Gross domestic product may be considered, a combination of three processes viz., long-run trend, business cycles and short-run shocks. The series of GDP can be decomposed in to its three components by using some statistical method. Such a decomposition of real GDP of Pakistan reveals that the Pakistan’s economy has a declining growth in long-run trend since early 1980s that however, is expected to start rising in 2001-02. Pakistan is also facing a recessionary phase of third business cycle, which is expected to end in 2004-05.business cycles; growth; pakistan

Arby, Muhammad Farooq

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
STATE BANK OF PAKISTAN 
 
 
 
Muhammad Farooq Arby 
Long-Run Trend, Business Cycles and 
Short-Run Shocks in Real GDP 
September, 2001 No. 01 
SBP Working Paper SeriesSBP Working Paper Series 
 
Editor:   Riaz  Riazuddin 
 
The objective of the SBP Working Paper Series is to stimulate and generate discussions, on 
different aspects of macroeconomic issues, among the staff members of the State Bank of 
Pakistan. Papers published in this series are subject to intense internal review process. The 
views expressed in the paper are those of the author(s) and do not necessarily reflect those of 
the State Bank of Pakistan. 
 
© State Bank of Pakistan 
All rights reserved. 
 
 
Price per Working Paper 
 
 Pakistan:  Rs  50  (inclusive  of  postage) 
  
Foreign:  US$ 20 (inclusive of postage) 
 
 
Purchase orders, accompanied with cheques/drafts drawn in favor of State Bank of Pakistan, 
should be sent to: 
 
Chief Spokesperson 
Corporate Services Department, 
State Bank of Pakistan, 
I.I. Chundrigar Road, P.O. Box No. 4456, 
Karachi 74000. Pakistan 
 
For all other correspondence: 
 
Editor, 
SBP Working Paper Series 
Research Department, 
State Bank of Pakistan, 
I.I. Chundrigar Road, P.O. Box No. 4456, 
Karachi 74000. Pakistan 
 
Published by: Editor, SBP Working Paper Series, State Bank of Pakistan, I.I. Chundrigar 
Road, Karachi, Pakistan. 
 
 
 
http://www.sbp.org.pk 
 
 
Printed at the SBPBSC (Bank) – Printing Press, Karachi, Pakistan  2 
 
 
 
 
 
 
State Bank of Pakistan Working Paper No. 1/01, September 2001 
 
 
 
Long-run Trend, Business Cycles and Short-run Shocks in Real GDP 
 
 
By 
Muhammad Farooq Arby 
Assistant Director 
General Economic Research Department 
State Bank of Pakistan 
Central Directorate 
Karachi 
Email: farooq.arby@sbp.org.pk * 
 
 
 
 
Abstract: 
Gross domestic product may be considered, a combination of three processes viz., long-run 
trend, business cycles and short-run shocks. The series of GDP can be decomposed in to its 
three components by using some statistical method. Such a decomposition of real GDP of 
Pakistan reveals that the Pakistan’s economy has a declining growth in long-run trend since 
early 1980s that however, is expected to start rising in 2001-02. Pakistan is also facing a 
recessionary phase of third business cycle, which is expected to end in 2004-05. 
 
 
 
 
 
Views expressed in this Working Paper are the author’s personal views and do not necessarily reflect those of the 
State Bank of Pakistan. 
* The author of this paper welcomes comments & suggestions.  3 
 
 
 
 
 
 
he path of economic growth for any country depends on a number of factors including 
structural changes in the economy, natural calamities, political instabilities, global 
recessionary trends, self-feeding business cycles, etc., and the combined effect of all these 
factors is most commonly represented in the country’s Gross Domestic Product. In statistical 
terms, however, the annual data series of GDP can be considered a combination of three 
processes; a long-run trend, business cycles, and short-run shocks to the economy, which can be 
separated from each other by using statistical techniques. The objective of this paper is to 
decompose real Gross Domestic Product of Pakistan into its above-mentioned components, and 
also to project them for determining future path of real GDP. Such type of dialysis gives more 
insights to understand the changing pattern of economic growth. Although some very broad 
comments have been made in the paper on the behaviour of GDP components during the past 
decades, a more detailed investigation is left for future research
1.  
In the literature, a number of methods have been proposed for separating the trend from the 
cyclical component of an economic time series. The most popular of these is the Hodrick-
Prescott (1997); while others include Rotemberg (1999), Baxter-King filter (1995), etc. This 
study has used the Hodrick-Prescott filter
2. A brief summary of the methodology used is 
provided in the following section. Results are presented and explained in section 3, while the 
last section concludes the paper. 
 
2.  Methodology 
The methodology consists of two steps; first to dissect the real GDP to get its components, and 
second to project the components into future. It is assumed that annual series of real GDP is an 
                                                 
1 The scope of this paper is limited to decompose the real GDP statistically and to project it into future. However, the 
results of the study raises a number of unanswered questions and pave way for future research in this area which may 
include use of alternate methods of decomposition, co-integration between trend and cycles exist in GDP, 
consumption, investment, M2, etc, and of course a detailed explanation of shocks, cycles and trends with respect to 
structural, political, social, and global events.  
2 See Pedregal & Young (2000), Pederson (1998), and Reeves et all (2000) for some useful comments on HP Filter. 
T  4 
aggregate of three components viz. Trend, Cyclical movements, and Irregular movements
3. In 
symbolic form; 
 
  Yt      = Tt  + Ct  + It         . 1  
 
where  Tt      = Long-run trend 
  Ct      = Cyclical movements 
  It       = Irregular movements (shocks) 
All are in natural log form.  
 
The HP filter is used in two stages to separate these components; first to extract the long-run 
trend (Tt) from the original series and then to filter out cycles (Ct) from the rest. The HP filter 
proceeds as follows; 
It assumes that a series (say Xt) has two components; a smooth one (St) and deviations (Dt) from 
St, i.e.  
Xt = St + Dt         . 2  
such that over a long period of time the sum of deviations (Dt) is near zero. 
In order to filter out St from Xt, it minimizes the following: 
Min:  Σ Dt
2 + λ Σ [∆
2St]
2       . 3  
The parameter λ is a positive number, which penalizes variability in the smooth component (St). 
∆ is the difference operator, power of which shows the order of differentiation. The higher the 
value of λ, the smoother is the solution series. Hodrick and Prescott suggested λ = 100 for 
annual data. 
We have applied the HP filter on the original series of real GDP to extract trend (Tt) component 
from it. By subtracting the trend from the original series (Yt), we get a new series (Zt) that 
contains cyclical and irregular components. 
Zt = Yt – Tt = Ct + It        . 4  
                                                 
3 This assumption is similar to that adopted by U.S. Bureau of Census in its seasonal adjustment program (the latest 
version of which is X-12-ARIMA).  In a seasonal adjustment program, a series is usually assumed to have four 
components: long-run trend, business cycle, seasonal variations, and irregular movements. However, in case of 
annual data there will be no seasonal component, leaving only three types of variations.  5 
We again apply the HP filter on Zt. In this second stage the HP filter wheedles out oscillations 
around the smooth component that is nothing but Cycles Ct. The difference between Zt and Ct 
represents shocks or Irregular component (It)   
The next step is to project trend and cycles into future over a ten-years’ period. For this purpose, 
ARIMA models have been used. Following the usual procedure of selecting a time series 
model
4, we have identified the following models for components; 
 
For trend component (Tt)
5: 
(1-α1L-α2L
2 -α3L
4) (1-L)
2 Tt = α0 + (1+β1L+β2L
4)ε    .5 
 
For cyclical component (Ct) 
(1-φ1L-φ2L
2 -φ3L
3-φ4L
4) Ct = φ0 + (1+π1L+π2L
2+π3L
3) ε    .6 
 
Data of real GDP at prices of 1980-81 for years 1949-50 to 2000-01 has been used
6. 
  
3. Results 
The three components of Pakistan’s real GDP have been shown in Figure-1. As expected, it has 
a positive long-run trend throughout the period. However, it may be noted that though trend 
GDP is increasing over time, its rate of increase as depicted in Figure-2 has different behaviour 
in different periods. During the first half of 1960s, the growth of trend component was rising 
while the second half witnessed a slow down. This pattern of growth has some bearings on 
structural developments in early 60s including the green revolution, the industrial revolution, 
the development of financial institutions, etc., and the impact of 1965 war on the later half of 
the 60s.  
 
                                                 
4 The procedure includes establishing order of integration by unit root test, identification of model with the help of 
autocorrelation and partial autocorrelation functions, and diagnostics etc. 
5 L is lag operator and ε is error term, normally distributed around constant mean.  
6 Data source for 1949-50 to 1994-95 is ’50 Years of Pakistan, Volume 1 – Summary, by Federal Bureau of Statistics 
(June 1998); for 1995-96 onward Economic Survey – 2000-01, by Economic Affairs Division, Ministry of Finance 
(June 2001).  6 
Figure 1: Components of Real GDP 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Note: Unit of Y-axis is natural log of million rupees.
Long-run Trend
10
10. 5
11
11. 5
12
12. 5
13
13. 5
14
Business Cycle
-0 .02
-0 .015
-0 .01
-0 .005
0
0. 005
0. 01
0. 015
0. 02
Short-run Shocks
-0 .05
-0 .03
-0 .01
0. 01
0. 03
0. 05 7 
  
Figure 2: Trend Growth rate (%) &  Public Investment (% of GDP) 
 
Another very intriguing result is the increasing trend growth during 1970s – a poorly rated 
decade by economists. There may be more explanations to it; one is the role of public fixed 
investment. Public fixed investment was 12.4 percent of GDP during 1973-74 to 1983-84 
compared with 9.7 percent and 9.4 percent during the two adjacent periods (Figure-2). It 
suggests that some positive structural changes occurred during this period. However, as 
mentioned below, the 1970s also witnessed a recession of second business cycle, which may 
have some fainting effects on the overall economic performance. 
Since 1983-84, the trend growth is declining, despite high overall GDP growth of 1980s. It 
suggests that high growth of 1980s may have been due largely to some transitory factors, 
including large inflow of remittances and foreign aid, instead of structural changes in the 
economy that could support long run growth. 
As regards the cyclical movements, it is shown that real GDP in Pakistan has completed at least 
two business cycles; one ending with a peak in 1968-69, and a second ending in 1990-91. Since 
1991-92, the economy is in recessionary phase of a third business cycle. The following table 
gives a time frame of phases of business cycles in Pakistan. 
3
3.5
4
4.5
5
5.5
6
6.5
1
9
5
0
1
9
5
1
1
9
5
2
1
9
5
3
1
9
5
4
1
9
5
5
1
9
5
6
1
9
5
7
1
9
5
8
1
9
5
9
1
9
6
0
1
9
6
1
1
9
6
2
1
9
6
3
1
9
6
4
1
9
6
5
1
9
6
6
1
9
6
7
1
9
6
8
1
9
6
9
1
9
7
0
1
9
7
1
1
9
7
2
1
9
7
3
1
9
7
4
1
9
7
5
1
9
7
6
1
9
7
7
1
9
7
8
1
9
7
9
1
9
8
0
1
9
8
1
1
9
8
2
1
9
8
3
1
9
8
4
1
9
8
5
1
9
8
6
1
9
8
7
1
9
8
8
1
9
8
9
1
9
9
0
1
9
9
1
1
9
9
2
1
9
9
3
1
9
9
4
1
9
9
5
1
9
9
6
1
9
9
7
1
9
9
8
1
9
9
9
2
0
0
0
2
0
0
1
% grow th
0
2
4
6
8
10
12
14
% of GDP
Grow th of Trend (%)
Average public investment (% of GDP)
12.4 %
9.2 %
9.4 %
12.6 % 8 
 
Table 1: Time Frame of Business Cycles in Pakistan 
 
Business Cycle  Recession  Trough  Recovery  Peak 
First B. Cycle 
(1949-69) 
1949-50 to 1959-60 
(11 years) 
1959-60  1960-61 to 1968-69 
(9 years) 
1968-69 
Second B. Cycle 
(1969-1991) 
1969-70 to 1978-79 
(10 years) 
1978-79  1979-80 to 1990-91 
(12 years) 
1990-91 
Third B. Cycle 
(1991 - ?) 
1991-92 to 2004-05 * 
(14 years) 
2004-05 *  2005-06 to ?   
*  Estimated 
 
The above chart reveals the following features of business cycles in Pakistan. 
 
1.  Pakistan’s economy went into recession soon after the independence. The whole decade 
of 1950 witnessed economic sluggishness that may be attributed to communal upsets, 
lack of infrastructure, weak (or virtually absent) industrial base, lack of private sector 
confidence on the infant economy, etc.  
2.  The economy started recovering by 1960. Interestingly, the recovery period is shorter 
than the recession. It may be postulated that appropriate economic planning and its 
effective implementation helped the economy recover quickly.  
3.  During 1970s the economy fell into recession almost as quickly as it had recovered 
during the last decade. Separation of East Pakistan and the nationalization of industrial, 
financial and other institutions could have adversely affected the business confidence 
during this period.  
4.  It took 12 years for the economy to recover from second recession compared with a 9-
year recovery period in the first cycle. Particularly, the economy slowed down in late 
1980s, and did not achieve even the peak level of last cycle that it fell into next 
recession.  
5.  Third recession started in early 1990s and is projected to continue till 2004-05. 
According to our projection, it will be the deepest recession of all. (Figure-3).  
 
 
  9 
Figure 3: Projections of Trend and Business Cycle 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
-0 .02
-0 .015
-0 .01
-0 .005
0
0. 005
0. 01
0. 015
0. 02
Projected
Business Cycles
-2
0
2
4
6
8
10
12
Overall GDP Growth (%)
Projected
Note: : Unit of primary Y-axis is natural log of million rupees 
10
10.5
11
11.5
12
12.5
13
13.5
14
1
9
5
0
1
9
5
1
1
9
5
2
1
9
5
3
1
9
5
4
1
9
5
5
1
9
5
6
1
9
5
7
1
9
5
8
1
9
5
9
1
9
6
0
1
9
6
1
1
9
6
2
1
9
6
3
1
9
6
4
1
9
6
5
1
9
6
6
1
9
6
7
1
9
6
8
1
9
6
9
1
9
7
0
1
9
7
1
1
9
7
2
1
9
7
3
1
9
7
4
1
9
7
5
1
9
7
6
1
9
7
7
1
9
7
8
1
9
7
9
1
9
8
0
1
9
8
1
1
9
8
2
1
9
8
3
1
9
8
4
1
9
8
5
1
9
8
6
1
9
8
7
1
9
8
8
1
9
8
9
1
9
9
0
1
9
9
1
1
9
9
2
1
9
9
3
1
9
9
4
1
9
9
5
1
9
9
6
1
9
9
7
1
9
9
8
1
9
9
9
2
0
0
0
2
0
0
1
2
0
0
2
2
0
0
3
2
0
0
4
2
0
0
5
2
0
0
6
2
0
0
7
2
0
0
8
2
0
0
9
2
0
1
0 0
1
2
3
4
5
6
7
%
 
g
r
o
w
t
Projected
Trend
% Growth in trend
Long-run Trend 10 
Figure-3 also shows the projection of long-run trend. It is 
estimated that the trend growth will start rising from year 2001-
02. Although the cyclical component of the GDP is projected to 
decline further in coming years, the dominance of trend will 
drive the overall GDP growth up (Table-2)
 7. The projection is 
based on the assumption that the economy will not suffer from 
positive or negative shocks during that period.   
 
Figure-4 shows the irregular component of the GDP that 
represents short-run shocks to the economy.  Pakistan’s economy 
has witnessed number of positive and negative shocks during the  
 
Figure 4: Irregular Component of GDP and Cotton Production 
Primary Y –axis = natural log of million rupees; Secondary Y-axis = million bales 
 
past decades. Although explaining each and every shock is outside the scope of this study, one 
important source of shocks is identified as cotton production in Pakistan. When there was a 
bumper cotton crop, the growth rose sharply (as in 1992 and 1996); and when it failed, growth 
                                                 
7 The projection shows a sharp jump in GDP growth during 2001-02, which comes down then to the onset 
of a smooth path. The reason may be very nature of the time series models, which keep in memory the 
past data generating process.  Sharp rise in growth during 2001-02 is possibly the lagged impact of some 
previous process, which is smoothed out subsequently. 
Table2: Projected real GDP 
Growth 
Year %  Growth 
2001-02 4.251 
2002-03 3.528 
2003-04 3.692 
2004-05 3.897 
2005-06 4.111 
2006-07 4.308 
2007-08 4.464 
2008-09 4.564 
2009-10 4.601 
-0 .05
-0 .04
-0 .03
-0 .02
-0 .01
0
0. 01
0. 02
0. 03
0. 04
0. 05
0
2
4
6
8
10
12
14
Short-run Shocks
Cotton production  11 
was depressed. A comparison of cotton production and irregular component of the GDP 
(Figure-4) clearly shows co-movements
8 of both the series indicating the power of cotton of 
driving the real GDP above/below its trend and cyclical path.  
 
4. Conclusion 
The paper has decomposed, statistically, the real GDP of Pakistan into three components viz., 
long-run trend, business cycles and short-run shocks. It also projected GDP growth on the basis 
of projected trend and business cycle. It is found that trend growth of real GDP, though positive, 
is declining since early 1980s. The reversal of trend growth is however, expected from year 
2001-02. The results also show that the economy of Pakistan has undergone two complete 
business cycles since its independence, and is now facing the recessionary phase of a third 
business cycle, which began in the early 1990s. It is projected that the current recession will 
continue until 2004-05, and then recovery will take place. However, since the dominant 
component of real GDP, the trend is projected to gain strength from 2001-02, the overall GDP 
growth is projected to rise gradually in coming years. The paper identifies a number of positive 
and negative shocks to the economy during past decades, and also finds a significant correlation 
between cotton production and shocks. 
                                                 
8 Correlation coefficient of cotton production and irregular component is +0.21.  12 
References 
Baxter, M & King R.G. (1995); Measuring business cycles approximate Bank-Pass filters for 
economic time series, NBER, WP 5022, February 1995 
 
Box G.E.P. & Gwilyn M. Jenkins (1970); Time series analysis, forecasting and control, San 
Francisco, Holden Day, 1970 
 
Hodrick, R. J. & Edward Prescott (1997); Post-war business cycle: an empirical investigation, 
Journal of Money, Credit & Banking 29 (1), February 1997 
 
Lucas, Robert E. (1981); Studies in business cycle theory, Cambridge, Mass; The MIT Press, 
1981 
 
Rotemberg, J.J. (1999); A heuristic method for extracting smooth trends from economic time 
series, NBER, WP 7439, December, 1999. 
 
Reeves J.J., Blyth A. C., Triggs M. C, & Small P.J. (2000); The Hodrick-Prescott Filter, a 
Generalization and a New Procedure for Extracting an Empirical Cycle from a Series; Studies in 
Nonlinear Dynamics and Econometrics, April 2000, 4(1): 1-16 
 
Pederson M. Torben (1998); The Hodrick-Prescott Filter, the Slutzky-effect and the 
distortionary effect of filters; DP No. 9/1998; Institute of Economics, University of Cpenhagen, 
November, 1998 
 

Measuring business cycles approximate Bank-Pass filters for economic time series, NBER, WP 5022,

The Hodrick-Prescott Filter, a Generalization and a New Procedure for Extracting an Empirical Cycle from a Series; Studies in Nonlinear Dynamics and Econometrics,

Long-run trend, Business Cycle & Short-run shocks in real GDP

Abstract

Similar works

Full text

Available Versions

Research Papers in Economics