COMMENTARY
Recent Trends in Indian GDP and Its Components: An Exploratory Analysis
Chandan Mukherjee
break. Alternatively, one may derive clues by visually examining the data and statistically test the break point indicated by the graph. The second approach looks for evidence from the data by a sequential testing procedure without any a priori assumption based on theory or visual query. In other words, the second approach is about deriving the break point endogenously rather than
There has been some discussion about when India’s growth began to slow down – did the deceleration occur before or after the onset of the global crisis? This article subjects quarterly GDP estimates to a statistical analysis to identify the break point in growth. It also illustrates the possibilities of examining break points in a trend in an interactive manner.
Chandan Mukherjee (chandan.mukherjee@ gmail.com) is at the National Institute of Public Finance and Policy, New Delhi.
1 The Context
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such data (time-patterns in a random walk,2 for example, can lead to a misleading impression of a trend).
Broadly speaking, there are two approaches to the statistical analysis to examine a structural break. One is based on a priori assumption. For example, pre- and post-reform growth paths. In this case, of course, one has a theoretical basis to anticipate a structural testing for a break point given exogenously.
Chow Test
The Chow (1960) Test is most commonly used for exogenous break point in different variations. Over the past two decades or so, there has been a substantial growth of literature on the methodology of determining structural breaks endogenously (See Bai (1997), Bai and Perron (2003), Altissimo and Corradi (2003), among many others.) However, the supremacy of any single approach is yet to emerge to establish itself as the “best practice” in the post Chow-test era. As a result, for a practitioner, there is the dilemma of choosing between pre-specified break point(s) which can vary from one researcher to another, and the endogenously determined break point(s) which can vary from one test to another. In such a situation, a middle road seems to be a practical approach. In the exploration presented here, a simple-minded mix of smoothing approaches is used to describe the trend. Visual judgment is complemented by statistical tests in the process of creating the descriptions. However, the statistical tests used here should probably be considered only as indicative exercises as the underlying assumptions of these tests are not strictly valid, in general.
For brevity of presentation, only the essential results are included in this note. Detailed results can be downloaded by the
Figure 1: GDP (Total): Quarter-on-Quarter Growth Rate and Lowess
Growth Rate (%)
12 10
8
6
4
2
1997q1 2002q3 2006q1 2006q4 2008q4 1997q1 means 1997-98 Quarter 1.
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COMMENTARY
Figure 2: GDP (Total) – Quarter-on-Quarter Growth Rate & Trend Fit
interested readers from http://www.think-D1 = (t-27) if t > 27
Growth Rate (%) ingwithdata.com/gdpbreak-results.pdf. = 0 otherwise 12 Dm = (t-m) if t>m 2 Exploring Trends and Breaks = 0 otherwise 10
Figure 1 (p 13) presents the quarter-on-The break point ‘m’ in the quarter growth rate of GDP i e, the relative above specification is the con-8 change in GDP of a given quarter over the cern of this exercise. The fit
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same quarter in the previous year, and a was estimated for each of the “lowess”3 smoother. The time path of the values of m from 41 to 45 i e, 4 growth rate as well as the trend exhibited corresponding to all the four by the lowess indicate that after a signifi-quarters of 2006-07 and the 2 cant rise from around the beginning of first quarter of 2007-08. The 1997q1 2002q3 2006q1 2006q4 2008q4
1997q1 means 1997-98 Quarter 1.
2002-03, a definite decline began sometime least residual sum of squares
Figure 3: Seasonally Adjusted GDP (Total) – Quarter-to-Quarter Growth
during 2006-07. A further step to check this turned to be for m=44 i e, Rate and Lowess Smoother
Growth Rate (%)
observation can be to fit a piece-wise linear 2006-07: Quarter 4. The 4 trend and test for the statistical significance results of this fit are given in of the change in the slope.4 Taking clues Figure 2 and Table 1. The 3 from the lowess, a piece-wise linear trend is Breusch-Godfrey test for the specified as given below. Since the trend fit residuals is insignificant for 2 by OLS left autocorrelated residuals, autore-lags 1 to 4 at 5% level. In other gressive components of lag 1 and 4 were words, there is no indication of 1 added to the specification based on the au-autocorrelated error or non
0
tocorrelation function plot. stationarity. However, the rePiece-wise linear trend specification siduals indicated heteroscada--1 with autoregressive components: sticity according to the Breusch
1997q1 means 1997-98 Quarter 1.
G = a + b.D1 + c.Dm + d.G1 + e.G4 + u Pagan/Cook-Weisberg test. This where is the reason why White’s correction is over the successive quarters, is considered
G: Quarter-on-Quarter GDP growth rate; used to estimate the standard errors, shown instead of quarter-on-quarter. The former is G1: G with lag 1; in Table 1. All the estimated coefficients possible when the seasonality factor is elimi-G4: G with lag 4; were significant at 5% level against null nated. With regard to the method of removt = 1, 2,…., 54 corresponding to 1996-hypothesis of zero. On the whole, there-al of the seasonal component in a series,
97: Q1 to 2008-09: Q4 fore, the above exploration seems to indi-there are several methods readily available cate that the growth in from the shelf nowadays – beginning with
Table 1: Trend in Quarter-on-Quarter GDP Growth Rate – OLS Regression Results
Indian GDP started de-the simplest one (and the earliest method)
Source SS df MS Number of obs = 44
clining from the fourth of seasonal dummy variables.
F( 4, 39) = 23.76 Model 149.311264 4 37.327816 Prob > F = 0.0000 quarter of 2006-07. However, the possibility of the existence Residual 61.2576052 39 1.57070782 R-squared = 0.7091 Quarter-on-quarter of seasonal unit roots in the quarterly GDP
Adj R-squared = 0.6792 growth rate is consid-series is indicated by the HEGY test. There-Total 210.568869 43 4.89695045 Root MSE = 1.2533
ered mainly to elimi-fore, X-12 Arima, one of the commonly used
Robust G Coef Std Err t P>|t| [95% Conf Interval] nate the season ality methods in contemporary practice, is used D1 .3249788 .0655888 4.95 0.000 1923129 .4576446 factor in the series. De-in this exercise to de-seasonalise the quar-D44 -.8259013 .1488925 -5.55 0.000 -1.127065 -.5247378
pending on the statisti-terly GDP series.5
G1 .2645806 .1271104 2.08 0.044 .0074757 .5216856
cal nature of the season-Figure 3 presents the time path of the
G4 -.4438917 .1354895 -3.28 0.002 -.717945 -.1698385
ality factor, it is possible quarter-to-quarter growth rate of the de
_cons 6.585088 1.024482 6.43 0.000 4.512878 8.657299
that the de-seasonalised seasonalised GDP and a lowess. The declin-
Table 2: Trend in Quarter-to-Quarter Seasonally Adjusted GDP Growth Rate – GDP series exhibits a ing pattern from the first quarter of 2006-07 OLS Regression Results
different time path of looks very similar to the one we noted in the
Source SS df MS Number of obs = 51
growth. In order to quarter-on-quarter growth rates (Figure 1)
F( 2, 48) = 4.66
check the robustness but the declining slope seems to begin earlier.
Model 8.59220051 2 4.29610025 Prob > F = 0.0142
of the above result,
Residual 44.2988079 48 .922891831 R-squared = 0.1625
Table 3: Recent Break Points in GDP – Total,
the same exercise is
Adj R-squared = 0.1276 Manufacturing and Infrastructure
Total 52.8910084 50 1.05782017 Root MSE = .96067 repeated for the de-GDP Series Quarter-on-Quarter Quarter-to-Quarter Robust
Growth Rate of Growth Rate of G Coef. Std. Err t P>|t| [95% Conf. Interval] seasonalised GDPseries. Original Series Seasonally Adjusted Series D1 .0977 .0214913 4.55 0.000 .0544888 .1409112 But, this time quarter-Total 2006-07: Q4 2005-06: Q4 D40 -.2000417 .0442699 -4.52 0.000 -.2890524 -.1110311 to-quarter growth rate Manufacturing 2007-08: Q1 2006-07: Q4 _cons 1.331198 .204864 6.50 0.000 .9192915 1.743105 Infrastructure 2003-04: Q3 2004-05: Q1
i e, relative change
october 10, 2009 vol xliv no 41
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1997q1 2002q3 2006q1 2006q4 2008q4 COMMENTARY
Figure 4: Seasonally-Adjusted GDP (Total) – Quarter-to-Quarter Growth techniques, probably has its Rate and Trend Fit
(Growth Rate, %) own place in the discourse.
MANOHAR
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3
2
1
0
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1997q1 means 1997-98 Quarter 1.
The same specification as before, for fitting the trend, is used with the de-seasonalised series with the difference that the autoregressive components are dropped as there was no evidence of autocorrelation in the residuals. This time, however, the least residual sum of squares is found to correspond to the break point m = 40, i e, the fourth quarter of 2005-06.
Figure 4 and Table 2 (p 14) present the fit and the results. The residuals pass the tests of Breusch-Godfrey at the level of 5%. Jarque-Bera test for normality of the residuals is also insignificant at the same level. All the estimated coefficients are significant at 5% level against the null hypothesis of zero.
Given the evidence so far, one is inclined to emphasise not so much the specific quarter6 when the decline began
1997q1 2002q3 2005q3 2006q4 2008q4
Notes
1 Data Source: Ministry of Statistics and Programme Implementation, Government of India, June 2009.
2 A time series is called a random walk when, from one period to the next, it merely takes a random “step” away from its last recorded position. Since, the series remembers all the previous random steps taken, it can easily produce a pattern in the time path which will look like a trend though it is in fact an accumulation of the random steps. A genuine trend in the time series means that the series fluctuates randomly around a trend-path.
3 Smoothing a time series means a way to dampen the fluctuations, in order make the trend, if any, discernible. The simplest way to smooth a time series is to consider the moving averages of a given length. A step further in this direction is to consider weighted moving average. Lowess, which is an abbreviation of Locally Weighted Scatterplot Smoothing, introduced first by Cleveland (1979), developed further in Cleveland and Devlin (1988), does the smoothing by fitting (moving) weighted least squares models instead of averaging over the length.
4 The piece-wise linear specification is adopted from Boyce (1986).
5 X-12 Arima was developed by the US Census Bureau and it is widely used in the published official statistics in the US.
6 In fact, the residual sum of squares is fairly close to one another for the quarters 2, 3 and 4 of 2006-07, the values being 62.26, 61.69 and 61.26, respectively, in the case of quarter-on-quarter GDP growth rate. They are 44.33, 44.29 and 44.37, respectively, for quarters 2005-06:Q3, Q4 and 2006-07: Q1, in the case of quarter-to-quarter growth rate.
References
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but that the decline in India’s GDP began prior to the beginning of 2007-08.
The same steps are followed to create descriptions of trend (and breaks) in the GDP component series of manufacturing and infrastructure (electricity, gas, water supply and construction). The results are summarised in Table 3 (p 14). As mentioned earlier, the detailed results can be downloaded from the internet.
The analysis presented here indicates that the deceleration in the Indian GDP growth indeed began before 2007-08. Methodologically, this note is about the possibilities of examining breaks in the trend in an interactive way. Of course, formal rigorous statistical tests can complement the exploratory analysis under one set of (critical) assumptions or another. However, the process of such analysis is opaque to the general reader and a large number of users of the findings. In this respect, an analysis which is transparent and accessible to anyone with a basic familiarity with the statistical
Altissimo, F and V Corradi (2003): “Strong Rules for Detecting the Number of Breaks in a Time Series”, Journal of Econometrics, Vol 117.
Bai, J (1997): “Estimating Multiple Breaks One at a Time”, Econometric Theory, Vol 8.
Bai, J and P Perron (2003): “Computation and Analysis of Multiple Structural Change Models”, Journal of Applied Econometrics, Vol 18.
Bhanumurthy, N R and L Kumawat (2009): “Global Economic Crisis and Indian Economy”, Review of Market Integration (forthcoming). See also, “Economic Outlook, India 2008-2010”, India Link, Fall Forecast, October 2008, Delhi School of Economics and Institute of Economic Growth, India.
Boyce, K James (1986): “Kinked Exponential Models for Growth Rate Estimation”, Practitioner’s Corner, Oxford Bulletin of Economics and Statistics, Vol 48, No 4.
Cleveland, W S (1979): “Robust Locally Weighted Regression and Smoothing Scatterplots”, Journal of the American Statistical Association, 74 (368): 829-36.
Cleveland, W S and S J Devlin (1988): “Locally-Weighted Regression: An Approach to Regression Analysis by Local Fitting”, Journal of the American Statistical Association, 83 (403): 596-610.
Gregory, C Chow (1960): “Tests of Equality Between Sets of Coefficients in Two Linear Regressions”, Econometrica 28(3): 591-605.
Rakshit, Mihir (2009): “India Amidst the Global Crisis”, Economic & Political Weekly, Vol XLIV, No 13, 28 March-3 April.
Srinivasan, T N (2009): “Remarks at the Panel on India’s Budget for 2009-10” (New York: Asia Society), 8 July.
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