This is not the document you are looking for? Use the search form below to find more!

0.00 (0 votes)

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.

- Added:
**April, 18th 2010** - Reads:
**367** - Downloads:
**2** - File size:
**304.70kb** - Pages:
**29** - content preview

- Username: samanta
- Name:
**samanta** - Documents:
**1258**

Related Documents

This paper studies optimal monetary policy responses in an economy featur- ingsectorial heterogeneity in the frequency of price adjustments. It shows that a central bank facing heterogeneous nominal ...

5.0 out of 5

|Koh Samui Beach Villa Holiday Rental on Thailand's Most Beautiful Tropical Island: Baan Dalah}|Koh Samui Luxury Beachfront Apartment Living: Apartment Osho Holiday Rental}

Panoramic, tropical sea and island sights, the pulse of the waves advancing and retreating from the ...

Jes Extender - My 2-Second Strategy With Jex Extender

The paper examines the sources of fluctuations in inflation and output in Poland and Hungary. Using a rational expectations, dynamic open economy aggregate supply-aggregate demand model and ...

This paper contributes to fill the huge existing gap in the literature on the Brazilian natural rate of unemployment. It reveals not only that the Brazilian Phillips curve (PC) has broken down since ...

India's main index edged higher on Monday, recovering from an earlier fall of as much as 1.4% to snap three day of losses, as hopes for rate cuts sparked gains in banks, while bargain-hunting ...

Ford Motor Company, a global auto maker based in Dearborn, Mich., manufactures and distributes automobiles in 200 markets across six continents. With about 300,000 employees and 108 plants worldwide, ...

Contrary to the common belief that more information is always better, Gigerenzer et al. (1999) showed that simple decision strategies which rely on little information can be quite successful. ...

This statement reaffirms the general business principles that govern how Shell in Malaysia and each of the Shell companies which make up the Royal Dutch/Shell Group of Companies conduct their affairs ...

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 *+ 0.10755*lpmb t *+ 0.31963*lavwag 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.

Forecasting ThailandТs Core Inflation

© 2004 International Monetary Fund

WP/04/90

Asia and Pacific Department

Prepared by Tao Sun1

Authorized for distribution by Alessandro Zanello

May 2004

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.

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 -

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

Thailand’s core inflation has proved

3.5

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.

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

0–3½ percent,

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

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 (

(

reserve money (

(

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).

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 (

average wage (

is calculated and added to Model 3.

Table 4 lists fourth-order augmented Dickey-Fuller statistics for the three variables mentioned

above (

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 (

(

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 (

adjustment coefficients (

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

indeed cointegrated with

equals to 31.822, with a

The coefficients

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

- 9 -

disequilibrium in the cointegrating relationship does not feed back onto the associated

variable. Restriction test on alpha shows that the corresponding variables

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:

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 (

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 (

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 (

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

## Add New Comment