(DRAFT - DO NOT CITE OR CIRCULATE) Product innovation, prices and factor reallocations

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1 (DRFT - DO NOT CITE OR CIRCULTE) Product innovation, prices and factor reallocations Clemens C. Struck September 16, 2015 bstract There is overwhelming evidence of substantial heterogeneity in production technologies across industries. Can we use a single production function to represent all these different industries on aggregate? nd, how can the economy have stable aggregate features when there are continuous reallocations of production factors (structural change) across these industries? To address these questions I use a framework of heterogeneous industries and endogenous growth. I underline a key implication of the economic growth literature: to reconcile the industry heterogeneity with aggregate economic outcomes (balanced growth) productivity growth needs to be biased towards labor. I show that this means that productivity growth needs to be higher in industries that are more labor intensive. In standard post-war U.S. data, however, I find no evidence that supports such a relation. Yet, I illustrate that productivity estimates based on these data suffer from measurement issues - likely because of underlying measurement problems in inflation. I show that downward revising aggregate inflation mechanically biases the estimates of productivity growth towards the labor intensive industries. ssuming that inflation is annually overstated by 1 percentage point can already restore the theoretically required allocation of productivity growth. Using numerical techniques, I then illustrate how adjusted productivity estimates can simultaneously induce balanced growth and structural change in the post-war U.S. environment of substantial heterogeneity in industry production technologies. JEL: E1, E13, E31, O31 Keywords: biased technological change, inflation bias, structural change, allocation of innovation struckc@tcd.ie, Department of Economics, Trinity College Dublin. n earlier version of this paper is part of my PhD thesis. ll errors are my own. 1

2 1 Introduction There is strong evidence of substantial heterogeneity in production technologies across industries (see e.g. Ricardo (1821), Heckscher (1919), Ohlin (1933), Helpman and Krugman (1985) and Melitz (2003)). Figure 1 shows that industries differ in labor intensity, capital-labor elasticity and productivity. Can we use a single production function to represent all these different industries on aggregate? nd, how can the economy have stable aggregate features when there are continuous reallocations of production factors (structural change) across these industries? To reconcile the industry heterogeneity with aggregate economic outcomes (balanced growth), I highlight a key implication of the economic growth literature: more productivity growth needs to occur in industries that are more labor intensive. 1 Yet, in the post-war U.S. industry data - an economy with standard aggregate economic outcomes 2 - I find no evidence that supports such a relation. The evidence I find rather supports the presumption of Baumol (1969), Balassa (1964) and Samuelson (1964) that productivity growth is not particularly high in the labor intensive industries. 3 In this essay, I show that downward revising aggregate inflation mechanically biases the estimates of productivity growth towards the labor intensive industries. ssuming that aggregate inflation is annually overstated by 1 percentage point can already restore the theoretically required allocation of productivity growth. To support my point, I present evidence that suggests that productivity estimates based on the standard data are mismeasured, likely because of measurement problems in inflation: 8 out of 20 industries exhibit either no or negative productivity growth during the 60 year post-war period. 4 My argument is 1 Uzawa (1961), cemoglu (2002) and Jones (2005) show that labor augmenting productivity growth is a prerequisite of balanced growth. I show that an implication of labor augmenting progress is that productivity growth is higher in industries that depend more on labor. To illustrate this, suppose the production function is Cobb-Douglas, i.e. Y = K α (L) α. Then if technical progress is purely labor augmenting, the measured rate of technical change, ( t t ) α, is higher in industries where α is higher. 2 Some recent studies such as Elsby et al. (2013) and Karabarbounis and Neiman (2014), among others, argue that the U.S. labor share has trend declined since the late 1970s and early 1980s. This evidence is sometimes taken as evidence against balanced growth. The size of this decline, however, amounts to less than 5 percentage points which can be viewed as normal medium-term behavior. The evidence of Piketty and Zucman (2014), for example, suggests that medium-term movements of this magnitude are a frequent phenomenon and can already be observed in the 19th century in the U.K. and in France. Gomme and Rupert (2004) show that this decline can be interpreted as a measurement issue. In 2012 Rupert reiterates this point on his blog. He recalculates the U.S. labor share based on the methodology of Gomme and Rupert (2004) and finds that the labor share in 2010 is close to its long-term average. 3 These papers assume that productivity growth in the service sector, which constitutes a large part of the non-tradable sector is low relative to the manufacturing sector which constitutes a major part of of the tradable sector. In this paper, I split the economy into labor and capital intensive industries. The main part of services lies in the labor intensive sector to which also fast growing sectors such as durable goods and transportation belong. 4 There is a large literature concerned with this issue to which, among many others, Baumol et al. (1985), Berndt et al. (2001), Hulten et al. (2001), Triplett and Bosworth (2003), Lebow and Rudd (2003), Griliches (1992), Griliches (1998), hmad et al. (2003), Wölfl (2005) and Oulton (2001) contribute. main theme in this literature is that the problem of negative long-run productivity growth rates is likely the result of a problem in measuring real variables in services (which constitute a substantial part of the labor intensive industries in this essay), i.e. measurement problems in inflation. I follow this literature in assuming that measurement problems in inflation are the cause of negative productivity growth rates. 2

3 vs B vs ln PK ω /P ω Y ω corr=0.9 PK ω /P ω Y ω corr= Capital Labor Elasticity, σ ω PK ω /P ω Y ω ln TFP C vs corr= Capital Labor Elasticity, σ ω ln TFP D vs PK ω /P ω Y ω corr=0.08 Notes: the panels show the author s calculations based on data drawn from the U.S. Bureau of Economic nalysis (BE). The 2-digit NICS industry level is denoted by τ. The data are 10-year averages at the beginning and end of the sample period. Panel plots the dispersion of the the capital-labor elasticity, σ τ, and the change in the capital output ratio lnp K τ P τ Y τ. Panel B plots the dispersion of the capital-output ratio, P K τ P τ Y τ. Panel C plots the relation between total factor productivity growth, lnt F P, and the capital-labor elasticity. Panel D plots the relation between productivity growth and the capital-output ratio. Figure 1: Industry level heterogeneity. laid out in three main parts. First, I use a standard framework of heterogeneous industries to illustrate that balanced growth requires more productivity growth in the more labor intensive industries. I then show analytically that this allocation emerges endogenously when technology spillovers are symmetric across industries. Next, I study the allocation of productivity growth in the standard post-war U.S. data. I conduct several robustness tests to establish that there is no relation between the capital-labor elasticity, the capital-output ratio and the allocation of productivity growth in the standard data. I then show that adjusting the data in a quantitatively reasonable way biases the estimates of productivity growth towards the labor intensive industries. Finally, I employ numerical techniques to illustrate how adjusted productivity estimates can simultaneously induce balanced growth and structural change in the post-war 3

4 U.S. environment of substantial heterogeneity in industry production technologies. Why does downward adjusting the standard data asymmetrically affect the productivity estimates? When inflation is overstated, the adjusted capital stock is larger across all industries than the standard data reveal. Because capital has a similar price index across industries, it increases commensurately as a result of adjusting prices. The change in capital is asymmetrically fortified by the cross-industry differences in capital intensities and capital-labor elasticities. The adjustment therefore asymmetrically affects the estimation of productivity growth. This effect is even stronger when taking into account that 6 industries in the labor intensive sector that account for 27.6% of GDP but only 2 industries within the capital intensive sector that account for 10.2% of GDP exhibit no or negative productivity growth in the standard data. 5 To illustrate that the effect of downward adjusting inflation is not a byproduct of a particular technique I reduce inflation directly in the data. The effect rather comes from two empirically grounded assumptions. First, I assume that capital has a similar price index across industries and, thus, adjusts commensurately when correcting inflation. Second, I assume that an inflation adjustment biases real output growth slightly to the labor intensive industries at the sectoral level. By how much do I need to reduce aggregate inflation? I theoretically show that productivity growth in labor intensive industries needs to be approximately twice as high as in capital intensive industries. This differential can already be reached when aggregate inflation is overstated by 1 percentage point annually and there is a slight asymmetry in the adjustment at the sectoral level. Related literature. The model of industry heterogeneity that I use to guide my analysis is an extension of cemoglu and Guerrieri (2006) and, thus, is particularly close to the models in the literature on structural change. This literature mainly emphasizes two different mechanisms. The model is close to theories of structural change in which factor reallocations emerge as a consequence of technological change. Papers that employ this mechanism are, among others, Baumol (1969), cemoglu and Guerrieri (2008), Ngai and Pissarides (2007), Duarte and Restuccia (2010), Carvalho and Gabaix (2013), Balassa (1964), Samuelson (1964), Matsuyama (2009) and Vollrath (2009). common alternative way of modeling structural change is taken by Kongsamut et al. (2001) who, among others, argue that preferences for goods change in the level of development and that these changes cause factor reallocations. 6 Herrendorf et al. (2013) 5 gain, this assumption is also in line with the results of the literature on productivity mismeasurement that I cite in the previous footnote. 6 t the core of this approach is an income effect. The models in this literature usually rely on a form of non-nomothetic preferences to replicate dynamics that comply with Engel s law. Examples of this literature are Laitner (2000), Foellmi and Zweimüller (2008), Matsuyama (1992), Matsuyama (2002), Caselli and Coleman (2001), Gollin et al. (2002) and Buera and Kaboski (2012). 4

5 point out that these two approaches comply with either value-added or final expenditure interpretations of the data. Buera and Kaboski (2009) and Boppart (2014) study both drivers of structural change in a joint framework. The main point of departure from this literature is in focusing on how to reconcile the industry heterogeneity in production technologies with balanced growth. 7 To generate balanced growth and structural change simultaneously in the non-balanced growth framework of cemoglu and Guerrieri (2006), I augment the model with a new technology spillover structure and with CES production functions at the industry level. In contrast to most papers in this literature I do not directly attempt to model the output composition shifts of Services, griculture and Manufacturing. Instead, I show that an economy that exhibits balanced growth can be decomposed into two representative industries of heterogeneous productions technologies and stable output shares. I show analytically that the technology spillover structure generates a bias of technical change that induces stable output shares within the economy when production is Cobb-Douglas. I then numerically show that the bias of technical change induces balanced growth while heterogeneity in capital-labor substitutability across industries simultaneously generates factor reallocations when production is CES. There are few studies that acknowledge the role of the endogenous allocation of productivity in the context of structural change. Young (2014) argues that workers self-select into industries upon their relative productivity in different tasks. This idea relates to the work on the allocation of skill by Roy (1951), Heckman and Sedlacek (1985) and, more recently, Hsieh et al. (2013). Ghironi and Melitz (2005) argue that more productive firms self-select into the export industry. Earlier research endogenizes the allocation of productivity across factors. In cemoglu (2002) and cemoglu (2003) technological progress is directed towards labor and macroeconomic stability is reached only in the absence of technology spillovers across industries. In a setup similar to the one used here, cemoglu and Guerrieri (2006), cannot restore balanced growth even in the absence of cross-industry technology spillovers. I show that balanced growth can be reached in the cemoglu and Guerrieri (2006) setup when there are symmetric technology spillovers 7 The recent literature on structural change usually bypasses the observed heterogeneity in production technologies across industries. Instead it assumes a Cobb-Douglas production technology that is identical across industries. The literature thereby subconsciously imposes balanced growth on the economy, at least in one key dimension. Given that the aggregate labor share is an output-weighted average of the industry labor shares, it is not surprising that the aggregate labor share is stable when the industry labor shares are identical and constant by assumption. The empirical evidence of Figure 1 clearly shows that a theory of balanced growth needs a stable labor share to emerge from an environment of continuous factor reallocations across heterogeneous industries. In cemoglu and Guerrieri (2006), however, balanced growth emerges only asymptotically after all but one sector has disappeared. lvarez-cuadrado et al. (2014) use heterogeneous CES functions at the sectoral level. What restores balanced growth in their model is the assumption that technical change is labor biased. They can recover labor biased technical change from the data, but only after the estimation is set to match the data. 5

6 across industries. 8 I then take the model to the data and show how the industry decomposition offers a way to empirically determine the bias of technical change in the data which is the primary contribution of this essay. The essay, thus, indirectly contributes also to the literature that attempts to determine the aggregate degree of substitution between capital and labor. The empirical evidence of Oberfield and Raval (2014), Klump et al. (2007), rrow et al. (1961), Sato (1970) and Lucas (1969), among others, points to an elasticity of less than unity, i.e. complementarity of capital and labor. There are few theoretical studies of this issue. Jones (2005) and Lagos (2006) present models based on Houthakker (1955) and Kortum (1997) in which productivity levels are drawn from Pareto distributions which implies that production takes a Cobb-Douglas form, i.e. the elasticity of substitution between capital and labor is unity. While innovation has been studied extensively in the endogenous growth literature, this literature usually does not quantify its empirical implications regarding price growth which I argue are important in the context of the allocation of productivity growth. Instead, the majority of contributions concerned with the effects of innovation on price growth focuses on empirically adjusting prices. Boskin (1998) identifies categories in the CPI, which constitutes a large part of output prices, and finds, after weighting different biases by categories, a bias in a range of 0.8 to 1.6pp. Estimating Engel curves, Bils and Klenow (2001) find that the inflation is overstated by 2.2pp among the 66 durable goods they examine. Using new data, Broda and Weinstein (2010) estimate a cost-of-living index to be 0.8pp lower than the CPI. Lebow and Rudd (2003) review the literature and estimate the confidence interval ranging from 0.3 to 1.4 percentage points. 9 I depart from these papers in that I show that a quantitatively plausible inflation adjustment helps to restore the theoretically required allocation of productivity growth that induces balanced growth. key takeaway from this exercise is that estimates of the bias of technical change are sensitive to underlying measurement problems in the data. Griliches (1992), Griliches (1998), Wölfl (2005) and hmad et al. (2003), among many others, argue that productivity growth could well be higher in the labor intensive industries if measurement problems in real output are properly accounted for. nother explanation, made by Oulton (2001), is that low productivity growth in services is due to the market structure of services, i.e. that service industries produce intermediate, not final goods. lthough the measurement procedures are frequently updated, the negative long run productivity estimates indicate that the recent BE U.S. 8 This parameter choice is somewhat less restrictive than the parameter choices in previous setups. Ngai and Pissarides (2007), among others, illustrate that balanced growth would be knife edge even if all industries used identical Cobb-Douglas production functions. They reconcile their model with balanced growth under the assumption that the intertemporal elasticity of substitution (IES) takes the value of 1. This parameter choice contrasts with the broadly accepted estimates of Hall (1988), which suggest a rather low IES close to 0. 9 Other articles on adjusting data for quality and variety improvements are Feenstra (1994), Broda and Weinstein (2004), Schott (2004), Hummels and Klenow (2005), Hallak (2006), Khandelwal (2010) and Hallak and Schott (2011). Handbury et al. (2013), for example, find that the precision of the CPI bias is not constant but depends on the level of inflation. Bils (2004) estimates the quality growth to be 5.6pp annually. 6

7 post-war NIP data used in this essay are still affected by these problems. Outline. The essay proceeds as follows. Section 2 conducts a breakdown of the economy into heterogeneous that serves as the focal point for the analysis in this paper. In section 3, I present a standard model of industry level heterogeneity and macroeconomic stability that follows this approach. First, I derive a condition for the allocation of productivity growth that induces balanced growth. I then characterize this allocation as an endogenous outcome. In Section 4, I test the model s implications. I establish that the standard data reveal a disconnect between productivity growth and other industry production characteristics. I then show that revising aggregate inflation downward biases the productivity estimates towards the labor intensive industries. In section 5, I use these estimations to illustrate that the adjusted allocation of productivity growth simultaneously generates macroeconomic stability and structural change in post-war U.S. environment of substantial industry heterogeneity. Section 6 concludes. 2 Preliminaries In this section, I show that an economy with stable aggregate factor shares can be decomposed into two industries of heterogeneous production technologies and stable output shares. This decomposition serves as the focal point for the analysis in this essay. It differs from a typical decomposition of the economy into industries such as griculture, Manufacturing and Services. 10 In the theoretical analysis below I explain this decomposition as an endogenous outcome. In particular, I show that this decomposition arises when technological progress is biased towards the industries that rely more on labor. In the empirical analysis further bellow I show how this decomposition can easily be recovered from the standard post-war U.S. industry data. I then empirically study the condition - labor biased technical change - that leads to it. The decomposition follows from a simple accounting identity. Suppose, there is a finite set of industries τ = {,,..., N}. The aggregate wage rate for the whole economy is w, total labour supply is L, the aggregate price level is P and total output is Y. Variables with subscript τ denote the industry level. The aggregate labor share can be expressed as an output-weighted sum of the industry labor shares: 10 I mainly rely on an alternative decomposition because of the difficulty of distinguishing different goods categories in practice. Final goods are often a combination of the intermediate goods of different categories and the intermediate goods are the output of a production network that links inputs from different categories together. Thus, what classifies as Manufacturing, Services or griculture is somewhat arbitrary. 7

8 w t L t P t Y t τ τ aggregate labor share w τ,t L τ,t P τ,t Y τ,t ) ] ) industry τ s labor share P τ,t Y τ,t P t Y t ) ] ) industry τ s output share. (1) From this decomposition I now derive two propositions that reveal the presence of two industries of heterogeneous production technologies with stable output shares in the data. Proposition 1 (Cobb-Douglas): Suppose that the labor share differs across industries and that aggregate and industry labor shares are constant. Then, if there exists a decomposition of the economy with changing output shares, there simultaneously exists another decomposition with constant output shares. Proof: see ppendix.1. Proposition 2 (CES): Suppose that the labor share differs across industries and changes over time and that the aggregate labor share is constant. Then, if there exists a decomposition of the economy with changing output shares, there simultaneously exists another decomposition with constant output shares and where industry labor shares increase in some industries and decrease in others. Proof: see ppendix.1. 3 The Model Consider an economy in which aggregate output is a composite of the output of two intermediate industries τ =,. The output of the intermediate industries can be combined to form a final good that can be used for consumption, investment and research. The intermediate industries differ in their labor intensity. In each industry τ, there are M τ,t symmetric firms i (, M τ,t at time t. The number of infinitely living consumers grows at an exogenously given constant rate, n. 3.1 Industries In this subsection I present a special case of this model - a standard neoclassical model of heterogeneous industries - to highlight the key condition that induces balanced growth. The standard model is basically 8

9 the industry representation of the full endogenous growth model. In the next section I provide an endogenous growth foundation for this model by introducing firm varieties within the industries. The final good, Y, is a composite of the output of the perfectly competitive intermediate industries Y and Y. Formally, Y t = (γ ε Y ε ε,t + ( γ ) ε Y ε ε,t ) ε ε, (2) with ε being the elasticity of substitution between industries and γ the share of good in final output. Different industries exhibit strong complementarity as I show in an estimation of the elasticity of substitution in Section 4.2. In line with this finding, I assume throughout the theoretical analysis that industries are complements. ssumption 1. The output of the intermediate industries is complementary, i.e. ε <. Each industry produces output using a constant elasticity of substitution production technology, Y τ,t = τ,t Kτ,t ατ ατ Lτ,t, (3) where K τ,t is the capital stock of industry τ; L τ,t is the amount of labor used by an industry. τ,t is the productivity. α τ is the share of capital in production. Thus, there are two sources of heterogeneity in production: i) the industry specific share of capital and ii) the level of productivity. ssumption 2. The labor intensity differs across industries, i.e. α > α. For simplicity, I derive the main analytical points of this essay under the assumption that the elasticity of substitution between capital and labor, σ τ, equals unity, i.e. that production takes the Cobb-Douglas form. In the empirical analysis below, I begin with the Cobb-Douglas case and then continue with the more general CES case. In ppendix.4, I present the derivation details of the model under the assumption that σ τ is not unity, 11 i.e. when production takes a more general CES form, στ στ Y τ,t = τ,t ] α τ Kτ,t στ στ + ( α τ )Lτ,t στ στ {. (4) 11 lvarez-cuadrado et al. (2014) is the first article in the literature on structural change that uses CES production functions at the industry level. Examining plant level data in the U.S., Oberfield and Raval (2014) reject an capital-labor elasticity that equals unity in the manufacturing industry. 9

10 The derivation details of the analytical solution are contained in ppendix.2. The key result is that, under standard consumer preferences, balanced growth emerges when productivity growth is labor augmenting. This means that productivity growth is higher in the more labor intensive sector such that relative productivity growth equals the relative labor share: = α α. (5) Proposition 3. Suppose ssumptions 1 and 2 hold. Then, for the standard model to exhibit balanced growth, i.e. K K = K K = K K, Y Y = Y Y = Y Y, P P = P P, more productivity growth needs to occur in the more labor intensive industries such that relative productivity growth equals the relative labor share. Derivation details: see ppendix Firms I now show how balanced growth and Proposition 3 can be derived as an endogenous outcome. Suppose that output of each industry is produced by a continuum of monopolistically competitive firms, Y τ,t = i= M τ,t φ φ φ yτ,i,t di} φ, (6) where y i,τ,t is the output of firm i in industry τ; φ > denotes the firm elasticity of substitution; M τ,t is the number of firms in industry τ at time t. firm i in industry τ produces output using a constant elasticity of substitution production technology, y τ,i,t = k ατ ατ τ,i,tlτ,i,t (7) where k τ,i,t is the capital stock that firm i in industry τ uses for production; l τ,i,t is the amount of labor used by a firm; M τ,t is still the number of varieties in industry τ. Each firm maximizes profits π τ,i,t π τ,i,t = p τ,i,t y τ,i,t w τ,i,t l τ,i,t r τ,i,t k τ,i,t. (8) where p τ,i,t is the price of firm i in industry τ; w τ,i,t is the price of labor; r τ,i,t is the price of capital. The profit of firm i in industry τ can be expressed as a function of industry output (ppendix.3 shows the derivation details), 10

11 π τ,i,t = φ P τ,t Y τ,t M τ,t. (9) t the industry level, production can be expressed as in the standard setup, that is, Y τ,t = M φ τ,t Kτ,t ατ ατ Lτ,t τ,t Kτ,t ατ ατ Lτ,t. (10) Research production takes the form of M M = b M ν M μ X and M M = b M ν M μ X, (11) where X τ denotes the research expenditure in industry τ; b τ is a positive parameter that governs the costs of research; ν, μ are parameters that measure the degree of state dependence. When μ =, there are no spillovers across industries. The spillover structure generates balanced growth as I illustrate below. It differs from the structures chosen by cemoglu (2002), cemoglu (2003) and cemoglu and Guerrieri (2006) in that it allows for research spillovers across industries. This earlier literature finds that balanced growth emerges only in the absence of technology spillovers across industries and in the presence of extreme state-dependence. ssuming that the value function is differentiable in time, the net present discounted value of profits of monopolist i starting at time t is given by V τ,i,t = π τ,i,t + V τ,i,t r t. (12) One unit spent on research in industry leads b M ν M μ units of new monopolists. One unit spent on research in industry leads b M ν M μ units of new monopolists. Free entry into research then implies that the profits from new monopolists equals the research expenditures (assuming research expenditure is positive): V,i = M ν M μ b and V,i = which hold as equalities as long as research expenditure is positive. M ν M μ b, (13) 3.3 Consumers The number of workers in the economy grows at an exogenously given rate, L t = e nt L. (14) 11

12 ll workers have identical preferences over the aggregate consumption good. These preferences can be represented as the utility function of a single consumer: e (ρ n)t c t θ θ dt, (15) where c t denotes the per-capita level of real consumption; ρ denotes the time preference parameter; θ is the inverse of the inter temporal elasticity of substitution. Labor is inelastically supplied. The representative consumer faces the following budget constraint: K + K + C + X + X = w L + w L + r K + r K +, (16) where X and X denote the research expenditures in industries and, respectively; C t = L t c t is aggregate real consumption; K τ is the change in the sector τ s capital stock; w τ is the wage rate; r τ is the return to capital; denote the economy s profits. The wealth of the consumer, W, is the sum of the aggregate capital stock and the value of the firms in the two industries and is given by where K = τ K τ ; the no-ponzi condition therefore takes the form of W t = K t + V,t + V,t, (17) {W t ] t The growth rate of consumption is given by t s= (r(s) n)ds{ (. (18) Thus, per-capita consumption growth is constant, as long as rt P t 3.4 Market Clearing c c = θ ( r t P t ρ). (19) is constant. ll factor markets are competitive, thus, capital and labor markets clear, L t = L,t + L,t i= M,t l,i,tdi + i= M,t l,i,t di, K t = K,t + K,t i= M,t k,i,tdi + i= M,t k,i,t di. (20) 12

13 The sum of firm profits in the two industries equal aggregate profits t =,t +,t i= M,t π,i,tdi + i= M,t π,i,t di. (21) Since firms within industries are symmetric, industry output can be expressed as the output of firm i premultiplied by an indicator of the quantity of firms in the industry Y t = Y,t + Y,t y,i,tm φ φ,t φ φ + y,i,t M,t. (22) Because the key derivation details of this model are contained in cemoglu and Guerrieri (2006), I use a rather short equilibrium definition and then mainly focus on how to restore balanced growth in this framework. 3.5 Equilibrium dynamic equilibrium is defined by time paths of prices, {{w τ,i,t } Mτ,t i=, {r τ,i,t} Mτ,t i=, {p τ,i,t} Mτ,t i=, P τ,t} t=, for all industries τ =,, and quantities, {c t, {k τ,i,t } Mτ,t i=, {l τ,i,t} Mτ,t i=, {y τ,i,t} Mτ,t i=, Y τ,t, L τ,t, K τ,t, X τ,t, M τ,t } t= given the labor supply {L t } t= such that i) p τ,i, k τ,i, l τ,i, maximize the profits of the monopolistically competitive firms ii) X, X, L, L, K, K and c maximize representative consumer s intertemporal problem iii) demand for the perfectly competitive intermediate industries, Y and Y, maximizes the use of the final good Y iv) output of the monopolistically competitive firms, y τ,i, maximizes the supply of the intermediate industries Y τ v) markets clear. 3.6 Long run behavior To ensure that output growth rates are asymptotically positive, I impose an additional parameter restriction. ( ( α )(ν + μ) (φ ) (( ε)(φ ) μ + ν) (α α )( ε)(φ )μ > (23) This restriction is part of the following assumption that ensures the model is asymptotically well behaved. ssumption 3. symptotic output growth is positive, i.e. Y Y >, and the transversality condition holds, i.e. ρ n > Y Y. 13

14 I now present the central proposition of this essay on the bias of productivity growth within the economy. The intuition for this proposition goes back to the assumption that labor cannot be accumulated like capital, i.e. the assumption that labor is scarce relative to capital. This assumption particularly limits the output of the industry with the higher labor intensity. By contrast, in the industry with the higher capital intensity, the scarcity of labor does not constrain output as much. Since both industries exhibit gross complementarily, the consumer wants both industries to grow commensurately. To achieve this, more productivity growth needs to occur in the industry that is more constraint by the scarcity of labor. Productivity growth in the two industries is given by (φ ) ( ε)( α ) ( α )(φ )μ + ( α )(φ )ν L = ( ( α )(ν + μ) (φ ) (( ε)(φ ) μ + ν) (α α )( ε)(φ )μ L, (24) = (φ ) ( ε)( α ) ( α )(φ )μ + ( α )(φ )ν L ( ( α )(ν + μ) (φ ) (( ε)(φ ) μ + ν) (α α )( ε)(φ )μ L, (25) These two equations show that the allocation of productivity growth is driven by the technology spillover structure, i.e. by the parameters ν and μ. s cemoglu (2002) illustrates, the absence of technology spillovers leads to balanced growth in a similar setup. The results of the setup here are more general as balanced growth can also be achieved despite the presence of technology spillovers. I now focus on a special case: technology spillovers are symmetric across industries. This symmetry implies that the percent increase in productivity for a given unit of the final good spent on innovation is always the same in both industries. Under symmetric technology spillovers the model therefore exhibits balanced growth as in a model in which there are no spillovers at all. Proposition 4. Suppose ssumptions 1, 2 and 3 hold. Then, for the endogenous growth model to exhibit balanced growth, i.e. K K = K K = K K, Y Y = Y Y = Y Y, P P = P P, technology spill-overs need to be symmetric, i.e. μ = ν. Derivation details: see ppendix.3. In the following section, I focus on determining empirically whether or not productivity growth is really labor biased. 14

15 4 Empirical nalysis In this section I use the post-war U.S. NIP (National Income and Product ccounts) data to test whether the condition that induces balanced growth is satisfied empirically. I describe the data in Section 4.1. Because some of the exercises that follow rely on an estimate of the goods elasticity of substitution, I estimate this elasticity across industries in Section 4.2. The main analysis is then split into two parts. First, in Section 4.3, I discuss the potential of the allocation of productivity growth to generate balanced growth. In particular, in this section I break down the economy into two main industries of approximately stable output shares that closely correspond to the hypothetical decomposition that Propositions 1 and 2 purport. This section reveals a fundamental disconnect between the allocation of productivity growth and production characteristics such as the industry labor intensity which makes it difficult to generate balanced growth. I then present evidence that suggests inflation is likely mismeasured. Second, in Section 4.4, I show that downward revising aggregate inflation biases the productivity estimates towards the labor intensive industries. 4.1 The Data The empirical analysis employs the U.S. Bureau of Economic nalysis NIP post-war data. This dataset contains information on prices as well as on nominal and real variables of output, capital and labor at the 2-digit industry level. For both, the analysis at the aggregate and disaggregate level, I use this dataset. To study the long run change of key economic variables, I compare 10-year averaged data at the beginning and end of the sample period. For the starting period of the data, I choose t =, while I set the end period to t =. For the entire sample period, data on a total of 26 industries are available. s a robustness check, I also consider a later initial period, t =. The advantage being that 86 industries are available from I split the industries into two categories - labor intensive and capital intensive - which not only differ in their capital intensity but also in their capital-labor elasticity. 4.2 The Goods Elasticity of Substitution Since the model assigns key importance to the goods elasticity of substitution in shaping the allocation of production factors and innovation, I now focus on determining its magnitude. Because the estimation procedure involves the use of the standard price data that may well overstate inflation, the estimates that I obtain in this section can only be considered as reference points. I establish that the goods elasticity of substitution is rather close to zero. To back out the elasticity, I impose the industry demand structure of Eq. (2) on the data, 15

16 Using the BE data on 26 industries, I run the following specification P τ,t Y τ,t = γ τ ( P ε τ,t ). (26) P t Y t P t ln P τ,ty τ,t P ty t P τ,t Y τ,t P t Y t =. (. +. (. ln P τ,t P t P τ,t P t + λ t, (27) where λ t is white noise; t-values are in brackets. Regressing changes in nominal expenditure on changes in prices across industries, I find a regression coefficient of., implying a goods elasticity of substitution, ε, of.. Because the goods elasticity is crucial for the analysis of this essay, I test the robustness of the previous estimate starting the sample period in I obtain an estimate of ε =.. These estimates are somehow lower than those in previous studies. cemoglu and Guerrieri (2008) obtain a confidence interval of [ ] from a static regression. 12 Because the productivity estimates that are the main focus of this essay are estimated independent of the goods elasticity, the key results of this essay remain unaffected by using different values of this elasticity. 4.3 The llocation of Productivity in Standard Data Using the standard post-war U.S. data, I now present evidence that closely corresponds to the hypothetical decomposition of the economy described in Propositions 1 and 2. Table 1 ranks industries by their labor intensity. It also breaks down the economy into two roughly stable fractions: a labor intensive and a capital intensive industry. The labor intensive industry has an average labor share of. and its share in output amounts to roughly of all private industries. The capital intensive industry s labor share is. and it takes up the remaining output share of about. Between and , the change in the output shares of both industries amounts to less than 2 percentage points. For the purposes of this essay, this is a reasonably close approximation of a decomposition into two industries with stable output shares. 12 The estimation procedure of cemoglu and Guerrieri (2008) has two main drawbacks relative to the one employed in this essay: first, their estimate relies on the ratio of the real output of industries. Since the U.S. data measure the price index, not the level of prices, the relative real output of industries is more of a pseudo measure that is derived from dividing relative nominal output by the price indexes. I can circumvent this problem, by using the change in time. This allows me to avoid calculating the relative real output. Instead, I use the change in the relative real output which is consistent with the intention of price indexes to capture the real change in time, not the level. Second, they need to estimate an additional time-invariant parameter - the ratio of the shares of goods in the CES basket. This parameter drops out when I estimate the change over time. 16

17 vs B vs corr= corr= 0.05 ln TFP ln TFP Capital Labor Elasticity, σ ω Capital Labor Elasticity, σ ω 4.5 C vs D vs ln TFP corr=0.08 ln TFP corr= PK ω /P ω Y ω PK ω /P ω Y ω Notes: the panels show the author s calculations based on data drawn from the U.S. Bureau of Economic nalysis (BE). The figures plot the change in the total factor productivity shares, lnt F P, in post-war U.S. industries against the industry capital-output ratio, P K τ P τ Y τ, and the industry capital-labor elasticity, σ τ. The industry level is denoted by τ. Figure 2: U.S. industry productivity growth and industry production characteristics. To address the question whether or not the model can meet the conditions necessary to generate balanced growth, I now focus on the allocation of productivity growth within the economy. Figure 2 plots the relation between TFP growth, the capital-labor elasticity and the capital share at the industry level. The figure indicates that there is a disconnect between productivity growth and production characteristics, i.e. there is no tendency for productivity growth to be higher in the more labor intensive industries. In the light of Proposition 4, this is bad news as it means that the allocation of productivity growth implies a set of technology spillovers which seems to work against balanced growth. Based on the relative labor intensity, Eq. (5) implies that productivity growth in the more labor intensive industry needs to be ( α ) ( α ) =.. =. higher than in the capital intensive industry. The productivity growth rates 17

18 of the standard data of Table 1 (Column 9) indicate that the productivity growth differential only amounts to ln(.) ln(.) =.. Given that the model assigns a central role to quality improvements, the standard data employed here may not be well-suited to capture what the model describes. This becomes apparent in the productivity estimates that suggest that the productivity in 8 out of 20 industries has declined or remained stable during the post-war period. 13 If this was really true, then we would need to explain how less effective technologies survive more effective ones in the long-run. I am not following this path but instead assume that the standard data are mismeasured because they do not, among other things, appropriately account for quality and variety improvements in output as Broda and Weinstein (2010) and Boskin (1998) argue. This is why I adjust the data in the next section. 4.4 The Effects of Downward djusting ggregate Inflation Cobb-Douglas. In this section, I subtract 1 percentage point from aggregate inflation in each year during To illustrate how this adjustment affects the sectoral productivity estimates, I have to make assumptions about capital and output inflation at the industry level. While I assume that capital inflation symmetrically falls symmetrically by 1 percentage point across industries 15 I make two alternative assumptions about output inflation. The first assumption serves as a hypothetical benchmark while the second assumption is empirically grounded: i) output inflation at the industry level symmetrically falls by 1 percentage point ii) output inflation at the industry level asymmetrically falls by 1.26pp in the labor intensive industry and by 0.61pp in the capital intensive industry. The key result of the adjustment procedure is that relative productivity growth increases in the more labor intensive industries under both assumptions. The effect is stronger under the second assumption though. I re-estimate productivity growth at the industry level employing two standard neoclassical production functions. One for each industry: Y t, = t, ( K α t, ) Y t, t, K t, ( L α t, ) L t,, (28) 13 Column (9) of Table 1 shows that productivity growth, t t, is equal or below unity in 8 out of 20 industries meaning that it is either absent or negative percentage point lies within a range determined as plausible by the empirical literature on the inflation bias. Boskin (1998), for example, finds, after weighting different biases by categories, a bias in a range of. to.pp for the CPI, which constitutes a large fraction of overall output prices. Lebow and Rudd (2003) review the literature and estimate the confidence interval ranging from. to. percentage points. 15 This assumption is key and plausible for two reasons: i) changes in the price of capital in Column (5) of Table 1 are uncorrelated (the correlation coefficient is 0.12) with changes in the price of output in Column (4) ii) the change in the price of capital in the labor intensive sector is very similar to the change in the price of capital in the capital intensive sector,. and., respectively. 18

19 Table 1: Industry Decomposition of post-war private U.S. economy by NICS industries (BE) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Industry NICS Pτ Yτ P Y Pτ Yτ P Y ατ ατ Pt PK,t Yt Kt Lt t Pt PK,t Yt Kt Lt t (BE) (BLS) (CD) Educational services % 1.1 % Health care and social assistance % 7.2 % Management of companies & enterprises % 1.9 % dministrative, waste management % 3.2 % Construction % 5.4 % rts, entertainment, and recreation % 1.1 % Other services, except government % 2.8 % Professional, scientific, technical services % 7.5 % Retail trade 44, % 7.5 % Transportation and warehousing 48, % 3.3 % Durable goods 33, 321, % 8.9 % ccommodation and food services % 3.2 % Wholesale trade % 6.8 % Finance and insurance % 8.4 % Information % 5.6 % Nondurable goods 31, % 6.8 % griculture, forestry, fishing, and hunting % 1.1 % Mining % 1.8 % Utilities % 1.9 % Real estate and rental and leasing % 14.4 % labor intensive 58.4 % 59.9 % capital intensive 41.6 % 40.1 % private industries % % Notes: the panels show the author s calculations based on data drawn from the U.S. Bureau of Economic nalysis (BE). The level of disaggregation is 2-digit NICS. For the initial period, I take t =, while I set the end period to t =. ατ (BE) are the author s calculations of the labor share based on the NIP data ατ (BLS) is the labor share calculated by the BLS t t (CD) are the productivity estimates based on Cobb-Douglas (CD) production functions. 19

20 Y t, = t, ( K α t, ) ( L α t, ). (29) Y t, t, K t, L t, i) output inflation falls symmetrically across industries. ggregate and industry price growth symmetrically falls after adjusting the standard data for an inflation bias. This fall implies, that the postadjustment increase in real output growth on the LHS of the last two equations is commensurate. This increase must be matched by an equal increase on the RHS. Since capital in both industries is deflated by the same price index, the capital stock increases by the same percent. The asymmetric adjustment in productivity comes from the difference in the power on the capital stock. higher power (a higher capital intensity) amplifies the post-adjustment increase in the capital stock by more than a lower power. Because the LHS has increased commensurately, this difference in the increase in capital on the RHS must be matched by an asymmetric increase in productivity. ii) output inflation falls asymmetrically across industries. Industry price growth asymmetrically falls after adjusting the standard data for an inflation bias. In particular, I assume that the increase on the LHS is higher in the more labor intensive industry. This assumption is plausible given that 6 industries in the labor intensive sector that account for 27.6% of GDP during but only 2 industries within the capital intensive sector that account for 10.2% of GDP exhibit no or negative productivity growth in the standard data. Moreover, this assumption of an asymmetric adjustment on the LHS is also supported by Griliches (1992), Griliches (1998), Wölfl (2005) and hmad et al. (2003) who argue that measurement issues in real variables, i.e. inflation, are likely to cause the service sector (which predominantly lies in the labor intensive industries) to exhibit negative productivity growth rates. The assumption of an asymmetric output adjustment implies that the direction of the productivity adjustment is the same as under assumption i), but that the effect is stronger. Relative productivity growth of the labor intensive industry therefore increases by more than previously. Results (Cobb-Douglas). The results are reported in Table 2. For simplicity, I assume that output and capital have the same price index. That is the price index of output. Without any adjustment, relative productivity growth is (Column 5) is ln(.) ln(.) =.. ssuming that aggregate inflation is pp lower, relative productivity growth increases to ln(.) ln(.) =.. I now assume that the overall adjustment is 1pp, but that output adjustment is slightly asymmetric at the sectoral level, i.e. 1.26pp in the labor intensive industry but only 0.61pp in the capital intensive industry. I assume that capital is still adjusted with the aggregate output deflator. s a result, productivity 20