The cyclicality of R&D investment revisited

1 INTRODUCTION

The relation between research & development investments (R&D) and the business cycle has been studied in a large number of papers. From a theoretical point of view, Schumpeter (1939) argued that investments in innovation were countercyclical since the opportunity costs in times of a recession were lower than in an upswing. Empirical evidence on the relation between R&D and economic growth, however, suggests procyclicality. Fabrizio and Tsolmon (2014), henceforth denoted by FT, listed many references that concluded that there was a positive relation between R&D and industry output growth. From a theoretical point of view, Francois and Lloyd-Ellis (2009) reconciled Schumpeter's theory with the empirical findings by pointing out that innovation was more than only R&D and that other innovative activities might exhibit different business cycle properties. On the other hand, if we look at the empirical literature the evidence is much more heterogeneous than pointing only at procyclicality. For example, Aghion, Askenazy, Berman, Cette, and Eymard (2012) allowed for heterogeneous impacts of the business cycle and found mixed results, whereas Kraiczy, Hack, and Kellermanns (2015), for example, found no relation between R&D and the business cycle. On closer inspection, FT also found mixed effects: Although for most firms procyclical R&D investments are estimated, for some firms countercyclical R&D investments are found. Because in FT the marginal effects depend on (i) the levels of patent protection, (ii) the rate of product obsolescence, and (iii) the degree of external financing, cyclicality is heterogeneous.

There are several reasons why such ambiguous results are found. In general it can be stated that none of the studies above use the same model. Differences can be found in the definition of the dependent variable (R&D, log(R&D), yes or no R&D, etc.), differences in the covariates (none, only lags, lags and leads, firm characteristics, etc.), and functional form (linear, nonlinear). Furthermore, the character of the data (time series, cross-section, panel) and the estimation method (random effects, fixed effects, ignoring the panel character) can differ. In this investigation we will compare the methods used in two related papers to establish whether the conclusions of the papers hold in different settings. We will analyze the research of FT more deeply and compare it with Barlevy (2007). FT starts from the model used by Barlevy and allows for the effect of output growth to be different across the levels of patent protection, product obsolescence, and external financing of the industry that the firm belongs to experiences. Apart from using a different data set, FT also use a different, but related, estimation technique and use controls that are different in one important aspect: They use first-differenced explanatory variables instead of level variables in their specification. To make the analysis comparable we will estimate the model of Barlevy and extend it according to the suggestions of FT using the same data and the same estimation method. The results are in Section 2. In Section 3, we improve on the treatment of missing values of R&D expenditures, and reestimate the models to see whether the conclusions are robust. In Section 4 we discuss some related models and specifications, and Section 5 concludes.

2 THE MODELS OF FABRIZIO AND TSOLMON 2014 AND BARLEVY 2007

The starting point of FT in their analysis of the cyclicality of R&D is the first-differenced model of R&D based on Barlevy (2007) and reads

(1)

where Δ is the first-differencing operator, R&D_kt is the natural logarithm of real R&D investments of firm k in year t, X_it is the log industry output relating to the industry i to which firm k belongs in year t, and M_kt denote firm-level controls, contemporary and one period lagged. τ_t are time fixed effects. This model is extended with some interaction terms that will be discussed later and then estimated by pooled ordinary least squares (OLS). Note that the addition of the constant β₀ indicates that FT allow for the possibility that there is a trend in the level of R&D expenditures.

The model of Barlevy (2007) actually differs in some important aspects. First, Barlevy estimates the relation between the growth in R&D and the growth in output using a fixed-effects or within estimator. Furthermore, Barlevy uses related but different controls. His model reads

(2)

where α_k denote firm-specific effects. The presence of the constant β₀ is questionable, but this bears no significance because it is not identified in a fixed-effects estimation as employed by Barlevy. This means that if firm-specific effects exist and if they correlate with one or more of the regressors, estimating Equation 1 with pooled OLS—that is, what is actually done by FT—will yield biased estimates, whereas estimation of Equation 2 with the fixed-effects estimator still gives unbiased results. Finally, note that Barlevy uses level controls and not first-differenced controls in his specification.

Cyclicality of R&D expenditure is represented by a nonzero effect of industry output (growth): β₁ ≠ 0. Procyclicality would be represented by β₁ > 0 and countercyclicality by β₁ < 0.

As revealed in footnote 4 of FT, the first-differenced model is only introduced because the model in levels displays autocorrelation and heteroskedasticity. 1In fact, it further removes possible endogeneity due to higher-order fixed effects. To show this, rewrite Equation 1 in level variables:

(3)

First differencing this model gives Model 1 with τ_t = θ_t − θ_t − 1 and ω_kt = ς_kt − ς_kt − 1. Note that first differencing takes care of the potential endogeneity due to the correlation between the firm-specific effect η_k and X_it and/or M_kt, and that η_k creates autocorrelation for sure and quite likely creates heteroskedasticity. If we compare the models in Equations 1-3, they are clearly related and Model 2 seems to be a special mix of Models 1 and 3. It allows for what is known as incidental trends (α_k), whereas Model 1 does not.

From rewriting the model in level variables it is also clear that the constant added to the model by FT, their β₀ in the first-differenced specification, represents a time trend in R&D. FT then proceed by adding their most important variables to the model: measures of industry-level obsolescence (Ob_i), patent effectiveness (PE_i) and external financing (EF_i) both as interactions with growth in industry output and as level variables. These last variables are not explicitly stated in the equation listed on page 666 (second column) of FT, but their inclusion is clear from the regression output in table 5 of FT and from the supplementary material provided by the authors. Adding the level variables is sound econometrics but, as we will see in a moment, it has some unintended consequences for the starting model that uses R&D in levels. The most elaborate model of FT is

(4)

What FT do is to allow for heterogeneous effects of industry output growth on the growth in R&D expenditures where the heterogeneity depends in Ob, PE, and EF. FT expect β₄ > 0—that is, with higher degree of obsolescence, firms will be more sensitive to changes in demand—and β₅ < 0; that is, with higher degree of patent protection, firms will be less sensitive to changes in demand. No discussion of the expected signs of β₆, δ₄, δ₅, and δ₆ is provided; in fact, they are not mentioned at all by FT except in the estimation output. As a consequence of the interaction effects, the effect of the cyclicality of R&D expenditure has become heterogeneous. The marginal effect of industry output growth on R&D growth is now

and, depending on the sign of the parameters and the level of the covariates, it can indicate procyclicality for some firms and countercyclicality for others.

The meaning of δ₄, δ₅, and δ₆ becomes clear if we reformulate Model 4 in level variables. As in the case of the added constant, adding the time constant variables to a first-difference specification gives rise to a trend in the level variable. In the present case, there is not only a pure time trend β₀·t but also three heterogeneous incidental time trends: δ₄·Ob_i·t , δ₅·PE_i·t and δ₆·EF_i·t. This specification can be correct, but FT do not provide theoretical or empirical arguments why adding these variables to the specification is a good idea. On top of that, the effects of these variables are only identified if no incidental trends are present. If we would actually follow the estimation method of Barlevy (2007)—that is, using a fixed-effects estimation—we would allow for firm-specific effects in Equation 1 which might potentially be correlated with the explanatory variables of Equation 1. If there is indeed correlation, then pooled OLS is not the correct estimation method to use, and a fixed-effects or first-difference estimation will not identify the constant and the parameters of Ob_i, PE_i and EF_i. Consequently, the estimation results of FT are only correct under the additional assumption of no incidental trends that Barlevy does not make.

We will now proceed with a replication of the estimation results of FT. In the next section we present estimation results of some alternative models that are less deviant from Barlevy (2007) to investigate whether the results of FT hold under less restrictive assumptions and alternative specifications.

3 TREATING MISSING OBSERVATIONS DIFFERENTLY

A simple diagnostic scatter graph of the dependent variable and the fitted values reveals an interesting problem. The scatter plots in Figure 1 display the dependent variable in the regressions in Table 1 (x-axis) and the fitted values from the regression of Model 1 (y-axis). In the left figure, on both the y- and x-axis there is an unusual concentration of points. Closer inspection of the files supplied by FT in the data archive of the Review of Economics and Statistics reveals that missing observations on R&D expenditures and some other variables are replaced by zeros. This results in a large number of zero R&D observations (38.2% of the 71,264 observations) and this explains the concentration of points on the y-axis. Another consequence of putting the log R&D expenditures to zero are extreme positive and negative changes in the R&D growth rates: If for a certain firm R&D is not observed in a certain year and it is observed in the next year, the growth rate is calculated to be huge if R&D is set to zero. The other way around generates very negative growth rates. 2We corrected the data by leaving the missing observations untouched, and this resulted in 40,922 remaining observations that are plotted in the right-hand scatter in Figure 1. Although the growth rates are still quite large in absolute value in some cases, the problem appears to have been solved to a large extent. We will use this restricted data set in the remaining part of this paper and indicate it by OGGB in Tables 2 and 3.

Columns (4)–(6) in Table 1 and columns (5)–(8) in Table 2 contain the same estimations as in the earlier columns but using the corrected data. If we only look at the estimated signs of the coefficients in Table 1, by and large the conclusions with respect to the FT specification do not change. The estimated coefficients are usually closer to zero and the significance appears to have reduced somewhat despite the calculated standard errors being smaller. We also find smaller R²s. The significance of obsolescence and patent effectiveness remains. If we concentrate on the full model as displayed in column (6), actually only obsolescence and patent effectiveness themselves have a significant impact. However, the significance of the interaction terms is lost. Note that none of the variables related to output growth are significant. For most firms there is procyclicality of the R&D expenditures, and this is stronger if the corrected data are used and if we judge this by the number of firms with procyclical R&D. However, the average marginal effect of output growth has reduced to 9%. Table 2, columns (5)–(8) display larger and more significant results than Table 2, columns (1)–(4). As in Barlevy (2007), the estimates of the effect of output growth while controlling for balance sheet variables are now strongly significant.

4 RECONCILIATION AND ALTERNATIVE SPECIFICATIONS

We will now proceed with estimating some alternative models to make the analyses more comparable. We start by rewriting the model estimated by FT in levels and then proceed to estimate this equation with a fixed effects estimation. A crucial observation here is that FT introduce a constant and three time-constant explanatory variables (Patent Effectiveness, Obsolescence, and External Financing) in the model they estimate. 3 If we rewrite the model actually estimated by FT—that is, the model in Equation 4—in level variables we obtain

(5)

As such, this model can make perfect sense, but in their discussion of R&D investments, indeed as a level variable, the growth in R&D investment is only introduced when discussing their empirical model. FT do not discuss time trends in general and time trends related to patent effectiveness, obsolescence and external financing in particular. If we review the results in Table 1, we can conclude that there is in general a negative trend in R&D expenditures but that this negative trend is less negative or even positive for firms with relatively high degrees of patent effectiveness, obsolescence and/or external financing.

The model in Equation 5 is, as far as we are aware, never used in the literature on R&D investments. Furthermore, as becomes clear from footnote 4 of FT, the authors are actually interested in estimating R&D in levels but resort to using first-differenced variables to mitigate the problems of autocorrelation and heteroskedasticity. 4If we estimate Equation 5 with a first-difference estimation, the results of FT as they presented in table 5 will be found, apart from the standard errors that are calculated somewhat differently. Now consider a model which is in line with the discussion of FT 5

(6)

The difference from Equation 5 is that we deleted all variables related to the trend. We estimate this model using the fixed-effects estimator. Due to using this estimator the effects of the time-constant explanatory variables cannot be estimated. 6The relevant estimation results are presented in Table 3, column (1). Note that the estimations now are performed on 45,061 observations. The conclusions we can draw from the estimation results in Table 3, column (1) are quite different from the conclusions from Table 1, column (6). The effect of industry output growth remains insignificant, although the sign has changed. The effect of patent effectiveness and obsolescence on the impact of industry output growth has also changed: Using a fixed-effect estimation reverses the sign and maintains insignificance. The signs are now contrary to the theoretical predictions of FT. This can signal two things: Either the model estimated is not the correct model and the model estimated by FT represents reality better, or there is a tendency in the direction of acyclical R&D expenditures for firms in industries with higher patent effectiveness and with lower levels of obsolescence. Finally, the effect of external financing remains positive but has become strongly significant. With respect to heterogeneity we can conclude from the average marginal effects of output growth on R&D expenditures that the procyclicality of R&D is even stronger in this alternative model: Procyclicality is found for 95.2% of the firms whereas it was 88% in Table 1.

We now turn to using the same controls as Barlevy (2007). Instead of controls specified as first differences, Barlevy uses level variables. The results, using pooled OLS as FT do, are presented in Table 3, column (2). The results are far from significant, apart from the interaction term relating to external financing. The effect of obsolescence in combination with output growth is again corresponding to the theoretical expectations of FT, although far from significant. The average marginal effect of output growth for this model is quite large (almost 24%), and the number of firms with countercyclical R&D is very small (2.5%).

If we now estimate the same model using a fixed-effects estimation, which is the estimation method used by Barlevy (2007), except that three interactions are used as additional regressors, we obtain Table 3, column (3). All significance of the reported coefficients is lost and incidental trends appear to be nonexistent. Note that the R² is in line with the previous results, so any significance derives from the control variables.

The same conclusion follows if we estimate the model of FT, see Table 1, and therefore use controls in differences, but not applying pooled OLS but the fixed-effects estimator. The results are in Table 3, column (4). As explained before, the effects of the time-constant explanatory variables cannot be estimated.

Due to the lack of significance, we conclude that it is not necessary to allow for second-order fixed effects as suggested by Barlevy (2007). If we concentrate only on the signs of the estimated coefficients, the conclusions are very similar to those following from Table 1. There is almost a one-to-one correspondence of the signs (14 out of 16 cases). However, as noted, almost all significance is lost. With respect to heterogeneity, only the external financing cross term is significant but this is precisely the variable that is not emphasized in FT. In fact, it is hardly discussed by them apart from entries in regression tables.

Although not very well known in economics, 7it is actually possible to estimate the effect of time-constant explanatory variables while allowing for fixed effects. In a complete linear setting this was first discussed by Mundlak (1978). He proved that if the fixed effects are linearly related to the time averages of the time-varying explanatory variables, adding these time averages to the model and estimating with either random-effects estimation or the pooled-regression estimation will yield the fixed-effect estimates. These are the estimated effects of the time-varying explanatory variables. What appears to be less well known is that Mundlak's assumption of linearity is superfluous. The result actually holds without specifying the relation between the fixed effects and the explanatory variables. Furthermore, even the standard errors calculated in the random-effects estimation are correct; that is, they are the same as the standard errors calculated if the fixed-effects estimator would have been used. 8Because we can actually use a random-effects estimator to calculate the fixed-effects estimator, we can also add time-invariant explanatory variables and their effects are indeed identified. However, for consistency we need to make the assumption that these time-invariant explanatory variables are not correlated with the fixed effects. Note that this assumption is implicitly made by FT also. The model in the Mundlak specification reads

The random-effect estimator gives the following effects of time-constant variables: Obsolescence: −0.562 (SE = 0.427), Patent Effectiveness: 8.993 (SE = 1.498), and External Financing:−0.282 (SE = 0.241) on R&D. Only the effect of Patent Effectiveness is significant and has the same sign as reported in FT.

Our conclusion is that if the same explanatory variables and appropriate estimation methods are used, the heterogeneity of cyclicality of R&D investment found by FT is reduced considerably. Heterogeneity appears to be dependent especially on the external financing of the firm. Just like FT, we do find procyclicality for the vast majority of firms.

Finally, we conduct two robustness checks as suggested by one of the referees. Barlevy (2007) and Fabrizio and Tsolmon (2014) both relate R&D to industry output. Although this reduces firm-specific idiosyncrasies, using firm-specific output appears to be the more direct measure and this is more in line with the hypotheses of Schumpeter (1939). In Table 4, columns (1)–(4), we therefore present estimates of the same specifications as in Table 3 but replacing industry output by firm output. The estimation results are very similar: The vast majority of firms appear to display procyclical R&D investments and there is heterogeneity but mainly with respect to external financing. Compared to Table 3, the sign of this variable has changed, indicating that depending more on external financing tends to make R&D expenditures less procyclical.

From Table 2 of FT it is clear that the growth in R&D attains some unrealistically high values in absolute sense: the minimum of the growth rate is −1,169% and the maximum 1,294%. As discussed, these large growth rates are partly due to replacing missing observations on R&D by zeros and adding 1 to the logarithm. Apart from our doubt regarding whether these figures can be correct, there is also another problem. The difference of the year-to-year log of R&D only measures the growth rate for relatively small changes. To investigate this we restrict the sample to R&D growth rates of 50% or less (in absolute values). 8This reduces the number of observations from about 45,000 to about 37,000. The estimation results, again for the same specification as in Table 3, are in columns (5)–(8) of Table 4. The overall conclusions do not change: More than 90% of the firms display procyclical R&D expenditures and there is heterogeneity again, but only due to external financing.

5 CONCLUSION

In this paper we replicated Fabrizio and Tsolmon (2014) and Barlevy (2007). The results of FT were retrieved almost precisely whereas significance was lost in the Barlevy specification. Significance of the Barlevy estimates was restored after having corrected the data, whereas the overall conclusion of FT remained the same after this correction. If we use suitable (fixed-effects) estimation methods, no significance was found for the key factors of Fabrizio and Tsolmon obsolescence and patent effectiveness. Heterogeneity of the cyclicality of R&D expenditures remained due to the external financing interaction term. These conclusions were corroborated when we generalized to firm-specific output growth instead of industry-specific output growth and when we restricted the sample to more realistic growth numbers of R&D.

Finally, our replication confirms the procyclicality of R&D expenditures as found by Barlevy (2007) and the heterogeneity of the procyclicality as found by Fabrizio and Tsolmon (2014), although the heterogeneity estimated by econometrically sound specification and estimation methods is quite different in nature.