COMPROBACIÓN DEHIPÓTESIS:

Following the growth accounting framework introduced by Solow (1957) and Jorgen- son - Griliches (1967), logarithmic di¤erentiation is applied to the accounting identity (4.4) in order to calculate the growth contributions of the input factors (L; K; R) in the production function (4.3). Thereby two crucial assumptions are needed: constant returns to scale and factor compensation according to their marginal return on GVA. 79_{It will become clear in the next sections that the compensation of traditional tangible capital}

R&D as investment in Growth Accounting 91

Then the sources of growth equation equals

lnYt=sLt lnLt+sKt lnKt+sRt lnRt+ lnt (4.5)

with indicating the changes between periods t and t 1 and with s as revenue shares. lnt represents the contribution of TFP. The revenue shares s are de…ned in the following way as two-period averages:

sL_t = 1 2 PL t Lt PY t Yt + P L t 1Lt 1 PY t 1Yt 1 (4.6) sK_t = 1 2 P_tKKt PY t Yt + P K t 1Kt 1 PY t 1Yt 1 sR_t = 1 2 PR t Rt PY t Yt +P R t 1Rt 1 PY t 1Yt 1

Due to the assumption of constant returns to scale it is ensured that these shares sum up to one. This speci…cation has also been used in the EU KLEMS database on which this chapter will build in the next sections80_{. The analysis is conducted on the industry}

level whereby industry-subscripts are omitted for clarity purposes.

How can this procedure be implemented? As described in the next section, the primary source of data are national accounts which provide data on GVA on the in- dustry level as well as on labour compensation (PL

t Lt). The di¤erence between these

two must be equal to total capital compensation (PK

t Kt+PtRRt). Having data on the

(R&D) capital stock and estimates on the user cost of the respective stock (PK t and

PR

t ) allows us to split this sum into its di¤erent asset types. Thereby, also tangible

capitalK can be divided into several asset types, for example in IT and Non-IT assets. Here, it is reasonable to assume that investors are indi¤erent between two investment opportunities if they yield the same return such that the following arbitrage condition must hold by de…ningPU

k;t as user cost andPk;tInv as investment price of assetk at time

t:

P_k;tInv +P_k;tU₊₁+ (1 k)Pk;tInv+1 =itPk;tInv (4.7)

R&D as investment in Growth Accounting 92

So, an investor is indi¤erent between an investment in asset k purchased at its invest- ment pricePInv

k;t (PtI w.r.t. tangible capital investment andPtN w.r.t. R&D investment

following the previous notation), lending this asset which generates revenues accord- ing to its user cost PU

k;t+1 and selling the depreciated asset in the next period for

(1 k)Pk;tInv+1 on the one hand and earning a nominal rate of return i by using the

money for an alternative investment opportunity on the other hand. This must hold for every asset type k, either tangible capital or R&D capital. Solving (4.7) for PU

k;t

gives the cost of capital equation as used by EU KLEMS:

P_k;tU =P_k;tInv₁it+ kPk;tInv (P Inv k;t P

Inv

k;t 1) (4.8)

Now, it must be clari…ed which nominal rate of return i is applied here. There are two competing procedures: either an appropriate exogenous value is assumed ex- ante or the rate of return is calculated endogenously ex-post as a residual. The …rst approach uses, for example, government bond rates. The latter, which is used in this chapter, ensures perfect consistency between income and production accounts81_.

Therefore i is calculated as a residual such that overall capital compensation for all assets (calculated as GVA minus labour compensation) is exhausted and the arbitrage condition (4.7) holds. Due to this procedure the ex-post calculated rate of return is also called internal rate of return. Following the EU KLEMS procedure (see EU KLEMS 2007, p.34) but integrating R&D as an asset type k and de…ning Cap as the sum of tangible capital K and R&D capitalR, the nominal rate of return becomes

it= PY t Yt PtLLt+ P k (PInv k;t Pk;tInv1)Capk;t P k PInv k;t kCapk;t P k PInv k;t 1Capk;t (4.9)

with P_tYYt PtLLt as the equivalent for total capital compensation. This rate of

return must be the same for all assets but it is allowed to vary across industries (and countries) because the procedure presented in this section is applied separately on the industry level. Of course, one might argue that the arbitrage condition (4.7) should also hold across industries. But this would, of course, violate the consistency between

R&D as investment in Growth Accounting 93

income and production accounts and contradict the general assumption in classical growth accounting that production factors are paid according to their social marginal productivity.

Finally, in order to aggregate several asset types into one measure of capital services, as for example lnKt in (4.5), the di¤erent marginal products (as for example of

investments in IT and machineries) must be considered by an appropriate weighting procedure which employs the corresponding user cost of capital calculated in (4.8). R&D capital might be integrated in this procedure as well or be treated separately in order to identifyRt in (4.5). The aggregation looks as follows:

lnKt = X k vk;t lnKk;t with k 6=R&D (4.10) vk;t = 1 2(vk;t+vk;t 1) and vk;t=P U k;tKk;t=( X k P_k;tUKk;t)

In the …nal parts of this section, I will discuss some crucial assumptions that are essential in the growth accounting framework and especially focus on the depreciation rate of (R&D) capital.