1

Differential equation potential output 1

A Differential Equation Approach to Thailand’s Potential Output

An Application to Bank of Thailand’s Macro Economic Model

Differential equation potential output 2

Purpose

To estimate potential output with economic intepretation that can be implemented within the Bank of Thailand macro model

2

Differential equation potential output 3

Outline

1. Previous attempts

2. Current application

3. The k ratio

4. Model performances

Differential equation potential output 4

Previous attempts

1. Frontier production function

2. Structural Var

3. Natural rate of unemployment

4. HP – multivariate

Each approach is related to different definition.

Period ends 2000q4

3

Differential equation potential output 5

Frontier

Def. Maximum output attained.

500

550

600

650

700

750

800

850

900

93Q1 94Q1 95Q1 96Q1 97Q1 98Q1 99Q1 2000Q1

RGDPFrontier

Differential equation potential output 6

Output Gap

Definition

Percentage diffent of actual output from estimated potential output

4

Differential equation potential output 7

Output Gap

-2

0

2

4

6

8

93Q1 Q4 Q3 Q2 96Q1 Q4 Q3 Q2 99Q1 Q4 Q3

Frontier

Differential equation potential output 8

Frontier

No

NoNo

NoYesEconomic

interpretaion

Linear

function

Model

Compatable

Determined within model

No estimation of data

Output Gap = 0.5

2000:q4

5

Differential equation potential output 9

Structural Var

Def Demand shocks in GDP do not change potential output

600

650

700

750

800

850

96Q1 Q3 97Q1 Q3 98Q1 Q3 99Q1 Q3 2000Q1 Q3

RGDPSVAR

Differential equation potential output 10

Output gap

-8

-6

-4

-2

0

2

4

6

8

10

12

93Q1 94Q1 95Q1 96Q1 97Q1 98Q1 99Q1 2000Q1

FrontierSVAR

6

Differential equation potential output 11

Svar

No

YesNo

NoYesEconomic

interpretaion

Linear

function

Model

Compatable

Determined within model

No estimation of data

Output Gap = -0.7

2000:q4

Differential equation potential output 12

Natural rate of unemployment

500

700

900

1100

1300

1500

1700

93Q1 94Q1 95Q1 96Q1 97Q1 98Q1 99Q1 2000Q1

NAIRURGDP

Def. Maintain rate of employment; no pressure on prices.

7

Differential equation potential output 13

Output gap

-10

-5

0

5

10

15

20

25

93Q1 94Q1 95Q1 96Q1 97Q1 98Q1 99Q1 2000Q1

FrontierSVARNairu

Differential equation potential output 14

Nairu

No

YesNo

NoYesEconomic

interpretaion

Linear

function

Model

Compatable

Determined within model

No estimation of data

Output Gap = 6

2000:q4

8

Differential equation potential output 15

HP multivariate

600

650

700

750

800

850

96Q1 97Q1 98Q1 99Q1 2000Q1

RGDPHP

Def. Long term trend imposing price trade off

Differential equation potential output 16

Output gap

-10

-5

0

5

10

15

20

25

93Q1 94Q1 95Q1 96Q1 97Q1 98Q1 99Q1 2000Q1

FrontierSVARNairuHP

9

Differential equation potential output 17

HP multivariate

No

YesNo

NoNoEconomic

interpretaion

Linear

function

Model

Compatable

Determined within model

No estimation of data

Output Gap = -6.5

2000:q4

Differential equation potential output 18

HP splicing (current)

Def. Combination of long term trend; transitory variations are excluded.

600

650

700

750

800

850

93Q1 95Q1 97Q1 99Q1 2001Q1

GDPRHSM

10

Differential equation potential output 19

Output gap

-10

-5

0

5

10

15

20

25

FrontierHSM HSMSA

Differential equation potential output 20

HP splicing

Yes

YesNo

NoNoEconomic

interpretaion

Linear

function

Model

Compatable

Determined within model

No estimation of data

Output gap = 1.62000Q4

=4.8 2002Q3

11

Differential equation potential output 21

Observation facts

1. Functional form specifications lead to different conclusions.

2. Nations use trends to form potential output.

Differential equation potential output 22

Neo classical growth

In the steady state, the average product of capital ratio is constant .

Differential is used to model convergent rate.

Convergent rate and steady Y/K ratio come from past experience

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Differential equation potential output 23

Net capital stock

5000

6000

7000

8000

9000

10000

1993 1994 1995 1996 1997 1998 1999 2000 2001

Differential equation potential output 24

Growth decomposition

GDP growth

Trend

Transitory

Changes in K (investment)

Changes in efficiency (Y/K)

Changes in resource utilization

13

Differential equation potential output 25

Output capital ratio

9

11

13

1994 1997 2000 2003

Downturn is temporary and growth is a sign of returning to trend.Pre-crisis

inefficiency

Differential equation potential output 26

Larger gap

600

650

700

750800

850

900

950

93Q1 95Q1 97Q1 99Q1 2001Q1

GDPRHSMGKY

14

Differential equation potential output 27

Output gap

-10

0

10

20

30

40

94Q1 Q4 Q3 Q2 97Q1 Q4 Q3 Q2 2000Q1 Q4 Q3 Q2

HSM GKY

Differential equation potential output 28

YK ratio

Yes

NoYes

YesYesEconomic

interpretaion

Linear

function

Model

Compatable

Determined within model

No estimation of data

Output gap = 10.7(14) 2000Q4

=13.6 (10) 2002Q3

( ) GDPRSA

15

Differential equation potential output 29

Output gap (sa)

-10

0

10

20

30

94Q1 Q4 Q3 Q2 97Q1 Q4 Q3 Q2 2000Q1 Q4 Q3 Q2

HSM GKY

Differential equation potential output 30

Prelim. results

In sample

Better fit infation (headline & core), GDP (private investment)

Out of sample

No major change in GDP

Lower forecasts in inflatrion rates

16

Differential equation potential output 31

Gains1. Economic implications on potential output

trend.

2. No major lost of forecasts property.

3. Basic of steady state research.