ESTIMATING INDEXES OF COINCIDENT AND LEADING INDICATORS FOR BARBADOS COTRIE, Gladys 1* CRAIGWELL, Roland**
MAURIN, Alain*
Abstract
In recent times, a number of studies have focused on describing and modelling the business cycles of developing countries. However, to date very few of the small economies of the Caribbean have been the subject of this type of empirical application. In this regard, the current paper's contribution is to conduct an analysis of the cyclical fluctuations in Barbados, focusing on the prediction of such fluctuations. To this end, the authors construct coincident and leading indicators for the Barbadian economy, using the Stock and Watson (1989, 1991) method, as well as another alternative procedure (Mongardini and Saadi-Sedik, 2003) derived thereof. The results obtained show that the proposed indicators possess excellent properties and accurately reflect the reference cycle of the Barbadian economy.
Keywords: Business Cycle, Coincident and Leading Indicators JEL: E32, E4 JEL Codes:
1. Introduction
Economic facts, past and present, show that the economy of each country in the world goes through many different phases characterised by alternating periods of more or less steady growth and recessions of varying impact. It is important for different economic agents to follow and predict these fluctuations and their consequences, especially those shocks – internal or external - that may affect the fluctuations. Indeed, it is vital for governments to pay close attention to the manner in which growth evolves since this determines the amount of tax revenue and has consequences for the level of unemployment. For their part, firms must rely on analysis and forecasts in order to manage their business optimally. Finally, households will alter their saving and consumption strategies by taking into account the economic climate and the evolution of the labour market.
The above suggests that the exercise of forecasting turning points is crucial and would fully justify the many economic research projects undertaken the world over that focus on developing appropriate forecasting methodologies such as leading indicators. Of course, in the special case of developing countries, it is perhaps easier to appreciate the necessity of such an exercise. As Williams (2006, p.1) points out, “While good official statistics are a valuable public resource in any national context, their role in guiding the formulation of public policy gives them an even greater importance in developing countries, where the impact of public policy decisions tends to be amplified in the presence of large economic
* Laboratoire d’Economie Appliquée au Développement (LEAD), U.F.R. des Sciences Juridiques et Economiques, Campus de Fouillole, BP 270, 97157, Pointe-a-Pitre, Cedex, GUADELOUPE, email: [email protected]; [email protected]
** University of the West Indies Cave Hill Barbados [email protected]
and social imbalances. Good statistical systems, therefore, tend to provide a relatively higher social return in countries such as those of the Caribbean.”
Leading indicators were developed as a convenient response to the unwieldy structural models that for a long time were used to make short-term economic forecasts. The construction and use of these indicators in the most economically advanced countries is now a well established activity and reflects a plurality of economic agents such as government organisations, private institutions, central banks and large commercial banks.
On the other hand, the literature in this domain is quite sparse when it comes to developing countries. In fact, leading indicators for such countries appeared for the very first time after 2000, following the financial crisis in South East Asia in 1997 and in South America at the turn of the 21st century, especially after the Argentina crisis of 2001-2002. Authors like Burkart and Coudert (2002) and even more recently Marongiu (2005) have proposed the use of leading indicators to prevent the onset of financial crisis.
In the same spirit, countries like Malaysia and the Philippines have agreed to put in place systems for the generation of leading indicators like those that currently exist in the Organisation of Economic Co-operation for Development OECD countries (Zhang and Zhuang, 2002).
In a recent paper, Cotrie, Craigwell and Maurin (2007) discuss the almost total absence of leading indicators used in the Caribbean basin. To this day, among the 15 CARICOM member states, a leading indicator exists only for Trinidad and Tobago and has been constructed by the Caribbean Money Market Brokers, a private financial company. This article seeks to address the absence of such indicators by constructing coincident and leading indicators for Barbados and to discuss their performance.
The structure of the paper is as follows. Section 2 presents a chronology of the Barbadian business cycle. Section 3 discusses some aspects of the coincident and leading indicators methodology. Section 4 shows the construction of the coincident and leading indicators using the Stock and Watson (1989, 1991) (hereafter SW) procedure. Section 5 develops a simplified version of SW approach due to Mongardini and Saadi-Sedik (2003), and compares these results with those from the SW estimation. Section 6 concludes.
2. Chronology of the Barbados Business Cycle
Coincident and leading indicators are developed from a reference series, so it is necessary to describe the characteristics of the reference chronology. The reference variable selected for the Barbados economy is real gross domestic product (GDP). From data covering the period 1974 to 2003, a chronology of the Barbados business cycles has been established in the paper of Craigwell and Maurin (2007a) and is reported and described in Tables 1 and 2.
Table 1: Durations of the Phases of the Barbadian Real GDP Cycle
Expansions Contractions Total
Period Duration in Quarters
Period Duration in Quarters
Duration in Quarters
1975:1-1981:3 26 1981:4-1982:3 3 29
1982:4-1988:4 24 1989:1-1992:3 14 38
1992:4-2000:2 30 2000:3-2002:1 6 36
2002:2- 10(+)
Source: Craigwell and Maurin (2007a)
Table 2: Descriptive Characteristics of the Phases of the Barbadian Business Using the Bry and Boschan Approach Cycle
Expansion Contraction Total
Average duration 29.7 10.3 36.3
Median duration 26 6 38
Max duration 30 14 40
Min duration 24 3 31
Proportion of time 74.16% 25.84% 100
Ratio expansion/contraction 2.87
Average amplitude 28.49% -12.18%
Steepness 0.96 -1.18
Source: Craigwell and Maurin (2007a)
There are four troughs (1975:1, 1982:3, 1992:3 and 2002:1) and three peaks (1981:3, 1988:4 and 2000:2) in the Barbados economy during the sample period. Table 1 also shows the durations of the different phases of the cycles: the complete cycles from trough to trough and peak to peak, the expansionary phases between trough and peak and the recessionary phases covering the periods from peak to trough.
In Table 2 one can observe that a notable feature of the Barbadian business cycle is the strong asymmetry between phases, with the expansionary phases generally being much longer in duration than the recessionary phases. The expansionary phases consist of between 24 and 30 quarters, whereas the recessionary phases, which are much more variable, lasted between 3 and 14 quarters.
These upturn and downturn phases correspond to the stylised facts of the Barbados economy. The period 1974-1982 is an era of rapid growth and high employment, emanating from the diversification of sugarcane cultivation to manufacturing, tourism and financial services. 1983-1992 relates to a decline in real output as a result of the international recession that was associated with the stagnation of commodity markets, oil shocks and world - wide inflation. The period 1993 - 2003 is an era of expansions and small contractions, driven mainly by the tourist industry and financial services, helped by the IMF austerity measures of the structural adjustment programme.
Craigwell and Maurin (2007a,b) have also done comparative observations of the characteristics of the Barbadian business cycle with those of other countries. Firstly, they found that the Barbadian business cycle is somewhat different from those of other developing countries. Considering, for example, a varied group of countries in Africa (Côte d’Ivoire, Malawi, Nigeria, South Africa and Zimbabwe), South America (Chile, Colombia, Mexico, Peru and Uruguay), as well as Asia and North Africa (India, South Korea, Malaysia, Morocco and Pakistan), Rand and Tarp (2002), using the Bry and Boschan procedure, showed that the average duration of their cycles was between 7 and 18 quarters. Conversely, the characteristics of the Barbadian cycle appear to be more similar to those of developed countries, like Australia (see Harding and Pagan (2002)) and France and Spain (see Harding and Pagan (2001)). Secondly, the main difference that appears between the Barbados cycle and the business cycles of developed countries relate to the characteristics of the contraction phase where Barbados stands out as having longer contractions with more pronounced amplitude. Thirdly, there is significant synchronization of the different phases of the Barbadian and U.S. business cycles. More precisely, this synchronization reflects the strong influence exerted by the U.S. economy
on the Barbadian economy. A growth or a recession in the U.S.’s economy is followed by a similar variation in the Barbadian economy, with a lag of some quarters.
3. Methodological Aspects
While the use of coincident and leading indicators may be perceived as commonplace in the field of business cycle analysis, finding effective methods for developing these indicators remains a core area of activity for economic policymakers in developed countries. This is so because the performance of such indicators is subject to two significant constraints, which business cycle analysts are perpetually seeking to overcome.
The first issue relates to the system for collecting the economic statistics representing the various components of the coincident and leading indicators. The observations of the reference series (for example, GDP) are collected with a lag; it is therefore necessary to identify candidate variables to serve as leading indicators, which can predict the turning points of the reference series. The candidate variables whose profiles satisfy this objective are those which have some economic linkage with the reference series and which is, above all, readily available, with a monthly or quarterly frequency and with historical data from as far back as the reference series. In developed countries the collection and diffusion processes for economic data are subject to continuous evaluation of their efficacy.
The second constraint relates to the methodology employed. In this regard, economic research has sought to improve on the techniques used for constructing coincident and leading indicators. Since the seminal work of Moore and Shishkin (1967), the literature has been enriched by a large number of procedures that provide (or not) the econometric foundations and allow (or not) for the simultaneous use of quantitative and qualitative data.
Today, the NBER and Stock and Watson (1989, 1991) procedures are the two most popular methods used. Both are founded in the abstract concept of the “state of the economy” which is an unobservable variable and they both propose estimating this variable using a range of available economic indicators. To this end, NBER economists have adopted a non-parametric approach. The coincident and leading indicator corresponding to the desired estimator of the unobserved variable is calculated using a weighted average of the selected series. The weights are fixed using scoring: a score is attributed to each indicator according to its behaviour vis-à-vis the expected characteristics of an effective indicator. The Stock and Watson (SW) estimator also relates to a weighted average of the selected variables. However, the weights are established using a more rigorous procedure, which employs dynamic factor analysis like state-space models (Kalman filter) or the principal components approach. Hence, this paper has chosen to apply the SW method (with principal components) for constructing composite indicators for Barbados. As shall be seen in the following paragraph, the method comprises two stages, each one suggesting the selection of particular economic indicators as candidates for inclusion in the composite indicators.
The Stock and Watson Approach
The Stock and Watson (1989, 1991) procedure is a special case of the econometric approach of construction of composite indicators and has become an important reference
method. On the basis of the principle that the business cycle results from the combination of the movements of several macroeconomic variables, these authors proposed a model that is based on the decomposition of several series into a common component and an idiosyncratic component. By noting that Yt is the vector of n initial series, in logarithms,
Ct
their common unobservable component, representative of the current state of the economy and, ut the vector of the idiosyncratic components, the specification of Stock and Watson model is written as
( ) ( )
( )
t t t
t t
t t
Y L C u
D L u
L C
(1)
This specification has its mathematical underpinnings in the set of tools and concepts associated with state-space modelling, which assumes that models are structured around space equations (for example, the first equation in (1)) and equations pertaining to transition between states (for instance, the other two equations in (1)). Moreover, Stock and Watson (1989,1991) make a number of fairly strong assumptions: (i) there is no autocorrelation between the error terms t and t; (ii) Ct and the errors u1t,...,untare not auto-correlated or serially correlated among themselves; (iii) Ct is the only component common to all the series and represents the only source of dynamism in the system, and; (iv) the series Y iit, 1,...,n may be integrated but they are not co- integrated.
The first stage of the Stock and Watson (1989, 1991) approach is to obtain a coincident indicator using the estimated value of Ct conditional on the information available at time t and denoted asCt t| , which represents a linear combination of the present and past values of the different components of the vector:
| ( )
t t t
C W L Y
(2) where W(L) is the vector of weights. Stock and Watson (1989, 1991) computed the coincident indicator utilising state-space models. In this paper the simpler principal components analysis (PCA) is employed to calculate the coincident indicator. The discussion on PCA below draws heavily on Nardo et al (2005).
The objective of PCA is to explain the variance of the observed data through a few linear combinations of the original data. In particular, much of the variation of Q variables, x1, x2 ,...xQ , should be accounted for by a smaller number of variables called principal components, or linear relations of the original data, Z1, Z2 ,...ZQ that are uncorrelated.
Formally,
Z1= a11 x1+ a12 x2+ ... +a1Q xQ
Z2= a21 x1+ a22 x2+ ... +a2Q xQ (3)
………..
ZQ= aQ1 x1+ aQ2 x2+ ... +aQQ xQ
where the weights aij (also called component or factor loadings) applied to the variables xj
in Equation (3) are chosen so that the principal components Z i satisfy the following
conditions:
(i) they are uncorrelated (orthogonal), (ii) the first principal component accounts for the maximum possible proportion of the variance of the set of xs, the second principal component accounts for the maximum of the remaining variance and so on until the last of the principal component absorbs all the remaining variance not accounted for by the preceding components, and
α2i1+ α2i2+ …+ α2iQ = 1, i=1,2,…Q
Mathematically, PCA involves finding the eigenvalues, αj , j=1,…,Q, of the sample
covariance matrix CM,
QQ Q
Q
Q Q i
cm cm
cm
cm cm
cm
cm cm
cm
...
....
....
. 2 1
2 22
21
1 12
1
(4)
where, the diagonal element cmii is the variance of xi and cmij is the covariance of variables x i and x j . The eigenvalues of the matrix CM are the variances of the principal components and can be found by solving the characteristic equation, CM −λI = 0 where I is the identity matrix with the same order as CM, and λ is the vector of eigenvalues.
The second step of the Stock and Watson method is to compute the synthetic leading indicator by estimating the future growth of the coincident indicator for the next 6 months (two quarters). The indicator is in fact simply the expected difference between the value of the coincident indicator in 6 months and its current value
Ct6|tCt t|
. Thus, their estimator is not a prediction of the level of economic activity but rather a forecast of the growth in Ctover six months. The two are, however, closely linked, since the leading indicator is defined by
Ct6|tCt t|
, the coincident indicator is given by Ct t| and the sum of the two indicates the predicted level of future economic activityCt6|t.Empirically, this second stage involves the estimation of a vector autoregressive (VAR) model:
1 1
( ) ( )
t c cc t cy t ct
C
L C
L Y V (5)
t yy
t ytyc y
t L C LY V
Y 1 1
where Yt is a vector of stationary leading indicators, Vct and Vyt are non-serially correlated error terms, and cc( )L ,cy( )L ,yc( )L and yy( )L are lag polynomials whose orders are determined empirically using statistical criteria such as that of Akaike.
Finally, having calculated the value of the coincident indicator Ct in the first stage, one can then determine the value of the leading indicator Yt by solving the equations of the VAR model in (5) above.
Variable Choice
As one might expect, the construction of a composite indicator for developing countries is a much more challenging exercise. Very recently, in a study carried out for the main emerging markets (Brazil, China, Indonesia, Russia and South Africa), Nilsson and Brunet (2006) highlighted the many practical difficulties they had to succumb. In the first instance, they pointed out that the databases used in the construction of composite indicators for OECD member countries were composed of several dozen macroeconomic
indicators stored under fourteen different headings. Secondly, they report that “the coverage of potential cyclical indicators for the major OECD non-member economies included in the MEI database is however not broad enough to obtain a reasonable number of leading indicators for each country in order to calculate a composite indicator (p.32).”
For Barbados, the pre-selection of candidate variables was similarly dependent on these variables meeting certain criteria: economic relevance on the one hand and availability of statistics on the other. In this regard, the Barbadian statistical series were reviewed by examining their statistical and economic properties in order to determine their usefulness in predicting future fluctuations in economic activity. First, reference was made to the customary leading variables as discussed in Craigwell, Cotrie and Maurin (2007). Around twenty candidate variables including, inter alia, production variables, monetary and financial indicators and trade variables, were examined. Second, the behaviour of the variables relative to the reference cycle was assessed; a complete characterisation of the variables is given in Craigwell and Maurin (2007a). In this investigation, both cross- spectral analysis and the NBER approach of measuring and describing the phase divergences and linkages between the cycles of two time series were utilised. These approaches provided robust methods for identifying and characterising the leading, coincident or lagging nature of a given series vis-à-vis a particular reference series.
Application of Cross-spectral Analysis
The most commonly used measures in co-spectral analysis are the coherence and mean delay statistics. The coherence statistic ranges between 0 and 1. A high value implies that a large proportion of the variance of the reference series is explained by the series under examination. The mean delay statistic is useful for measuring the degree to which the indicator lags or leads the reference series. A value close to zero is indicative of strong similarities between the movements of the two variables and, conversely, a positive (or negative) number suggests that the indicator leads (or lags) the reference series.
The calculated values for the candidate series are shown in Table 3. Decision rules similar to those used by Nilsson and Brunet (2006) are applied; in particular, the coherence statistic is restricted to values above 0.4. Thus, only CONSTRUC, FINANCE, LSV and RETAIL display cyclical behaviours that explain fluctuations in the GDP of Barbados to a significant degree. Based on the assumption that absolute values greater than 0.33 quarters (that is, about one month) for the mean delay statistic indicate leading or lagging behaviour, the majority of the variables were found to be coincident.
Application of the NBER Approach
Cross-correlations and turning point analyses constitute the two basic pillars of the NBER approach. They allow for an understanding of the degree of synchronisation between the movements of the two variables, by measuring the extent to which changes in one tend to coincide with changes in the other. The instantaneous correlations are shown in Table 3.
The highest values (greater than 0.5) are obtained for CONSTRUC, FINANCE, LSV and TOUR, followed by the values for TRANSCOM, SUG, M1 and IMPORT, which range between 0.46 and 0.49. Table 3 also reveals the value and the lead or lag associated with the maximum correlation. Based on these values, the different variables are characterised as follows: CPI, ELEC, EXPORT, MINING and SUG are leading indicators, while CONSTRUC, FINANCE, IPI, LSV, M1 and TOUR are coincident indicators.
Table 3: Bivariate Statistics with the Reference GDP Series (data adjusted with the HP filter) Coherence Mean Delay Cross-correlation
Series 2 Y-8 Y Decision 2 Y-8 Y Decision r0 rmax tmax(1)
CONSTRUC 0.58 YES -0.04 COIN 0.66 0.66 0 CPI 0.12 NO -6.68 LAG -0.25 -0.33 3 CSP 0.23 NO 0.26 COIN 0.29 0.38 1 ELECT 0.19 NO 0.49 LEAD 0.14 0.43 6 EXPORT 0.00 NO -3.09 LAG 0.06 -0.16 6 FA 0.04 NO 0.72 LEAD 0.05 0.19 -5 FINANCE 0.57 YES -0.11 COIN 0.73 0.73 0
GOV 0.34 NO 0.01 COIN 0.26 0.42 -1 IMPORT 0.39 NO -0.26 COIN 0.48 0.48 0 IPI 0.26 NO 0.03 COIN 0.40 0.40 0 LSV 0.58 YES 0.23 COIN 0.59 0.59 0 M1 0.39 NO 0.11 COIN 0.46 0.46 0 M2 0.21 NO -0.21 COIN 0.31 0.45 -6 MANU 0.28 NO 0.18 COIN 0.33 0.41 1 MINING 0.00 NO 2.20 LEAD 0.00 0.16 2 NAGRF 0.01 NO -2.49 LAG -0.05 -0.46 -3 RETAIL 0.48 YES -0.05 COIN 0.38 0.51 -1 SUG 0.12 NO -0.32 COIN 0.46 0.47 4 TBR 0.07 NO -4.95 LAG -0.06 0.36 -5 TOUR 0.55 YES 0.19 COIN 0.65 0.65 0 TRANSCOM 0.41 NO -0.50 LAG 0.49 0.61 -1 Note: (1) the + (-) sign refers to a lead (lag) with respect to the reference series
Table 4 reports the results of an analysis of turning point sequences for each candidate variable with respect to the Barbadian GDP series. Based on the median delay statistic, which is more robust than the average delay, the following classification is derived:
CONSTRUC, CPI, GOV, RETAIL, SUG, TBR and TRANSCOM are leading indicators and EXPORT, FA, FINANCE, IMPORT, LSV, M2 and TOU are coincident indicators.
The Bry and Boschan algorithm was applied in order to identify the turning points. It should also be noted that this classification remains largely unchanged if the data are considered in levels or filtered with the Hodrick-Prescott procedure.
At this point, the least that can be said is that these different measures of the synchronisation of the cycles of various variables with that of GDP do not always provide the same results. Nevertheless, using moderate assumptions and taking into consideration the findings of other studies, it is possible to arrive at a “correct” classification. In their study, Nilsson and Brunet (2006) carried out a classification exercise in relation to 148 indicators for the six large non-OECD members previously mentioned and found that:
- Series based on opinion polls were often leading indicators
- Real sector indicators (e.g. production, construction, transport, labour, prices) were, in 50% of cases, leading indicators
- External trade variables were often coincident
- Financial variables were rarely leading and often coincident
Table 4: Analysis of Turning Point Sequences with respect to the Reference GDP series (data adjusted with the HP filter)
Average Lag Median Lag
Reference Series Peaks Troughs All Peaks Troughs All CONSTRUC 7.00 0.33 3.67 5.50 -2.50 5.00
CPI 1.33 6.00 4.00 -5.50 5.00 3.50 CSP -6.33 -6.50 -6.43 -6.50 -6.00 -6.50 ELECT -0.75 2.20 0.89 -1.00 -2.00 -1.50 EXPORT 0.50 1.40 1.00 0.50 -0.50 0.50
FA 3.00 -2.00 0.50 0.50 -2.00 -0.50 FINANCE -0.33 -2.00 -1.29 -0.50 -2.00 -0.50
GOV 3.50 0.00 1.75 6.00 -1.50 1.50
IMPORT -1.00 1.00 0.11 -1.00 -0.50 -0.50 IPI -5.33 -4.25 -4.71 -12.00 -3.50 -7.50 LSV 2.25 -0.80 0.56 1.00 -1.50 0.00
M1 0.50 -2.00 -0.89 -0.50 -2.50 -2.00 M2 -0.25 0.40 0.11 0.50 -1.50 0.00 MANU -2.25 -0.20 -1.11 -3.50 -1.50 -1.50 MINING -0.67 0.75 0.14 -3.00 0.00 -1.50 NAGRF 0.67 -4.50 -1.40 -5.50 -4.50 -5.50 RETAIL 3.33 0.50 1.71 1.50 1.00 1.00
SUG 2.67 5.33 4.00 -0.50 1.50 3.50
TBR 3.25 3.40 3.33 5.00 2.50 2.50
TOUR 4.67 -1.75 1.00 1.00 -0.50 -0.50 TRANSCOM 4.50 2.33 3.20 4.50 1.00 2.50 Final selection of coincident variables
Given all of the points discussed above, the following variables are selected to include in the two types of composite indicators.
Table 5: Coincident and Leading Indicators
Coincident Indicators Leading Indicators
RETAIL, LSV, CONSTRUC, M1 CPI, EXPORT, TBT, TRANSCOM, US-LCI As regards the coincident components, the variables chosen are those that reflect the current economic situation in Barbados. In effect, the tourism and construction sectors are strongly correlated with GDP and allow for a reasonable representation of the economic situation. Along with the real growth in retail sales, these variables are representative of Barbadian economic growth. In terms of the leading indicators, all of the variables selected correspond to the present variables used in the composite leading indexes of many countries. It should be noted that the LCI for the US is included, rather than the LCI produced by Canada (Conference Board) or the Euro Zone (OECD). This is based on a result in Craigwell and Maurin (2007a) who found that fluctuations in Barbados economy are linked closely to those of the US.
4. Construction of Coincident and Leading Indicator Indexes with the Stock and Watson Methodology
The Coincident Indicator Index
A precondition for a valid composite index for the coincident indicators (CCI) is that the
4 series developed from the BUSY software given above, that is, RETAIL, LSV, CONSTRUC and M1, be non-stationary and co-integrated. The results of the Augmented Dickey and Fuller’s unit root test suggest that the log seasonally adjusted series need to be difference once to be stationary. Furthermore, the Johansen’s co-integration test indicates that the 4 series are co-integrated at the 5% level of significance (see Appendix 1).
The next step is to use the dynamic factor analysis discussed above to derive weights for the 4 indicators. Formally, the coincident indicator Ct t/ W L( )Yt where W (L) is a weighting vector that gives the contribution of each variable to the composition of the index. Applying the factor analysis gives:
∆C = 0.3436∆CONSTRUC + 0.2892∆LSV + 0.3021∆M1 + 0.1559∆RETAIL The dynamics of the estimated coincident growth rate index exhibits similar properties to the GDP growth rate (see Figure 1). Given this result, a simple procedure can be used to derive the index: the initial value of the index is set equal to the equivalent observation for real GDP; subsequent observations are then derived by multiplying the previous observation by the CCI quarterly growth rate. The CCI1 so derived is shown in Figure 2.
Figure 1: Comparison of Change of GDP and Change of the Coincident Indicator
-.15 -.10 -.05 .00 .05 .10 .15 .20 .25
1975 1980 1985 1990 1995 2000
DCCI DGDP
Figure 2: Comparison of Level of GDP and Level of Coincident Indicator
140 160 180 200 220 240 260 280
1975 1980 1985 1990 1995 2000 GDP CCI1
From Figure 2, the coincident indicator index displays similar business cycle characteristics of the Barbadian economy as the reference series, real GDP.
The Leading Indicator Index
In order to construct the leading indicator index (LCI), a VAR is undertaken using Equations 2 and 5. As is customary, the variables identified as leading indicators – CPI, EXPORT, TBR, TRANSCOM and US-LCI- and CCI1 are first checked for stationarity.
The results in Appendix 2 indicate that all the variables, except TBR, which is I(0) stationary, are stationary in first difference form. Also, the Johansen co-integration tests
indicate no co-integration at conventional significance levels, justifying that a VAR in first differences is appropriate. Based on various model selection criteria, the optimal model of the VAR is with 4 lags. The results of the VAR are given in Appendix 2.
LCI1t+2 is an estimation of the growth of the coincident index, two quarters ahead. It’s clear from Figure 3 that the leading indicator is not the same as the growth rate of GDP but picks up most of the expansions and contractions of the economy.
Figure 3: Comparison of Change of GDP and Change of Leading Indicator
-. 08 -. 04 . 00 . 04 . 08 . 12 . 16
1975 1980 1985 1990 1995 2000
DGDP DLCII
In order to obtain the evolution of LCI1, the same operation that was done for CCI1 is repeated. Figure 4 shows this adjustment and indicates the closeness of the two series.
Figure 4: Comparison of Level of GDP and Level of Leading Indicator
160 180 200 220 240 260 280
1980 1985 1990 1995 2000
LCII GDP
To see more clearly how well the leading indicator predicts GDP, Figure 5 presents a sub sample between 2000 and 2003. Note most peaks and troughs are predicted.
Figure 5: Comparison of Level of GDP and Level of Leading Indicator (2000-2003)
210 220 230 240 250 260 270
00:1 00:3 01:1 01:3 02:1 02:3 03:1 03:3
LEI1 GDP
An evaluation for the post sample period of 2004 is given in Figure 6. The results indicate
that the leading composite indicator (LEI1) forecasts a peak in 2003:3 for GDP which is realised in 2004:1, that is, two quarters after the change in LEI1.
Figure 6: Predicting the Change of Leading Indicator (Post-sample)
-.06 -.04 -.02 .00 .02 .04 .06 .08
03:1 03:2 03:3 03:4 04:1 04:2 04:3 04:4
DCEI1VAR DGDP
5. A Comparison with Mongardini and Saadi-Sedik Method The Coincident Index
Mongardini and Saadi-Sedik (2003), hereafter MS, provides a simplification of the SW method, and they argued that it could be used when there is a limited sample size. It assumes that the reference series are highly correlated with GDP and have a similar evolution. The same indicators in the SW method are utilised here but only industrial production has these features. Hence, a reduced form equation is estimated as follows:
1
t t t
t t t
IPI LCI u
u
(6)
It’s a simple regression of the reference series on other indicators that represent the state of the economy. IPI is the growth rate of the seasonally adjusted industrial production index, LCIt is a vector of the seasonally adjusted coincident indicators expressed in growth rates, ut is an error term with a moving average component of order 1. As the error term is not normally distributed in the regression, the standard errors and covariance matrix are estimated using the Newey-West heteroskedastic-consistent procedure. For the coincident indicators, those obtained from the BUSY software was the point of departure. However, the findings of this model was quite poor (R2=0.12). Hence, after some experimentation, an alternative model was derived.
The results of this estimation are given in Table 6 below. The coefficients are statistically significant and correctly signed, and therefore, can provide appropriate weights. Figure 7 shows that the fitted value closely tracks the actual data, although not as good as the SW approach above. Nevertheless, it is close enough that the fitted values of the regression can be interpreted as the growth rates of the composite index.
The final step is to derive the coincident indicator in levels (CEI2) from the regression results. As in the SW approach, a simple procedure is used to calculate the index: the initial value of the index is set equal to the equivalent observation for industrial production; multiplying the previous observation by the fitted quarterly growth rate then derives subsequent observations. The coincident indicator index so computed is shown in Figure 8.
Table 6: Estimation of Coincident Economic Indicator Dependent Variable: DIPI. Method: Least Squares
Sample (adjusted): 1974:2 2003:4. Convergence achieved after 6 iterations Newey-West HAC Standard Errors & Covariance (lag truncation=4)
Variable Coefficient Std. Error t-Statistic Prob.
DMANU 0.683771 0.075074 9.108009 0.0000
DRV 0.077451 0.038957 1.988146 0.0492
C 0.002413 0.001023 2.358516 0.0200
MA (1) -0.676025 0.070122 -9.640710 0.0000 R-squared 0.714818 Mean dependent var 0.004127 Adjusted R-squared 0.707378 S.D. dependent var 0.058525 S.E. of regression 0.031659 Akaike info criterion -4.034581 Sum squared resid 0.115260 Schwarz criterion -3.941165
Log likelihood 244.0576 F-statistic 96.08368
Durbin-Watson stat 2.060661 Prob (F-statistic) 0.000000 Inverted MA Roots .68
Figure 7: Estimation of Change of Coincident Economic Indicator
-.10 -.05 .00 .05 .10 .15
-.2 -.1 .0 .1 .2
1975 1980 1985 1990 1995 2000 Residual Actual Fitted
Figure 8: Comparison of Coincident Indicator and Index of Industrial Production
50 60 70 80 90 100 110
1975 1980 1985 1990 1995 2000 CEI2 IPI
The index seems to represent the state of the economy relatively well. Most of the turning points in the cyclical GDP are predicted by the CEI2. Note, a visual comparison between Figures 2 and 8 give Figure 2 the edge in terms of its ability to track the reference series.
The Leading Indicator Index
As in the estimation of the CEI2, the economic activity variable is measured by the IPI.
The statistical relationship is then formulated in the form of the following reduced form equation:
2 1
t t t
t t t
IPI LLI u
u
(7) where IPIt2 is the growth rate of the seasonally adjusted IPI two quarters ahead,
LLIt
is a vector of seasonally adjusted leading indicators and ut is an error term with a moving average component of order 1. The procedure to estimate equation (7) is the same as that used to determine CEI2 and LEI1 above.
Table 1: Estimation of Leading Economic Indicators Dependent Variable: DIPI (2). Method: Least Squares
Sample (adjusted): 1974:2 2003:2. observations: 117 after adjusting endpoints Convergence achieved after 11 iterations
Newey-West HAC Standard Errors & Covariance (lag truncation=4)
Variable Coefficient Std. Error t-Statistic Prob.
DLSV -0.058389 0.022191 -2.631271 0.0097
DM2 0.082828 0.055830 1.483563 0.1407
DRPI 0.038370 0.145390 0.263912 0.7923
DFA 0.006224 0.017762 0.350408 0.7267
MA (1) -0.442295 0.088161 -5.016916 0.0000
R-squared 0.281790 Mean dependent var 0.004303
Adjusted R-squared 0.256140 S.D. dependent var 0.058996 S.E. of regression 0.050883 Akaike info criterion -3.076793 Sum squared resid 0.289973 Schwarz criterion -2.958751 Log likelihood 184.9924 Durbin-Watson stat 2.079603 Inverted MA Roots .44
Unlike the CEI2, most of the variables in the estimation (see Table 7) are not statistically significant. However, the fitted value and the growth of the IPI appear to be highly correlated (see Figure 9).
Figure 9: Estimation of Change of Leading Economic Indicator
-.2 -.1 .0 .1 .2
-.2 -.1 .0 .1 .2
1975 1980 1985 1990 1995 2000
Residual Actual Fitted
Hence, it seems possible to construct the index with this simplified method as done above for the more sophisticated SW. The results are given in Figure 10.
Figure 10: Comparison of Leading Indicator and Index of Industrial Production (LEI2 lagged two quarters forward)
40 50 60 70 80 90 100 110
1975 1980 1985 1990 1995 2000 IPI LEI2
Note that the evolutions of the two series, although not identical, are quite close. Figure 11 gives a better view. For the period 2000 to 2003, one can see that when the LEI2 predicts the increase in 2000:3, the same expansion is realised in 2000:2 for the leading index.
Figure 11: Comparison of Leading Indicator and Index of Industrial Production (2000 -2003)
50 60 70 80 90 100 110
00:1 00:3 01:1 01:3 02:1 02:3 03:1 03:3 LEI2 IPI
An evaluation for 2004 is given in Figure 12. The LEI2 forecasts a peak in 2003:3 for GDP and it is obtained in 2004:1, implying that the prediction is realized two quarters before the event occurs.
Figure 12: Predicting the Change of Leading Indicator (Post-sample)
-8 -4 0 4 8 12
03:1 03:2 03:3 03:4 04:1 04:2 04:3 04:4 DIPI DLEI2
6. Conclusion
This paper establishes that there is a need to develop leading economic indicators in the countries of the Caribbean. Elsewhere in the world, especially in the industrialized economies, the use of these indicators is already an ancient tradition. Recognising that the Stock and Watson (1989, 1991) method is one of the best for developing leading economic indicators, it is applied to Barbadian data. More precisely, a coincident
indicator and a leading indicator of the business cycle of Barbados are developed and compared with an alternative methodology. Although both procedures map the reference series well the Stock and Watson (1989, 1991) method appeared to have performed more creditably.
References
Agenor, P., J. C. McDermott and E. S. Persad (2000), Macroeconomic Fluctuations in Developing Countries: Some Stylised Facts, The World Bank Economic Review, Vol. 14, No. 2, pp. 251-85.
Burkart O. and V. Coudert (2002), Leading indicators of currency crises for emerging countries, Emerging Markets Review, Vol. 3, Issue 2, pp…
Cotrie, G., Craigwell, R. and A. Maurin (2007), A Review of Leading Composite Indicators:
Making a Case for Their Use in Caribbean Economies, Central Bank of Barbados Economic Review, Vol.XXXIV, No. 3, pp.27-44.
Craigwell, R. and A.Maurin (2007a), A Comparative Analysis of the Barbados and United States Business Cycles, Revue d'Economie Régionale et Urbaine, No.1, pp. 57-78 Craigwell, R. and A.Maurin (2007b), A Sectoral Analysis of Barbados’ GDP Business Cycle, Journal of Eastern Caribbean Studies, Vol. 32, No.1, pp. 21-52.
Harding, D. and Pagan, A. (2001), Extracting, Analysing and Using Cyclical Information, Melbourne Institute of Applied Economics and Social Research, mimeo.
Harding, D. and Pagan, A. (2002), A Comparison of Two Business Cycle Dating Methods, Journal of Economic Dynamics and Control, Vol. 27 No. , pp. 1681-1690.
Marongiu, F., (2005), Towards A New Set Of Leading Indicators Of Currency Crisis For Developing Countries: An Application To Argentina, Center for the Implementation of Public Policies promoting Equity and Growth, School of Economic Sciences, Universidad de Buenos Aires, Argentina, Working Paper 0512011
Mongardini, J. and T.Saadi-Sedik, (2003), Estimating Indexes of Coincident and Leading Indicators: An Application to Jordan, IMF Working Paper No. 170.
Moore, G. H. and J. Shriskin (1967), Indicators of Business Expansions and Contractions, National Bureau of Economic Research, Occasional Paper No. 103.
Nardo, M., M. Saisana, A. Saltelli, S. Tarantola, A. Hoffman and E.Giovannini (2005), Handbook On Constructing Composite Indicators: Methodology and User Guide, OECD Statistics Working Paper, No.3.
Nilsson, R. and O. Brunet (2006) Composite Leading Indicators for Major OECD Non-Member Economies, OECD Statistics Working Paper, No.1.
Nilsson R. and Brunet O. (2005), Composite Leading indicators for major OECD non-member economies : Brasil, China, India, Indonesia, Russian Federation, South Africa, OECD Statistics Working Paper, December.
Rand J. and Tarp, F. (2002), Business Cycles in Developing Countries: Are They Different? World Development, Vol.30, No12, pp.2071-2088.
Stock, J. H. and M. W. Watson, (1989), “New Indexes of Coincident and Leading Economic Indicators,” NBER Macroeconomic Annual Report, Cambridge, Massachusettes: National Bureau of Economic Research, pp. 351-394.
Stock, J. H. and M. W. Watson, (1991), A Procedure for Predicting Recessions with Leading Indicators: Econometric Issues and Recent Experience, National Bureau of Economic Research, Working Paper No. 4014.
Williams E. (2006), Feature address at the Launch of Caribbean Money Market Brokers, Central Bank of Trinidad and Tobago, January 24, 2006
Zhang W. and Zhuang J. (2002), Leading Indicators of Business Cycles in Malaysia and the Philippines, Asian Development Bank, ERD Working Paper Series, N° 32.
On line Annex at the journal Website: http://www.usc.es/economet/aeid.htm
Appendix 1
Table 1A: Results of Augmented Dickey-Fuller Test
Variables Level First difference
RETAIL -1.493 -5.900
CONSTRUC -1.135 -2.900
LSV -1.476 -12.738
M1 4.536 -3.390
Note: The critical test at 5% is -2.887
Table 1B: Johansen Co-integration Trace Test Sample (adjusted): 1975Q2 2003Q4
Included observations: 115 after adjustments Trend assumption: Linear deterministic trend Series: LSV M1 CONSTRUC RETAIL Lags interval (in first differences): 1 to 4 Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None * 0.169327 48.78571 47.85613 0.0408
At most 1 0.139119 27.45103 29.79707 0.0911 At most 2 0.057961 10.22408 15.49471 0.2639 At most 3 0.028774 3.357576 3.841466 0.0669 Trace test indicates 1 cointegrating eqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
Appendix 2
Table 2A: Results of Augmented Dickey-Fuller Test
Variables Level First difference
TBR -3.524 -5.647
TRANSCOM -0.641 -5.537
CPI -2.061 -10.060
EXPORT -2.527 -5.273
US_LCI -0.038 -6.914
CCI1 -0.553 -4.918
Note: The critical test at 5% is -2.887
Table 2B: Johansen Co-integration Trace Test Sample (adjusted): 1975Q4 2003Q4
Included observations: 113 after adjustments Trend assumption: Linear deterministic trend
Series: CCI1 CPI EXPORT TBR TRANSCOM US_LCI Lags interval (in first differences): 1 to 4
Unrestricted Cointegration Rank Test (Trace)
Hypothesized Trace 0.05
No. of CE(s) Eigenvalue Statistic Critical Value Prob.**
None 0.269252 83.54498 95.75366 0.2561
At most 1 0.194241 48.09842 69.81889 0.7179 At most 2 0.087804 23.69369 47.85613 0.9487 At most 3 0.068420 13.30891 29.79707 0.8770 At most 4 0.040214 5.300262 15.49471 0.7762 At most 5 0.005843 0.662158 3.841466 0.4158 Trace test indicates no cointegration at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values
Table 2c: Vector Autoregression Estimates Sample (adjusted): 1975Q4 2003Q4; t- statistics in [ ]
D(CCI1) D(CPI) D(EXPORT) D(TBR) D(TRANSCOM) D(US_LCI) D(CCI1(-1)) -0.206153 -0.002067 -10.42544 0.024992 -0.015887 -0.003594
[-
1.89388] [-0.07511] [-0.02783] [ 1.50226] [-1.99012] [-0.14983]
D(CCI1(-2)) -0.071148 0.021232 427.3900 0.020913 0.005099 -0.012862 [-
0.64197] [ 0.75765] [ 1.12050] [ 1.23467] [ 0.62735] [-0.52665]
D(CCI1(-3)) -0.211727 -0.012330 -323.4523 0.037482 0.054650 -0.025217 [-
1.89369] [-0.43612] [-0.84058] [ 2.19345] [ 6.66494] [-1.02349]
D(CCI1(-4)) 0.063049 0.006691 -237.7136 0.008538 0.016946 -0.031172 [ 0.48678] [ 0.20430] [-0.53327] [ 0.43129] [ 1.78400] [-1.09212]
D(CPI(-1)) 0.090025 0.021693 1882.537 0.021022 -0.002087 -0.016235 [ 0.21304] [ 0.20301] [ 1.29440] [ 0.32549] [-0.06733] [-0.17434]
D(CPI(-2)) 0.013753 -0.087657 -537.3235 0.011488 0.021527 -0.031455 [ 0.03206] [-0.80819] [-0.36398] [ 0.17524] [ 0.68431] [-0.33278]
D(CPI(-3)) -0.728429 -0.067869 -1036.179 0.146406 0.002614 -0.012316 [-
1.72314] [-0.63493] [-0.71220] [ 2.26605] [ 0.08433] [-0.13220]
D(CPI(-4)) 0.399479 0.015911 1035.264 0.053800 0.039226 -0.017341 [ 0.95627] [ 0.15063] [ 0.72007] [ 0.84265] [ 1.28037] [-0.18837]
D(EXPORT(-1)) -1.12E-05 1.05E-05 -0.297025 -9.28E-06 -2.33E-06 4.35E-06 [-
0.36630] [ 1.36543] [-2.83327]
[-
1.99379] [-1.04214] [ 0.64806]
D(EXPORT(-2)) -1.49E-05 4.73E-06 0.038105 -5.25E-06 -2.56E-06 -1.22E-05 [-
0.47905] [ 0.60315] [ 0.35715]
[-
1.10747] [-1.12772] [-1.77920]
D(EXPORT(-3)) -2.12E-05 5.43E-06 0.370831 1.02E-06 -1.58E-06 3.09E-06 [-
0.68170] [ 0.69075] [ 3.46274] [ 0.21353] [-0.69338] [ 0.45050]
D(EXPORT(-4)) -7.86E-06 -1.73E-07 0.007349 -3.08E-06 4.30E-06 -7.63E-07 [-
0.25315] [-0.02206] [ 0.06879]
[-
0.64898] [ 1.88928] [-0.11161]
D(TBR(-1)) -0.676491 0.152435 1618.870 0.546385 -0.080311 -0.177077 [-
1.03710] [ 0.92419] [ 0.72112] [ 5.48068] [-1.67885] [-1.23190]
D(TBR(-2)) 0.078928 0.105672 -595.3554 0.042427 0.017906 0.019932 [ 0.10506] [ 0.55627] [-0.23026] [ 0.36951] [ 0.32499] [ 0.12040]
D(TBR(-3)) -1.195994 0.043968 -2293.412 -0.059128 0.098738 -0.152444 [-
1.61741] [ 0.23515] [-0.90118]
[-
0.52320] [ 1.82076] [-0.93552]
D(TBR(-4)) 0.151052 0.192106 3486.093 -0.193068 -0.044107 -0.143262 [ 0.22607] [ 1.13705] [ 1.51599]
[-
1.89064] [-0.90013] [-0.97298]
D(TRANSCOM(-
1)) 1.470487 -0.085294 4925.035 0.274440 -0.345789 0.098878 [ 1.13768] [-0.26097] [ 1.10714] [ 1.38926] [-3.64791] [ 0.34715]
D(TRANSCOM(-
2)) 0.310319 -0.021788 3472.457 0.196237 -0.291159 0.098780 [ 0.26911] [-0.07472] [ 0.87498] [ 1.11348] [-3.44296] [ 0.38873]
D(TRANSCOM(-
3)) -1.965840 -0.225542 1116.543 0.174989 -0.371210 0.250712 [-
1.81174] [-0.82204] [ 0.29899] [ 1.05520] [-4.66489] [ 1.04851]
D(TRANSCOM(-
4)) 1.392045 -0.035438 5693.977 0.088126 0.383467 0.425413 [ 1.14900] [-0.11568] [ 1.36559] [ 0.47593] [ 4.31589] [ 1.59342]
D(US_LCI(-1)) 0.262339 0.101219 2056.511 -0.049109 -0.006967 0.447482 [ 0.55620] [ 0.84868] [ 1.26687]
[-
0.68125] [-0.20140] [ 4.30520]
D(US_LCI(-2)) -0.600902 -0.161037 -2595.439 0.048086 0.064997 -0.254064 [-
1.17610] [-1.24648] [-1.47600] [ 0.61580] [ 1.73463] [-2.25651]
D(US_LCI(-3)) 0.899762 0.102332 3471.202 -0.092358 -0.049636 0.220884 (0.51216) (0.12950) (1762.66) (0.07828) (0.03756) (0.11286)
[ 1.75680] [ 0.79018] [ 1.96930]
[-
1.17990] [-1.32150] [ 1.95709]
D(US_LCI(-4)) -0.134149 -0.101366 -1959.940 -0.117852 0.020885 -0.260045 [-
0.28412] [-0.84903] [-1.20612]
[-
1.63315] [ 0.60314] [-2.49926]
C 1.028559 0.819108 -1692.811 -0.209704 0.033113 0.399138 [ 1.15962] [ 3.65214] [-0.55454]
[-
1.54693] [ 0.50905] [ 2.04203]
R-squared 0.417238 0.130772 0.294930 0.536386 0.859458 0.385443 Adj. R-squared 0.258302 -0.106290 0.102638 0.409946 0.821128 0.217836 Sum sq. resids 1719.135 109.9184 2.04E+10 40.15660 9.246122 83.48428 S.E. equation 4.419913 1.117619 15211.67 0.675518 0.324144 0.974005 F-statistic 2.625205 0.551635 1.533762 4.242210 22.42275 2.299689 Log likelihood -314.1437 -158.7779 -1234.382 -101.8851 -18.91018 -143.2358 Akaike AIC 6.002544 3.252706 22.28994 2.245754 0.777171 2.977625 Schwarz SC 6.605948 3.856110 22.89335 2.849158 1.380576 3.581030 Mean dependent 0.848286 0.676903 785.0221 -0.027705 0.097876 0.450980 S.D. dependent 5.132161 1.062574 16058.06 0.879409 0.766421 1.101317 Determinant resid covariance
(dof adj.) 2.21E+08
Determinant resid covariance 49318370 Log likelihood -1962.870 Akaike information criterion 37.39594 Schwarz criterion 41.01636
