Forecasting South African Inflation
Geoffrey Woglom
Richard S. Volpert ’56 Professor of Economics
Amherst College
(grwoglom@amherst.edu)
Abstract: This paper looks at what variables are useful for forecasting inflation starting in
1990. I show that the output gap, a measure of real economic conditions, does seem to
provide useful information for forecasting inflation. This is good news for the Reserve
Bank, since the primary way that the Reserve Bank tries to affect future inflation is through
real economic conditions. In addition, short-term interest rates and import price inflation
also seem to provide useful information. The most accurate of these forecasts suggests a
root mean square forecast error of 1-2% for 1-year ahead inflation, which is within the
Reserve Bank’s current target range.
I. Introduction
In order for inflation targeting to be successful, a central bank must be able to
generate reasonably accurate forecasts of future inflation. Ideally, however, these forecasts
of inflation should also depend on variables over which the central bank has some control.
This distinction in forecast accuracy can be illustrated with the help of a standard, modern
Phillips curve:
 t   te   (u N  ut )  vt ,
(1)
where t is the rate of inflation, et is inflationary expectations, uN is the natural rate of
unemployment (assumed for convenience to be a constant) , ut is the unemployment rate,
and vt captures “supply shocks,” such as an increase in the price of imported oil. Suppose
equation (1) were the basis of a very accurate inflation forecast, but all of the variance in the
inflation forecast was due to exogenous changes in oil prices. While the central bank would
have an accurate forecast of inflation, it would have little influence over the actual inflation
rate, and little hope of achieving the target on a consistent basis.
Therefore, a central bank with an inflation target hopes to find a forecasting equation
for inflation that includes variables over which the bank has some control. Again, equation
(1) can be used to illustrate this point with the help of the Reserve Bank’s most recent
statement of monetary policy’s effects on inflation (Smal and de Jager [2001]). That
document presents a diagram depicting 6 channels of monetary policy effects on inflation.
Four of these channels work by affecting the “demand and supply of goods and services.”
In terms of equation (1), relative aggregate supply and demand are measured by the natural
rate of unemployment relative to the actual unemployment rate (so-called cyclical
unemployment). These 4 separate channels only differ by the way in which monetary policy
affects aggregate demand: e.g., via the effect of interest rates on asset prices leading to
2
wealth effects on spending, as opposed to interest rate effects on the exchange rate leading
to a change in net exports. All of these channels, however, affect inflation by altering the
balance of aggregate supply and demand.
The other two channels depicted in the diagram are: 1) direct effects of exchange
rate changes on domestic prices; 2) the effect on inflationary expectations. The direct
exchange rate effect can be thought of as captured in the vt term in equation (1), and
inflationary expectations are explicitly a part of equation (1). Changes in the exchange rate
tend to be passed through to the domestic price of imports, thereby directly affecting the
inflation rate, as well as affecting the inflation rate with a lag through the so-called “knockon” effects of import price changes on other prices and wages. Inflationary expectations
have been emphasized as a determinant of inflation ever since the early 70’s new classical
revolution in macroeconomics. It is worth noting, however, that one of the early claims of
rational expectations, costless disinflation, has come to be seen as implausible. The
hypothesis of costless disinflation would argue that with credible monetary policy,
expectation effects would become the sole, systematic determinant of inflation. A more
modern view is that while expectational effects may be quite important, they only work to
the extent that a central bank is willing and able to alter real economic conditions to affect
the rate of inflation (Ball [1994])1. And, the predominant way that central banks alter real
economic conditions to affect inflation is by changing aggregate demand relative to aggregate
supply. In previous work (Woglom[2003]), I showed that there is strong evidence that
Reserve Bank policy is affected by real economic conditions, suggesting that they are
responding to real conditions in order to affect future inflation.
I should note that Akinboade and Siebrits (2004) in a recent paper find a sacrifice ratio for South Africa of
essentially zero during the 1990s using Ball’s methodology.
1
3
Therefore, my strategy is to try to identify an accurate forecasting equation that is
based on a variation of the Phillips curve in equation (1), where there is a significant role for
the variables measuring the balance between aggregate demand and aggregate supply. An
immediate problem of empirically implementing equation (1) in the South African context,
however, is the lack of accurate and timely data on unemployment (see for example Hodge
[2002]). In addition, interpreting South African unemployment in terms of aggregate supply
and demand is complicated because of the predominance of structural unemployment. It is
important, however, to recall that cyclical unemployment appears in equation (1) as a
measure of aggregate excess demand because of the historical precedents of early
investigations of the Phillips curve. More modern empirical work has successfully used
“output gaps” to measure the balance of aggregate supply and demand as a substitute for
unemployment rates. In the United States, Okun’s Law provides a direct link between
cyclical unemployment and the output gap, the percentage by which output falls below full
employment output. And, Stock and Watson (1999) (whose paper serves as a model for this
paper), show that a number of detrended output series can be used as measures of the
output gap to forecast US inflation more accurately than can be done with the US
unemployment rate. Consequently, I use detrended measures of South African output to
measure the output gap in my empirical Phillips curves.
The rest of the paper is organized as follows: The next section presents estimates of
the Phillips curve using quarterly data and the detrended log of real GDP as the measure of
the output gap. The third section then describes a forecasting experiment, that attempts to
simulate ex ante forecasts to see whether the estimated Phillips curves can be useful in
forecasting. In this section I compare the accuracy of the baseline Phillips curve equation
(without supply shock terms) to alternate simple forecasts: 1) a naïve forecast that inflation
4
next year will be the same as inflation over the previous four quarters; 2) a forecast based on
a simple autoregression of past inflation rates. Given the success of the Phillips curve
approach, I then examine in section 4 forecasts that are based on the baseline forecasts
where alternative economic indicators replace the output gap term, what I will call biavriate
forecasts. The fifth section compares the accuracy of the baseline Phillips curve forecasts to
the survey data on inflationary expectations compiled by the Bureau of Economic Research
(Kershoff [2000]). The sixth section examines the extent to which the results from the
quarterly data can be replicated with monthly data. While the Phillips curve does appear to
have useful information for forecasting inflation, both with the monthly and quarterly data,
none of these relatively simple forecasts are very accurate. Therefore in section 7, I look at
constructing an “optimal” forecast by looking for a multivariate forecast that is the most
accurate. This section is more speculative because of the problem of data mining. While it
is unclear whether the best forecasts for the most recent period will remain the most
accurate, the results do tell us something about how accurate these forecasts are likely to be.
In addition, in these most accurate forecasts, the output gap still plays a significant and
substantial role in forecasting future inflation. Section 8 concludes.
2. A Phillips Curve for South Africa?
In the empirical work, I make two further modifications to equation (1). First
because we are interested in forecasting future inflation, the dependent variable is the
inflation rate over a longer time interval (one year) than the sampling period (either quarterly
or monthly). Second, because there is substantial evidence that inflation has a unit root (see
for example Akinboade et. al. [2002]), the primary tests of the model will be based on a
differenced version of the Phillips curve, or
 t4   t 1     ( L) t   gapt 1  vt 1 +e t+4
(2)
5
where t4 is the 1-year ahead inflation rate at time t (for quarterly data). t4=100ln(Pt+4/Pt), t-1
is the previous period’s inflation rate ((=400ln(Pt/Pt-1), and where consumer prices in
metropolitan areas is the measure of the price level.(L) is a polynomial in the lag operator
L, gapt-1 is a detrended measure of lagged output, and vt-1 is a measure of lagged supply
shocks. In my baseline estimates I use the percentage appreciation of the nominal effective
exchange rate and the percentage increase in the dollar price of oil as supply shock variables.
The lagged inflation terms in equation (2) are meant as a crude way of capturing inflationary
expectations and other sources of inflation inertia. The differenced specification of equation
(2) is equivalent to the restriction that the sum of the coefficients on lagged inflation is equal
to one. To measure the output gap term in (2) for my baseline Phillips curve, I use the
Hodrick-Prescott (HP) filter (Hodrick and Prescott [1981]) to detrend the log of real GDP.
Because of all of the changes that South Africa has experienced, I use only data since
1990 in my analysis. For want of a better reason, this date corresponds roughly with the
start of Chris Stals’ tenure as governor of the Reserve Bank. With such a relatively short
sample period, I need to be careful to avoid specifications that “over fit” the sample period.
Therefore, in choosing lags lengths I have picked the shortest length where either the
Schwarz-Bayes or Akakie information criteria achieved a local minimum.
Table 1 presents estimates of equation (2) using quarterly data from the 1990s. Each
regression includes 6 lagged values of the change in the quarterly inflation rate (coefficients
not shown). The “t” statistics reported in parentheses are based on standard errors adjusted
for heteroskedasticity and the built-in moving average nature of the errors.
6
Table 1, South African Phillips Curves (I(1) Specification)
(1)
(2)
(3)
(4)
(5)
(6)
1-Year Ahead
1991:4-2003:1
-1.11
(3.35)
Gap-1
App-1
-1.12
(3.55)
-0.04
(1.63)
-1.09
(3.44)
-0.04
(1.62)
0.00
(0.93)
0.74
0.73
Poil-1
Adj. R2
0.66
0.73
(7)
91:498:4
-1.22
(4.12)
1-Qrt Ahead
1991:2-2003:4
-0.32
(0.97)
0.82
0.15
0.14
Std Error 2.76
2.47
2.41
2.44
1.81
3.61 3.63
of Reg
Chow
1.58
1.86
2.63** 2.19*
N.A.
1.22 1.09
Test
* and ** represent “F” statistics that are significant at the 10 and 5% levels
Column (1) is a simple, univariate autoregression with 6 lags to explain future inflation.
Column (2) illustrates that one lag of the output gap is statistically significant over this time
period and that the resulting estimated Phillips curve passes tests for structural stability,
albeit barely at the 10% level of significance. Including the “supply shock” terms (columns
(3) and (4)) marginally improves the fit of the regression and these terms enter with the
correct a priori signs, but the problem of structural instability worsens. Column (5) shows
the estimate of the baseline regression at the start of the forecasting period.
Columns (6) and (7) show the results for the simple autoregression and the simple
Phillips curve for the change in the quarterly inflation rate. While the coefficient on the
output gap is not identified very precisely, it does provide an estimate of the quantitative
importance of the gap for future inflation. In particular, Figure 1 plots the predicted
reduction in quarterly inflation (measured at annual rates) if the output gap is increased by 1
7
percentage point and is maintained at that level for subsequent quarters. This figure shows
that a 1% gap that is maintained for 1 year lowers the inflation rate by less than 1 percentage
point by the end of a year, which implies the so-called sacrifice ratio appears to be high.
While the size of the sacrifice ratio is discouraging, in general, the results of Table 1
suggest that a Phillips curve approach may be a fruitful method for forecasting inflation in
South Africa. Unfortunately, the most direct measures of supply shocks terms are
problematic. Therefore, I take the simple Phillips curve in column (2) as a baseline around
which to measure alternative forecasts and forecasting procedures.
For comparison, Table 2 reproduces the results of Table 1, where the restriction
implied by the unit root for inflation has been relaxed (i.e. lagged inflation replaces lagged
differences in inflation in (2)) as independent variables. While all of the variables for the year
ahead inflation rate enter with the correct sign, none is statistically significant either
individually or jointly.
Table 2: I(0) Specifications of the Phillips Curve
(1)
(2)
(3)
(4)
(5)
Gap-1
1-Year Ahead
1991:4-2003:1
-0.47
(1.62)
App-1
-0.51
(1.81)
-0.02
(1.31)
-0.51
(1.83)
-0.03
(1.34)
0.00
(0.37)
Poil-1
(6)
(7)
91:498:4
-0.45
(1.17)
1-Qrt Ahead
1991:2-2003:4
0.10
(0.23)
Adj. R2
0.80
0.81
0.81
0.81
0.85
0.14
0.12
Std Error
of Reg
Chow
Test
2.12
2.08
2.05
2.08
1.69
3.63
3.66
1.96*
1.62
1.67
1.87*
NA
2.81**
2.51**
8
The results from Table 2 suggest that any conclusions about forecasting inflation using the
unit root restriction should be checked against forecasting procedures that do not impose
this restriction.
3. A Forecasting Experiment
Tables 1 and 2 indicate the ex post ability of various measures to explain historical
rates of inflation. The Reserve Bank, however, must be concerned with its ability to forecast
prospective inflation. Unless the assumptions of a constant structure and correctly specified
model are fulfilled (which is highly unlikely), the correlations in Tables 1 and 2 will overstate
the ability of these equations to forecast on an ex ante basis. We can, however, use the
historical data to perform a “what-if” experiment to provide some evidence on ex ante
forecasts. The “what-if” experiment asks the question suppose a forecaster had been using
the regressions in Tables 1 or 2 to forecast inflation, how good would those ex ante forecasts
have been? I perform this “what-if” experiment starting in 1999, the date by which the
Reserve Bank was probably starting, albeit informally, to target the inflation rate (as Tito
Mboweni was preparing to replace Chris Stals).
The forecasts are ex ante in the sense that they are based on data and information
dated prior to the time at which the forecast would have been made. Thus, for example,
suppose I had been using the baseline Phillips curve of Table 1, column 2 to forecast the 1year ahead rate of inflation for the first quarter of 1999 (1999:1). I would have to base my
forecast on the information that was available by the end of the fourth quarter of 1998.
Therefore, my hypothetical ex ante forecast would differ in two ways from the fitted value for
1999:1 of the regression in column (2) of Table 1. Firstly, the regression available to me in
the first quarter of 1999 would have to be based on data from through 1998:4 (i.e., the
regression in column (5)). Secondly, my measure of the output gap, even for this shorter
9
sample period, would be different than the output gap measure used in the regression for
column (2) of Tables 1 and 2. This difference results from the fact that the HP filter uses all
of the sample data to determine the entire sample estimate of trend output. More
specifically, the estimate of trend output for the first observation depends on the level of
output for the last observation in the sample.
Therefore, to fulfill my “what-if” experiment I use the estimate of the output gap
based on the HP detrended output through 1998:4. To generate a series of such ex ante
forecasts, each subsequent period I add one more period of data to my sample and then reestimate detrended output and then the Phillips curve. The re-estimated Phillips curve is
then used to provide one more forecast of inflation over the next year. Thus, my ex ante
forecast of 1-year ahead inflation for 1999:2 is based on data through 1999:1 and an estimate
of the baseline Phillips curve of column (2) of Table 1.
It is important to note that this “what-if” experiment is still a long ways from a true
ex ante forecast for two separate but related reasons. First, I don’t worry at all about time
lags in the availability of data. In point of fact, the Reserve Bank did not have the data on
1998 fourth quarter real GDP at the start of the first quarter of 1999. Secondly, the
historical data that I use has been revised from its first publication. And, clearly these
revisions to the originally reported data are substantially important, particularly for CPI
inflation. Nevertheless, the experiment should help to identify sample correlations that have
not been stable and/or reliable and a misspecified model.
Table 3 reports the results of using the regressions of columns 2 in Tables 1 and 2
(the baseline forecasts) in an ex ante experiment, along with two simpler, alternative forecasts.
The top panel reports results for the specification where the unit root restriction is imposed
(the I(1) specification) and the bottom panel where this restriction is relaxed (the I(0)
10
specification). The simple alternative forecasts are based on univariate autoregressions (the
regressions in columns (1) in Tables 1 and 2) and on a so-called naïve forecast, which
assumes that the 1-year ahead rate of inflation will equal the rate of inflation over the past
four quarters. RMSE is the root mean square error of the baseline forecast. Relative MSE is
the ratio of the mean squared error of the alternative forecast to the baseline forecast. When
this number is greater than one, the alternative forecast is less accurate than the baseline.
Finally, the column labeled  indicates the information content in the alternative forecast
relative to the baseline Phillips curve forecast.  is the estimated coefficient (with adjusted
standard errors in parentheses) from the regression:
 t4   t 1  (1   ) F BASELINE + F ALTERNATE
(3) ,
where F stands for a forecast. If the alternative forecast has no information that is not
already contained in the baseline forecast  will equal zero, or alternatively if the baseline
forecast contains no additional information  will equal 1.
The top panel of Table 3 indicates that the baseline Phillips curve forecast is more
accurate than either of the other two simple alternatives and contains information not
contained in the other two. The bottom panel shows similar results for the I(0)
specification, but also shows that the I(0) specification provides more accurate forecasts of
inflation than the I(1) specification, at least over this forecast interval.
11
Table 3
Baseline Forecasts I(1) Specifications: 1999:1-2003:1
RMSE Baseline Phillips Curve = 3.12 % pts
Variable:
Relative MSE
Simple:
Univariate
1.18
Naïve
2.60
Baseline Forecasts I(0) Specifications: 1999:1-2003:1
RMSE Baseline Phillips Curve = 2.69 % pts
Variable:
Relative MSE
Baseline I(1)
1.34
Specification
Univariate
1.14
Naïve
3.48

0.12
(0.38)
0.15
(0.11)

0.24
(0.30)
-0.49
(0.76)
-0.16
(0.22)
Figures 2 and 3 show the forecasts underlying the statistics in Table 3. In Figure 2,
the Phillips curve forecasts are not radically different from the forecasts from the
autoregressionn, but the Phillips curve approach helps during the pickup in inflation during
2000 (relative to the forecasts made in 1999) and during the sharp rise in inflation during
2002. Figure 3 shows that for the I(0) specification the Phillips curve forecast really only
adds information to the forecasts made in 1999.
It might at first glance seem reasonable that the unrestricted regression would
provide better forecasts than the restricted regression, but this is not in fact the case in
principle. The unrestricted regression will always fit the entire sample period better than the
restricted specification, as is illustrated by the higher R2, in the respective columns of Table 2
relative to the same columns in Table 1. But the forecasts are based on out-of-sample
properties, and if the unit-root specification is in fact correct, it should provide more
12
accurate out-of-sample forecasts to an incorrectly specified regression equation. Stock and
Watson (1999), however, find a similar result, that the I(0) specification provides more
accurate forecasts of US inflation in their more recent forecasting period. Regardless of how
one views the unit root issue, the results in Table 3 suggest that the output gap does provide
useful information for forecasting South African inflation. In the next section, I look at
whether any other economic variables provide more accurate forecasts of inflation based on
information that is not contained in the baseline forecasts.
Before turning to that question, however, it is worth commenting on the accuracy of
these forecasts. The root mean square errors are not large relative to the standard errors of
the regressions in columns 2 of Tables 1 and 2. They are, however, large relative to the
target range of only 3 percentage points. Unless the Reserve Bank has forecasts of inflation
that are much more accurate, these forecasts errors suggest that the Reserve Bank is likely to
miss its targets relatively frequently.
4. Bivariate Inflation Forecasts with Alternative Economic Indicators.
In this section, I look at alternative economic indicators to see whether they contain
information that is useful in forecasting inflation. Therefore, the strategy for the alternative
forecast is to use a regression equation similar to the baseline Phillips curve and then to
substitute one lagged value of an alternate indicator for the lagged output gap. Table 4
presents results for alternative forecasts based on variations in the baseline Phillips curve.
For example, the first panel of the table uses different measures of the output gap. These
results show that the total production index or just the durables component of the index as
the output measure yields somewhat more accurate forecasts of inflation than the baseline
13
Table 4: Forecasting Performance of Phillips Curve Variations (I(1)
Specification), 1999:1-2003:1
RMSE Baseline Phillips Curve = 3.12 % pts.
Variable:
Transformation
Relative MSE

Real Activity
Vol. of
Production
HP filter
0.92
1st Difference of
Log
HP filter
1.15
1st Difference of
Log
HP filter
1.12
1st Difference of
Log
HP filter
1.23
None
1.22
HP filter
0.95
Leading
None
0.83
Coincident
None
1.02
Lagging
None
1.32
Appreciation
None
1.19
Appreciation
1st Difference
1.26
Oil Price
Inflation ($)
Oil Price
Inflation ($)
None
1.18
1st Difference
1.19
Vol. of Prod.
Durables
Vol. of Prod.
Non-Durabl.
Total
Employment
Capacity
Utilisation
Capacity
Utilisation
Business
Cycle Indic.
Supply
Shocks
0.91
1.13
1.13
1.02
(0.52)
0.19
(0.32)
1.05
(0.35)
0.18
(0.38)
0.02
(0.48)
0.06
(0.42)
0.18
(0.34)
-0.28
(0.73)
0.74
(0.35)
0.70
(0.43)
0.43
(0.32)
-0.21
(0.60)
0.14
(0.31)
0.02
(0.43)
0.09
(0.58)
0.10
(0.39)
14
Phillips curve and virtually all of the information in the baseline forecast is contained in the
alternative. Detrended capacity utilization and the untransformed leading indicator series
also provide more accurate forecasts, but it is not as conclusive that these alternative
forecasts contain all of the information contained in the baseline forecasts. Somewhat
surprisingly, the last panel of Table 4 indicates that the supply shock terms that play a
prominent role in discussions of South African inflation do not seem to contain information
not contained in the baseline forecasts.
Table 5 presents results to see if there are economic indicators of cost-push inflation
that could be useful in forecasting inflation. Total producer price inflation and the import
components appear to contain useful information, but not all the information contained in
the baseline forecasts. Somewhat surprisingly, measures of wage inflation do not appear
useful in forecasting consumer price inflation.
15
Table 5: Forecasting Performance of Producer Prices and Wages
(I(1) Specification), 1999:1-2003:1
RMSE Baseline Phillips Curve = 3.12% pts.
Variable:
Transformation
Relative MSE

Prod. Price
Inflation
Total
Food
Imports
Wage
Inflation
Remuneration
Unit Labor
Costs
None
0.94
1st Difference
1.20
None
1.10
1st Difference
1.21
None
0.98
1st Difference
1.11
None
1.20
1st Difference
1.21
None
1.22
1st Difference
1.26
0.61
(0.28)
0.16
(0.27)
0.31
(0.24)
0.07
(0.40)
0.52
(0.24)
0.35
(0.10)
0.09
(0.38)
0.06
(0.41)
0.05
(0.42)
0.10
(0.33)
Finally, Table 6 looks at financial market variables as possible indicators of future
inflation. The first panel uses the growth of financial aggregates, which conceivably could be
better indicators of real economic activity than the lagged output gap. The growth rate of
M3 produces as accurate forecasts as the baseline, but does not appear to contain all of the
same information as in the baseline.
16
Table 6: Forecasting Performance of Financial Variables (I(1)
Specification), 1999:1-2003:1
RMSE Baseline Phillips Curve = 3.12% pts.
Variable:
Transformation
Relative MSE

Aggregate
Growth Rates
M3
None
1.00
1st Difference
1.24
None
1.46
1st Difference
1.20
3 month
None
0.69
6 month
None
0.71
12 month
None
0.70
12 month –
3 month
12 month –
6 month
6 month 
3 month
None
1.05
None
1.16
None
1.01
Total Credit
Short-Term
CD Rates
0.51
(0.42)
-0.00
(0.46)
-0.23
(0.41)
0.09
(0.37)
0.99
(0.29)
0.96
(0.29)
0.97
(0.30)
0.39
(0.24)
0.21
(0.26)
0.48
(0.23)
Short-term interest rates could improve inflation forecasts for two possible reasons.
First they could also be indicators of future real economic activity. In addition, however,
through the Fisher relationship, they contain an alternate measure of inflationary
expectations. The results seem to indicate that the short-term interest rates provide more
accurate forecasts of inflation that contain virtually all of the information in the baseline
forecasts. The last 3 rows of the table are interesting because the slope of the yield curve is
apparently less useful than the levels of the individual short-term interest rates. In some
countries the slope of the yield curve has provided accurate forecasts of future economic
activity (i.e., Stock and Watson [1989]).
17
As noted in the discussion of Table 3, there are differences in the forecast accuracy
based on the unit-root restriction. Therefore, Table 7 presents results to check whether the
key results from Tables 4-6 are sensitive to the unit root restriction. These results indicate
the there are fewer variables that add much information to the baseline forecasts (which are
not very different from the forecasts from the autoregressions). In the I(0) specification, the
product price variables, however, seem to be more important than under the alternate
specification, but the differences are small.
Table 7: Forecasting Performance of I(0) Forecasts, 1999:1 2003:1
RMSE Baseline Phillips Curve = 2.69% pts
Variable:
Transformation
Relative MSE

Phillips
Curve Var.
Volume of
Production
Leading
Indicator
Oil Price ($)
Inflation
Appreciation
HP Filter
1.06
None
1.19
None
1.17
None
1.19
Total
None
0.90
Imports
None
0.82
M3 growth
None
1.15
r12
None
0.95
Prod Price
Inflation
Financial
Variables
0.01
(0.96)
-0.49
(0.58)
-0.27
(1.17)
-0.49
(0.58)
0.84
(0.92)
0.74
(0.45)
-0.75
(0.47)
0.64
(0.47)
The results of our ex ante experiment are promising: 1) Detrended output, a
variable over which the Reserve Bank has some influence, does help to forecast future
18
inflation. 2) Product price inflation and short-term interest rates also appear to have
important information concerning future inflation. The bad news is none of these simple
bivariate forecasts are very accurate.
5. Phillips Curve Forecasts versus BER Surveys of Inflationary Expectations
Since the third quarter of 2000, the Bureau of Economic Research at Stellenbosch
Unversity has conducted surveys of business people, labor leaders and households to gauge
inflationary expectations. The business and labor surveys ask respondents to forecast
average inflation for the current calendar year and over the next calendar year. From these
data I inferred a 1-year ahead forecast by taking a geometric weighted average of the two
forecasts. For example, the estimated 1-year ahead forecast from the 2000:4 survey is:
F 2000:4  ({[1  F 2000 )(1  F 2001 )3 ]}0.25  1
The household survey asks respondents just for their expectations over the current calendar
year, which I use as their one-year ahead forecast.
Table 8 shows the relative performance of the survey expectations to the baseline
Table 8: Forecasting Performance of BER Forecasts, 2000:3-2003:1
RMSE Baseline I(1) Phillips Curve = 3.77 % pts.
Variable:
Relative MSE

Simple
Univariate
1.15
Naïve
1.92
Business
Financial
Sector
NF
Business
Labor
0.85
Average
1.00
Households.
3.47
0.99
1.17
-3.55
(1.65)
0.11
(0.23)
0.58
(0.21)
0.50
(0.21)
0.42
(0.20)
0.50
(0.21)
-0.60
(0.26)
19
Phillips curve forecasts using the I(1) specification. Not surprisingly the forecasts from the
financial sector appear to be the most accurate, and all of the business and labor forecasts
appear to have information, not contained in the baseline forecast.
Table 9: Forecasting Performance of BER Forecasts, 2000:3-2003:1
RMSE Baseline I(0) Phillips Curve = 2.88 % pts.
Variable:
Relative MSE

Simple
Univariate
0.97
Naïve
3.28
Business
Financial
Sector
NF
Business
Labor
1.46
Average
1.71
Households.
5.94
1.70
2.00
1.48
(0.93)
-0.46
(0.18)
0.16
(0.32)
0.09
(0.30)
-0.08
(0.26)
0.04
(0.29)
-0.24
(0.18)
Unfortunately, these results are specific to the I(1) specification. As is shown in Table 9,
when one relaxes the unit root restriction none of the survey forecasts is as accurate as the
baseline Phillips curve and none appears to provide information relative to the baseline
forecast. Although I should note that over this sample period, the Phillips curve model
doesn’t seem to add information to the simpler forecast based on an autoregression.
Figure 4 graphs the two Phillips curve forecast along with the most accurate BER
forecast, that of the Financial Analysts. The figure shows that the BER forecast does a better
job of predicting the acceleration of inflation during 2002, but misses badly on the
20
subsequent fall in inflation. The Phillips curve forecasts are somewhat more accurate
because while they don’t predict the rise in inflation during 2002, they are not that far off
when the inflation rate declines during 2003.
6. Monthly Data
In this section, I look at the extent to which the results from the quarterly data can
be replicated with monthly data. The starting place is to see whether the data indicate that
there is anything like a Phillips curve relationship in the monthly data. For this analysis the
index of total production is used instead of the unavailable GDP data. Table 10 presents
Table 10: Phillips Curves – Monthly Data:
I(1) Specification
1-yr Ahead
1-month Ahead
1991:4-2003:2
1990:8-2003:12
(1)
(2)
(3)
(4)
Gap-1
-0.23
-0.14
(0.93)
(1.69)
Adj. R2
0.67
0.68
0.27
0.27
Std Error of
3.18
3.15
Reg
Chow Test
1.85**
1.55*
I(0) Specification
1-yr Ahead
1991:4-2003:2
(1)
(2)
4.94
4.94
2.36**
1.95**
Gap-1
1-month Ahead
1990:8-2003:12
(3)
(4)
-0.22
(1.09)
-0.23
(1.59)
Adj. R2
0.79
0.79
0.31
0.31
Std Error of
Reg
Chow Test
2.56
2.55
4.81
4.80
4.65**
4.14**
2.22**
2.03**
21
results for estimates of basic Phillips curves for the two specifications of unit roots for
inflation. In this case, the optimal lag length for the autoregression was 14 months.
Monthly inflation rates are more volatile and the estimates of the effect of output gaps are
less precise. Although none of the estimated coefficients on the output gap is statistically
significant, they all have the correct a priori sign. The Chow tests, however, indicate that the
estimates may suffer from structural instability, particularly the I(0) specification.
The detailed results for the ex ante bivariate forecasts are relegated to the Appendix.
The forecasts from the baseline Phillips curves (based on the regressions in column 2 in
Table 10) are not much more accurate than the autoregressions and none of the available
monthly economic indicators appears to add much information, with two interesting
exceptions, short-term interest rates and the producer price of imported goods.
7. “Optimal” Forecasts
In the previous sections, I showed that Phillips curve effects seem to be a
determinant of South African inflation, and that the output gap provides useful information
for forecasting future inflation. Unfortunately, as Figures 3 and 4 illustrate, these forecast
are not very accurate, and none of these simple forecasts was able to capture the sharp runup
in inflation in 2002, nor its subsequent decline. Therefore, in this section, I ask a somewhat
more speculative question: In hindsight, how could one have forecasted inflation more
accurately and how accurate might these “optimal” forecasts have been. In other words, on
the basis of the bivariate tests, can one identify a small number of indicators to forecast
inflation more accurately? Since I am basing my choices on the basis of the performance in
the bivariate tests, the choice of variables may well not be reliable for the future. In any
22
event, this analysis does provide information about how accurate an ex ante forecast is likely
to be.
To construct these so-called “optimal” forecasts, I started with the basic Phillips
curve equation with an ex ante estimate of the output gap. I then added the 12-month CD
rate, which appeared to be one of the most successful indicators in the bivariate forecasts. I
then searched among the other indicators to see if I could find an indicator that would
improve on this trivariate forecast. The search was relatively easy because the only indicator
that improved the trivariate forecast was producer price inflation of imported goods.
Table 11 provides information about the accuracy of these forecasts. In each case,
the accuracy and information of the forecast is compared to the respective “baseline”
forecast from a simple Phillips curve specification with an output gap term. The tables show
that these alternative forecasts substantially increase forecast accuracy. This exercise is, of
course, subject to problems of data mining. Data mining, however, is liable to lead to
misspecified forecasting equations that are not stable over time. We can check on some of
these problems by looking at the reasonableness of the regression equation underlying these
forecasts.
Table 12 shows the full sample estimate of the forecasting equation (i.e., the equation
used for the last ex ante forecast) and these estimates appear reasonable. All of the estimated
coefficients enter with the correct a priori signs and are statistically significant. The Chow
tests, however, indicate the equations suffer from problems of structural instability, which
could be associated with over fitting the sample period.
While the Chow tests are signaling that one must be cautious in interpreting these
estimates, it is worth noting that these estimates are very encouraging. The estimated
coefficients on the output gap are about twice the size of the simple Phillips curve estimates
23
in Table 1. If these coefficients are stable, they suggest a much more sanguine view of the
sacrifice ratio. In addition, the negative and substantial coefficient on the interest rate is
interesting for two reasons: 1) It suggests that the interest rate is not acting as a proxy for
inflationary expectations; 2) Instead, it suggests that the interest rate is capturing the effects
of the current real interest rate on future levels of aggregate demand. If this turns out to be
true it is important: it implies that the Reserve Bank by changing short-term nominal
interest rates can change the rate of inflation relative to the rate expected in financial
markets.
Table 11: “Optimal” Forecasts
Quarterly Data
1999:1-2003:2
(1)
(2)
I(1)
I(0)
RMSE
2.38%
1.99%
Relative
0.58
0.54
MSE
0.95
1.08

(0.39)
(0.25)

Monthly Data:
1999:1-2003:2
(4)
(5)
I(1)
I(0)
3.12%
3.02%
0.62
0.81
1.27
(0.29)
1.14
(0.43)
Table 12: “Optimal” Forecasting Equations
Quarterly Data
Monthly Data:
1991:4-2003:2
1991:4-2003:2
(1)
(2)
(4)
(5)
I(1)
I(0)
I(1)
I(0)
Gap-1
-1.37
-0.75
-0.33
-0.23
(4.53)
(4.99)
(3.13)
(2.09)
r12-1
-0.57
-0.30
-0.51
-0.22
(3.57)
(3.84)
(3.77)
(1.40)
Producer
0.11
0.15
0.07
0.07
Import
(2.95)
(5.16)
(3.29)
(3.87)
Inflation-1
Adj. R2
0.88
0.90
0.77
0.82
Std Error of
Reg
Chow Test
1.65
1.49
2.68
2.33
5.00**
3.71**
1.17
4.99**
24
Figure 5 shows that not only are the quarterly, forecasts more accurate, but they do a
much better job of capturing turning points: the run up of inflation during 2002 and the
subsequent decline. One would expect that the presence of the import price inflation is
helping to capture the effects of the exchange rate. But the fact that these ex ante forecasts
seem to be tracking turning points suggest that they may be valuable in forecasting future
inflation. Unfortunately, the results from the monthly forecasts are not as encouraging.
While the forecasts are substantially more accurate (at least in the I(1) specification) than the
baseline forecasts in terms of mean square error, Figure 6, shows this is an artifact of
estimating the average level of inflation more accurately. None of the monthly forecasts are
able to track turning points very accurately.
8. Conclusion
In spite of all of the recent changes that have affected the South African economy,
the evidence from this paper suggests that the current output gap is related to future
inflation, as is suggested by the theory of the modern Phillips curve In addition, short-term
interest rates and the rate of inflation of imported producer goods also appear to have
significant forecasting power. The price of imported goods is most likely capturing
information on the effect of the exchange rate on domestic price inflation. Short-term
interest rates appear to be capturing the effects of current monetary policy on future levels
of aggregate demand.
That is the goods news. Unfortunately, the simple Phillips curve forecasts are not
terribly accurate and the regression equations of the more accurate, augmented Phillips
curves (in Table 12) appear to suffer from instability. Therefore, one must interpret with
caution, the forecasting performance of the “optimal” forecasts analyzed in section 7. Those
results are, however, encouraging because if they hold up they suggest mean squared forecast
25
errors on the order of 1-2 percentage points for year-ahead inflation rates. They also imply
much more substantial effects of the current output gap and real interest rates on future
inflation than the simple, baseline Phillips curve. If those results prove to be stable, the
Reserve Bank should be able to forecast inflation accurately and affect future inflation in
ways to bring those forecasts within the target range.
26
Figure 1: Reduction in Inflation from
1% Output Gap
0.5
0
1
2
3
4
5
7
6
Percentage Points
-0.5
-1
-1.5
-2
-2.5
Quarters
8
9
10
11
12
27
Figure 2: Forecasts of CPI Inflation
14
12
10
1-Year Ahead Inflation
6
Baseline Forecast
Simple Autoregression
4
2
/0
4
/0
3
20
02
/0
2
20
02
/0
1
20
02
/0
4
20
02
/0
3
20
01
/0
2
Date of Forecast
20
01
/0
1
20
01
/0
4
20
01
/0
3
20
00
/0
2
20
00
/0
1
20
00
/0
4
20
00
/0
3
19
99
/0
2
19
99
/0
1
19
99
-2
19
99
at
e
0
D
Percent
8
28
Figure 3:Forecasts of CPI Inflation
(I(0) Specification)
14
12
8
1-Year Ahead Inflation
Baseline Forecast
Simple Autoregression
6
4
2
/0
4
02
/0
3
20
02
/0
2
20
02
/0
1
20
02
/0
4
20
01
/0
3
20
01
/0
2
Date of Forecast
20
01
/0
1
20
01
/0
4
20
00
/0
3
20
00
/0
2
20
00
/0
1
20
00
/0
4
20
99
/0
3
19
99
/0
2
19
99
19
19
99
e
/0
1
0
D
at
Percent
10
29
Figure 4: Forecasts of CPI Inflation versus BER Survey Data
14
12
10
Percent
8
1-Year Ahead Inflation
I(1) Specification
6
I(0) Specification
BER Financial Analysts
4
2
0
2000/03
2000/04
2001/01
2001/02
2001/03
2001/04
2002/01
-2
Date of Forecast
2002/02
2002/03
2002/04
2003/01
30
Figure 5: "Optimal" Quarterly Forecasts of Inflation
14
12
10
8
1-Year Ahead Inflation
4
I(1) Specification
I(0) Specification
2
-4
-6
Date of Forecast
01
20
03
/
03
04
20
02
/
20
02
/
02
20
02
/
04
01
20
02
/
20
01
/
03
20
01
/
02
20
01
/
04
01
20
01
/
20
00
/
03
20
00
/
01
02
20
00
/
20
00
/
04
19
99
/
02
03
19
99
/
-2
19
99
/
01
0
19
99
/
Percent
6
19
99
/0
19 1
99
/0
19 3
99
/0
19 5
99
/0
19 7
99
/0
19 9
99
/1
20 1
00
/0
20 1
00
/0
20 3
00
/0
20 5
00
/0
20 7
00
/0
20 9
00
/1
20 1
01
/0
20 1
01
/0
20 3
01
/0
20 5
01
/0
20 7
01
/0
20 9
01
/1
20 1
02
/0
20 1
02
/0
20 3
02
/0
20 5
02
/0
20 7
02
/0
20 9
02
/1
20 1
03
/0
1
Percent
31
Figure 6: "Optimal" Monthly Forecasts
14
12
10
8
1-Yr Ahead Inflation
I(1) Specification
6
I(0) Specification
4
2
0
Date of Forecast
32
Appendix:
A. Data and Methods
All data with the exception of the dollar price of oil were taken from the South
African Reserve Bank’s Web site. Monthly data, with the exception of interest rates, were
transformed into quarterly data by taking 3-month averages before any transformations of
the basic data were done. For example, the quarterly CPI observation for the first quarter of
2001 is given by:
CPI2001,Q1 = CPI2001,Jan + CPI2001,Feb + CPI2001,Mar
Inflation rates and other growth rates were calculated as continuously compounded annual
rates, so that the rate of inflation for the first quarter of 2001 is given by:
2001,Q1 = 400[ln(CPI2001,Q1/ CPI2000,Q4)-1]
One-year ahead inflation rates were calculated similarly. So, for example, the 1-year ahead
inflation rate for January of 2001 is given by:
2001,JAN = ln(CPI2002,JAN/ CPI2001,JAN)-1
The interest rate data are weekly and the monthly data and quarterly observations are given
by the interest rate on the first week of the month or quarter.
The raw employment, remuneration and unit labour cost series are not comparable
pre and post 2001:2. Therefore, I assumed that the rate of change of each of these series
during 2002:3 was the average of the rate of change of the two adjacent quarters. For the
employment series, I then adjusted the index for 2002:3 using this assumption and the
2002:2 level of the index. Subsequent values of the index were given by the actual
percentage increase times the level of the index in the previous quarter.
The oil price data are daily data that were taken from a US Department of Energy
web site (http://www.eia.doe.gov/oil_gas/petroleum/info_glance/crudeoil.html). Monthly
33
averages were calculated from the daily data, and quarterly average from the 3 monthly
averages. Inflation rates were then calculated as detailed above.
The specific series used are detailed below:
Prices:
Consumer Prices:
7032N
Producer Prices:
Total:
7050N
Food:
7049N
Imports
7045N
Oil Price Europe Brent Spot Price FOB ($/bbl)
Output Measures:
Real GDP
Index of tot. Product.:
Index of Product, Dur:
Index of Product. Ndur:
Capacity Utilization:
Tot. Non-agric. Employment:
Business Cycle Indicators:
Leading:
Coincident:
Lagging
Labor Costs:
Money and Finance
Remuneration
Unit Labour Costs
6006D
7075N
7073N
7074N
7078L
7009L
7090N
7091N
7092N
7012L
7015L
M3
1374N
Tot. credit extended by montry instits:1368M
3-month Negotiable CD rate:
1411W
6-month Negotiable CD rate:
1412W
12-month Negotiable CD rate:
1413W
Exchange Rate
Nominal effective exchange rate
5369M
34
B. Bivariate Forecasts Monthly Data
Table B.1.: Forecasting Performance of Phillips Curve Monthly
Data, 1999:1-2003:2 I(1)
RMSE Baseline Phillips Curve = 3.95 % pts
Variable:
Transformation
Relative MSE

Simple
Univariate
1.11
Naïve
1.70
Prod. Price
Inflation
Total
1.02
Food
1.13
Imports
0.99
Supply
Shocks
Oil Price
Inflation ($)
Appreciation
Financial
Variables
1.13
1.11
M3 growth
1.12
r3
0.79
r6
0.79
r12
0.79
r12-r3
1.06
r12-r6
1.08
-3.50
(1.42)
-0.22
(0.28)
0.04
(1.48)
-2.47
(1.10)
0.64
(0.90)
-3.19
(1.65)
-4.79
(1.62)
-2.81
(0.95)
1.48
(0.71)
1.50
(0.69)
1.49
(0.72)
-1.98
(1.06)
-2.07
(0.78)
35
Table B.2 Forecasting Performance of Phillips Curve Monthly Data,
1999:1-2003:2 I(0)
RMSE Baseline Phillips Curve = 3.37 % pts
Variable:
Relative MSE

Baseline
1.49
-0.23
from Table
(0.49)
A.1
Simple
Univariate
1.03
Naïve
2.34
Prod. Price
Inflation
Total
0.96
Food
1.06
Imports
0.89
Supply
Shocks
1.06
Oil Price
Inflation ($)
Appreciation
-2.71
(2.86)
-0.52
(0.36)
3.09
(2.20)
-0.69
(1.25)
1.54
(0.39)
-2.55
(1.61)
1.03
-3.25
(3.21)
M3 growth
1.04
r3
0.98
r6
0.98
r12
0.97
-1.85
(1.62)
0.84
(1.38)
0.86
(1.31)
0.92
(1.30)
r12-r3
1.06
r12-r6
1.08
Financial
Variables
-3.41
(2.54)
-2.21
(1.49)
36
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