Monetary policy and inflation expectations: impact and causal analysis of heterogeneous economic agents’ expectations in South Africa

Figures & data

Figure 1. Economic variables of inflation expectation and the repo rate. Note the economic variables are $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$, which is the inflation expectations for financial agents one year ahead; $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$, which is the inflation expectations for business agents one year ahead, and $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdunln\mathrm{\_}rr$, which is the inflation expectations for trade union agents one year ahead. On the other hand, $CI$ is a confidence interval, $f\mathrm{\_}v$ is the filter value, $infl\mathrm{\_}ub$ is the inflation upper band, and $infl\mathrm{\_}lb$ is the inflation lower band. Composed by the authors, data sourced from (SARB, 2023).

Table 1. Economic variables utilised.

Variable	Description	Sourced
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}{f}_{t+1}$	Inflation expectations for financial agents for one year ahead	SARB (2023)
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}{b}_{t+1}$	Inflation expectations for business agents one year ahead	SARB (2023)
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdunln\mathrm{\_}r{r}_{t+1}$	Inflation expectations for trade union agents for one year ahead	SARB (2023)
$ln\mathrm{\_}r{r}_t$	Repo rate
$l\mathrm{\_}ln\mathrm{\_}ri{r}_t$	Lag real interest rate.	Own computation
$ln\mathrm{\_}gdp\mathrm{\_}ga{p}_t$	Gross domestic product gap, percent change, quarterly, seasonally adjusted annual rate	Own computation
$ln\mathrm{\_}unemp{l}_t$	Official unemployment rate	SARB (2023)
$ln\mathrm{\_}inf{l}_t$	inflation rate
$ln\mathrm{\_}{g}_t$	General government final consumption expenditure percentage of gross domestic product	SARB (2023)

Table 2. Descriptive statistics.

Variable	Obs	Mean	Std. Dev.	Min	Max	Skewness	Kurtosis	Shapiro‒Wilk
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	90	1.671	0.153	1.131	2.152	0.387	0.011	0.019
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	90	1.815	0.202	1.308	2.241	0.505	0.358	0.035
$ln\mathrm{\_}nfl\mathrm{\_}e\mathrm{\_}trdun$	90	1.772	0.234	1.194	2.37	0.589	0.268	0.015
$ln\mathrm{\_}rr$	92	1.948	0.342	1.253	2.603	0.913	0.364	0.081
$l\mathrm{\_}ln\mathrm{\_}rir$	91	1.588	0.463	0.394	2.46	0.072	0.975	0.203
$ln\mathrm{\_}gdp\mathrm{\_}gap$	91	0.024	0.293	−0.478	.808	0.026	0.524	0.016
$ln\mathrm{\_}unempl$	91	3.256	0.116	3.045	3.564	0.002	0.253	0.002
$ln\mathrm{\_}infl$	92	1.604	0.54	−0.836	2.595	0.000	0.000	0.000
$ln\mathrm{\_}g$	91	2.893	0.082	2.741	3.153	0.873	0.295	0.000

The authors compiled the results.

Table 3. Matrix of correlations.

Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	1.000
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	0.520	1.000
$ln\mathrm{\_}nfl\mathrm{\_}e\mathrm{\_}trdun$	0.521	0.965	1.000
$ln\mathrm{\_}rr$	0.400	0.524	0.578	1.000
$l\mathrm{\_}ln\mathrm{\_}rir$	−0.129	−0.126	−0.099	0.544	1.000
$ln\mathrm{\_}gdp\mathrm{\_}gap$	−0.485	−0.498	−0.558	−0.306	−0.012	1.000
$ln\mathrm{\_}unempl$	−0.388	−0.196	−0.283	−0.456	−0.322	0.725	1.000
$ln\mathrm{\_}infl$	0.516	0.442	0.480	0.296	−0.420	−0.333	−0.124	1.000
$ln\mathrm{\_}g$	−0.179	−0.103	−0.195	−0.730	−0.577	0.173	0.524	−0.061	1.000

The authors compiled the results.

Table 4. Conventional unit root and structural break.

Test		Dickey-Fuller test for unit root		Phillips-Perron test for unit root		Structural break		Perron test
Variable		Test Stat	5% Critical Value	Test Stat	5% Critical Value	Break	P value	Test Stat	5% Critical Value
$d.ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	Z(t)	−4.453	−2.900	−4.453	−2.900	2019q3	0.00	−10.937	−2.900
$d.ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	Z(t)	−4.969	−2.900	−4.969	−2.900	2018q2	0.00	−7.892	−2.900
$d.ln\mathrm{\_}nfl\mathrm{\_}e\mathrm{\_}trdun$	Z(t)	−5.484	−2.900	−5.484	−2.900	2018q4	0.00	−8.483	−2.900
d.$ln\mathrm{\_}rr$	Z(t)	−4.567	−2.900	−4.567	−2.900	2009q4	0.00	−4.609	−2.900
$d.l\mathrm{\_}ln\mathrm{\_}rir$	Z(t)	−7.372	−2.900	−7.372	−2.900	2008q2	0.00	−9.118	−2.900
$d.ln\mathrm{\_}gdp\mathrm{\_}gap$	Z(t)	−6.344	−2.900	−6.344	−2.900	2008q4	0.00	−25.463	−2.900
$d.ln\mathrm{\_}unempl$	Z(t)	−8.984	−2.900	−8.984	−2.900	2019q2	0.00	−13.285	−2.900
$d.ln\mathrm{\_}infl$	Z(t)	−5.899	−2.900	−5.899	−2.900	2004q2	0.00	−6.308	−2.900
$d.ln\mathrm{\_}g$	Z(t)	−9.087	−2.900	−9.087	−2.900	2010q1	0.00	−13.625	−2.900

Note that d is the difference in the first-order condition. The authors compiled the results.

Table 5. Lag-order selection criteria.

lag	LL	LR	df	p	FPE	AIC	HQIC	SBIC
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$
0	202.514	0.000	−4.5	−4.466	−4.347
1	864.345	1323.700	49	0.000	0.000	−18.799	−18.156	−17.201
2	1083.580	438.470	49	0.000	0.000	−22.758	−21.552	−19.761
3	1235.160	303.17*	49	0.000	3.1e-20*	−25.1433*	−23.3746*	−20.7483*
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$
0	197.313	0.000	−4.5	−4.450	−4.329
1	855.255	1315.900	49	0.000	0.000	−19.030	−18.378	−17.409
2	1067.810	425.110	49	0.000	0.000	−22.924	−21.703	−19.886
3	1226.840	318.060	49	0.000	0.000	−25.544	−23.752	−21.0873*
4	1330.320	206.960	49	0.000	6.4e-21*	−26.841	−24.4795*	−20.967
$ln\mathrm{\_}nfl\mathrm{\_}e\mathrm{\_}trdun$
0	188.432	0.000	−4.3	−4.290	−4.168
1	832.202	1287.500	49	0.000	0.000	−18.704	−18.048	−17.072
2	1037.770	411.130	49	0.000	0.000	−22.476	−21.247	−19.416
3	1196.370	317.210	49	0.000	0.000	−25.117	−23.314	−20.6294*
4	1294.760	196.780	49	0.000	1.1e-20*	−26.308	−23.9308*	−20.392

Compiled by the authors.

Table 6. Johansen tests for cointegration.

Maximum rank	Params	LL	Eigenvalue	Trace statistic	Critical value 5%
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$
0	105	1140.7723	0.0000	188.7824	124.24
1	118	1171.0061	0.50496	128.3148	94.15
2	129	1199.7746	0.48780	70.7779	68.52
3	138	1213.1351	0.26707	44.0569*	47.21
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$
0	105	1150.7296	0.0000	208.2535	124.24
1	118	1192.4228	0.62077	124.8670	94.15
2	129	1214.9091	0.40722	79.8946	68.52
3	138	1229.7856	0.29246	50.1414	47.21
4	145	1241.4968	0.23841	26.7192*	29.68
$ln\mathrm{\_}nfl\mathrm{\_}e\mathrm{\_}trdun$
0	105	1127.9321	0.0000	213.9315	124.24
1	118	1173.1126	0.65031	123.5704	94.15
2	129	1196.2224	0.41576	77.3507	68.52
3	138	1211.3003	0.29577	47.1951*	47.21

Compiled by the authors.

Table 7. Long-run estimations of VEC.

Estimation	(1)	Estimation	(2)	Estimation	(3)
Variable	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	Variable	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	Variable	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$
$ln\mathrm{\_}rr$	−5.00709**	$ln\mathrm{\_}rr$	3.217125	$ln\mathrm{\_}rr$	0.05391***
	(−8.38)		(0.309466)		(5.556029)
$l\mathrm{\_}ln\mathrm{\_}rir$	2.610707*	$l\mathrm{\_}ln\mathrm{\_}rir$	−1.07985**	$l\mathrm{\_}ln\mathrm{\_}rir$	−2.49872
	(7.78)		(4.17848)		(0.330152)
$ln\mathrm{\_}gdp\mathrm{\_}gap$	0.752205**	$ln\mathrm{\_}gdp\mathrm{\_}gap$	1.604874	$ln\mathrm{\_}gdp\mathrm{\_}gap$	−2.0386
	(1.28)		(0.383199)		(0.705103)
$ln\mathrm{\_}unempl$	−1.60786**	$ln\mathrm{\_}unempl$	−1.49038*	$ln\mathrm{\_}unempl$	7.034806***
	(−1.55)		(8.70831)		(2.265198)
$ln\mathrm{\_}infl$	4.024137***	$ln\mathrm{\_}infl$	−2.08427	$ln\mathrm{\_}infl$	−2.36513
	(13.19)		(0.165142)		(0.285433)
$ln\mathrm{\_}g$	−2.6345	$ln\mathrm{\_}g$	−4.12963***	$ln\mathrm{\_}g$	−9.72697*
	(−1.27)		(6.263472)		(2.353076)
$dmmy\mathrm{\_}ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	−0.68864*	$dmmy\mathrm{\_}ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	0.56658	$dmmy\mathrm{\_}ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	0.679938
	(−3.1)		(0.16943)		(0.304165)
$dmmy\mathrm{\_}ln\mathrm{\_}gdp\mathrm{\_}gap$	−3.90001**	$dmmy\mathrm{\_}ln\mathrm{\_}gdp\mathrm{\_}gap$	2.770337	$dmmy\mathrm{\_}ln\mathrm{\_}gdp\mathrm{\_}gap$	−4.50543
	(−6.33)		(0.309134)		(0.552148)
$dmmy\mathrm{\_}ln\mathrm{\_}infl$	2.199556*	$dmmy\mathrm{\_}ln\mathrm{\_}infl$	−1.30161**	$dmmy\mathrm{\_}ln\mathrm{\_}infl$	−1.45619
	(5.89)		(5.22913)		(0.421555)
$dmmy\mathrm{\_}ln\mathrm{\_}g$	2.098428**	$dmmy\mathrm{\_}ln\mathrm{\_}g$	0.292862	$dmmy\mathrm{\_}ln\mathrm{\_}g$	4.91827
	(4.23)		(0.218817)		(0.408688)
$\mathrm{\_}cons$	9.343239*	$\mathrm{\_}cons$	12.99339*	$\mathrm{\_}cons$	12.56705**
	(4.23)		(4.23)		(4.23)
$N$	86	$N$	86	$N$	86

t statistics in parentheses and * p < 0.05, ** p < 0.01, *** p < 0.001. Please note that only significant results for the relevant variables are reported and compiled by the authors due to space constraints.

Table 8. Wald tests of Granger causality for$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$.

Equation	Excluded	chi2	df	Prob>Chi2
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$ln\mathrm{\_}rr$	3.124	1	0.077
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$l\mathrm{\_}ln\mathrm{\_}rir$	0.028	1	0.867
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$ln\mathrm{\_}gdp\mathrm{\_}gap$	6.592	1	0.010
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$ln\mathrm{\_}unempl$	0.120	1	0.729
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$ln\mathrm{\_}infl$	1.257	1	0.262
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$ln\mathrm{\_}g$	5.321	1	0.021
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	$ALL$	26.698	6	0.000
$ln\mathrm{\_}rr$	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$	7.449	1	0.006
$ln\mathrm{\_}rr$	$l\mathrm{\_}ln\mathrm{\_}rir$	2.142	1	0.143
$ln\mathrm{\_}rr$	$ln\mathrm{\_}gdp\mathrm{\_}gap$	1.481	1	0.224
$ln\mathrm{\_}rr$	$ln\mathrm{\_}unempl$	0.110	1	0.740
$ln\mathrm{\_}rr$	$ln\mathrm{\_}infl$	2.182	1	0.140
$ln\mathrm{\_}rr$	$ln\mathrm{\_}g$	18.176	1	0.000
$ln\mathrm{\_}rr$	$ALL$	37.988	6	0.000

Compiled by the authors.

Table 9. Wald tests of Granger causality for $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$ and $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$.

Equation	Excluded	chi2	df	Prob>Chi2	Equation	Excluded	chi2	df	Prob>Chi2
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$ln\mathrm{\_}rr$	6.245	1	0.012	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$ln\mathrm{\_}rr$	3.676	1	0.055
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$l\mathrm{\_}ln\mathrm{\_}rir$	0.729	1	0.393	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$l\mathrm{\_}ln\mathrm{\_}rir$	6.017	1	0.014
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$ln\mathrm{\_}gdp\mathrm{\_}gap$	1.418	1	0.234	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$ln\mathrm{\_}gdp\mathrm{\_}gap$	3.580	1	0.058
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$ln\mathrm{\_}unempl$	0.000	1	0.993	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$ln\mathrm{\_}unempl$	1.415	1	0.234
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$ln\mathrm{\_}infl$	50.060	1	0.000	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$ln\mathrm{\_}infl$	3.830	1	0.050
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$ln\mathrm{\_}g$	18.952	1	0.000	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$ln\mathrm{\_}g$	3.295	1	0.069
$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	$ALL$	128.500	6	0.000	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	$ALL$	44.317	6	0.000
$ln\mathrm{\_}rr$	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$	0.041	1	0.840	$ln\mathrm{\_}rr$	$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdun$	0.561	1	0.454
$ln\mathrm{\_}rr$	$l\mathrm{\_}ln\mathrm{\_}rir$	0.224	1	0.636	$ln\mathrm{\_}rr$	$l\mathrm{\_}ln\mathrm{\_}rir$	0.038	1	0.846
$ln\mathrm{\_}rr$	$ln\mathrm{\_}gdp\mathrm{\_}gap$	1.291	1	0.256	$ln\mathrm{\_}rr$	$ln\mathrm{\_}gdp\mathrm{\_}gap$	0.310	1	0.578
$ln\mathrm{\_}rr$	$ln\mathrm{\_}unempl$	1.553	1	0.213	$ln\mathrm{\_}rr$	$ln\mathrm{\_}unempl$	0.155	1	0.693
$ln\mathrm{\_}rr$	$ln\mathrm{\_}infl$	2.201	1	0.138	$ln\mathrm{\_}rr$	$ln\mathrm{\_}infl$	1.859	1	0.173
$ln\mathrm{\_}rr$	$ln\mathrm{\_}g$	24.627	1	0.000	$ln\mathrm{\_}rr$	$ln\mathrm{\_}g$	8.305	1	0.004
$ln\mathrm{\_}rr$	$ALL$	56.241	6	0.000	$ln\mathrm{\_}rr$	$ALL$	18.349	6	0.005

Compiled by the authors.

Figure 2. Shock of inflation expectations for financial agents for one year ahead on economic variables. Note that economic variables are$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}f$which is the inflation expectations for financial agents for one year ahead, $ln\mathrm{\_}rr$ is the repo rate, $l\mathrm{\_}ln\mathrm{\_}rir$ is the lag real interest rate, $ln\mathrm{\_}gdp\mathrm{\_}gap\hspace{0.17em}$ gross domestic product gap, percent change, quarterly, seasonally adjusted annual rate, $ln\mathrm{\_}unempl$ is the official unemployment rate, $ln\mathrm{\_}infl$ is the inflation rate and is the $ln\mathrm{\_}g$ general government final consumption expenditure percentage of gross domestic product. Compiled by the authors.

Figure 3. Shock of inflation expectations for business agents one year ahead on economic variables. Note that economic variables are $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}b$, which is the inflation expectations for business agents one year ahead, $ln\mathrm{\_}rr$ is the repo rate, $l\mathrm{\_}ln\mathrm{\_}rir$ is the lag real interest rate, $ln\mathrm{\_}gdp\mathrm{\_}gap\hspace{0.17em}$ gross domestic product gap, percent change, quarterly, seasonally adjusted annual rate, $ln\mathrm{\_}unempl$ is the official unemployment rate, $ln\mathrm{\_}infl$ is the inflation rate. It is the $ln\mathrm{\_}g$ general government final consumption expenditure percentage of gross domestic product. Compiled by the authors.

Figure 4. Shock of inflation expectations for trade union agents for one year ahead on economic variables. Note that economic variables are$ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdunln\mathrm{\_}rr$, which is the inflation expectations for trade union agents for one year ahead, $ln\mathrm{\_}rr$ is the repo rate, $l\mathrm{\_}ln\mathrm{\_}rir$ is the lag real interest rate, $ln\mathrm{\_}gdp\mathrm{\_}gap\hspace{0.17em}$ gross domestic product gap, percent change, quarterly, seasonally adjusted annual rate, $ln\mathrm{\_}unempl$ is the official unemployment rate, $ln\mathrm{\_}infl$ is the inflation rate and is the $ln\mathrm{\_}g$ general government final consumption expenditure percentage of gross domestic product. Compiled by the authors.

Figure A1. Period where a break in the data is considered. Note that this is with 95% confidence bands around the null. Where economic variables are $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdunln\mathrm{\_}rr$, which is the inflation expectations for trade union agents one year ahead; $ln\mathrm{\_}rr$ is the repo rate; $l\mathrm{\_}ln\mathrm{\_}rir$ is the lag real interest rate; $ln\mathrm{\_}gdp\mathrm{\_}gap$ is the gross domestic product gap, percent change, quarterly, seasonally adjusted annual rate; $ln\mathrm{\_}unempl$ is the official unemployment rate; $ln\mathrm{\_}infl$ is the inflation rate and is the $ln\mathrm{\_}g$ general government final consumption expenditure percentage of gross domestic product. Compiled by the authors.

Figure A2. Period where there is no break in the data that is considered. Note that this is with 95% confidence bands around the null. Where economic variables are $ln\mathrm{\_}infl\mathrm{\_}e\mathrm{\_}trdunln\mathrm{\_}rr$, which is the inflation expectations for trade union agents one year ahead; $ln\mathrm{\_}rr$ is the repo rate; $l\mathrm{\_}ln\mathrm{\_}rir$ is the lag real interest rate; $ln\mathrm{\_}gdp\mathrm{\_}gap$ is the gross domestic product gap, percent change, quarterly, seasonally adjusted annual rate; $ln\mathrm{\_}unempl$ is the official unemployment rate; $ln\mathrm{\_}infl$ is the inflation rate and is the $ln\mathrm{\_}g$ general government final consumption expenditure percentage of gross domestic product. Compiled by the authors.

Figure A3. Stability of the ECV model estimation. Compiled by the authors.

Sarb. (2023). Online Statistical Query (Historical Macroeconomic Time Series Information) [Retrieved March 20, 2023]. https://www.resbank.co.za/Research/Statistics/Pages/OnlineDownloadFacility.aspx .

 Google Scholar

Data availability statement

Data will be supplied upon request.