– Ronald Coase: ‘How Should Economists Choose?’

I Introduction

II Methodology and Data

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m

case, the choice is correlated with the data, and the Chow Test is likely to validate a breakdate when none in fact exists. The problem with the second method is that it assumes that the exogenous event has had an impact on the parameters of the model, and that at that point in time it is the only causal factor. When this is not true an observed structural change may have little to do with the exogenous event itself. Moreover, it has been demonstrated that this procedure can lead to erroneous conclusions.4 All of this points to the importance of the proper identification of the breakdate. Continuing with the Chow Test, we may now apply the test at every possible point in a sample and to choose the data point corresponding to the maximum valued F-statistic as the breakdate. While this does generate for us an endogenously identified breakdate the procedure can be used to estimate only one break at a time. Of course, the method may be applied repeatedly to estimate more than one break, but this is cumbersome and the procedure non-standard. On the other hand, we now have a methodology that can estimate simultaneously multiple structural breaks in a series which is described below.

Bai and Perron (1998, 2003) have developed an approach to the problem of identifying breaks in a series based on the least squares principle common to regression analysis. Its superiority draws from the feature that it allows for the simultaneous estimation of multiple breaks. The breakdates are estimated as global minimisers of the sum of squared residuals from an OLS regression of (1) using a dynamic programming algorithm [Bai and Perron 2003]. The procedure is as follows. Given the number of breaks m, for each partition (T1, …,T) denoted {TP} the associated

mleast squares estimates βp = (a, g)p are obtained by minimising

the sum of squared residuals Σm+1 Σ Tj [lnYt – aj – gjt]2. The

j=1

t=Tj-1+1 resulting estimates ^ β

are used to compute the sum of squared residuals – denoted STp(T1, …,T) – associated with the partition

m

^ ^

{TP}. Now the estimated breakpoints (T1, …,T) are such that

m^^

(T1, …,T), = argmin(T1, …,Tm) ST(T1, …,T), where the

mmminimisation is over all possible partitions (T1, …, T) such that

mTi – Ti –1 ≥ h. Note that h is the minimum length assigned to a segment and Ti is the i-th breakpoint. The procedure considers all possible combination of segments and selects the partition that minimises the sum of squared residuals. Thus the leastsquares estimates of breakdates are those that minimise the fullsample sum of squared residuals in (1). As we are working with a trending series the following may be noted. First, Bai (1997) has demonstrated that stationarity of regressors or disturbances is not required (p 553) for consistency of the breakpoints estimated under the above procedure. Secondly, the asymptotic distribution of the breakpoint estimator, needed for construction of the confidence interval, has been derived by the author without assuming stationarity of the disturbances. The above procedure is used to sequentially estimate the optimal break points for the series starting from one to the maximum allowed by T and h. The next step is to select the number of breaks in the time series. When the number of break points is unknown, a test based on the supF statistic has been proposed [Bai and Perron 1998], to choose the number of breakpoints. This testing procedure assumes non-trending regressors and is therefore inapplicable in the present context. An alternative approach which accommodates trending regressors is to use the

Bayesian Information Criteria (BIC). This has been demonstrated to be superior to other information criteria in the determination of the number of structural breaks [Wang 2006]. Here the number of breaks selected is that for which BIC is at a minimum. We adopt this procedure to choose the number of breaks, starting from zero to the maximum.5 The criterion is particularly appropriate when multiple breaks are considered because it introduces a penalty factor for additional break points which necessarily reduces the sum of squared residuals,6 as is apparent from below:

BIC(m) = lnσ^ 2 (m) + p*ln(T)/T

P* = (m + 1) q + m + p ^

T σ2 = T–1 Σ û2tt=1 where m is the number of breaks, q is the number of explanatory variables whose coefficients are subjected to shift and p is the number of explanatory variables whose coefficients are constant. Before proceeding to the estimation we consider another issue. This relates to the question of whether we are faced with what has been referred to in the literature as a “partial” versus “pure” structural break. In the present context this translates into the following question. We are concerned with a change in the rate of growth of output which implies a shift in the slope coefficient. When this is accompanied by an intercept shift in the data generating process, it is important to allow for this level shift in the estimation of the breakdate. Simulation results of Perron and Zhu (2005) show that incorporation of a level shift of more than 0.3 in absolute value improves the accuracy of breakdate estimation. However, a practical problem is that the estimated change in the intercept cannot be a good guide due to contamination and feedback effects between the estimated level shifts and breakdates. Here, along with an examination of the estimated intercept shift a visual comparison of the actual and fitted series has been suggested to verify whether the intercept shift is a true level shift rather than a random deviation away from the trend line [Perron and Zhu 2005]. We adopt this approach. The study covers the period from 1950-51 to 2003-04. The choice of time period follows from two considerations. First, we are interested in growth regimes after the launching of a development programme in independent India so that we may track the effect of changes in the policy regime. Secondly, it has already been established [Hatekar and Dongre 2005] that when the entire 20th century is taken the dominant break occurs around the year 1950. Data on gross domestic product (GDP) at the aggregate and sectoral levels and sectoral shares in total GDP up to 1999-2000 were obtained from National Account Statistics of India, an electronic database supplied by the Economic and Political Weekly Research Foundation and the data for the remaining years were taken from National Account Statistics, published by the Central Statistical Organisation (CSO). The level of disaggregation adopted in this study is determined by the data availability. All the figures are in 1993-94 prices. In our estimation of the breakdates the minimum length of a segment, h, has been fixed at 8. This implies a maximum of five breaks or six growth regimes in our sample extending over 1950-51 to 2003-04. A trimming of 15 per cent of the total observations, implied by h = 8, is considered appropriate for a sample size of the present study [Bai and Perron 2003]. Also, a minimum of eight years per segment seems reasonable to us when studying long-run growth. We are aware that an element of judgment is involved here; however, the sensitivity of the

Economic and Political Weekly July 14, 2007

III Results and Their Interpretation

available. This finding is at odds with the reported finding of Wallack that no trend break can be established in the disaggregated GDP series. If true, that would imply that there is no underlying dynamism to growth in the economy. That is, all the sectors grow at a constant rate. However, the growth rate of aggregate GDP yet accelerates as the fast(er) growing sectors come to occupy larger shares of the economy. An acceleration of the overall growth rate when the sectoral growth rates remain constant is purely an “artefact” of accounting, due to the reallocation of output from the slow-growing to the fast-growing sectors of the economy. Our estimates conclusively suggest that the observed acceleration in the growth of GDP is not such an artefact. We find change in the trend growth rate across all sectors in the economy. Not only is this plausible, it is also in keeping with conventional wisdom among researchers of the Indian economy that shifts in the Indian growth data such as “the green revolution” and “industrial stagnation since the mid-1960s” represent trend breaks.

(3) Agricultural growth shows a trend break in 1964-65 when growth accelerates. As the estimates of a structural break come with an associated confidence interval we need not hold fast to the point estimate and we are open to the interpretation that the break takes place “some time in the mid-1960s”. However, the point estimate does suggest the interpretation that the acceleration of agricultural growth may not be entirely due to the miracle seeds with which the green revolution tends to be identified. It may also owe something to the steady expansion in irrigated area in the decade and half preceding the mid-1960s. Clearly, the methodology of generating structural breaks in the data endogenously has proved decisive in this understanding. The traditional practice is to measure the rate of growth of agriculture prior to 1965-66 and after 1966-67, these two years – being ones of severe drought when output was well below trend – having been excluded from the time series on output in both segments. The usual result is to find the rate of growth higher in the second period and to conclude that the acceleration has occurred in 1967-68. This is

Table 3: Sectoral Contribution to the Changein GDP Growth from 1979-80

(In per cent) Contribution

The regressions presented in Table 4 are the parsimonious representation of an original specification in which output growth in each sector was regressed on the current values of output growth in the other sectors and its own lagged values. Allowing for simultaneity the model was first estimated by GMM using instrumental variables for all current-dated variables. Except for the secondary sector in which the current growth of the tertiary sector was found to be statistically significant, for the primary and tertiary sectors the current output growth of the other sectors was found to not matter. So, for the sake of uniformity, we choose to exclude current output growth from the specification altogether. With current-dated variables out of the specification OLS is sufficient, and the resulting estimates are presented11 in Table 4. Note that the independent variables from lag one to three were entered along with the lagged dependent variable. The model was then reduced to the more parsimonious representation reported.

From the regressions reported in Table 4 the following may be inferred. First, primary sector growth displays a certain autonomy with neither the secondary nor tertiary sectors entering into its determination; however, growth of the primary sector enters the growth of the tertiary. Secondly, growth of the tertiary sector enters growth of the secondary but not growth of the primary. Finally, secondary sector growth does not significantly enter into growth of the other two sectors of the economy. Together, these regressions lead us to conclude that secondary-sector growth has not driven tertiary-sector growth during the period under consideration, so it could not have influenced the growth shifts in the Indian economy even indirectly. We wager that it will be found that “Tertiary-sector growth Granger-causes secondarysector growth but secondary-sector growth does not Granger-cause tertiary-sector growth”. Our results suggest a recursive model.

IV Conclusion

Using a method developed by Bai and Perron we have identified growth regimes in India since 1950. The hallmark of this method is that no extraneous information is imposed on the data, i e,

Table 4: Inter-sectoral Growth Relations

Explanatory Variables Dependent Variables PtSt Tt

-0.596* 0.060 0.066*

Pt-1 (-5.25) (1.36) (2.23)

-0.224 0.168 -0.068

St-1 (-0.77) (1.19) (-1.12)

0.307 0.429* 0.524*

Tt-1

(0.47) (2.16) (3.58) -0.219

Pt-2 (-1.72)

-0.198

St-2 (-1.56)

0.265*

Tt-2

(2.19)

0.24 0.10 0.49

R

Breusch-Godfrey LM test for Autocorrelation First order 2.02 (0.16) 0.28 (0.59) 0.07 (0.79) Second order 3.17 (0.21) 0.36 (0.83) 1.88 (0.39) No Observations 50 50 50

Notes:(1) P, S, and T,respectively, denote the growth rate of Primary, Secondary and Tertiary sector output.

in the language of econometric practice, we have “allowed the data to parametrise the model”. Our results suggest the following data-congruent narrative. There is across-the-board dynamism in the Indian economy during this period in that all the major sectors show an acceleration in their rate of growth. This diverges strongly from the finding of the only other comparable study, by Wallack, that no break in the growth rate can be established for individual sectors. It implies that the acceleration in the economy-wide growth rate from 1979-80 identified in this study is not an artefact of the reallocation of output across sectors. However, at least two of the three main components of GDP accelerate prior to that date giving us some idea of the factors underlying the acceleration in aggregate growth. These are the primary and tertiary sectors, or at least their major components. The secondary sector, largely constituted by manufacturing, shows a positive break only after 1980.

These results provide some vital clues and building blocks for a narrative on Indian economic growth. The sequence of accelerations, the order being primary, tertiary and secondary, suggests the following story of growth in India since 1950. The acceleration of growth in the primary sector, occurring as early as the mid-1960s provided the original stimulus, via supply and demand linkages, to growth in the other sectors of the economy. This is confirmed by our econometric exercise. Growth of the primary sector enters into the growth of the tertiary sector which in turn enters into the growth of the secondary sector. The secondary sector does not in turn enter either of the other; nor does the tertiary sector enter into the growth of the primary sector. This implies a recursive model of growth and a certain causality is implied by these results.

After a propulsion driven by acceleration of primary sector growth services growth has been quite unstoppable in India. As our decomposition exercise shows, it has contributed overwhelmingly to the estimated shift in the aggregate growth rate since 1979-80. Manufacturing has very likely played less of a role in bringing about the growth transition in India as has been argued by some researchers. It accelerates after the acceleration in the other sectors which between them manage to raise the economy-wide growth rate well before the reforms12 said to have been initiated in the 1980s. The results of our research strategy indicate little role for a liberalised trade and industrial policy having been the trigger of a new growth dynamic in India via faster manufacturing growth, at least up to the mid-1990s. We conclude with two observations. Note that our results are a direct outcome of our methodology of generating the break date(s) endogenously. A very different reading would emerge were we to break the data arbitrarily ostensibly following a judgment13 on the timing of a shift in the policy regime which is believed to have stimulated growth. Clearly, therefore, methodology matters. We consider this an important result in itself. Secondly, some researchers have rhetorically queried whether services may emerge as the engine of economic growth in the future [Dasgupta and Singh 2005]. We find that services have proved to be the engine of growth already! Among the few authors who have recognised this is Rakshit (2007), however, in light of our results, he dates this to too recent a date. Our results show that services have led growth in India for at least two decades by now. Acknowledging this is a prerequisite to understanding economic growth in India. Central to it all is the proper identification of growth regimes, which has been the focus of this paper.

Economic and Political Weekly July 14, 2007

Appendix A1. Decomposition of Change in Aggregate Growth Rate

⎛− ⎞

YYt t −1

Y

⎝ t1− ⎠

n1 n1

⎛⎞ ⎛⎞

−1 −1

⎠ =

gY2

+ (w g − w g ) …(5)

T2T2 T1 T1

A2. Computation of the Confidence Interval of the Breakdates

Confidence interval for breakdates, where trended regressors are

present, are computed using the procedure given in Bai (1997).

^ This can be explained as follows. Let Tj be the j-th breakpoint,^ ^ ^ ^ ^ ^

βj = (aj, gj), δj= (βj+1 – βj) and ztj = (1, tj), where tj is the value ^ ^ ^^ ^ T^

of t at j-th break. Define, Lj = (δjz'tjztjδ'j)/σ2 where σ2 = T–1Σu2

from (1). Now the 100(1 – α)% confidence interval is given by^ ^ ^^

[Tj – (c/Lj) – 1, Tj + (c/Lj) + 1], where c is the (1 – α/2)th quantile of the distribution (at 5 per cent level c = 11). Note that it is assumed that the variance of the error term is the same across segments. It is of course possible to construct the confidence interval without this assumption of uniformity [Bai 1997], but we have not done so to maintain computational ease.

lli

Email: pbkrishnan@yahoo.com parameswaran@cds.ac.in

Log Income

13.5

12.5

12

1950 1960 1970 1980 1990 2000 Year (1950 = 1950-51)

Note:The vertical dashed line indicates the breakpoint.

Notes

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Economic and Political Weekly July 14, 2007