Estimating Production Functions. Paul Schrimpf. Paul Schrimpf. UBC Economics 565. January 12, 2017

Transcription

1 Estimating UBC Economics 565 January 12, 2017

2 1 Introduction Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications 2 Setup 3 Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions 4 Selection OP selection 5 Applications

3 Introduction Setup Simultaneity Instrumental variables Panel data Section 1 Fixed effects Dynamic Control functions Critiques extensions Introduction Selection OP selection Applications

4 Introduction Why estimate functions? Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Primitive component of economic model Gives estimate of firm productivity useful for understing economic growth Stylized facts to inform theory, e.g. Foster, Haltiwanger, Krizan (2001) Effect of deregulation, e.g. Olley Pakes (1996) Growth within old firms vs from entry of new firms, e.g. Foster, Haltiwanger, Krizan (2006) Effect of trade liberalization, e.g. Amiti Konings (2007) Effect of FDI Javorcik (2004)

5 These slides based on: Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Aguirregabiria chapter 2 Ackerberg et al. (2007) section 2 Van Beveren (2012) Applications

6 Introduction Setup Simultaneity Instrumental variables Panel data Section 2 Fixed effects Dynamic Control functions Critiques extensions Setup Selection OP selection Applications

7 Introduction Setup Simultaneity Cobb Douglas Y it = A it K β k it Lβ l it Setup Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications In logs, y it = β k k it + β l l it + ω it + ε it with log A it = ω it + ε it, ω it known to firm, ε it not Problems: 1 Simultaneity: if firm has information about log A it when choosing inputs, then inputs correlated with log A it, e.g. price p, wage w, perfect information ( p ) L it = w β la it K β 1 1 β k l it 2 Selection: firms with low productivity will exit sooner 3 Others: measurement error, specification

8 Introduction Setup Simultaneity Instrumental variables Panel data Section 3 Fixed effects Dynamic Control functions Critiques extensions Simultaneity Selection OP selection Applications

9 Simultaneity solutions Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection 1 IV 2 Panel data 3 Control functions Applications

10 Instrumental variables Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Instrument must be Correlated with k l Uncorrelated with ω + ε Possible instrument: input prices Correlated with k, l through first-order condition Uncorrelated with ω if input market competitive Other possible instruments: output prices (more often endogenous), input supply or output dem shifter (hard to find)

11 Problems with input prices as IV Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Not available in some data sets Average input price of firm could reflect quality as well as price differences Need variation across observations If firms use homogeneous inputs, operate in the same output input markets, we should not expect to find any significant cross-sectional variation in input prices If firms have different input markets, maybe variation in input prices, but different prices could be due to different average productivity across input markets Variation across time is potentially endogenous because could be driven by time series variation in average productivity

12 Fixed effects Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Have data, so should consider fixed effects FE consistent if: 1 ω it = η i + δ t + ωit 2 ωit uncorrelated with l it k it, e.g. ωit only known to firm after choosing inputs 3 ωit not serially correlated is strictly exogenous Problems: Fixed productivity a strong assumption Estimates often small in practice Worsens measurement error s Bias(ˆβ k FE ) β k Var( ε) Var( k) + Var( ε)

13 Dynamic : motivation I Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications General idea: relax fixed effects assumption, but still exploit Collinearity : Cobb-Douglas, flexible labor capital implies log labor log capital are linear functions of prices productivity (Bond Söderbom (2005)) If observed labor capital are not collinear then there must be something unobserved that varies across firms (e.g. prices), but that would invalidate monotonicity assumption of control function

14 Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications See Blundell Bond (2000) Dynamic : moment conditions Assume ω it = γ t + η i + ν it with ν it = ρν i,t 1 + e it, so y it = β l l it + β k k it + γ t + η i + ν it + ε it subtract ρy i,t 1 rearrange to get y it =ρy i,t 1 + β l (l it ρl i,t 1 ) + β k (k it ρk i,t 1 )+ + γ t ργ t 1 + η i (1 ρ) + e }{{} it + ε it ρε i,t 1 }{{} =ηi =w it Moment conditions: Difference: E[x i,t s w it ] = 0 where x = (l, k, y) Level: E [ x i,t s (η i + w it )] = 0

15 Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Adjustment costs V(K t 1, L t 1 ) = Dynamic : economic model I max P t F t (K t, L t ) P K t (I t + G t (I t, K t 1 )) I t,k t,h t,l t ψe [V(K t, L t ) I t ] W t (L t + C t (H t, L t 1 )) + s.t. K t = (1 δ k )K t 1 + I t L t = (1 δ l )L t 1 + H t Implies P t F t L t W t C t L t =W t + λ L t F t P t P K G t t =λ K t K t K t ( [ ]) λ L 1 (1 δ l )ψe t+1 I t ( 1 (1 δ k )ψe λ L t [ ]) λ K t+1 I t λ K t

16 Introduction Dynamic : economic model II Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Current productivity shifts F t L t (if correlated with ] I t future) the shadow value of future labor E [ λ L t+1 λ L t Past labor correlated with current because of adjustment costs

17 Dynamic data: s Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Problems: Sometimes imprecise (especially if only use difference moment conditions) Differencing worsens measurement error Weak instrument issues if only use difference moment conditions but levels stronger (see Blundell Bond (2000))

18 Control functions Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications From Olley Pakes (1996) (OP) Control function: function of data conditional on which endogeneity solved E.g. usual 2SLS y = xβ + ε, x = zπ + v, control function is to estimate residual of reduced form, ˆv then regress y on x ˆv. ˆv is the control function Main idea: model choice of inputs to find a control function

19 OP assumptions Introduction y it = β k k it + β l l it + ω it + ε it Setup Simultaneity Instrumental variables 1 ω it follows exogenous first order Markov process, Panel data Fixed effects Dynamic Control functions Critiques extensions Selection p(ω it+1 I it ) = p(ω it+1 ω it ) 2 Capital at t determined by investment at time t 1, OP selection Applications k t = (1 δ)k it 1 + i it 1 3 Investment is a function of ω other observed variables i it = I t (k it, ω it ), is strictly increasing in ω it 4 Labor variable non-dynamic, i.e. chosen each t, current choice has no effect on future (can be relaxed)

20 OP estimation of β l Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Invertible investment implies ω it = I 1 t (k it, i it ) y it =β k k it + β l l it + I 1 t (k it, I it ) + ε it =β l l it + f t (k it, i it ) + ε it Partially linear model Estimate by e.g. regress y it on l it series functions of t, k it, i it Gives ˆβ l, ˆf it = ˆf t (k it, i it )

21 OP estimation of β k Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Note: ˆf t (k it, i it ) = ˆω it + β k k it By assumptions, ω it = E[ω it ω it 1 ] + ξ it = g(ω it 1 ) + ξ it with E[ξ it k it ] = 0 Use E[ξ it k it ] = 0 as moment to estimate β k. OP: write function as y it β l l it =β k k it + g(ω it 1 ) + ξ it + ε it =β k k it + g (f it 1 β k k it 1 ) + + ξ it + ε it Use ˆβ l ˆf it in equation above estimate ˆβ k by e.g. semi-parametric nonlinear least squares ] : use E [ˆξ it (β k )k it = 0

22 Critiques extensions Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Levinsohn Petrin (2003): investment often zero, so use other inputs instead of investment to form control function : control function often collinear with l it for it not to be must be firm specific unobervables affecting l it (but not investment / other input or else dem not invertible cannot form control function) Navarro, Rivers : relax scalar unobservable in investment / other input dem Wooldridge (2009): more efficient joint estimation Maican (2006) Jaumreu : endogenous productivity

23 Introduction Setup Simultaneity Instrumental variables Panel data Section 4 Fixed effects Dynamic Control functions Critiques extensions Selection Selection OP selection Applications

24 Selection Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Let d it = 1 if firm in sample. Stard conditions imply d = 1{ω ω (k)} Messes up moment conditions All estimators based on E[ω it Something] = 0, observed data really use E[ω it Something d it = 1] E.g. OLS okay if E[ω it l it, k it ] = 0, but even then, E[ω it l it, k it, d it = 1] =E[ω it l it, k it, ω it ω (k it )] =λ(k it ) 0 Selection bias negative, larger for capital than labor

25 Selection in OP model Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Estimate β l as above Write d it = 1{ξ it ω (k it ) ρ(f i,t 1 β k k it 1 ) = h(k it, f it 1, k it 1 )} Propensity score P it E[d it k it, f it 1, k it 1 ] Similar to before estimate β k, from y it β l l it =β k k it + g (f it 1 β k k it 1, P it ) + + ξ it + ε it

26 Introduction Setup Simultaneity Instrumental variables Panel data Section 5 Fixed effects Dynamic Control functions Critiques extensions Applications Selection OP selection Applications

27 Applications Introduction Setup Simultaneity Instrumental variables Panel data Fixed effects Dynamic Control functions Critiques extensions Selection OP selection Applications Olley Pakes (1996): productivity in telecom after deregulation Söderbom, Teal, Harding (2006): productivity exit of African manufacturing firms, uses IV Levinsohn Petrin (2003): compare estimation methods using Chilean data Javorcik (2004): FDI productivity, uses OP Amiti : trade liberalization in Indonesia, uses OP Aw, Chen, Roberts (2001): productivity differentials firm turnover in Taiwan Kortum Lerner (2000): venture capital innovation

28 Part II Navarro, Rivers from Selected applications extensions Amiti Jaumreu

29 Navarro, Rivers from Amiti Jaumreu 6 7 Navarro, Rivers from 8 9 Amiti 10 Jaumreu

30 Section 6 Navarro, Rivers from Amiti Jaumreu

31 Navarro, Rivers from Frazer (2015): contributions Document collinearity in OP Levinsohn Petrin (2003) Need l it, f it (k it, i it ) not collinear, i.e. something causes variation in l, but not k Propose alternative estimator Relates estimator to dynamic (Blundell Bond, 2000) approach Illustrates estimator using Chilean data Amiti Jaumreu 0 These slides are based on the working paper version Frazer (2006).

32 I Navarro, Rivers from Amiti Jaumreu OP assume i it = I t (k it, ω it ) Symmetry, parsimony suggest l it = L t (k it, ω it ) Then l it = L t (k it, I 1 t (k it, i it )) = g t (k it, i it ) y it = β l l it + f t (k it, i it ) + ε it l it collinear with f t (k it, i it ) Worse in Levinsohn Petrin (2003) Uses other input m it to form control function y it =β l l it + β k k it + β m m it + ω it + ε it m it =M t (k it, ω it ) Even less reason to treat labor dem differently than other input dem

33 Navarro, Rivers from Amiti Jaumreu II Collinearity still with parametric input dem Plausible models that do not solve collinearity Input price data Must include in control function to preserve scalar unobservable Same logic above implies m l are functions of both prices, so still collinear Adjustmest costs in labor Need to add l it 1 to control function Change in timing assumptions Measurement error in l (but not m) Solves collinearity, but makes ˆβ l inconsistent Potential model change that removes collinearity Optimization error in l (but not m) m chosen, l specific shock revealed, l chosen OP only: l it chosen at t 1/2, l it = L t (ω it 1/2, k it ), i it chosen at t

34 Navarro, Rivers from Amiti Jaumreu Idea: like capital, labor is harder to adjust than other inputs Model: l it chosen at time t 1/2, m it at time t Implies m t = M t (k it, l it, ω it ) Estimation: 1 y it = β k k it + β l l it + f t (m it, k it, l it ) +ε it gives }{{} Φ t(m it,k it,l it) ˆω it (β k, β l ) = ˆΦ it β k k it β l l it 2 Moments from timing Markov process for ω it assumptions: ω it = E[ω it ω it 1 ] + ξ it E[ξ it k it ] = 0 as in OP E[ξ it l it 1 ] = 0 from new timing assumption ˆξit (β k, β l ) as residual from nonparametric regression of ˆω it on ˆω it 1 Can add moments based on E[ε it I it ] = 0

35 estimators Navarro, Rivers from Amiti Both derive moment conditions from assumptions about timing information set of firm Dealing with ω Dynamic : AR(1) assumption allows quasi-differencing Control function: makes ω estimable function of observables Dynamic allows fixed effects, does not make assumptions about input dem Control function allows more flexible process for ω it Jaumreu

36 Navarro, Rivers from Amiti Jaumreu Chilean plant level data Compare OLS, FE, LP, ACF, dynamic estimators LP ACF using three different inputs (materials, electricity, fuel) for control function Results: 311=food, 321=textiles, 331=wood, 381=metal Expected biases in OLS FE ACF LP significantly different ACF less sensitive to which input used for control function Dynamic closer to ACF than LP, but still significant differences

37 TABLE 1 Industry 311 Capital Labor Returns to Scale Estimate SE Estimate SE Estimate SE OLS FE ACF M ACF E ACF F LP M LP E LP F DP Industry 321 Capital Labor Returns to Scale Estimate SE Estimate SE Estimate SE OLS FE ACF M ACF E ACF F LP M LP E LP F DP Industry 331 Capital Labor Returns to Scale Estimate SE Estimate SE Estimate SE OLS FE ACF M ACF E ACF F LP M LP E LP F DP

38 TABLE 2 Industry 311 Industry 321 M E F M E F ACF vs OLS ACF vs OLS K K L L RTS RTS ACF vs LP ACF vs LP K K L L RTS RTS ACF vs DP ACF vs DP K K L L RTS RTS Industry 331 Industry 381 M E F M E F ACF vs OLS ACF vs OLS K K L L RTS RTS ACF vs LP LP vs ACF K K L L RTS RTS ACF vs DP ACF vs DP K K L L RTS RTS Note: Value is the % of bootstrap reps where ACF coeff is less than OLS, LP, or DP coef. A value either above 0.95 or below 0.05 indicates that coefficients are significantly different from each other.

39 Section 7 Navarro, Rivers Navarro, Rivers from Amiti Jaumreu

40 Navarro, Rivers Navarro, Rivers from Amiti Show that control function method is not nonparametrically identified when there are flexible inputs Propose alternate estimate that uses data on input shares information from firm s first order condtiion Show that value-added gross output functions are incompatible Application to Colombia Chile Jaumreu

41 Assumptions Navarro, Rivers from 1 Hicks neutral productivity Y jt = e ω jt+ε jt F t (L jt, K jt, M jt ) 2 ω jt Markov, ε jt i.i.d. 3 K jt L jt determined at t 1, M jt determined flexibly at t K L play same role in the model, so after this slide I will drop L 4 M jt = M t (L jt, K jt, ω jt ), monotone in ω jt Amiti Jaumreu

42 Navarro, Rivers from Amiti Jaumreu Reduced form Let h(ω jt 1 ) = E[ω jt ω jt 1 ], η jt = ω jt h(ω jt 1 ) log output y jt =f t (k jt, m jt ) + ω jt + ε jt =f t (k jt, m jt ) + h(m 1 t 1(k jt 1, m jt 1 )) +η jt + ε jt }{{} =h t 1 (k jt 1,m jt 1 ) Assumptions imply Reduced form E[η jt k jt, k jt 1, m jt 1,...k j1, m j1 ] = 0 }{{} =Γ jt E[y jt Γ jt ] =E[f t (k jt, m jt ) Γ jt ] + h t 1 (k jt 1, m jt 1 ) (1) : given observed E[y jt Γ jt ] is there a unique f t, h t 1 that satisfies (3)?

43 Navarro, Rivers from Amiti Jaumreu Let f t (k, m) = β k k + β m m Example: Cobb-Douglas I Assume firm is takes prices as given First order condition for m gives m = constant + Put into reduced form E[y jt Γ jt ] =C + β k 1 k + ω 1 β m 1 β m β k 1 β m k jt + β m 1 β m E[ω jt Γ jt ] + h t 1 (k jt 1, m jt 1 ω Markov ω jt 1 = M 1 t 1(k jt 1, m jt 1 ) implies E[ω jt Γ jt ] =E[ω jt ω jt 1 = M 1 t 1(k jt 1, m jt 1 )] = =h t 1 (k jt 1, m jt 1 ) (2)

44 Example: Cobb-Douglas II Navarro, Rivers from Amiti Which leaves E[y jt Γ jt ] =constant + from which β k, β m are not identified β k 1 k jt + h t 1 (k jt 1, m jt 1 ) 1 β m 1 β m Rank condition fails, E[m jt Γ jt ] is colinear with h t 1 (k jt 1, m jt 1 ) After conditioning on k jt, k jt 1, m jt 1, only variation in m jt is from η jt, but this is uncorrelated with the instruments (3) Jaumreu

45 Navarro, Rivers from Amiti Jaumreu from first order conditions I Since m flexible, it satisfies a simple static first order condition, ρ t =p t F t M E[eε jt ]e ω jt log ρ t = log p t + log F t M (k jt, m jt ) + log E[e ε jt ] + ω jt Problem: prices often unobserved, endogenous ω Solution: difference from output equation to eliminate ω, rearrange so that it involves only the value of materials the value of output (which are often observed) s jt }{{} log ρ tm jt pty jt = log G t (k jt, m jt ) + log E[e ε jt ] }{{}}{{} E ( M t Ft M ) /F t ε jt

46 Navarro, Rivers from Amiti Jaumreu from first order conditions II Identifies elasticity up to scale, G t E ε jt which identifie E Integrating, mjt m 0 G t (k jt, m)/m = f t (k jt, m jt ) + c t (k jt ) identifies f up to location Output equation mjt y jt = m 0 G t (k jt, m)/m c t (k jt ) + ω jt + ε jt mjt c t (k jt ) + ω jt = y jt G t (k jt, m)/m ε jt } m 0 {{ } Y jt

47 from first order conditions III Navarro, Rivers from where the things on the right have already been identified Identify c t from Y jt = c t (k jt ) + h t (Y jt 1, k jt 1 ) + η jt Amiti Jaumreu

48 Value added: Navarro, Rivers from Amiti Jaumreu VA jt =p t Y jt ρ t M jt =p t F t (K jt, M t (K jt, ω jt ))e ω jt+ε jt ρ t M t (K jt, ω jt ) Envelope theorem implies elasticity Y e ω elasticityva e ω (1 ρ tm jt p t Y jt ) Problems Hicks-neutral productivity does not imply value-added Hicks-neutral productivity Ex-post shocks ε jt not accounted for in approximation

49 Navarro, Rivers from Look at tables Value-added estimates imply much more productivity dispersion than gross (90-10) ratio of 4 vs 2 Amiti Jaumreu

50 Section 8 Navarro, Rivers from Amiti Jaumreu

51 Navarro, Rivers from public_events/ fifth-annual-microeconomics-conference/grieco-p_0. pdf Amiti Jaumreu

52 Navarro, Rivers from Amiti Jaumreu My thoughts while reading I How they got the data Incentive shifters may be correlated with quality productivity Time since inspection + Inspect recently higher quality incentive - Low productivity low quality more inspections Referral rate Section 5.2: incentive shifters can be correlated with productivity, only need that shape of possibilities frontier is invariant Should hemoglobin level be controlled for when measuring quality? Anemia (low hemoglobin) is risk-factor for infection Anemia can be treated through diet, iron supplements (pills or IV), EPO, etc Are dialysis facilities responsible for this treatment?

53 Navarro, Rivers My thoughts while reading II In data average full-time dieticiens = 0.5, average part-time = 0.6 Estimation details: Step 1: Estimate α q y jt Ê[y h jt, i jt, k jt, l jt, x jt ] = α q (qjtê[q h jt, i jt, k jt, l jt, x jt ]) + ε jt from Amiti Jaumreu Drop observations with h jt = 0 (not invertibility) Okay here, because selecting on ω, residual, ε jt is uncorrelated with ω Problematic in last step? No, see footnote 49 Step 2: Estimate β k, β l from y jt + ˆα q + β k k jt + β l l jt = g(ˆω jt 1 (β)) + η jt + ε jt

54 My thoughts while reading III Navarro, Rivers from Amiti Only have hatω jt 1 (β) when h jt 1 0, okay because ε jt η jt are uncorrelated with ω jt 1, would be if using ˆω jt Nothing about selection number of centers, 4270, vs center-years, 18295, implies there must be entry exit Would like to see some results related to productivity dispersion e.g. Decompose variation in infection rate into: productivity variation, incentive variation, quality-quantity choices, rom shocks Compare strengthening incentives vs closing least productive facilities as policies to increase quality Jaumreu

55 Section 9 Navarro, Rivers Amiti from Amiti Jaumreu

56 Overview Navarro, Rivers from Amiti Jaumreu Effect of reducing input output tariffs on productivity Reducing output tariffs affects productivity by increasing competition Reducing input tariffs affects productivity through learning, variety, quality effects Previous empirical work focused on output tariffs; might be estimating combined effect Input tariffs hard to measure; with Indonesian data on plant-level inputs can construct plant specific input tariff

57 Navarro, Rivers from Amiti Jaumreu Methodology Estimate TFP using Olley-Pakes Output measure is revenue may confound productivity markups Estimate relation between TFP tariffs log(tfp it ) =γ 0 + α i + α tl(i) + γ 1 (output tariff) tk(i) + + γ 2 (input tariff) tk(i) + ε it (4) k(i) = 5-digit (ISIC) industry of plant i l(i) = isl of plant i Explore robustness to: Different productivity measure Specification of 4 Endogeneity of tariffs

58 Data tariff measure Navarro, Rivers from Indonesian annual manufacturing census of 20+ employee plants , after cleaning 15, 000 firms per year Input tariffs: Data on tariffs on goods, τ jt, but also need to know inputs 1998 only: have data on inputs, use to construct input weights at industry level, w jk Industry input tariff = j w jkτ jt Amiti Jaumreu

59 Results Navarro, Rivers from Amiti Jaumreu Look at tables Input tariffs have larger effect than output, ˆγ , ˆγ Robust to: Productivity measure Tariff measure Including/excluding Asian financial crisis Less robust to instrumenting for tariffs Qualitatively similar, but larger coefficient estimates Explore channels for productivity change Markups (maybe), product switching/addition (no), foreign ownership (no), exporters (no)

60 Criticism Navarro, Rivers from Methodology: Could use LP, ACF, or dynamic methods to estimate TFP Stard errors in productivity regression appear to ignore uncertainty from estimating TFP Measurement error in tariffs could be taken more seriously (is this why IV estimates are larger?) Amiti Jaumreu

61 Section 10 Navarro, Rivers Jaumreu from Amiti Jaumreu

62 Overview Navarro, Rivers from Amiti Estimable model of endogenous productivity, which combines: Knowledge capital model of R&D OP & LP productivity estimation Application to Spanish manufacturers focusing on R&D Large uncertainty (20%-60% or productivity unpredictable ) Complementarities increasing returns Return to R&D larger than return to physical capital investment Jaumreu

63 Navarro, Rivers from Amiti Jaumreu Cobb-Douglas : Model (simplified) I y it = β l l it + β k k it + ω it + ε it Controlled Markov process for productivity, p(ω it+1 ω it, r it ), ω it = g(ω it 1, r it 1 ) + ξ it Labor flexible non-dynamic Value function V(k t, ω t, u t ) = max i,r Π(k t, ω t ) C i (i, u t ) C r (r, u t ) ρ E [V(k t+1, ω t+1, u t+1 ) k t, ω t, i, r, u t ]

64 Navarro, Rivers from Amiti Jaumreu Model (simplified) II u scalar or vector valued shock u not explicitly part of model, but identification discussion (especially p10 footnote 6) implicitly adds it u independent of? k, l? across time? Control function incorporating Cobb-Douglas assumption ( perfect competition): ω it = h(l it, k it, w it p it ; β) = λ 0 +(1 β l )l it β k k it +(w it p it ) Form moments based on y it = β l l it +β k k it +g (h(l it 1, k it 1, w it 1 p it 1 ; β), r it 1 )+ξ it +ε i No collinearity because: Parametric h Variation in k, r due to u Estimated model adds

65 Model (simplified) III Navarro, Rivers from Material input instead of labor for control function h based on imperfect competition Comparison to OP, LP, ACF Amiti Jaumreu

66 Results Navarro, Rivers from Look at tables figures Large uncertainty (20%-60% or productivity unpredictable ) Complementarities increasing returns Return to R&D larger than return to physical capital Amiti Jaumreu

67 Navarro, Rivers from Amiti Jaumreu D., K. G. Frazer Structural identification of functions. URL D., C. Lanier Benkard, S. Berry, A. Pakes Econometric tools for analyzing market outcomes. Hbook of econometrics 6: URL pii/s Ungated URL Daniel A., Kevin Garth Frazer Properties of Recent Function Estimators. Econometrica 83 (6): URL Aguirregabiria, Victor Empirical Industrial Organization: Models, Methods, Applications. URL courses/eco2901/teaching_io_toronto.html.

68 Navarro, Rivers from Amiti Jaumreu Amiti, Mary Jozef Konings Trade Liberalization, Intermediate Inputs, Productivity: Evidence from Indonesia. The American Economic Review 97 (5):pp URL Aw, Bee Yan, Xiaomin Chen, Mark J. Roberts Firm-level evidence on productivity differentials turnover in Taiwanese manufacturing. Journal of Development Economics 66 (1): URL pii/s Blundell, R. S. Bond GMM estimation with persistent data: an application to functions. Econometric Reviews 19 (3): URL

69 Navarro, Rivers from Amiti Jaumreu Bond, Steve Måns Söderbom Adjustment costs the identification of Cobb Douglas functions. IFS Working Papers W05/04, Institute for Fiscal Studies. URL Ulrich Jordi Jaumreu R&D Productivity: Estimating Endogenous Productivity. The Review of Economic Studies 80 (4): URL abstract. Foster, L., J.C. Haltiwanger, C.J. Krizan Aggregate productivity growth. Lessons from microeconomic evidence. In New developments in productivity analysis. University of Chicago Press, URL

70 Navarro, Rivers from Amiti Jaumreu Foster, Lucia, John Haltiwanger, C. J. Krizan Market Selection, Reallocation, Restructuring in the U.S. Retail Trade Sector in the 1990s. The Review of Economics Statistics 88 (4):pp URL A., S. Navarro, D. Rivers On the of : How Heterogeneous is Productivity? URL https: //sites.google.com/site/econsalvador/research/ _9_25_13_FULL.pdf?attredirects=0. Grieco, Paul LE Ryan C Productivity Quality in Health Care: Evidence from the Dialysis Industry. Review of Economic Studies (forthcoming) URL 08/MS17933manuscript.pdf.

71 Navarro, Rivers from Amiti Jaumreu Javorcik, Beata Smarzynska Does Foreign Direct Investment Increase the Productivity of Domestic Firms? In Search of Spillovers through Backward Linkages. The American Economic Review 94 (3):pp URL Kortum, Samuel Josh Lerner Assessing the Contribution of Venture Capital to Innovation. The RAND Journal of Economics 31 (4):pp URL Levinsohn, James Amil Petrin Estimating Using Inputs to Control for Unobservables. The Review of Economic Studies 70 (2):pp URL Maican, F.G Productivity dynamics, r&d, competitive pressure. ECONOMIC STUDIES DEPARTMENT OF ECONOMICS SCHOOL OF BUSINESS, ECONOMICS AND LAW UNIVERSITY OF GOTHENBURG.

72 Navarro, Rivers from Amiti Jaumreu Olley, G.S. A. Pakes The dynamics of productivity in the telecommunications equipment industry. Econometrica 64 (6): URL Söderbom, Måns, Francis Teal, Alan Harding The Determinants of Survival among African Manufacturing Firms. Economic Development Cultural Change 54 (3):pp URL Van Beveren, I Total factor productivity estimation: a practical review. Journal of Economic Surveys URL x/full. Wooldridge, Jeffrey M On estimating firm-level functions using proxy variables to control for unobservables. Economics Letters 104 (3): URL pii/s