plant The traditional view of the cement industry is that the combination of economies of scale with high transportation costs creates within the US a set of regional oligopolies (recen
35、t papers in this tradition include McBride (1983); Koller 5 j n and Weiss (1989); Rosenbaum (1994). However, whether the oligopolies are small enough to support market power is an empirical issue. The decreasing importance of domestic and international transportation costs is likely to have increase
36、d the size of the regional markets and increased the effect of potential competition from outside the markets (e.g. Peck and McGowan (1967); Prentice (1996). Hence, following Das (1992), the cement plant is assumed to be a price taker. The first implication of this assumption is that production and
37、retirement decisions are made independently of decisions made for other kilns within the plant or across plants. Second, the production and retirement decisions simplify to two simple rules (see Das (1991a). Denote as the discount factor, T* as the (endogenous) retirement date, if not retired in the
38、 current period, and SVt the scrap value at time t. The output and retirement decisions can be expressed as follows: k if P w w f 0 Q = n t f ,t vn,p o,t p (4) n,t 0 otherwise. T Retire if Et j t P wf , jvn, p wop f k SVt 0. (5) j t Equation (4) states if price exceeds the average cost of operating
39、the kiln, the kiln operates at full capacity. Otherwise, nothing is produced. The production decision is a discrete choice that depends on price relative to average cost. Similarly, equation (5) states the kiln is retired if the expected present value of its operating is less than the current scrap
40、value. These decision rules correspond to the output and shutdown rules in the continuous production decision case. Furthermore, equation (4) in combination with equation (3) implies an ordering for the use of kilns the Kiln Use Rule. In effect all of the kilns at a plant are ranked and operated in
41、order of their efficiency. As the price of cement rises above the marginal cost of each kiln, that kiln is operated, in addition to all younger kilns at the plant. For a given price, the oldest kiln that is profitable to operate, is referred to as the marginal kiln for that plant. All younger kilns
42、are operated, and all kilns older than the marginal kiln are idled. This is illustrated in Figure 1. With an output price, 6 f P, the first two kilns, with capacities k1 and k2, feature marginal costs below P and are operated at full capacity. Kiln 2 is the marginal kiln. The third kiln, with a marg
43、inal cost greater than P, is not operated. Empirical support for the Kiln Use Rule is provided in Das (1992). After allocating plant output to kilns according to the Kiln Use Rule, most kilns are found to either operate at or near capacity or not at all. The kiln retirement rule, equation (5), impli
44、es older kilns are retired before newer kilns, and wet and dry process kilns are retired before preheater/precalciner kilns. This pattern is generally observed over the sample period. However, there are striking examples of new kilns being closed, and kilns more than 50 years old continuing to opera
45、te. Anomalous plants must feature lower or higher than average marginal costs or kiln fixed costs due to plant specific factors such as the quality of their raw materials. The connection between plant productivity and plant exit has been highlighted in recent work. Griliches and Regev (1995), workin
46、g with a panel of Israeli manufacturers, note plants closing during the sample period have significantly lower labor productivity than other plants. Olley and Pakes (1996) estimate a production function, including an adjustment for unobserved productivity differences based on plant investment, and a
47、chieve significantly better results. In Section 4.4, the kiln retirement rule is used to correct for the unobserved productivity differences across plants. Finally, it is worth noting some further characteristics of the equilibrium underlying this characterisation of the industry. There may seem to
48、be some tension between the assumption of price taking behavior and observed extensive heterogeneity as competition would drive out the more costly equipment and plants. Salter (1966) resolves this tension. With expenditure on capital equipment at least partially sunk, if demand exceeds capacity and price rises above average cost, Ricardian rents will be earned. In Figure 1, the rent earned by the firm on each kiln is equal to RTn P wvn, p wop k f * kn (6) n 7 Unless entrants expect the rents subsequently earned by the ki
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