Intellectual capital and total factor productivity

Figures & data

Table 1. Variable definitions and data sources.

Variable	Definition	Data Source
Y	Output-side real GDP at chained PPPs (in mil. 2017US$)	PWT 10.0
K	Capital stock at current PPPs (in mil. 2017US$)	PWT 10.0
L	Number of persons engaged (in millions)	PWT 10.0
(1-α)	Share of labor varying across units and time	PWT 10.0
top	Total factor productivity level (dependent variable)	Derived
tfp_g	Total factor productivity growth (dependent variable)	≫
ic	National intellectual capital level (independent var.)	≫
ic_g	National intellectual capital growth (independent var.)	≫

Source: Feenstra et al., 2015.

Table 2. Descriptive statistics of variables.

Variable	Mean	Std. dev	Min	Max
tfpl	238.8091	257.9822	8.086	1282.04
lntfpl	4.811024	1.224316	2.090	7.15621
tfp_g	0.0035538	0.0486834	−0.2897	0.233879
ic	1.428746	0.5453389	0.4367	2.77262
lnic	0.2795242	0.4027394	−0.8284	1.01979
ic_g	0.0152826	0.0482072	−0.6579	0.2532

Source: Current Data.

Table 3. Mean TFP and IC (level and growth) by income level and region.

Income Category	Obs	tfpl	ic	tfp_g	ic-g
Low-Income Countries (LIC)	62	28.18	0.68	0.0019	0.024
Lower Middle-Income Countries (LMIC)	186	63.79	0.93	0.0003	0.008
Upper Middle-Income Countries (UMIC)	248	129.13	1.28	0.0022	0.018
High-Income Countries (HIC)	403	419.48	1.87	0.0061	0.016
AEC (Singapore, Thailand & S. Korea)	93	214	1.80	0.0086	0.021

Source: Current Data.

Figure 1. The level of IC index across income level and time.

Table 4. The CD and slope homogeneity test.

Model	Variable	Definition	CD statistic	α	Delta
1	lntfpl	natural log of TFP level	4.54**	0.64	5.42**
	lnic	natural log of IC level	86.96**	0.99	adj. 6.10**
2	tfp_g	TFP growth	23.34**	0.77	3.97**
	Ic_g	IC growth	10.54**	0.75	adj. 4.47**

**refers to a 1% level of sig. 0.5 < = α < 1 → strong cross-sectional dependence.

Table 5. Sequential test for multiple breaks (Ditzen et al., 2021).

	Test Statistic		Bai & Perron Critical Values
	Model1	Model2	1%	5%	10%
F(1/0)	0.19	1.29	12.29	8.58	7.04
F(2/1)	7.30	4.69	13.89	10.13	8.51
F(3/2)	4.89	0.31	14.80	11.14	9.41
F(4/3)	0.55	7.61	15.28	11.83	10.04
F(5/4)	0.53	2.52	15.76	12.25	10.58

Detected number of breaks: No breaks found.

Table 6. Panel Unit Root Tests.

		CIPS		Karavias and Tzavalis (2014)
Model	Var	no trend	trend	break	no trend	trend
1 (level)	lntfpl	−0.1	−0.4	1	−3.16**	−2.20
	L.lntfpl	−1.3	−2.4**	2	−3.15**	−2.51
	lnic	−2.5**	−5.0**	1	−35.39**	−5.88**
	L.lnic	−1.2	−1.9*	2	−33.87**	−7.26**
1^st diff	d.lntfpl	−15.0**	−12.8**	1	−42.56**	−24.74**
	d.lntfpl	−10.0**	−7.5**	2	−41.58**	−23.34**
2 (level)	tfp_g	−13.6**	−12.5**	1	−43.77**	−25.96**
	L.tfp_g	−6.0**	−4.7**	2	−42.83**	−24.21**
	ic_g	−20.7**	−18.5**	1	−47.51**	−27.41**
	L.ic_g	−13.3**	−10.1**	2	−45.74**	−25.32**

* & ** refers to 1% 5% level of sig.

Table 7. Co-integration tests.

Statistic	Gt	Ga	Pt	Pa
M1	−2.1*	−8.9*	−9.4	−5.9*
M2	−3.8**	−21.2**	−21.0**	−22.0**

H0: no co-integration. * & ** refers to 5% and 1% level of sig.

Table 8. Dynamic CCE estimation result (lntfpl as dependent).

MG effect	Variables	DCC-MG	CS-ARDL	CS-DL	CS-ECM
Short Run Est.	lntfpl (Std. Errors)	0.434** (0.0608)	0.434** (0.0608)
	lnic (Std. Errors)	0.521** (0.17043)	0.521** (0.1704)
	L.lnic (Std. Errors)	0.165 (0.2011)	0.165 (0.2011)	−0.334 (0.24889)	−0.165 (0.2011)
Adjust.Term	lr_lntfpl (Std. Errors)		−0.566** (0.0608)		−0.566** (0.0608)
Long Run Est.	lr_lnic(Std. Errors)		3.085** (0 .9016)	0.998** (0.29891)	3.085** (0.9016)
	CD Statistic	−1.55	−1.55	−1.53	−1.55
	R^2 (MG)	0.91	0.91	0.86	0.51
Observations		783	783	783	783

*& ** refers to a 5% and 1% level of significance, respectively.

Table 9. Dynamic CCE estimation result for 2nd model (tfp_g as dependent).

Mean group effect	Variables	DCC-MG	CS-ARDL	CS-DL	CS-ECM
Short Run	L.tfp_g	0.022	0.022
		(0.0571)	(0.0571)
	ic_g	0.083**	0.083**
		(0.0351)	(0.0351)
	L.ic_g	0.059*	0.059*	−0.045	−0.059*
		(0.0340)	(0.0340)	(0.0378)	(0.0340)
Adjust.Term	lr_tfp_g		−0.978***		−0.978***
			(0.0571)		(0.0571)
Long Run Est	lr_ic_g		0.171***	0.143***	0.171***
			(0.0641)	(0.0542)	(0.0641)
CSD	CD Statistic	−1.05	−1.05	−1.55	−1.05
R-squared (MG)		0.73/0.34	0.83/0.33	0.82/0.32	0.34/0.66
Total Observations		812	812	812	812

*,** &*** refers to 10%, 5% & 1% significance level and the values in (.) indicate Std. Errors.

Figure 2. Graphs for sample low income countries.

Figure 3. Graphs for sample upper middle income countries.

Figure 4. Graphs for sample HIC.

Figure 5. Shows the relationship between IC and TFP is linear after the natural log.

Table 10. CS-ARDL results for 10 advanced countries.

Mean Group Effect	Ln (TFP level) as dependent		TFP growth as the dependent variable
	Coef	Std. Err	Var	Coef	Std. Err
L.lntfpl	0.86***	0.033	L.tfp_g	0.44**	0.179
lnic	0.61***	0.139	Ic_g	−0.006	0.134
Adj. Term	−0.14***	0.033	Adj. term	−0.56***	0.179
lr_lnic	4.26***	0.566	lr_ic_g	0.43**	0.211
Total obs.	250			250
R2-(MG)	84			81

** & *** refers to 5% and 1% level of significance.

Table A1. Sample countries by income group and region.

Income group	SSA	MENA	LA	Asia	Europe	NA
LIC (< =$1085)	Ethiopia 3 Malawi 6
LMIC ($1086–$4255)	Ghana 13 Kenya 5 Senegal 15	Morocco10		Indonesia 4 Philippines26
UMIC ($4256–13,205)	Mauritius 9 S.Africa 12		Brazil 1 Mexico 7 Colombia2 Peru 11	Malaysia 8 Thailand 14
HIC (> =$13,205)			Chile 28	Japan 25 S. Korea 27 Singapore 29	Germany19 France18 UK 23 Netherlands20 Sweden22 Denmark16 Italy17 Spain21	USA 24

Source: Income level according to 2023 WB classification.

Table A2. Compositions of intellectual capital index.

Code		Indicators and or proxies	relation	Measures
Renewal capital (RC)	1	Payments + receipts for the use of intellectual property + technical cooperation grants	Positive	BoP, current US$
	2	Design applications (resident + non resident)	Positive	count
	3	Patent applications (resident + non resident)	Positive	count
	4	Research and development expenditure	Positive	% of GDP
	5	Scientific and technical journal articles	Positive	counts
Process Capital (PC)	1	Communications, computer, etc.	Positive	% serv export & import
	2	Cost of business start-up procedures	Negative	% of GNI per capita
	3	Internet + tele subscribers	Positive	per 100 people
	4	Procedures to build, register business & property	Negative	Number
	5	Time to register business & property	Negative	Days
	6	Corruption perception index	Negative	Number
Marketing Capital (MC)	1	Trade to GDP ratio	Positive	% of GDP
	2	Domestic credit to the private sector	Positive	% of GDP
	3	Market capitalization	Positive	% of GDP
	4	Foreign direct investment, net inflows	Positive	% of GDP
	5	ICT goods & service exports	Positive	% service exports
	6	Medium and high-tech exports	Positive	% manufacturing exports
Human Capital (HC)	1	Population ages 15-64	Positive	% of the total population
	2	Mortality rate, infant	Negative	per 1,000 live births
	3	Pupil-teacher ratio, 1°,2ry & tertiary	Negative	Number
	4	School enrollment, 1°,2ry & tertiary	Positive	% gross
	5	Researchers & Technicians in R&D	Positive	per million people

Source: Adapted from Ståhle et al. (2015) and Global competitiveness index.

Feenstra, R. C., Inklaar, R., & Timmer, M. P. (2015). The next generation of the Penn World Table. American Economic Review, 105(10), 3150–3182. https://doi.org/10.1257/aer.20130954

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Ståhle, P., Ståhle, S., & Lin, C. (2015). Intangibles and national economic wealth – a new perspective on how they are linked. Journal of Intellectual Capital, 16(1), 20–57. https://doi.org/10.1108/JIC-02-2014-0017

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Data availability statement

The data that support the findings of this study are openly available in figshare at 10.6084/m9.figshare.25048061.