An Alternative Theory of the Plant Size Distribution, with Geography and Intra- and International Trade. Holmes and Stevens (2012)

Transcription

1 An Alternative Theory of the Plant Size Distribution, with Geography and Intra- and International Trade Holmes and Stevens (2012) Standard Theory of the Within Industry Size Distribution New plants enter an industry and obtain a productivity draw. Plants that get good draws choose to be big. Lucas (1978) This idea has widespread use in international to explain trade facts. Melitz Bernard, Eaton, Jensen Kortum (BEJK)

2 This Paper Observation: Even when we go to narrowly-defined industries, big plants often do not look like homothetic expansions of smaller plants Plants of different size tend to do different functions. (Piore and Sable (1984)) Small plants: Specialty goods, craft production, (custom, retail-like) Large plants: Standardized goods for inventory, mass production

3 Example Industry that gets extra attention Wood Furniture Factories in North Carolina with 1000 plus employees make stock furniture pieces Small craft shops scattered around the country, like Amish furniture shops. NAICS industry classification puts them both in NAICS

4 What We Do Theory of Geography and Trade applied to locations in the U.S. Standardized goods (off-the-shelf BEJK) Specialty goods Estimate the model UseCensusmicrodataontheCommodityFlowData

5 Result 1: Estimate the share of establishment counts in the specialty good segments In most industries, more then half the plants are specialty good plants In most industries, the share is growing. Concerns the plant size/industry concentration re- Result 2: lationship Pure BEJK special case bombs quantitatively (can get this qualitatively) Model with specialty goods segment added fits this Result 3: What happens when imports from China begin flowing into an industry?

6 As an illustration, the impact of China on the wood furniture industry... U.S. industry has collapsed over period Standard model predicts NC share of what is left should rise. Big screwup! Places like High Point, N.C. vs. places like New York.

7 Four Basic Facts about the Within-Industry (6-digit NAICS) Size Distribution 1. Enormous variation in plant size. Variance in ln(emp)=1.55 in overall manufacturing. 82% remains when difference out industry means. 2. Skewed right, large fraction of small plants. Overall average size=46 emp, yet 67% of plants = 20 emp 423 out of 473 industries (90% of emp), at least 26% of plants =20.

8 3. Small plants tend to ship locally Bernard and Jensen (1995) on exports Holmes and Stevens (2012) on domestic shipments 4. Small plants are geograpically diffuse, large plants concentrated Holmes and Stevens (2002). Table

9 Table 1 Mean Location Quotient by Plant Size for Three Groups of Industries Industry Grouping Plant Size Categor y Number of Establishm ents Mean Location Quotient NAICS Fixed Effect Raw All Industries (473 Industries) All 361, , , , ,

10 Model: Locations There are locations indexed by 0 is distance beween and 0.

11 Model: Industry Segments Indexed by Below we group industry segments into Industries. But that is a concern for the Census. Consumers think about industries Utility Cobb-Douglas for composite good of industry segment with spending share. Each industry segment follows the model of BEJK.

12 BEJK Model of Each Industry Segment (drop for now). Segment is a CES composite of continuum of differentiated products [0 ]( variety). locations vary in productivity parameter,wages. Transportation costs: ( ) is iceberg transportation cost of shipping miles Fixed set of potential entrants at each location for product, each gets a productivity draw. First best, second best, drawn from a distribution depending on.

13 Bertrand competition for each customer so most efficient producer at a destination gets the job (at price no more than second most efficient producer s cost) Frechet Distribution assumption yields clean analytical formulae

14 Everything Boils Down To... : cost efficiency index 0 = ( ( 0 ) ) : distance adjustment from to 0. Then the probability that 6= is lowest cost to a particular point at is 0 = 0 P =1 0 This is also the sales share.

15 SalesandPlantCountsAcrosslocations Sales to 0 0 = 0 0. Sales from source across all destinations = X =1. Plant counts at, =

16 for a scaling parameter equal to the ratio of overall variety to goods per plant,. In summary, for each industry segment have: A model of segment sales from each location to each location Amodelofplantcountsateachlocation

17 Industry Industry a set of segments in industry Primary segment ( =1) Speciality segment =2 Assume the following about spending share X =2.

18 Model 1 of Speciality Segment: High Transportation Cost Parameters of speciality the same as primary EXCEPT spending share of transportation cost (and variety) ( ) = 1 ( ), Parameter magnifies transportation cost Introduce internal geography at each location. land area. Let be

19 Result for Model 1 Proposition 1. Suppose holds, and that transportation cost in segment is given by as above for transportation magnification parameter. Assume the remaining parameters for specialty segment are the same as for the primary sector, except for perhaps 6= 1. (i) If variety is weakly higher in the specialty segment, 1, then average plant size (sales revenue per plant) in the specialty segment is smaller than in the primary segment. (ii) Assume that for any arbitrary point ( )inagivencity, mean efficiency ( ) atdistance is continuously differentiable

20 and strictly positive. Consider making large, while rescaling variety in segment according to = ³ 2, for a constant. Then lim = 2 2, (1) where is the measure of plant counts in segment in industry at city.

21 Suppose = 0 1. (have estimate 1 = 7) Yields a relationship between population and plant counts for lim = 1 (2)

22 Model 2 of Speciality Segment: Niche with Idiosyncratic Sources of Supply Assume cost efficiency vector Γ =( 1 2 )forsegment 1 drawn from a distribution satisfying P = 0 0 P 0 0. (3) Suppose speciality segments in an industry, each has spending share given by =. Suppose for a given, variety in segment is equal to =.

23 Proposition 2. Assume transportation cost is zero for specialty segments, i.e., ( ) = 1, all 0, 2. Suppose for each 1, Γ is drawn i.i.d. across from a distribution satisfying (3). (i) If transportation cost in the primary segment is also zero, and if there are fewer primary segment varieties than the overall specialty segment total, 1, then average plant size of specialty plants is smaller than primary plants. (ii) If the number of specialty segments is large, plant counts for specialty goods as a whole approximately equal (4) for 1 P 0 0.

24 Data 1997 Census of Manufactures (CM): Plant level data of the universe of plants (sales, location, etc.) 1997 Commodity Flow Survey (CFS): Sample of Shipments from a sample of (15,000) plants origin and destination and link to CM after conditioning on industry and distance, we use 500,000 observations for structural estimates

25 Data Selections Industry defined at 6-digit NAICS level (North American Industry Classification System). Pick 172 (out of 473) industries where demand approximately follows population is population share Locations defined at level of Bureau of Economic Analysis Economic Area =177 Based on MSAs, except rural counties get included in the partition

26 Seven Industries that Get Extra Attention 1997 changed from SIC to NAICS, a production based system. Plants using the same production technology grouped inthesameindustry SIC system did this sometimes (sugar from beets and from cane different industries) missed other times, some chocolate factories, wood furniture stores, etc. placed in retail under SIC 1997 micro data, for these seven industries for each plant have NAICS and SIC. Use this to classify plants as R or M depending on SIC. Take R as a proxy for speciality.

27 NAICS Industry Classification Table 2 Descriptive Statistics for the 1997 Reclassification Industries by R and M Status Classification Based on SIC Number of Plants Mean Plant Employ. Export Share Mean Location Quotient Chocolate Candy R (NAICS ) M Nonchocolate Candy R (NAICS ) M Kitchen Cabinets R 2, (NAICS ) M 5, Upholstered Household Furniture R (NAICS ) M 1, Wood Household Furniture R (NAICS ) M 3,

28 Quantitative Analysis Model of distance adjustment for, ln 0 = loglog ln 0 which yields a constant distance elasticity loglog. The second is a semi-log specification, ln 0 = semi,1 0 semi,2 ( 0 )2, First-stage estimates: Constrained model with only primary segment (one segment model) Pick and Γ =( )to: fit sales distribution across locations perfectly (have the universe). Use iterative procedure to back out Γ.

29 maximize conditional likelihood of the destinations in the shipment sample conditioned on 100 for shipments

30 Table 4 First Stage Results for the Seven Reclassification Industries Reclassification Industries LogLog Case Constant Elasticity Semi- Log Case Elasticity 100 miles Semi- Log Case Elasticity 500 miles LogLog Case LogLike Semi- Log Case LogLike Number of Shipment Obs. Chocolate Candy (311330) ,633 Nonchocolate Candy (311340) Curtains(314121) Other Apparel (315999) Kitchen Cabinets (337110) Upholstered Household Furn.(337121) Wood Household Furn.(337122) , , , , , ,624

31 Table 5 Summary Statistics for First Stage Results Sample of Industries Full Sample (466 Industries) LogLog Case Constan t Elasticit y Semi- Log Case Elasticit y 100 miles Semi- Log Case Elasticit y 500 miles Mean th Percentile 50 th Percentile 75 th Percentile Mean Diffuse Demand (172 Industries) Mean Non- Diffuse Demand (294 Industries)

32 Stage 2: Estimate plant count model Baseline estimates, take limit where sales revenue share of specialty is zero. So and Γ same as for one segment model of just primary segment. Specialty segment still factors into plant counts. Pick and to fit = (Γ )+ + +, (5) Also consider an alternative where make assumptions on size of speciality plants and difference them out of sales, with little difference in results.

33 Source: See Table 6 Second-Stage Estimates of the Plant Count Parameters and Related Model and Data Statistics Constant ξ Reclassification Industries Chocolate Candy (311330).4 (.2) Nonchocolate Candy (311340).1 (.1) Regression Results (s.e. in Parentheses) Slope Slope Speciality Primary λ S λ P (52.3) (31.2) 76.6 (13.0) 62.6 (7.9) R 2 Estimated Specialty Count Share (Percent) Curtains(314121) -.9 (.3) Other Apparel (315999) -1.8 (.4) Kitchen Cabinets 1.5 (337110) (1.2) (56.4) (110.8) (230.5) 20.9 (8.1) (20.4) (21.5) Upholstered Household Furn. (337121) -1.3 (.5) (94.7) (8.6)

34 Wood Household Furn.(337122) -1.1 (.8) (138.9) (24.7) Mean Reclass. Industries (N=7) All Industries (N=466) Mean Minimum th Percentile th Percentile th Percentile th Percentile th Percentile Maximum Mean Diffuse Demand Industries (N=172) Mean Non-Diffuse Demand Industries (N=294) Source: See Supplementary Web Appendix

35 Plan Compare Estimated industry model with only primary segment Estimated industry modwl with specialty segment Examine plant size/geographic concentration relationship Examine effect of China surge

36 Table 7 Sales, Count and Size Quotients in Data, Size Quotients for Two Models in High Concentration Industry/Locations Data Primary Only Revenue Model BEA Economic Area Share Q rev Q count Q size Q size Full Model Industry Q size Chocolate Candy Harrisburg, PA Nashville, TN (NAICS ) Chicago, IL Philadelphia, PA San Francisco, CA Kitchen Cabinets Harrisburg, PA (NAICS ) Wood Household Furn. (NAICS ) Dallas, TX High Point, NC Charlotte, NC Toledo, OH

37 Summary Statistics Reclass.Industries (N=7 Industries) All Industries (N = 466 Industries) Diffuse Demand Industries N = 23 Industry/Locations Mean Median N=1708 Industry/Locations Mean Median N=589 Industry/Locations Mean Median (N = 172 Industries) Non-Diffuse N=1119 Demand Industry/Locations Industries Mean (N = 294 Median Industries) Source: See Supplementary Web Appendix

38 Modeling China Surge Baseline: distribute imports across ports. Model growth in imports from China as a new source of supply. Solve for to match change in imports P 0 =1 0 0 P 0 =1 0 0 = + P 0 =1 0 0 (6) We calculate by taking the weighted average of (6) across all destinations. We start by plugging in the estimated domestic cost-efficiency parameters 0 for 1997 into (6).

39 Next let =ˆ, where is the share in the 2007 data of manufacturing imports from China going through customs at location. We solve for the scaler ˆ so that the implied value of equals the China new-import share for industry. Stochastic transition of cost efficiency. To explicitly take into account this force, we employ the following procedure. We start with those 88 industries in the bottom category of Table 8forwhichthenewChinashareiszero. Wetakemakea grid of the cost efficiencies in 1997 and 2007 and estimate a stochastic transition process for the cost efficiencies over the grid. We then assume the same transition matrix applies for the other industries, and run 10,000 different simulations, taking averages over simulations for each location and industry.

40 Table 8 Summary Statistics for 6-Digit NAICS Industries Classified by New China Share Category Count of Industries Mean of New China Share Mean of New All- Country Share Mean Industry Employment Growth (percent) All Industries By New China Share Category (percent) 50 to to to to >0 to None * * There are 12 industries in which the new China share is negative. In all of these cases, the value is negligible. (The minimum is and the mean is ) For these cases we truncate the new China share at zero. Analogously, we truncate the new all-country share at zero. There are 465 industries in this table rather than 466, because NAICS , Laboratory apparatus & furniture mfg had no data for 2007 because the industry was discontinued and the plants were reassigned to other industries.

41 Table 9 Cell Counts by Plant Size in 1997 and 2007 For the United States as a Whole and at the Primary Location of An Industry For Wood Furniture and for the 46 Industries with New China Share above 25 Percent Panel A: Wood Furniture Industry Plant Size Cell Counts in United States Plant Size Cell Counts in Primary Location (High Point) Employment Size Class All Plants 3,835 3, to 19 3,091 3, to to to to to ,000 and above Panel B: All 46 Industries with New China Share Above 25 Percent

42 Plant Size Cell Counts in United States Plant Size Cell Counts in Primary Location Employment Size Class All Plants 24,192 16,534 1, to 19 16,258 12,674 1, to 49 3,300 1, to 99 1, to 249 1, to to ,000 and above Source: The cell counts are based on public tabulations from the Census discussed in Appendix B. The High Point, NC Area consists of the BEA Economic Area containing High Point, NC (consisting of 22 counties). For each industry, the Primary Location is the Economic Area with the highest sales revenue location quotient, among locations with at least 5 percent of U.S. sales.

43 Table 10 Actual Values in Data for High Concentration Industry/Cities Size and Count Quotients and Change in Count Quotients Means Across New China Share Categories Number of High Concen. Industry/ Cities Q size 1997 Q count 1997 Q count 2007 Percent Change in Count Shares All By New China Share Category (percent) 50 to to to to >0 to None Source: See Supplementary Web Appendix

44 Table 11 Predicted Values of Various Models for High-Concentration Industry/Cities Percent Change in Count Shares Between 1997 and 2007 Means Across New China Share Categories By New China Share Category (percent) Number of High Concen. Industry/ Cities Primary-Only- Segment Model China Only RTM Only China +RTM China Only RTM Only Full Model China +RTM China +RTM Population 50 to to to to >0 to None Source: See Supplementary Web Appendix

45 Table 12 Estimated Primary Segment Plant Count Share for 1997 and 2007 By New China Share Categories New China Share Category (percent) Total Establishment Count (1,000 plants) Estimated Primary Segment Count Share (percent) Change in Percent Primary to to to to >0 to None Source: See Supplementary Web Appendix