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# Understanding Economic Growth in India: A Prerequisite

#### This article follows a recent development in the estimation and testing of multiple structural breaks in linear models to identify phases of growth in India since 1950. The noteworthy feature of the methodology is that it allows the data to parametrise the model, thus yielding results that are immune to the prior beliefs of the researcher. The resulting estimates reveal that there are two growth regimes in India since 1950. The authors then decompose by sector the contribution to the change in the growth rate across these regimes. Finally, by means of a simple econometric model, they test a hypothesis that emerges from their estimation and testing for structural break in the main sectors of the economy to provide an explanation of the growth transition in India. In passing, the authors consider the bearing of their results on extant explanations of the same transition.

PULAPRE BALAKRISHNAN, M PARAMESWARAN

If you torture the data enough, nature will always confess.

– Ronald Coase: ‘How Should Economists Choose?’

#### I Introduction

#### II Methodology and Data

The growth rates of aggregate and sectoral GDP may be estimated using the exponential function lnYt = a + gt + ut, where lnY, g, t and u denote the log of income, growth rate, time trend and random disturbance term, respectively. The subscript t denotes time. The parameters of the above regression model – a and g

– would vary from one growth regime to another, making it necessary to identify the change point. Therefore, we first estimate the breakdates of the above model for aggregate and sectoral GDP and accordingly partition the data to estimate the periodwise growth rates. The methodology for estimating the breakdates is explained in detail below.

The exponential growth model containing m+1 growth regimes and m break dates (T1,…, T) can be written as follows:

mlnYt = a1 + g1t + ut, t = 1,…,T1

lnYt = a2 + g2t + ut, t = T1 + 1,…,T2 ...(1)

.

.

. lnYt = am+1 + gm+1t + ut,t = T + 1,…,T

m

Here we adopt the convention that T0 = 0 and Tm+1 = T the total number of observations. The number of break points m and the break dates (T1,…,T) are treated as unknown and estimated

mfrom the data. The conventional approach to establishing a structural break in a time series regression model is to perform the test for a statistically significant difference in its parameters across two periods. This is referred to as the “Chow Test”.2 In recent years, however, this approach has come under scrutiny [Hansen 2001]. The issue of concern is the method of identification of the breakdate. One of two approaches is followed. The first is to identify the breakdate based on some known feature of the data, such as an observed inflexion in the graph of a series. The other is to choose the breakdate based on the occurrence of some exogenous event expected to cause structural change in the model. An example would be to treat the first oil shock of 1973 as signalling a break in the growth rate of the oil-importing OECD economies, and then proceeding to test for the same. Both these procedures3 for choice of breakdate is problematic. In the first

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

estimated breakdates to the choice of interval length may be subjected to analysis as will be done by us. Now the search for possible break would be confined to the period 1957-58 to 1995-96. The growth rates across regimes are estimated by imposing kinks at the estimated breakpoints according to a procedure due to Boyce (1986). This maintains the continuity of the exponential trend line at the break points.

#### III Results and Their Interpretation

The estimated breakdates7 are presented in Table 1 and the growth rates for the associated sub-periods in Table 2. The breakdate has been estimated allowing for a shift in the intercept alongside a change in the slope coefficient, the case of a pure structural change. Our visual comparison of the fitted series and actual series showed that in almost all cases the change in the slope is accompanied by a shift in the intercept.8 Furthermore, in the overwhelming majority of instances (50 out of a total 71 intercept shifts for the 24 series) the change in the intercept exceeded the absolute value 0.3 found by Perron and Zhu (2005) to be the critical value beyond which the accuracy of the breakdate estimates can be affected if the intercept shift is not allowed for.9

Table 1: Estimated Breakdates

First Break | Second Break | Third Break | Fourth Break | ||
---|---|---|---|---|---|

GDP | 1978-79 (+) | ||||

[1977/78-1979/80] | |||||

1.1 | Agriculture | 1964-65 (+) | |||

[1963/64-1965/66] | |||||

1.2 | Forestry and logging | 1964-65 (+) | 1976-77 (-) | 1988-89(+) | |

[1963/64-1965/66] | [1975/76-1977/78] | [1987/88-1989/90] | |||

1.3 | Fishing | 1958-59 (-) | 1973-74 (-) | 1982-83 (+) | 1992-93 (-) |

[1957/58-1959/60] | [1972/73-1974/75] | [1981/82-1983/84] | [1991/92-1993/94] | ||

2 | Mining and quarrying | 1959-60 (+) | 1969-70 (-) | 1980-81 (+) | 1988-89 (-) |

[1958/59-1960/61] | [1968/69-1970/71] | [1978/79-1980/81] | [1988/89-1990/91] | ||

3 | Manufacturing | 1965-66 (-) | 1982-83 (+) | 1994-95 (-) | |

[1964/65-1966/67] | [1981/82-1983/84] | [1993/94-1995/95] | |||

3.1 | Registered | 1965-66 (-) | 1982-83 (+) | 1994-95 (-) | |

[1964/65-1966/67] | [1981/82-1983/84] | [1993/94-1995/96] | |||

3.2 | Unregistered | 1964-65 (-) | 1986-87 (+) | 1994-95 (-) | |

[1963/64-1965/66] | [1985/86-1987/88] | [1993/94-1995/96] | |||

4 | Electricity, gas and water supply | 1957-58 (+) | 1967-68 (-) | 1983-84 (+) | 1991-92 (-) |

[1956/57-1958/59] | [1966/67-1968/69] | [1982/83-1984/85] | [1990/91-1992/93] | ||

5 | Construction | 1969-70 (-) | 1981-82 (+) | ||

[1968/69-1970/71] | [1980/81-1982/83] | ||||

6 | Trade, hotels and restaurants | 1962-63 (-) | 1971-72 (+) | 1994-95 (+) | |

[1961/62-1963/64] | [1970/71-1972/73] | [1993/94-1994/95] | |||

6.1 | Trade | 1962-63 (-) | 1971-72 (+) | 1994-95 (+) | |

[1961/62-1963/64] | [1970/71-1972/73] | [1993/94-1995/96] | |||

6.2 | Hotels and restaurants | 1959-60 (-) | 1971-72 (+) | 1984-85 (+) | 1994-95 (+) |

[1951/52-1967/68] | [1970/71-1972/73] | [1983/84-1985/86] | [1993/94-1995/96] | ||

7 | Transport, storage and communication | 1961-62 (-) | 1973-74 (+) | 1993-94 (+) | |

[1960/61-1962/63] | [1972/73-1974/75] | [1992/93-1994/95] | |||

7.1 | Railways | 1961-62 (-) | 1984-85 (+) | 1992-93 (-) | |

[1960/61-1962/63] | [1983/84-1985/86] | [1991/92-1993/94] | |||

7.2 | Transport by other means | 1957-58 (+) | 1973-74 (+) | 1993-94 (+) | |

[1955/56-1959/60] | [1972/73-1974/75] | [1992/93-1994/95] | |||

7.3 | Storage | 1974-75 (+) | 1984-85 (-) | ||

[1973/74-1975/76] | [1983/84-1985/86] | ||||

7.4 | Communication | 1962-63 (-) | 1987-88 (+) | 1995-96 (+) | |

[1960/61-1964/65] | [1986/87-1988/89] | [1994/95-1996/97] | |||

8 | Financing, Insurance, real estate and | 1966-67 (+) | 1979-80 (+) | 1992-93 (-) | |

business services | [1965/66-1967/68] | [1978/79-1980/81] | [1991/92-1993/94] | ||

8.1 | Banking and Insurance | 1965-66 (-) | 1979-80 (+) | 1995-96 (-) | |

[1958/59-1972/73] | [1978/79-1980/81] | [1994/95-1996/97] | |||

8.2 | Real estate, ownership of dwelling and | 1966-67 (+) | 1980-81(+) | 1993-94 (-) | |

business services | [1965/66-1967/68] | [1979/80-1981/82] | [1992/93-1994/95] | ||

9 | Community and personal services | 1961-62 (+) | 1976-77 (+) | 1992-93 (+) | |

[1960/61-1962/63] | [1975/76-1977/78] | [1991/92-1993/94] | |||

9.1 | Public administration and defence | 1961-62 (-) | 1986-87 (-) | 1995-96 (+) | |

[1960/61-1962/63] | [1985/86-1987/88] | [1994/95-1996/97] | |||

9.2 | Other services | 1957-58 (+) | 1968-69 (-) | 1980-81 (+) | 1992-93 (+) |

[1956/57-1958/59] | [1967/68-1969/70] | [1979/80-1981/82] | [1991/92-1993/94] |

Notes: (1) 95 per cent confidence interval of the estimated breakdate is provided in the brackets. Confidence intervals are computed using the asymptotic distribution derived using the “shrinking magnitude of shift” framework [for details of this see Perron and Zhu 2005 and Deng and Perron 2005].

(2) The signs plus and minus, in parentheses, indicate acceleration and deceleration, respectively.

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 2: Estimated Growth Rates

Sector | Period 1 | Period 2 | Period 3 | Period 4 | Period 5 | |
---|---|---|---|---|---|---|

GDP | 3.34 | 5.20 | ||||

[1950/51-1978/79] | [1979/80-2003/04] | |||||

1.1 Agriculture | 1.73 | 2.78 | ||||

[1950/51-1964/65] | [1965/66-2003/04] | |||||

1.2 Forestry and logging | 1.57 | 2.46 | -2.31 | 1.33 | ||

[1950/51-1964/65] | [1965/66-1976/77] | [1977/78-1988/89] | [1989/90-2003/04] | |||

1.3 Fishing | 5.63 | 3.93 | 2.14 | 6.18 | 5.10 | |

[1950/51-1958/59] | [1959/60-1973/74] | [1974/75-1982/83] | [1983/84-1992/93] | [1993/94-2003/04] | ||

2 | Mining and quarrying | 4.82 | 5.44 | 3.14 | 8.65 | 4.90 |

[1950/51-1959/60] | [1960/61-1969/70] | [1970/71-1980/81] | [1981/82-1988/89] | [1989/90-2003/04] | ||

3 | Manufacturing | 6.27 | 4.26 | 6.76 | 6.07 | |

[1950/51-1965/66] | [1966/67-1982/83] | [1983/84-1994/95] | [1995/96-2003/04] | |||

3.1 Registered | 7.76 | 4.53 | 7.53 | 6.13 | ||

[1950/51-1965/66] | [1966/67-1982/83] | [1983/84-1994/95] | [1995/96-2003/04] | |||

3.2 Unregistered | 4.63 | 4.09 | 5.96 | 5.83 | ||

[1950/51-1964/65] | [1965/66-1986/87] | [1987/88-1994/95] | [1995/96-2003/04] | |||

4 | Electricity, gas and water supply | 8.51 | 12.21 | 7.03 | 9.23 | 5.64 |

[1950/51-1957/58] | [1958/59-1967/68] | [1968/69-1983/84] | [1984/85-1991/92] | [1992/93-2003/04] | ||

5 | Construction | 6.59 | 2.00 | 5.05 | ||

[1950/51-1969/70] | [1970/71-1981/82] | [1982/83-2003/04] | ||||

6 | Trade, hotels and restaurants | 5.79 | 3.80 | 5.12 | 8.40 | |

[1950/51-1962/63] | [1963/64-1971/72] | [1972/73-1994/95] | [1995/96-2003/04] | |||

6.1 | Trade | 5.71 | 3.84 | 5.10 | 8.23 | |

[1950/51-1962/63] | [1963/64-1971/72] | [1972/74-1994/95] | [1995/96-2003/04] | |||

6.2 | Hotels and restaurants | 5.42 | 4.67 | 4.45 | 6.74 | 9.91 |

[1950/51-1959/60] | [1960/61-1971/72] | [1972/73-1984/85] | [1985/86-1994/95] | [1995/96-2003/04] | ||

7 | Transport, storage and | 6.12 | 5.50 | 5.55 | 9.21 | |

communication | [1950/51-1961/62] | [1962/63-1973/74] | [1974/75-1993/94] | [1994/95-2003/04] | ||

7.1 Railways | 5.81 | 3.68 | 4.01 | 3.78 | ||

[1950/51-1961/62] | [1962/63-1984/85] | [1985/86-1992/93] | [1993/94-2003/04] | |||

7.2 Transport by other means | 5.94 | 6.16 | 6.21 | 6.85 | ||

[1950/51-1957/58] | [1958/59-1973/74] | [1974/75-1993/94] | [1994/95-2003/04] | |||

7.3 Storage | 3.09 | 9.99 | 1.15 | |||

[1950/51-1974/75] | [1975/76-1984/85] | [1985/86-2003/04] | ||||

7.4 | Communication | 7.13 | 6.17 | 7.41 | 19.41 | |

[1950/51-1962/63] | [1963/64-1987/88] | [1988/89-1995/95] | [1995/96-2003/04] | |||

8 | Financing, insurance, real estate | 3.06 | 3.44 | 8.88 | 8.00 | |

and business services | [1950/51-1966/67] | [1967/68-1979/79] | [1979/80-1992/93] | [1993/94-2003/04] | ||

8.1 Banking and insurance | 6.65 | 5.83 | 11.01 | 9.19 | ||

[1950/51-1965/66] | [1966/67-1979/80] | [1980/81-1995/96] | [1996/97-2003/04] | |||

8.2 Real estate, ownership of dwelling | 2.29 | 2.79 | 7.77 | 5.92 | ||

and business services | [1950/51-1966/67] | [1967/68-1980/81] | [1981/82-1993/94] | [1994/95-2003/04] | ||

9 | Community and personal | 4.20 | 4.46 | 5.95 | 6.86 | |

services | [1950/51-1961/62] | [1962/63-1976/77] | [1977/78-1992/93] | [1993/94-2003/04] | ||

9.1 | Public administration and | 6.53 | 6.23 | 4.96 | 6.48 | |

defence | [1950/51-1961/62] | [1962/63-1986/87] | [1987/88-1995/96] | 6[1996/97-2003/04] | ||

9.2 | Other services | 2.41 | 3.97 | 2.83 | 5.01 | 7.43 |

[1950/51-1957/58] | [1958/59-1968/69] | [1969/70-1980/81] | [1981/82-1992/93] | [1993/94-2003/04] | ||

Notes: (i) All estimates are significant at 1 per cent level, and (ii) in brackets is the concerned period for the reported growth. | ||||||

2918 | Economic and Political Weekly | July 14, 2007 |

interpreted as the impact of the Green Revolution, the principal feature of which is seen as the spreading use of high-yielding varieties of seed and the application of fertiliser, both introduced in the years of food shortage in the mid-1960s. It is, however, difficult to assume that this package alone could have raised the rate of growth permanently. Our finding here that the growth rate of the agricultural sector accelerates from 1964-65 suggests that the conventional finding of an acceleration of agricultural growth from 1967-68 is an artefact of the method of using exogenous information to partition the time series. We consider it an intuitive appeal of our estimate(d breakdate) that the growth acceleration is initiated in a year of fast growth. The data show that in 1964-65 agricultural output increases by over 10 per cent.

of the acceleration varies from mild in the case of “Transport, Storage and Communication” to dramatic in the case of “Financing, Insurance, Real Estate and Business Services” (Table 2). We consider this evidence of the timing of a break in the components of the tertiary sector as prima facie evidence of services having led the acceleration in the growth of GDP in India. Following this lead we undertake two exercises. First, we perform a decomposition of the contribution by sector to the change in the aggregate GDP growth rate from 1979-80. Secondly, we perform an econometric test of the relationship between sectoral growth rates that must hold if aggregate growth is services led.

Using the expression derived in the Appendix, the change in the average growth rate of aggregate GDP from 1979-80 onwards is decomposed into the contribution by constituent sectors. The results of this exercise are reported in Table 3. Find that the contribution by the tertiary sector overwhelms the contribution by the other sectors. In particular, note that the contribution exceeds that of manufacturing by a factor exceeding four. The above exercise appears conclusively to have established that the acceleration of aggregate GDP was not led by manufacturing. Methodologically, we have not reached this stage yet though, for the results of the decomposition undertaken must be read along with the caveat that what may be established from the exercise is only the direct contribution of each sector to the change in the aggregate growth rate. Per se we cannot rule out that tertiarysector growth may have been in turn stimulated by manufacturing growth, even though our earlier finding is that services growth had broken ground before manufacturing. Taking into account this weakness of the decomposition exercise, we undertake some econometric exercises the results of which are presented in Table 4. For the purpose of these exercises we have aggregated the data according to the standard classification “primary”, “secondary” and “tertiary” as this makes the analysis of the data more manageable. For a clear description of what each of these sectors contain the reader may refer to Table 3.

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

(In per cent) Contribution

I Primary sector -25.95

1.1 Agriculture -26.41

1.2 Forestry and logging -3.94

1.3 Fishing 0.63 2 Mining and quarrying 3.76 II Secondary sector 25.66 3 Manufacturing 24.65

3.1 Registered 18.79

3.2 Unregistered 5.86 4 Electricity, gas and water supply 4.44 5 Construction -3.43 III Tertiary sector 100.29 6 Trade, hotels and restaurants 23.08

6.1 Trade 20.83

7.2 Transport by other means 7.58

7.3 Storage -0.12

9.2 Other services 12.28

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

Consider two periods 1 and 2, respectively consisting of n1 and n2 years. Denote aggregate GDP, primary, secondary, and tertiary sector incomes by Y, P, S, and T. Let wit denote the share of sector i (i = P, S, T) in Y in year t and g denote the growth rate. Y in year t can be written as follows:

Yt = Pt + St + Tt …(1)

From (1), the growth rate of Y can be written as:

gYt = wptgpt + wst gst + wTt gTt …(2)

⎛− ⎞

YYt t −1

where gYt =⎜ ⎟ is the growth rate of Y in year t and gPt,

Y

⎝ t1− ⎠

gSt and gTt are defined similarly. Using (2), the average annual growth rate for the period 1 ( gY1 ) can be written as follows. Where a bar over notations has been used to denote average value.

gY1 = wP1gP1 + wS1 gS1 + wT1 gT1 …(3)

where,

n1 n1

⎛⎞ ⎛⎞

−1 −1

g = n1 g wg = n1 wg

Y1 ⎜∑ Yt ⎟, and i1 i1 ⎜∑ it it ⎟ . ⎝ t1=⎝ t1 ⎠

⎠ =

Similarly, can be written as below,

gY2

gY2 = wP2 gP2 + wS2 gS2 + wT2gT2 …(4)

In (4), averages are taken over n2 observations in period two. Subtracting (3) from (4),

(gY2 − gY1 ) = (wP2gP2 − wP21gP1 ) + (wS2 gS2 − wS1 gS1 )

+ (w g − w g ) …(5)

T2T2 T1 T1

Dividing (5) throughout by the left-hand side value and multiplying it by 100 gives the percentage contribution of each sector to the change in the average growth rate of Y in period two over that in previous period.

###### 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

t

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

u t=1

[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.

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

Log Income

###### Figure A1

GDP: Actual and Fitted Values

14

13.5

13

12.5

12

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

Note:The vertical dashed line indicates the breakpoint.

#### Notes

[This paper was first presented at the south and south east Asia meetings of the Econometric Society held at Chennai over December 18-20, 2006. We are grateful to Arunava Sen for inviting us to organise a special session titled ‘Understanding Economic Growth in India’ and for giving us the opportunity to present this paper there. Subsequently, the paper was presented at the Delhi Centre of the Indian Statistical Institute where we benefited from the comments of the seminar participants. Abdul Aziz, Kaushik Basu and K L Krishna read the paper and generously gave us comments. An anonymous referee’s observations have led to greater clarity in our presentation. Support from our institutions is acknowledged. Errors and omissions would be ours.]

1 See Hansen (2001) for an accessible discussion of developments in the associated econometrics. 2 Decades ago T N Srinivasan had pointed out to one of us that this is a misnomer as the test had been first devised by C R Rao!

3 For an example of the use of each of these approaches in the context of identifying growth regimes in India see Virmani (2006) and Kaur (2007). At this stage we might mention that having misunderstood the procedure, Kaur attributes to Balakrishnan (2005) a similar arbitrariness, when actually he had explicitly adopted a methodology that generates a breakpoint endogenously. See Balakrishnan (2005), p 3969.

4 See Ben-David and Papell (1998). 5 For an application see Uctum et al (2006). 6 See Bai and Perron (2003) for a comparison of the performance of the

BIC and supF statistics.

7 Estimation of the breakdates were done using the software package ‘strucchage in R’ written by Zeileis, Leisch, Hansen, Hornik, Kleiber and Peters. For details see Zeileis et al (2005).

8 To save space we present a representative graph of fitted and actual series of GDP in the Appendix, Figure A1. The figures for the remaining series are available from us upon request.

9 We are aware of an additional empirical issue. In the case of multiple breaks it is conceivable that there is an intercept shift between some segments and not between others. However, our methodology does not allow us to accommodate this, forcing us to allow for an intercept shift for every break in a series.

10 A sensitivity analysis performed by us showed that in all the series estimated breakdates are invariant to h = 4 and 5, given the number of breaks estimated when h = 8.

11 All results reported here are available from the authors upon request.

12 Interestingly, there is no agreement on the nature of the reforms. While some have seen this as liberalisation Rodrik and Subramanian (2005) argue that the policy changes of the 1980s were actually pro-business, and therefore not competition inducing.

13 See Acharya (2002) and Kohli (2006) for instances. Indeed the decadewise periodisation adopted by these authors leaves the researcher with little option other than to conclude that the acceleration of growth in India in the 1980s has been strongly led by faster growth of agriculture (the main component of the primary sector). For, agricultural growth not only doubles in the decade of the 1980s but this acceleration is greater by far than that in the other two principal sectors of the economy (see Acharya op cit, Table 2). In 1980-81 the primary sector was the largest.

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Economic and Political Weekly July 14, 2007