### Test for stationarity

Recall that an implication of Eq. (4) is that semi-endogenous models hold true if TFP ((lnA)) is a unit root [I(1)] process, so that, by extension, the R&D and patent variables ((lnRD) and (lnPATENT)) are I(1) processes. Similarly, Eq. (4) implies that Schumpeterian models hold if the R&D intensity measures (i.e. (RD/Y), (RD/L) (RD/AL), (PATENT/Y), (PATENT/L), and (PATENT/AL)) and TFP ((lnA)) are I(0), or stationary, processes (Ang and Madsen 2011). We can test these implications using unit root tests. Figures 2 and 3 show that the variables do not evolve along a smooth path and are hence best tested using unit root tests, which accommodate this behaviour. We draw on two structural break unit root tests, namely, the tests of Perron (1989) and Narayan and Popp (2010, NP), to examine the unit root properties of the variables. The Perron and NP tests account for one and two structural breaks, respectively.

Table 1 shows the test results. The Perron test fails to reject the null hypothesis of no unit root for (lnA). This finding is supported by the NP test results, which means that TFP is nonstationary, consistent with semi-endogenous growth theory. R&D expenditures are also nonstationary, based on both tests. However, the evidence of unit roots in patent applications is unclear, because, whereas the Perron test finds the variable to be stationary, the NP test suggests mixed conclusions. In other words, the M1 statistics are consistent with the Perron test, but the M2 test is not. With regards to the R&D intensity measures, the Perron test suggests that (RD/Y), (RD/L), and (RD/AL) are nonstationary, whereas (PATENT/Y), (PATENT/L), (PATENT/L), and (PATENT/AL) are. The NP test results suggest mixed conclusions by appearing to support the nonstationarity of the R&D intensity measures. Overall, both tests appear to support the semi-endogenous growth models.

### Cointegration results

The unit root tests in the preceding section (i.e. Sect. 5.1), which also double as tests for structural breaks, indicate that the variables are subjected to structural breaks. This finding is also supported by the evolution of the variables as depicted in Figs. 2 and 3.^{Footnote 15} Aside from this, TFP and the R&D indicators appear to co-move over time. This finding demands formal nonlinear testing to establish a long-run relation between TFP and the R&D indicators. In addition, Eq. (5) suggests that semi-endogenous growth theory is valid if (lnX) and (lnA) are cointegrated and the cointegrating vector is ((1, left( {phi – 1} right)/sigma)), such that the second element carries a negative sign. Similarly, Eq. (6) suggests that Schumpeterian growth theory is valid if (lnX) and (lnQ) are cointegrated, with the cointegrating vector being (1, − 1). However, as argued in Sect. 3, these are stricter conditions, which are rarely observed in practice. Thus, following Juhro et al. (2020), we find adequate cointegration evidence to conclude in favour of either model.

We apply two nonlinear cointegration tests to verify that TFP and the R&D indicators share common long-run relationships. Specifically, we apply the Gregory–Hansen and nonlinear autoregressive distributed lag (NARDL) bounds tests. The Gregory–Hansen test has a null hypothesis of no cointegration, which is tested against the alternative of cointegration with regime shifts. The NARDL test has the null hypothesis of no cointegration against an alternative of cointegration. The main intuition underlying this test is that negative and positive changes in a predictor have a nonlinear impact on the predictand. Table 2 reports the results of these tests. Both tests show strong evidence of cointegration between TFP and the R&D indicators at the conventional levels of statistical significance. In other words, the cointegration tests support both growth models, such that the necessary conditions for semi-endogenous growth and Schumpeterian theories are satisfied within the nonlinear cointegration framework.

### Long-run elasticities

Equations (5) and (6) imply that (lnX_{t} = mu lnQ_{t} + kappa lnA_{t} + e_{t}), where (kappa = left( {1 – phi } right)/sigma) (Zachariadis 2003, 2004). Within this framework, semi-endogenous growth theory is valid if (kappa > 0) and (mu = 0), and (e_{t}) is a stationary error term. Similarly, the Schumpeterian theory hypothesis holds if (kappa = 0) and (mu = 1). This means that we can verify the validity of both theories by estimating (mu) and (kappa), the product variety and technical elasticities of R&D/innovation.

Because the endogenous growth theories imply a long-run relation between TFP and innovation, the most appropriate way of estimating the elasticities should account for this long-run property. To this end, we draw on the dynamic least squares approach when estimating the elasticities. Table 3 reports these results. We report the results of the fully specified regression and the piecewise regressions (i.e. Eqs. (5) and (6)) in Panels A and B, respectively. The results suggest that TFP and product variety are critical determinants of R&D expenditure. This finding refutes the joint hypothesis under the semi-endogenous and Schumpeterian growth theories. None of the conditions is satisfied if product variety is measured as (Y) (i.e. (kappa < 0) and (mu > 0)), while semi-endogenous growth theory is partly satisfied if product variety is measured as (AL) (i.e. (kappa > 0) and (mu > 0)). Considering the piecewise regressions in Panel B, none of the Schumpeterian conditions (i.e. (kappa = 0) and (mu = 1)) is satisfied but the semi-endogenous conditions ((kappa > 0) and (mu = 0)) are partly satisfied; that is, we cannot reject the condition that (kappa > 0). Hence, the evidence seems to favour semi-endogenous growth theory. This evidence is consistent with that documented by Juhro et al. (2020) for Indonesia.

### The impact of EPU on TFP growth

Having established that Sri Lanka’s growth is best explained by semi-endogenous growth theory, we now turn to testing our hypothesis that EPU determines the impact of R&D investment on TFP growth. The usual way of completing the test of endogenous growth theories is to regress TFP growth on R&D, R&D intensity, and technology frontier indicators (Juhro et al. 2020). However, such a regression would ignore the role of EPU in TFP growth. Hence, we extend the regression to capture the impact of EPU, proxied by the news-based world uncertainty index for Sri Lanka constructed by Ahir et al. (2018), by interacting the R&D indicator with an EPU indicator. As discussed earlier, policy uncertainty has been persistent in Sri Lanka. We accommodate policy uncertainty persistence by including three lags of the interaction term in our model.

We report estimates of our model, that is, Eq. (7), in Table 4. In Column (1), we include only the contemporaneous interaction term, while, in Column (4), we include the contemporaneous interaction term and its lagged terms of up to three. The estimates suggest that EPU reduces TFP growth via its impact on R&D, as indicated by the coefficient of the contemporaneous interaction term, which is negative and statistically significant. Over time, the economy adjusts to the EPU shock, such that its impact on TFP growth via R&D is no longer negative but positive, as shown by the coefficients of the lagged interaction terms, which are positive and significant up to the second lag. By the third year (third lag), the economy becomes immune to EPU, as shown by the coefficient of the third lagged interaction term, which is positive but statistically nonsignificant.

In terms of economic significance, these estimates suggest that a unit standard deviation increase in EPU would contemporaneously decrease TFP growth by − 3.43% of its sample mean (i.e. 0.79%) via a reduction in R&D investment.^{Footnote 16} One and two years after the unit standard deviation increase in EPU, TFP growth increases by 4.57% and 4.20%, respectively, of its sample mean of 0.79%. It is clear that Sri Lanka is a peculiar case. The country has undergone prolonged periods of uncertainty, to the extent that its TFP growth and economic indicators have fully absorbed the impact of uncertainty. Our estimates show that, although EPU affects TFP growth, as shown by the sum of the coefficients of the interaction terms, (delta), the impact is not sufficiently detrimental to overturn the positive impact of R&D expenditures on TFP growth. In terms of economic significance, a unit standard deviation increase in EPU would increase TFP growth by 5.44% of its sample mean of 0.79% through R&D investment in the long term.

The negative contemporaneous impact of EPU on R&D investment and TFP growth is in line with the theoretical prediction of the real options literature, where firms are generally cautious about investing during periods of uncertainty (Sarkar 2000; Bloom et al. 2007; Iyke and Ho 2020). In this case, it appears that the government’s initial hesitation to invest in R&D in response to an increase in EPU undermines TFP growth in the country. Over time, since the government, unlike firms, is more concerned about the social benefits of R&D investments, it should internalise the EPU and increase R&D investments to stimulate TFP growth, consistent with the estimated positive impact of R&D.

In addition to the impact of EPU, we find that domestic R&D intensity, measured as R&D scaled by labour (i.e. (lnleft( {X/Q} right)^{d})), is an important determinant of TFP growth in Sri Lanka. This reflects the difficulty in clearly distinguishing endogenous growth theories in Sri Lanka, as observed in the preceding analysis. What can be said with certainty is that R&D is an important source of TFP growth in the country. Hence, policies aimed at fortifying R&D investment would drive the country towards a higher long-term growth path.

We examine the sensitivity of these estimates to two alternative R&D intensity indicators, namely, R&D scaled by the GDP ((RD/Y)) and R&D scaled by the product of TFP and labour ((RD/AL)). Table 5 reports the estimates. These estimates are consistent with those in Table 4. Specifically, Panel A, which shows the estimates based on (RD/Y), suggests that EPU has a negative contemporaneous impact on TFP growth via R&D investment. For the first and second lags, the impact of EPU on TFP growth via R&D is positive and statistically significant, but this significance dissipates for the third lag (see Panel A). The joint impact of EPU on TFP growth via R&D is positive and statistically significant, as shown by the sum of coefficients of the interaction terms (i.e. (delta)). In other words, the detrimental impact of EPU is overturned in the long term as the economy internalises the impact; hence R&D boosts long-term TFP growth despite the heightened EPU. We draw the same conclusions from the estimates in Panel B, which are based on (RD/AL).

It is worth noting that domestic R&D intensity does not appear to significantly determine TFP growth using (RD/Y) and (RD/AL) as indicators of R&D intensity.^{Footnote 17} In other words, we are better able to validate the semi-endogenous growth theory using these alternative R&D intensity indicators. Overall, our finding that EPU influences the impact of R&D investment on TFP growth is not driven by the measure of R&D intensity.

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