Input-biased technical progress and the aggregate elasticity of substitution: Evidence from 14 EU Member States

Transcription

1 Input-biased technical progress and the aggregate elasticity of substitution: Evidence from 14 EU Member States Grigorios Emvalomatis University of Dundee December 14, 2016

2 Background & Motivation Two key notions in economic growth models: The elasticity of substitution The direction of technical progress

3 Background & Motivation Two key notions in economic growth models: The elasticity of substitution has been associated with: factor returns in international markets effectiveness of employment-creation policies changes in factor income shares over time sustainability of growth The direction of technical progress

4 Background & Motivation Two key notions in economic growth models: The elasticity of substitution has been associated with: factor returns in international markets effectiveness of employment-creation policies changes in factor income shares over time sustainability of growth The direction of technical progress has been associated with: welfare consequences of new technologies changes in factor income shares (Adapted from León-Ledesma, McAdam, and Willman; 2010)

5 Background & Motivation Little consensus has been reached with regards to the values of these parameters/measures. Theoretical considerations: Practical considerations:

6 Background & Motivation Little consensus has been reached with regards to the values of these parameters/measures. Theoretical considerations: balanced growth path either with labor-augmenting progress (Solow growth model) or with unitary elasticity of substitution Acemoglu (2002, 2003): in the short run technical progress could be capital augmenting Hicks/Kennedy: factor prices and price-induced innovation Jones (2005): long-run elasticity of substitution equal to one Practical considerations:

7 Background & Motivation Little consensus has been reached with regards to the values of these parameters/measures. Theoretical considerations: balanced growth path either with labor-augmenting progress (Solow growth model) or with unitary elasticity of substitution Acemoglu (2002, 2003): in the short run technical progress could be capital augmenting Hicks/Kennedy: factor prices and price-induced innovation Jones (2005): long-run elasticity of substitution equal to one Practical considerations: non-identification theorem (Diamond, McFadden, Rodriguez) impose either labor-augmenting progress or σ = 1 impose a functional path on input-augmenting process (Klump et al., 2007) use dual information (cost minimization or profit maximization) short- vs. long-run elasticity of substitution

8 Objectives & Outline Objectives: Outline: examine the direction of technical progress ( ) in 14 European economies provide an estimate of the elasticity of substitution between labor and capital test the hypothesis of price-induced innovation Definitions: elasticity of substitution, input-augmenting progress, biased progress The non-identification theorem and panel data Modelling approach Data, results & extensions Conclusions

9 The elasticity of factor substitution σ = log(k/l) logmrs LK σ = log(k) logmrs LK K y Y L L k K L σ =1.5 σ =0.9 σ =0.6 Inputs are: gross complements if σ < 1 gross substitutes if σ > 1

10 Input-Augmenting Progress Consider a neoclassical production function: Y = F (K,L,t)

11 Input-Augmenting Progress Consider a neoclassical production function: Y = F (K,L,t) Technical change is factor augmenting if the production function can be written as: Y = F (A(t)K,B(t)L) where A and B are capital and labor efficiency indexes

12 Input-Augmenting Progress Consider a neoclassical production function: Y = F (K,L,t) Technical change is factor augmenting if the production function can be written as: Y = F (A(t)K,B(t)L) where A and B are capital and labor efficiency indexes Technical progress can be: labor-augmenting if Ȧ = 0, Ḃ > 0 capital-augmenting if Ȧ > 0, Ḃ = 0

13 Input-Augmenting Progress Consider a neoclassical production function: Y = F (K,L,t) Technical change is factor augmenting if the production function can be written as: Y = F (A(t)K,B(t)L) where A and B are capital and labor efficiency indexes Technical progress can be: labor-augmenting if Ȧ = 0, Ḃ > 0 capital-augmenting if Ȧ > 0, Ḃ = 0 factor-augmenting if Ȧ > 0, Ḃ > 0

14 Input-Augmenting Progress Consider a neoclassical production function: Y = F (K,L,t) Technical change is factor augmenting if the production function can be written as: Y = F (A(t)K,B(t)L) where A and B are capital and labor efficiency indexes Technical progress can be: labor-augmenting if Ȧ = 0, Ḃ > 0 capital-augmenting if Ȧ > 0, Ḃ = 0 factor-augmenting if Ȧ > 0, Ḃ > 0 Hicks neutral if Ȧ = Ḃ, t Y = C(t)F (K,L)

15 Input-Biased Progress Technical progress can be: Hicks neutral if the MRS LK is constant (over time) along any fixed K-L ratio: D(K,L,t) dlogmrs LK dt = 0

16 Input-Biased Progress Technical progress can be: Hicks neutral if the MRS LK is constant (over time) along any fixed K-L ratio: D(K,L,t) dlogmrs LK = 0 dt capital-biased/labor-saving if: D(K,L,t) dlogmrs LK > 0 dt labor-biased/capital-saving if: D(K,L,t) dlogmrs LK dt < 0

17 Input-Biased Progress Technical progress can be: Hicks neutral if the MRS LK is constant (over time) along any fixed K-L ratio: D(K,L,t) dlogmrs LK = 0 dt capital-biased/labor-saving if: D(K,L,t) dlogmrs LK > 0 dt labor-biased/capital-saving if: D(K,L,t) dlogmrs LK dt < 0 When progress is factor augmenting: D(K,L,t) = σ 1 σ ] [Ȧ A Ḃ B

18 Labor-Augmenting Progress with σ < 1 K y Y L L k K L

19 Labor-Augmenting Progress with σ < 1 K y Y L L k K L

20 Labor-Augmenting Progress with σ < 1 K y Y L L k K L dk dl = MRS LK = labor saving

21 The Non-Identification Theorem given the time series of all observable market phenomena for a single economy with classical aggregate production function, [...] the same time series could have been generated by an alternative production function having an arbitrary elasticity or bias at the observed points

22 The Non-Identification Theorem given the time series of all observable market phenomena for a single economy with classical aggregate production function, [...] the same time series could have been generated by an alternative production function having an arbitrary elasticity or bias at the observed points t 3 K t 3 t2 t 1 y Y L t 1 t 2 L k K L

23 The Non-Identification Theorem given the time series of all observable market phenomena for a single economy with classical aggregate production function, [...] the same time series could have been generated by an alternative production function having an arbitrary elasticity or bias at the observed points K y Y L L k K L

24 The Non-Identification Theorem given the time series of all observable market phenomena for a single economy with classical aggregate production function, [...] the same time series could have been generated by an alternative production function having an arbitrary elasticity or bias at the observed points K y Y L L k K L

25 The Non-Identification Theorem With panel data there is enough information to identify σ and the direction of technical progress. t 3 K t 3 t2 t 1 y Y L t 2 t 3 t 1 t 2 t 3 t 2 t 1 t 1 L k K L

26 The Non-Identification Theorem With panel data there is enough information to identify σ and the direction of technical progress. K y Y L L k K L

27 The Normalized CES Production Function The normalized CES production function is: [ ( )σ 1 ( ] σ )σ 1 σ 1 Y = Ỹ σ BL σ π +(1 π) AK K L where: A and B are capital and labor efficiency indexes K is capital stock and L labor use at the point of normalization (base period) Ỹ is output and π is the share of capital in income at the point of normalization (base period) Y, K, L, A, B implicitly depend on time

28 The Normalized CES Production Function The normalized CES production function is: [ ( )σ 1 ( ] σ )σ 1 σ 1 Y = Ỹ σ BL σ π +(1 π) AK K L where: A and B are capital and labor efficiency indexes K is capital stock and L labor use at the point of normalization (base period) Ỹ is output and π is the share of capital in income at the point of normalization (base period) Y, K, L, A, B implicitly depend on time In per worker terms: [ y = ỹ π ( ] σ )σ 1 σ 1 A k σ +(1 π) B k where: y = Y/L, ỹ = Ỹ/ L k = K/L, k = K/ L

29 Estimation using Dual Information The first-order conditions for cost minimization lead to: ) ) log(k) = σlog( π 1 π (σ 1)log( k +σlog ( ) ( w r +(σ 1)log A B)

30 Estimation using Dual Information The first-order conditions for cost minimization lead to: ) ) log(k) = σlog( π 1 π (σ 1)log( k +σlog ( ) ( w r +(σ 1)log A B) The first-order conditions for profit maximization lead to: log ( ) (Ỹ K) K Y = σlogπ +(σ 1)log σlog(r)+(σ 1)logA log ( ) (Ỹ L) L Y = σlog(1 π)+(σ 1)log σlog(w)+(σ 1)logB

31 Estimation using Dual Information The first-order condition for cost minimization can be written as: log(k) = δ +σlog ( ) w r +(σ 1) h(t) where: ( ) ) π δ = σlog (σ 1)log( k becomes a parameter h(t) = log 1 π ( A(t) B(t) ) describes the input-augmentation process

32 Estimation using Dual Information The first-order condition for cost minimization can be written as: log(k) = δ +σlog ( ) w r +(σ 1) h(t) where: ( ) ) π δ = σlog (σ 1)log( k becomes a parameter h(t) = log 1 π ( A(t) B(t) ) describes the input-augmentation process However, the cost minimization problem assumes that adjustment of the K L ratio is instantaneous

33 Estimation using Dual Information The first-order condition for cost minimization can be written as: log(k) = δ +σlog ( ) w r +(σ 1) h(t) where: ( ) ) π δ = σlog (σ 1)log( k becomes a parameter h(t) = log 1 π ( A(t) B(t) ) describes the input-augmentation process However, the cost minimization problem assumes that adjustment of the K L ratio is instantaneous there is no way of modeling the effect of relative input prices on the process of innovation (creation or adoption)

34 Estimation using Dual Information The first-order condition for cost minimization can be written as: log(k) = δ +σlog ( ) w r +(σ 1) h(t) where: ( ) ) π δ = σlog (σ 1)log( k becomes a parameter h(t) = log 1 π ( A(t) B(t) ) describes the input-augmentation process However, the cost minimization problem assumes that adjustment of the K L ratio is instantaneous there is no way of modeling the effect of relative input prices on the process of innovation (creation or adoption) in the presence of adjustment costs, σ is the short-run elasticity of substitution

35 Econometric Model: State-Space Formulation Observed equations: logk it = δ +σlog( wit r it )+(σ 1)s t +ε it

36 Econometric Model: State-Space Formulation Observed equations: logk it = δ +σlog( wit r it )+(σ 1)s t +ε it Hidden-state equation: s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: ) s t log( At B t D t σ 1 σ (s t s t 1 )

37 Econometric Model: State-Space Formulation Observed equations: logk it = δ +σlog( wit r it )+(σ 1)s t +ε it Hidden-state equation: s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: s t log( At B t ) D t σ 1 σ (s t s t 1 ) s 1 = 0 to normalize A t and B t

38 Econometric Model: State-Space Formulation Observed equations: logk it = δ +σlog( wit r it )+(σ 1)s t +ε it Hidden-state equation: s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: s t log( At B t ) D t σ 1 σ (s t s t 1 ) s 1 = 0 to normalize A t and B t z t includes ( additional ) drivers of the hidden state, eg. z t = t or wt q z t = log r t q

39 Econometric Model: State-Space Formulation Observed equations: logk it = δ +σlog( wit r it )+(σ 1)s t +ε it Hidden-state equation: s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: s t log( At B t ) D t σ 1 σ (s t s t 1 ) s 1 = 0 to normalize A t and B t z t includes ( additional ) drivers of the hidden state, eg. z t = t or wt q z t = log r t q δ, σ, ζ 1, ζ 2, ζ 3 are parameters to be estimated

40 Econometric Model: State-Space Formulation Observed equations: logk it = δ +σlog( wit r it )+(σ 1)s t +ε it Hidden-state equation: s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: s t log( At B t ) D t σ 1 σ (s t s t 1 ) s 1 = 0 to normalize A t and B t z t includes ( additional ) drivers of the hidden state, eg. z t = t or wt q z t = log r t q δ, σ, ζ 1, ζ 2, ζ 3 are parameters to be estimated ε it and v t are white-noise error terms

41 Data AMECO: Annual macro-economic database of the European Commission EU countries: EU-15 except Germany

42 Data AMECO: Annual macro-economic database of the European Commission EU countries: EU-15 except Germany Variables: output (Y): GDP in billions of 2010 Euros capital stock (K): billions of 2010 Euros labor (L): thousands of persons shares of inputs in GDP input prices w, r; using output-weighted input-price ratios

43 Results 1 Parameter Mean 5% 95% π σ ζ ζ σ ε σ v

44 Results 1 Parameter Mean 5% 95% π σ ζ ζ σ ε σ v one lag two lags Mean 5% 95% Mean 5% 95% π σ ζ ζ ζ σ ε σ v

45 Results D(K,L,t) ) t log ( w r

46 Results D(K,L,t) ) t 1 log ( w r

47 Results D(K,L,t) ) t 2 log ( w r

48 Results D(K,L,t) ) t 3 log ( w r

49 Results D(K,L,t) ) t 4 log ( w r

50 Results D(K,L,t) ) t 5 log ( w r

51 Discussion & and Extensions Main findings: reasonable estimate of the aggregate elasticity of substitution technical progress is labor augmenting (σ < 0 labor saving) A there is large variability over time in A Ḃ B relative input prices affect the direction of technical progress

52 Discussion & and Extensions Main findings: reasonable estimate of the aggregate elasticity of substitution technical progress is labor augmenting (σ < 0 labor saving) A there is large variability over time in A Ḃ B relative input prices affect the direction of technical progress Criticism: the technology is the same for all countries and the relative weighted input prices drive innovation (creation & adoption) allowing the direction of technical progress to be country-specific reintroduces the non-identification problem

53 Discussion & and Extensions Main findings: reasonable estimate of the aggregate elasticity of substitution technical progress is labor augmenting (σ < 0 labor saving) A there is large variability over time in A Ḃ B relative input prices affect the direction of technical progress Criticism: the technology is the same for all countries and the relative weighted input prices drive innovation (creation & adoption) allowing the direction of technical progress to be country-specific reintroduces the non-identification problem Two alternatives: break the 14 Member States into homogeneous subgroups allow for country-specific points of normalization

54 Results 2: Subgroups of Member States DK, FI, SE, UK BE, FR, NL EL, ES, IE, IT, PT Parameter Mean Std. Dev. Mean Std. Dev. Mean Std. Dev. π σ ζ ζ ζ σ ε σ v

55 The Role of the Normalization Point The normalization point defines the location of the isoquant and the shape of the per-worker production function

56 The Role of the Normalization Point The normalization point defines the location of the isoquant and the shape of the per-worker production function From a fixed point we get a family of curves that differ only by the elasticity of substitution K y Y L L k K L σ =0.2 σ =0.5 σ =0.8

57 The Role of the Normalization Point The normalization point defines the location of the isoquant and the shape of the per-worker production function From a fixed point we get a family of curves that differ only by the elasticity of substitution K y Y L L k K L σ =0.2 σ =0.5 σ =0.8

58 The Role of the Normalization Point The normalization point defines the location of the isoquant and the shape of the per-worker production function From a fixed point we get a family of curves that differ only by the elasticity of substitution K y Y L L k K L σ =0.2 σ =0.5 σ =0.8

59 A Putty-Clay Model Suggestion from literature: chose the normalization points from the data, prior to estimation. Instead we can estimate them

60 A Putty-Clay Model Suggestion from literature: chose the normalization points from the data, prior to estimation. Instead we can estimate them If the global production function is Cobb-Douglas, its normalization point is irrelevant

61 A Putty-Clay Model Suggestion from literature: chose the normalization points from the data, prior to estimation. Instead we can estimate them If the global production function is Cobb-Douglas, its normalization point is irrelevant This is not the case when the global production function is CES with σ 1 K y Y L L k K L σ =0.8 σ =0.3 σ =0.2 σ =0.2

62 Results 3: Country-Specific Normalization Points logk it = δ +σlog( wit r it )+(σ 1)s t +ε it s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: ( ) π ) δ = σlog (σ 1)log ( ki 1 π

63 Results 3: Country-Specific Normalization Points logk it = δ +σlog( wit r it )+(σ 1)s t +ε it s t = ζ 1 +ζ 2 s t 1 +ζ 3 z t +v t where: ( ) π ) δ = σlog (σ 1)log ( ki 1 π Common Country-Specific Normalization Point Normalization Point Parameter Mean 5% 95% Mean 5% 95% π σ ζ ζ ζ σ ε σ v

64 Discussion & Conclusions A step forward towards identifying the elasticity of substitution with panel data: reasonable estimates of the elasticity of substitution relative input prices affect the direction of technical progress

65 Discussion & Conclusions A step forward towards identifying the elasticity of substitution with panel data: reasonable estimates of the elasticity of substitution relative input prices affect the direction of technical progress Criticism: the composition of the labor force has changed over the period of analysis; manifested as labor augmentation the price of capital was imputed from the share of capital and capital stock no markup