Peter Brouwer
Henry Nieuwenhuijsen
The computations for this study were carried out at CEREM (Centre for Research of Economic Micro-data of Statistics Netherlands). The views expressed in this paper are those of the authors and do not necessarily reflect the policies of Statistics Netherlands.
Research Report 9908/E
Modelling returns to R&D:
an application on size effects
ISBN: 90-371-0762-1 Price: NLG 20.-Order number: H9908
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Contents
1 Introduction . . . .4
2 Modelling productivity effects of R&D . . . .5
3 Data . . . .8
4 Results . . . .10
5 Summary . . . .17
References . . . .18
Appendices I Chow test for parameter stability . . . .19
Modelling returns to R&D: an application on size effects
1
Introduction
Since Schumpeter in his book Capitalism, Socialism and Democracy
(1942) put forward the hypothesis that large enterprises are the most effective innovators much research has been done on the theme size and R&D. Many authors discovered through empirical research that the share of firms doing R&D increases with size class and in the highest size classes the share is exactly one (e.g. Villard (1958), Nelson et al. (1967), Bound et al. (1984) and Cohen et al. (1987)). These empirical results have been interpreted as support for Schumpeter. However, studies show also that the relation between R&D and size is proportional (Scherer (1984), Bound et al. (1984) and Cohen et al. (1987)). Moreover, some authors found that the number of innovations per dollar of R&D is disproportional with size (e.g. Acs and Audretsch, 1991). The last two theses can be interpret-ed as a rejection of Schumpeter’s hypothesis. Cohen and Klepper (1996) recently put forward the idea that, because of cost spreading, large firms do have an advantage in conducting R&D, which is con-form Schumpeter. Furthermore there is the hypothesis of Nooteboom (1994). He stated the idea that there is an indication of dynamic com-plementarity between large and small firms in the innovative process. This means that large and small firms are more effective innovators at different stages in the life cycle of a technology or product. In sum we conclude that earlier studies on R&D and size give no unambigu-ous results. The question remains whether large or small firms prof-it more from their specific R&D activprof-ities.
In this study we deal with the direct effects on productivity of the in-house R&D expenditures of firms. In particular the differences in the output elasticities of R&D expenditures between large and small firms are investigated.
The outline of the paper is as follows. Section 2 discusses the mod-elling of the productivity effects of R&D. In section 3 we present the data used for the estimations. Finally, the results are presented in sec-tion 4. The paper ends with a summary.
2
Modelling productivity effects
of R&D
In order to assess the effects of R&D activities on productivity most studies employ a Cobb-Douglas production function1. The advantage of estimating a production function is that it is relatively simple and the data necessary for estimation are usually available. In its stan-dard form the production function relates the volume of production to the input factors labour, capital and material consumption. By including a measure of R&D as additional explanatory variable in the production function we can obtain an estimate of the output elastic-ity of R&D.
As a measure of R&D the concept of a stock of knowledge capital (Hall and Mairesse (1995)) is used. It is assumed that past R&D expenditures form a stock of knowledge in a way similar to the for-mation of the stock of physical capital through investments. The knowledge stock increases each year by new R&D expenditures. Furthermore a certain depreciation rate for knowledge capital is assumed. Hall and Mairesse (1995) show that, using the Perpetual Inventory Method (PIM), the initial knowledge stock is proportional to the initial R&D expenditures. This implies that in cross sections R&D expenditures can be used as a measure of R&D in the produc-tion funcproduc-tion.
The production function can be estimated at different levels of aggre-gation. For our purpose of estimating the effects of R&D activities on production it is best to use data at the firm level. Using aggregated data can introduce an aggregation bias due to a skewed distribution of R&D expenditures across firms. In this case, a small number of large firms with high R&D expenditures will dominate the results. When these firms operate at a multinational level, aggregated data are not suitable for measuring the productivity effects of R&D, since R&D activities in one country will affect productivity in another country. In the Netherlands most R&D expenditures are concentrat-ed within five multinational companies (see Minne (1997)). Clearly, estimating a Cobb-Douglas production function is a simplifi-cation of reality. This simplifisimplifi-cation can lead to biased estimates of the output elasticity of R&D expenditures caused by the influence of
variables not included in the production function. To correct for the omission of variables that are related to the characteristics of the par-ticular sector in which a firm operates we can include sector dum-mies when estimating the production function.
Besides sector-specific characteristics there may also be firm-specific characteristics that influence the estimations of the output elasticity of R&D expenditures. However, including a dummy variable for each firm is not feasible since that would introduce too many coefficients to be estimated. When panel data are available the firm-specific char-acteristics can be eliminated by using either growth figures (first dif-ferences) or variables related to their mean (within transformation) in the estimation. Unfortunately both methods are rather sensitive to measurement errors. To avoid the influence of measurement errors one can use so-called ‘long differences’ of variables. This entails using mutations of variables over a longer period of time and requires the observation of firms at two moments several years apart. Especially for smaller firms, of which only samples are surveyed, this is often unfeasible.
Another assumption made implicitly when using a production func-tion concerns the exogeneity of the input factors. The producfunc-tion function determines the level of output based on the level of the dif-ferent input factors. However, in practice there can also be a reverse relationship between output and input factors, i.e. the level of output may determine the level of input factors employed. This is true espe-cially for the input factors labour and materials. The interdependence of the levels of output and input factors is usually referred to as the problem of simultaneity.
It will be clear that the advantage of the simple estimation of a pro-duction function to assess the productivity effect of R&D comes at the cost of possible biases in the estimates of the output elasticities. Besides the already mentioned complicating factors, R&D not only influences production, but it will most likely have an effect on the demand for the products of a firm as well. In fact, increasing the demand by introducing new products is probably one of the main reasons for firms to engage in R&D activities.
Van Leeuwen and Nieuwenhuijsen (1999) propose a model compris-ing a production function and a demand function, both includcompris-ing R&D as an additional explanatory variable. By estimating this model in its reduced form and using long differences and within transfor-mations of the variables, they take into account both the
ity issue and the influence of firm-specific characteristics, while incorporating the demand effects of R&D. The sample available in Van Leeuwen and Nieuwenhuijsen (1999) consists of large enter-prises.
In our study we want to distinguish between the productivity effects of in-house R&D for small and medium-sized enterprises (SMEs) and large enterprises (LEs). Only data for a single year (1994) are avail-able. We therefore start by estimating the Cobb-Douglas production function, including R&D expenditures in 1994 as additional explana-tory variable, for the cross section. Since the estimates for the output elasticities of R&D expenditures obtained in this way may be biased we also estimate a version of the model by Van Leeuwen and Nieuwenhuijsen. This allows to determine how the estimated output elasticities are affected by taking into account several of the issues discussed in this section and consequently how much confidence we can have in the estimates from the extended Cobb-Douglas produc-tion funcproduc-tion.
3
Data
Data are used of Dutch manufacturing firms at the firm level for 1994. They are available from Statistics Netherlands. The database links data from the R&D survey with selected variables from the Production Statistics. From the R&D survey data are available of the number of R&D and other employees and the amount of in-house R&D expenditures. R&D expenditures are divided into labour costs, costs of materials and investments. The variables from the Production Statistics include sales, number of employees, capital depreciation costs and material consumption.
With this dataset it is possible to avoid estimation biases caused by double-counting of R&D inputs1. In the estimations labour and mate-rial inputs are adjusted for the amounts used for R&D. For capital input the adjustment could not be made since no data was available for total investments in fixed capital. However, R&D investments in fixed capital comprise only 10 percent of total R&D expenditure. Hence, we are able to solve the double-counting problem for 90 per-cent.
The total number of firms available is 203. Table 1 shows the distri-bution of the number of firms for different size classes, based on the total number of employees of a firm. We define small and medium-sized enterprises (SMEs) as firms consisting of less than 100 employ-ees, while large enterprises (LEs) consist of 100 or more employees. From table 1 we see there are no data available for firms with less than 10 employees, so our sample of SMEs consists mainly of medi-um-sized enterprises.
Table 1 Number of firms in dataset by size class
Number of employees Number of firms in dataset
10-<20 3 SMEs 20-<50 9 50-<100 65 100-<200 61 LEs 200-<500 45 500 and more 20
Modelling returns to R&D: an application on size effects
1 See Schankerman (1981). See also Bartelsman et al. (1996) and Hall and Mairesse (1995) for a comparison of empirical results with and without adjusting for double-counting.
Summary statistics for SMEs and LEs are presented in table 2. The statistics indicate some notable differences between SMEs and LEs, supporting that the influence of R&D expenditures on productivity differs between these groups of firms. Not surprisingly it is immedi-ately clear that LEs are more capital-intensive than SMEs are, as evi-denced by the higher average depreciation costs per employee for these firms. It is striking to note that SMEs show a higher average R&D intensity, as defined by the in-house R&D expenditures as per-centage of sales. Furthermore, we see that labour productivity for SMEs is 20% smaller than for LEs.
Table 2 Summary statistics (averages)
SMEs LEs
Number of firms 77 126
Number of employees 68 606
Sales (x NLG 1,000,000) 21 182
In-house R&D-expenditures (x NLG 1,000) 418 12761 Value added per employee (x NLG 1,000) 103 129 Depreciation costs per employee (x NLG 1,000) 11 19
R&D intensity (% of sales) 2.36 2.02
Source: Statistics Netherlands.
In our estimations we use sector dummies to account for differences between sectors that might influence the estimates of the effects of R&D expenditures on productivity. We define four sectors based on the two-digit Standard Industrial Classification (SIC) of Statistics Netherlands. The four sectors are: Food, Beverages and Tobacco (SIC 15 and 16), Chemical Industry and Allied (SIC 23-25), Metal Industry (SIC 27-35) and Other Manufacturing: textiles, wearing apparel, wood products, paper and paper products, printing and publishing, furniture and manufacture of building materials (SIC 17-22, 26, 36 and 37).
4
Results
We estimate the productivity effects of R&D expenditures by employ-ing an extended Cobb-Douglas production function, with R&D as additional explanatory variable besides labour, capital and materials. This production function is given by
where:
Qs, C, L, K, M: Volume of production, capital, labour, R&D
expen-ditures and volume of material consumption, respectively
α, β, γ, δ: Output elasticity of capital, labour, R&D expendi-tures and material consumption, respectively
A: Constant term of production function
i: Index denoting firm.
Equation (1) is estimated in its loglinear form using capital depreci-ation costs as proxy for capital and including sector dummies to account for sector-specific characteristics. It is estimated for the com-plete sample and for SMEs and LEs separately. The results are pre-sented in table 3.
Table 3 Estimates of Cobb-Douglas production functions for 1994*,**
Variable Complete sample SMEs LEs
Output elasticity: Material consumption (δ) 0.645 0.641 0.650 (42.042) (22.961) (34.622) Labour (β) 0.233 0.243 0.248 (10.715) (4.662) (8.874) Capital (α) 0.102 0.093 0.100 (8.198) (3.549) (7.184) R&D expenditures (γ) 0.045 0.035 0.048 (5.110) (1.951) (4.841) Number of observations .203 ...77 .126 R2 0.99 0.97 0.99
* Estimated in loglinear form, including sector dummies. ** t-values in parentheses.
From table 3 we see a significant positive productivity effect of R&D expenditures (γ) for the entire sample of 0.045. This result is compa-rable to the magnitude of the productivity effects of R&D found by Van Leeuwen and Nieuwenhuijsen (1999) for mainly large Dutch manufacturing firms.
Examining the productivity effects of R&D expenditures for SMEs and LEs separately it appears from table 3 that this effect is larger for the larger firms. The estimated output elasticities of R&D expendi-tures for SMEs and LEs are 0.035 and 0.048, respectively. To test whether the difference in productivity effects for SMEs and LEs is sig-nificant we apply two Chow tests for parameter stability1. We first test the hypothesis that the extended Cobb-Douglas production func-tion is the same for SMEs and LEs. Assuming the same producfunc-tion function for all firms amounts to restricting all parameters of the pro-duction function to be equal. This hypothesis cannot be rejected at the 5%-significance level as the value of the Chow test statistic is 1.03, whereas the 5% critical value for the F8,187distribution is 1.99. We then test the hypothesis of an equal output elasticity of R&D expenditures for SMEs and LEs, while assuming all other parameters of the production function to be equal. This hypothesis cannot be rejected either at the 5%-significance level, as the value of the Chow test statistic 1.09 is less than 3.89, the 5% critical value for the F1,194 distribution. Hence, the Chow test does not reject the hypothesis of equal output elasticities of R&D expenditures for SMEs and LEs. The insignificance of the differences in estimates between SMEs and LEs may result from the high concentration of medium-sized firms in the sample (see table 1 in section 3). There are especially few small firms in the dataset.2
Furthermore using an extended Cobb-Douglas production function to assess the productivity effects of R&D expenditures leaves out possi-ble complicating factors, which might lead to biased estimates of these effects (see section 2).
First, the demand effects of R&D are ignored. It is likely that the intro-duction of new products will have a positive effect on the demand for products of a given firm. Not including the demand effects might result in biased estimates for the productivity effects.
Second, the production function does not account for possible simul-taneity. By using a production function we assume that the produc-tion factors labour, capital, materials and R&D are exogenous vari-ables which determine the volume of production. The reverse may also be true, i.e. the levels of the production factors may be influ-enced by the volume of production. This simultaneity can influence
the estimates of the output elasticities. The problem of simultaneity mainly arises when using time-series data.
Third, although we do account for sector-specific characteristics by including sector dummies there may also be an influence of cific characteristics. When panel data are available, these firm-spe-cific influences can be eliminated by estimating equation (1), using either growth figures or deviations from firm-specific averages of the variables. However, both methods are sensitive to measurement errors in the data.
The first two of these problems (demand effects and simultaneity) can be dealt with by estimating a more extensive system of equa-tions, proposed by Van Leeuwen and Nieuwenhuijsen (1999). Besides a production function, analogous to equation (1), a demand equation is introduced which includes R&D as an additional explana-tory variable:
Where:
Qd, K: Volume of demand and R&D expenditures
D: Constant determining position of demand curve
P: Relative price of final product (compared to competitors)
η: Demand elasticity of price of final products
φ: Effects of R&D capital on position of demand curve
i: Index denoting firm.
The system of equations (1) and (2) can be represented in its loglin-ear form, with lower case letters representing the natural logarithms of variables:
Equations (3) and (4) cannot be estimated in a straightforward fash-ion since it remains unclear which variables are exogenous and endogenous. However, assuming profit maximisation, short-term constant physical capital and production being equal to demand, three equations can be derived that can be estimated directly. Appendix II provides a detailed explanation of the derivation. In the derived model, turnover, employment and material consumption depend on R&D capital, tangible capital, material prices and wages (indices are left out):
wland wmrespectively denote wages and price of materials (inter-mediate goods). πq, πl and πmare constants in equations (5) through (7). εequals 1+1/η.
In short, the equations can be written as:
All coefficients in equations (5a)-(7a) can be expressed in terms of the structural parameters in equations (3) and (4). By estimating the system of equations (5)-(7) we take into account both the demand effects of R&D expenditures and the issue of simultaneity. To deal with firm-specific characteristics as well, we can include wages at the firm level. This will probably cause biases in the estimates of the output elasticity of labour (β), as it will incorporate the influences of the firm-specific characteristics. This is of no great concern, howev-er, since we are not particularly interested in the estimates of β.
Table 4 shows the estimates of the structural parameters of equations (1) and (2) for both SMEs and LEs. These estimates are obtained by estimating the system of equations (5)-(7), including wages at the
firm level and sector dummies, using a Seemingly Unrelated
Table 4 SUR estimates of structural parameters for 1994*,**
Variable SMEs LEs
Output elasticity: Material consumption (δ) 0.896 0.876 (1.584) (12.999) Labour (β) -1.807 -0.016 (-0.457) (-0.245) Capital (α) 0.620 0.109 (0.475) (4.639) R&D expenditures (γ) 0.112 0.045 (0.488) (3.176) Price elasticity of demand (η) -9.174 -6.665
(-2.257) (-5.988) R&D elasticity of demand (φ) -0.030 0.160
(-0.174) (2.101) * Estimated with wages at the firm level and including sector dummies. ** t-values in parentheses.
From the results for SMEs in table 4 we conclude that the extensive system of equations cannot be estimated meaningfully for these firms. The only parameter significant at the 5%-significance level is
η, the price elasticity of demand. Together with the value of η
(-9.174) this indicates that SMEs may be operating under conditions close to perfect competition1. Since we find no significant demand effects of R&D expenditures for SMEs, it seems at least partially jus-tified to assess the productivity effects of R&D expenditures for SMEs by estimating an extended Cobb-Douglas production function. For LEs the estimation of equations (5)-(7) does yield significant esti-mates for most structural parameters. The unfeasible (and insignifi-cant) estimate of β(-0.016) is probably due to inclusion of wages at the firm level, as a result of which it incorporates the influences of firm-specific characteristics. LEs do exhibit a significant influence of R&D expenditures on demand (0.160), even though the price elastic-ity of demand is also substantial (-6.665). However, of most interest to us is the estimate of the output elasticity of R&D expenditures (γ). The estimate of γobtained from estimating the extensive system of equations for LEs (0.045) is very close to the estimate found by esti-mating the extended Cobb-Douglas production function (0.048). Furthermore the results for LEs are comparable with the results found by Van Leeuwen and Nieuwenhuijsen (1999). They used a panel of large Dutch manufacturing firms comprising information for the years 1985, 1989 and 1993. Their within estimates are presented
Results
together with our results for LEs in table 5. The table shows that the estimates of the impact of R&D on demand and productivity are almost equal. The output elasticity of labour is different. This is caused by the firm-specific effects that biases the output elasticity in the cross-sectional estimates. Because in Van Leeuwen and Nieuwenhuijsen a panel is available they can make a correction for firm-specific effects by using within estimates.
Table 5 Estimates of structural parameters LEs; cross section 1994 and within estimates 1985-1993*
cross section** within estimates***
Variable 1994 1985-1993 Output elasticity: Material consumption (d) 0.876 0.775 (13.0) (13.5) Labour (β) -0.016 0.081 (-0.25) (0.8) Capital (α) 0.109 0.066 (4.6) (6.9) R&D expenditures (γ) 0.045 0.047 (3.2) (2.1)
Price elasticity of demand (η) -6.665 -1,717
(-6.0) (-8,1)
R&D elasticity of demand (φ) 0.160 0.192
(2.1) (4.3)
* t-values in parentheses.
** Estimated with wages at the firm level and including sector dummies. *** Estimated with firm-specific effects (within transformation: deviation of mean
score of variable), sectoral wages and dynamic sector dummies. Source: Van Leeuwen and Nieuwenhuijsen (1999).
In sum, the estimations of the extended Cobb-Douglas production functions provide evidence for a larger output elasticity of R&D expenditures for large firms. However, the difference in parameter estimates for SMEs and LEs is not statistically significant at the 5%-significance level. The estimates may be biased due to the omission of demand effects of R&D expenditures, simultaneity and the influ-ence of firm-specific characteristics. When estimating a more elabo-rate system of equations to account for these issues, we find no sig-nificant estimates for SMEs due to the high price elasticity of demand. This indicates that the demand effects of R&D are of limit-ed importance for SMEs. For LEs we do find significant demand effects of R&D, but the estimated output elasticity of R&D is very close to the estimate found using the extended Cobb-Douglas
who investigated mainly large firms. The findings indicate that the extended Cobb-Douglas production function is an adequate model for estimating the output elasticity of R&D expenditures. The esti-mates of the output elasticities of R&D expenditures obtained in this way do not reveal a significant difference between SMEs and LEs. However, this may be due to the high concentration of medium-sized firms in our sample.
5
Summary
It is generally accepted that R&D contribute to economic growth. R&D activities lead to improvements in production processes and introduction of new products. R&D activities influence the own per-formance of the R&D firm, but via spill-overs the perper-formances of other firms (in- or outside the sector) are also influenced.
This report is about the direct effects of R&D at the firm level. The main object of the study is to measure productivity effects of R&D. In particular the differences in the output elasticities of R&D expen-ditures between large and small firms are investigated.
To measure the output elasticity of R&D a Cobb Douglas production function is estimated. We use data of 203 Dutch manufacturing firms for 1994, available from Statistics Netherlands. We find positive and significant productivity effects of R&D for both large and small firms. Small firms are defined as firms with less than 100 employees, while large firms have 100 or more employees. The estimated output elas-ticities are 0.038 for small firms and 0.048 for large firms. Testing the significance of the difference between small and large firms points out that the difference is not significant.
Some tests on robustness of the results are done. A model incorpo-rating both productivity effects and demand effects of R&D is also estimated. The model corrects for simultaneity and missing vari-ables. A disadvantage of the model is that it can be used only if there is a demand effect of R&D. Hence in situations closely to perfect competition the model is not suitable. In this study the model is estimated for both small and large firms. The model gives no inter-pretable results for small firms. It appears that for the population of small firms the market situation is close to perfect competition. For the large firms plausible results are found. The estimate of the out-put elasticity for large firms is 0.045 and the estimate of the demand effect is 0.160. These results are close to the results found by Van Leeuwen and Nieuwenhuijsen (1999). They used data for especially large firms. In sum we conclude that the Cobb-Douglas estimates of the output elasticity of R&D expenditures for small and large firms are robust.
References
Acs, Z.J., and D.B. Audretsch (1991), R&D, firm size and innovative activity, in Acs, Z.J., and D.B. Audretsch (ed.), Innovation and Technological Change: An International Comparison, New York: Harvester Wheatsheaf.
Bound, J., C. Cummins, Z. Griliches, B.H. Hall and A. Jaffe (1984), Who does R&D and who patents?, in Z. Griliches (ed.), R&D, Patents, and Productivity, The University of Chicago Press for the National Bureau of Economic Research.
Cohen, W.M., and S. Klepper (1996), A reprise of size and R&D, The Economic Journal, vol. 106, pp. 925-951.
Cohen, W.M., R. Levin and D. Mowery (1987), Firm size and R&D-intensity: a re-exa-mination, Journal of Industrial Economics, vol. 35, pp. 543-565.
Griliches, Z., and J Mairesse (1984), Productivity and R&D at the Firm Level, in Z. Griliches (ed.), R&D, Patents, and Productivity, The University of Chicago Press for the National Bureau of Economic Research.
Hall, B.H., and J. Mairesse (1995), Exploring the relationship between R&D and pro-ductivity in French manufacturing firms, Journal of Econometrics, vol. 65, pp. 263-293. Minne, B. (1997), International battle of giants. The role of investment in research and fixed assets, Onderzoeksreeks Directie Marktwerking, Ministry of Economic Affairs (The Hague).
Nelson, R.R., M.J. Peck and E.D. Kalachek (1967), Technology, Economic Growth and
Public Policy, Washington D.C.: Brookings Institution.
Leeuwen, G. van, and H.R. Nieuwenhuijsen (1999), Distinguishing between
productivi-ty and demand effects of R&D, Research paper no. 9905, Statistics Netherlands. Nooteboom, B. (1994), Innovation and Diffusion in Small Firms: Theory and Evidence,
Small Business Economics, vol. 6, pp. 327-347.
Scherer, F.M. (1984), Innovation and Growth: Schumpeterian Perspectives, Cambridge,
Mass.: MIT Press.
Schankerman, M. (1981), The effect of double counting and expensing on the measured returns to R&D, Review of Economics and Statistics, vol. 63, pp. 454-458.
Schumpeter, J.A. (1942), Capitalism, Socialism and Democracy,Harper and Row (New
York).
Stewart, J. (1991), Econometrics,Philip Allan (Hertfordshire).
Villard, H. (1958), Competition oligopoly and research, Journal of Political Economy, vol. 66, pp. 483-497.
Appendix I: Chow test for
para-meter stability
The Chow test for parameter stability tests the hypothesis that the parameters of a model are equal for different subsamples of the data1. When m categories can be distinguished, based on some qual-itative variable, one can estimate m separate regressions for all dif-ferent subsamples. The Chow test statistic can then be written as fol-lows:
Where
Sr: Sum of squared residuals of regression for complete
sam-ple, i.e. the parameters are restricted to be equal for all subsamples
Si: Sum of squared residuals of regression for subsample i
n: Number of observations
m: Number of subsamples
k: Number of regressors in the model
i: Index denoting subsample.
The null hypothesis that all parameters are equal for all different sub-samples is rejected when the test statistic exceeds the critical value of the F(m-1)k,n-mkdistribution.
In the context of our study, we test the hypothesis that the parame-ters of the Cobb-Douglas production function are equal for SMEs and LEs. The total number of observations (n) equals 203, we distinguish two subsamples (m), namely SMEs and LEs, and the number of regressors (k), including sector dummies and the constant term, in our model is eight. This implies that we must compare the test sta-tistic with the critical value of the F8,187distribution.
Instead of allowing all parameters to vary for the different subsam-ples under the alternative hypothesis, one can also test the alterna-tive hypothesis that the value of only one parameter may have dif-ferent values for difdif-ferent subsamples. In this case one can estimate a restricted model, with all parameters equal for all subsamples, and
allowed to vary. The test statistic is, analogously to equation (A.1), written as
where Srand S represent the residual sum of squares for the restrict-ed and unrestrictrestrict-ed regression, respectively. The value of this test sta-tistic must be compared with the critical value of the Fm-1,[n-(k+m-1)] distribution.
For our study (with n=203, m=2 and k=8, as before) this means we must compare the test statistic with the critical value of the F1,194 distribution.
Appendix II: Derivation of
produc-tion funcproduc-tion and
demand equation
In the underlying appendix, we present the relation between the parameters in the structure model and the reduced model. The struc-ture model consists of a production function and a demand equation. The reduced model consists of three equations. The model has been presented earlier by Van Leeuwen and Nieuwenhuijsen (1999). We start with the following equations for the variables in volumes:
Where:
Qs, Qd,C, L, K, M: Volume of production, demand, capital, labour,
R&D capital1 and intermediate (material) con-sumption
α, β, γ, δ: Output elasticity of capital, labour, R&D capital and material consumption
µ: Disembodied technological development
A: Constant term of production function
D: Constant determining position of demand curve
P: Relative price of final product (compared to
com-petitors)
η: Demand elasticity of price of final products
φ: Effect of R&D capital on position of demand curve
i,t: Indices denoting industry and year.
In logarithms we obtain:
The parameters in equations (3) and (4) cannot be estimated direct-ly since it is not clear which variables are exogenous and endoge-nous. Based on the hypotheses of profit maximization and short-term constant physical and R&D capital, a system of three equations can be derived that can be directly estimated. Derivation is presented below (indices i and t will henceforth be omitted).
We maximize the so-called Lagrangian function and assume that qs
= qd= q:
Appendix II: Derivation of production function and demand equation
Furthermore, lower case symbols refer to the logarithmic transforma-tion of variables. First-order conditransforma-tions give:
We rewrite the demand curve
and define:
Including equations (10) and (11) in equation (8) gives:
For mwe include equations (10) and (11) in equation (9):
With respect to q, including equations (12) and (13) in equation (3) gives:
and
The constants πq, πl and πm in equations (14) through (16) are
important; they depend on sector and year. In the case of panel esti-mates, the constant can even be included in a firm-specific way. In the case of perfect competition and zero impact of R&D on enter-prise sales-opportunities, the equations are less complicated (η=−∞,
ε=1andφ=0). Our data set allows for a complete estimation of the correct system as presented in section 4:
The coefficients πql, πqm, πqc, πqk, πll, πlm, πlc, πlk, πml, πmm, πmcand
πmk are functions of the structure parameters. Equations (17)
through (19) are rewritings of equations (14) through (16).
Equations (15) and (16) prove that, among others, the following rela-tions hold for the coefficients in equarela-tions (17) through (19):
Equation (21) implies that a rise in R&D capital has identical effects on labour and material intermediate consumption. On the basis of equation (20) this also holds for physical capital.
List of Research Reports
The research report series is the successor of both the research paper and the ‘research-publicatie’ series. There is a consecutive report numbering followed by /x. For /x there are five options:
/E: a report of the business unit Strategic Research, written in English;
/N: like /E, but written in Dutch;
/F: like /E, but written in French;
/A: a report of one of the other business units of EIM/Small Business Research and
Consultancy;
/I: a report of the business unit Strategic Research for internal purposes; external avail-ability on request.
9301/E The intertemporal stability of the concentration-margins relationship in Dutch
and U.S. manufacturing; Yvonne Prince and Roy Thurik
9302/E Persistence of profits and competitiveness in Dutch manufacturing; Aad
Kleijweg
9303/E Small store presence in Japan; Martin A. Carree, Jeroen C.A. Potjes and A. Roy
Thurik
9304/I Multi-factorial risk analysis and the sensitivity concept; Erik M. Vermeulen, Jaap Spronk and Nico van der Wijst
9305/E Do small firms’ price-cost margins follow those of large firms? First empirical results; Yvonne Prince and Roy Thurik
9306/A Export success of SMEs: an empirical study; Cinzia Mancini and Yvonne Prince
9307/N Het aandeel van het midden- en kleinbedrijf in de Nederlandse industrie; Kees
Bakker en Roy Thurik
9308/E Multi-factorial risk analysis applied to firm evaluation; Erik M. Vermeulen, Jaap Spronk and Nico van der Wijst
9309/E Visualizing interfirm comparison; Erik M. Vermeulen, Jaap Spronk and Nico
van der Wijst
9310/E Industry dynamics and small firm development in the European printing
indus-try (Case Studies of Britain, The Netherlands and Denmark); Michael Kitson, Yvonne Prince and Mette Mönsted
9401/E Employment during the business cycle: evidence from Dutch manufacturing;
Marcel H.C. Lever and Wilbert H.M. van der Hoeven
9402/N De Nederlandse industrie in internationaal perspectief: arbeidsproduktiviteit,
lonen en concurrentiepositie; Aad Kleijweg en Sjaak Vollebregt
9403/E A micro-econometric analysis of interrelated factor demand; René Huigen, Aad
Kleijweg, George van Leeuwen and Kees Zeelenberg
9404/E Between economies of scale and entrepreneurship; Roy Thurik
9405/F L’évolution structurelle du commerce de gros français; Luuk Klomp et Eugène
Rebers
9406/I Basisinkomen: een inventarisatie van argumenten; Bob van Dijk
9407/E Interfirm performance evaluation under uncertainty, a multi-dimensional frame-work; Jaap Spronk and Erik M. Vermeulen
9408/N Indicatoren voor de dynamiek van de Nederlandse economie: een sectorale
analyse; Garmt Dijksterhuis, Hendrik-Jan Heeres en Aad Kleijweg
9409/E Entry and exit in Dutch manufacturing industries; Aad Kleijweg and Marcel
Lever
9410/I Labour productivity in Europe: differences in firm-size, countries and industries; Garmt Dijksterhuis
9411/N Verslag van de derde mondiale workshop Small Business Economics; Tinbergen
Instituut, Rotterdam, 26-27 augustus 1994; M.A. Carree en M.H.C. Lever
9412/E Internal and external forces in sectoral wage formation: evidence from the
Netherlands; Johan J. Graafland and Marcel H.C. Lever
9413/A Selectie van leveranciers: een kwestie van produkt, profijt en partnerschap?;
F. Pleijster
9414/I Grafische weergave van tabellen; Garmt Dijksterhuis
9501/N Over de toepassing van de financieringstheorie in het midden- en kleinbedrijf;
Erik M. Vermeulen
9502/E Insider power, market power, firm size and wages: evidence from Dutch
manu-facturing industries; Marcel H.C. Lever and Jolanda M. van Werkhooven
9503/E Export performance of SMEs; Yvonne M. Prince
9504/E Strategic Niches and Profitability: A First Report; David B. Audretsch, Yvonne M. Prince and A. Roy Thurik
9505/A Meer over winkelopenstellingstijden; H.J. Gianotten en H.J. Heeres
9506/I Interstratos; een onderzoek naar de mogelijkheden van de Interstratos-dataset;
Jan de Kok
9507/E Union coverage and sectoral wages: evidence from the Netherlands; Marcel H.C.
Lever and Wessel A. Marquering
9508/N Ontwikkeling van de grootteklassenverdeling in de Nederlandse Industrie; Sjaak
Vollebregt
9509/E Firm size and employment determination in Dutch manufacturing industries;
Marcel H.C. Lever
9510/N Entrepreneurship: visies en benaderingen; Bob van Dijk en Roy Thurik
9511/A De toegevoegde waarde van de detailhandel; enkele verklarende theorieën tegen
de achtergrond van ontwikkelingen in distributiekolom, technologie en externe omgeving; J.T. Nienhuis en H.J. Gianotten
9512/N Haalbaarheidsonderzoek MANAGEMENT-model; onderzoek naar de
mogelijkheden voor een simulatiemodel van het bedrijfsleven, gebaseerd op gedetailleerde branche- en bedrijfsgegevens; Aad Kleijweg, Sander Wennekers, Ton Kwaak en Nico van der Wijst
9513/A Chippen in binnen- en buitenland; De elektronische portemonnee in kaart
gebracht; een verkenning van toepassingen, mogelijkheden en consequenties van de chipcard als elektronische portemonnee in binnen- en buitenland; drs. J.
9601/N Omzetprognoses voor de detailhandel; Pieter Fris, Aad Kleijweg en Jan de Kok 9602/N Flexibiliteit in de Nederlandse Industrie; N.J. Reincke
9603/E The Decision between Internal and External R&D; David B. Audretsch, Albert J. Menkveld and A. Roy Thurik
9604/E Job creation by size class: measurement and empirical investigation; Aad
Kleijweg and Henry Nieuwenhuijsen
9605/N Het effect van een beursnotering; drs. K.R. Jonkheer
9606/N Een Micro-werkgelegenheidsmodel voor de Detailhandel; drs. P. Fris
9607/E Demand for and wages of high- and low-skilled labour in the Netherlands;
M.H.C. Lever and A.S.R. van der Linden
9701/N Arbeidsomstandigheden en bedrijfsgrootte. Een verkenning met de
LISREL-methode; drs. L.H.M. Bosch en drs. J.M.P. de Kok
9702/E The impact of competition on prices and wages in Dutch manufacturing
indus-tries; Marcel H.C. Lever
9703/A FAMOS, een financieringsmodel naar grootteklassen; drs. W.H.J. Verhoeven
9704/N Banencreatie door MKB en GB; Pieter Fris, Henry Nieuwenhuijsen en Sjaak
Vollebregt
9705/N Naar een bedrijfstypenmodel van het Nederlandse bedrijfsleven; drs. W.H.M.
van der Hoeven, drs. J.M.P. de Kok en drs. A. Kwaak
9801/E The Knowledge Society, Entrepreneurship and Unemployment; David B.
Audretsch and A. Roy Thurik
9802/A Firm Failure and Industrial Dynamics in the Netherlands; David B. Audretsch,
Patrick Houweling and A. Roy Thurik
9803/E The determinants of employment in Europe, the USA and Japan; André van Stel
9804/E PRISMA’98: Policy Research Instrument for Size-aspects in Macro-economic
Analysis; Ton Kwaak
9805/N Banencreatie bij het Klein-, Midden- en Grootbedrijf; Henry Nieuwenhuijsen,
Ben van der Eijken en Ron van Dijk
9806/A Milieumodel; drs. K.L. Bangma
9807/A Barriers for hiring personnel; Jacques Niehof
9808/A Methodiek kosten en baten Arbowetgeving; drs. K.M.P. Brouwers, dr. B.I. van
der Burg, drs. A.F.M. Nijsen en ir. H.C. Visee
9809/E Business Ownership and Economic Growth; An Empirical Investigation; Martin
Carree, André van Stel, Roy Thurik and Sander Wennekers
9810/E The Degree of Collusion in Construction; M.H.C. Lever, H.R. Nieuwenhuijsen
and A.J. van Stel
9811/E Self-employment in 23 OECD countries; Ralph E. Wildeman, Geert Hofstede,
Niels G. Noorderhaven, A. Roy Thurik, Wim H.J. Verhoeven and Alexander R.M. Wennekers
9812/E SICLASS: Forecasting the European enterprise sector by industry and size class; Niels Bosma and Ton Kwaak
9901/E Scanning the Future of Entrepreneurship; drs. N.S. Bosma, drs. A.R.M.
Wennekers and drs. W.S. Zwinkels
9902/E Are Small Firms Really Sub-optimal?; Compensating Factor Differentials in Small Dutch Manufacturing Firms; David B. Audretsch, George van Leeuwen, Bert Menkveld and Roy Thurik
9903/E FAMOS; A size-class based financial analysis model; W.H.J. Verhoeven and E.A.
van Noort
9904/E Conduct and Performance in Dutch Manufacturing; An Application of
Appelbaum 1982 with a Plausibility-Check; Frank A. Hindriks, Henry R. Nieuwenhuijsen and Adriaan J. van Stel
9905/E Non-competitive Rents in Dutch Manufacturing; Conduct and Performance in
the New Empirical Industrial Organization; Frank A. Hindriks
9906/E A human-resource-based theory of the small firm; Charlotte Koch and Jan de
Kok
9907/N Van werknemer naar ondernemer; Een hybride of directe start?; ir. H.C. Visee
en drs. W.S. Zwinkels
