Assessing measurement errors in the CDM research–innovation–productivity relationships

ABSTRACT

The Crépon-Duguet-Mairesse 1998 article, known as CDM, initiated a structural econometric framework to analyze the relationships among research, innovation and productivity, which has been estimated most generally on the basis of cross-sectional innovation survey-type data. Some econometric implementations of the CDM approach have suggested that such data give useful but imprecise measures of the innovation output (share of innovative sales), and to a lesser degree of the innovation input (R&D). These ‘measurement errors’ may result in attenuation biases of the estimated R&D and innovation impact elasticities in the two basic CDM ‘roots’ relations of R&D to innovation and innovation to productivity, as well as in the extended production function à la Griliches linking directly R&D to productivity. Using a panel of three waves of the French Community Innovation Survey (CIS), we assess these biases and the magnitude of the underlying measurement errors, assuming mainly that they are ‘white noise’ errors. We do so by comparing two pairs of usual panel estimators (Total and Between) in both the cross-sectional and time dimensions of the data (Levels and Differences). We find large measurement errors on innovation output in the innovation–productivity equation, resulting in large attenuation biases in the related elasticity parameter. We also find smaller but sizeable measurement errors on R&D, with significant attenuation biases in the corresponding elasticity estimates, in the R&D–innovation equation and the extended production function. Simulations suggest that the measurement errors on innovation and R&D are unaffected by similar measurement errors on the capital variable.

KEYWORDS:

• Measurement errors
• classical errors-in-variables
• attenuation bias
• R&D
• innovation and productivity

JEL CLASSIFICATION:

• C18
• C23
• C33
• O30
• O31
• O33

Notes

1. Mairesse (1990) discusses the importance of measurement errors on physical capital stocks in Cobb–Douglas production functions estimated with panel data.

2. In addition, ‘intermediate’ CIS (CIS 2006 and CIS 2010) have been conducted, but they generally involve a smaller number of firms and/or a lighter questionnaire than the ‘regular’ CIS. There also is, a prototype innovation survey that was conducted in 1991 and is known as CIS 0 or CIS1990. This survey is the one that has been used in the original CDM study.

3. We have also used the prototype survey CIS1990 to construct a companion panel data sample to the one used here, in order to assess innovation persistence and to use the firm innovation binary indicator in 1990 to control for initial conditions in our three R&D, innovation and productivity relations, instead of including firm fixed effects. Besides showing a very high degree of persistence the differences we find in the estimated parameters of interest are actually not striking and we only report them in the working paper version of this analysis.

4. This is because R&D and innovation persistence (or autocorrelation) measured over four years can be expected to be less than over two years. See Mairesse (1990) and Griliches and Mairesse (1998), who strongly make the point that the OLS attenuation biases from classical (or approximately classical) errors-in-variables are strongly exacerbated when one performs regressions in first-differences instead of levels, or, alternatively, when one controls for fixed effects. The variability of the variables affected by measurement errors is much reduced relatively to that of such errors, insofar as these variables are often very persistent (that is strongly autocorrelated) while the measurement errors are non-autocorrelated or weakly so.

5. Note also that r is also the residual of the regression of x* on all other regressors since it is assumed that e is not correlated with x, nor with possible errors of measurement in other regressors, such as for us here the stock of physical capital.

6. We could have also computed the Within Level (WL) and Within Difference (WD) estimators, and have basically compared any pair of estimates of the six usual panel data estimates (TL), (BL), (WL), (TD), (BD) and (WD) to retrieve an estimate of the relative size of the measurement error (assuming it is the only source of misspecification). We thought clearer and preferable to do as we do here, since the pair of (TL) and (BL) estimators do not take into account firm fixed effects, while the pair of (TD) and (BD) estimators take care of them. Note that the (WL) estimator takes care of fixed effects and the (WD) estimator takes care of both firm fixed effects and firm fixed time trends.

7. Since our panel is very short (T=3), note that the variance of the measurement error is always twice . Note also that is only three times higher than and that it is also equal to and not higher as it would be in panels with a longer time dimension.

8. Note that if can assume that x follows an AR(1) stable autoregressive process of order 1:

we can obtain formulas that generalize the ones for σ² _e in the four dimensions TL, BL, TF and BD of the panel data we consider. Under this assumption, we can also write that:

Hence for an approximate value of (ρ⁴ _x) we can compute (ρ_x) and thus the estimates of λ_TD and λ_BD we would have obtained if we had in Difference a panel of one-year differences instead of a panel of four-year differences. Hence λ_TD, if we could compute it over one-year differences, would be (1/ ρ³ _x) higher than λ_TD as we actually estimate on four-year differences. For example, with (ρ⁴ _x) = 0.66, the order of magnitude we observe for R&D, we have (ρ_x) = 0.9 and the one-year difference λ_TD would be about equal to 1.35 times the four-year difference λ_TD.

9. CIS surveys also provide a binary indicator of the introduction of an innovation, and allow researchers to build a dummy variable indicating whether a firm performs R&D on a continuous basis or not. It seems that these two dummy variables are likely to be less biased by measurement errors than the two continuous variables on which we focus here (see Mairesse, Mohnen, and Kremp 2005). These continuous variables, however, have been used in the original CDM model and are usually preferred by researchers.