The productivity–wage relationship in South Africa: an empirical investigation

Figures & data

Hypothesised causal relations among real wages, productivity and unemployment

Causal direction	Expected sign	Rationale
PROD → RW	+	Performance‐based pay; bargaining
PROD → UR	+	Greater efficiency implies reduced labour demand
	−	Positive output effect on employment
RW → PROD	+	Efficiency wages
RW → UR	+	Higher labour costs cause factor substitution
UR → RW	−	Surplus labour weakens union bargaining power
UR → PROD	+	Workers increase effort to secure jobs;
		less productive workers are fired first

Real wages, productivity, employment and unemployment, 1970–2002

Growth in productivity and real wages, 1970–2002

Average year‐on‐year growth rates of productivity and real wages

Variable	1971–9	1980–9	1990–2002
Productivity	0,30%	0,22%	3,38%
Real wages	−0,40%	0,26%	2,04%
Source: SARB (2003).

Pairwise correlation coefficients

Variables	1971–9	1980–9	1990–2002	1983–2002
RW‐PROD	−0,09^1	0,21^1	0,97	0,98
RW‐UR	–	−0,25^1,2	0,90	0,88
UR‐PROD	–	0,462	0,88	0,89
Notes: 1. Insignificant at the 10 per cent level. All other coefficients are significant at 1 per cent. 2. 1983–9. Sources: SARB (2003); DBSA (2003); StatsSA (1999, 2002) and own calculations.

Testing for order of integration, 1983–2002

Variable	Test	I(1) vs I(0)	I(1) vs I(0) + trend	I(2) vs I(1)
LPROD	DF	3,51*	−0,99	−6,54*
	ADF(1)	2,40	−1,01	−4,79*
	ADF(4)	1,57	−0,98	−2,94*
LRW	DF	−0,29	−2,41	−9,78*
	ADF(1)	0,01	−2,22	−6,71*
	ADF(4)	0,53	−1,90	−5,49*
UR	DF	0,02	−1,36	−3,89*
	ADF(1)	−0,52	−2,79	−3,18*
	ADF(4)	−0,28	−2,37	−3,48*
5 per cent critical value		−2,90	−3,47	−2,90
Notes: *Significant at the 5 per cent level. Bold print test statistics correspond to the ‘best’ regression specification chosen by the Akaike information criterion (AIC), Schwarz Bayesian criterion (SBC) and Hannan–Quinn criterion (HQC).

Testing for order of integration, 1990–2002

Variable	Test	I(1) vs I(0)	I(1) vs I(0) + trend	I(2) vs I(1)
LPROD	DF	1,92	−3,20	−5,53*
	ADF(1)	1,40	−3,07	−4,09*
	ADF(4)	0,24	−2,93	−2,16
LRW	DF	−0,76	−4,44*	−9,03*
	ADF(1)	−0,37	−3,70*	−6,02*
	ADF(4)	0,06	−3,38	−4,78*
UR	DF	−1,59	−1,23	−3,29*
	ADF(1)	−1,43	−2,45	−2,68
	ADF(4)	−1,34	−2,00	−2,95*
5 per cent critical value		−2,92	−3,50	−2,92
Notes: *Significant at the 5 per cent level. Bold print test statistics correspond to the ‘best’ regression specification chosen by the Akaike information criterion (AIC), Schwarz Bayesian criterion (SBC) and Hannan–Quinn criterion (HQC).

Testing for lag order in the VAR

Test statistics and choice criteria for selecting the order of the VAR model
Order	LL	AIC	SBC	LR test	Adjusted LR test
4	795,6347	753,6347	704,6893	—	—
3	788,3159	755,3159	716,8588	CHSQ(9) = 14,6376[,101]	11,9412[,217]
2	784,7229	760,7229	732,7541	CHSQ(18) = 21,8237[,240]	17,8035[,469]
1	754,1743	739,1743	721,6938	CHSQ(27) = 82,9208[,000]	67,6459[,000]
0	397,8210	391,8210	384,8288	CHSQ(36) = 795,6275[,000]	649,0646[,000]
Notes: AIC = Akaike information criterion, SBC = Schwarz Bayesian criterion. Based on 76 observations from 1984/Q1 to 2002/Q4. Order of VAR = 4. List of variables included in the unrestricted VAR: LRW, LPROD, UR. List of deterministic and/or exogenous variables: C, D90.

Cointegration tests for LRW, LPROD and UR, 1983–2002

Specification of the cointegrating VAR	Eigenvalue	Trace	AIC	SBC	HQC
Restricted intercepts, no trends	1	1	3	1	2
Unrestricted intercepts, no trends	0	1	2	0	2
Unrestricted intercepts, restricted trends	0	2	3	0	3
Unrestricted intercepts, unrestricted trends	0	0	2	0	2
Note: Figures refer to the number of cointegrating vectors (r) indicated by each test.

Cointegration test using ‘unrestricted intercepts, no trends’, 1983–2002

Eigenvalue test:
			Critical values
Null	Alternative	Eigenvalue	5%	10%
r = 0	r = 1	18,81	21,12	19,02
r≤1	r = 2	13,49	14,88	12,98
r≤2	r = 3	1,05	8,07	6,50
Trace test:
			Critical values
Null	Alternative	Trace	5%	10%
r = 0	r≥1	33,35	31,54	28,78
r≤1	r≥2	14,53	17,86	15,75
r≤2	r = 3	1,05	8,07	6,50

Cointegration test using ‘unrestricted intercepts, no trends’, 1990–2002

Eigenvalue test:
			Critical values
Null	Alternative	Eigenvalue	5%	10%
r = 0	r = 1	17,35	21,12	19,02
r≤1	r = 2	13,70	14,88	12,98
r≤2	r = 3	0,63	8,07	6,50
Trace test:
			Critical values
Null	Alternative	Trace	5%	10%
r = 0	r≥1	31,67	31,54	28,78
r≤1	r≥2	14,32	17,86	15,75
r≤2	r = 3	0,63	8,07	6,50

Cointegrating vector Z = LRW −0,85 LPROD +0,75 UR

Cointegration test for LRW and LPROD, 1990–2002

Eigenvalue test:
			Critical values
Null	Alternative	Eigenvalue	5%	10%
r = 0	r = 1	15,53	14,88	12,98
r≤1	r = 2	2,76	8,07	6,50
Trace test:
			Critical values
Null	Alternative	Trace	5%	10%
r = 0	r≥1	16,64	17,86	15,75
r≤1	r = 2	1,11	8,07	6,50

Cointegrating vector Z = LRW −0,58 LPROD

Error correction models for LRW and LPROD, 1990–2002

1990/Q1 – 2002/Q4; n = 52	Dependent variable
Regressor	DLRW	DLPROD
CONSTANT	0,72*	−0,21*
	(2,52)	(−2,22)
DLRW(−1)	−0,14	−0,14*
	(−0,85)	(−2,65)
DLPROD(−1)	0,34	0,24
	(0,84)	(1,77)
ECM(−1)	−0,37*	0,11*
	(−2,50)	(2,30)
R‐squared	0,19	0,20
Adjusted R‐squared	0,14	0,15
F(3, 48)	3,87	3,92
p value of F	0,02	0,01
Standard error	0,0208	0,0068
Note: *Significant at 5 per cent; t‐statistics in parentheses.

Decomposition of gross value added into wage bill and gross operating surplus

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