Competition, Technological Change and Productivity Gains: A Sectoral Analysis

The empirical relationship between competition intensity and the rate of productivity growth across 30 sectors of the French economy between 1978 and 2015 displays an inverted U-shape. This implies that there exists an optimal level of competition for each sector, defined by the price markup that maximises the growth rate of hourly labour productivity. As there is a significant and strong positive correlation between optimal markups and technical progress rates in each sector, it follows that sectors with high technical progress require higher markups to maximise their labour productivity growth rate. The persistence of non-optimal markups in French sectors is associated with a 0.4% loss in aggregate annual labour productivity growth during the period (1.86%). French long-term productivity growth could have reached 2.25% had markups been at their optimal level. As a result, policies to foster innovation and productivity should aim at enabling the optimal level of markup (or market power), particularly in high-innovation sectors.

Open Access funding provided by ZBW -Leibniz Information Centre for Economics. * The views expressed do not necessarily refl ect those of the institutions with which the authors are affi liated. 1 The markup also refl ects market power, as the ability of a fi rm to set a price above its marginal cost. It represents the difference between prices under imperfect and perfect competition. A higher markup implies lower competition intensity. Conversely, a lower markup implies higher competition intensity.
in competition intensity harms labour productivity growth. These optimal markups are strongly correlated with the sector rate of technical progress and maximise the growth rate of labour productivity in each sector. Sectors with higher rates of technical progress thus have higher optimal markups. Such sectors necessitate suffi ciently high markups to maximise their labour productivity growth. A long-term disconnect between actual and optimal sector markups would be detrimental to aggregate labour productivity growth. Some sectors, such as digital sectors, are more conducive to technical progress than others and require higher investment and hence a higher markup to maximise their labour productivity growth.

Estimation strategy
The estimation strategy to demonstrate that the empirical relationship between competition (markups) and the rate of labour productivity growth is specifi c to each sector and can be represented by an inverted U-shaped curve is as follows: fi rst, actual sector markups are estimated following the methodology of Roeger (1995). Second, a nonparametric identifi cation of the relationship between markups and labour productivity growth rates provides evidence of an inverted U-shape when sectors are grouped according to their rate of technical progress. Third, we estimate an econometric model showing that the inverted U relationship between competition and productivity growth is signifi cant. 2 This allows the calcula-

Figure 1 Hourly labour productivity growth and markups by sector
Source: Authors' own elaboration.
tion of the markup that maximises the inverted U curve for each sector (the optimal markups). Fourth, a strong positive and signifi cant correlation between the optimal markups and the technical progress rates in each sector is evidenced based on our own computation of the average level of Hicks-neutral technical progress for each sector. 3 This result suggests that a sector with a higher technical progress rate requires a higher optimal markup to maximise its own rate of labour productivity growth. Finally, the correlation between technical progress and optimal markups is used to estimate the losses in productivity growth due to unsuitable markups in each sector during the whole period.
A nonparametric identifi cation of the markup and labour productivity growth rate relationship As a fi rst approach, the relationship between competition and productivity growth can be represented by a scatter plot of the sector markups and the compound annual growth rate of hourly labour productivity during the seven periods running from 1978 to 2015 ( Figure 1). The scatter plot shows 210 points (30 sectors observed during the seven periods), and each point on the fi gure represents a sector observed during each of the seven specifi c periods.
At fi rst glance, the scatter plot does not provide any obvious or robust result regarding the link between competition and productivity growth. However, by grouping sectors according to their level of technical progress, it appears that an inverted U-shaped relationship actually characterises the effect of markups on the rate of hourly labour productivity growth ( Figure 2). This graph suggests that the relationship between competition intensity and labour productivity growth may vary across sectors subject to their specifi c rate of technical progress. Hence, markups over marginal costs or perfect competition prices could be related to sector-specifi c characteristics, meaning that higher markups do not necessarily imply the existence of static monopoly rents. by markup x i and annual productivity growth y i , denoted (x i , y i ), is shifted to point (X i , Y j ) following: Relationship between hourly labour productivity growth and markup according to the level of technical progress Note: 'High technical progress' set groups together sectors with a technical progress rate higher than 2.5%; 'Medium-high technical progress' set groups sectors with a rate between 2.5% and 1.86%; the 'Medium-low technical progress' set groups sectors with a rate between 1.86% and 1.5%; and the 'Low technical progress' set groups sectors with a rate lower than 1.5%.
cal progress' set. 5 The smoothing of the moving averages reduces the volatility of the observations and reveals the trends of the effects of markups on productivity growth. Each smoothed moving average exhibits an inverted Ushape with a peak corresponding to a higher markup for higher technical progress. Indeed, the peak of the 'Low technical progress' set is reached for a markup close to 1.10; the peak of the 'Medium-low technical progress' set is reached for a markup close to 1.15; the peak of the 'Medium-high technical progress' set is reached for a markup close to 1.24; and the peak of the 'High technical progress' set is reached for a markup close to 1.34. This result suggests that an increase in the rate of technical progress in turn increases the markup level that maximises the hourly productivity growth of the sector.

Estimation of optimal sector markups
The optimal levels of markup in each of the 30 sectors are obtained by estimating an econometric model based on a quadratic function. This specifi cation allows for the estimation of the effect of variations in the markups on the rate of labour productivity growth for each sector. A dum-my variable is associated with the squared markup term, which allows the estimated coeffi cient to vary across sectors. The following Equation (1) (1) is estimated where i {1, 2, ..., 30} is the index of the sector, p {1, 2, ..., 7} is the index of the period, CAGRprod ip is the compound annual growth rate of production at current prices of sector i, markup ip is the estimated markup for sector i and intbub is a dummy variable that captures the impact of the Internet bubble, which might have affected the information technology sectors during the fi fth period (2000)(2001)(2002)(2003)(2004). During the fi fth period, intbub = 1 (intbub = 0 otherwise) for each sector in the information technology category, which includes 'Computer, electronic and optical products', 'Publishing, audio-visual and broadcasting activities', and 'Telecommunications; IT and other information services'. In this equation, the individual (sector) fi xed effects have been removed to avoid interactions with the dummy indicator. The term d i represents the dummy indicator of sector i, d p is a period fi xed effect, β is the coeffi cient of the markup that is common to all sectors, α i is the coeffi cient of the squared markup specifi c to sector i, c is a constant and ε ip is the residual. The optimal markup for sector i is then determined by the following term: As a result, the corresponding maximum level of hourly productivity growth is defi ned by The results of the estimation are presented in Table 1. The fi rst column provides the explanatory variables; the second column provides the estimated coeffi cients of Equation (1) with detailed sector-specifi c squared markups; the third column provides the associated standard error; the fourth column provides the optimal markup for each sector, calculated on the basis of the estimated markup coeffi cients; the fi fth column provides the associated standard error; the sixth column provides the annual average growth rate of maximised labour productivity; and the last column provides the associated standard error.  Technical Progress all highly signifi cant. As a result, the estimates confi rm a nonlinear, inverted U-shaped relationship between competition and labour productivity, which captures the actual rate at which technical progress is adopted in the economy.
The optimal markup is strongly correlated with the rate of technical progress Figure 3 represents the correlation between the optimal markup and the average rate of technical progress (denoted θg) for each sector.
The line indicates the linear fi t of the scatter plot. The correlation coeffi cient between the sector-specifi c optimal markup and the rates of technical progress is 0.67, which is above the 1% signifi cance threshold (0.416), for the 30 observations. The correlation between average markups and the technical progress rate is positive but weakly signifi cant. In other words, average markups are weakly correlated with technical progress, while the optimal markups that we calculated are strongly correlated with technical progress. Such a strong correlation suggests that sectors experiencing higher rates of technical progress require higher optimal markups to maximise their productivity growth rate.
Indeed, labour productivity growth refl ects improvements in production techniques, which require investment.
Markups have two contrary effects on investment. On the one hand, they tend to reduce investment, in line with the 'escape competition' effect. On the other hand, they tend to increase investment, in line with the Schumpeterian effect. The markup that maximises investment refl ects an underlying trade-off between those two effects in each sector. As the productivity impact of technical progress occurs through investment, a higher rate of technical progress strengthens the Schumpeterian effect more than the 'escape competition' effect. As a result, the trade-off in a sector with a higher rate of technical progress tends to shift towards higher markups (Jeanjean, 2020).

Labour productivity losses due to unsuitable markups
In the previous section, we calculated the optimal markup for each sector. This means that when the markup is above or below this level, productivity growth is not reaching its maximum level. The gap between observed productivity growth and maximum productivity growth can be considered a productivity loss. To estimate the productivity losses for each sector in each period, it is necessary to compute, on the one hand, the difference in each period and for each sector between the actual markup and the optimal markup: On the other hand, it is necessary to compute the difference between the hourly labour productivity growth rate and the maximum labour productivity growth rate, which is simply the difference between the hourly labour productivity growth and the rate of productivity growth that is achieved when markups coincide with their optimal levels in each sector: If markupmax i is the optimal markup, one can expect that the fi rst difference CAGRprod ip is increasing when markup ip < 0 and decreasing when markup ip > 0. Hence, an increase in the variation rate of markups leads to a decrease in the variation rate of labour productivity. Figure 4 presents the variations in hourly labour productivity growth as a function of the markup over perfectly competitive prices.
The scatter plot points to the impact of the difference between the actual sector markups and the optimal markups on the growth rate of labour productivity. The origin point of the graph represents the estimated optimal markup and the corresponding hourly productivity growth for each sector. An upward or downward deviation from this optimal markup results in a decrease in the rate of hourly labour productivity growth. Equation (2) allows for an estimation of the losses in productivity growth caused by unsuitable markups.
The Internet bubble may have increased productivity growth in the information technology sector during the fi fth period (2000)(2001)(2002)(2003)(2004) independently of the markup levels. This effect can be corrected with the dummy variable Figure 3 Correlation between optimal markups and total productivity growth by sector Source: Authors' own elaboration. intbub, introduced in Equation (1). The term markup ip may be either positive or negative depending on the period. The absolute value of the difference between the actual and the optimal level of markup in each sector allows to analsye the impact of the distance from these sector-specifi c optimal markups on the growth rate of labour productivity, irrespective of the sign of the difference. The equation is estimated for fi rst differences of the dependent variable, i.e. the hourly labour productivity growth rate.
The results are presented in Table 2, which provides ordinary least squares estimates of Equation (2). Specifi cation (1) does not include the dummy variable that captures the effect of the Internet bubble, whereas specifi cations (2) and (3) include it. The coeffi cient of | markup |, as expected, is negative and signifi cant in all specifi cations, which confi rms that hourly labour productivity growth decreases as soon as markups deviate from their estimated optimal levels. The loss of productivity growth is estimated on average at 0.373% for a deviation of 0.1 points from the optimal markup. In specifi cations (2) and (3), the Internet bubble dummy has a positive and signifi cant coeffi cient. In summary, there exists a markup that maximises the growth rate of hourly labour productivity growth for each sector. Hence, a difference between the actual level of markups and the optimal markups in a given sector induces a divergence between the observed productivity growth rate and the maximum productivity growth rate. Figure 3 suggests that the rate of technical progress determines the potential productivity growth that could be achieved by an optimal markup, and Figure 4 shows that a deviation from this optimal markup prevents the realisation of full productivity growth.

Average annual productivity losses for each sector
Differences between actual and optimal levels of markups entail losses in labour productivity growth. It is possible to estimate the average annual labour productivity growth that is lost due to unsuitable markup levels in each sector between 1978 and 2015. First, it is necessary to compute the mean of the differences between observed markups and optimal markups. However, as these differences may be positive in some periods and negative in others, it is necessary to compute the fi rst differences in absolute values: Second, we calculate the mean of the differences between observed productivity growth and maximum productivity growth: p=1 CAGRprod ip / 7 . Figure 5 presents the productivity losses due to unsuitable markups. This graph shows that hourly labour productivity growth decreases when the markups deviate from their optimal levels. The correlation between the average distance from the optimal markup and the loss of productivity growth is highly signifi cant. The coeffi cient of determination is R 2 = 0.86. The impact of the productivity loss on the global economy can be estimated by weighting each sector by its share of the global economy.

Technical Progress
Empirical results on productivity losses due to unsuitable markups The relationship between markups and the rate of labour productivity growth across 30 sectors of the French economy over the period 1978-2015 has an inverted U-shaped form, which implies that there is an optimal markup for each sector. These markups depend on the sector-specifi c rate of technical progress: sectors with higher rates of technical progress require higher markups to maximise their labour productivity growth. A markup that differs from its optimal level tends to reduce the growth rate of labour productivity.
The average annual loss of productivity growth due to unsuitable markups in the French economy over the period 1978-2015 is estimated at 0.4% (with an average difference of 0.152 from the optimal markup). As the average annual growth rate of French labour productivity was 1.86% over the period, such growth could have reached 2.25% had markups been at their optimal levels.
A direct policy implication is that sectors with strong technical progress should be allowed to adjust their competition intensity to their rate of technical progress. Otherwise, they could be prevented from achieving the full productivity gains derived from the adoption of technologies. In particular, digital sectors, which have high productivity growth rates (i.e. high technical progress), require suffi ciently high markups (market power) to maximise their labour productivity growth.

Public policy to enhance innovation and productivity
Public debate on competition policy is currently addressing concerns about how competition policies should adapt to the digital transformation of the economy, driven by the development of algorithms and data in all industries. Our research advocates that the assessment of competition intensity should take into account the technological progress measured in each sector. In digital sectors, specifi cally, the rate of innovation is high, and the trend of productivity growth is essentially driven by investment in technologies (dynamic effi ciency) rather than price competition, which hinders markups above perfectly competitive prices (static effi ciency; Jeanjean, 2015;Houngbonon and Jeanjean, 2016). In such sectors, higher prices do not necessarily refl ect higher monopoly rents, and higher markups may refl ect the expected return on risky investment in innovation (Ciriani and Lebourges, 2016).
Competition policies that aim at lowering prices to marginal costs (i.e. eliminating market power) could shift competition intensity beyond its optimal level and thus impede the expected profi t margins necessary to sustain current and future investments in innovation. In sectors with a high innovation rate, investments in technologies may be curtailed due to markups below the optimal level. Moreover, reduced investment in technologies in these sectors should also have a negative impact on other sectors.