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Skill complementarity in production technology: New empirical evidence and implications

  • Andrey Stoyanov and Nick Zubanov ORCID logo EMAIL logo
Published/Copyright: October 15, 2021
German Economic Review
From the journal German Economic Review Volume 23 Issue 2

Abstract

Danish manufacturing firm data reveal that 1) industries differ in within-firm worker skill (= wage) dispersion, and 2) within-firm skill dispersion positively correlates with firm productivity in industries with higher average skill dispersion. We argue that these patterns reflect technological differences between industries: firms in the “skill complementarity” industries profit from hiring similarly able workers, while the “skill substitutability” firms thrive on skill differences. Our study produces a robust, data-driven and theoretically validated classification of industries into the complementarity and substitutability groups, unveils hitherto unnoticed technological heterogeneity between industries within the same economy, and illustrates its importance through simulations.

Keywords: skill dispersion; complementarity; production technology; firm productivity
Appendix A

A.1 The model behind simulations in Section 4.4

Consider an economy with two perfectly competitive industry sectors, indexed by i = 1 , 2, with linear demand functions:

(10) Q i = a i − b i p i

where Q i is the quantity of good i consumed, and a i > 0 and b i > 0 are the demand function parameters.

The output Y i in each sector is produced by combining two types of labor, A and B, using a production technology similar to that specified in equations (2) and (3) in the main text:

(11) Y i = L i L ˆ i

where L i = L i A + L i B is the total employment in sector i, L i k is the amount of type-k labor used in sector i, L ˆ i = θ i A s A ρ i + θ i B s B ρ i 1 ρ i is the labor efficiency term, θ i k = L i k L i is the share of type-k labor in total employment, ρ i is the parameter that captures the degree of complementarity between the two types of labor in sector i, and s k > 0 are the type-specific labor productivity parameters. Note that the total factor productivity in each sector is fixed to one, so that industries differ only in the degree of complementarity between the two types of labor, captured by parameters ρ i , and in the demand conditions, a i , b i . Each type of labor is supplied inelastically: there are L ‾ A and L ‾ B units of each type, and full employment.

Firms within each sector are symmetric. Given the production technologies defined above, firm j operating in industry i chooses the level of employment for each type of labor in order to maximize its profit function

π i j = p i Y i − w A L i j A − w B L i j B

where p i is the market price of a good produced by sector i, and w k is the wage rate earned by workers of type k.

Taking the first-order conditions of the profit function with respect to L i j A and L i j B and summing across all firms within an industry, we obtain the demand functions for each type of labor in each sector:

(12) p i Y i L i 1 + θ i n 1 ρ i L i L ˆ i s k ρ i − s n ρ i = w k , n ≠ k

The marginal production costs in sector i are then equal to

(13) m c i = w A L i A + w B L i B Y i

The equilibrium in this simple model is defined as a set of resource allocations L i k , market prices p i , wages for each type of labor w k , output levels by sector Y i , and consumption of each good Q i such that, given production technologies and market demand functions:

  1. the labor markets clear

    (14) L 1 A + L 2 A = L ‾ A L 1 B + L 2 B = L ‾ B ,

  2. the goods markets clear

    (15) Y i = Q i ,

  3. firms maximize profits

    (16) p i = m c i .

Equilibrium conditions (10), (12), (14), (16), and (15) provide a system of twelve equations with twelve unknowns, p i , w k , Y i , Q i , L i A , L i B .

A.2 Additional figures and tables

Figure A1

Figure 3 replicated for different measures of skill complementarity.

Figure A2

Figure 3 replicated for different measures of within-firm skill dispersion.

Figure A3

Figure 3 replicated for the unrestricted version of equation (6).

Table A1

Estimation results by specification from unconstrained specification.

Measure of skill complementarity Measure of skill dispersion ρ H ρ L p-value for ρ H = ρ L Shares of industries with skill substitutability in the total
Output Employment # of firms
Panel A: estimation results for NLLS
PCA skill1 8.26 −0.45 0.00 0.728 0.700 0.678
skill2 2.30 −5.21 0.00 0.728 0.700 0.678
skill3 1.93 −2.24 0.02 0.728 0.700 0.678
skill4 2.06 −0.97 0.17 0.728 0.700 0.678
Impact skill1 3.99 −2.54 0.00 0.221 0.172 0.107
skill2 9.16 −8.39 0.00 0.221 0.172 0.107
skill3 6.88 −2.42 0.00 0.221 0.172 0.107
skill4 7.01 −3.20 0.00 0.221 0.172 0.107
Teamwork skill1 8.71 −0.78 0.00 0.754 0.739 0.731
skill2 8.88 −5.47 0.00 0.754 0.739 0.731
skill3 11.21 −2.20 0.00 0.754 0.739 0.731
skill4 5.52 −0.97 0.00 0.754 0.739 0.731
Contact skill1 6.52 −0.74 0.00 0.508 0.549 0.581
skill2 14.96 −5.36 0.00 0.508 0.549 0.581
skill3 9.37 −2.30 0.00 0.508 0.549 0.581
skill4 9.82 −3.13 0.00 0.508 0.549 0.581
Communication skill1 3.79 −2.63 0.00 0.204 0.151 0.090
skill2 8.57 −8.08 0.00 0.204 0.151 0.090
skill3 6.42 −2.39 0.00 0.204 0.151 0.090
skill4 6.63 −3.08 0.00 0.204 0.151 0.090
Panel B: estimation results for NLLS with control function
PCA skill1 1.39 −0.43 0.00 0.491 0.405 0.285
skill2 1.85 −5.77 0.00 0.491 0.405 0.285
skill3 1.59 −1.99 0.07 0.491 0.405 0.285
skill4 1.22 −2.64 0.04 0.491 0.405 0.285
Impact skill1 1.39 0.19 0.33 0.367 0.260 0.155
skill2 1.87 −4.50 0.00 0.367 0.260 0.155
skill3 1.50 −1.63 0.03 0.367 0.260 0.155
skill4 1.20 −2.41 0.08 0.367 0.260 0.155
Teamwork skill1 1.97 0.12 0.11 0.754 0.739 0.731
skill2 4.08 −3.45 0.00 0.754 0.739 0.731
skill3 3.12 −1.44 0.00 0.754 0.739 0.731
skill4 2.74 −0.56 0.00 0.754 0.739 0.731
Contact skill1 1.44 0.18 0.06 0.723 0.694 0.671
skill2 2.78 −3.58 0.00 0.723 0.694 0.671
skill3 2.03 −1.71 0.00 0.723 0.694 0.671
skill4 1.75 −0.75 0.09 0.723 0.694 0.671
Communication skill1 1.55 −0.58 0.06 0.204 0.151 0.090
skill2 2.57 −5.50 0.00 0.204 0.151 0.090
skill3 1.88 −1.75 0.00 0.204 0.151 0.090
skill4 1.55 −2.52 0.00 0.204 0.151 0.090

  1. Notes: Each line in the table presents the threshold regression estimation results for different measures of complementarity, skill dispersion, and econometric estimators. The first column describes the measure of skill complementarity used in the estimation, with PCA standing for the aggregate measure obtained by grouping all four measures into one using a principal component analysis (PCA). The second column describes the measure of skill dispersion: skill1 is measured as worker fixed effect from log wage equation; skill2 is worker fixed effects and observables (net of occupation effects) from log wage equation; skill3 is log wage net of firm fixed effect from log wage equation; skill4 is the log wage. The p-value for the test of ρ H = ρ L is obtained through bootstrap using 100 repetitions.

Table A2

Skill complementarity index by industry.

3-digit NACE industry code Industry name Skill complementarity index = frequency of being in the complementarity group
241 Manufacture of basic chemicals 1
242 Manufacture of pesticides and other agro-chemical products 1
243 Manufacture of paints, varnishes and similar coatings, printing ink and mastics 1
244 Manufacture of pharmaceuticals, medicinal chemicals and botanical products 1
246 Manufacture of other chemical products 1
247 Manufacture of man-made fibres 1
300 Manufacture of office machinery and computers 1
332 Manufacture of instruments and appliances for measuring, checking, testing, navigating and other purposes, except industrial process control equipment 1
245 Manufacture of soap and detergents, cleaning and polishing preparations, perfumes and toilet preparations 0.9
297 Manufacture of domestic appliances n.e.c. 0.9
311 Manufacture of electric motors, generators and transformers 0.9
312 Manufacture of electricity distribution and control apparatus 0.9
316 Manufacture of electrical equipment n.e.c. 0.9
313 Manufacture of insulated wire and cable 0.875
314 Manufacture of accumulators, primary cells and primary batteries 0.875
315 Manufacture of lighting equipment and electric lamps 0.8
351 Building and repairing of ships and boats 0.8
266 Manufacture of articles of concrete, plaster and cement 0.7
267 Cutting, shaping and finishing of stone 0.7
268 Manufacture of other non-metallic mineral products 0.7
271 Manufacture of basic iron and steel and of ferro-alloys 0.7
272 Manufacture of tubes 0.7
273 Other first processing of iron and steel 0.7
274 Manufacture of basic precious and non-ferrous metals 0.7
275 Casting of metals 0.7
291 Manufacture of machinery for the production and use of mechanical power, except aircraft, vehicle and cycle engines 0.6
293 Manufacture of agricultural and forestry machinery 0.6
294 Manufacture of machine-tools 0.6
295 Manufacture of other special purpose machinery 0.6
331 Manufacture of medical and surgical equipment and orthopaedic appliances 0.6
152 Processing and preserving of fish and fish products 0.575
153 Processing and preserving of fruit and vegetables 0.575
154 Manufacture of vegetable and animal oils and fats 0.575
155 Manufacture of dairy products 0.575
156 Manufacture of grain mill products, starches and starch products 0.575
157 Manufacture of prepared animal feeds 0.575
262 Manufacture of non-refractory ceramic goods other than for construction purposes 0.5
263 Manufacture of ceramic tiles and flags 0.5
264 Manufacture of bricks, tiles and construction products 0.5
265 Manufacture of cement, lime and plaster 0.5
281 Manufacture of structural metal products 0.5
282 Manufacture of tanks, reservoirs and containers of metal; manufacture of central heating radiators and boilers 0.5
283 Manufacture of steam generators, except central heating hot water boilers 0.5
284 Forging, pressing, stamping and roll forming of metal; powder metallurgy 0.5
285 Treatment and coating of metals; general mechanical engineering 0.5
286 Manufacture of cutlery, tools and general hardware 0.5
287 Manufacture of other fabricated metal products 0.5
292 Manufacture of other general purpose machinery 0.5
342 Manufacture of bodies (coachwork) for motor vehicles; manufacture of trailers and semi-trailers 0.5
343 Manufacture of parts and accessories for motor vehicles and their engines 0.5
352 Manufacture of railway and tramway locomotives and rolling stock 0.5
353 Manufacture of aircraft and spacecraft 0.5
354 Manufacture of motorcycles and bicycles 0.5
355 Manufacture of other transport equipment n.e.c. 0.5
362 Manufacture of jewellery and related articles 0.5
366 Miscellaneous manufacturing n.e.c. 0.5
212 Manufacture of articles of paper and paperboard 0.4
261 Manufacture of glass and glass products 0.4
252 Manufacture of plastic products 0.3
201 Sawmilling and planing of wood; impregnation of wood 0.2
202 Manufacture of veneer sheets; manufacture of plywood, laminboard, particle board, fibre board and other panels and boards 0.2
203 Manufacture of builders’ carpentry and joinery 0.2
204 Manufacture of wooden containers 0.2
205 Manufacture of other products of wood; manufacture of articles of cork. straw and plaiting materials 0.2
361 Manufacture of furniture 0.2
251 Manufacture of rubber products 0.1
151 Production, processing and preserving of meat and meat products 0
174 Manufacture of made-up textile articles, except apparel 0
175 Manufacture of other textiles 0
177 Manufacture of knitted and crocheted articles 0
182 Manufacture of other wearing apparel and accessories 0
211 Manufacture of pulp, paper and paperboard 0
221 Publishing 0
222 Printing and service activities related to printing 0

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Published Online: 2021-10-15
Published in Print: 2022-05-31

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Articles
  3. Do balanced-budget fiscal stimuli of investment increase its economic value?
  4. A macro-level analysis of language learning and migration
  5. Skill complementarity in production technology: New empirical evidence and implications
  6. The effect of retirement on social relationships
  7. The estimation of reaction functions under tax competition
https://doi.org/10.1515/ger-2020-0102
Keywords for this article
skill dispersion; complementarity; production technology; firm productivity

Articles in the same Issue

  1. Frontmatter
  2. Original Articles
  3. Do balanced-budget fiscal stimuli of investment increase its economic value?
  4. A macro-level analysis of language learning and migration
  5. Skill complementarity in production technology: New empirical evidence and implications
  6. The effect of retirement on social relationships
  7. The estimation of reaction functions under tax competition
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