Performance and Strategy: Simultaneous Equations Analysis of Long-lived Firms

Abstract

A simultaneous equations model of performance, strategy and size is tested using fieldwork evidence on long-lived firms in Scotland. Estimation is by I3SLS, with correction for sample selection bias. The contributions of this paper are that it: (a) grounds estimation on fieldwork evidence; (b) calibrates performance and competitive strategy; (c) tests and models endogeneity; and (d) computes robust trade-off elasticities between firm size and performance. It shows how this trade-off provides the entrepreneur with two strong incentives: (i) to seek greater efficiency typically by an increase in the human capital of the ‘core’ workforce; (ii) to achieve higher levels of performance by adopting more diverse competitive strategies.

Key Words:

• Performance
• Size
• Competitive Strategy
• Simultaneity
• Mature Firms

JEL classifications:

• C42
• D21
• G33
• L2
• M13
• M21

This research was undertaken with the generous support of Enterprise Ireland, to whom the authors make grateful acknowledgement. We should also like to thank the many owner-managers of small firms in Scotland, who gave generously of their time, to allow us to collect high quality data in the field. Finally, the work on which this paper is based has benefitted from the comments of numerous people, in conferences (e.g., Scottish Economic Society, Irish Economic Society, Royal Economic Society, European Association for Research in Industrial Economics, European Economic Society), seminars and workshops (e.g., Universities/Colleges of Aberdeen, Babson, Barcelona, Birmingham, Copenhagen, Cork, Durham, Lancaster, Limerick, Nice, St Andrews, Strathclyde, Warwick), in workshop and research centre discussions (e.g., ZEW Mannheim, CREM Caen) and in private correspondence. They are all thanked for their inputs, but absolved of any responsibility for the form this paper takes.

Notes

1. Storey (1994) found that 4% of the fast-growing firms in his sample create about 50% of the employment in this cohort over a decade.

2. SMEs are defined in accordance to the European Commission’s definition 2003/361/EC definition where medium-sized enterprises consists of enterprises which employ fewer than 250 persons and which have either an annual turnover not exceeding 50 million euro, or an annual balance sheet total not exceeding 43 million euro. Small enterprises are defined as enterprises which employ fewer than 50 persons and whose annual turnover or annual balance sheet total does not exceed 10 million euro. Micro enterprises are defined as enterprises which employ fewer than 10 persons and whose annual turnover or annual balance sheet total does not exceed 2 million euro.

3. See the online appendix for a more detailed presentation of the exact survey question and all 28 items included in this multidimensional performance measure.

4. Specifically, the Cronbach’s (1951) alpha was 0.78, exceeding the level recommended by Nunnally (1978) of 0.7 and the data fitted yardstick measurement models (cf. Chrisman, Bauerschmidt, and Hofer 1998; Sandberg and Hofer 1987) well, [χ²(16) = 9.9762; p-value = 0.868].

5. In practice the test is implemented as follows: Suppose a structural equation is

y₁ = δX₁ + βy₂ + u.

where y₁ and y₂ are vectors of suspected endogenous variables, X₁ is a matrix of exogenous and predetermined variables, and u a vector of error terms. Let ${\widehat{y}}_2$ be the vector of fitted values of y₂ from a reduced form regression of y₂ against all the exogenous and predetermined variables in the system. The DWH test is simply an F test that the coefficient π on ${\widehat{y}}_2$ is equal to zero (i.e., test $\widehat{\mathit{\pi }}=0$) in an estimation of the following regression $y_1={\mathit{\delta }}_{}{X}_1+\mathit{\beta }{y}_2+\mathit{\pi }{\widehat{y}}_2+u$.

6. F_(1,60) statistic = 0.17, H_o could not be rejected.

7. F_(1,60) statistic = 0.57, H_o could not be rejected.

8. Maximum likelihood methods are invariant to reparameterisation whereas instrumental variables are not.

9. The I3SLS estimation and the associated diagnostic tests were conducted on Shazam whereas the I3SLS estimation with the correction for sample selection was undertaken in LIMDEP.

10. When higher that 2 iterations are used the significance of the performance and size variables increase rapidly due to rounding errors.

11. Single R² measures are not appropriate in an equation system. The R² from a particular equation computed could be negative since with system estimation in general it is not the case within each equation the sum of the residuals is zero. The numerator could be larger than the denominator that is the unexplained variation can be larger than the total variation implying a negative R². This is because single equation systems minimises e'e and therefore maximises the R² in general. System estimation methods do not minimise e'e. The maximum likelihood estimator minimises the determinant of the residual cross products matrix; that is ML minimises det E'E. Hence ML does not maximise the individual equation R² values. Since single equation R² measures are flawed in the equation system context, a different goodness of fit measure should be employed viz. ${\tilde{R}}^2=1-\frac{\left|E^{\prime }E\right|}{\left|y^{\prime }y\right|}$

The system ${\tilde{R}}^2$ reported is defined as

$\tilde{R}=1-\left|\widehat{\sum }\right|/\left|{\left(Y-\overline{Y}\right)}^{{}^{\prime }}\left(Y-\overline{Y}\right)\right|$

where Y is an n x k matrix and $\overline{Y}$ contains the sample means.

12. The Chi-square statistic is calculated using the following formula:

${\mathit{\chi }}^2=-N\left(log\left(1-{\tilde{R}}^2\right)\right)$.

13. The Lagrange Multiplier statistic is computed as $L{M}^{\ast }=N{R}_u^2$ where $R_u^2$is the un-centred $R_{}^2$or $R_u^2=y^{\prime }X{\left(X^{\prime }X\right)}^{-1}{X}^{\prime }y/y^{\prime }y$ (see Cameron and Trivedi 2005). Under the null hypothesis of a diagonal covariance structure the statistic has an asymptotic ${\mathit{\chi }}_{(M(M-1)/2)}^2$distribution where M is the number of equations in the system.

14. This stability condition can be expressed:

(dP/dS)_7a = –0.2141 > –0.5070 = (dP/dS)_8.

Additional information

Funding

This work was supported by Enterprise Ireland under Grant [IC/2001/060].