14.452 Economic Growth: Directed Technological Change
14.452 Economic Growth: Lecture 12, DirectedTechnological ChangeDaron AcemogluMITDecember 8, 2009.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.1 / 71
Directed Technological ChangeIntroductionIntroductionThus far have focused on a single type of technological change (e.g.,Hicks-neutral).But, technological change is often not neutral:12Benefits some factors of production and some agents more than others.Distributional effects imply some groups will embrace new technologiesand others oppose them.Limiting to only one type of technological change obscures thecompeting effects that determine the nature of technological change.Directed technological change: endogenize the direction and bias ofnew technologies that are developed and adopted.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.2 / 71
Biased Technological ChangeImportanceSkill-biased technological changeOver the past 60 years, the U.S. relative supply of skills has increased,but:12there has also been an increase in the college premium, andthis increase accelerated in the late 1960s, and the skill premiumincreased very rapidly beginning in the late 1970s.Standard explanation: skill bias technical change, and an accelerationthat coincided with the changes in the relative supply of skills.Important question: skill bias is endogenous, so, why hastechnological change become more skill biased in recent decades?Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.3 / 71
Biased Technological ChangeImportanceSkill-biased technological changeCollege wage premiumRel. supply of college skills.8.6.5.4.4.2.3R e l. su p p ly o f c o lle g e s killsC o lle g e w a g e p r e miu m.6039495969year798996Courtesy of Princeton University Press. Used with permission.Figure 15.1 in Acemoglu, Daron. Introduction to Modern Economic Growth.Princeton, NJ: Princeton University Press, 2009. ISBN: 9780691132921.Figure:R elative S upply of C ollege S kills and C ollege Prem iumDaron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.4 / 71
Biased Technological ChangeImportanceUnskill-biased technological changeLate 18th and early 19th unskill-bias:“First in firearms, then in clocks, pumps, locks, mechanical reapers,typewriters, sewing machines, and eventually in engines and bicycles,interchangeable parts technology proved superior and replaced theskilled artisans working with chisel and file.” (Mokyr 1990, p. 137)Why was technological change unskilled-biased then andskilled-biased now?Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.5 / 71
Biased Technological ChangeImportanceWage push and capital-biased technological changeFirst phase. Late 1960s and early 1970s: unemployment and share oflabor in national income increased rapidly continental Europeancountries.Second phase. 1980s: unemployment continued to increase, but thelabor share declined, even below its initial level.Blanchard (1997):Phase 1: wage-push by workersPhase 2: capital-biased technological changes.Is there a connection between capital-biased technological changes inEuropean economies and the wage push preceding it?Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.6 / 71
Biased Technological ChangeImportanceImportance of Biased Technological Change: moreexamplesBalanced economic growth:Only possible when technological change is asymptoticallyHarrod-neutral, i.e., purely labor augmenting.Is there any reason to expect technological change to be endogenouslylabor augmenting?Globalization:Does it affect the types of technologies that are being developed andused?Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.7 / 71
Biased Technological ChangeImportanceDirected Technological Change: Basic Arguments ITwo factors of production, say L and H (unskilled and skilledworkers).Two types of technologies that can complement either one or theother factor.Whenever the profitability of H-augmenting technologies is greaterthan the L-augmenting technologies, more of the former type will bedeveloped by profit-maximizing (research) firms.What determines the relative profitability of developing differenttechnologies? It is more profitable to develop technologies.12when the goods produced by these technologies command higher prices(price effect);that have a larger market (market size effect).Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.8 / 71
Biased Technological ChangeImportanceEquilibrium Relative BiasPotentially counteracting effects, but the market size effect will bemore powerful often.Under fairly general conditions:Weak Equilibrium (Relative) Bias: an increase in the relative supply ofa factor always induces technological change that is biased in favor ofthis factor.Strong Equilibrium (Relative) Bias: if the elasticity of substitutionbetween factors is suffi ciently large, an increase in the relative supply ofa factor induces suffi ciently strong technological change biased towardsitself that the endogenous-technology relative demand curve of theeconomy becomes upward-sloping.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.9 / 71
Biased Technological ChangeImportanceEquilibrium Relative Bias in More Detail ISuppose the (inverse) relative demand curve:wH /wL D (H/L, A)where wH /wL is the relative price of the factors and A is a technologyterm.A is H-biased if D is increasing in A, so that a higher A increases therelative demand for the H factor.D is always decreasing in H/L.Equilibrium bias: behavior of A as H/L changes,A (H/L)Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.10 / 71
Biased Technological ChangeImportanceEquilibrium Relative Bias in More Detail IIWeak equilibrium bias:A (H/L) is increasing (nondecreasing) in H/L.Strong equilibrium bias:A (H/L) is suffi ciently responsive to an increase in H/L that the totaleffect of the change in relative supply H/L is to increase wH /wL .i.e., let the endogenous-technology relative demand curve bewH /wL D (H/L, A (H/L)) D̃ (H/L) Strong equilibrium bias: D̃ increasing in H/L.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.11 / 71
Biased Technological ChangeBasics and DefinitionsFactor-augmenting technological changeProduction side of the economy:Y (t ) F (L (t ) , H (t ) , A (t )) ,where F / A 0.Technological change is L-augmenting ifL F (L, H, A) F (L, H, A). AA LEquivalent to:the production function taking the special form, F (AL, H ).Harrod-neutral technological change when L corresponds to labor andH to capital.H-augmenting defined similarly, and corresponds to F (L, AH ).Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.12 / 71
Biased Technological ChangeBasics and DefinitionsFactor-biased technological changeTechnological change change is L-biased, if: F (L,H ,A )/ L F (L,H ,A )/ H 0. ASkill premiumRelative supplyof skillsω’ωRelative demandfor skillsSkill-biased tech. changeH/LCourtesy of Princeton University Press. Used with permission.Figure 15.2 in Acemoglu, Daron. Introduction to Modern Economic Growth.Princeton, NJ: Princeton University Press, 2009. ISBN: 9780691132921.Figure: The effect of H-biased technological change on relative demand andrelative factor prices.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.13 / 71
Biased Technological ChangeBasics and DefinitionsConstant Elasticity of Substitution Production Function ICES production function case: σσ 1 σ 1σ 1σσY (t ) γL (AL (t ) L (t )), γH (AH (t ) H (t ))whereAL (t ) and AH (t ) are two separate technology terms.γi s determine the importance of the two factors, γL γH 1.σ (0, ) elasticity of substitution between the two factors.σσσσσ , perfect substitutes, linear production function is linear. 1, Cobb-Douglas, 0, no substitution, Leontieff. 1, “gross substitutes,” 1, “gross complements”.Clearly, AL (t ) is L-augmenting, while AH (t ) is H-augmenting.Whether technological change that is L-augmenting (orH-augmenting) is L-biased or H-biased depends on σ.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.14 / 71
Biased Technological ChangeBasics and DefinitionsConstant Elasticity of Substitution Production Function IIRelative marginal product of the two factors: σ 1 1MPHAH ( t ) σH (t ) σ, γMPLAL ( t )L (t )(1)where γ γH /γL .substitution effect: the relative marginal product of H is decreasing inits relative abundance, H (t ) /L (t ).The effect of AH (t ) on the relative marginal product:If σ 1, an increase in AH (t ) (relative to AL (t )) increases therelative marginal product of H.If σ 1, an increase in AH (t ) reduces the relative marginal product ofH.If σ 1, Cobb-Douglas case, and neither a change in AH (t ) nor inAL (t ) is biased towards any of the factors.Note also that σ is the elasticity of substitution between the twofactors.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.15 / 71
Biased Technological ChangeBasics and DefinitionsConstant Elasticity of Substitution Production Function IIIIntuition for why, when σ 1, H-augmenting technical change isL-biased:with gross complementarity (σ 1), an increase in the productivity ofH increases the demand for labor, L, by more than the demand for H,creating “excess demand” for labor.the marginal product of labor increases by more than the marginalproduct of H.Take case where σ 0 (Leontieff): starting from a situation in whichγL AL (t ) L (t ) γH AH (t ) H (t ), a small increase in AH (t ) will createan excess of the services of the H factor, and its price will fall to 0.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.16 / 71
Biased Technological ChangeBasics and DefinitionsEquilibrium BiasWeak equilibrium bias of technology: an increase in H/L, inducestechnological change biased towards H. i.e., given (1):d (AH (t ) /AL (t ))dH/Lσ 1σ 0,so AH (t ) /AL (t ) is biased towards the factor that has become moreabundant.Strong equilibrium bias: an increase in H/L induces a suffi cientlylarge change in the bias so that the relative marginal product of Hrelative to that of L increases following the change in factor supplies:dMPH /MPL 0,dH/LThe major difference is whether the relative marginal product of thetwo factors are evaluated at the initial relative supplies (weak bias) orat the new relative supplies (strong bias).Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.17 / 71
Baseline Model of Directed Technical ChangeEnvironmentBaseline Model of Directed Technical Change IFramework: expanding varieties model with lab equipmentspecification of the innovation possibilities frontier (so none of theresults here depend on technological externalities).Constant supply of L and H.Representative household with the standard CRRA preferences: 0exp ( ρt )Aggregate production function: Y ( t ) γ L YL ( t )C (t )1 θ 1dt,1 θε 1ε γ H YH ( t )ε 1ε(2) ε ε 1,(3)where intermediate good YL (t ) is L-intensive, YH (t ) is H-intensive.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.18 / 71
Baseline Model of Directed Technical ChangeEnvironmentBaseline Model of Directed Technical Change IIResource constraint (define Z (t ) ZL (t ) ZH (t )):C (t ) X (t ) Z (t ) Y (t ) ,(4)Intermediate goods produced competitively with: N (t ) L11 βxL (ν, t )YL (t ) d ν Lβ1 β0and1YH (t ) 1 β N H (t )0xH (ν, t )1 β d ν H β,(5)(6)where machines xL (ν, t ) and xH (ν, t ) are assumed to depreciate afteruse.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.19 / 71
Baseline Model of Directed Technical ChangeEnvironmentBaseline Model of Directed Technical Change IIIDifferences with baseline expanding product varieties model:12These are production functions for intermediate goods rather than thefinal good.(5) and (6) use different types of machines—different ranges [0, NL (t )]and [0, NH (t )].All machines are supplied by monopolists that have a fully-enforcedperpetual patent, at prices pLx (ν, t ) for ν [0, NL (t )] and pHx (ν, t )for ν [0, NH (t )].Once invented, each machine can be produced at the fixed marginalcost ψ in terms of the final good.Normalize to ψ 1 β.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.20 / 71
Baseline Model of Directed Technical ChangeEnvironmentBaseline Model of Directed Technical Change IVTotal resources devoted to machine production at time t are N (t ) N H (t )LX (t ) (1 β )xL (ν, t ) d ν xH (ν, t ) d ν .00Innovation possibilities frontier:ṄL (t ) η L ZL (t ) and ṄH (t ) η H ZH (t ) ,Value of a monopolist that discovers one of these machines is: s Vf (ν, t ) exp r s ds π f (ν, s )ds,t(7)(8)twhere π f (ν, t ) pfx (ν, t )xf (ν, t ) ψxf (ν, t ) for f L or H.Hamilton-Jacobi-Bellman version:r (t ) Vf (ν, t ) V̇f (ν, t ) π f (ν, t ).Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.(9)21 / 71
Baseline Model of Directed Technical ChangeEnvironmentBaseline Model of Directed Technical Change VNormalize the price of the final good at every instant to 1, which isequivalent to setting the ideal price index of the two intermediatesequal to one, i.e., εγLε (pL (t ))1 ε γH(pH (t ))1 ε 1 1 ε 1 for all t,(10)where pL (t ) is the price index of YL at time t and pH (t ) is the priceof YH .Denote factor prices by wL (t ) and wH (t ).Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.22 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium IAllocation. Time paths of[C (t ) , X (t ) , Z (t )]t 0 ,[ NL (t ) , NH (t )]t 0 , pLx (ν, t ) , xL (ν, t ) , VL (ν, t )andt 0,ν [0,N L (t )][χH (ν, t ) , xH (ν, t ) , VH (ν, t )] t 0, , andν [0,N H (t )][r (t ) , wL (t ) , wH (t )]t 0 .Equilibrium. An allocation in whichAll x existing research firms choosepf (ν, t ) , xf (ν, t )for f L, H to maximize profits,t 0,ν [0,N f (t )][NL (t ) , NH (t )]t 0 is determined by free entry[r (t ) , wL (t ) , wH (t )]t 0 , are consistent with market clearing, and[C (t ) , X (t ) , Z (t )]t 0 are consistent with consumer optimization.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.23 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium IIMaximization problem of producers in the two sectors:maxL,[xL (ν,t )]ν [0,N N L (t )0L (t ) ]pL (t ) YL (t ) wL (t ) L(11)pLx (ν, t ) xL (ν, t ) d ν,andmaxH ,[xH (ν,t )]ν [0,N N H (t )0H (t ) ]pH (t ) YH (t ) wH (t ) H(12)pHx (ν, t ) xH (ν, t ) d ν.Note the presence of pL (t ) and pH (t ), since these sectors produceintermediate goods.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.24 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium IIIThus, demand for machines in the two sectors: 1/βL for all ν [0, NL (t )] and all t, (13) 1/βHpL ( t )xL (ν, t ) pLx (ν, t )andpH ( t )xH (ν, t ) pHx (ν, t )for all ν [0, NH (t )] and all t. (14)Maximization of the net present discounted value of profits implies aconstant markup:pLx (ν, t ) pHx (ν, t ) 1 for all ν and t.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.25 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium IVSubstituting into (13) and (14):xL (ν, t ) pL (t )1/β L for all ν and all t,andxH (ν, t ) pH (t )1/β Hfor all ν and all t.Since these quantities do not depend on the identity of the machineprofits are also independent of the machine type:π L (t ) βpL (t )1/β L and π H (t ) βpH (t )1/β H.(15)Thus the values of monopolists only depend on which sector they are,VL (t ) and VH (t ).Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.26 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium VCombining these with (5) and (6), derived production functions forthe two intermediate goods:YL (t ) andYH ( t ) Daron Acemoglu (MIT)1 β1p L ( t ) β NL ( t ) L1 β(16)1 β1pH (t ) β NH (t ) H.1 βEconomic Growth Lecture 12December 8, 2009.(17)27 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium VIFor the prices of the two intermediate goods, (3) imply 1pH ( t )YH ( t ) εp (t ) γpL ( t )YL ( t ) 1ε1 β NtH()H γ p (t ) βNL (t ) L βεβNH (t ) H σ γσ,NL ( t ) L(18)where γ γH /γL andσ ε ( ε 1) (1 β ) 1 (ε 1) β.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.28 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium VIIWe can also calculate the relative factor prices:ω (t ) wH (t )wL (t )NH ( t )NL ( t ) σ 1 σ1εNH ( t ) σHσ γ.NL (t )L p (t )1/β(19)σ is the (derived) elasticity of substitution between the two factors,since it is exactly equal toσ Daron Acemoglu (MIT) d log ω (t )d log (H/L)Economic Growth Lecture 12 1.December 8, 2009.29 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumEquilibrium VIIIFree entry conditions:η L VL (t ) 1 and η L VL (t ) 1 if ZL (t ) 0.(20)η H VH (t ) 1 and η H VH (t ) 1 if ZH (t ) 0.(21)andConsumer side:Ċ (t )1 (r (t ) ρ ) ,C (t )θ(22)and lim exp t t0r (s ) ds (NL (t ) VL (t ) NH (t ) VH (t )) 0,(23)where NL (t ) VL (t ) NH (t ) VH (t ) is the total value of corporateassets in this economy.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.30 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumBalanced Growth Path IConsumption grows at the constant rate, g , and the relative pricep (t ) is constant. From (10) this implies that pL (t ) and pH (t ) arealso constant.Let VL and VH be the BGP net present discounted values of newinnovations in the two sectors. Then (9) implies that1/β1/ββpL LβpH HVL and VH , r r(24)Taking the ratio of these two expressions, we obtainVH VLDaron Acemoglu (MIT) pHpL 1βEconomic Growth Lecture 12H.LDecember 8, 2009.31 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumBalanced Growth Path IINote the two effects on the direction of technological change:12The price effect: VH /VL is increasing in pH /pL . Tends to favortechnologies complementing scarce factors.The market size effect: VH /VL is increasing in H/L. It encouragesinnovation for the more abundant factor.The above discussion is incomplete since prices are endogenous.Combining (24) together with (18): ε 1 σ 1VH1 γ σ NH σ H σ .(25)VLγNLLNote that an increase in H/L will increase VH /VL as long as σ 1and it will reduce it if σ 1. Moreover,σ 1 ε 1.The two factors will be gross substitutes when the two intermediategoods are gross substitutes in the production of the final good.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.32 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumBalanced Growth Path IIINext, using the two free entry conditions (20) and (21) as equalities,we obtain the following BGP “technology market clearing” condition:η L VL η H VH .(26)Combining this with (25), BGP ratio of relative technologies is NHNL σ ε η γ HL σ 1,(27)where η η H /η L .Note that relative productivities are determined by the innovationpossibilities frontier and the relative supply of the two factors. In thissense, this model totally endogenizes technology.Daron Acemoglu (MIT)Economic Growth Lecture 12December 8, 2009.33 / 71
Baseline Model of Directed Technical ChangeCharacterization of EquilibriumSummary of Balanced Growth PathProposition Consider the directed technological change model describedabove. Supposeβ εγH(η H H )σ 1 γLε ( η L L)σ 1εand (1 θ ) β γH(η H H )σ 1 γLε (η L L)σ 1 σ 1 1 σ 1 1ρ (28) ρ.Then there exists a unique BGP equilibrium in which therelative technologies are given by (27), and consumption andoutput grow at the rate 11σ 1σ 1 σ 1εεg β γHηH γηL ρ. (29)( H )L( L )θDaron Acemoglu (MIT)Economic Growth
Standard explanation: skill bias technical change, and an acceleration that coincided with the changes in the relative supply of skills. Important question: skill bias is endogenous, so, why has technological change become more skill biased in recent decades? Daron Acemoglu (MIT) Economic Growth Lecture 12 December 8, 2009. 3 / 71.
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