Does recession drive convergence in firms' productivity?

Does recession drive convergence in firms’ productivity? Evidence from Spanish manufacturing firms Álvaro Escribano & Rodolfo Stucchi

Journal of Productivity Analysis ISSN 0895-562X Volume 41 Number 3 J Prod Anal (2014) 41:339-349 DOI 10.1007/s11123-013-0368-5

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Author's personal copy J Prod Anal (2014) 41:339–349 DOI 10.1007/s11123-013-0368-5

Does recession drive convergence in firms’ productivity? Evidence from Spanish manufacturing firms ´ lvaro Escribano • Rodolfo Stucchi A

Published online: 22 October 2013 Springer Science+Business Media New York 2013

Abstract This paper provides evidence on the effect of recessions and expansions on the productivity growth rate of productivity leaders and followers. We use data of a representative sample of the Spanish manufacturing sector for the period 1991 and 2005. These data allow us to estimate firm level productivity for a relatively long period of time and provide us with firm level perception of the business cycle. We find that productivity tends to converge in recessions because, in these periods, the productivity growth of followers is higher than the productivity growth of leaders. This fact is consistent with theoretical models of managerial incentives and competition. A recession can be seen as an exogenous increase in competition that reduces demand and poses a threat of liquidation. This threat is higher for followers and is high enough to create asymmetric incentives to become more productive. We test the robustness of our results to sample selection and different productivity measure. Keywords Productivity Business cycle Competition Convergence Recessions Spain

The views expressed in this paper are those of the authors and do not necessarily represent those of the Inter-American Development Bank, its Executive Directory or the countries they represent. ´ . Escribano A Department of Economics, Universidad Carlos III de Madrid, C/Madrid, 126, 28903 Getafe, Madrid, Spain e-mail: [email protected] R. Stucchi (&) Office of Strategic Planning and Development Effectiveness, Inter-American Development Bank, Av. Pedro de Valdivia 0193, Providencia, Santiago, Chile e-mail: [email protected]

JEL Classification M20

D22 D24 E32 L25 L60

1 Introduction The high heterogeneity in firms’ productivity even within narrowly defined industries is one of the most documented facts about firms’ productivity. It is also well known that this heterogeneity is highly persistent (Baily et al. 1992; Bartelsman and Dhrymes 1998; Bartelsman and Doms 2000; Syverson 2011). However, as many averages do, these facts hide interesting patterns about the evolution of firms’ productivity. The simple observation of any industry suggests several possibilities about the evolution of firms’ productivity. In fact, some firms become more productive than others, some firms far from the frontier become more productive and catch up with the firms at the frontier, and some highly productive firms become even more productive and diverge from the rest of firms. Some of these facts have been studied in the literature. The catch up in productivity, for example, has been studied by Oulton (1998), Fung (2005), Girma and Kneller (2005), Chevalier et al. (2009), and Iacovone and Crespi (2010). Figure 1 shows the distribution of Spanish manufacturing firms’ total factor productivity1 in 1991, 1996, 2000, and 2005. This Figure shows three interesting facts. First, the distribution moved to the right as the productivity improved over time. Second, the productivity growth rate dropped after 1995. While the largest shift in the distribution took place between 1991 and 1996, the distribution in 2000 was almost identical to the distribution in 1996. 1 See Sect. 2 for a detailed definition of firms’ total factor productivity.

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Fig. 1 Evolution of the total factor productivity distribution. Notes: In this figure total factor productivity is measured as the difference between each firm’s total factor productivity (in logs) defined in Sect. 2 and the average level of the industry (2-digit industries)

Finally, the shift from 1991 to 1996 was larger in the lower tail of the productivity distribution; this could be showing that the productivity growth rate of firms with productivity levels below the average of each industry was higher than the productivity growth rate of firms with productivity above the industry average. This shift was even more evident for large firms. The variance of productivity within industries dropped 67 % between 1991 and 1995 and after this period there was no additional reduction in the dispersion of firms’ productivity. The fall in productivity growth after 1995 affects the growth rate of the economy and therefore many researchers studied the productivity of Spanish firms from different angles. For example, Huergo and Jaumandreu (2004) and Doraszelski and Jaumandreu (2013) focused on innovation, Ornaghi (2006) studied the diffusion of technology, Delgado et al. (2002) compared the level and growth of productivity between exporters and non-exporters, Farinãs and Ruano (2005) and Lopez-Garcıá et al. (2007) studied dynamics of firms’ productivity focusing on entry and exit, and Dolado et al. (2012) focused on the relationship between temporary workers and productivity. Instead of focusing on the fall of the productivity growth rate, in this paper we focus on the third fact; i.e. we pay special attention to the asymmetric shift in the productivity distribution between 1991 and 1995. One important characteristic of this period is the recession that occurred in 1992 and 1993 (Ferraz and Ortega 2006). The economy showed negative growth rates in the last quarter of 1992 and the first two quarters of 1993. More than half of the manufacturing firms reported that their markets were in recession during those years. The average annual growth rate of the Spanish GDP in the first half of the 1990s was less than one third of the growth rate of the second half and less than one half of growth rate of the early 2000s. We aim at understanding whether the asymmetric shift and convergence in productivity was associated to the business

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cycle. To do this, we evaluate the effect of recessions and expansions on the productivity growth of firms with different levels of productivity and test whether less productive firms tend to catch up with more productive firms during recessions. There are theoretical reasons why it is possible to observe convergence in productivity during a recession. Schmidt (1997) presented a model in which competition affects managerial effort. In addition, he claims that recessions can be interpreted as an increase in the degree of competition; lower and more price elastic demand together with overcapacities lead to more intense competition. Therefore the threat of liquidation in a recession gives managers direct incentives to work harder for a cost reduction. Furthermore, the disutility of liquidation for managers and workers increases in recessions, reinforcing the threat of liquidation effect. Therefore, it is possible to observe reorganization programs implemented more frequently during recessions. Although the same cost-reduction programs could be feasible in booms, they are more costly. Then, if the threat of liquidation is more credible for less productive firms one should expect convergence in productivity during recessions. There are several papers that focused on the relationship between the incentives created by an increase in competition and productivity. Schmitz (2005) showed how, after an important increase in competition, iron ore producers more than doubled their productivity. Similarly, Bloom and Van Reenen (2007) found that managerial practices are strongly associated with firm level productivity and that poor management practices are more prevalent when product market competition is weak. Finally, Oulton (1998) and Syverson (2004) also found that competition reduces the dispersion in firms’ productivity. We use firm level data obtained from the ‘‘Survey on Business Strategies’’ (Encuesta sobre Estrategias Empresariales, ESEE). This survey has three main advantages for our

Author's personal copy J Prod Anal (2014) 41:339–349

study. First, it provides us with a representative sample of the Spanish manufacturing sector for a long period; it covers the period 1991–2005. Second, firms annually report whether their markets are in recession or expansion and the resulting timing of the business cycle based on firms’ perceptions is consistent with the timing of the business cycles defined in terms of the GDP growth rate. Finally, firms are asked about the price variation in their main five output markets. With this information we constructed a Paasche firm level price index that allows us to obtain physical total factor productivity (Foster et al. 2008). We find that the recession in the early 1990s drove the convergence in firms’ productivity. Our results show that followers have higher productivity growth during recessions and therefore they tend to catch up with leaders in those periods. The exit of less productive firms could also imply a reduction in the variance of firms’ productivity. Given that the exit of less productive firms is also higher during recessions, it could also explain the reduction in the variance in the early 1990s. However, our findings are robust to sample selection. In fact, we also find that followers tend to catch up with leaders in recessions if we consider firms in the balanced panel or if we control for sample selection using the Heckman’s (1979) two step procedure. This finding is important for the interpretation of the results: the threat-ofliquidation during a recession, that is higher for followers, creates asymmetric incentives to become more productive. We also tested the consistency of our results to a different productivity measure and other identification strategy. Our paper contributes to the literature that studies the heterogeneity of firms’ productivity and its evolution (Oulton 1998; Bartelsman and Dhrymes 1998; Fung 2005; Syverson 2004; Girma and Kneller 2005; Chevalier et al. 2009; Iacovone and Crespi 2010), the literature that studies the cyclical patterns of productivity (Basu 1996; Basu and Fernald 2001; Baily et al. 2001), and the literature that studies the incentives created by an increase in competition and productivity (Syverson 2004; Schmitz 2005; Bloom and Van Reenen 2007). The rest of the paper is organized as follows. Section 2 describes the dataset and presents some descriptive statistics. Section 3 studies the effect of recessions and expansions on the productivity growth of productivity followers and leaders. Section 4 provides three robustness checks. Finally, Sect. 5 concludes. 2 Data and descriptive statistics 2.1 Data We use firm level data from the ‘‘Survey on Business Strategies’’ (Encuesta sobre Estrategias Empresariales,

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ESEE) which is an annual survey based on a representative sample of the Spanish manufacturing sector conducted by SEPI Foundation. In this survey, firms with more than 200 employees in the first year (1990) were asked to participate. The rate of participation reached approximately 70 % of the population of firms within that size category. Firms that employed between 10 and 200 employees were sampled randomly by industry and size strata. The sample covered 5 % of the population. Another important feature of the survey is that after 1990 the properties of the initial sample have been maintained. Newly created firms have been added annually with the same sampling criteria as in the base year. There are exits from the sample coming from shutdown and no reporting. Therefore, due to this entry and exit process, the dataset is an unbalanced panel of firms. Even though when the first year of the survey is 1990, we use the information from 1991 to 2005 because the data corresponding to 1990 is not perfectly comparable with that of subsequent years. We follow five rules to select the sample for our empirical analysis. First, we exclude those firms that declared that they moved from one industry to another. Second, we exclude observations with negative value added or negative intermediate consumption. Third, we exclude observations with ratios of labor cost to sales or material cost to sales larger than one. Fourth, we exclude the observations for which the firm reports an incomplete year—i.e., the firm reports that was active for less than 1 year—in a year different than the one in which the firm leaves the market. Finally, we exclude the observations of those firms that do not report all the information needed to compute productivity or if the firm only provides information for 1 year. An important advantage of our dataset is that it is possible to construct firm level price indices for output and materials (Doraszelski and Jaumandreu 2013). Firms are asked about the price changes they did during the year in up to 5 separate markets in which they operate. The price index for output is computed as a Paasche-type index of the responses and normalized by the average value for each firm. Firms are also asked about the changes during the year for raw materials and therefore the same type of index is computed for materials. Although these firm level price indices capture the price variation for each firm, they do not capture price differences across firms. We compute total factor productivity (TFP) using the Solow’s residual extended to control for the degree of capacity utilization. The correction for variable capacity utilization is important in our analysis because it changes over the business cycle. In particular, the log of firm i’s TFP in period t (tfpit) is defined as, tfpit ¼ yit al lit am mit ak ðkit þ jit Þ

ð1Þ

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Table 1 Descriptive statistics 1991–1995 Mean

1996–2000

SD

CV

Mean

2001–2005

SD

CV

Mean

SD

CV

Small (less than 50 employees but more than 10) TFP (in logs)

3.54

0.56

TFP (annual growth rate, in percentage)

1.86

22.20

0.158 11.90

3.62

0.57

1.45

16.79

0.157 11.56

3.69

0.55

1.56

17.25

0.149 11.03

Medium (less than 200 employees but more than 50) TFP (in logs)

3.65

0.53

0.145

3.69

0.53

0.144

3.73

0.51

0.137

TFP (annual growth rate, in percentage)

2.99

16.52

5.53

1.57

13.13

8.35

1.43

12.41

8.66

3.55

0.55

0.155

3.67

0.54

0.147

3.69

0.53

0.143

2.34

14.73

6.29

1.45

8.94

6.15

1.16

11.04

9.54

Large (more than 200 employees) TFP (in logs) TFP (annual growth rate, in percentage)

Firms for which it is possible to compute TFP for at least two consecutive years

where y is the log of output, l, m, and k are the log of labor, materials, and capital, j is the log of the annual average capacity utilization rate reported by each firm, and ax (x = {l, m, k}) are input–output elasticities. We measure input–output elasticities using industry average cost shares over the sample period.2 Output is measured by the value of goods and services produced during the year deflated using the firm price index of output. Labor is measured in hours, capital as the firm’s value of the capital stock deflated using the price index of investment in equipment goods, and materials as the value of intermediate consumption deflated using the firm price index of materials. Having firm level price indexes is an important advantage over traditional TFP measures that deflate nominal variables with industry level price indexes. In this sense, our productivity measure is close to the ‘‘physical productivity’’ defined in Foster et al. (2008). This productivity measure rests on the assumption of constant returns to scale. We are confident of this assumption because several papers tested this assumption for the same dataset and did not find evidence against it (see, for example, Doraszelski and Jaumandreu 2013). 2.2 Descriptive statistics Table 1 highlights some interesting facts about TFP and its growth rate. First, there is large heterogeneity in the level of TFP. The heterogeneity in terms of growth rates is even larger; the coefficient of variation of the growth rates is ten times larger than the coefficient of variation of the level. Second, small firms have on average the lowest 2

Alternatively, the input–output elasticities can be obtained by estimating the production function (see Olley and Pakes 1996; Levinsohn and Petrin 2003; Doraszelski and Jaumandreu 2013). The main advantage of the Solow’s residual is simplicity and the fact that it is not necessary to assume perfect competition in the output market.

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productivity growth rates. Third, after 1995 there is a stable reduction in the productivity growth rate of every size group but the small firms; these firms showed an average growth rate in 2001–2005 larger than in 1996–2000. Table 2 tests for convergence in firms’ productivity. The convergence literature provides us with two convergence tests: b and r-convergence (Barro and Sala-i-Martin 1992). b-convergence tests for a negative correlation between the average productivity growth rate and the initial level of productivity. The implied speed of convergence in the period 1991–1995 is considerably higher than the speed of convergence in the periods 1996–2000 and 2001–2005. The main drawback of b-convergence is that it is a necessary but not sufficient condition for a reduction in the variance. r-convergence, on the other hand, directly tests for a reduction in the variance of firms’ productivity. To test for a reduction in the variance we use the T2 and T3 statistics developed by Caree and Klomp (1997).3 The null hypothesis of no convergence is H0: var(tfp0)/var(tfpT) = 1 and the alternative hypothesis of convergence is H1: var(tfp0)/ var(tfpT) [ 1. When the estimated var(tfp0)/var(tfpT) is lower than one we test for r-divergence. The alternative hypothesis in this case is H1: var(tfp0)/var(tfpT) \ 1. We test for r-convergence in productivity deviations with respect to the industry average instead of considering each industry 3

Given that productivity in period T depends on productivity in period 0, and therefore variance in T depends on variance in 0, the ratio of variances does not converge to an F-distribution and therefore we cannot apply the standard test to compare variances. To control for this dependence, Caree and Klomp (1997) proposed two statistics: pffiffiffi 2 2 ðr^2 r^2 Þ2 N ðr^0 =r^T 1Þ pffiffiffiffiffiffiffiffi T2 ¼ ðN 2:5Þ log 1 þ 0:25 2 0 2 T 2 and T3 ¼ 2 r^0 r^T r^0T

2 1p^

where r^20 , r^2T and r^0T are the sample variance of tfp0 and tfpT and the sample covariance between tfp0 and tfpT, respectively. Finally, p^ is the estimate of the autoregressive coefficient of tfpT on tfp0. The assumption behind these statistics is that firms’ productivity follows a first order autoregressive process. Under the null hypothesis of no d

d

convergence, T2 ! v2 ð1Þ and T3 ! Nð0; 1Þ.


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Table 2 Convergence tests

Fit ¼ 1½In period t firm i is in Q1jt ; Q2jt ; Q3jt ; or Q4jt

1991–1995

1996–2000

2001–2005

b

-0.143***

-0.116***

-0.092***

R2

0.55

0.32

0.18

No. of Obs

459

645

838 0.77

b-Convergence

r-Convergence (within industry) var(tfp0)/var(tfpT)

1.67

0.94

T2

70.00***

1.08

20.12***

T3

10.32***

-1.01

-4.18***

(1) Firms for which is possible to compute TFP for at least five consecutive years. (2) b-convergence: The estimating equation is Dtfpi = a ? b tfpi,0 ? a0 xi,0 ? ui where Dtfpi is the growth rate of firm i’s productivity between periods 0 and T and x includes industry and size dummies, age, age squared, foreign capital, human capital, and dummies for incorporated company, entry, merger, and demerger; all these variables evaluated at the initial year (0) of each sub-period. Inference was done using heteroskedasticity robust standard errors. (3) r-convergence: To analyze productivity within industries we consider the difference between productivity and the average productivity of each industry for each period. When the variance of productivity in period T is lower (higher) than the variance of productivity in period 0, we test the null hypothesis of equality of variance against the alternative hypothesis of r-convergence (r-divergence). (4) Significance levels: * = 10 %; ** = 5 %; *** = 1 %

separately because the number of observations in each industry might not be sufficiently large. The ratio of variances confirms the reduction in variance showed in Fig. 1 between 1991 and 1995. The reduction was quantitatively large; the ratio of variances is 1.67—i.e. the variance in 1991 was 67 % larger than the variance in 1995—and statistically significant. During the period 1996–2000 there was no convergence or divergence. Finally, from 2001 to 2005 the variance of productivity within each industry increased. However, the increase was considerably lower than the reduction in the variance between 1991 and 1995.

3 Productivity leaders and followers during business cycle Let Qsjt (s = 1, 2, …, 5) be the quintile s of the productivity distribution of firms in industry j in period t. We define two dummy variables, Lit and Fit, that take value 1 when firm i in period t is a productivity leader or a productivity follower, respectively, and take value zero otherwise. We classify as followers those firms in quintiles 1, 2, 3 and 4 of the productivity distribution of their industry and as leaders those firms in the fifth quintile. That is, if firm i belongs to industry j then it will be a follower or a leader in period t according with the following definitions:

Lit ¼ 1½In period t firm i is in Q5jt

ð2Þ

where 1½ is an indicator function. An important feature of our dataset is that firms provide information about the dynamism of the market in which they work.4 In fact, they need to report if they are working in recessive, stable, or expansive markets. This information provides us with firm level perception of the business cycle. Given that the perception could be affected by the productivity of the firm and therefore it could be endogenous in a productivity equation, we aggregate firms’ perception at the industry level. In particular, we define Rjt and Ejt as the proportion of firms in industry j and period t that report that their markets are in recession and expansion, respectively. These variables are exogenous to each firm because the contribution of each firm to this average is small and equal for every firm in the industry.5 These variables are highly correlated with the growth rate of the Spanish GDP; in 1992 and 1993 more than 50 % of the firms reported that they markets were in recession. There is no other year with such a large number of firms reporting recession. An advantage of the proportion of firms in recession and expansion is that these variables vary across time and industries and therefore they provide us with important cross-section information to identify the effect of the business cycle. The relationship between convergence and the business cycle can be analyzed using the following regression model: Dtfpit ¼ aF Fi;t1 þ aL Li;t1 þ aR Rjt þ aE Ejt þ aFR Fi;t1 Rjt þ aLR Li;t1 Rjt þ aFE Fi;t1 Ejt þ aLE Li;t1 Ejt þ ax xi;t1 þ az zit þ uit ;

ð3Þ

where D tfpit is the growth rate of productivity, and xi,t-1 is a set of control variables that includes a dummy variable for incorporated companies, the proportion of foreign capital, human capital (the proportion of engineers and workers with a college degree), and a dummy variable for process innovation. Using lagged variables helps to avoid inconsistency problems caused by possible endogenous variables. Vector zit includes a set of exogenous variables like size, year, and industry dummies, and age and its square. It also includes dummies for firms involved in a merger or demerger process and for entrants and exiting firms. The coefficients aFR and aLR measure the effect of recessions on the growth rate of productivity of followers and leaders, respectively. The coefficients aFE and aLE 4

Given that each firm can serve more than one market, ESEE provides a weighted index of the dynamism of the markets as reported by the firm for the markets in which it operates. 5 The contribution of each firm to the average of a dummy variable is equal to the inverse of the number of firms in each industry.

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Table 3 The effect of recessions and expansions on productivity followers and leaders

Dependent variable: D tfp Follower t - 1 Follower t - 1 9 recession Follower t - 1 9 expansion

[1]

[2]

0.00724

0.105***

[0.0191]

[0.0236]

0.294***

0.226***

[0.0420]

[0.0496]

0.119***

0.0739

[0.0438]

[0.0532]

Q1 in t - 1 Q2 in t - 1 Q3 in t - 1

(1) Dependent variable is D tfpit. (2) All regressions include age, age squared, dummy variables for year, industry, size, incorporated companies, entry, exit, mergers, and demergers. They also include the proportion of foreign capital, the proportion of skilled workers, and a dummy for process innovation; all these variables lagged one period. (3) Followers are those firms in quintiles 1, 2, 3, and 4 of the productivity distribution. (4) Heteroskedasticity robust standard errors. (5) Significance levels: * = 10 %; ** = 5 %; *** = 1 %

[4]

0.0568**

0.263***

[0.0230]

[0.0296]

0.0150

0.167***

[0.0211]

[0.0256]

0.00155

0.0959***

[0.0208]

[0.0248]

Q4 in t - 1

-0.00840

0.0636***

[0.0208]

[0.0239]

Q1 in t - 1 9 recession

0.359*** [0.0499]

0.200*** [0.0608]


0.306***

0.204***

[0.0464]

[0.0552]


0.250***

0.222***

[0.0451]

[0.0519]


0.221***

0.186***

[0.0455]

[0.0514]

Q1 in t - 1 9 expansion

0.146***

0.0382

[0.0527]

[0.0661]

Q2 in t - 1 9 expansion

0.122**

0.0589

[0.0481]

[0.0568]

0.102**

0.0824

[0.0473]

[0.0547]

0.0832*

0.0453

[0.0472]

[0.0533]

Q3 in t - 1 9 expansion Q4 in t - 1 9 expansion Recession

-0.274*** [0.0447]

-0.228*** [0.0517]

-0.264*** [0.0446]

-0.214*** [0.0508]

Expansion

-0.103**

-0.0670

-0.102**

-0.0660

[0.0448]

[0.0528]

[0.0450]

[0.0522]

Firm level fixed effects

No

Yes

No

Yes

R2

0.07

0.11

0.12

0.21

Number of observations

15,837

15,837

15,837

15,837

Number of firms

2,395

2,395

2,395

2,395

measure the corresponding effect of expansions. Given that Li,t-1 = 1 - Fi,t-1, this expression can be rewritten in a more convenient way that allows us to directly test for catching up in recessions and expansions, i.e., Dtfpit ¼ aL þ ðaF aL ÞFi;t1 þ ðaR þ aLR Þ Rjt þ ðaE aLE Þ Ejt þ ðaFR aLR ÞFi;t1 Rjt þ ðaFE aLE ÞFi;t1 Ejt þ ax xi;t1 þ az zit þ uit : ð4Þ The differential effect of recessions and expansions on the productivity growth rate of leaders and followers can be

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[3]

analyzed directly by the sign of the coefficients (aFR - aLR) and (aFE - aLE). If (aFR - aLR) is larger than zero, followers catch up with leaders in recessions. On the other hand, if (aFE - aLE) is lower than zero, followers fall behind leaders in booms. Table 3 presents the results of estimating Eq. (3). Columns [1] and [2] show the OLS and fixed-effect estimates of Eq. (4). The fixed-effect estimate allows for more persistence in productivity differences. The coefficient of the follower dummy variable is positive and statistically


significant in the fixed-effect estimation. This reflects some degree of mean reversion. The coefficient of the interaction term between the followers dummy and the proportion of firms in recession is positive. This finding shows that the difference in the growth rate of productivity between followers and leaders is positive in recession and therefore followers tend to catch up with leaders during recessions. It is important to mention that this is true even after capturing mean reversion. The coefficient of the interaction term between the follower dummy and the proportion of firms in expansion is statistically non-significant. Therefore, we can conclude that there is no convergence or divergence during expansions. The literature has documented that productivity is procyclical (see, for example, Basu 1996; Baily et al. 2001; Basu and Fernald 2001). The marginal effect of recessions and expansions are (aR ? aLR) ? (aFR - aLR) Fi,t-1 and (aE aLE) ? (aFE - aLE) Fi,t-1, respectively. Therefore these marginal effects depend on whether the firm is follower or leader. In the case of followers, the marginal effect of recessions is (aR ? aLR) ? (aFR - aLR) = aR ? aFR. Table 3 shows that this marginal effect is -0.003 (=0.225 - 0.228). In the case of leaders, the marginal effect of recessions is (aR ? aLR). In this case, the coefficient is considerably large, -0.228, and statistically significant at 1 %. Therefore, when the proportion of firms in recession in each industry increases, keeping the rest of variables constant, there is a reduction in the expected productivity growth rate of leaders. On the other hand, the marginal effect of the proportion of firms in expansions is statistically not different from zero both for leaders and followers. The definition of followers in Eq. (2) covers a wide range of firms. The main advantage is that with two groups of firms is clear how to test for convergence in recessions. We could get a better understanding of the convergence during recessions if we study the effect of recessions on every quintile of the productivity distribution. In this direction, columns [3] and [4] in Table 3 show analogous results to columns [1] and [2] but instead of estimating the effect of recessions and expansions on followers and leaders’ productivity growth rates, we estimate the differential effect of recession and expansion on each quintile of the productivity distribution. We do this by including the interaction term between the variables reflecting the percentage of firms in recessions (Rjt) and expansions (Ejt) and a set of dummy variables indicating the corresponding quintile of the industry productivity distribution of the previous year, Qsi,t-1 with s = 1, 2, …, 5. We focus on the fixed-effect estimation in column [3] that allows for persistence in the heterogeneity. These results confirm that less productive firms had higher productivity growth rate. In fact, the coefficients of the quintiles are decreasing as the quintile approaches to the top. This finding also captures mean reversion. More important, the interactions

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between productivity quintiles 1, 2, 3, 4 (quintile 5 is the omitted category) and the proportion of firms in recession are positive and therefore they reflect the convergence in productivity during recessions. These results also show that the heterogeneity within followers is important; the firms less affected by the recession are those in quintile 3 followed by firms in quintiles 2 and 1. The interactions between quintiles and the proportion of firms in expansions are not significant. Finally, the coefficient of the proportion of firms in recession is negative and statistically significant. These findings confirm that followers tend to catch up with leaders during recessions. This catch up was sufficiently large during the recession in the early 1990s and explained the reduction in the dispersion showed in Table 2.

4 Robustness analysis In this section we present three robustness checks. First, we check if our results are driven by sample selection. As we mentioned above, Fig. 1 shows a large shift in the productivity distribution from 1991 to 1995 with higher shift in the lower tail of the distribution. Table 3 provides evidence showing that the asymmetric shift was explained by a higher productivity growth rate of the firms in the lower tail of the productivity distribution during the recession that took place in 1992 and 1993. However, this asymmetric change could also occur if firms in the lower tail exit the market between 1991 and 1995. Columns [1] and [2] in Table 4 show the same estimates of Table 3 considering only firms in balanced sample. All the results are robust to considering only those firms that stayed in the market from 1991 to 2005. Columns [3] and [4] in Table 4 control for sample selection using a two steps Heckman’s (1979) procedure. This two steps procedure consists in estimating the Mill’s inverse ratio (first step) and then controlling for selection by including the inverse Mill’s ratio as an additional regressor in Eq. (4) (second step).6 The inverse 6

The Mill’s ratio is obtained from the estimation of the survival probability through a Probit model that uses as regressors the same variables included in Eq .(4) plus the excluded variables. We used as excluded variables the log of the firm’s debt and a dummy variable that takes value one if the firm is an exporter. These variables are correlated with survival and do not enter in the productivity growth equation. The dummy exporter can be excluded from the productivity growth equation because there is evidence showing that while more productive firms are able to export, the fact that a firm is exporting does not imply it will increase its productivity (see Delgado et al. 2002). In the case of the log of debt, it can be excluded because there are no theoretical reasons why debt should affect productivity growth. The Mill’s ratio is equal to /(cw)/A(c•w) where /(.) and A(.) are the normal density and normal cumulative distribution functions, respectively, w is a vector that contains all the variables in Eq. (4) plus the excluded variables, and c are the estimated coefficients from the Probit model for survival.

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Table 4 Robustness checks Robustness check (1): sample selection Dependent variable: Dtfp [1] Follower t - 1

[2]

[3]

Robustness check (2): revenue TFP Dependent variable:D rtfp [4]

[5]

0.0813***

0.140***

[0.0296]

[0.0256]

[0.0239]

Follower t - 1 9 recession

0.229*** [0.0656]

0.218*** [0.0525]

0.203*** [0.0527]

Follower t - 1 9 expansion

0.0409

0.0279

0.0614

[0.0691] Q1 in t - 1

[6]

0.113***

[0.0560]

[0.0528]

0.219***

0.308***

[0.0451]

[0.0326]

[0.0297]

Q2 in t - 1

0.0951***

0.201***

0.187***

[0.0342]

[0.0282]

[0.0256]

Q3 in t - 1

0.0632**

0.124***

0.120***

[0.0295]

[0.0272]

[0.0251]

Q4 in t - 1

0.0353

0.0899***

0.0843***

[0.0308]

[0.0264]

[0.0236]

0.134

0.0748

0.155**

[0.0866]

[0.0627]

[0.0627]


0.290***


0.238***

0.154***

0.176***


[0.0768] 0.223***

[0.0589] 0.205***

[0.0570] 0.201***

[0.0669]

[0.0557]

[0.0549]

0.195***

0.188***

0.129**

[0.0705]

[0.0561]

[0.0544]

-0.0316

-0.0587

0.0230

[0.102]

[0.0704]

[0.0655]

Q4 in t - 1 9 recession Q1 in t - 1 9 expansion Q2 in t - 1 9 expansion Q3 in t - 1 9 expansion Q4 in t - 1 9 expansion Recession

0.0927

-0.0141

0.0508

[0.0790]

[0.0618]

[0.0563]

0.0586

0.0202

0.0447

[0.0675]

[0.0585]

[0.0545]

0.0453

-0.0148

0.0152

[0.0704]

[0.0574]

[0.0521]

-0.257***

-0.249***

-0.358***

-0.268***

-0.221***

-0.195***

[0.0664]

[0.0662]

[0.0570]

[0.0561]

[0.0546]

[0.0535]

Expansion

-0.0376

-0.0455

-0.0289

0.00905

-0.0398

-0.0270

Inverse Mill’s ratio

[0.0658] –

[0.0668] –

[0.0540] 1.552***

[0.0541] 0.898***

[0.0522] –

[0.0513] –

[0.140]

[0.140]

Firm level fixed effects

Yes

Yes

Yes

Yes

Yes

Yes

R

0.11

0.17

0.14

0.21

0.11

0.21

Number of observations

6,387

6,387

14,475

14,475

15,837

15,837

Number of firms

508

508

2,330

2,330

2,395

2,395

2

(1) Dependent variables. Columns [1] to [4]: Dtfp. Columns [5] and [6]: Drtfp, where rtfp is revenue total factor productivity. (2) All regressions include age, age squared, dummy variables for year, industry, size, incorporated companies, entry, exit, mergers, and demergers. They also include the proportion of foreign capital, the proportion of skilled workers, and a dummy for process innovation; all these variables lagged one period. (3) Followers are those firms in quintiles 1, 2, 3, and 4 of the productivity distribution. While in columns [1] to [4] productivity is measured by tfp, in columns [5] and [6] productivity is measured by rtfp. The same applies for the quintiles Q1, Q2, Q3, and Q4. (4) The excluded variables in the selection equation are the log of debt and an exporter dummy. (5) Heteroskedasticity robust SE. (6) Significance levels: * = 10 %; ** = 5 %; *** = 1 %

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347

Mill’s ratio is statistically significant. However, all the findings are robust to this additional control. Therefore, although less productive firms exited the market in the recession, this fact cannot explain the convergence in productivity. Second, we check the robustness of our results to deflating output and materials using industry deflators instead of firm level price indices. If we use industry level price indices to deflate output and materials and then we use Eq. (1) to obtain productivity, we obtain the Revenue total factor productivity (see, Foster et al. 2008). Columns [5] and [6] in Table 4 shows the same estimates of Table 3 considering Revenue total factor productivity. All the results are robust. Therefore, although firms adjusted prices in recession, this fact cannot explain the convergence of productivity in recession. Finally, a possible concern is that the convergence in productivity could be explained by other factors that could generate a trend in the dynamic of firms’ productivity rather than the recession in the early 1990s. In fact, Chevalier et al. (2009) found that in France the speed of convergence slowed down during the 1990s and they attribute this fact to globalization and the ICT revolution that may have benefited more productive firms. To address this issue we see how the speed of convergence changes over time and how the recession affects its evolution. A time varying speed of convergence can be obtained estimating recursively the following equation: Dtfpit ¼ ct þ bt tfpi;t1 þ a0xt xit1 þ a0zt zit þ uit ;

ð5Þ

with t = 1992, 1993, …, 2005 and xit1 and zit including the same control variables used to estimate Eq. (4) above. The evolution of estimated coefficients bt is shown in Panel (a) of Fig. 2. The closer is the value of bt to zero the lower the convergence rate. The estimated coefficient bt increases over time from -0.45 in 1992 to -0.20 in 2005. This finding is consistent with the fact that from 1991 to 1995 the convergence rate was sufficiently large to imply a reduction in the dispersion of firms’ productivity and after 1996 the speed of convergence was not sufficiently high to reduce the dispersion of productivity. Panel (a) also shows the evolution of the proportion of firms declaring that their markets are in recession. There is a clear negative relationship bt and the proportion of firms in recession; i.e. a positive correlation between the speed of convergence and the proportion of firms in recession. To evaluate whether the high absolute value of the coefficient b in the early 1990s is related to the recession, we estimated Eq. (5) for each industry and obtained a coefficient bjt for t = 1992, …, 2005 and j = 1, …, 18. Panel (b) in Fig. 2 shows the relationship between these coefficients and the proportion of firms in recessions in each industry. This panel confirms the negative relationship between the

Fig. 2 Convergence of firm’s productivity and recessions. a The evolution of b and the proportion of firms in recession. b Relationship between b and the proportion of firms in recession. Notes: a Coefficient bt in the following regressions: Dtfpit = ct ? bt tfpi,t-1 ? at xit ? vit, t = 1992, 1993, …, 2005. This is a b-convergence equation considering consecutive periods, in xijt we included age, age squared, the proportion of skilled workers, the proportion of foreign capital, a dummy for incorporated companies, and for process innovation in the previous period, and industry dummies. b Coefficient bjt in the following regressions: Dtfpijt = cjt ? bjt tfpij,t-1 ? atjt xit ? vit, t = 1992, 1993, …, 2005; j = 1, 2, …, 18 (industries). This is a b-convergence equation considering consecutive periods and estimated for each industry j, in xijt we included age, age squared, the proportion of skilled workers, the proportion of foreign capital, a dummy for incorporated companies, and for process innovation in the previous period. The closer the value of bjt to zero the lower the speed of convergence

proportion of firms in recession and the coefficient b. To test this relationship, we run two regressions: (1) bjt on a set of industry dummies and time dummies for the periods before 1995 and between 1996 and 2000, and (2) bjt on the same set of variables as before and the percentage of firms in industry j reporting that their markets are in recession. In the first regression, the coefficient of the dummy for the period before 1995 was equal to -0.11 and statistically significant at 1 %. This result confirms that before 1995 the value of bjt was lower. In the second regression, the coefficient of the percentage of firms in recessions was -0.288 and

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statistically significant at 1 % and the coefficient for the period before 1995 was not significant. Then, it is possible to conclude that the lower value of the coefficient in the period before 1995 is due to the large proportion of firms reporting their markets are in recession; i.e., the recession drove the higher convergence rate before 1995.

5 Conclusions This paper studies the evolution of the dispersion of firms’ productivity in the Spanish manufacturing sector during the period 1991–2005 and its relation with the business cycle. We evaluate the effect of the business cycle on the productivity growth of productivity leaders and followers. We use a rich dataset that allows us to construct firm level price indices and therefore to obtain physical productivity. This dataset also provides us with firm level perception of the business cycle and therefore allows us to obtain business cycle variables that vary by industry. The main findings of the paper can be summarized as follows: (1) There was an asymmetric shift of the productivity distribution from 1991 to 1995; the larger shift was in the lower tail of the distribution. (2) In the same period, the variance of productivity within each industry shrunk. (3) This convergence in productivity was explained by the recession in 1992 and 1993 that created incentives for followers to reduce costs and become more productive. This result is consistent with the implications of Schmidt (1997) model of managerial incentives and competition and the fact that the recession imposed higher threat of liquidation on followers. This result is also consistent with other papers that found that competition drives higher productivity (Schmitz 2005) and lower dispersion of firms’ productivity (Oulton 1998; Syverson 2004). (4) The exit of less productive firms during the recession did not explain the reduction in the variance of firms’ productivity. (5) There was no convergence during expansions. The reason for no convergence during expansions could be related to the fact the innovation is pro-cyclical (Geroski and Walters 1995; Barlevy 2007) and more productive firms are usually more innovative than less productive firms. (6) The productivity of the Spanish manufacturing firms was not procyclical during expansions. The mechanism behind this fact is beyond the objective of this paper. However, understanding it could shed light on the poor performance in productivity of the Spanish economy after 1995. (7) We tested the robustness of our results in several directions; in addition to sample selection, we also used different productivity measure and different identification strategy. Acknowledgments We thank Ce´sar Alonso, Eric Bartelsman, Samuel Bentolila, Juan J. Dolado, Jose´ C. Farinãs, Jesu´s Gonzalo,

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J Prod Anal (2014) 41:339–349 Jordi Jaumandreu, Juan Jimeno, Jacques Mairesse, Ricardo Mora, Carlos Velasco, the associate editor, two anonymous referees, and participants in seminars and conferences at Universidad Carlos III de Madrid, Universidad de Oviedo, Sant’ Anna School of Advanced Studies, XXII Jornadas de Economıá Industrial (Barcelona), workshop on ‘‘Entrepreneurship, Firm Demography and Industrial Location’’ (Vienna), and conference ‘‘Organization and Performance: Understanding the Diversity of Firms’’ (Tokyo) for helpful comments. Financial support from the Telefonica-UC3M Chair on Economics of Telecommunications (Escribano) and from Consejerıá de Educacioń de la Comunidad de Madrid (Stucchi) is gratefully acknowledged.

Appendix: Variable definitions TFP Total factor productivity. Described in Sect. 2, see Eq. (1). Output Value of goods and services produced computed as sales plus the variation of inventories deflated by the firm’s price index of output. Labor Effective total hours worked computed as the number of workers times the average hours per worker. The average hours per worker is computed as the normal hours plus average overtime minus average working time lost at the workplace. All these variables are reported by firms. Intermediate materials Value of firm’s intermediate consumption deflated by the firm’s price index of materials. Capital Capital at current replacement values CKit is computed recursively from an initial estimate and the data on current investments in equipment goods Iit. We update the value of the past stock of capital by means of the price index of investment PIt as CKit = (1 - d) PIt/PIt-1 CKit-1 ? Iit-1, where d is an industry-specific estimate of the rate of depreciation. Capital in real terms is obtained by deflating capital at current replacement values by the price index of investment as Kit = CKit/PIt. See Martıń-Marcos and Suarez (1997) and Escribano and Stucchi (2011) for more details. Investment Value of current investment in equipment goods. Wages Firm’s hourly wage rate (total labor cost divided by effective total hours of work) deflated by the firm’s price index of output. User cost of capital Weighted long-term interest rate of banks and other long-term debts plus the industry-specific depreciation rate minus the investment inflation rate. Age Difference between the current year and the year of birth declared by the firm. Size Firms are classified in 3 size categories. Large firms: Firms with more than 200 employees. Medium-sized firms: firms with less than 200 but more than 50 employees. Small firms: firms with less than 50 employees.


Industry Firms are classified in 17 industries: (1) Nonmetallic products, (2) Chemical products, (3) Metallic products, (4) Agricultural and industrial machinery, (5) Office machinery and data processing machinery, (6) Electrical material and electrical accessories, (7) Vehicles and motors, (8) Other transport material, (9) Meat and meat products, (10) Food and tobacco, (11) Beverages, (12) Textiles and apparels, (13) Leather products and shoes, (14) Wood and furniture, (15) Paper, paper products and printing products, (16) Plastic products and rubber, (17) Other manufactured products. Recession and expansion Firms report whether they operate in expansive, stable, or recessive market. Recession (expansion) is the proportion of firms that work in a market in recession (expansion) at the industry level. Human capital Proportion of engineers and workers with a university degree. Foreign capital Proportion of foreign capital. Process innovation Dummy variable that takes value one when the firm reports that has introduced a process innovation. Incorporated company Dummy variable that takes value one when the firm is an incorporated company. Merger Dummy variable that takes value one when the firm has been involved in a merger process. Demerger Dummy variable that takes value one when the firm has been involved in a demerger process. Entry Dummy variable that takes value one if the firm have entered in the market after 1990. Exit Dummy variable that takes value one if the firm exit the market during the period 1991–2005. Exporter Dummy variable that takes value one if the firm exports part of its production.

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