Innovation, competition and technical efficiency

Contradictory empirical and theoretical evidence on the relationship between innovation and competition has been reconciled in a model that yields an inverted U-shaped curve. I test whether the predictions of the model are supported by the data with an unbalanced panel of firms for 1990–2003 in a high productivity growth, high-tech industry, Finnish ICT manufacturing. In particular, I investigate how well alternative, yet rigorous measures of innovation and the technology gap, such as R&D intensity, R&D elasticity, technical change, technical efficiency and total factor productivity fare with respect to competition measured by the Lerner index. The results prove sensitive to the choice of variable. Overall, the model is not supported by the empirical evidence of the industry. Subjects: Industrial Economics; Microeconomics; Production Research & Economics


Introduction
By definition, fully efficient firms form the global technology frontier. Since the frontier represents the state of the art in technology, it responds to innovation only. Meanwhile, neoclassical theory postulates competition to reduce productive inefficiency. Yet, the Schumpeterian paradigm (Schumpeter, 1934) recognized monopoly rent prospects of the innovator as the central innovation incentive. Hence, firms at the frontier are frequently sheltered from intense competition. The theoretical model of , postulating an inverted U-curve-shaped relationship between innovation and competition, has proposed a way to reconcile controversial empirical findings

ABOUT THE AUTHOR
Elina Berghäll is a senior research fellow with the VATT Institute for Economic Research (VATT) in Helsinki. The article is a part of her research on the Finnish ICT industry. Her research fields cover a range of topics from innovation policy, R&D and physical investment, ICT, technology frontier, productivity, technical efficiency, environment and sustainable development, economic growth, infrastructures, tax competition, regional policy, urban economics to international capital flows. In addition to VATT, she has worked among others for the OECD, the Association of Finnish Local and Regional Authorities and the UNU/ WIDER. Her research results have been presented and published on various international fora and publications. She has taken part in a number of scientific and policy-oriented working groups and acted as referee to numerous international journals.

PUBLIC INTEREST STATEMENT
The assumption that competition reduces slack while innovation depends on it, is fairly common. By definition, efficiency improvements narrow the gap with the technology frontier. On the other hand, the technology frontier shifts with innovation, which can generate at least temporary monopoly power. This somewhat contradictory relationship between innovation and competition has been reconciled by Aghion, Bloom, Blundell, Griffith, and Howitt (2005) into a model that yields an inverted U-shaped curve. I test the predictions of the model with a panel of Finnish ICT firms for 1990-2003, when radical innovation in mobile phones accelerated technological change and productivity growth. Since the model is not supported by the empirical evidence of the industry, I conclude that the model predictions do not represent stylized facts of the relationship between competition and innovation. between innovation and growth and the contradictions of industrial organization (e.g. Dixit & Stiglitz, 1977) and endogenous growth models (e.g. Aghion & Howitt, 1992;Grossman & Helpman, 1991;& Romer, 1990). The purpose of this paper is to explore the robustness of the predictions of the model on empirical evidence from an innovative industry subject to intense competition from abroad. According to the model, new technological breakthroughs can establish significant leads in competition and increasing returns for a while, until laggards copy and catch up with the innovators. Innovation increases at low levels of competition, reaches an optimum and thereafter declines as competition intensifies and begins to discourage innovations as monopoly rents from innovation decline. The inverted U-shaped interrelationship emerges from the escape competition effect at low levels of competition, which turns into a Schumpeterian effect as higher levels of competition begin to discourage R&D investment. As empirical predictions of the inverted U-model, Aghion and Griffith (2005, p. 57) list that (1) additional product market competition (PMC) in frontier industries increases innovation; (2) Vice versa, additional PMC in lagging industries reduces or increases innovation only weakly; (3) An increase in PMC in the economy on average reduces the share of frontier industries and raises the average technological gap. "The average fraction of frontier sectors decreasesnamely, the average technological gap between incumbent firms and the frontier in their respective sectors increases-when competition increases"; (4) As a result, the general effect of additional PMC on the economy follows an inverted U-shape. Additional PMC encourages innovation at low levels of competition, but discourages it at high levels of PMC.
In efficiency terms, this means that additional PMC in efficient industries increases innovation, and vice versa additional PMC in inefficient industries reduces or increases innovation less, and that additional PMC in the economy on average reduces the share of frontier firms or raises average inefficiency. In other words, there is a positive relationship between inefficiency and (additional) competition at the industry or economy-wide level. The more efficient the economy on average, the more inefficiency increases as a result of competition.  refer to productivity in the context of the innovation-competition dichotomy. They (p. 49) state that while competition appears to be effective at improving productivity levels in satisficing firms (those plagued with agency and managerial slack problems), this does not automatically translate into higher rates of productivity growth in such firms relative to more profitmaximizing ones. In other words, competition can be effective in raising productivity in inefficient firms relative to more efficient firms, but not its growth rate. Innovation has been proxied by the level and growth rate of TFP also by Nickell (1996), who found evidence that more intense PMC is reflected in more rapid TFP growth. In practice, while innovation may raise productivity, high innovation input or output does not automatically translate into TFP growth. In addition, the use of productivity for innovation confuses the relationship of innovation with the frontier, also referred to in the Aghion et al. model. In economic theory, inefficiency is a relative term that measures the gap between the production possibilities frontier and the realized output. Productivity improvements, in contrast, reduce inefficiency in lagging firms, but increase it if the improver is a frontier firm. If firms are inefficient, competition is more likely to raise efficiency. Moreover, although all may be pushed to seek ways to improve their efficiency, the gap between successful firms and the rest may widen and average inefficiency increases.
In addition to productivity,  applied patents as a measure of innovation and the Lerner index as a measure of competition. Subsequent literature, surveyed in the next section, has applied further measures of innovation and technology gaps. Tingvall and Poldahl (2006) test the predictions of the model on firm-level data, and find that the inverted U-shaped relation is supported by a Herfindahl index measure of competition, but not by a price-cost margin.
I contribute to the literature by testing whether results correspond to the theory if more rigorous determinants of innovation and technology gaps are applied, such as R&D intensity and technical efficiency. In particular, I apply frontier methodology to estimate the technology gap, and R&D intensity, R&D elasticity and technical change as proxies for innovation. The data-set is from an innovative and competitive industry, the Finnish ICT manufacturing industry during a period of rapid technological change, 1990-2003. At the time, the industry attracted technology adopters from abroad in the form of FDI. Hence, one can assume it to have been close to the frontier, while being open to intense competition from abroad.
According to the predictions of the theory, if the industry was indeed at the frontier at the time, average technical efficiency in Finnish ICT manufacturing should be high, competition neck-andneck on the upward sloping part of the inverted U-curve. That is, additional competition should increase innovation. I seek answers to questions, such as is average technical efficiency high in the industry? Has competition increased technical inefficiency or innovation? Does technical inefficiency or total factor productivity (TFP) provide a good measure of innovation? The results prove sensitive to the choice of variable. Overall, the model is not supported by the empirical evidence of the industry.
The next section reviews empirical applications of the theory. I present the data and variables in the Section 3, and methodology in the Section 4. The Section 5 summarizes the results and their implications are briefly discussed in Section 6.

Related theories and empirical findings
The literature on firm performance, competition, sources of innovation and industrial organization extends beyond the Schumpeterian paradigm (Schumpeter, 1934), which recognized monopoly rent prospects of the innovator as the driving force of innovation. Arrow (1962) identified the profit appropriation opportunity of the new comer to arise from the public good properties of knowledge (spillovers). Bain (1951) found that rates of return of firms in relatively more concentrated industries were significantly higher than those in un-concentrated ones, interpreting it as evidence in favour of the now so-called structure conduct performance paradigm in industrial organization theory. Demsetz (1973) and Demsetz (1974) challenged this view by arguing that abnormal profits reflect higher efficiency levels rather than monopoly profits, and that researchers need to distinguish between the impacts of efficiency on performance from those of market power. To test the cause, if collusion is present, then smaller firms should earn similar (if not higher) rates of return than large firms. If in contrast, efficiency is driving the rates of returns, then a positive correlation with the industry rate of return should only emerge for large firms. Similarly, Carlsson (1972) found productive efficiency to increase with producer concentration, and explained it by the small size of the Swedish market relative to economies of scale in manufacturing. Caves (2007) has argued that efficiency rents and monopolistic profits (due to the dominance of one large buyer firm over many suppliers), may also coexist. The resource-based view (RBV) of the firm holds that if short-run competitive advantages are heterogeneous in nature and not perfectly mobile, they can be transformed into a sustained competitive advantage generating abnormal returns (Peteraf, 1993, p. 180).
Most traditional models of PMC and innovation predicted a detrimental impact from competition on innovation and growth. These include, e.g. the Hotelling linear model and the monopolistic competition model by Dixit and Stiglitz (1977). Dasgupta and Stiglitz (1980) propose that the anticipation of future competition deter entry and hence competition today. In the mid-1990's, empirical findings began to contradict these theories, but the models applied so far suffered from linearity. The only exception was Scherer (1965), who showed how patenting activity increases with firm size, but with diminishing patenting relative to size. He questioned the role of large monopolistic conglomerates in technological progress, i.e. the Schumpeterian (Mark II) model of competition, innovation and growth. His view received support from subsequent empirical research .
Empirical findings of a positive relationship between PMC and productivity growth have generated new models and theories on gradual technological progress that evolves step by step. That is first, lagging firms need to catch-up with market/technology frontier leaders by means of imitation, before they attempt to escape competition by means of innovation. (See e.g. Aghion, Harris, & Vickers, 1997;or Aghion, Harris, Howitt, & Vickers, 2001). Also in line with the theory,  evaluate the predictions listed above with patent data on the UK firms, and find that the inverted U-curve is steeper in more neck-and-neck (efficient) industries. For example, the curve is steeper in the food and beverages sector, than in electronics and electrical products. Other positive evidence for the inverted U-curve has been found by Kilponen and Santavirta (2007), who found that R&D subsidies to have adverse effects on competition in only extreme cases, but generally positive influences on innovation.
In contrast, Gorodnichenko, Svenjar, and Terrell (2010) claim to find no evidence on an inverted U-curve for emerging markets firms, although what they find is in accordance with the downward sloping part of the inverted u-curve. That is, competition has a negative effect on innovation, especially for firms further from the frontier, but they do not rule out an inverted U-relationship in more pro-business environments. Bos, Kolari, and Van Lamoen (2013) proxy innovation with input-based (cost minimization) technical efficiency, and estimate the presence of an inverted U-curve between competition and technology gaps in the US banking industry. They find consolidation to have reduced innovation. Similarly, Badunenko, Fritsch, and Stephan (2006) consider efficiency as an overall measure of innovativeness, resulting from high productivity in the production and sale of highly priced innovative goods and services. It is unexpected that the technology gap has been used to proxy innovation, since it is a rather common presumption that efficiency and innovativeness are contradictory, because innovation requires some degree of slack. Particularly, industrial organization theories typically expect innovation to decline with efficiency enhancing competition .
Well before them, research by Hanusch and Hierl (1992) suggests that the relationship between profit margins and technical efficiency is not linear. Hanusch and Hierl analysed the relationship between profitability and technical efficiency in German electronics and machinery industries and found it to be convex, i.e. enterprises enjoy increasing returns to their attempts to raise efficiency. They concluded suggestively that leading enterprises may be subject to strong efficiency pressures to maintain profitability relative to competition. Their data on R&D expenditures was sufficient only for the machinery industry. Since deviations from the production frontier were small, they concluded that the sample firms' best strategy is innovation as opposed to imitation, in order to ensure technological leadership and above average profitability.

The data and variables
Empirical evidence is sought from a fairly homogenous innovative high-tech industry in the small country that is subject to intense competition from abroad. Asset seeking FDI into the industry during the sample period suggests it to have been close to a technology frontier, characterized by intense and rapidly evolving innovation and competition (Berghäll, 2015). It, therefore, offers potential to test the predictions of the model in a concise setting with few disrupting unknowns. While external validity requires more extensive evidence on other industries and countries, the empirical research needs to be carried out separately by industry to avoid unrealistic production function assumptions with respect to underlying technologies. The present exercise therefore contributes to the literature with an example of an innovative industry, which may have counterparts in other countries and high-tech industries.

The ICT industry data
The  Table 1.
In the production function, real value-added measures output (Y), the dependent variable. There are three main independent variables: Non-R&D labour (L), the physical capital stock (K) and the R&D stock (R). Labour input is proxied by total firm personnel due to data shortages on hours worked. As R&D was included as an input, R&D employees were deducted from the total number of labour input to avoid double-counting (see e.g. Hall & Mairesse, 1995). The LDPM database provides proxies for physical capital, built from machine and equipment investments using the perpetual inventory method with a 10% depreciation rate, i.e. K t = (1δ)K t−1 + I t , where δ is the depreciation rate. Similarly, R&D capital stocks were built from total intramural R&D investments, available in the R&D panel, based on the perpetual inventory method. The initial R&D stock was based on data from 1985 to 1989 when available, and estimated with a 30% depreciation rate, in line with rapid technological development (confirmed by the results) and a prior finding for electrical products Bernstein and Mamuneas (2006). 3 Firm level data on capital and labour was obtained by summing up plant levels in the LDPM database by firm. Analysis at the firm level avoids the questionable division of R&D capital plant-wise, as well as the comparison of units within the same firm as if they competed.
Due to data shortages, as well as for homogeneity of the sample, the analysis concerns only innovative firms with at least 20 employees. Large firms dominate the industry in terms of sales and R&D. Though small and microfirms are large in number, 89% in 1993 and 86% in 2004, their share of total employees was only 12 and 7%, respectively, and even less of total turnover 6 and 2%, or total wage costs 9 and 5%, respectively, for 1993 and 2003. Their exclusion, therefore, cuts out only about 10% of total economic activity in the industry. In 2003, the true number of firms operating in the industry rose to almost 1,700, and 233 if only firms with over 20 employees are considered. Larger firms cover over 90% of the private R&D carried out in the industry, which in turn represents over half of total corporate R&D in Finland. The exclusion of smaller firms does not confuse the analysis because estimation results showed most results to be (strictly) increasing in size, and consequently, the potential direction of microfirms' impact is rather obvious.
To avoid selectivity bias caused by the exclusion of loss-making and indebted firms when logarithms are taken, Lerner values and debt ratios were adjusted by adding the maximum loss or maximum debt to all observations plus one, as is recommended in the literature. About 3-4% of observations were removed due to negative or missing values when logarithms were taken, extreme annual variation or impossible value-added figures. Due to data secrecy requirements, there was no other basis for the exclusion of outliers other than their extremeness in value. In frontier analysis, such a cause is even more suspect than usual, as it could lead to the removal of frontier firms defeating the purpose of the exercise. Nominal variables were deflated with sectoral producer price indices at the 2 and 3 digit levels (1995 = 100), with the exception of R&D prior to 1995, for which the general earnings level index was used (due to the unavailability of alternatives).
In consequence, panel firms can be assumed to be subject to similar (minimal) regulation, demonstrate similar behaviour, i.e. profit or revenue maximizing, allowing me to apply an output distance function, i.e. an output-oriented efficiency measure. In addition, firms can be assumed to fit into the same functional form of the production function for their relative efficiencies to be comparable. Aghion et al. use patents, i.e. an innovation output measure for innovation. Innovation output can also be approximated by technical change and R&D elasticity. Innovation, however, may refer to the innovation inputs, for which R&D provides more accurate estimates. Innovation input is measured by R&D intensity (R&D Capital/No. of Personnel), which does not vary by the model applied, though it is not constant over time and firm size (Figure 1). In contrast, innovation output measures (implemented innovative activity), which is measured by R&D elasticity and technical change were estimated.

Innovation variables
Various other firm characteristics are listed in Table 2 such as firm size (number of employees, six categories), firm age (four categories) and the firm leverage (debt ratio).  have argued firm leverage to be positively related with innovation to escape the risk of bankruptcy. Also, firm size and age are expected to have a significant impact on innovation, the direction varying by technological regime. The Schumpeterian hypothesis deems firm size to be conducive to R&D, while the so-called Schumpeterian Mark I regime characterizes situation in which technological progress emerges from new technology-based firms through a process of creative destruction (see e.g. Nelson and Winter, 1982). Although most formal R&D is concentrated in large corporations, Acs and Audretsch (1991) argue that small firms account for a disproportionate share of new product innovation, given their low formal R&D expenditures. Audretsch (1995) confirms that the empirical evidence on their role as engines of innovative activity in certain industries is robust, and yet the link between R&D and innovation disappears as the unit of observation is reduced to the firm level, particularly with small firms. Small is typically new, but since it proved impossible to establish an exact age for each firm, firms were merely grouped into four age categories.

Competition variables
The primary competition measure was specified as a firm-specific Lerner index based on firm operating profit divided by the value of gross output (turnover), i.e. profit margin. Operating profit was derived from firm value added minus factor input costs, i.e. expenses including payroll taxes and social security payments incurred by the firm, as well as capital costs as indicated by financing expenses in firm profit and loss statements. The Lerner Index is common to the literature due to its significant advantages in measurement (Aghion & Griffith, 2005, p. 22) and is in accordance with the microeconomic principle that high profit margins equal imperfect competition. For example, domestic market shares are rather irrelevant since the share of international trade in the industry is high. The Lerner index overcomes the difficulties inherent in input and output price measurements, and quality change, since the measure of competition is defined by the profits of firms. Since all firms operate in the same country, general price level and foreign exchange conditions are the same for all firms. In accordance with the microeconomic principle that high profit margins equal imperfect competition, increased competition is expected to reduce profit margins. Rates of returns are indicated similar to  with a firm-specific Lerner index, which is common to the literature due to its significant advantages in measurement (Aghion & Griffith, 2005, p. 22). Here, the Lerner index is based on firm operating profit divided by the value of gross output (turnover), i.e. profit margin, price cost margin or mark-up.
In contrast, domestic market shares, such as the Herfindahl index, are rather deceptive measures of competition when most of it originates from abroad. Moreover, according to survey results by Gilbert (2006), empirical research based on market concentration to proxy competition has not reached definite conclusions on the relationship between market structure and R&D, once industry characteristics, technological opportunities and appropriability were controlled for.
In 1990-1993, the economy plunged into a deep recession. Yet, profitability was rapidly regained in the industry (Figure 2) with radical innovation. Net entry into the industry was high until mid-1990's, falling subsequently to exit levels by the end of the decade. Entry-based competition revived only after 2005. Thereafter, profitability gradually declined and competition intensified. While average competition (1-Log Lerner) has intensified very gradually, competition actually declined for the largest firms as Figure 3 above shows over the sample period. On average, production growth (gy) correlates significantly (0.30) with the Lerner index, showing boom times to raise profitability. In contrast, recessions intensify competition, as one would expect. Low profitability is expected to signal intense competition.
Another determinant of inefficiency related to global competition is foreign ownership. Data on foreign firms is available for 1993-2002, with an emphasis observable for 1997-2002, but since the entire industry is subject to global competition, foreign ownership is of little relevance. Related research has found inward FDI into the industry to have been most likely asset-seeking (see Berghäll, 2015).

Determinants of the technology gap
Technological gaps between leaders and followers are measured by Battese-Coelli (1995) technical inefficiencies following the inverted U-curve-shaped theoretical predictions of the relationship between innovation and competition. Thus, technical inefficiency also estimates innovation impacts.  Technical efficiency results were compared with other reasonable indicators of innovation, such as technical change (implemented innovative activity), R&D intensity, an input measure and R&D elasticity, an innovation output measure.
The analysis concerns only innovative firms. Since the industry is highly R&D intensive, the R&D requirement does not introduce a selectivity bias. It has the beneficial corollary that panel firms can be assumed to be subject to similar (minimal) regulation, demonstrate similar behaviour. In addition, I can assume the firms to fit into the same functional form of the production function for their relative efficiencies to be comparable.

Methodology
The inverted U-curve model does not argue causality. I am, therefore, only interested in correlations of competition and innovation in this context. Technology gaps, in contrast, are estimated with parametric and non-parametric methodologies. Otherwise estimation methods depend on the estimator. Technical change and R&D elasticity are estimated with maximum likelihood. The impact of competition on the technology gap is estimated with true fixed and Battese-Coelli efficiency.

Firm-level estimates
The key insight Farrell (1957) proposed was to extract information from extreme observations of the data to determine the best practice production frontier, rather than having to rely on some hypothetical production possibilities curve. A flexible translog functional form was assumed to approximate the production technology, following Heshmati, Kumbhakar, and Hjalmarsson (1995): where Y it is the output of the i-th firm observed in period t, f(.) represents the production technology, K is the physical capital, L is the non-R&D labour, R is the R&D capital input and θ is a vector of parameters to be estimated. The following flexible translog (transcendental) production function was assumed to approximate production technology: where the β's denote parameter estimates of the production function, i is the company, j and h denote inputs (i.e. logarithms of physical capital (k), non-R&D labour (l) and R&D capital (r)), and t is the time period (i.e. the year concerned). Also, Cobb-Douglas forms of the model were tested and found to apply only for the international data comparison. R&D elasticity, i.e. the percentage change of output divided by the percentage change of R&D, was obtained from the first derivative of the production function with respect to R&D: where E ijt is firm-, input-and time-varying, respectively.
The rate of exogenous technical change was obtained as follows: (1) where TC it is neutral, if β jt = 0 for all inputs j. In other words, technical change merely represents the change in the production function with respect to time.

Data envelopment analysis for technical efficiency measures
Several estimation methods were used to confirm and check results. State-of-the-art true fixed and random effects estimate of technical efficiency proved unreasonable. Instead, for consistency and comparability of results, as well as to abstain from potentially distorting assumptions, non-parametric data envelopment analysis (DEA) was applied to estimate technical efficiency. DEA applies linear programming to compare relative performance when the production process involves multiple inputs and outputs. In contrast to stochastic frontier modelling, there is no need to specify a mathematical form for the production function beforehand, since the method simply seeks the points that maximize output given inputs (output-oriented measure) or minimize inputs given output (inputoriented measure). Hence, DEA efficiency results do not depend on the above formulation of the production function. Several programmes are available to carry out the linear programming problem. Hence, its complexity in terms of the number of inputs and outputs causes no constraint. Most efficient firms receive a score of one, and less efficient a score somewhere below one, but above zero. At the same time, the major drawback of the method is the fact that there is no adjustment for outliers. Yet, it is simple to check visually how the efficiency estimates are distributed and how "unreasonable" outliers are.
The original constant returns DEA methodology was developed by Charnes, Cooper and Rhodes (1978). In 1984, Banker, Charnes and Cooper developed it further into a variable returns to scale (VRS) version. The differences in the input and output-oriented measures reveal whether returns to scale are not constant, decreasing or increasing. When input-based efficiency is smaller than the output-based, returns to scale are decreasing. 4 If returns to scale appear to be increasing, output-based efficiency measures are generally higher, but there is no clear rule on which measure should be selected.
As a robustness check, so-called order-m efficiencies were also estimated. The methodologies are described in more detail, for instance, in Daraio and Simar (2007).

Results
According to the predictions of the model, if the industry is indeed at the frontier, average technical efficiency should be high, competition neck-and-neck and firms located on the upward sloping part of the inverted U-curve. That is, additional competition should increase innovation. Whether this is the case, is inspected by seeking answers to the following questions: Is average technical efficiency high in the industry? Has competition increased technical inefficiency or innovation? Does technical inefficiency or TFP provide a good measure of innovation?

Is average technical efficiency high in the industry?
Parametric efficiency estimates vary greatly by the methodology chosen. Hence, the assumptions underlying them appear to influence results significantly. Therefore, after checking for outliers, results for non-parametric DEA measures are presented (Figure 4). Both input-and output-based DEA measures are high. The input-based measure showed the smallest firms as most efficient, while the output measure showed the largest firms to huddle closest to the frontier. Since their difference suggests increasing returns to scale, and firm size clearly contributes to efficiency, the largest firms appear to be the most efficient, and the output-based measure more reliable.

Has competition increased technical inefficiency on average?
Determinants of inefficiency show competition to contribute significantly to inefficiency in the Battese-Coelli inefficiency model estimated with maximum likelihood. Efficiency is an increasing function of profit margins. In contrast, foreign ownership and exporter status did not prove to be (4)  significant determinants of inefficiency (Table 3). Exposure to global competition does not seem to affect technical efficiency. Moreover, the correlation between competition and technical efficiency was significant and negative: input-based DEA −0.15 and output-based DEA −0.40 (Table 4). Competition increases technical inefficiency, but the relationship is not linear, as Hanusch and Hierl (1992) have suggested. These results run counter to the neoclassical assumption that efficiency increases with competition, but are in line with the inverted U-curve pp. 71-72), i.e. increasing the threat of competition advances innovation in the more efficient firms, but dampens it in inefficient firms. Yet, Figures 5-7 provide a better fit than inverted U-curves.

Table 3. Maximum likelihood estimates on panel data and determinants of Battese-Coelli and DEA technical inefficiency 1 (N = 928; δ = 30% R&D depreciation rates)
Notes: The positive delta, e.g. for debt ratio indicates that the more indebted firms in the sample tend to be less efficient. A negative delta for a dummy variable like size and age imply an opposite relationship with inefficiency. A negative delta for the Lerner Index indicates that the higher the firm's profitability, the lower its inefficiency.

Can inverted U-curves be found between competition and innovation?
Results with respect to innovation are somewhat contradictory. As Table 4 shows, the correlation is contradictory with respect to innovation and competition. While competition is associated with significantly increased R&D intensity (1% level), and R&D elasticity (at the 5% significance level), competition is associated with significantly decelerated technical change (1% level). It may be that product related innovation is conducive to intense competition, but when it comes to process innovation (technical change), competition decelerates it. Yet, as Figures 8-10 below show, an inverted U-curve relationship between innovation and competition could only be found for technical change and competition. For R&D intensity and elasticity, the relationship was more of a U-curve. In all cases, however, the fit was not convincing.

Does technical inefficiency provide a good measure of innovation? The relationship between technical efficiency and technical change
Results do not support technical efficiency as an appropriate measure of innovation. As Table 4 shows, input-based DEA correlates significantly at the 1% level, but negatively with R&D elasticity (−0.14) and technical change (−0.28). Its correlation with R&D intensity is insignificant and almost zero. Hence, input-based DEA technical efficiency is not a proxy to innovation. As for output-based DEA, it correlates positively and significantly at the 1% level with technical change (0.22), and positively and significantly, at the 5% level with R&D intensity (0.08). Its correlations with R&D elasticity is insignificant and almost zero. Hence, output-based DEA may proxy technical change and perhaps R&D intensity, but the correlations are fairly small.
The finding that technical efficiency is not a good measure of innovation questions the external validity of estimations of Bos et al. (2013), which used input-based (cost minimization) technical efficiency to proxy innovation to estimate the presence of an inverted U-curve between competition and technology gaps. Even in this respect, the relationship resembles that of a (non-inverted) U-curve. As Figure 11 shows, competition is minimized at a higher efficiency level. 5 In other words, most efficient firms have indeed escaped competition. Even if technical efficiency could proxy innovation, the relationship between technical efficiency and competition is far from a robust inverted U-curve. An important factor that distinguishes efficiencies is firm size. As Figure 12 shows, the most (output-based DEA) efficient largest and smallest firms enjoy actually the most rapid technical change. This is the result also on average for the sample. The positive relationship is pronounced only for the largest firms with respect to input-based DEA. Even with a quadratic function the relationship is straightforward, more efficiency is good for innovation ( Figure 13).
For R&D elasticity, a vaguely inverted U-curve could be traced only for input-based DEA (Figure 14). There seems to be an efficiency optimum that maximizes innovation below full efficiency. Outputbased DEA shows inefficient firms as typically small. Input-based DEA, however, showed the   smallest firms as most efficient. Profit margins increased with efficiency across the board regardless of firm size, and small firms have been more R&D intensive on average. Thus, contrary to the predictions of the inverted U-curve theory, small firms that have on average been furthest from the frontier have also been most keen to escape competition by means of innovation.
In sum, the predictions of the inverted U-curve theory are controversial in relating innovation and the concept of efficiency. TFP and technical efficiency do not appear to provide adequate proxies of innovation. Output-based DEA may proxy technical change, and perhaps R&D intensity, but the correlations are small though significant. Output-based TFP correlates significantly (at the 1% level) and positively with technical change (0.20), but not with R&D intensity or R&D elasticity. TFP may proxy technical change, but the correlation is rather small.

Does TFP provide a good measure of innovation?
Innovation has also been proxied by the level and growth rate of TFP. For example, Nickell (1996) found evidence in line with the neoclassical postulation that more intense PMC is reflected in more rapid TFP growth. In my sample, in contrast, there is little correlation between TFP and innovation. Output-based TFP correlates positively significantly at the 1% level and with technical change (0.20), but not with R&D intensity or R&D elasticity (Table 4). As Figures 15-18 below show, a slight positive correlation could be detected only for technical change. In conclusion, TFP would not appear to provide a good measure of innovation.

Discussion and conclusions
Average technical efficiency is high in the industry. Competition increases technical inefficiency on average. In these respects, the evidence with respect to the industry being on the technology frontier is clear, but overall, the evidence in support of the inverted U-curve relationship is weak and contradictory. Results are sensitive to the proxies and methodologies applied. In conclusion, I   In addition to Schumpeterian models and the inverted U-curve, the finding that the most profitable firms and plants are also to be the most efficient, combined with the finding that profit margins increased with efficiency across the board regardless of firm size, are in line with so-called RBVs of the firm, in contrast to traditional structure conduct performance or contemporary industrial organization views. Efficient small firms are also profitable, although large firms are generally the most efficient. Hence, the causality may run from efficiency (and innovativeness) to profit margins and firm growth, i.e. there are efficiency rents that firms may be able to transform into long-term competitive advantages that generate abnormal returns. Overall, the industry seems to reflect the Schumpeterian Mark II hypothesis of creative accumulation, rather than creative destruction.
Competitive and innovation conditions can, at least to some extent, be tampered with, by, e.g. generous R&D support to bridge the disincentive gap between private and social returns-hence their appeal. This evidence suggests, however, that tampering with competitive conditions to raise innovation is futile. Innovation within smaller firms is already relatively high in terms of R&D intensity, while technical change is R&D saving and the two correlate negatively.
One should not confuse productivity with efficiency when discussing the beneficial effects of competition. Competition may, e.g. increase productivity, but not necessarily average efficiency. Second, when there are large differences in technical efficiencies that are due to other factors than innovation and competition, such as simple scale efficiencies, technological gaps may provide insufficient guidance on the impact of competition on innovation. Efficiency measures distance from the technology frontier, while it is technological progress that expands the production possibilities frontier through innovation. The most efficient firms are likely to be highly innovative, but for the rest, efficiency change merely measures imitation-based catch-up with frontier firms. Some level of slack may even be necessary in highly innovative industries. Efficiency-raising may be counterproductive to innovation.