Productivity Dynamics, R&D, and Competitive Pressure

Transcription

1 Knowledge for Growth Industrial Research & Innovation (IRI) Productivity Dynamics, R&D, and Competitive Pressure CONTRIBUTED PAPER FOR THE 2007 CONFERENCE ON CORPORATE R&D (CONCORD) <CONFERENCE STRAND> File name: <FlorinMaican_CONCORD_ doc> Author: <Florin Maican> Status: <Draft> Last updated: < > Organisation: <Göteborg University> Page 1 of 34

2 TABLE OF CONTENTS 1 Introduction Overview of the Industries Modeling Framework Estimation Estimation Approach Empirical Results Discussion and Conclusions Appendix A Appendix B LIST OF ANNEXES Annex 1 Annex 2 Page 2 of 34

3 1 Introduction The link between spending on research and development (R&D) and performance is one of the most studied topics in industrial organization. Business magazines and newspapers emphasize the belief in the myth that higher R&D spending ensures competitive advantage: "The European Commission will today appeal to E.U. countries to increase spending on research and development, or face being out paced by competitors such as China" Financial Times, July 2005 Complexity of customer demand and shorter product life cycles are factors that increase the competitive value of a fast and effective innovation engine. Sweden is one of the countries spending the most on R&D, 1 with sixteen manufacturing firms in the 2005 EU Scoreboard rank, which is a list of the EU 700 group of firms ranked by their R&D spending in the 2004 financial year (see EU (2005)). Little work, however, has been done on the impact of R&D on firm performance in Sweden. This paper investigates the distribution of future productivity conditional on current R&D, current productivity, and competition pressure in three Swedish manufacturing industries. The analysis of the productivity distribution helps to understand the firm dynamics investment in R&D and physical capital. In the theoretical firm dynamics models proposed by Ericson and Pakes (1995), Hopenhayn (1992), and Jovanovic (1982), the stochastic evolution of firm productivity determines the success or failure of the firm in an industry. Analyzing the effects of competitive pressure on a firm s incentive to invest in product and process innovations, Bonne (2000) derives the conditions under which a rise in competitive pressure increases each firm s investments in process innovations to improve efficiency. He finds that the effects of a rise in competitive pressure on firm s incentive to innovate depend on the firm s type, which is determined by its efficiency level relative to that of its opponents. 2 Geroski (1990) and Nickell (1996) find empirical evidence that increases in competition are good for innovation. Structural dynamic models with R&D and capital investments based on production function approach neglect competitive pressure that may lead to inconsistent coefficient estimates. The theoretical focus of this paper I propose an underlying dynamic model that allows for the effects of competitive pressure on R&D spending and productivity. This paper provides an extension of Olley and Pakes (1996) (OP) semiparametric algorithm for estimating production function parameters which account for the self selection induced by liquidation, the simultaneity induced by the endogeneity of input demands, and competitive pressure. A further improvement to previous work is that we explicitly incorporate the effect of competitive pressure on the choice of inputs in Buettner (2004) s algorithm. Buettner (2004) extends the OP method by allowing the distribution of the future productivity to evolve endogenously over time the firm s R&D spending affects the distribution of future productivity conditional on the current productivity. 1 R&D investments were around 4% of GDP in Vives (2004) analyzes the effects of competition on R&D effort for a variety of market structures. His findings are: an increasing number of firms tend to reduce R&D spending provided that the total market for varieties does not shrink; an increasing total market size increases both the R&D effort and the number of varieties. Page 3 of 34

4 R&D and competitive pressure influence the stochastic evolution of the unobserved productivity state. 3 While in the OP setting two firms with the same current productivity and different capital stock will have different distributions of future productivity, in the Buettner (2004) setting current capital influences R&D spending that affects future productivity. In my setting the decision to invest and how much to invest in R&D and physical capital depends on the competitive pressure faced by a firm. In other words, we partly endogenize the Markov process for the productivity dynamics. 4 I show that under few restrictions on the model primitives, the policy function for capital investments generated by the structural model is still invertible. I can express the unobserved productivity state as a function of capital, investment, and competitive pressure. The endogenous productivity choice model justifies the retention of observations with nonpositive investment when competitive pressure is included. I employ semiparametric estimation to account for unobserved firm heterogeneity. In the empirical part of the paper I estimate a production function to obtain a measure of firm productivity. I incorporate firm exit and competitive pressure in the estimation to correct for the selection problem induced by liquidated firms. Even if R&D spending enhances plant productivity, such improvements do not occur without costs associated with the exit of firms and large reallocations as well as displacements of labor and capital. From a policy perspective, it is therefore important to evaluate the distribution of future productivity. Analysis of the effect of R&D spending and competitive pressure on the entire distribution of future productivity gives a complete picture of the stochastic nature of R&D outcomes. I relate how the distribution of future productivity changes in respect to current productivity, R&D spending, and competitive pressure. My data cover , a period of significant adjustment, and include all Swedish firms with five or more employees in three important manufacturing industries machinery and equipment, electrical and optical equipment, and transport equipment. The comprehensive nature of the data enables us to analyze the dynamics of small plants that are often unobserved due to data limits. In order to obtain a measure of firm level productivity I estimate a production function in which firm efficiency is modeled as an unobserved firm specific effect. As discussed in detail in Section 4 of this paper, a firm s private knowledge of its productivity and competitive pressure affects its behavior and thus bias the estimates of the coefficients on inputs such as labor and capital in the production function. Since the measure of productivity depends on these estimates, their consistency is crucial for the analysis. My research yields several important findings. First, I find support for productivity improvements related to R&D and competitive pressure. I estimate my dynamic model including different measures of competitive pressure and accounting for the dynamics of inputs. I accept my dynamic model for the machinery and equipment, and for the electrical and optical industries. Long run elasticity of value added with respect to R&D is approximately 0.02 for the machinery and equipment industry and 0.14 for the electrical and optical equipment industry. I find that the optimal share of resources to invest in 3 Early literature on the effect of R&D on productivity was largely focused on estimating the average or expected returns (private or social) to R&D spending. (See Griliches (1998) for a survey of the effect of R&D on productivity.) Does competition affect productivity? There exists a theoretical basis for competition enhancing productivity, but the empirical evidence is not strong enough. 4 I do not have detailed data to introduce an technological indicator following the Ackerberg, Benkard, Berry, and Pakes (2005) s suggestion and have two Markov processes one controlled and another exogenous. Page 4 of 34

5 research is estimated to be one to six times larger than the actual amount invested by the Swedish manufacturing industries. Second, I find that firm exit also contributes to the reshuffling of resources within the economy. The reallocation of market shares and resources from less to more efficient firms is an important channel of productivity: the covariance grew by 1.7% in the machinery and equipment industry, 4.2% in the electrical and optical equipment industry, and by 1.6% in the transport equipment industry. Third, the results show that failure to account for competition pressure faced by a firm causes bias in quasi inputs estimation for the Swedish manufacturing industries. Moreover, selection bias induced by firm closings and simultaneity bias induced by firm dynamics significantly affect the magnitude of the capital coefficient in the production function. The results emphasize that failure to adequately account for the dynamics of unskilled labor or/and technical labor can lead to severe under estimations of capital stock (see Ackerberg, Caves, and Fraser (2005)). In the reminder of this paper, Section 2 describes the data and presents an overview of three Swedish industries and documents some changes in their structures. The dynamic modeling framework used to compute productivity is outlined in Section 3, while Section 4 discusses econometric implementation of the theoretical model. Section 5 presents test results of future productivity distribution conditional on R&D, current productivity, and competitive pressure. Section 6 summarizes the paper and draws conclusions. 2 Overview of the Industries This section provides an overview of the industries and helps motivate my empirical strategy. I choose the empirical strategy based on the information provided by entries, exits, and R&D to sales ratios. This paper draws on a census of Swedish manufacturing firms employing five or more workers, provided by Statistics Sweden, Financial Statistics(FS) and Regional Labor Statistics(RAMS). While RAMS contains information on employee education and wages, FS contains information about firm input and output. My panel data set covers from 1996 to A unit of observation is a firm; however, over 99% of the firms are single plant establishments. Appendix A gives more information about the data as well as variable definitions. Table 1 presents characteristics of the data for all industries. The machinery and equipment industry is the largest, and transport equipment is the smallest. In all industries the largest amount of R&D was spent after During 2000 and 2001 the Swedish economy had entered acyclical downturn. The slowdown was partially explained by weaker international demand. Another impact on the Swedish economy during this period was the bursting of the IT bubble on the stock exchanges. International companies like Atlas Copco (mining and construction equipment) and Tetra Laval (liquid food packaging and dairy equipment) dominate the machinery and equipment industry. In 2002, the industry produced a value added of SEK 47.6 billion, employed 87,741 people in Sweden, and spent SEK 4.6 billion on R&D. The electrical and optical industry is dominated by international companies like ABB (power and automation equipment) and Electrolux (appliances). In 2002, this industry produced a value added of SEK 30.3 billion, employed 86,156 people in Sweden, and spent SEK 34.7 billion on R&D. Transport equipment is one of the most important industries in Sweden. It includes cars, trucks and buses, aircrafts, trains, and marine and aircraft engines. Volvo, Saab, and Page 5 of 34

6 Scania dominate final vehicle assembly. Its many subcontractors underscore the importance of the industry. In the past few years, the industry has undergone rapid restructuring. Ford Motor acquired Volvo Car Corporation and General Motors acquired Saab Automobile. Also subcontractors suffer from extensive restructuring since final vehicle makers tend to cut down on the number of suppliers when introducing new models. In 2002, the industry produced a value added of SEK 46.9 billion, employed 91,474 people in Sweden, and spent SEK 24.2 billion on R&D. Table 2 presents an analysis of the entrants in all three industries. Around 8% of the firms active in 2001 in the machinery industry entered in 1973 or before, accounting for 31% of the technical employment and 63% of R&D spending in Of the firms active in 2001, the proportion that entered after 1996 is constant around 3%. The share of R&D spending is smaller than 1% after In the electrical and optical industry, around 2% of the firms active in 2001 entered in 80s account for 33% of the sales and 60.12% of R&D spending. The highest share of the employment in 2001, 20%, is given by the firms that entered in They have 7% of the technical employment and around 1.5% of the R&D spending in the industry in Around 15% of the 2001 R&D spending in the transport equipment industry came from firms that entered in The firms that entered after 1997 and that were still active in 2001 seem to not be R&D incubators because they have nearly 0% of the R&D spending in They might be subsidiaries of the larger firms in this industry. In all three industries, the high share of 1996 entry firms that were active in 2001 is due to the sample selection prior to The data contain all firms active in these industries after Most of the post 1996 entrants in the database are small firms, accounting for no more than 8% of 2001 employment. On the other hand, the transport equipment industry is the only industry where the large share of R&D spending does not imply a large share of technical employment. Table 3 provides information about the exit process. It suggests that exit seems to play an important role in the adjustment process after Around 29% of the firms in all industries that were active in 1997 did not survive until These firms spent about 20% of the 1997 R&D and produced about 30% of the 1997 output in the machinery, and the electrical and optical equipment industries. The lowest amount of R&D spent by incumbent firms in 2000 that did not survive until 2001 was in the in transport equipment industry (1% of the 2000 R&D spending). The scale effect (R&D to sales ratios) analysis gives us information about the advantages of the newcomers in the industries. Table 4 provides information about the evolution of R&D to sales ratios for firms with sales below and above the median. In all three industries, firms that are larger than the median (on the basis of sales) tend to spend a higher share of sales on R&D than those that are smaller than the median, except for in 2001, when the opposite occurred. The electrical and optical equipment, and the transport equipment industries present large differences in spending. In the transport equipment industry, the larger than median firms spent more than double the proportion of sales on R&D than the smaller than median ones. In the electrical and optical industry, firms spent more than double the proportion of sales on R&D than in the machinery industry. What does large R&D spending yield in the three Swedish industries? Spending more does not necessarily help, while spending too little will hurt. My data emphasize that R&D budget levels vary substantially, even within sub industries. There is not a certain approach to spending money on innovation development, but there are some successful stories in the discussed industries. I want to find if there exists a statistical relation between R&D spending and future productivity at the industry level. Page 6 of 34

7 3 Modeling Framework This section presents the structure of the behavioral model of firms. First I introduce assumptions and structural properties of the stochastic dynamic model, and then derive theoretical results that justify the empirical work in the rest of the paper. I assume a stochastic dynamic single agent model for the industry. A firm maximizes the expected discounted value of future net cash flows. Productivity and the capital stock are the firm s state variables. The dynamic model is formulated by the following Bellman equation with the discount factor : 5 (1) where denotes the random next period state, where the probabilities associated with the next period state are conditioned on starting state and choosing action ; is competitive pressure; is the R&D spending function; is the cost of physical capital; is the investment choice of the firm; and the discount factor is. The firm makes a discrete decision whether to exit or continue in operation after it observes its state variables at the beginning of each period. The firm receives a termination value if it exits. If the firm continues in operation, it earns the net profit in state when action is selected. The action represents the choice of the next period s productivity through R&D spending,, and the decision to invest in capital,. I assume that the profit function,, is bounded from above, non decreasing in,, and, strict supermodular, and continuously differentiable. A rise in competitive pressure raises profits. The firm adapts to increased competitive pressure by raising its productivity. The cost of physical capital is bounded from below, nondecreasing in and decreasing in, submodular, and continuously differentiable. The R&D spending function is non negative, non decreasing in and decreasing in, submodular and strictly submodular on the set. Investment in capital has a deterministic effect on future capital stock. Spending on R&D influences future productivity stochastically. Both investments depend on competitive pressure. In each period, the firm chooses how much to invest in capital stock (and indirectly the next period s capital stock), the quantity of intermediate inputs, labor, and distribution of the next period s productivity through its R&D spending. The accumulation equation for capital is given by 5 See Ericson and Pakes (1995). Page 7 of 34

8 where denotes the next period s capital stock; is the rate of capital depreciation; and is the investment choice of the firm at the beginning of the current period that enters in capital stock at the end of the current period. The firm invests in R&D to improve its productivity in the future years, but the outcomes of the research process are uncertain. The distribution of conditional on information at time depends upon productivity, R&D spending, competitive pressure, and physical investment in capital. For simplicity we introduce a single index as in Buettner (2004), which implies that both R&D spending and productivity affect the distribution for only through. is a controlled Markov process and its primitives are given by the family of conditional distributions, The family is assumed be stochastically increasing in for each value (increases in investment lead to better, in stochastic dominance sense, distribution for future efficiency), stochastically increasing in for each given (conditional on the higher choice the better the distribution of tomorrow s ), stochastically increasing in for each given (conditional on and the higher pressure the better the distribution of tomorrow s ), and continuous in the sense that when integrated against a continuous bounded function of, it produces a continuous bounded function of,, and. The return to research and development are uncertain, and the probability distribution over future productivity is parametrized by competitive pressure. Competitive pressure indexes the sensitivity of the probability distribution to future distribution choice : higher values of competitive pressure correspond to probability distributions where future distribution choice is more effective at shifting probability weights towards high realizations of productivity. Let be the optimal policy. Then we rewrite the Bellman equation can be rewritten in terms of the expected value of profits in the following period and the continuation thereafter (2) Page 8 of 34

9 I want to find a set of alternative programs that leave the last term in this expression unchanged. The distribution of conditional on and each alternative policy is the same as the distribution of conditional on and optimal policy. I choose optimal policy such that where and are chosen such that at. The optimal policy produces a distribution of conditional as a convolution of and. This implies that we obtain the same convoluted distribution by perturbing and by and and by. Lemma 1 The value function is bounded under, non decreasing in productivity and capital, supermodular, and unique. Proof: see appendix B. Lemma 2 The optimal physical investment choice conditional on,, and (3) is non decreasing in,, and. Proof: see appendix B. Lemma 3 The policy function for the choice of distribution is non decreasing in and strictly non decreasing in on the set,,,. Proof: see appendix B. Theorem 1 The policy function for the investment choice,, is non decreasing in and strictly non decreasing in on the set, ;. Proof: see appendix B. Solving the dynamic model we obtain the following policy functions: Page 9 of 34

10 (4) (5) I denote with the threshold productivity. For each capital stock and competition pressure there exists an exit threshold productivity: if the value of productivity is below, then the firm exits; otherwise it stays in operation. Summarizing, as in Olley and Pakes (1996) and Buettner (2004) I prove the monotonicity for the physical investment function including the competition pressure. The policy functions for investment choice (5Error! Reference source not found.) is strictly non decreasing in productivity. The results from theorem 1 suggest that I can use also the data with zero physical investment when I control for competitive pressure. Muendler (2005) finds the same result, but he uses a dynamic framework with quadratic adjustment cost including fixed adjustment cost, and without R&D data. My results indicate that the productivity function is strictly non decreasing when competitive pressure increases and the firm invests in R&D. (6) 4 Estimation Olley and Pakes (1996) introduce an approach based on the explicit models of input choices and exit decisions. The strict monotonicity of the optimal investment or intermediate inputs choice allows us to obtain the estimates of production function parameters and of the unobserved productivity states. Production Function: I assume a Cobb Douglas production technology: where is value added, capital stock, and labor. represents the Hicksian neutral efficiency level of firm, and is not observed by the econometrician. The economies of scale is captured by. The physical output is not observed and is usually replaced by deflated revenue using an industry price deflater. 6 Taking the natural logs in expression (7Error! Reference source not found.) and indexing my variables by time yield (7) 6 I use value added as output instead of deflated sales. Bond and Söderbom (2005) argue that it is impossible to identify coefficients on perfectly variable (and non dynamic) inputs in a Cobb Douglas framework. Page 10 of 34

11 where lowercase symbols represent natural logs of variables and, and represents the observed value added per firm. can be interpreted as the mean efficiency level across firms, and is the deviation from that mean for firm in period. The unobserved is divided into two components: and. The unobservables that are neither observed nor predictable by the firm before input and exit decisions at time are represented by. The component is observed by the firm when it chooses inputs or makes exit decisions. It represents unobserved productivity, and the endogeneity problems are consolidated into it and not into. The component represents either a serially uncorrelated additional productivity shock or measurement error which can be serially correlated. Output, input factors, productivity, and error terms are time and firm specific. Production coefficients are constant across time and firms. Assumptions: Three types of assumptions are important in this approach. First, the assumption that refers to the points in time when inputs are chosen by the firm relative to when they are used in production. Second, there is a scalar assumption that limits the dimensionality of the econometric unobservables that impact firm behavior. The third assumption is a strict monotonicity on the investment demand or on one of the intermediate inputs choice demand investment (intermediate inputs choice) is strictly monotonic in the scalar unobservable for a firm whose investment (intermediate inputs choice) is strictly positive. 7 At the beginning of each period, the firm observes its state variables productivity state, the capital stock, and market conditions. Then it decides whether it continues operations or exits. If it continues operations, then it decides the levels of investment in capital, intermediate inputs, how much of the variable factor labor to employ, and R&D spending given market conditions. The shock is realized after these choices are made. Thus, the labor responds and is correlated with the productivity state, but it is uncorrelated with the error term. The investment decision in period must be made at the end of period based on the information available at that time the productivity and the values of the competitive pressure. 8 9 In other words, capital will respond to productivity via investment violating the consistency condition. Furthermore, the shock is uncorrelated with and with previous s. Correlation of the unobserved productivity with the labor and the capital biases the OLS estimates if one does not control for unobserved productivity. The bias in OLS estimates has three parts. First, Marschak and Andrew (1944) point out that the endogeneity of input choices might cause problems in estimation of (8Error! Reference source not found.). The highly productive firms invest more in physical capital, and the future capital stock is positively correlated with. On the other hand, the highly productive firms have higher employment conditional on capital because they (8) 7 While OP assumes strict monotonicity of the investment demand function, Levinsohn and Petrin (2003) assume strict monotonicity of intermediate inputs choice demand. 8 See Levinsohn and Petrin (2003) for a detailed discussion about the timing of data collection and of the actual investment decisions. These details about data collection are not known in my case, but the investment decision affects the proxy s implementation. 9 Current investment is ordered before the productivity shock in period is known. Page 11 of 34

12 have a higher marginal product of labor in (Error! Reference source not found.8). Second, the selection of firms through exit is another source of bias. A firm optimally decides to exit if its productivity is less than the exit threshold, which is a function of its capital stock and competitive pressure. The exit threshold is decreasing in capital because the firm s profit is strictly increasing in capital. It follows that the lower bound on the range of productivity realizations for surviving firms in the data is decreasing in capital. Therefore, average productivity among survivors is decreasing in the capital stock leading to a downward bias in the capital coefficient. 10 Third, if the firm has some pricing power, then the estimates of will be biased because the inputs might be correlated with the price a firm charges. The bias is called an omitted price variable bias Estimation Approach To solve the bias problem we can use different approaches for the estimation of production functions: fixed effects, or the Blundell and Bond (2000) instrumental variable approach. 13 The OP estimation procedure solves the problem of firm specific time varying unobserved productivity in the estimation of the production functions. I extend the OP framework proposed by Buettner (2004) including the effect of competitive pressure on R&D spending and on physical capital. Ackerberg, Benkard, Berry, and Pakes (2005)(ABBP) give a detalied estimation methodology of OP framework and discuss possible extensions. However, they do not discuss the link between productivity and competitive pressure. The estimation strategy is to control for the unobserved productivity, non parametrically exploiting the monotonicity property of the investment function or one input demand function. I express the unobserved productivity as a function of the current investment, actual capital stock, and competitive pressure : where the functional form is unknown. This function depends in a complex way on all the primitives of the structural model. I assume that labor has dynamic implications to avoid the collinearity problems discussed in ACF. Labor, a component of in my case, is also a function of the state variables and the proxy variable: (9) (10) Rewriting the production function (8Error! Reference source not found.) yields: 10 This is not necessary in my model with R&D spending and competitive pressure. 11 See Klette and Griliches (1996). 12 The firm level price deviation from the industry wide price is captured in the error term. If this price variation is correlated with the inputs, the estimated coefficients will be biased. Intermediate inputs and labor are negatively correlated with the unobserved price yielding a downward bias in intermediate inputs and labor coefficients. For comparison reasons, I do not correct for this bias. It works in an opposite direction than a simultaneity bias, making any prior on the direction of the bias hard. 13 See Ackerberg, Caves, and Fraser (2005) and Levinsohn and Petrin (2003) for a detailed discussion. Page 12 of 34

13 where. The function combines all the dynamic production terms (labor and capital), investment, and competitive pressure. Equation (12Error! Reference source not found.) is a partially semiparametric model where the functional forms and are unknown. An estimate of the unknown function can be obtained from equation (12Error! Reference source not found.). Since the labor and capital have dynamic implication, they cannot be estimated in the first stage as in Robinson (1988). I estimate and in the second stage. I assume that productivity follows a first order Markov process, and, that capital does not immediately respond to the innovation in productivity. The innovation in productivity over last period s expectation is given by, where the index implies that the R&D and current productivity affect the distribution of future productivity only through. For any value of and, the conditional expectation can be computed. Identification of and depends on whether self selection of firms through exit is a concern and whether we consider a model with or without R&D data. Rearranging the production function (12Error! Reference source not found.) and taking the expectation in (13Error! Reference source not found.) conditional on information at and survival until, the expression becomes (11) (12) where denotes the information set in. By assumption, the choice distribution in is sufficient to characterize the distribution of given the competitive pressure. Since productivity follows a Markov process, the second stage estimation becomes (13) The expected productivity conditional on survival is an unknown function. To estimate it, I use the non parametrical approach as in stage one. As Buettner (2004) notes, the key of the model with R&D spending is that the distribution function of future productivity depends on the choice variable. The presence of in the expectation term in the case of model with a R&D spending causes a problem in the identification of. I present the models where self selection of firms through exit is an issue. In this case, the expectation of productivity conditional on past information and survival becomes Page 13 of 34

14 The bias term is a function of state variables and. To control for the impact of the unobservable on selection, I need a measure of productivity that makes the firm indifferent between continuing and selling off. First, I discuss the approach to control for selection in the model without R&D data. As in OP, I need a separate estimate of the survival probability to obtain a proxy for the second index : The proxy variable appears in the last expression because,,. According to this expression, I obtain estimates for the survival probabilities by regression survival in on polynomial extension in,,,, and. The probability of survival is strictly decreasing in the exit threshold. This implies that the threshold can be obtained inverting the survival probability :. I can write the stage estimation equation as where is an unknown non parametric function in,, and. I express the empirical analogue of these moments as (14) The first stage of estimation (see equation (Error! Reference source not found.12)) gives us the values of. The values are the predicted values from the non Page 14 of 34

15 parametric regression of on and. I obtain the estimation of the residual from the following equation: The residuals are functions of parameters. The estimation of gives us the candidate values for. Estimation: To identify and, I use the following two moment conditions: and. The first moment condition that helps to identify assumes that fixed dynamic variables(state variables) i.e capital do not respond to the innovation in productivity. The second moment condition implies that the lagged variable and dynamic inputs i.e. labor should be uncorrelated with the innovation in productivity. This is true because is a part of a firm s information set at and should be uncorrelated with. I get estimates of minimizing the GMM criterion function: where indexes firms; indexes the instruments; and index the first and ante last period firm is observed; and. Buettner (2004) suggests the following way to proxy for (15) without having to use. First, use data on R&D spending. The distribution choice is obtained by inverting R&D function,, where denotes the observed R&D spending of firm in period. In this case, the second stage estimation becomes where is an unknown non parametric function in,,, and. The estimates of are obtained by minimizing the GMM criterion function (17Error! Reference source not found.), where I assume that R&D spending is uncorrelated with the error term in (18Error! Reference source not found.). R&D spending and error are correlated if R&D spending is used in the construction of the value added measure. (16) Page 15 of 34

16 In the case where R&D spending does not exist, none of the terms is a function of and in the Bellman equation (Error! Reference source not found.1). I use the threshold function combined with the fact that the following equation for the second stage:. This yields (17) which is the same equation as for the non selection case. As above, we obtain the estimates of by minimizing the GMM criterion function (Error! Reference source not found.17) using. This is my preferred model to estimate productivity in the empirical part of the paper. 5 Empirical Results This section presents my empirical results. Table 5 presents estimates of the input coefficients from the production function using the OLS, OP, LP, ACF and Buettner (2004) methods. I estimate the production function on the two digit industry level for the following industries: machinery and equipment, electrical and optical equipment, and transport equipment. This implies that firms producing various two digit goods use the same factor proportions, but are imperfect substitutes in consumption, which can lead to different behavior investment in physical capital and in R&D within an industry. On the other hand, differences in their exposure to domestic and international competition might lead to differences in their behavior and differences in their productivity response to international shocks. I include the following factors of production: non technical, technical labor, materials, and energy. Table 5 reports the estimates of the coefficients based on OLS and different semiparametric methods using value added as the left hand side variable, and the full sample (unbalanced panel). According to the theory, the coefficients on variable inputs such as labor should be biased upwards in the OLS estimation. But the direction of the bias on the capital coefficient is ambiguous. My results confirm this. The estimates of the coefficient on labor and capital based on semiparametric estimation differ from OLS, changing in a direction that points to successful elimination of simultaneity and selection bias. On the one hand, the coefficient on capital is lower than OLS (machinery and equipment: LP m, LP all, ACF m, B 1, B 2, B 3; electrical and optical equipment: OP, ACF m, B 1, B 2, B 3; and Transport Equipment: LP all, ACF m, ACF e, ACF all, B 2, B 3). The estimated capital coefficient drops drastically to unreasonable levels when I introduce lagged R&D spending to control for expected productivity in the Buettner (2004) specification. On the one hand, this might be due to an endogeneity problem with respect to R&D, if R&D data are used in the construction of the value added measure. On the other hand, production function estimation with these data might suffer from persistent unobserved shocks that vary within firms but resist treatment and cause bias. Muendler Page 16 of 34

17 (2005) suggests that firm level capital investment interacted with sector level competition variables is a superior candidate model to capture a firm s individual market expectations and to correct for transmission bias. He neither allows for R&D nor accounts for rivalry variables, however. The degree of rivalry in a market is difficult to determine with precision, and cannot be captured by one variable. Following Geroski (1990), I use four measures of rivalry: (i) the extent of market penetration by entrants, (ii) the relative number of small (less than 100 employees) firms, (iii) within period percentage change in concentration ratio, and (iv) the four firm concentration ratio. All variables are computed using five digit information. The firms competitive environment is also captured by the following variables: foreign market penetration, aggregate demand, and real exchange rate (see Muendler (2005)). Table 6 reports the estimates of the coefficients based on one of the semiparametric methods discussed in Section 4.1. The selected method captures the effect of R&D spending and also controls for selection in my model by putting the current capital stock in the nonparametric function, and accounts for competitive pressure. I estimate different specifications with the competitive pressure variables mentioned earlier and present only the significant results. Taking account of competitive pressures gives better estimates for capital; further, the labor coefficients move in a direction suggested by theory. Though early literature on R&D and productivity studied the average effect of R&D on productivity, my approach and Buettner (2004) treat R&D subject to stochastic accumulation. This allows us to estimate the entire conditional distribution of productivity realizations, and gives us a a more complete picture of the effect of R&D on productivity. Considering the productivity s estimates from Table 6, we should investigate whether the empirical conditional distribution of future productivity is stochastically increasing in R&D spending. Table 8 presents the distributions conditional on survival and positive investments. I do not control for censoring of the distribution through exit or through negative investments. I run OLS and quantile regressions of future productivity on current productivity, R&D spending, and competitive pressure variables. The OLS regression estimates the mean effect of current productivity and R&D spending on future productivity, while the quantile regressions estimate the effect of R&D spending on different quantiles of the conditional distribution. The null hypothesis implies that none of the coefficients on R&D is significantly positive, or at least that one of the coefficients is significantly negative, while the alternative implies first order stochastic dominance of future productivity in R&D spending. My regressions are simplistic and assume that there is a linear relationship between the conditional quantiles and the dependent variable. In the context of my model, I assume that the choice can be expressed as a linear function of current productivity, R&D spending, and competitive pressure variables, and a linear relationship between and the quantiles. The coefficient for R&D is positive in OLS specifications and in each of the quantile regressions for the machinery and the electrical and optical industries. On the other hand, the coefficient on R&D is positive, but is not significant in all quantile regressions for the transport equipment industry. This implies that even if there are some successful firms in this industry, R&D spending has a low effect on future productivity. The standard errors reported in Table 8 are bootstrapped. I are able to specify out of versions of the bootstrap in which the sample size of the bootstrap samples is different (typically smaller) compared to the original sample size. This "sub sampling" approach has a number of advantages, for example that it can be considerably faster than the full out of version. For the machinery and the electrical and optical industries, the R&D coefficients are positive and significant in most of the regressions. According to Page 17 of 34

18 this, I can reject the null of a non positive coefficient at conventional significance levels and conclude that the conditional productivity distribution is stochastically increasing in R&D for the machinery and equipment, and for the electrical and optical industries. Table 8 shows that I cannot accept the hypothesis that the conditional productivity distribution is increasing in R&D spending for transport equipment. On the other hand, I accept the hypothesis that the conditional productivity distribution is increasing in competitive pressure (aggregate demand, market share, number of small firms) for all industries. Since I accept my dynamic model for the machinery and equipment, and for the electrical and optical industries, the OLS coefficients on R&D from Table 8 give a crude estimate of the effect of R&D on expected productivity. This is a rough approximation of the elasticity of the expected value added in the next period with respect to R&D: elasticity is about for machinery and equipment and for electrical and optical equipment. Both estimates are low, but they are only a measure of short run returns to R&D. If I assume that the one period "shift" in the distribution of productivity is permanent, then the long run return to R&D in terms of value added would be the discounted value of the permanent increase in value added. Let us assume a 10 % discount rate. Then a long run elasticity of value added with respect to R&D is approximately 0.02 for the machinery and equipmet industry and 0.14 for the electrical and optical equipment industry. My results indicate that aggregate demand plays an important role in shifting future productivity in the electrical and optical and the transport equipment industries. Do the manufacturing industries engage too much or too little R&D? I try to find how much private investment in research differs from optimal investment. I estimate the private rate of return to R&D,, using the regression. 15 Large rates of return to R&D suggest substantial underinvestment. Jones and Williams (1998) emphasize that represents an underestimate of the true rate of return to R&D with a maximum downbias equal to the rate of growth of output. They define the optimal amount of research as given by the condition that the rate of return is equal to the real interest rate. The actual rate of investment in research by the industry,, satisfies the equation, where is the productivity growth. 16 The optimal rate of investment in R&D along a balanced growth path is, where is the output growth. Therefore, the ratio of optimal investment to actual investment in research is (18) Having the estimate of, we can compute a lower bound on this ratio. The denominator is no greater than the real rate of return for the economy. The average real return on the stock market was around in Table 9Error! Reference source 15 I have to distinguish between the private return and the social return to R&D. In my case, I estimate the private return to R&D using firms own share as the explanatory variables. The social return to R&D captures inter firms technology spillovers by focusing on the industry level and alleviates measurement problems. 16 is a parameter in the production function for new ideas and the presence of may reflect duplication of effort in research process the social marginal product of R&D may be less than the private marginal product (see Jones and Williams (1998) for more details). Page 18 of 34

19 not found. implies a estimate of of about six for the machinery and equipment, two for the electrical and optical equipment, and four for the transport equipment. Even if we double the private rate of return to 15%, the ratios remain high three for the machinery and equipment, one for the electrical and optical equipment, and two for the transport equipment. Hence, the optimal share of resources to invest in research is estimated to be one to six times larger than the actual amount invested by the Swedish manufacturing industries. To check the importance of productivity gains stemming from the reshuffling of resources from the less to the more efficient firms, I compute aggregate industry productivity measures for each year. The aggregate industry productivity is a weighted average of firms individual unweighted productivities with an individual firm s weight corresponding to its share of the total industry output. As in Olley and Pakes (1996), I decompose the weighted aggregate measure into two parts: the unweighted aggregate productivity measure and the total covariance between a firm s share of the industry output and its productivity: where the bar over a variable denotes a mean of all firms in a given year. The covariance component represents the contribution to the aggregate weighted productivity resulting from the reallocation of market share and resources across firms of different productivity levels. A positive covariance indicates that more output is produced by the more efficient firms. The results of the productivity decomposition for the industries in our sample are reported in Table 7 in terms of growth relative to 1996; therefore the growth measures for each industry are normalized. First, my results indicate that the aggregate weighted productivity increased in all industries from 1996 to The aggregate productivity gains over seven years range from 1.8% in the electrical and optical equipment industry, to 2.6% in the machinery and equipment industry, and to 4% in the transport equipment industry. The growth in aggregate productivity was driven by a small growth in unweighted productivity only in the machinery and transport equipment industries; otherwise it resulted from the reallocation of the resources and market share from less to more productive firms over time. More productive firms produced an increasing share of output in all industries: the covariance grew by 1.7% in the machinery and equipment industry, 4.2% in the electrical and optical equipment industry, and by 1.6% in the transport equipment industry. 6 Discussion and Conclusions This paper suggests a method for getting reliable estimates on productivity accounting for competitive pressure. The model focuses on structural techniques suggested by Olley and Pakes (1996). In many industries firms engage in R&D with the aim of improving future productivity, and they decide how much to spend taking competitive pressure into account. If one believes that the true underlying model of firm dynamics should include R&D and competitive pressure, then without an explicit model it is unclear whether the OP or the Buettner (2004) approach can be applied. In addition to the vast literature on estimating Page 19 of 34

20 production functions correcting for simultaneity bias, I control for competitive pressure on a firm s decision to invest in physical capital and R&D. In this way, I get estimates for productivity corrected for persistent unobserved shocks. My main contributions are the following: First, I study how R&D and competitive pressure influence the stochastic evolution of the unobserved productivity state. In other words, I partly endogenize the Markov process for the productivity dynamics. I show that under few restrictions on the model primitives, the policy function for capital investments generated by the structural model is still invertible. I can express the unobserved productivity state as a function of capital, investment and competitive pressure. Second, the endogenous productivity choice model justifies the retention of observations with nonpositive investment when competitive pressure is included. I apply this methodology on three Swedish manufacturing industries. I analyze the distribution of future productivity conditional on R&D spending, current productivity, and competitive pressure. The results demonstrate that the omission to account for competitive pressure leads to inconsistent estimates of the production coefficients. In addition, I find that firm exit contributes to the reshuffling of resources within the economy. Most importantly, I present evidence that R&D enhances performance in Swedish manufacturing industries R&D and competitive pressure improve productivity. References ACKERBERG, D., L. BENKARD, S. BERRY, AND A. PAKES (2005): Econometric Tools for Analyzing Market Outcomes, Forthcoming Handbook Of Econometrics. ACKERBERG, D., K. CAVES, AND G. FRASER (2005): Structural Identification of Production Functions, mimeo, UCLA. ATHEY, S. (2000): Characterizing Properties of Stochastic Objective Functions, mimeo, MIT and NBER. BLUNDELL, R., AND S. R. BOND (2000): GMM Estimation with Persistent Panel Data: An Application to Production Functions, Econometric Reviews, 31(3), BOND, S., AND M. SÖDERBOM (2005): Adjustment Costs and the Identification of Cobb Douglas Production Functions, Discussion paper, The Institute of Fiscal Studies, Working Paper Series No.05/04. BONNE, J. (2000): Competitive Pressure: The Effects on Investments in Product and Process Innovation, RAND Journal of Economics, 31, BUETTNER, T. (2004): R&D and the Dynamics of Productivity, mimeo, LSE. ERICSON, R., AND A. PAKES (1995): Markov Perfect Industry Dynamics: A Framework for Empirical Work, Review of Economic Studies, 62, EU (2005): Monitoring Industrial Research: The 2005 EU Industrial R&D investment Scoreboard, Volume I: Analysis, Discussion paper, European Commission. GEROSKI, P. A. (1990): Innovation, Technological Opportunity, and Market Structure, Oxford Economic Papers, 42(3), GRILICHES, Z. (1998): R&D and Productivity. The University of Chicago Press, Chicago. HOPENHAYN, H. A. (1992): Entry, Exit and Firm Dynamics in Long Run Equilibrium, Econometrica, 60(5), HULTEN, C., AND F. WYKOFF (1981): chap. The measurement of Economic Depreciation, in C. Hulten ed., Depreciation, Inflation, and Taxation of Income from Capital, Urban Institute Press, Washington D.C. JONES, C., AND J. WILLIAMS (1998): Measuring the Social Return to R&D, The Quarterly Journal of Economics, pp JOVANOVIC, B. (1982): Selection and the Evolution of Industry, Econometrica, 50(5), Page 20 of 34

21 KLETTE, T., AND Z. GRILICHES (1996): The Inconsistency of Common Scale Estimators when Output Prices are Unobserved and Endogenous, Journal of Applied Econometrics, 11(4), LEVINSOHN, J., AND A. PETRIN (2003): Estimating Production Functions Using Inputs to Control for Unobservables, The Review of Economic Studies, 70(2), MARSCHAK, J., AND W. H. ANDREW (1944): Random Simultaneous Equations and the Theory of Production, Econometrica, 12(3 4), MUENDLER, M. (2005): Estimating Production Functions when Productivity Change is Endogenous, mimeo, University of California, San Diego and CESifo. NICKELL, S. J. (1996): Competition and Corporate Performance, Journal of Political Economy, 104(4), OLLEY, S., AND A. PAKES (1996): The Dynamics of Productivity in the Telecommunications Equipment Industry, Econometrica, Vol. 64(No. 6), ROBINSON, P., M. (1988): Root N Consistent Semiparametric Regression, Econometrica, 56, SMITH, J. E., AND K. J. MCCARDLE (2002): Structural Properties of Stochastic Dynamic Programs, Operations Research, 50(5), VIVES, X. (2004): Innovation and Competitive Pressure, mimeo, INSEAD and Centre for Economic Policy Research. Page 21 of 34

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31 7 Appendix A I now describe the variables used. Value added is total shipments, adjusted for changes in inventories, minus the cost of materials. Real value added is constructed by deflating value added by a five digit industry output deflater. The deflectors are taken from Statistics Sweden. The technical labor variable is the total number of employers with at least 3 years of technical school education. The non technical labor defines the remaining employees. Data on the research and development variable stem from FS and covers all firms with at least one employee active in R&D activities at a minimum of 50% full time. The FS is updated annually and it is compulsory for firms to reply. Firms must give an exact figure for R&D spending or to answer in an interval scale. I deflated the R&D spending, sales, and investment by the consumer price index(cpi) from IMF CDROM The capital measure is constructed using a perpetual inventory method,. Since the capital data distinguish between buildings and equipment, all calculations of the capital stock are done separately for buildings and equipment. As suggested by Hulten and Wykoff (1981) buildings are depreciated at a rate of and equipment at In order to construct capital series using the perpetual inventory method, I need an initial capital stock. Some of the firms in FS since I set the initial capital stock to the first occurrence in FS. I define entry when the year of entry in FS is the same as the year of first data collection. FS contain all firms in different industries after Appendix B Lemma 1 The value function is bounded under, non decreasing in productivity and capital, supermodular, and unique. Proof: The proof is a consequence of the proposition 5 in Smith and McCardle (2002). I reformulate Smith and McCardle (2002) s proposition in proposition Error! Reference source not found.. All the properties in the lemma Error! Reference source not found. are closed convex cone properties. Definition 1 is a closed convex cone property ( ) if the set of functions satisfying forms a closed convex cone in the topology of pointwise convergence. Proposition 1 (Smith(2002)) Let be a set of functions on satisfying a CCC property, and let be a joint extension of on. If, for all, (a) the net profit functions satisfy and (b) the transitions and satisfies, then each satisfies and, if it exists, also satisfies. In my case the properties and are the following: is bounded, increasing in and, and supermodular; and for each and, is bounded, nondecreasing in and, and supermodular. Page 31 of 34

32 The net profit function is bounded above because the profit function is bounded above, cost and R&D functions are nonnegative. The expected net present value of the future one period return is bounded above due to the fact that. In addition, puts a lower bound on the value function so that is bounded. The net profit is a non decreasing function of the current state, and are supermodular (see Athey (2000)); this combination of properties is the that I want to show that the value function satisfies. Each of these properties is a single point property, and is as well. The joint extension of requires that holds for each action. The net profit function satisfies for each choice of action and therefore satisfies.. From lemma 2 and lemma 3 I have that the transitions and satisfies. Thus, I obtain each satisfies and also satisfies Lemma 2 The optimal physical investment choice conditional on,, and is non decreasing in,, and. Proof: The value function is supermodular. The integral is supermodular in because is stochastically non decreasing in and (see Athey (2000)). This implies that the optimal investment choice is non decreasing in capital ( is supermodular implying that the objective function is supermodular), non decreasing in and. Lemma 3 The policy function for the choice of distribution is non decreasing in and strictly non decreasing in on the set Proof:,,,. The objective function is supermodular in. It is a sum of supermodular functions ( By assumption, the R&D spending is supermodular and the profit function is also supermodular). This implies that the objective function is non decreasing in and. To prove strict monotonicity I use an Euler equation for a perturbation of the optimal between periods and. We want to see what are the implications of an increasing in productivity on the Euler equation. Euler equation has to remain satisfied for an increasing in productivity. The choice of distribution Page 32 of 34

33 and competitive pressure affect the stochastic evolution of the future productivity. The future productivity affects the future pressure. I construct an alternative programme that leaves the joint distribution of the state variables from the periods onwards unchanged (conditional on the state in ). If the perturbation Let us define denotes the choice distribution under the optimal programme, let us consider. The next period productivity has the distribution under this perturbation. where,,, and is differentiable as and are differentiable. The difference in period between the value function of the original and alternative programme is This expression must be non negative in a neighborhood of the because the original programme is optimal. Its derivative with respect to at must be zero, which implies the Euler equation. for each. is a continuous, strictly increasing function of for every. For fixed and increase in has to trigger change in and for to remain satisfied. In addition to Buettner (2004), my setting accounts for the effect of competitive pressure on the firm s profit when I have an increase in productivity. The choice distribution is non decreasing in on the set. Page 33 of 34

34 Theorem 1 The policy function for the investment choice,, is non decreasing in and strictly non decreasing in on the set, ; Proof: I know from lemma 2 and 3 that the investment choice. is non decreasing in, which is non decreasing in and. This implies that the optimal investment choice is non decreasing in and. Let us consider the following alternative programme:, (actual investment affects future productivity that affects competitive pressure),,, and. The difference in period between the value function of the original and alternative programme is This expression must be non negative in a neighborhood of the because the original programme is optimal. Its derivative with respect to at must be zero, which implies the Euler equation. for each. is a continuous, strictly increasing function of for every. For fixed and increase in has to trigger change in and for to remain satisfied. Page 34 of 34