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Forecasting Thailand's Core Inflation

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This paper develops an approach for forecasting in Thailand core inflation. The key innovation is to anchor the projections derived from the short-term time-series properties of core inflation to its longer-run evolution. This involves combining a short-term model, which attempts to distill the forecasting power of a variety of monthly indicators purely on goodness-of-fit criteria, with an equilibrium-correction model that pins down the convergence of core inflation to its longer-run structural determinants. The result is a promising model for forecasting Thai core inflation over horizons up to 10, 24, and 55 months, based on a root mean-squared error criterion as well as a mean absolute error criterion.
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Content Preview
WP/04/90


Forecasting ThailandТs Core Inflation

Tao Sun



© 2004 International Monetary Fund
WP/04/90


IMF Working Paper

Asia and Pacific Department

Forecasting Thailand’s Core Inflation

Prepared by Tao Sun1

Authorized for distribution by Alessandro Zanello

May 2004


Abstract

This Working Paper should not be reported as representing the views of the IMF.
The views expressed in this Working Paper are those of the author(s) and do not necessarily represent
those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are
published to elicit comments and to further debate.

This paper develops an approach for forecasting in Thailand core inflation. The key
innovation is to anchor the projections derived from the short-term time-series properties of
core inflation to its longer-run evolution. This involves combining a short-term model, which
attempts to distill the forecasting power of a variety of monthly indicators purely on
goodness-of-fit criteria, with an equilibrium-correction model that pins down the convergence
of core inflation to its longer-run structural determinants. The result is a promising model for
forecasting Thai core inflation over horizons up to 10, 24, and 55 months, based on a root
mean-squared error criterion as well as a mean absolute error criterion.

JEL Classification Numbers: C53, E37

Keywords: Forecasting, Core Inflation

Author’s E-Mail Address: tsun@imf.org; suntao@pbc.gov.cn




1 Many thanks are due to Alessandro Zanello, Alessandro Rebucci, and Varapat Chensavasdijai
for guidance, comments, suggestions, and encouragement. Nickolay Nedelchev and
Teresa Del Rosario provided excellent assistance in compiling the database.

- 2 -
Contents Page

I. Introduction....................................................................................................................4

II. Data...... ..........................................................................................................................5

III. Modeling
Core
Inflation ................................................................................................6
A.
Short-Run
Dynamics..........................................................................................6
B.
Long-Run
Dynamics..........................................................................................7
C.
Robustness
Checks...........................................................................................10

IV.
Conclusions..................................................................................................................10

References................................................................................................................................28

Figures

1.
BOT’s Core Inflation Projections and Actuals ..............................................................4
2.
Chow Test of Model 4 .................................................................................................16
3. Actual
and
Fitted
Value of Model 4 ............................................................................16
4.
Residual Density and the Residual Correlogram of Model 4 ......................................17
5. Forecasting
Performance of Model 4...........................................................................17
6. Cointegration
Relations
of Core Inflation, Import Price Index, and Average Wage...18
7.
Chow Test of Model 3 .................................................................................................18
8. Forecasting
Performance of Model 3...........................................................................19
9.
Chow Test of Model 2 .................................................................................................19
10. Forecasting
Performance of Model 2...........................................................................20
11.
Chow Test of Model 1 .................................................................................................20
12.
Forecasting Performance of Model 1...........................................................................21
13.
Chow Test of Model 4 (1995m5–2001m10) ...............................................................21
14.
Forecasting Performance of Model 4 (2001m11–2003m10).......................................22
15.
Chow Test of Model 4 (1995m5–1999m3) .................................................................22
16.
Forecasting Performance of Model 4 (1999m4–2003m10).........................................23

Tables

1. Data
Description
and Transformation..........................................................................11
2.
RMSE and MAE of Four Models ................................................................................13
3.
Diagnostic Statistics for the Single-Equation Inflation Model 4.................................13
4.
ADF (4) Statistics for Testing for a Unit Root in Various Time Series ......................14
5.
F and Related Statistics for the Sequential Reduction from the Fourth-Order
VAR
to
the
First-Order VAR...........................................................................14
6. Standard Statistics and Estimates of Cointegration Analysis to First-Order VAR


Cointegration Analysis, 1995 (5) to 2003 (10) ................................................14

- 3 -
7.
Coefficients of Cointegration Vectors Beta and Corresponding Adjustment
Coefficients
Alpha ...........................................................................................15
8.
Comparison of Forecasting Performance by Model 4 in Different Time Horizons ....15

Appendices

I. Model
1 ........................................................................................................................24
II. Model
2 ........................................................................................................................25
III. Model
3 ........................................................................................................................26
IV. Model 4 ........................................................................................................................27

- 4 -

I. INTRODUCTION
Forecasting inflation is a key task for a central bank with an inflation-targeting framework,
such as the Bank of Thailand (BOT). Under inflation targeting, the conduct of policy is
informed by the general direction of future inflation, with due disregard for transitory
fluctuations in the inflation rate or the price level. The BOT combines judgment and the
output of a structural econometric model to produce quarterly forecasts of core inflation—the
bank’s intermediate target—over the next eight quarters. These forecasts are published in a
quarterly Inflation Report and widely discussed in the press.
Forecasting with precision
4.0
4.0
Figure 1. BOT's Core Inflation Projections and
Thailand’s core inflation has proved
3.5
Actuals
3.5
difficult. A comparison of the
BOT's four-quarter-
BOT’s published forecasts with
3.0
3.0
ahead forecast
expost realizations of quarterly core
2.5
Actual
2.5
inflation rates shows that forecast
2.0
2.0
errors have been persistent and one-
sided (Figure 1).
1.5
1.5
1.0
1.0
This paper develops an alternative
approach for forecasting Thai core
0.5
0.5
inflation. The key innovation is to
0.0
0.0
anchor the projections derived from
01q2 01q3 01q4 02q1 02q2 02q3 02q4 03q1 03q2 03q3 03q4 04q1 04q2 04q3 04q4
the short-term time-series properties
of core inflation with its longer-run evolution. This involves combining a short-term model,
which attempts to distill the forecasting power of a variety of high-frequency indicators purely
on goodness-of-fit criteria, with an equilibrium-correction model that pins down the
convergence of core inflation to its longer-run structural determinants. As such, the approach
attempts to bridge the gap between an analysis that focuses purely on the time-series
properties of a variable at the expense of an economic interpretation of its dynamics and an
analysis that focuses exclusively on a structural representation at the expense of forecasting
power. The approach in this paper could be applicable to other countries that have adopted an
inflation-targeting framework.
The starting point is to select a parsimonious specification of an unrestricted model of the
data-generating process driving Thailand’s core inflation. This has been done following the
General-to-Specific methodology (Hendry, 2001) as implemented in the PcGets software.
PcGets selects a data-congruent model even though the precise formulation of the
econometric relationship among the variables of interest is not known a priori.2

2 A congruent model will have as main attributes constant parameters and conditionally
homoscedastic, serially uncorrelated, and normally distributed errors.


- 5 -
Starting from a general model that is data congruent, PcGets eliminates statistically
insignificant variables, with diagnostic tests checking the validity of these “reductions” to
preserve the data congruency of the final specification. The General-to Specific process of
streamlining an initial unrestricted model follows either a “liberal strategy,” which minimizes
the non-deletion probability of relevant variables, or a “conservative strategy,” which
minimizes the non-deletion probability of irrelevant variables.
Both strategies have been followed in this paper, with an additional innovation. The common
components of the variables discarded by PcGets (extracted through a principal component
analysis) are then reintroduced as a potentially significant regressor in the PcGets-reduced
model. The augmented model is then subject again to the PcGets selection process to assess
whether the principal components add to the forecasting power.
The last enhancement of the forecasting model adds to the final selection an equilibrium-
correction term (ECM term) that captures the long-run determinants of Thai core inflation.
The ECM (identified through cointegration analysis) adds an economic interpretable element
to the model and pins down the long-term forecast. As such, it reduces the chances of a
structural bias in the forecasts.
The result of this hybrid approach is a model for forecasting inflation over horizons up to 10,
24 and 55 months that is promising, based on a root mean-squared error criterion as well as a
mean absolute error criterion. The parsimonious model formulated generates out-of-sample
forecasts that appear to be broadly satisfactory. Reliance on monthly variables in the model
allows for a prompt update of core inflation forecasts and—thus—could help in monetary
policy evaluation in the context of IMF surveillance work on Thailand.
The paper is organized as follows. Section II documents the variables used in the model
selection and data transformation. Section III describes the best-performing model. It shows
that the progressive addition of an error correction term, the lagged core inflation, and the
principal components of an array of excluded variables improve the forecasting accuracy of
the model. Section IV concludes and presents possible extensions of the paper’s approach by
focusing on quarterly data and a larger dataset.
II. DATA
The dependent variable in the forecasting regressions is the series of seasonally adjusted,
monthly percent changes in Thailand’s consumer price index, purged of its raw food and
energy components. This series is referred to as “core inflation” and corresponds to the policy
target chosen by the BOT in July 2000, when it officially embraced an inflation-targeting
framework. Although the BOT aims at keeping quarterly core inflation in the range of
0–3½ percent, monthly changes are the focus of this paper’s modeling exercise in order to
capitalize on information embedded in a variety of high-frequency indicators. The exercise is
later repeated with quarterly inflation rates to cross-check the robustness of the results.
A group of potential explanatory variables available at a monthly frequency has been selected
before the specification search. These include commodity and asset prices, indicators of cost
pressures in product or labor market (such as industry selling price indexes, wages, unit labor
costs, and import prices), and measures of pressure on the demand side (such as the money
supply and other financial indicators).

- 6 -
Appropriate transformations of the raw data have been made to produce approximately
uniform variability in the series over the sample range. All data are seasonally adjusted. Since
we are dealing with series in terms of their month-on-month growth rates,
“log-differences” of all variables used (except the nominal interest rate) have been taken.3
Table 1 gives the names, description, units, sources, and transformation of the time series
considered in the econometric applications.
Data availability and required transformations limit the period used for model estimation and
testing to May 1995 to October 2003. For example, some variables of interest (namely, the
retail petroleum price index, the producer price index, and the farm price index) are not
available prior to January 1995. The introduction of lags in explanatory variables further
limits the sample period. The final sample period, however, is broadly consistent with that
used to estimate the BOT’s quarterly structural model, which takes 1994Q1 as the starting
point. 4
III. MODELING CORE INFLATION
A. Short-Run Dynamics
The specification search for a strong forecasting performance involved a comparison among
four alternative models. Model 1 is obtained from the PcGets elimination of statistically
irrelevant variables from a General Unrestricted Model (GUM). Model 2 is Model 1 with
additional explanatory variables: seven principal components (with three lags) capturing the
common comovements in the variables that appeared in the general model but were rejected in
the reduction. Model 3 is Model 2 with the three lags of core monthly inflation. Finally,
Model 4 is Model 3 augmented by an equilibrium-correction term.
These models are compared in terms of their out-of-sample forecasting accuracy. Forecasting
performance is measured by their root mean-squared error (RMSE) and mean absolute error
(MAE). On both criteria Model 4 outperforms the others (Table 2).
Model 4 performs well in terms of diagnostic tests (Table 3). Figure 2 shows that the
parameters in Model 4 are constant. Empirically, the residuals are normally distributed,
homoscedastic, and serially uncorrelated, and the null hypothesis of no omitted variables is
easily accepted for a wide variety of variables. Figure 3 plots the fitted and actual values of
monthly core inflation and illustrates how well Model 4 explains the data. Figure 4 records the
residuals density and the residual correlogram of Model 4, pointing to lack of serial
correlation and near-white-noise properties. Figure 5 shows the out-of-sample forecasting

3 However, in cointegration analysis, the logarithm of the levels of the consumer price index
(net of the food and energy components), an import price index, and the average wage are
used.
4 Within the framework of this model, the BOT has chosen the following variables to forecast
core inflation: lagged core inflation, an estimate of the GDP gap, the import price index, the
raw food consumer price index, and an error-correction term.

- 7 -
power is very good and consistent with the long lead needed to conduct of a forward-looking
monetary policy.
At the root of Model 4’s strong performance lies the fact that it supplements the (statistical)
short-run analysis of its competitors with a consideration of the (economic) long-run effects of
the error-correction term. In other words, it captures the economically meaningful view that
inflation is ultimately determined by pressures in labor costs and the nominal exchange rate,
while its shorter-run evolution may be also influenced or described by other variables.
In order to put in perspective the performance of Model 4, it is useful to present its genesis as
a progressive enhancement of the simpler Models 1, 2, and 3.
Model 1—the starting model—is produced by reduction of a general model involving all the
20 variables in Table 1, with three lags. The choice of lagged variables has been informed by
preliminary unit root tests, and ensures that all variables are stationary. In the reduction
process leading to Model 1, PcGets follows the “liberal strategy” so as to keep as many
variables as possible and avoid loss of information (Appendix I reports key statistics for this
model as well as the individual parameter values).
Model 2 adds to Model 1 the seven first principal components of variables that PcGets
excludes, to capture the information content of the variables dropped out.5 In the case of
Model 1, principal components are extracted from 10 variables. These variables are the
percent changes in: the capacity utilization rate (dlcu), the nominal effective exchange rate
(dlneer), the world export unit value for manufactures (dlmuv), and housing price (dlacomm),
reserve money (dlrm), the import price index (dlpmb), a world commodity price index
(dlcomm), the average wage (dlavwag), and stock price index (dlstp). Seven stationary
principal components are enough to explain 95 percent of comovements in all these variables.
To match Model 1’s lag structure, three lags of the principal components are included, and
another PcGets regression with the conservative strategy is run.6 The resulting model is
Model 2 (details are in Appendix II).
Model 3 adds lags of the endogenous variable to allow for persistence in core inflation (details
are in Appendix III).
B. Long-Run Dynamics
Model 4 is the final stage in this search process. It augments Model 3 with an equilibrium-
correction term lagged once. The rationale for this addition is as follows. Model 1, 2, and 3
are statistical models that ignore the long-run determinants of inflation and simply aim at
capturing the best possible description of the short-run dynamics of this variable. As such,

5 Basically, principle component regression is used for solving possible multicollinearity
problems that may lead to the insignificance of individual variables—and hence, their
elimination in the PcGets search.
6 Since there are lots of variables here, I use the “conservative strategy” to get rid of the least
significant variables and arrive at as parsimonious a parametrization as possible.

- 8 -
they are statistically useful but not necessarily informative from an economic point of view.
To remedy this limitation, the equilibrium-correction term gives an economic underpinning to
the forecast, at least over the longer run.
The equilibrium-correction term is derived through cointegration analysis. Once unit root tests
assured that the variables of interest have the same order of integration, Johansen’s maximum
likelihood procedure tests for cointegration among (the log of): the consumer price index
excluding its food and energy subcomponents (lccpi), the import price index (lpbm), and the
average wage (lavwag). Using the estimated cointegrating equation, an error-correction term
is calculated and added to Model 3.
Table 4 lists fourth-order augmented Dickey-Fuller statistics for the three variables mentioned
above (lccpi, lpmb, and lavwag). The deviation from unity of the estimated largest root
appears in parentheses below each Dickey-Fuller statistic. This deviation should be
approximately 0 if the series has a unit root. Unit root tests are given for the original variables
(all in logs), and for their changes.
Table 4 suggests that all variables appear to be integrated of order 1. Notwithstanding their
nonstationarity, these variables may still be linked by a linear relationship that could be
recovered through cointegration analysis.
Cointegration analysis aims at capturing the presence of a long-run relationship between a
group of nonstationarity economic time series. The (log of) the price index excluding food and
energy (lccpi), the (log of) the import price index (lpmb), and the (log of) the average wage
(lavwag) forms such a group and—on economic grounds—one would expect a relationship
linking them in the long run. Figure 6 is suggestive of this relationship.
To establish the existence of a statistical long-run relationship among these three variables,
the Johansen’s (1988) procedure is run on a four-order vector autoregression (VAR), based on
a preliminary analysis showing that it is statistically acceptable to simplify the specification to
a first-order VAR (see Table 5).
Table 6 reports standard statistics and estimates for Johansen’s procedure applied to this first-
order VAR. The maximal eigenvalue and trace eigenvalue statistics strongly reject the null
hypothesis of no cointegration in favor of at least one cointegrating relationship. There is
some evidence of the existence of two cointegrating relationship, but it is weak and has been
safely ignored.
Table 7 reports the coefficient of the cointegrating vector (beta, in the table), and standardized
adjustment coefficients (alpha, in the table). The coefficient appears in the first part of the
second column in Table 7 under the header “A.” The null hypothesis of zero coefficients for
the import prices and wages is strongly rejected, supporting the idea that lpmb and lavwag are
indeed cointegrated with lccpi. The relevant Chi-square statistics with two degrees of freedom
equals to 31.822, with a p-value of 0.0000.
The coefficients alpha in the lower portion of second column (under the header “A”) of the
table measure the feedback effects of the (lagged) disequilibrium in the cointegrating relation
onto the variables in the VAR. A test of weak exogeneity of a given variable checks whether
or not the column corresponding to alpha in Table 7 (under the header “B”) is 0. If so,

- 9 -
disequilibrium in the cointegrating relationship does not feed back onto the associated
variable. Restriction test on alpha shows that the corresponding variables lpmb and lavwag are
weakly exogenous.7 Weak exogeneity implies that the cointegrating vector and the feedback
coefficients enter only the price index equation. Thus, modeling the long-run equilibrium
process for inflation can be limited to the specification of a single equation linking consumer
prices to import prices and wages.
From the cointegration analysis and the exogeneity result, one obtains:
Equilibrium Correction Term t = lccpi t + 0.10755lpmb t + 0.31963lavwag t.

The equation demonstrates that the import price index and average wage are cointegrated with
the core inflation. The import price index coefficient is lower that that of average wage. This
equation implies an equilibrium-correction term that captures the long-run dynamics of
Thailand’s core inflation, namely its convergence to a long-run equilibrium.

Added to a forecasting model, this term allows discrepancies between the log-level of the
consumer price index (net of food and energy) and its long-run determinants to affect core
inflation, while ensuring that in the long run the level of price index remains in line with its
structural determinants. In other words, the addition of the equilibrium-correction term to the
forecasting model anchors the forecasts over a long horizon to the long-run evolution of the
price level. Thus, Model 4 supplements the forecasting exercise based on the statistical
properties of the time series for Thailand’s core inflation in Model 3 with an economic
underpinning.

The superior performance of Model 4 is supported by additional evidence on the performance
of the alternative Models 1, 2, and 3. These are best discussed in reverse order, moving from
the model closest to Model 4 to less comprehensive specifications.
As discussed earlier, by dropping the equilibrium-correction term lagged once (ecm(1)) from
Model 4, we get Model 3. Although the Chow test (Figure 7) shows that the parameters in
Model 3 are still constant, its root mean-squared error rises from 0.002642 to 0.002799
(Figure 8), suggesting a weaker forecasting power.
By dropping the core inflation lagged three times (ccpi(3)) from Model 3, we get Model 2.
The relevant Chow test for stability of coefficients shows that the parameters are constant
(Figure 9), while its root-mean squared error rises from 0.002799 to 0.002951 (Figure 10).
Finally, by dropping the (lagged) principal components (PC) of the variable eliminated in the
reduction process from Model 2, we obtain Model 1. Although the Chow test (Figure 11)
shows that parameters are constant in this case too, its root mean-squared error rises from
0.002951 to 0.004288 (Figure 12). Overall, the progressive enhancements from Model 1 to
Model 4 improve the forecasting power by some 62 percent ((0.004288/0.002642 -1)*100).

7 The relevant chi-square test statistics equal to 4.0697 with a p-level of 0.1307.

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