The impact of public R&D subsidy on small firm productivity: evidence from Korean SMEs

Abstract

This paper explores the effects of R&D promotion policy on SME performance. We use a large panel data set on public R&D subsidies to Korean manufacturing firms. We control for counterfactual outcomes employing the DID (difference in differences) estimation procedure as well as for the endogeneity of the R&D investment and the R&D subsidy using the 2-stage Tobit/Logit DPD (dynamic panel data) procedure. We find significant evidence for positive effects of the public R&D subsidy on both the R&D expenditure and the value added productivity of Korean manufacturing SMEs. The policy thus appears to have been successful in fostering technological advancement and in promoting economic growth.

Appendices

Appendix 1

In this appendix we show the equivalence in estimating policy parameter γ ₂ between the first difference estimator and the standard panel estimator used in this paper.

Let D _i,t be a zero–one indicator that equals unity if firm i received the subsidy at time t and zero otherwise. Adding a cross-product term of private R&D investment and public subsidy to reflect the fact that the subsidy can affect labor productivity indirectly by promoting private R&D investment, and re-expressing Eq. (1) gives us the following dynamic labor productivity model:

$$q_{i,t} = \beta_{0} + \gamma_{1} R_{i,t} + \gamma_{2} { (}D_{i,t} \times R_{i,t} ) + X_{i,t}^{\prime } \beta + \eta_{i} + \varepsilon_{i,t}$$

(3)

where labor productivity q = ln(Q/L), R&D investment per employee R = ln(R&D/L), γ ₂ reflects the indirect subsidy effect on productivity, X is a vector of explanatory variables such as capital intensity ln(K/L), number of employees ln(L), education and job training expenses per employee ln(Edu/L) and Age ln(Age), η _i denotes a time-invariant effect unique to firm i, and ε _i,t is a time varying error distributed independently across firms and independently of all η _i.

Estimation of model (1.1) as a special case of the error component model has been discussed in the literature. When η _i is a random component with a distribution independent of the observed right-hand side variables, then conventional generalized least squares produces a consistent and efficient estimator.

However, if the firm specific effect, η _i is correlated with ε _i,t then OLS estimation of the policy parameter γ ₂ in Eq. (3) could produce simultaneity bias. A popular way of getting consistent estimators involves first differencing Eq. (1) (main section) over time:

$$\Delta q_{i,t} = \gamma_{1} \Delta R_{i,t} + \gamma_{2} { (}\Delta D_{i,t} \times \Delta R_{i,t} ) + \Delta X_{i,t}^{\prime } \beta + \Delta \varepsilon_{i,t}$$

(4)

The first differencing eliminates the unobservable time-invariant firm-specific effects which can cause endogeneity of R _i,t or D _i,t in Eq. (1). Suppose, for simplicity, that the sample consists of only two periods: period (t − 1) which is before the firm receives the subsidy for technology development and period t. Let the group S represent the firms which are subsidized and the group N represent the firms which are not subsidized. As Lach (2002) suggests, if Eq. (3) is applied to the firms without a subsidy at (t − 1), D _i,t−1 = 0, then ΔD _i,t  = D _i,t and thus we get:

$$\Delta q_{i,t} = \gamma_{1} \Delta R_{i,t} + \gamma_{2} { (}D_{i,t} \times \Delta R_{i,t} ) + \Delta X_{i,t}^{\prime } \beta + \Delta \varepsilon_{i,t}$$

(5)

From (5), it follows that:

$$\begin{array}{*{20}l} {E(\Delta q_{i,t}^{s} - \Delta q_{i,t}^{N} ) = E(\Delta q_{i,t}^{s} |\Delta X,\Delta R,D_{i,t} = 1, \, D_{i,t - 1} = 0) + E(\Delta q_{i,t}^{N} |\Delta X,\Delta R,D_{i,t} = 0, \, D_{i,t - 1} = 0)} \hfill \\ {\quad = \gamma + E(\Delta \varepsilon_{i,t}^{s} |\Delta X,\Delta R,D_{i,t} = 1, \, D_{i,t - 1} = 0) - E(\Delta \varepsilon_{i,t}^{N} |\Delta X,\Delta R,D_{i,t} = 0, \, D_{i,t - 1} = 0)} \hfill \\ \end{array}$$

Under the assumption that ε _i,t is mean independent of the subsidy dummy variable D _i,t at time t, the expected difference conditional on ΔX and D _i,t−1 = 0 between the growth rate of subsidized (Δ$q_{i,t}^{S}$) and non-subsidized firms (Δ$q_{i,t}^{N}$) can be identified as policy parameter γ ₂:

$$\begin{aligned} E(\Delta \varepsilon_{i,t}^{s} |\Delta X,\Delta R,D_{i,t} = 1, \, D_{i,t - 1} = 0) = E(\Delta \varepsilon_{i,t}^{N} |\Delta X,\Delta R,D_{i,t} = 0, \, D_{i,t - 1} = 0) \hfill \\ E(D_{i,t} \times \varepsilon_{i,t} ) = 0, \, \forall t) \hfill \\ \end{aligned}$$

(6)

If D _i,t−1 = 0, and E(X _i,t ε _i,t ) = 0 (Lach 2002), then both the first differencing estimator and the DID estimator are equivalent, meaning that the traditional panel analysis can be applied.

Appendix 2

See Table 8.

Table 8 R&D subsidy by firm size

Appendix 3

See Table 9.

Table 9 R&D subsidy Effect on labor productivity using DID sample: RE & FE Model