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Estimating entrants' productivity when prices are unobserved
ECMODE-03047; No of Pages 8 Economic Modelling xxx (2013) xxx–xxx
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Estimating entrants' productivity when prices are unobserved☆ Umut Kılınç VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
a r t i c l e
i n f o
Available online xxxx JEL classification: D22 D24 L11 C51 Keywords: Productivity Price–cost markups Production function estimation Control function Firm entry
a b s t r a c t Entrant firms are constrained to set lower price–cost markups than incumbents due to idiosyncratic demand shocks faced in the startup phase. Productivity indices suffer from micro-level markup variation and underestimate entrants' productivity, when productivity is measured by nominal sales and expenditures but not quantities. This study makes the first attempt to estimate entrants' productivity by controlling for their markup difference, when prices or quantities are unobserved at the firm-level. The econometric methodology introduces demand side into a structural model of production to account for the price variation. The estimation routine deals with the endogeneity due to unobserved productivity using a control function approach, and retrieves average markups for entrants and incumbents together with a markup-adjusted productivity index. My findings show that entrants set on average lower markups than incumbents in Japanese manufacturing. When productivity is adjusted to markups, entrants are as productive as incumbents, while the standard measures of labor and total factor productivity indicate low productivity for entrant firms. © 2013 Published by Elsevier B.V.
1. Introduction The entry of new producers is widely thought to be a key source of productivity growth. Entrants can introduce new products and processes, up-to-date production technologies, managerial and organizational structures that may be costly to adopt by existing producers. Entrant firms have higher incentives to innovate and also tend to influence aggregate productivity growth through the dynamic process of creative destruction.1 One, however, rarely finds highly productive entrants in data especially by examining firm-level productivity indices.
☆ I would like to thank Eric Bartelsman, Jan Boone, Mika Maliranta and Sabien Dobbelaere for their valuable comments and discussions. I thank all the participants of the conference “Beyond the short run: Productivity growth, market imperfections and macroeconomic disequilibrium” for their useful feedback. E-mail address: [email protected]. 1 Theoretical models of industrial evolution bring an explanation to the static feature of mature firms. Older incumbents may suffer from low input quality and out-of-date production technology, and exhibit smooth or declining productivity performance throughout the life time unless hit by random shocks (e.g. Cooper et al., 1999; Doms and Dunne, 1998; Jovanovic, 1998). Incumbents may incur additional burden in the form of, for instance, liquidation costs, severance payments or labor training expenses while replacing the existing combination of production factors. Caballero and Hammour (1998) point out that production factors are generally specific to the existing match and the production technology which creates additional costs in the liquidation phase of the separated factors of production. Acemoglu and Cao (2010) argue that entrants engage in more radical innovations to replace incumbents.
Despite the advantages of being new, entrants' productivity performance has been shown to be poor in their first years.2 This is often attributed to the necessary tasks to be undertaken in the start-up phase such as the analysis of demand conditions, advertising new products to attract customers and learning-by-doing type activities. Thus, new firms are argued to exploit their productivity advantage, and catch up with the size and profitability scale of incumbents only after a start-up period. Recent empirical findings show that the adverse demand shocks faced in the start-up phase cause entrants to lag behind incumbents in terms of size and profits, but productivity as the technical efficiency in production is not necessarily affected by these demand side factors. Eslava et al. (2004) and Foster et al. (2008) compare two productivity indices that are based on revenues and quantities of outputs using a rare type micro-level production data that contains nominal and quantity-based indicators. Their findings show that entrant firms' productivity performance is poor according to revenue–productivity, but entrants are as productive as incumbents with respect to quantity–productivity. The difference between the revenue and quantity based productivity is attributed to firm-level price effects. Demand shocks faced in the start-up phase prevent entrants from charging
2 Bartelsman and Doms (2000), Foster et al. (2001) and Bartelsman et al. (2005) provide empirical support that entrants require some time to exploit their productivity advantage. Olley and Pakes (1996) show that entrants have initially poor productivity performance, but the ones that survive experience higher productivity growth than incumbents.
0264-9993/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.econmod.2013.09.027
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
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price–cost markups as high as incumbents, so that entrants' revenue– productivity is lower. In contrast, entrants are as productive as incumbents even in the start-up phase according to the quantity–productivity. The empirical evidence stresses that analyzing entrants' productivity requires disentangling price effects from productivity indices. Firmlevel prices or quantities, however, are generally unobservable, so that productivity is calculated by revenues and input expenditures that are price-adjusted by, at best, industry-level deflators. This may not constitute a vital issue, if the aim is to analyze aggregate productivity, since the distorting effects of unobserved price variation can be eliminated in the phase of aggregation. Price effects, however, could bias the productivity comparisons across firms within the same industry. For instance, if a particular firm group has a significantly different pricing behavior, within-industry comparisons based on nominal productivity indices would be misleading. This paper makes the first attempt to assess entrants' productivity performance by taking into account their possible price–cost markup variation, when prices or quantities are unobservable. My methodology consists of the structural estimation of a production relation, where the theoretical setup relies on Hall (1987, 1988) that introduces the demand side into a model of production to control for unobserved markups. The estimation method borrows from Levinsohn and Petrin (2003), so that the model is estimated by taking into account the endogeneity of inputs to productivity using a control function approach. The estimation routine retrieves markups individually for entrants and incumbents jointly with a productivity index that is adjusted to entrants' markup variation. In the empirical application, I use plant-level data from manufacturing industries of Japan. Recently, a considerable amount of research has been directed toward controlling for unobserved markups while estimating productivity. Griliches and Mairesse (1995) address the problems in the estimation of production functions due to the unobserved heterogeneity in firms' output prices. Griliches and Klette (1996) introduce demand side into the structural model of production to take into account the price variation. Katayama et al. (2003) point out that the implications derived from revenue-based productivity measures are misleading, and offer a structural approach to impute quantities from nominal data. Levinsohn and Melitz (2004) construct an empirical model of production that accounts for unobserved prices. Their model introduces a demand shifter into a production function, and factor elasticity parameters are estimated together with an average markup that is not necessarily equal to one but still the same for all firms in the sample. The structural model drawn in Griliches and Klette (1996) and modified in Levinsohn and Melitz (2004) is applied with various extensions. For instance, Dobbelaere (2004) takes into account labor market imperfections in the joint estimation of productivity and markups. Martin (2005) develops an alternative control function approach to take into account endogeneity as well as firm-level variation in factor elasticity parameters while controlling for imperfect competition. DeLoecker (2011) modifies the estimation methodology of Levinsohn and Melitz (2004) to account for multi-product firms. DeLoecker and Warzynski (2012) estimate production functions by allowing for internationally-trading firms to have markups different than the industry average. The econometric methodology described in the following section is developed to test the importance of demand side factors in the measurement of entrants' productivity performance. In the empirical application, the Japanese manufacturing sector is divided into two groups as high-and low-tech industries for which start-up conditions may differ, and the estimation results are interpreted comparatively. The next section presents the structural model with heterogeneous firms producing differentiated products and facing different demand conditions. The third chapter describes the data and provides preliminary evidence on the entrant plants' markup variation. The fourth section constructs the control function approach to deal with the endogeneity of inputs to unobserved productivity. In addition, the robustness of alternative production function estimation methods is discussed in the fourth section.
The fifth section elaborates the relative productivity performance of entrants in manufacturing industries of Japan. The fifth section also derives implications for firm-level productivity estimation by evaluating the results comparatively among alternative econometric approaches. 2. Structural model This section presents a structural model of production based on Hall (1987, 1988). Unlike Hall's original approach, the model in this part is formulated at the plant-level, and a reduced-form production relation is derived to estimate the within industry variation in price–cost markups. The model industry is populated by heterogeneous plants that operate under imperfect competition and produce according to a Cobb–Douglas type production function. αM αL
αK
Q it ¼ Θit M it it Lit it K it it :
ð1Þ
Eq. (1) represents plant i's production function that is homogenous L K of degree λit = αM it + αit + αit. t is the time index and αit stands for the factor elasticity that is variable over time and across plants. Qit, Mit, Lit and Kit are the output, intermediate inputs, labor and capital respectively. Θit is the total factor productivity. In the model industry, plants are assumed to produce differentiated products, and Pit(Qit) represents the plant-level inverse demand function. Assuming −ηit is the price elasticity of demand, and Cit is the price of intermediate inputs, the first order condition of plant i's static maximization problem for intermediate inputs is given as follows. ∂P it ∂Q it ∂Q it Q þ P it ¼ C it : ∂Q it ∂M it it ∂Mit
ð2Þ
Using the identity of factor elasticity, αM it = ∂QitMit/∂MitQit, one can derive the following condition to substitute αM it in production function with a composite term that consists of markups and observables. μ it
C it Mit M ¼ α it : P it Q it
ð3Þ
In Eq. (3), μit = (1 − 1/ηit)− 1 represents the markup and CitMit/ PitQit is the intermediate input expenditures to revenue ratio. I further assume that the condition given in Eq. (3) holds for labor input. Substituting Eq. (3) into the log of the production function, the reduced-form production relation can be written as follows. qit ¼ μ it
C it Mit W L m þ it it l P it Q it it P it Q it it
K
þ α it kit þ θit :
ð4Þ
In Eq. (4), Wit represents the plant specific wage, and the lowercase letters are the variables in logarithms. In the reduced-form production function, the factor elasticity of capital is not replaced by its expenditure share, mainly because the firm-specific user cost of capital is unobservable. In the next step, however, the elasticity of capital is replaced by αKit = λit − αLit − αM it where λit is the degree of total returns to scale (r.t.s). To simplify the notation, sJit is used to represent the expenditure share of input J ∈{M, L} in revenues, namely that sM it = CitMit/PitQit, and the production function takes the following form. h i M L qit ¼ μ it sit ðmit −kit Þ þ sit ðlit −kit Þ þ λit kit þ θit :
ð5Þ
In the derivation of the reduced form of the production function (Eq. (5)), the equilibrium identity for capital, μitsKit = αKit, is abandoned, mainly because the expenditure share to revenue ratio is not directly observable from data. In addition, the calculation of the user cost of capital at the firm-level has shortcomings such as the underlying assumption of fixed capital utilization rates for all firms. In the context of this paper, such a restrictive assumption on input expenditures
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
would be inconsistent, because the aim is to detect the variation in markups across firms, which is linked to the variation in expenditure shares. The equilibrium identity for capital is also invalid, if we adhere to conventional theory that capital is a dynamic input of production, so that the objective function of the maximization problem shall not be per-period profits. If this is the case, the variation in the r.t.s cannot be solely explained by markups and factor L K shares, namely that λit = μ it [sM it + s it + s it ] may not hold, but the functional form in Eq. (5) would be still consistent. One can also argue that labor is not a perfectly variable input, especially if one proxies it by the number of workers employed in a given plant. In this study, however, labor is proxied by a more flexible variable, total hours worked in a given year, which would minimize the errors due to the perfect variability assumption.3 3. Data and descriptive statistics on entry The empirical work in this study draws on annual plant-level data from manufacturing industries in Japan for the period from 1985 to 2007.4 The dataset is a combination of different sources and is prepared by Fukao et al. (2009). The output is represented by the total annual sales deflated by the 2-digit industry-level PPI. The labor input is reported as total working hours in a given year and the intermediate input is represented by the expenditures on materials deflated by the industry-level PPI. Fukao et al. (2009) construct the capital stock by the perpetual inventory method using time series of investments. The sample of establishments used in this study consists of 1987 plants, 863 of which are entrants that are established within the 23-year period between 1985 and 2007. Entrants are detected by the absence of data, so that if a firm's first year in the sample is not 1985, then it is classified as an entrant. This way of detecting entrants does not allow identifying the new firms in the first year of the sample, so that 1985 is omitted in the estimations. Descriptive statistics are given in App. Tables 1 and 2, and the detection of outliers is also discussed in Appendix A. In the empirical analysis, manufacturing industries are grouped into two major sectors, high- and low-tech, and the production function is estimated separately for each sector. The technology categorization of industries is mainly based on Hatzichronoglou (1997), namely that the high-tech consists of middle-high and high technology industries, and the low-tech contains middle-low and low technology industries. A list of the 2-digit industries contained in low- and high-tech groups can be found in Appendix A. Table 1 provides descriptive statistics on firm entry in the Japanese manufacturing sector. 40% of all the firms in the sample are entrants who are established within the 23-year period. The entrants, however, are small in terms of their labor share, so that the annual average labor-weighted entry rate is less than 1%.5 In particular, the entry rate within the high-tech sector is lower than the low-tech, possibly because entering into high-tech industries requires larger amounts of sunk investments. For an average entrant, there are 12.4 time observation in the sample, while this is slightly higher in low-tech industries. In the dataset, the shares of factor expenditures in total costs are provided at the firm-level. Thus, one can calculate an approximation of the profit margin that can be linked to price–cost markups for any firm 3 The appendix comparatively displays the coefficients of variation for labor and intermediate inputs at the 2-digit industry-level. The variations are not dramatically different. 4 The complete data is publicly available at the website of the Japan Centre for Economic Research (http://www.jcer.or.jp/eng/research/database070528.html). 5 The entry rate reported in Table 1 is the labor sum of entrants divided by the total labor of the industry. The entry rates are calculated based on the conventional definition, so that entrants are the firms in their first year, and they become incumbents starting from the second year of their life time. In the rest of the study, however, new firms are classified as entrants for their entire lifetime within the sample period. In this way, the start-up period in manufacturing industries is considered to last beyond the first year in the market.
3
group using the equilibrium identity.6 To establish such a link, however, one needs to assume a value for the degree of total returns to scale and approximate the user cost of capital. The profit margin (PM) calculations reported in this part, therefore, are based on the assumption that λ = 1 and employ an approximation of firms' user cost of capital. The descriptive statistics generated in this way are interpreted as preliminary insights into the markup variation between entrants and incumbents in the Japanese manufacturing. The top panel of Fig. 1 displays the variable profit margin as the ratio of revenues to variable costs that are the sum of the expenditures on labor and intermediate inputs. The lower panel is for the total profit margin that is the ratio of revenues to total costs including the approximated user cost of capital. According to the Figure, there is a considerable gap between the average PM of entrants and incumbents, so that the variable PM is around 1.83 for incumbents and 0.91 for entrants, while the total PM is 1.90 for incumbents and 0.92 for entrants. The two measures of the PM are rather fixed over time between 1986 and 2002 but decreasing after 2002 for both entrants and incumbents simultaneously. The magnitude of the gap between entrants' and incumbents' profitability, however, is roughly constant over the entire sample period. 3.1. OLS and fixed-effects estimations The estimation of Eq. (5) by the OLS or the fixed-effects would only provide aggregate level parameter estimates of μit and λit, but the main interest in this study is the variation in the markups for entrant firms. In addition, the r.t.s (λit) is defined to be heterogeneous across firms, so that it may also vary for entrants. Introduction of an entry dummy into Eq. (5) in the following way, therefore, enables to estimate entrants' markup and r.t.s variation. h i M L qit ¼ μ sit ðmit −kit Þ þ sit ðlit −kit Þ h i M L ent þμe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit ent e D þθ : þλk þ λk it
it
it
ð6Þ
it
In Eq. (6), Dent it represents the entry dummy that takes the value of 1 for all the years of an entrant and 0 otherwise. The parameter μ is the average markup of incumbents and μe stands for the average markup difference of entrants from incumbents. Similarly, the coefficient on kitDent it e are is expected to capture the variation in the r.t.s. Once μ, μe , λ and λ identified, one can retrieve a plant specific productivity index that is adjusted to the markup and r.t.s differences of entrants from incumbents.7 In the first step of the empirical section, Eq. (6) is estimated by the OLS and the firm fixed-effects model. Each estimation equation contains time and industry dummies, and the equations estimated by the OLS also include a constant and a separate dummy for entrants (Dent it ). In the OLS and fixed-effects model, θit represents the error term that contains unobserved productivity. In the top panel of Table 2, the estimation results by the OLS show that the average markup of entrants is significantly lower than incumbents for the entire manufacturing sector. The OLS also detects a significantly positive variation in the r.t.s for entrants. When manufacturing is separated into low- and high-tech sectors, however, the OLS finds that the coefficient representing the entrants' markup variation is positive and significant at 1% level for both industry groups. The estimate of e is significantly negative for the two sub-samples. the r.t.s. variation (λ) The lower panel of Table 2 demonstrates that the estimation results based on the fixed-effects model differ from the OLS for the low- and 6 L K The structural model provides the identity λit = μit[sM it + sit + sit] that links the profit L K margin (1/[sM it + sit + sit]) to markups (μit). The computation of the factor expenditure shares in revenue (sit) is discussed in the Appendix part. 7 Estimating the time variation in markups or r.t.s is not feasible in the specification given by Eq. (6). Nevertheless, the evidence provided in Fig. 1 implies that the average markups remain rather fixed over time within the sample period.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
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Table 1 Entrants' share in Japanese manufacturing.
#Observations #Firms #Entrants Avg. age of entrants Entry ratea (%) a
Table 2 Production function estimations by fixed-effects and OLS.
Total sector
Low-tech
High-tech
OLS
Markup (μ)
Markup diff. (μe)
r.t.s (λ)
e r.t.s diff. (λ)
34,433 1987 863 12.4 0.48
14,032 811 319 13 0.70
20,401 1191 544 12 0.39
Total sector
0.850* (0.005) 0.822* (0.003) 0.777* (0.004)
−0.072* (0.006) 0.014* (0.005) 0.044* (0.006)
0.876* (0.003) 0.949* (0.001) 0.947* (0.002)
0.039* (0.004) −0.033* (0.003) −0.038* (0.003)
Fixed-effects
Markup (μ)
Markup diff. (μe)
r.t.s (λ)
e r.t.s diff. (λ)
Total sector
0.835* (0.006) 0.841* (0.004) 0.820* (0.006)
−0.056* (0.008) −0.017* (0.008) −0.036* (0.010)
0.780* (0.006) 0.891* (0.004) 0.890* (0.007)
0.030* (0.006) −0.075* (0.008) −0.047* (0.010)
Low-tech High-tech
Entry rate is the annual average of the employment ratio of entrants to incumbents.
Variable PM
high-tech sectors. The fixed-effects model retrieves a negative markup difference between entrants and incumbents not only for the overall sector but also for the two sub-groups where the estimates of the markup gap are significant at 1% level. The r.t.s variation is estimated to be negative in the low- and high-tech industries, while it is positive for the overall sector. Assuming that capital is a perfectly variable factor of production, the profit margins can be computed through the equilibri L K ^ ^ um identity, namely that 1= sM it þ sit þ sit ¼ μ =λ. For incumbent firms in the full sample, the OLS yields a profit margin that is 0.85 / 0.876 = 0.97, and the profit margin is 1.07 according to the fixedeffects model. Entrants' profit margin in the full sample is 0.85 with the OLS and 0.96 with the fixed-effects. The OLS estimates of incumbents' average markup (μ) so that the estimated profit margin is low in comparison to the profit margin approximations based on factor expenditure shares given in Fig. 1. This can be an indication of the endogeneity issue in the estimation of the production function by the OLS. Namely, the input expenditure shares in revenue are negatively correlated with productivity that is contained in the error term in the OLS case, so that the OLS estimates of μ are biased downward, and the markup difference of entrants from incumbents (μe) is estimated to be considerably low. The fixed-effects model would be a solution to the endogeneity problem, unless productivity would follow a systematic pattern over time. The time variation in productivity, however, is still contained in the error term and the endogeneity issue persists in the fixed-effects model. Nevertheless, the fixed-effects model partially tackles the endogeneity by controlling for cross-sectional variation, so that the estimates of the markup gap are significantly negative for every firm group. The profit margins estimated by the fixed-effects model are higher in comparison to the OLS case, but they are still much lower than the approximations based on the expenditure shares given in Fig. 1. The estimation procedure described in the next part offers an alternative approach that also controls for the time dependence in the unobserved productivity.
High-tech
*Significant at 1%. **Significant at 5%. Standard errors are in parenthesis. Time and industry dummies are included.
4. A control function approach This section develops a control function approach to handle the endogeneity problem in the estimation of the reduced-form production function given by Eq. (6). The usage of control function approaches in production function estimations dates back to Olley and Pakes (1996) who invert the investment function to derive a proxy for unobserved productivity. The approach used in this paper, however, relies on an extension by Levinsohn and Petrin (LP) (2003) where intermediate inputs are employed as the proxy variable.8 The LP is based on a structural approach which models the endogeneity by assuming that the manager can partially observe her firm's productivity and uses this information while hiring production factors. Managers' decisions on the optimal amount of inputs generate a correlation between production factors and productivity that is fully unobserved by the researcher. Assuming the intermediate inputs is a monotone function of productivity and a function of the state variable capital, mit = m(θit,kit), the LP inverts m(·) to obtain the function to control for unobserved productivity that is θit = ϕ(mit,kit) where ϕ(·) = m−1(·). At this stage, I follow Ackerberg et al. (2006) and introduce lit as a state variable into the control function together with the entry dummy, the other state (capital) and the proxy (intermediate inputs) variables. The production function is written as follows h i M L qit ¼ μ sit ðmit −kit Þ þ sit ðlit −kit Þ þ λkit h i M L ent e Dent þμe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit þ λk it it ent þϕit mit ; lit ; kit ; Dit þ ε it :
ð7Þ
2 1.5 1
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2
Total PM
Low-tech
1.5 1
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 incumbents
entrants
Fig. 1. Average Profit Margin (PM) in the Japanese manufacturing sector.
In the above equation, ϕit(·) stands for the systematic part of productivity according to which the manager develops her expectations. εit is the random productivity shock that is fully unobservable and i.i.d. over time. The LP method has a critical timing assumption on the choice of the optimal amount of labor used in production. The LP assumes that labor is a predetermined factor, which allows the coefficient of labor to be identified in the first stage, whereas this aspect of the LP attracts much criticism (e.g. Ackerberg et al., 2006; Wooldridge, 2009). In the estimation, I abandon the LP's timing assumption and add labor into the control function, so that the factor elasticity of labor is identified in the final stage. In the first stage, the estimation equation, therefore, consists of a non-parametric function, g(·), that contains the production function and the systematic productivity isolated from random shocks. 8 Levinsohn and Petrin (2003) criticize the use of investment as a proxy for productivity, since investment is a control on the state variable capital, and a state variable is by definition costly to adjust.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
The function g(·) is approximated by a third order polynomial and estimated by the OLS ent qit ¼ g it mit ; lit ; kit ; Dit þ εit :
ð8Þ
The first stage of the estimation, therefore, separates the random shock component from the systematic and serially correlated part of productivity, but it does not identify any of the parameters that are subject to the analysis. An approximation of the systematic productivity can e in the following way be obtained for any given values of μ, μe, λ and λ h i ent M L θit ¼ g it mit ; lit ; kit ; Dit −μ sit ðmit −kit Þ þ sit ðlit −kit Þ h i M L ent e k Dent : −λ kit −μe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit −λ it it
ð9Þ
Productivity is assumed to evolve as a first-order Markov process e as follows.9 which can be written for given μ⁎, μe , λ⁎ and λ θit ¼ βθit−1 þ eit
ð10Þ
e , one, therefore, can retrieve the fitted For given μ⁎, μe , λ⁎ and λ values of Eq. (10) to be used as an estimate for the expectation of productivity conditional on the previous period's realization. Namely, ^ e and stands for the e, λ and λ, E θd it jθit−1 ¼ βθit−1 is a function of μ, μ productivity expectation of the manager. The second stage of the estimation routine can be written in the following form. h i M L qit ¼ μ sit ðmit −kit Þ þ sit ðlit −kit Þ þ λkit h i M L ent þμe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit e Dent þ E θd þλk it it it jθit−1 þ ε it þ eit
ð11Þ
Joint minimization of the error terms εit and eit provides the estie mates of μ, μe, λ and λ. " # H T X N h i 2 X 11X ðεit þ eit ÞZ it;h min TN t i μ;e μ ;λ;e λ h
ð12Þ
In the formulation of the GMM minimization problem, Eq. (12) employs a set of instruments (Zit,j where j = 1 to H) that contains the first and second lags of the production factors and the first lags of the expenditure shares. Moreover, the current capital stock is assumed to be determined by investments in t-1. The instrument matrix, therefore, L consists of Zit = {kit,kit − 1,mit − 1,lit − 1,sM it − 1,sit − 1,kit − 2,mit − 2,lit − 2}. The standard errors are calculated by block bootstrapping, namely, by resampling the dataset over randomly drawn plants, but using the entire times series observations of a drawn plant.10 In the following parts, the control function approach also is used to estimate a restricted version of Eq. (6) that excludes the variables capturing entrants' markup e variation. For the restricted version, the second lags are (μe) and r.t.s (λ) excluded from the instrument matrix, so that Zit = {kit,kit − 1,mit − 1, L lit − 1,sM it − 1,sit − 1}. 4.1. Production function estimation with control function The control function approach described in the previous part is applied to two different versions of the reduced-form production function. In addition to the original version given by Eq. (6), I estimate the
production function without variables capturing entry variation with the aim of comparing the productivity indices derived from these two versions. The top panel of Table 3 displays the estimation results of the production function with entry variation given by Eq. (6). In comparison to the OLS and the fixed-effects model, the control function estimates of the incumbents' markup rise to 1.998 for the entire manufacturing sector. This corresponds to a profit margin that is 1.81 for incumbents which is roughly identical to the average profit margin of incumbents approximated by factor expenditure shares. Entrants' average price– cost markup is estimated to be significantly lower than incumbents' average that is 1.998 − 1.556 = 0.442. Table 3 shows that there is a considerable difference in the markup estimates of firms in low- and high-tech industries, so that incumbents in low-tech industries have significantly higher markups than high-tech incumbents. Conversely, entrants in high-tech industries have higher markups than low-tech entrants. The profit margin estimations based on the control function approach is 0.54 for entrants in low-tech industries and 0.75 for high-tech entrants. Combining this with the entry rates reported in Table 1, one may argue that entry barriers are greater in high-tech industries, so that the average high-tech entrant has to set a higher markup than the average low-tech entrant. This could be because starting up in high-tech industries requires adopting more capital- or technology-intensive production methods, so that hightech entrants incur larger sunk costs than low-tech counterparts. Alternatively, competition in product market may be responsible for the markup difference between the two sectors. Intensive competition leads to a stricter market selection mechanism that only allows relatively highly profitable units to enter into the market. Competition is probably more intensive in high-tech industries, because the estimated overall markups given in the bottom panel of Table 3 are the highest for low-tech industries. The entry variation in the r.t.s that is estimated to be significantly positive in the OLS and the fixed-effects model for the entire sector is insignificant by the control function approach. The adjustment of production function parameters with the true markup variation, therefore, reduces or eliminates the difference in the r.t.s estimates.
5. Entrants' relative productivity This section is devoted to an analysis of entrants' relative productivity performance in the Japanese manufacturing using alternative productivity indices. Each total factor productivity (TFP) index is calculated by the
Table 3 Control function estimation results. Control function estimates with entry variation
Total sector Low-tech High-tech
Markup (μ)
e) Markup diff. (μ
r.t.s (λ)
e r.t.s diff. (λ)
1.998* (0.254) 1.919* (0.306) 1.589* (0.305)
−1.556 (0.338) −1.404 (0.543) −0.872** (0.353)
1.103* (0.158) 0.956* (0.171) 0.959* (0.156)
0.185 (0.170) 0.165 (0.135) 0.160 (0.144)
Control function estimates without entry variation
Total sector 9
In the estimation, I include a constant term into Eqs. (8) and (10). However, it is not possible to identify both intercepts individually with given restrictions. I omit the constants as well as industry and time dummies in the formulations but use them in the estimations. For details on the identification issue of the intercept see Levinsohn and Petrin (2003). 10 In the programming of the block bootstrapping routine, I utilize the code provided by Levinsohn et al. (2004).
5
Low-tech High-tech
Markup (μ)
r.t.s (λ)
1.112* (0.082) 1.315* (0.096) 0.944* (0.116)
0.776* (0.051) 0.678* (0.100) 0.814* (0.039)
*Significant at 1%. **Significant at 5%. Standard errors are in parenthesis. Time and industry dummies are included.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
Table 4 Entrants' relative productivity. Estimation method
Ent./Inc. Prod.
Control function with entry variation Control function without entry variation Levinsohn–Petrin Fixed-effects with entry variation Labor productivity
0.93 0.24 0.27 0.55 0.75
Labor Prod.
6
2 1.5 1 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
TFP
3
11 Estimation of productivity without entry variation implies that the estimating equaL ent tion is in the form of Eq. (6) but excludes the terms, [sM it (mit − kit) + sit(lit − kit)]Dit and kitDent it , which are capturing the markup and r.t.s difference of entrants from incumbents. 12 In the estimation of the standard TFP by Levinsohn and Petrin's (2003) approach, a general Cobb–Douglas type production function is employed and the factor elasticity coefficients are retrieved using the programming routine provided by Levinsohn et al. (2004).
2 1 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
TFP−markup
ratio of outputs to composite form of inputs whose functional form differs among alternative estimation methods. The TFP, therefore, is Θit = Qit / Fit(Mit,Lit,Kit). The statistics given in Table 4 are based on five different productivity indices that are estimated by the fixed-effects model with entry variation,11 the control function approaches with and without entry variation, the labor productivity that is the ratio of output (revenues deflated by 2-digit PPI) to labor (total annual working hours), and the standard total factor productivity index estimated by Levinsohn and Petrin's (2003) methodology without introducing demand side or controlling for markups.12 To compute the statistics reported in Table 4, first, the weighted average productivity is calculated for entrants and incumbents, and then, the ratio is taken between the productivity averages of the two firm groups. In the calculation of the weighted average productivity, firms' output shares are used as the weights for the TFP and the labor shares for the labor productivity. Table 4 presents the productivity ratios of entrants to incumbents for five different measures of productivity. The productivity index estimated by the control function approach with entry variation indicates the highest relative entrant productivity, while the control function without entry variation yields the lowest relative productivity for entrant plants. The difference between the two productivity indices estimated by the control function approaches with and without entry variation is somewhat expectable, since the control function without entry variation overestimates entrants' markups, as long as the actual markups of entrant firms are lower than incumbents. The fixed effects model with entry variation indicates that entrant's productivity is considerably low relative to incumbents. This is due to endogeneity issue in the fixed-effects model that drives down the absolute value of the estimates of the markup gap, so that entrants' markups are still overestimated. The labor productivity, however, reflects a higher relative productivity for entrants than those based on the fixed-effects model and the control function without entry variation. This is possibly because labor productivity is calculated by not deflated labor expenditures but annual working hours, so that the index does not suffer from unobserved input price variation. In other words, using a quantity based input indicator partially controls for unobserved markup variation in labor productivity, while this is not the case in the standard TFP that is measured by deflated nominal intermediate inputs and capital stock. Table 4 also reports entrants' relative productivity based on the TFP index estimated by Levinsohn and Petrin's (LP) (2003) algorithm. In the LP algorithm, the TFP is retrieved through the estimation of a log-linear Cobb–Douglas production function that is an extensively used specification in the applied literature. The entrants' relative productivity, however, is particularly low when it is measured by the standard version of the LP algorithm that does not take into account entrants' markup variation. Fig. 2 provides a closer look at the labor productivity and the two total
0.6 0.4 0.2 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 entrants
incumbents
Fig. 2. Entrants' vs. incumbents' productivity.
productivity indices that are estimated by the original LP method (TFP) and the control function approach with entry variation (TFPmarkup). Fig. 2 depicts the time paths of the weighted average productivity of entrants and incumbents for the three productivity indices. The top panel displays a considerable gap in labor productivity between entrants and incumbents. The labor productivity gap shrinks especially after 1998 that coincides with the East Asian financial crises. A similar time trend is also observed in the standard TFP displayed in the middle panel of Fig. 2, so that there is some degree of convergence between the average productivity levels of entrants and incumbents for the period after 1998. Nevertheless, the productivity difference of entrants is noticeably large for the entire sample period, when it is measured by the LP method. The TFP-markup estimated by the control function approach with entry variation, however, indicates that entrants are on average more productive than incumbents in the first three years of the sample. For the period between 1990 and 1998, entrants' TFP-markup performance slows down, while incumbents' average TFP-markup rises considerably. As in the time paths of the other two productivity indices, the TFP-markup reflects a convergence between entrants' and incumbents' productivity especially after 1998. The time path of the TFP-markup is different from those of labor productivity and the standard TFP especially for entrant firms. This is because in the estimation of the TFP-markup, the total returns to scale is fixed to λ, but the factor elasticity parameters can vary over time and across firms. Therefore, if a firm reacts to a productivity or demand shock by altering its factor shares in production, this is accounted for in the estimation of the TFP-markup but not in the standard TFP. Nevertheless, the time paths of the three indices shown in Fig. 2 provide evidence, to some degree, that the East Asian financial crisis alter the productivity trends in the Japanese manufacturing sector. This may be because of the cleansing effect of recession that clears the market from inefficient firms and facilitates entry. Recessions hit inefficient units more severely and induce exit, which releases a portion of resources to be recombined in more efficient producers (e.g. Caballero and Hammour, 1994). The cleansing effect, therefore, provides new firms with the opportunity to capture the released portion of the resources and to catch up with incumbents more quickly.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
6. Conclusions Since it was realized that the accumulation of inputs does not solely explain producers' production performance, productivity has been used to represent the immaterial factor, namely the efficiency in production. Besides contributing to our understanding of economic growth and welfare, the economics of productivity provides valuable insights into the patterns of industrial restructuring. However, although the theoretical concept of productivity is rather well established, its measurement in practice is ambiguous, especially when the quantities of inputs and outputs are unobservable. When measured by nominal sales, productivity involves price effects that are sensitive to demand-side factors. These factors can be in the form of idiosyncratic demand shocks that are neither determinants nor outcomes of the technical efficiency in production. Demand shocks, however, can be systematically different for some particular firms in an industry. Recent empirical evidence shows that in the startup phase, new firms face negative demand shocks which prevent them from setting markups as high as incumbents. As a ratio of sales to expenditures, the nominal productivity is a positive function of markups, and therefore, may underestimate entrants' actual productivity performance. If this is the case, deflating firm-level data by aggregate price indices would not eliminate the price effects; namely that micro-level markup variation would still persist in the productivity index that is based on deflated production data. This study attempts to answer whether entrant firms charge significantly lower markups in Japan's manufacturing sector, and derives implications of markup heterogeneity for the measurement of productivity. Since firms' prices or quantities are unobservable in the subject industry, the unobserved price variation is controlled for by introducing the demand side into the structural model of production. This enables to estimate price–cost markups using firms' nominal sales and input expenditures through a production function specification. A control function approach is applied to deal with the endogeneity of inputs to unobserved productivity, and a productivity index is estimated by taking into account the average markup gap between entrants and incumbents. My results show that entrants set on average lower markups than incumbents in Japanese manufacturing industries. The markup gap between entrants and incumbents is estimated to be the largest by the proposed control function approach, while the OLS and fixed effects model provide downward biased markup estimates due to the endogeneity issue. The results further show that according to the standard measures of labor and total factor productivity, the average productivity of entrant plants is lower than incumbents. The total factor productivity index that is estimated by accounting for the unobserved markup variation as well as by controlling for the endogeneity, however, indicates that entrants' average productivity is not significantly different from incumbents' average. The results of this study provide new insights on entrants' productivity dynamics and their contribution to aggregate productivity growth. Asymmetric demand shocks may break down the expected positive correlation between profitability and productivity for entrant firms. New firms may initially have low profitability but not necessarily low productivity, which implies that productivity gains from entry may be much higher than what is calculated by nominal or deflated output and input indicators. The empirical evidence on the distorting effects of unobserved prices in the measurement of entrants' productivity is limited to few studies that make use of rare type micro data containing quantities of outputs and inputs. The methodology proposed in this paper, however, does not require observing firms' quantities or prices and is applicable to a wide range of firm-level data. The findings of this paper highlight the importance of distortionary price effects in the measurement of productivity at the micro-level. This study only considers entrants as the group of plants that faces
7
different demand conditions, but one can rely on alternative classifications such as domestic and foreign, private and state-owned firms for which markups may differ even within narrowly defined industries. Firm-level productivity analysis, therefore, needs productivity indices that are controlled for micro-level price variations, especially when comparing productivity performances of firm groups within the same industry.
Appendix A. Constructing input expenditure shares and detecting outliers In the plant-level dataset of the Japanese manufacturing sector, the total hours worked and the price-adjusted capital, material expenditures and revenues are reported annually together with each input's expenditure share in total input expenditures. The proposed estimation procedure, however, requires the factor expenditure shares in total revenues but not in total costs. As explained in Fukao et al. (2009), expenditures on material inputs and revenues are deflated with the same price index (2-digit industry level PPI) which enables to retrieve the input expenditure to revenue ratios in the following way. The nominal material expenditure to revenue ratio is calculated by the ratio of the deflated material expenditures to deflated revenues, since both variables are adjusted by the same price index. Moreover, it is possible to calculate the ratio between labor and intermediate input expenditures, because the dataset contains the variables for each input's expenditure share in total input expenditures. Once, the labor to intermediate input expenditures ratio is obtained, the share of labor expenditures in revenue can be calculated simply by multiplying intermediate input expenditures' share in revenue with the ratio of labor to intermediate input expenditures. In the dataset, the capital input's cost share in total input expenditures is also reported, where the user cost of capital is calculated through an approximation over variables such as price deflators, interest and depreciation rates. Even though it is technically possible to retrieve capital expenditures to revenue ratio for each plant and time period in the same manner, I assumed and stated in the main text that the user cost of capital is not observable and subject to possible errors in its approximation. The user cost of capital, therefore, is only used for descriptive purposes, namely, in the approximation of the profit margin in Fig. 1. I detect the outliers according to firms' annual profit margins. I calculate the standard errors for each 2-digit industry and year, and select the observations that are 4 standard errors away from the mean as outliers. The entire time series of a firm is subtracted, if the firm is an outlier in at least one year. This leads 3.6% of all observations to be omitted from the sample. There are totally 94 firms detected as outliers that consist of 51 incumbents and 43 entrants.
App. Table 1 Summary statisticsa.
Incumbents
Entrants
a
Output (Jap. Yen) Labor (man-hours) Capital (Jap. Yen) Intermediate inp. (Jap. Yen) Output (Jap. Yen) Labor (man-hours) Capital (Jap. Yen) Intermediate inp. (Jap. Yen)
Mean
Std
Std/mean
145,521,097 4,640,546 60,498,151 117,346,015 33,967,779 1,152,528 7,882,472 26,219,664
445,960,489 11,247,325 183,097,337 368,243,060 143,951,857 2,604,955 27,815,184 123,309,612
3.07 2.42 3.03 3.14 4.24 2.26 3.53 4.70
Nominal variables are price-adjusted with the base year 2000.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
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U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
App. Table 2 Entry and exit rates (%) in Japanese industries. Code
Entry rate
Exit rate
C.V. of int. inputs
C.V. of labor
#Firms
#obs
Low-tech industries 6 Food 7 Textile & mill 8 Apparel 9 Lumber & wood 10 Furniture & fixtures 11 Paper 12 Printing & publish. 14 Petroleum & coal 15 Leather 16 Stone & clay & glass 17 Primary metal 18 Fabricated metal 24 Rubber & plastics
Definition
1.24 0.01 0.53 2.00 1.17 0.21 0.71 0.00 5.65 0.59 0.12 1.73 0.75
0.48 0.12 0.54 0.91 0.60 2.64 0.25 1.24 0.00 1.13 0.76 1.09 0.34
2.29 1.31 1.79 1.10 0.98 1.48 2.57 1.31 0.72 2.01 2.13 1.83 1.74
1.73 1.28 1.20 0.92 0.92 1.28 1.95 0.93 0.64 1.54 2.27 1.48 1.64
174 27 62 14 14 47 40 13 4 99 123 115 81
3075 534 922 210 256 781 600 224 67 1701 2249 1996 1417
High-tech industries 13 Chemicals 19 Non-elec. mach. 20 Electrical mach. 21 Motor vehicles 22 Tran. equip. & ordna. 23 Instruments 25 Misc. manufact.
0.29 0.35 0.27 0.44 0.38 0.67 1.78
0.86 0.56 0.45 0.29 0.78 0.58 1.17
1.73 2.88 3.56 3.07 1.42 1.46 1.76
1.42 2.37 2.97 2.07 0.92 1.12 1.76
262 285 335 131 33 74 76
4681 5063 5472 2433 633 1125 994
Entry and exit rates are the annual averages based on plants' labor shares. “C.V.” represents the coefficient of variation. “#Firms” and “#obs” stand for the number of firms and observations. “Code” is the industry codes.
References Acemoglu, D., Cao, D.V., 2010. Innovation by entrants and incumbents. NBER Working Papers 16411. National Bureau of Economic Research, Inc. Ackerberg, D., Caves, K., Frazer, G., 2006. Structural identification of production functions. MPRA Paper 38349. University Library of Munich, Germany. Bartelsman, E.J., Doms, M., 2000. Understanding productivity: lessons from longitudinal microdata. J. Econ. Lit. 38 (3), 569–594. Bartelsman, E.J., Haltiwanger, J., Scarpetta, S., 2005. Measuring and analyzing crosscountry differences in firm dynamics. In: Dunne, T., Jensen, J.B., Roberts, M. (Eds.), Producer Dynamics: New Evidence from Micro Data, NBER Chapters. National Bureau of Economic Research, Inc. Caballero, R.J., Hammour, M.L., 1994. The cleansing effect of recessions. Am. Econ. Rev. 84 (5), 1350–1368. Caballero, R.J., Hammour, M.L., 1998. The macroeconomics of specificity. J. Polit. Econ. 106 (4), 724–767. Cooper, R., Haltiwanger, J., Power, L., 1999. Machine replacement and the business cycle: lumps and bumps. Am. Econ. Rev. 89 (4), 921–946. DeLoecker, J., 2011. Product differentiation, multiproduct firms, and estimating the impact of trade liberalization on productivity. Econometrica 79 (5), 1407–1451. DeLoecker, J., Warzynski, F., 2012. Markups and firm-level export status. Am. Econ. Rev. 102 (6), 2437–2471. Dobbelaere, S., 2004. Estimation of price–cost margins and union bargaining power for Belgian manufacturing. Int. J. Ind. Organ. 10, 1381–1398. Doms, M.E., Dunne, T., 1998. Capital adjustment patterns in manufacturing plants. Rev. Econ. Dyn. 1 (2), 409–429. Eslava, M., Haltiwanger, J., Kugler, A., Kugler, M., 2004. The effects of structural reforms on productivity and profitability enhancing reallocation: evidence from Colombia. J. Dev. Econ. 75 (2), 333–371. Foster, L., Haltiwanger, J., Krizan, C.J., 2001. Aggregate productivity growth. lessons from microeconomic evidence. New Developments in Productivity Analysis, NBER Chapters. National Bureau of Economic Research, Inc., pp. 303–372. Foster, L., Haltiwanger, J., Syverson, C., 2008. Reallocation, firm turnover, and efficiency: selection on productivity or profitability? Am. Econ. Rev. 98 (1), 394–425. Fukao, K., Inui, T., Ito, K., Kim, Y.G., Yuan, T., 2009. An international comparison of the tfp levels and the productivity convergence of Japanese, Korean, Taiwanese and Chinese listed firms. Global COE Hi-Stat Discussion Paper Series gd09-089, Institute of Economic Research, Hitotsubashi University. Griliches, Z., Klette, T.J., 1996. The inconsistency of common scale estimators when output prices are unobserved and endogenous. J. Appl. Econ. 11 (4), 343–361.
Griliches, Z., Mairesse, J., 1995. Production functions: the search for identification. NBER Working Papers 5067. National Bureau of Economic Research, Inc. Hall, R.E., 1987. Productivity and the business cycle. Carn.-Roch. Conf. Ser. Public Policy 1, 421–444. Hall, R.E., 1988. The relation between price and marginal cost in U.S. industry. J. Polit. Econ. 96 (5), 921–947. Hatzichronoglou, T., 1997. Revision of the high-technology sector and product classification. OECD Science, Technology and Industry Working Papers 1997/2. OECD Publishing. Jovanovic, B., 1998. Vintage capital and inequality. Rev. Econ. Dyn. 1 (2), 497–530. Katayama, H., Lu, S., Tybout, J., 2003. Why plant-level productivity studies are often misleading, and an alternative approach to interference. NBER Working Papers 9617. National Bureau of Economic Research, Inc. Levinsohn, J., Melitz, M., 2004. Productivity in a Differentiated Products Market Equilibrium. Mimeo, Harvard University. Levinsohn, J., Petrin, A., 2003. Estimating production functions using inputs to control for unobservables. Rev. Econ. Stud. 70 (2), 317–341. Levinsohn, J., Petrin, A., Poi, B.P., 2004. Production function estimation in stata using inputs to control for unobservables. Stata J. 4 (2), 113–123. Martin, R., 2005. Productivity dispersion, competition and productivity measurement. CEP Discussion Papers dp0692. Centre for Economic Performance, LSE. Olley, G.S., Pakes, A., 1996. The dynamics of productivity in the telecommunications equipment industry. Econometrica 64 (6), 1263–1297. Wooldridge, J.M., 2009. On estimating firm-level production functions using proxy variables to control for unobservables. Econ. Lett. 104 (3), 112–114.
Umut Kılınç holds a Master of Philosophy degree in economics from Tinbergen institute, The Netherlands (2007). He conducted doctoral studies at Tinbergen Institute and VU University of Amsterdam where he was employed as a research and teaching assistant between 2007 and 2011. In September 2011, he received his Ph.D. degree in economics from VU University of Amsterdam and joined the STATEC (in Luxembourg) as a post-doc researcher. His research interests cover empirical topics in the economics of productivity and industrial organization.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
Contents lists available at ScienceDirect
Economic Modelling journal homepage: www.elsevier.com/locate/ecmod
Estimating entrants' productivity when prices are unobserved☆ Umut Kılınç VU University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
a r t i c l e
i n f o
Available online xxxx JEL classification: D22 D24 L11 C51 Keywords: Productivity Price–cost markups Production function estimation Control function Firm entry
a b s t r a c t Entrant firms are constrained to set lower price–cost markups than incumbents due to idiosyncratic demand shocks faced in the startup phase. Productivity indices suffer from micro-level markup variation and underestimate entrants' productivity, when productivity is measured by nominal sales and expenditures but not quantities. This study makes the first attempt to estimate entrants' productivity by controlling for their markup difference, when prices or quantities are unobserved at the firm-level. The econometric methodology introduces demand side into a structural model of production to account for the price variation. The estimation routine deals with the endogeneity due to unobserved productivity using a control function approach, and retrieves average markups for entrants and incumbents together with a markup-adjusted productivity index. My findings show that entrants set on average lower markups than incumbents in Japanese manufacturing. When productivity is adjusted to markups, entrants are as productive as incumbents, while the standard measures of labor and total factor productivity indicate low productivity for entrant firms. © 2013 Published by Elsevier B.V.
1. Introduction The entry of new producers is widely thought to be a key source of productivity growth. Entrants can introduce new products and processes, up-to-date production technologies, managerial and organizational structures that may be costly to adopt by existing producers. Entrant firms have higher incentives to innovate and also tend to influence aggregate productivity growth through the dynamic process of creative destruction.1 One, however, rarely finds highly productive entrants in data especially by examining firm-level productivity indices.
☆ I would like to thank Eric Bartelsman, Jan Boone, Mika Maliranta and Sabien Dobbelaere for their valuable comments and discussions. I thank all the participants of the conference “Beyond the short run: Productivity growth, market imperfections and macroeconomic disequilibrium” for their useful feedback. E-mail address: [email protected]. 1 Theoretical models of industrial evolution bring an explanation to the static feature of mature firms. Older incumbents may suffer from low input quality and out-of-date production technology, and exhibit smooth or declining productivity performance throughout the life time unless hit by random shocks (e.g. Cooper et al., 1999; Doms and Dunne, 1998; Jovanovic, 1998). Incumbents may incur additional burden in the form of, for instance, liquidation costs, severance payments or labor training expenses while replacing the existing combination of production factors. Caballero and Hammour (1998) point out that production factors are generally specific to the existing match and the production technology which creates additional costs in the liquidation phase of the separated factors of production. Acemoglu and Cao (2010) argue that entrants engage in more radical innovations to replace incumbents.
Despite the advantages of being new, entrants' productivity performance has been shown to be poor in their first years.2 This is often attributed to the necessary tasks to be undertaken in the start-up phase such as the analysis of demand conditions, advertising new products to attract customers and learning-by-doing type activities. Thus, new firms are argued to exploit their productivity advantage, and catch up with the size and profitability scale of incumbents only after a start-up period. Recent empirical findings show that the adverse demand shocks faced in the start-up phase cause entrants to lag behind incumbents in terms of size and profits, but productivity as the technical efficiency in production is not necessarily affected by these demand side factors. Eslava et al. (2004) and Foster et al. (2008) compare two productivity indices that are based on revenues and quantities of outputs using a rare type micro-level production data that contains nominal and quantity-based indicators. Their findings show that entrant firms' productivity performance is poor according to revenue–productivity, but entrants are as productive as incumbents with respect to quantity–productivity. The difference between the revenue and quantity based productivity is attributed to firm-level price effects. Demand shocks faced in the start-up phase prevent entrants from charging
2 Bartelsman and Doms (2000), Foster et al. (2001) and Bartelsman et al. (2005) provide empirical support that entrants require some time to exploit their productivity advantage. Olley and Pakes (1996) show that entrants have initially poor productivity performance, but the ones that survive experience higher productivity growth than incumbents.
0264-9993/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.econmod.2013.09.027
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
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U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
price–cost markups as high as incumbents, so that entrants' revenue– productivity is lower. In contrast, entrants are as productive as incumbents even in the start-up phase according to the quantity–productivity. The empirical evidence stresses that analyzing entrants' productivity requires disentangling price effects from productivity indices. Firmlevel prices or quantities, however, are generally unobservable, so that productivity is calculated by revenues and input expenditures that are price-adjusted by, at best, industry-level deflators. This may not constitute a vital issue, if the aim is to analyze aggregate productivity, since the distorting effects of unobserved price variation can be eliminated in the phase of aggregation. Price effects, however, could bias the productivity comparisons across firms within the same industry. For instance, if a particular firm group has a significantly different pricing behavior, within-industry comparisons based on nominal productivity indices would be misleading. This paper makes the first attempt to assess entrants' productivity performance by taking into account their possible price–cost markup variation, when prices or quantities are unobservable. My methodology consists of the structural estimation of a production relation, where the theoretical setup relies on Hall (1987, 1988) that introduces the demand side into a model of production to control for unobserved markups. The estimation method borrows from Levinsohn and Petrin (2003), so that the model is estimated by taking into account the endogeneity of inputs to productivity using a control function approach. The estimation routine retrieves markups individually for entrants and incumbents jointly with a productivity index that is adjusted to entrants' markup variation. In the empirical application, I use plant-level data from manufacturing industries of Japan. Recently, a considerable amount of research has been directed toward controlling for unobserved markups while estimating productivity. Griliches and Mairesse (1995) address the problems in the estimation of production functions due to the unobserved heterogeneity in firms' output prices. Griliches and Klette (1996) introduce demand side into the structural model of production to take into account the price variation. Katayama et al. (2003) point out that the implications derived from revenue-based productivity measures are misleading, and offer a structural approach to impute quantities from nominal data. Levinsohn and Melitz (2004) construct an empirical model of production that accounts for unobserved prices. Their model introduces a demand shifter into a production function, and factor elasticity parameters are estimated together with an average markup that is not necessarily equal to one but still the same for all firms in the sample. The structural model drawn in Griliches and Klette (1996) and modified in Levinsohn and Melitz (2004) is applied with various extensions. For instance, Dobbelaere (2004) takes into account labor market imperfections in the joint estimation of productivity and markups. Martin (2005) develops an alternative control function approach to take into account endogeneity as well as firm-level variation in factor elasticity parameters while controlling for imperfect competition. DeLoecker (2011) modifies the estimation methodology of Levinsohn and Melitz (2004) to account for multi-product firms. DeLoecker and Warzynski (2012) estimate production functions by allowing for internationally-trading firms to have markups different than the industry average. The econometric methodology described in the following section is developed to test the importance of demand side factors in the measurement of entrants' productivity performance. In the empirical application, the Japanese manufacturing sector is divided into two groups as high-and low-tech industries for which start-up conditions may differ, and the estimation results are interpreted comparatively. The next section presents the structural model with heterogeneous firms producing differentiated products and facing different demand conditions. The third chapter describes the data and provides preliminary evidence on the entrant plants' markup variation. The fourth section constructs the control function approach to deal with the endogeneity of inputs to unobserved productivity. In addition, the robustness of alternative production function estimation methods is discussed in the fourth section.
The fifth section elaborates the relative productivity performance of entrants in manufacturing industries of Japan. The fifth section also derives implications for firm-level productivity estimation by evaluating the results comparatively among alternative econometric approaches. 2. Structural model This section presents a structural model of production based on Hall (1987, 1988). Unlike Hall's original approach, the model in this part is formulated at the plant-level, and a reduced-form production relation is derived to estimate the within industry variation in price–cost markups. The model industry is populated by heterogeneous plants that operate under imperfect competition and produce according to a Cobb–Douglas type production function. αM αL
αK
Q it ¼ Θit M it it Lit it K it it :
ð1Þ
Eq. (1) represents plant i's production function that is homogenous L K of degree λit = αM it + αit + αit. t is the time index and αit stands for the factor elasticity that is variable over time and across plants. Qit, Mit, Lit and Kit are the output, intermediate inputs, labor and capital respectively. Θit is the total factor productivity. In the model industry, plants are assumed to produce differentiated products, and Pit(Qit) represents the plant-level inverse demand function. Assuming −ηit is the price elasticity of demand, and Cit is the price of intermediate inputs, the first order condition of plant i's static maximization problem for intermediate inputs is given as follows. ∂P it ∂Q it ∂Q it Q þ P it ¼ C it : ∂Q it ∂M it it ∂Mit
ð2Þ
Using the identity of factor elasticity, αM it = ∂QitMit/∂MitQit, one can derive the following condition to substitute αM it in production function with a composite term that consists of markups and observables. μ it
C it Mit M ¼ α it : P it Q it
ð3Þ
In Eq. (3), μit = (1 − 1/ηit)− 1 represents the markup and CitMit/ PitQit is the intermediate input expenditures to revenue ratio. I further assume that the condition given in Eq. (3) holds for labor input. Substituting Eq. (3) into the log of the production function, the reduced-form production relation can be written as follows. qit ¼ μ it
C it Mit W L m þ it it l P it Q it it P it Q it it
K
þ α it kit þ θit :
ð4Þ
In Eq. (4), Wit represents the plant specific wage, and the lowercase letters are the variables in logarithms. In the reduced-form production function, the factor elasticity of capital is not replaced by its expenditure share, mainly because the firm-specific user cost of capital is unobservable. In the next step, however, the elasticity of capital is replaced by αKit = λit − αLit − αM it where λit is the degree of total returns to scale (r.t.s). To simplify the notation, sJit is used to represent the expenditure share of input J ∈{M, L} in revenues, namely that sM it = CitMit/PitQit, and the production function takes the following form. h i M L qit ¼ μ it sit ðmit −kit Þ þ sit ðlit −kit Þ þ λit kit þ θit :
ð5Þ
In the derivation of the reduced form of the production function (Eq. (5)), the equilibrium identity for capital, μitsKit = αKit, is abandoned, mainly because the expenditure share to revenue ratio is not directly observable from data. In addition, the calculation of the user cost of capital at the firm-level has shortcomings such as the underlying assumption of fixed capital utilization rates for all firms. In the context of this paper, such a restrictive assumption on input expenditures
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
would be inconsistent, because the aim is to detect the variation in markups across firms, which is linked to the variation in expenditure shares. The equilibrium identity for capital is also invalid, if we adhere to conventional theory that capital is a dynamic input of production, so that the objective function of the maximization problem shall not be per-period profits. If this is the case, the variation in the r.t.s cannot be solely explained by markups and factor L K shares, namely that λit = μ it [sM it + s it + s it ] may not hold, but the functional form in Eq. (5) would be still consistent. One can also argue that labor is not a perfectly variable input, especially if one proxies it by the number of workers employed in a given plant. In this study, however, labor is proxied by a more flexible variable, total hours worked in a given year, which would minimize the errors due to the perfect variability assumption.3 3. Data and descriptive statistics on entry The empirical work in this study draws on annual plant-level data from manufacturing industries in Japan for the period from 1985 to 2007.4 The dataset is a combination of different sources and is prepared by Fukao et al. (2009). The output is represented by the total annual sales deflated by the 2-digit industry-level PPI. The labor input is reported as total working hours in a given year and the intermediate input is represented by the expenditures on materials deflated by the industry-level PPI. Fukao et al. (2009) construct the capital stock by the perpetual inventory method using time series of investments. The sample of establishments used in this study consists of 1987 plants, 863 of which are entrants that are established within the 23-year period between 1985 and 2007. Entrants are detected by the absence of data, so that if a firm's first year in the sample is not 1985, then it is classified as an entrant. This way of detecting entrants does not allow identifying the new firms in the first year of the sample, so that 1985 is omitted in the estimations. Descriptive statistics are given in App. Tables 1 and 2, and the detection of outliers is also discussed in Appendix A. In the empirical analysis, manufacturing industries are grouped into two major sectors, high- and low-tech, and the production function is estimated separately for each sector. The technology categorization of industries is mainly based on Hatzichronoglou (1997), namely that the high-tech consists of middle-high and high technology industries, and the low-tech contains middle-low and low technology industries. A list of the 2-digit industries contained in low- and high-tech groups can be found in Appendix A. Table 1 provides descriptive statistics on firm entry in the Japanese manufacturing sector. 40% of all the firms in the sample are entrants who are established within the 23-year period. The entrants, however, are small in terms of their labor share, so that the annual average labor-weighted entry rate is less than 1%.5 In particular, the entry rate within the high-tech sector is lower than the low-tech, possibly because entering into high-tech industries requires larger amounts of sunk investments. For an average entrant, there are 12.4 time observation in the sample, while this is slightly higher in low-tech industries. In the dataset, the shares of factor expenditures in total costs are provided at the firm-level. Thus, one can calculate an approximation of the profit margin that can be linked to price–cost markups for any firm 3 The appendix comparatively displays the coefficients of variation for labor and intermediate inputs at the 2-digit industry-level. The variations are not dramatically different. 4 The complete data is publicly available at the website of the Japan Centre for Economic Research (http://www.jcer.or.jp/eng/research/database070528.html). 5 The entry rate reported in Table 1 is the labor sum of entrants divided by the total labor of the industry. The entry rates are calculated based on the conventional definition, so that entrants are the firms in their first year, and they become incumbents starting from the second year of their life time. In the rest of the study, however, new firms are classified as entrants for their entire lifetime within the sample period. In this way, the start-up period in manufacturing industries is considered to last beyond the first year in the market.
3
group using the equilibrium identity.6 To establish such a link, however, one needs to assume a value for the degree of total returns to scale and approximate the user cost of capital. The profit margin (PM) calculations reported in this part, therefore, are based on the assumption that λ = 1 and employ an approximation of firms' user cost of capital. The descriptive statistics generated in this way are interpreted as preliminary insights into the markup variation between entrants and incumbents in the Japanese manufacturing. The top panel of Fig. 1 displays the variable profit margin as the ratio of revenues to variable costs that are the sum of the expenditures on labor and intermediate inputs. The lower panel is for the total profit margin that is the ratio of revenues to total costs including the approximated user cost of capital. According to the Figure, there is a considerable gap between the average PM of entrants and incumbents, so that the variable PM is around 1.83 for incumbents and 0.91 for entrants, while the total PM is 1.90 for incumbents and 0.92 for entrants. The two measures of the PM are rather fixed over time between 1986 and 2002 but decreasing after 2002 for both entrants and incumbents simultaneously. The magnitude of the gap between entrants' and incumbents' profitability, however, is roughly constant over the entire sample period. 3.1. OLS and fixed-effects estimations The estimation of Eq. (5) by the OLS or the fixed-effects would only provide aggregate level parameter estimates of μit and λit, but the main interest in this study is the variation in the markups for entrant firms. In addition, the r.t.s (λit) is defined to be heterogeneous across firms, so that it may also vary for entrants. Introduction of an entry dummy into Eq. (5) in the following way, therefore, enables to estimate entrants' markup and r.t.s variation. h i M L qit ¼ μ sit ðmit −kit Þ þ sit ðlit −kit Þ h i M L ent þμe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit ent e D þθ : þλk þ λk it
it
it
ð6Þ
it
In Eq. (6), Dent it represents the entry dummy that takes the value of 1 for all the years of an entrant and 0 otherwise. The parameter μ is the average markup of incumbents and μe stands for the average markup difference of entrants from incumbents. Similarly, the coefficient on kitDent it e are is expected to capture the variation in the r.t.s. Once μ, μe , λ and λ identified, one can retrieve a plant specific productivity index that is adjusted to the markup and r.t.s differences of entrants from incumbents.7 In the first step of the empirical section, Eq. (6) is estimated by the OLS and the firm fixed-effects model. Each estimation equation contains time and industry dummies, and the equations estimated by the OLS also include a constant and a separate dummy for entrants (Dent it ). In the OLS and fixed-effects model, θit represents the error term that contains unobserved productivity. In the top panel of Table 2, the estimation results by the OLS show that the average markup of entrants is significantly lower than incumbents for the entire manufacturing sector. The OLS also detects a significantly positive variation in the r.t.s for entrants. When manufacturing is separated into low- and high-tech sectors, however, the OLS finds that the coefficient representing the entrants' markup variation is positive and significant at 1% level for both industry groups. The estimate of e is significantly negative for the two sub-samples. the r.t.s. variation (λ) The lower panel of Table 2 demonstrates that the estimation results based on the fixed-effects model differ from the OLS for the low- and 6 L K The structural model provides the identity λit = μit[sM it + sit + sit] that links the profit L K margin (1/[sM it + sit + sit]) to markups (μit). The computation of the factor expenditure shares in revenue (sit) is discussed in the Appendix part. 7 Estimating the time variation in markups or r.t.s is not feasible in the specification given by Eq. (6). Nevertheless, the evidence provided in Fig. 1 implies that the average markups remain rather fixed over time within the sample period.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
4
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
Table 1 Entrants' share in Japanese manufacturing.
#Observations #Firms #Entrants Avg. age of entrants Entry ratea (%) a
Table 2 Production function estimations by fixed-effects and OLS.
Total sector
Low-tech
High-tech
OLS
Markup (μ)
Markup diff. (μe)
r.t.s (λ)
e r.t.s diff. (λ)
34,433 1987 863 12.4 0.48
14,032 811 319 13 0.70
20,401 1191 544 12 0.39
Total sector
0.850* (0.005) 0.822* (0.003) 0.777* (0.004)
−0.072* (0.006) 0.014* (0.005) 0.044* (0.006)
0.876* (0.003) 0.949* (0.001) 0.947* (0.002)
0.039* (0.004) −0.033* (0.003) −0.038* (0.003)
Fixed-effects
Markup (μ)
Markup diff. (μe)
r.t.s (λ)
e r.t.s diff. (λ)
Total sector
0.835* (0.006) 0.841* (0.004) 0.820* (0.006)
−0.056* (0.008) −0.017* (0.008) −0.036* (0.010)
0.780* (0.006) 0.891* (0.004) 0.890* (0.007)
0.030* (0.006) −0.075* (0.008) −0.047* (0.010)
Low-tech High-tech
Entry rate is the annual average of the employment ratio of entrants to incumbents.
Variable PM
high-tech sectors. The fixed-effects model retrieves a negative markup difference between entrants and incumbents not only for the overall sector but also for the two sub-groups where the estimates of the markup gap are significant at 1% level. The r.t.s variation is estimated to be negative in the low- and high-tech industries, while it is positive for the overall sector. Assuming that capital is a perfectly variable factor of production, the profit margins can be computed through the equilibri L K ^ ^ um identity, namely that 1= sM it þ sit þ sit ¼ μ =λ. For incumbent firms in the full sample, the OLS yields a profit margin that is 0.85 / 0.876 = 0.97, and the profit margin is 1.07 according to the fixedeffects model. Entrants' profit margin in the full sample is 0.85 with the OLS and 0.96 with the fixed-effects. The OLS estimates of incumbents' average markup (μ) so that the estimated profit margin is low in comparison to the profit margin approximations based on factor expenditure shares given in Fig. 1. This can be an indication of the endogeneity issue in the estimation of the production function by the OLS. Namely, the input expenditure shares in revenue are negatively correlated with productivity that is contained in the error term in the OLS case, so that the OLS estimates of μ are biased downward, and the markup difference of entrants from incumbents (μe) is estimated to be considerably low. The fixed-effects model would be a solution to the endogeneity problem, unless productivity would follow a systematic pattern over time. The time variation in productivity, however, is still contained in the error term and the endogeneity issue persists in the fixed-effects model. Nevertheless, the fixed-effects model partially tackles the endogeneity by controlling for cross-sectional variation, so that the estimates of the markup gap are significantly negative for every firm group. The profit margins estimated by the fixed-effects model are higher in comparison to the OLS case, but they are still much lower than the approximations based on the expenditure shares given in Fig. 1. The estimation procedure described in the next part offers an alternative approach that also controls for the time dependence in the unobserved productivity.
High-tech
*Significant at 1%. **Significant at 5%. Standard errors are in parenthesis. Time and industry dummies are included.
4. A control function approach This section develops a control function approach to handle the endogeneity problem in the estimation of the reduced-form production function given by Eq. (6). The usage of control function approaches in production function estimations dates back to Olley and Pakes (1996) who invert the investment function to derive a proxy for unobserved productivity. The approach used in this paper, however, relies on an extension by Levinsohn and Petrin (LP) (2003) where intermediate inputs are employed as the proxy variable.8 The LP is based on a structural approach which models the endogeneity by assuming that the manager can partially observe her firm's productivity and uses this information while hiring production factors. Managers' decisions on the optimal amount of inputs generate a correlation between production factors and productivity that is fully unobserved by the researcher. Assuming the intermediate inputs is a monotone function of productivity and a function of the state variable capital, mit = m(θit,kit), the LP inverts m(·) to obtain the function to control for unobserved productivity that is θit = ϕ(mit,kit) where ϕ(·) = m−1(·). At this stage, I follow Ackerberg et al. (2006) and introduce lit as a state variable into the control function together with the entry dummy, the other state (capital) and the proxy (intermediate inputs) variables. The production function is written as follows h i M L qit ¼ μ sit ðmit −kit Þ þ sit ðlit −kit Þ þ λkit h i M L ent e Dent þμe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit þ λk it it ent þϕit mit ; lit ; kit ; Dit þ ε it :
ð7Þ
2 1.5 1
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2
Total PM
Low-tech
1.5 1
1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 incumbents
entrants
Fig. 1. Average Profit Margin (PM) in the Japanese manufacturing sector.
In the above equation, ϕit(·) stands for the systematic part of productivity according to which the manager develops her expectations. εit is the random productivity shock that is fully unobservable and i.i.d. over time. The LP method has a critical timing assumption on the choice of the optimal amount of labor used in production. The LP assumes that labor is a predetermined factor, which allows the coefficient of labor to be identified in the first stage, whereas this aspect of the LP attracts much criticism (e.g. Ackerberg et al., 2006; Wooldridge, 2009). In the estimation, I abandon the LP's timing assumption and add labor into the control function, so that the factor elasticity of labor is identified in the final stage. In the first stage, the estimation equation, therefore, consists of a non-parametric function, g(·), that contains the production function and the systematic productivity isolated from random shocks. 8 Levinsohn and Petrin (2003) criticize the use of investment as a proxy for productivity, since investment is a control on the state variable capital, and a state variable is by definition costly to adjust.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
The function g(·) is approximated by a third order polynomial and estimated by the OLS ent qit ¼ g it mit ; lit ; kit ; Dit þ εit :
ð8Þ
The first stage of the estimation, therefore, separates the random shock component from the systematic and serially correlated part of productivity, but it does not identify any of the parameters that are subject to the analysis. An approximation of the systematic productivity can e in the following way be obtained for any given values of μ, μe, λ and λ h i ent M L θit ¼ g it mit ; lit ; kit ; Dit −μ sit ðmit −kit Þ þ sit ðlit −kit Þ h i M L ent e k Dent : −λ kit −μe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit −λ it it
ð9Þ
Productivity is assumed to evolve as a first-order Markov process e as follows.9 which can be written for given μ⁎, μe , λ⁎ and λ θit ¼ βθit−1 þ eit
ð10Þ
e , one, therefore, can retrieve the fitted For given μ⁎, μe , λ⁎ and λ values of Eq. (10) to be used as an estimate for the expectation of productivity conditional on the previous period's realization. Namely, ^ e and stands for the e, λ and λ, E θd it jθit−1 ¼ βθit−1 is a function of μ, μ productivity expectation of the manager. The second stage of the estimation routine can be written in the following form. h i M L qit ¼ μ sit ðmit −kit Þ þ sit ðlit −kit Þ þ λkit h i M L ent þμe sit ðmit −kit Þ þ sit ðlit −kit Þ Dit e Dent þ E θd þλk it it it jθit−1 þ ε it þ eit
ð11Þ
Joint minimization of the error terms εit and eit provides the estie mates of μ, μe, λ and λ. " # H T X N h i 2 X 11X ðεit þ eit ÞZ it;h min TN t i μ;e μ ;λ;e λ h
ð12Þ
In the formulation of the GMM minimization problem, Eq. (12) employs a set of instruments (Zit,j where j = 1 to H) that contains the first and second lags of the production factors and the first lags of the expenditure shares. Moreover, the current capital stock is assumed to be determined by investments in t-1. The instrument matrix, therefore, L consists of Zit = {kit,kit − 1,mit − 1,lit − 1,sM it − 1,sit − 1,kit − 2,mit − 2,lit − 2}. The standard errors are calculated by block bootstrapping, namely, by resampling the dataset over randomly drawn plants, but using the entire times series observations of a drawn plant.10 In the following parts, the control function approach also is used to estimate a restricted version of Eq. (6) that excludes the variables capturing entrants' markup e variation. For the restricted version, the second lags are (μe) and r.t.s (λ) excluded from the instrument matrix, so that Zit = {kit,kit − 1,mit − 1, L lit − 1,sM it − 1,sit − 1}. 4.1. Production function estimation with control function The control function approach described in the previous part is applied to two different versions of the reduced-form production function. In addition to the original version given by Eq. (6), I estimate the
production function without variables capturing entry variation with the aim of comparing the productivity indices derived from these two versions. The top panel of Table 3 displays the estimation results of the production function with entry variation given by Eq. (6). In comparison to the OLS and the fixed-effects model, the control function estimates of the incumbents' markup rise to 1.998 for the entire manufacturing sector. This corresponds to a profit margin that is 1.81 for incumbents which is roughly identical to the average profit margin of incumbents approximated by factor expenditure shares. Entrants' average price– cost markup is estimated to be significantly lower than incumbents' average that is 1.998 − 1.556 = 0.442. Table 3 shows that there is a considerable difference in the markup estimates of firms in low- and high-tech industries, so that incumbents in low-tech industries have significantly higher markups than high-tech incumbents. Conversely, entrants in high-tech industries have higher markups than low-tech entrants. The profit margin estimations based on the control function approach is 0.54 for entrants in low-tech industries and 0.75 for high-tech entrants. Combining this with the entry rates reported in Table 1, one may argue that entry barriers are greater in high-tech industries, so that the average high-tech entrant has to set a higher markup than the average low-tech entrant. This could be because starting up in high-tech industries requires adopting more capital- or technology-intensive production methods, so that hightech entrants incur larger sunk costs than low-tech counterparts. Alternatively, competition in product market may be responsible for the markup difference between the two sectors. Intensive competition leads to a stricter market selection mechanism that only allows relatively highly profitable units to enter into the market. Competition is probably more intensive in high-tech industries, because the estimated overall markups given in the bottom panel of Table 3 are the highest for low-tech industries. The entry variation in the r.t.s that is estimated to be significantly positive in the OLS and the fixed-effects model for the entire sector is insignificant by the control function approach. The adjustment of production function parameters with the true markup variation, therefore, reduces or eliminates the difference in the r.t.s estimates.
5. Entrants' relative productivity This section is devoted to an analysis of entrants' relative productivity performance in the Japanese manufacturing using alternative productivity indices. Each total factor productivity (TFP) index is calculated by the
Table 3 Control function estimation results. Control function estimates with entry variation
Total sector Low-tech High-tech
Markup (μ)
e) Markup diff. (μ
r.t.s (λ)
e r.t.s diff. (λ)
1.998* (0.254) 1.919* (0.306) 1.589* (0.305)
−1.556 (0.338) −1.404 (0.543) −0.872** (0.353)
1.103* (0.158) 0.956* (0.171) 0.959* (0.156)
0.185 (0.170) 0.165 (0.135) 0.160 (0.144)
Control function estimates without entry variation
Total sector 9
In the estimation, I include a constant term into Eqs. (8) and (10). However, it is not possible to identify both intercepts individually with given restrictions. I omit the constants as well as industry and time dummies in the formulations but use them in the estimations. For details on the identification issue of the intercept see Levinsohn and Petrin (2003). 10 In the programming of the block bootstrapping routine, I utilize the code provided by Levinsohn et al. (2004).
5
Low-tech High-tech
Markup (μ)
r.t.s (λ)
1.112* (0.082) 1.315* (0.096) 0.944* (0.116)
0.776* (0.051) 0.678* (0.100) 0.814* (0.039)
*Significant at 1%. **Significant at 5%. Standard errors are in parenthesis. Time and industry dummies are included.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
Table 4 Entrants' relative productivity. Estimation method
Ent./Inc. Prod.
Control function with entry variation Control function without entry variation Levinsohn–Petrin Fixed-effects with entry variation Labor productivity
0.93 0.24 0.27 0.55 0.75
Labor Prod.
6
2 1.5 1 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
TFP
3
11 Estimation of productivity without entry variation implies that the estimating equaL ent tion is in the form of Eq. (6) but excludes the terms, [sM it (mit − kit) + sit(lit − kit)]Dit and kitDent it , which are capturing the markup and r.t.s difference of entrants from incumbents. 12 In the estimation of the standard TFP by Levinsohn and Petrin's (2003) approach, a general Cobb–Douglas type production function is employed and the factor elasticity coefficients are retrieved using the programming routine provided by Levinsohn et al. (2004).
2 1 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
TFP−markup
ratio of outputs to composite form of inputs whose functional form differs among alternative estimation methods. The TFP, therefore, is Θit = Qit / Fit(Mit,Lit,Kit). The statistics given in Table 4 are based on five different productivity indices that are estimated by the fixed-effects model with entry variation,11 the control function approaches with and without entry variation, the labor productivity that is the ratio of output (revenues deflated by 2-digit PPI) to labor (total annual working hours), and the standard total factor productivity index estimated by Levinsohn and Petrin's (2003) methodology without introducing demand side or controlling for markups.12 To compute the statistics reported in Table 4, first, the weighted average productivity is calculated for entrants and incumbents, and then, the ratio is taken between the productivity averages of the two firm groups. In the calculation of the weighted average productivity, firms' output shares are used as the weights for the TFP and the labor shares for the labor productivity. Table 4 presents the productivity ratios of entrants to incumbents for five different measures of productivity. The productivity index estimated by the control function approach with entry variation indicates the highest relative entrant productivity, while the control function without entry variation yields the lowest relative productivity for entrant plants. The difference between the two productivity indices estimated by the control function approaches with and without entry variation is somewhat expectable, since the control function without entry variation overestimates entrants' markups, as long as the actual markups of entrant firms are lower than incumbents. The fixed effects model with entry variation indicates that entrant's productivity is considerably low relative to incumbents. This is due to endogeneity issue in the fixed-effects model that drives down the absolute value of the estimates of the markup gap, so that entrants' markups are still overestimated. The labor productivity, however, reflects a higher relative productivity for entrants than those based on the fixed-effects model and the control function without entry variation. This is possibly because labor productivity is calculated by not deflated labor expenditures but annual working hours, so that the index does not suffer from unobserved input price variation. In other words, using a quantity based input indicator partially controls for unobserved markup variation in labor productivity, while this is not the case in the standard TFP that is measured by deflated nominal intermediate inputs and capital stock. Table 4 also reports entrants' relative productivity based on the TFP index estimated by Levinsohn and Petrin's (LP) (2003) algorithm. In the LP algorithm, the TFP is retrieved through the estimation of a log-linear Cobb–Douglas production function that is an extensively used specification in the applied literature. The entrants' relative productivity, however, is particularly low when it is measured by the standard version of the LP algorithm that does not take into account entrants' markup variation. Fig. 2 provides a closer look at the labor productivity and the two total
0.6 0.4 0.2 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 entrants
incumbents
Fig. 2. Entrants' vs. incumbents' productivity.
productivity indices that are estimated by the original LP method (TFP) and the control function approach with entry variation (TFPmarkup). Fig. 2 depicts the time paths of the weighted average productivity of entrants and incumbents for the three productivity indices. The top panel displays a considerable gap in labor productivity between entrants and incumbents. The labor productivity gap shrinks especially after 1998 that coincides with the East Asian financial crises. A similar time trend is also observed in the standard TFP displayed in the middle panel of Fig. 2, so that there is some degree of convergence between the average productivity levels of entrants and incumbents for the period after 1998. Nevertheless, the productivity difference of entrants is noticeably large for the entire sample period, when it is measured by the LP method. The TFP-markup estimated by the control function approach with entry variation, however, indicates that entrants are on average more productive than incumbents in the first three years of the sample. For the period between 1990 and 1998, entrants' TFP-markup performance slows down, while incumbents' average TFP-markup rises considerably. As in the time paths of the other two productivity indices, the TFP-markup reflects a convergence between entrants' and incumbents' productivity especially after 1998. The time path of the TFP-markup is different from those of labor productivity and the standard TFP especially for entrant firms. This is because in the estimation of the TFP-markup, the total returns to scale is fixed to λ, but the factor elasticity parameters can vary over time and across firms. Therefore, if a firm reacts to a productivity or demand shock by altering its factor shares in production, this is accounted for in the estimation of the TFP-markup but not in the standard TFP. Nevertheless, the time paths of the three indices shown in Fig. 2 provide evidence, to some degree, that the East Asian financial crisis alter the productivity trends in the Japanese manufacturing sector. This may be because of the cleansing effect of recession that clears the market from inefficient firms and facilitates entry. Recessions hit inefficient units more severely and induce exit, which releases a portion of resources to be recombined in more efficient producers (e.g. Caballero and Hammour, 1994). The cleansing effect, therefore, provides new firms with the opportunity to capture the released portion of the resources and to catch up with incumbents more quickly.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
6. Conclusions Since it was realized that the accumulation of inputs does not solely explain producers' production performance, productivity has been used to represent the immaterial factor, namely the efficiency in production. Besides contributing to our understanding of economic growth and welfare, the economics of productivity provides valuable insights into the patterns of industrial restructuring. However, although the theoretical concept of productivity is rather well established, its measurement in practice is ambiguous, especially when the quantities of inputs and outputs are unobservable. When measured by nominal sales, productivity involves price effects that are sensitive to demand-side factors. These factors can be in the form of idiosyncratic demand shocks that are neither determinants nor outcomes of the technical efficiency in production. Demand shocks, however, can be systematically different for some particular firms in an industry. Recent empirical evidence shows that in the startup phase, new firms face negative demand shocks which prevent them from setting markups as high as incumbents. As a ratio of sales to expenditures, the nominal productivity is a positive function of markups, and therefore, may underestimate entrants' actual productivity performance. If this is the case, deflating firm-level data by aggregate price indices would not eliminate the price effects; namely that micro-level markup variation would still persist in the productivity index that is based on deflated production data. This study attempts to answer whether entrant firms charge significantly lower markups in Japan's manufacturing sector, and derives implications of markup heterogeneity for the measurement of productivity. Since firms' prices or quantities are unobservable in the subject industry, the unobserved price variation is controlled for by introducing the demand side into the structural model of production. This enables to estimate price–cost markups using firms' nominal sales and input expenditures through a production function specification. A control function approach is applied to deal with the endogeneity of inputs to unobserved productivity, and a productivity index is estimated by taking into account the average markup gap between entrants and incumbents. My results show that entrants set on average lower markups than incumbents in Japanese manufacturing industries. The markup gap between entrants and incumbents is estimated to be the largest by the proposed control function approach, while the OLS and fixed effects model provide downward biased markup estimates due to the endogeneity issue. The results further show that according to the standard measures of labor and total factor productivity, the average productivity of entrant plants is lower than incumbents. The total factor productivity index that is estimated by accounting for the unobserved markup variation as well as by controlling for the endogeneity, however, indicates that entrants' average productivity is not significantly different from incumbents' average. The results of this study provide new insights on entrants' productivity dynamics and their contribution to aggregate productivity growth. Asymmetric demand shocks may break down the expected positive correlation between profitability and productivity for entrant firms. New firms may initially have low profitability but not necessarily low productivity, which implies that productivity gains from entry may be much higher than what is calculated by nominal or deflated output and input indicators. The empirical evidence on the distorting effects of unobserved prices in the measurement of entrants' productivity is limited to few studies that make use of rare type micro data containing quantities of outputs and inputs. The methodology proposed in this paper, however, does not require observing firms' quantities or prices and is applicable to a wide range of firm-level data. The findings of this paper highlight the importance of distortionary price effects in the measurement of productivity at the micro-level. This study only considers entrants as the group of plants that faces
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different demand conditions, but one can rely on alternative classifications such as domestic and foreign, private and state-owned firms for which markups may differ even within narrowly defined industries. Firm-level productivity analysis, therefore, needs productivity indices that are controlled for micro-level price variations, especially when comparing productivity performances of firm groups within the same industry.
Appendix A. Constructing input expenditure shares and detecting outliers In the plant-level dataset of the Japanese manufacturing sector, the total hours worked and the price-adjusted capital, material expenditures and revenues are reported annually together with each input's expenditure share in total input expenditures. The proposed estimation procedure, however, requires the factor expenditure shares in total revenues but not in total costs. As explained in Fukao et al. (2009), expenditures on material inputs and revenues are deflated with the same price index (2-digit industry level PPI) which enables to retrieve the input expenditure to revenue ratios in the following way. The nominal material expenditure to revenue ratio is calculated by the ratio of the deflated material expenditures to deflated revenues, since both variables are adjusted by the same price index. Moreover, it is possible to calculate the ratio between labor and intermediate input expenditures, because the dataset contains the variables for each input's expenditure share in total input expenditures. Once, the labor to intermediate input expenditures ratio is obtained, the share of labor expenditures in revenue can be calculated simply by multiplying intermediate input expenditures' share in revenue with the ratio of labor to intermediate input expenditures. In the dataset, the capital input's cost share in total input expenditures is also reported, where the user cost of capital is calculated through an approximation over variables such as price deflators, interest and depreciation rates. Even though it is technically possible to retrieve capital expenditures to revenue ratio for each plant and time period in the same manner, I assumed and stated in the main text that the user cost of capital is not observable and subject to possible errors in its approximation. The user cost of capital, therefore, is only used for descriptive purposes, namely, in the approximation of the profit margin in Fig. 1. I detect the outliers according to firms' annual profit margins. I calculate the standard errors for each 2-digit industry and year, and select the observations that are 4 standard errors away from the mean as outliers. The entire time series of a firm is subtracted, if the firm is an outlier in at least one year. This leads 3.6% of all observations to be omitted from the sample. There are totally 94 firms detected as outliers that consist of 51 incumbents and 43 entrants.
App. Table 1 Summary statisticsa.
Incumbents
Entrants
a
Output (Jap. Yen) Labor (man-hours) Capital (Jap. Yen) Intermediate inp. (Jap. Yen) Output (Jap. Yen) Labor (man-hours) Capital (Jap. Yen) Intermediate inp. (Jap. Yen)
Mean
Std
Std/mean
145,521,097 4,640,546 60,498,151 117,346,015 33,967,779 1,152,528 7,882,472 26,219,664
445,960,489 11,247,325 183,097,337 368,243,060 143,951,857 2,604,955 27,815,184 123,309,612
3.07 2.42 3.03 3.14 4.24 2.26 3.53 4.70
Nominal variables are price-adjusted with the base year 2000.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027
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U. Kılınç / Economic Modelling xxx (2013) xxx–xxx
App. Table 2 Entry and exit rates (%) in Japanese industries. Code
Entry rate
Exit rate
C.V. of int. inputs
C.V. of labor
#Firms
#obs
Low-tech industries 6 Food 7 Textile & mill 8 Apparel 9 Lumber & wood 10 Furniture & fixtures 11 Paper 12 Printing & publish. 14 Petroleum & coal 15 Leather 16 Stone & clay & glass 17 Primary metal 18 Fabricated metal 24 Rubber & plastics
Definition
1.24 0.01 0.53 2.00 1.17 0.21 0.71 0.00 5.65 0.59 0.12 1.73 0.75
0.48 0.12 0.54 0.91 0.60 2.64 0.25 1.24 0.00 1.13 0.76 1.09 0.34
2.29 1.31 1.79 1.10 0.98 1.48 2.57 1.31 0.72 2.01 2.13 1.83 1.74
1.73 1.28 1.20 0.92 0.92 1.28 1.95 0.93 0.64 1.54 2.27 1.48 1.64
174 27 62 14 14 47 40 13 4 99 123 115 81
3075 534 922 210 256 781 600 224 67 1701 2249 1996 1417
High-tech industries 13 Chemicals 19 Non-elec. mach. 20 Electrical mach. 21 Motor vehicles 22 Tran. equip. & ordna. 23 Instruments 25 Misc. manufact.
0.29 0.35 0.27 0.44 0.38 0.67 1.78
0.86 0.56 0.45 0.29 0.78 0.58 1.17
1.73 2.88 3.56 3.07 1.42 1.46 1.76
1.42 2.37 2.97 2.07 0.92 1.12 1.76
262 285 335 131 33 74 76
4681 5063 5472 2433 633 1125 994
Entry and exit rates are the annual averages based on plants' labor shares. “C.V.” represents the coefficient of variation. “#Firms” and “#obs” stand for the number of firms and observations. “Code” is the industry codes.
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Umut Kılınç holds a Master of Philosophy degree in economics from Tinbergen institute, The Netherlands (2007). He conducted doctoral studies at Tinbergen Institute and VU University of Amsterdam where he was employed as a research and teaching assistant between 2007 and 2011. In September 2011, he received his Ph.D. degree in economics from VU University of Amsterdam and joined the STATEC (in Luxembourg) as a post-doc researcher. His research interests cover empirical topics in the economics of productivity and industrial organization.
Please cite this article as: Kılınç, U., Estimating entrants' productivity when prices are unobserved, Econ. Model. (2013), http://dx.doi.org/ 10.1016/j.econmod.2013.09.027