WIOD Consortium Meeting

Sevilla, 25 – 26, May, 2011

Embodied and induced technical change and the price of carbon

Kurt KratenaMichael Wueger

Literature: embodied and induced technical change• Models increasingly integrate features of endogenous technical

change:

WITCH (Bosetti et al., 2006), CGE (Otto, Loeschel and Reilly, 2008)

• Endogenous innovation: (i) energy saving R&D, (ii) learning by doing for carbon-free technologies

• Popp (2002): energy saving innovation, Sue Wing (2006): technical change induced by climate policy climate policy creates the cost savings of it’s own measures

Critical issues and questions

• Induced innovation or diffusion of (existing) technologies?

• Difference between substitution of factors (for example K and E) and technical change (Binswanger and Ruttan, 1978 and Sue Wing, 2006)

• Are K and E substitutes or complements ? Does embodied and induced technical change only work with K and E substitutability ?

Technical change in E3 modelling

K,L,E,M (Translog) model of production with embodied and induced technical change

• Factor bias & TFP (Binswanger and Ruttan, 1978; Jorgenson and Fraumeni, 1981, Jorgenson, 1984)

• Embodied technical change (Berndt, Kolstad and Lee,1993; Sue Wing and Eckaus, 2007)

• From embodied to induced technical change: K as short-run fixed factor plus investment function (first results with EUKLEMS data in Kratena, 2007)

• Model of dynamic factor demand (Pindyck and Rotemberg, 1983): forward looking, but no explicit adjustment costs

• Application to WIOD data (YL files, environmental satellites accounts) combining with EUKLEMS (release March 2008, including energy inputs) and IEA Energy Prices and Taxes

Technical change in E3 modelling

Dynamic factor demand model: general• Dynamic cost functions with short-run variable costs VC (prices pv of

variable factors L, E, M), investment costs (K = capital stock, pI = investment price), gross output Q, labour L (second nest: different skills) , energy E, TFP, returns to scale and technical change bias

• Shephard’s Lemma and Euler condition:

• Euler condition without explicit adjustment costs just states that the shadow price of K equals the user costs of K.

Technical change in production

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Translog model with non-constant returns to scale

Dynamic factor demand model

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Translog model with constant returns to scale

Dynamic factor demand model

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Dynamic factor demand model

Embodied and induced technical change•Derivation of the shadow price of capital derivation of the optimal stock K*:

•Impact of energy price on K* (long-run)

•Returns to scale ( measures the cost effect of Q):

•Increasing returns to scale: < 1.

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log)/log()/log(loglog

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Dynamic factor demand model

Capital stock adjustment and energy

•Forward looking adjustment of K to K*:

•Investment function (non-constant returns to scale)

•Input-output spill-overs of technical change through production of capital goods:

p = VC/Q + pKK/Q

•With Bij as the investment matrix (industries * commodities) for imports (MB) and domestic deliveries

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Dynamic factor demand model

Embodied and induced technical change:energy

•Elasticity of E to K:

•Long-run elasticity of E:

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sKE K

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Estimation methodology• Balanced panel for: AUT, DNK, FIN, NLD, GB, from 1980-2006

• GMM estimation with lagged exogenous (factor prices, output, capital stock, depreciation rate, rate of return) as instruments the expectation of K*t+1 is determined by all information in t capital stock adjustment can be due to expectation errors or shocks

• Estimating the full system with VC-function, factor demand for L and E and investment function ( log Kt+1) for non-constant and constant returns to scale

• Deriving returns to scale, own price elasticities, capital/energy and capital/labour elasticities (calculating shadow price of K), as well as long-run elasticities of E

• Restrictions: homogeneity, symmetry and concavity of the cost function (individual, for ‘problem cases’)

Dynamic factor demand model

Data from WIOD, EUKLEMS and IEA (energy prices)• Energy inputs in physical units (TJ) by about 20 energy carriers from

WIOD environmental accounts

• IEA Energy Prices and Taxes for most of the energy carriers/countries (estimating missing data to fill gaps)

• Constructing an aggregate energy input in current prices (pE *E), volumes (E), and price of energy pE. The volume measure is based on aggregation of energy contents effective input (‘energy services’ like ‘labour servives’ and ‘capital srvices’ in EUKLEMS)

• Capital stock, GFCF deflators, depreciation rate (capital input files from EUKLEMS), benchmark interest rate (EUROSTAT), deflated with VA deflator (YL files, WIOD) user costs pI(r + )

• ‘Labour services’ (L) , compensation of employees from (pL*L) price of labour (pL) , data from YL files, WIOD

Dynamic factor demand model

Estimation results: non-constant returns to scale

25 parameters out of 91 are insignificant

Embodied energy saving technical change: wood and cork, pulp and paper/printing, chemicals, rubber and plastics, basic metals and fabricated metal, electrical and optical equipment

Dynamic factor demand model

K LL LE EE KK KL KE

Food, beverages and tobacco -0.3064 0.0577 -0.0144 0.0121 -0.0337 0.0619 0.0148(0.1235) *** (0.0245) ** (0.0022) *** (0.0009) *** (0.0811) (0.0156) *** (0.0015) ***

Textiles, leather and footwear -0.7704 0.0168 -0.0051 0.0131 0.3874 0.0041 0.0025(0.1366) *** (0.0329) (0.0035) * (0.0018) *** (0.1214) *** (0.0160) (0.0017) *

Wood and cork -1.8256 0.1528 -0.0156 0.0110 -1.1409 0.0340 -0.0003(0.3106) *** (0.0262) *** (0.0061) *** (0.0000) *** (0.1446) *** (0.0173) ** (0.0045)

Pulp and paper, printing -1.1688 0.0109 0.0085 0.0250 0.6118 0.0421 -0.0045(0.6125) ** (0.0285) (0.0094) (0.0001) *** (0.3202) ** (0.0165) ** (0.0097)

Coke, refined petroleum and nuclear fuel -0.1471 -0.0091 -0.0526 0.0658 -0.8335 -0.0240 0.0050(1.0648) (0.0195) (0.0062) *** (0.0146) *** (0.2745) *** (0.0085) *** (0.0181)

Chemicals and chemical products 1.5429 0.1510 -0.0008 0.0229 1.2024 0.1722 -0.1248(0.2262) *** (0.0207) *** (0.0092) (0.0078) *** (0.2953) *** (0.0178) *** (0.0136) ***

Rubber and plastics -0.8230 0.0839 0.0027 0.0011 -1.1749 0.1260 -0.0149(0.6449) (0.0195) *** (0.0099) *** (0.0122) ** (0.4804) * (0.0259) *** (0.0275) *

Other non-metallic minerals -1.5436 -0.0326 -0.0249 0.0550 0.4000 0.0138 0.0441(0.2738) *** (0.0219) (0.0074) *** (0.0001) *** (0.1644) ** (0.0109) (0.0105) ***

Basic metals and fabricated metal -0.3972 0.1629 -0.0188 0.0417 -0.1735 0.1723 -0.0581(0.1947) ** (0.0211) *** (0.0074) *** (0.0052) *** (0.1242) (0.0104) *** (0.0063) ***

Machinery -0.2171 0.1076 -0.0012 0.0054 0.4780 0.1012 0.0000(0.2187) (0.0132) *** (0.0025) (0.0011) *** (0.1223) *** (0.0066) *** (0.0014)

Electrical and optical equipment -0.0358 0.0690 -0.0005 0.0070 -0.1320 0.0639 -0.0019(0.1468) (0.0316) (0.0045) (0.0000) *** (0.0443) *** (0.0130) *** (0.0017)

Transport equipment -0.2724 0.1700 0.0134 0.0072 -0.5835 0.0574 0.0009(0.3201) (0.0000) *** (0.0065) ** (0.0031) ** (0.1525) *** (0.0187) *** (0.0032)

Other manufacturing -1.2236 0.0358 -0.0082 0.0136 -0.1043 0.1448 0.0016(0.1927) *** (0.0328) (0.0076) (0.0006) *** (0.0295) *** (0.0144) *** (0.0057)

Estimation results: constant returns to scale

8 parameters out of 91 are insignificant

Embodied energy saving technical change: Coke, refined petroleum and nuclear fuel, chemicals, basic metals and fabricated metal

Dynamic factor demand model

Q LL LE EE KL KE QK

Food, beverages and tobacco 1.7855 0.0859 -0.0036 0.0151 0.0658 0.0090 0.8386(0.1243) *** (0.0100) *** (0.0017) ** (0.0000) *** (0.0058) *** (0.0006) *** (0.1582) ***

Textiles, leather and footwear 1.5012 -0.0390 -0.0060 0.0123 -0.0561 0.0030 0.2458(0.0785) *** (0.0213) * (0.0037) * (0.0013) *** (0.0118) *** (0.0011) *** (0.1347) *

Wood and cork 1.1515 0.1358 0.0060 0.0163 0.0125 0.0084 0.5162(0.2228) *** (0.0185) *** (0.0057) (0.0025) *** (0.0123) (0.0025) *** (0.4424)

Pulp and paper, printing 0.0481 -0.1672 0.0464 0.0212 -0.0966 0.0423 -1.2639(0.2789) (0.0392) *** (0.0181) ** (0.0107) ** (0.0124) *** (0.0038) *** (0.4518) ***

Coke, refined petroleum and nuclear fuel 3.3571 -0.0430 -0.0463 0.0393 -0.0272 -0.0080 3.7159(0.5714) *** (0.0177) ** (0.0066) *** (0.0095) *** (0.0075) *** (0.0124) (0.7940) ***

Chemicals and chemical products 0.9078 0.1553 0.0367 -0.0117 0.1763 -0.1656 -4.2503(0.0889) *** (0.0000) *** (0.0072) *** (0.0063) * (0.0146) *** (0.0130) *** (0.7219) ***

Rubber and plastics 0.9011 0.0542 0.0297 0.0266 0.0974 -0.0479 -0.1035(0.1146) *** (0.0174) *** (0.0102) *** (0.0082) *** (0.0154) *** (0.0169) *** (0.0553) *

Other non-metallic minerals 0.6591 0.1429 0.0101 0.0513 -0.0381 0.0160 -1.2287(0.2074) *** (0.0156) *** (0.0059) * (0.0001) *** (0.0077) *** (0.0041) *** (0.3890) ***

Basic metals and fabricated metal 1.1697 0.1699 -0.0115 0.0372 0.0914 -0.0325 0.3441(0.0752) *** (0.0000) *** (0.0112) (0.0040) *** (0.0071) *** (0.0034) *** (0.1777) *

Machinery -0.0441 0.1694 0.0205 0.0047 0.1205 0.0064 -1.7631(0.0976) (0.0141) *** (0.0018) *** (0.0013) *** (0.0057) *** (0.0008) *** (0.2056) ***

Electrical and optical equipment 1.1576 0.0766 0.0062 0.0061 0.0719 0.0008 -0.0281(0.0234) *** (0.0218) *** (0.0035) * (0.0013) *** (0.0106) *** (0.0010) (0.0127) **

Transport equipment 2.0841 0.1703 0.1035 0.0141 0.0339 0.0179 1.0262(0.1248) *** (0.0000) *** (0.0097) *** (0.0030) *** (0.0101) *** (0.0031) *** (0.1425) ***

Other manufacturing 1.0372 -0.0429 -0.0301 0.0132 0.1364 0.0188 0.4420(0.0730) *** (0.0224) * (0.0036) *** (0.0004) *** (0.0072) *** (0.0030) *** (0.0990) ***

Estimation results: non-constant returns to scale

Factor bias: (i) labour saving in all industries, (ii) energy saving in: chemicals, other non-metallic minerals, basic metals and fabricated metal, machinery, electrical and optical equipment, and transport equipment

Dynamic factor demand model

t tt tK tL tE

Food, beverages and tobacco -0.0380 0.0000 -0.0037 -0.0005 0.0006(-0.0025) *** (0.0001) (-0.0010) *** (0.0009) (-0.0001) ***

Textiles, leather and footwear -0.0236 -0.0002 0.0048 -0.0028 0.0005(-0.0053) *** (-0.0001) * (-0.0016) *** (-0.0011) *** (-0.0001) ***

Wood and cork -0.0287 0.0002 0.0022 -0.0038 0.0003(-0.0070) *** (-0.0001) * (0.0028) (-0.0007) *** (-0.0001) *

Pulp and paper, printing -0.0408 -0.0001 -0.0062 -0.0028 0.0003(-0.0144) *** (0.0001) (0.0058) (-0.0009) *** (0.0004)

Coke, refined petroleum and nuclear fuel 0.1636 -0.0020 -0.0067 -0.0009 0.0036(-0.0434) *** (0.0007) *** (0.0073) (0.0007) (0.0011) ***

Chemicals and chemical products 0.0146 0.0006 0.0161 -0.0037 -0.0030(0.0076) ** (0.0002) *** (0.0053) *** (0.0009) *** (0.0005) ***

Rubber and plastics -0.0591 0.0001 -0.0237 -0.0023 0.0006(0.0102) (0.0002) ** (0.0063) (0.0006) *** (0.0005)

Other non-metallic minerals -0.0179 -0.0001 0.0157 -0.0007 -0.0009(0.0045) *** (0.0001) (0.0019) *** (0.0006) (0.0003) ***

Basic metals and fabricated metal 0.0104 0.0004 -0.0088 -0.0046 -0.0003(0.0066) * (0.0001) *** (0.0027) *** (0.0007) *** (0.0003)

Machinery -0.0305 0.0002 -0.0012 -0.0059 -0.0002(0.0070) *** (0.0001) * (0.0025) (0.0003) *** (0.0001) ***

Electrical and optical equipment 0.0159 0.0013 0.0027 -0.0083 -0.0004(0.0127) (0.0001) *** (0.0026) (0.0012) *** (0.0002) ***

Transport equipment 0.0019 0.0003 0.0002 -0.0073 -0.0004(0.0056) (0.0002) ** (0.0022) (0.0006) *** (0.0002) **

Other manufacturing -0.0539 0.0001 -0.0103 -0.0033 0.0011(0.0053) *** (0.0002) (0.0021) *** (0.0011) *** (0.0003) ***

Estimation results: constant returns to scale

Factor bias: (i) labour saving in all industries except pulp and paper, (ii) energy saving in a majority of industries

Dynamic factor demand model

t tt tK tL tE

Food, beverages and tobacco 0.0014 0.0001 0.0143 -0.0017 0.0003(0.0047) (0.0002) (0.0039) *** (0.0005) *** (0.0001) ***

Textiles, leather and footwear 0.0159 -0.0008 0.0247 -0.0016 0.0004(0.0046) *** (0.0002) *** (0.0029) *** (0.0009) * (0.0001) ***

Wood and cork -0.0315 0.0011 -0.0176 -0.0037 -0.0002(0.0063) *** (0.0003) *** (0.0085) ** (0.0007) *** (0.0002)

Pulp and paper, printing -0.0178 0.0002 -0.0122 0.0041 -0.0013(0.0071) ** (0.0003) (0.0061) ** (0.0012) *** (0.0006) **

Coke, refined petroleum and nuclear fuel 0.0737 -0.0043 0.0465 -0.0004 0.0044(0.0222) *** (0.0013) *** (0.0186) ** (0.0006) (0.0007) ***

Chemicals and chemical products -0.0122 0.0011 0.0643 -0.0026 -0.0060(0.0031) *** (0.0002) *** (0.0113) *** (0.0004) *** (0.0004) ***

Rubber and plastics -0.0490 0.0026 -0.0062 -0.0013 -0.0017(0.0066) *** (0.0004) *** (0.0061) (0.0006) ** (0.0004) ***

Other non-metallic minerals -0.0298 0.0019 0.0109 -0.0044 -0.0014(0.0063) *** (0.0004) *** (0.0041) *** (0.0004) *** (0.0002) ***

Basic metals and fabricated metal -0.0331 0.0017 -0.0003 -0.0037 -0.0009(0.0036) *** (0.0002) *** (0.0030) (0.0003) *** (0.0003) ***

Machinery 0.0120 -0.0002 0.0217 -0.0061 -0.0004(0.0069) * (0.0002) (0.0057) *** (0.0004) *** (0.0001) ***

Electrical and optical equipment -0.0231 0.0014 0.0178 -0.0084 -0.0004(0.0019) *** (0.0001) *** (0.0012) *** (0.0008) *** (0.0001) ***

Transport equipment -0.0040 0.0007 0.0224 -0.0053 -0.0020(0.0044) (0.0002) *** (0.0036) *** (0.0004) *** (0.0002) ***

Other manufacturing -0.0371 0.0014 -0.0141 -0.0008 0.0020(0.0043) *** (0.0002) *** (0.0028) *** (0.0009) (0.0002) ***

Estimation results: elasticities, non-constant returns to scale

price elasticity of E : - 0.2, of L : - 0.5 .

Negative energy/capital elasticities (K and E are substitutes):

pulp and paper/printing, chemicals, rubber and plastics, basic metals and fabricated metal, machinery, electrical and optical equipment

Energy saving embodied technical change

Dynamic factor demand model

EE LL EK LK

Food, beverages and tobacco -0.2595 -0.4773 0.8845 0.3742 1.0165Textiles, leather and footwear -0.0791 -0.6458 0.1587 -0.0010 1.0126

Wood and cork -0.1494 -0.1316 0.0489 0.2075 0.8908Pulp and paper, printing -0.1339 -0.6706 -0.1159 0.1824 0.9614

Coke, refined petroleum and nuclear fuel -0.1092 -1.1677 0.2276 -0.3925 0.8844Chemicals and chemical products -0.5682 -0.0404 -1.9717 0.7897 1.0518

Rubber and plastics -0.4759 -0.4773 -0.2467 0.6514 0.7445Other non-metallic minerals -0.0160 -0.7898 0.5935 -0.0936 1.1096

Basic metals and fabricated metal -0.0742 -0.1115 -1.1123 0.7391 0.9279Machinery -0.4165 -0.3362 -0.0240 0.3023 1.0028

Electrical and optical equipment -0.0810 -0.4551 -0.1248 0.3502 0.8846Transport equipment -0.2061 -0.0220 0.1149 0.2678 1.0052Other manufacturing -0.0397 -0.6047 0.0783 0.3875 1.0005

Estimation results: elasticities, constant returns to scale

Negative energy/capital elasticities (K and E are substitutes): coke, refined petroleum and nuclear fuel, chemicals, rubber and plastics, basic metals and fabricated metal

Three industries show energy saving embodied technical change in both specifications: chemicals, rubber and plastics, basic metal/fabricated metal

Dynamic factor demand model

EE LL EK LK

Food, beverages and tobacco -0.0766 -0.3066 0.5721 0.4304Textiles, leather and footwear -0.1292 -0.8412 0.1972 -0.2049

Wood and cork -0.1035 -0.1998 0.5357 -0.0466Pulp and paper, printing -0.2587 -1.3081 1.5026 -0.2380

Coke, refined petroleum and nuclear fuel -0.1422 -2.0352 -0.0056 -0.6921Chemicals and chemical products -1.0836 -0.0191 -2.7513 0.6553

Rubber and plastics -0.1107 -0.5175 -1.5797 0.2704Other non-metallic minerals -0.0772 -0.2258 0.3545 -0.0330

Basic metals and fabricated metal -0.1676 -0.0853 -0.6477 0.3698Machinery -0.4928 -0.1390 0.5788 0.2823

Electrical and optical equipment -0.2030 -0.4283 0.1732 0.3288Transport equipment -0.0906 -0.0208 1.9192 0.1459Other manufacturing -0.0702 -0.7703 1.3564 0.4615

Estimation results: embodied and induced technical change

• Two industries with embodied energy saving technical change in the case of non-constant returns to scale, but not with constant returns: pulp and paper/printing, electrical and optical equipment

• Are non-constant returns to scale an additional source of technical change? (some industres with decreasing returns !)

• Main disadvantage of this approach:

• (Price) induced technical change is only possible, when K and E are substitutes and investment reacts positive to energy price shocks further reduction of number of industries with embodied plus induced energy saving technical change

Dynamic factor demand model

Estimation results: long-run price elasticities of E

Starting point: industries with embodied energy saving technical change

Is there also induced energy saving technical change ? =

Is the long-run price elasticity of E higher than the short-run ?

Dynamic factor demand model

non-constant rs non-constant rs constant rs constant rs EE EE EE EE

Food, beverages and tobacco -0.2595 0.1276 -0.0766 0.0503Textiles, leather and footwear -0.0791 -0.0801 -0.1292 -0.1309

Wood and cork -0.1494 -0.1494 -0.1035 -0.1036Pulp and paper, printing -0.1339 -0.1347 -0.2587 -0.2437

Coke, refined petroleum and nuclear fuel -0.1092 -0.1078 -0.1422 -0.1422Chemicals and chemical products -0.5682 -0.7728 -1.0836 -1.3512

Rubber and plastics -0.4759 -0.9150 -0.1107 -0.0920Other non-metallic minerals -0.0160 -0.0815 -0.0772 -0.1400

Basic metals and fabricated metal -0.0742 0.2981 -0.1676 -0.0022Machinery -0.4165 -0.4165 -0.4928 -0.4928

Electrical and optical equipment -0.0810 -0.0792 -0.2030 -0.2055Transport equipment -0.2061 -0.2059 -0.0906 0.5446Other manufacturing -0.0397 -0.0364 -0.0702 -0.0613

Embodied & induced technical change

Non-constant returns to scale

Starting point: industries with embodied energy saving technical change: pulp and paper/printing, chemicals, rubber and plastics, basic metals and fabricated metal, machinery, electrical and optical equipment

Long-run elasticity of E (EE) > short-run elasticity (EE) = induced technical change: pulp and paper/printing, chemicals, rubber and plastics, machinery

Dynamic factor demand model

Embodied & induced technical change

Constant returns to scale

Starting point: industries with embodied energy saving technical change: coke, refined petroleum and nuclear fuel, chemicals, rubber and plastics, basic metals and fabricated metal

Long-run elasticity of E (EE) > short-run elasticity (EE) = induced technical change: chemicals

Dynamic factor demand model

Conclusions and Future Research

Conclusions• Dynamic Translog factor demand model allows for diverse

sources/types of technical change: returns to scale, TFP, factor bias, embodied and induced technical change.

• Technical change/progress is only partly energy saving, also for embodied technical change

• Disadvantage: embodied technical change is only energy saving, if E and K are substitutes induced technical change is only energy saving, if E and K are substitutes plus if investment reacts positively to energy prices.

Future research• Allowing for embodied technical change in the case that E and K are

complements vintage model for aggregate K.