Download Calculating potential growth rates and output gap

Academy of Economic Studies
Doctoral School of Finance and Banking
Romania’s potential growth rates and output gap
MSc.: Catalin Condrache
Supervisor: Prof. Moisa Altar
Bucharest, July 2008
Contents
 Preliminary aspects
 Methods for estimating potential GDP
 Model Definition
 Modeling Romania’s situation
 Estimating and testing methodology
 Conclusions and future research
Abstract
 The present working paper sets a goal to assess the
impact of production progress, stock of capital,
employment in the economy and human capital,
within GDP formation. The approach is slightly different
from that used so far in estimating potential GDP in the
models for Romania’s production function, because in my
opinion the current approach reveals the evolution of the
potential GDP more realistically. In order to improve the
production function model for Romania, I augmented the
model by human capital approximation.
Preliminary aspects
 Definitions
Potential GDP – represents the level of real GDP which
the economy can produce without
generating inflationary pressures.
Output Gap – represents the difference, expressed in
percentage points, between actual real
GDP and potential GDP.
 Importance
The concept of potential GDP plays a key role in
understanding the economic long term growth theory.
According to this theory the long term growth rate in GDP is
explained by fundamentals factors, such as: the structure of
the economy, demographic and educational factors,
technology, etc.
Methods for estimating potential GDP
 Univariate Methods



Hodrick – Prescott Filter
Band Pass Filter
Models with unobserved components - Kalman Filter
 Multivariate Methods



Production Function, Cobb – Douglas
Multivariate unobserved components models
Structural Vector Autoregression model
Difficulties in estimating potential GDP

Short sample of usable data for Romania

Structural changes happened during the analyzed period

Official GDP data is published with a lag, being
subsequently subject to revision

Unreliable statistical data for capital stock
Model Definition

The types of production function used in the literature are
particular forms of the constant elasticity of substitution –CES

In all models, the Cobb – Douglas production function is used

(1 )

The following equation seems to be a better approximation:
Yt  At  K t  Lt
Yt  At  K t  H t  L1t  

In order to surprise the dynamic of GDP we take the log
log Yt  log At    log K t    log H t  (1     )  log Lt
Modeling Romania’s situation
 Data series: quarterly 1998 Q1 -2007 Q4

Real GDP (expressed in 2000 ct price)

Gross Formation of Fixed Capital (2000 ct price) - GFFC

Real accumulated capital

Employment in the economy

Human Capital
Modeling Romania’s situation
 Challenge –estimation of capital stock


Harberger (1978)- assumes a capital growth rate equal to
the average growth rate of real GDP.
Kt 
It
;
(g  )
K1 = K0 x (1 – φ) + I1

g = 4.70% (average growth rate of real GDP – for the period considered)

Φ = 5.0% (depreciation of fixed capital)
Modeling Romania’s situation

Evolution of labor force – structural brake
Adj Labor Force
Unadj Labor Force
12,000,000
9,800,000
9,600,000
10,000,000
8,000,000
9,400,000
9,200,000
9,000,000
6,000,000
4,000,000
8,800,000
8,600,000
8,400,000
2,000,000
8,200,000
8,000,000

7,800,000
19
98
19 Q1
98
19 Q3
99
19 Q1
99
20 Q3
00
20 Q1
00
20 Q3
01
20 Q1
01
20 Q3
02
20 Q1
02
20 Q3
03
20 Q1
03
20 Q3
04
20 Q1
04
20 Q3
05
20 Q1
05
20 Q3
06
20 Q1
06
20 Q3
07
20 Q1
07
Q
3
19
98
Q
19 1
98
Q
19 4
99
Q
20 3
00
Q
20 2
01
Q
20 1
01
Q
20 4
02
Q
20 3
03
Q
20 2
04
Q
20 1
04
Q
20 4
05
Q
20 3
06
Q
20 2
07
Q
20 1
07
Q
4
-
The series was adjusted by assuming zero growth between
2001 Q4 – 2002 Q1, and the data prior to 2001 Q4 was
recursively corrected using the quarterly difference taken from
the data based on the previous methodology
Modeling Romania’s situation

The following data sets likely to figure as human capital:

Share of capital education expenditure in GDP

Share of employed with secondary and university
education in the employment group over 15 years of age
(Eurostat data; in line with levels 3 – 6 of ISCDE 1997)

Share of employed with university education in the
employment group over 15 years of age

Share of employed with secondary and university education in
employment group over 25 years of age

Share of employed with university education in the
employment group over 25 years of age

Share of male with secondary and university education in the
employment group over 15 years of age
Estimating and testing methodology

Census – X12 algorithm has been used to seasonally adjust all
time series

The employment in the economy data series was adjusted for
structural break

In order to surprise the dynamic of GDP, I take a log of the
Cobb – Douglas function
Modeling and testing methodology

The firs estimation showed a Durbin–Watson =0.536 (autocorrelation)

Remedy for serial correlation: Cochrane-Orcutt
Yt  1   2  K t   3  Lt   4  H t   t
 t     t 1   t

ρ = 0.723194.
Variable Coefficient
RHO(-1) 0.732194
Std. Error t-Statistic
0.121095 6.04643
Prob.
0
Modeling and testing methodology

New error estimate
 t   t     t 1

New equation
Yt  Yt 1  1 (1   )   2 ( K t  K t 1 )   3 ( Lt  Lt 1 )   4 ( H t  H t 1 )   t
Yt*  1*   2  K t*   3  L*t   4  H t*  t

After all the adjustments were implemented, I obtained
LogGDP = 1.673 + 0.29*LogK + 0.11*LogL + 0.62*LogH

New DW = 1.975663
Modeling and testing methodology

The coefficients are statistically different from zero at a 5% significance level

The percentage of the total variation in the dependent variable explained by
the independent variables, R2, is at a good level of 84%

By adding the human capital to the C–D production function the R-squared
has improved, increasing the accuracy of the forecasting

Constant returns to scale assumption, was tested using Wald test
Wald Test:
Equation: COBB_DOUGLAS
T-Statistic
Value
F-statistic
0.007611
Chi-square
0.007611
Null Hypothesis Summary:
Normalized Restriction (= 0)
-1 + C(2) + C(3) + C(4)
df
(1, 36)
1
Probability
0.931
0.9305
Value
0.016221
Std. Err.
0.185927
Modeling and testing methodology

Normality test
7
Series: Residuals
Sample 1998Q2 2007Q4
Observations 39
6
5
4
3
2
1
0
-0.04

-0.02
0.00
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
-3.68e-16
0.000182
0.021764
-0.037896
0.014463
-0.448283
2.620932
Jarque-Bera
Probability
1.539725
0.463077
0.02
The residuals seems to be almost normally distributed



Kurtosis is almost 3
Skewness is very close to zero
Jarque-Berra – is at a small value
Calculating potential growth rates and output gap

Resulted production function

LogGDP = 1.673 + 0.29*LogK + 0.11*LogL + 0.62*LogH

The Total Factor Productivity (TFP) has the major impact

According to the GDP regression function, in order to create
sustainable economic growth for the medium term, the solution
is to rise human capital and stock of capital mainly

Country like Romania would attract capital and loose qualified
labor force
Calculating potential growth rates and output gap

Growth rates of real GDP and potential GDP
10.00%
10.00%
8.00%
8.00%
6.00%
6.00%
4.00%
4.00%
2.00%
2.00%
0.00%
0.00%
-2.00%
1999
2000
2001
2002
2003
2004
2005
2006
2007
-1.16%
0.88%
5.72%
5.10%
5.15%
8.45%
4.22%
7.86%
6.05%
Potential GDP 2.00%
3.20%
4.50%
5.10%
5.30%
5.70%
5.90%
6.00%
6.20%
Real GDP
-2.00%
Calculating potential growth rates and output gap

Output –gap
0.00%
-0.50%
-1.00%
-1.50%
-2.00%
-2.50%
-3.00%
-3.50%
-4.00%
-4.50%
-5.00%
1998
Output-gap -3.45%
1999
2000
2001
2002
2003
2004
2005
2006
2007
-3.62%
-4.45%
-3.34%
-3.34%
-3.48%
-0.97%
-2.54%
-0.83%
-0.97%
Conclusions and future research

The results show an increasing annual potential GDP growth rate, from
an average of 3.70% in the period 1998 – 2002, to values of around
6% in recent period

Romania experienced in the past 10 years, a potential GDP growth
rates above the those registered by new EU Central and Eastern
European member states in their periods of high growth

The factors with the biggest impact in growth rates of potential GDP
are total factor productivity, human capital and stock of capital

Estimating the production function, was the first step in understanding
and analyzing real convergence

The convergence process concept has its origin in the exogenous
model of growth of Robert Solow. According to it, the existence of
some economies that have similar characteristics in terms of
preferences and technologies, of some declining marginal efficiency as
well as of a perfect flexibility from the production factors generates a
reduction of the incomes differences between the countries (regions)
Thank you for your consideration!
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