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.
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Notes
See Sect. 2 for a detailed definition of firms’ total factor productivity.
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.
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:
\( T_{2} = (N - 2.5)\log \left( {1 + 0.25\frac{{(\hat{\sigma }_{0}^{2} - \hat{\sigma }_{T}^{2} )^{2} }}{{\hat{\sigma }_{0}^{2} \hat{\sigma }_{T}^{2} - \hat{\sigma }_{0T}^{2} }}} \right) \) and \( T_{3} = \frac{{\sqrt N (\hat{\sigma }_{0}^{2} /\hat{\sigma }_{T}^{2} - 1)}}{{2\sqrt {1 - \hat{\pi }^{2} } }} \)
where \( \hat{\sigma }_{0}^{2} \), \( \hat{\sigma }_{T}^{2} \) and \( \hat{\sigma }_{0T} \) are the sample variance of tfp 0 and tfp T and the sample covariance between tfp 0 and tfp T , respectively. Finally, \( \hat{\pi } \) is the estimate of the autoregressive coefficient of tfp T on tfp 0 . The assumption behind these statistics is that firms’ productivity follows a first order autoregressive process. Under the null hypothesis of no convergence, \( T_{2} \mathop \to \limits^{d} \chi^{2} (1) \) and \( T_{3} \mathop \to \limits^{d} N(0,1) \).
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.
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.
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 ϕ(γw)/Ф(γ∙w) where ϕ(.) and Ф(.) 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 γ are the estimated coefficients from the Probit model for survival.
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Acknowledgments
We thank César Alonso, Eric Bartelsman, Samuel Bentolila, Juan J. Dolado, José C. Fariñas, Jesús Gonzalo, 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 Economía 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 Consejería de Educación de la Comunidad de Madrid (Stucchi) is gratefully acknowledged.
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Appendix: Variable definitions
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 CK it is computed recursively from an initial estimate and the data on current investments in equipment goods I it . We update the value of the past stock of capital by means of the price index of investment P It as CK it = (1 − δ) P It /P It−1 CK it−1 + I it−1, where δ 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 K it = CK it /P It . See Martín-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) Non-metallic 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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Escribano, Á., Stucchi, R. Does recession drive convergence in firms’ productivity? Evidence from Spanish manufacturing firms. J Prod Anal 41, 339–349 (2014). https://doi.org/10.1007/s11123-013-0368-5
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DOI: https://doi.org/10.1007/s11123-013-0368-5