Kamil Adiloglu
email: kamil.adiloglu@inria.fr

Emmanuel Vincent
email: emmanuel.vincent@inria.fr

AN UNCERTAINTY ESTIMATION APPROACH FOR THE EXTRACTION OF SOURCE FEATURES IN MULTISOURCE RECORDINGS

We consider the extraction of individual source features from a multisource audio recording by combining source separation with feature extraction. The main issue is then to estimate and propagate the uncertainty over the separated source signals, so as to robustly estimate the features despite source separation errors. While state-of-the-art techniques were designed for scenarios involving one prominent source plus background noise, we focus on under-determined mixtures involving several sources of interest. We apply either Gibbs sampling or variational Bayes to estimate the posterior probability of the sources and subsequently derive the expectation of the features either by sampling or by moment matching. Experiments over stereo mixtures of three sources show that variational Bayes followed by either feature sampling or moment matching provides the best results for convolutive mixtures, while no improvement is obtained on instantaneous mixtures compared to deterministic feature computation.

INTRODUCTION

Audio information retrieval (AIR) covers a wide range of applications, from speech/speaker recognition to music genre classification. All these applications are typically achieved by extracting features describing the audio content and exploiting them for e.g. classification. However, most audio signals consist of a mixture of several sound sources, which have their own characteristics. Applying source separation prior to feature extraction can increase retrieval accuracy. For example, the separation of target speech from background noise is known to improve speech recognition performance [START_REF] Kolossa | Independent component analysis and timefrequency masking for speech recognition in multitalker conditions[END_REF], while the separation of harmonic and percussive sounds improves music genre classification [START_REF] Rump | Autoregressive MFCC models for genre classification improved by harmonic-percussion separation[END_REF].

The problem at hand is then to robustly estimate the features of each source despite source separation errors. This can be achieved in a probabilistic framework by estimating the uncertainty over the separated source signals and propagating it to the features. Because source separation is usually achieved in the time-frequency domain, the uncertainty must be expressed in that domain. The pioneering approach of Cooke et al. [START_REF] Cooke | Robust automatic speech recognition with missing and unreliable acoustic data[END_REF][START_REF] Eggink | Application of missing feature theory to the recognition of musical instruments in polyphonic audio[END_REF] relied on a binary uncertainty model, where each time-frequency coefficient of each source was considered either as reliable or not reliable. Deng et al. [START_REF] Deng | Dynamic compensation of HMM variances using the feature enhancement uncertainty computed from a parametric model of speech distortion[END_REF] and Kolossa et al. [START_REF] Kolossa | Independent component analysis and timefrequency masking for speech recognition in multitalker conditions[END_REF] proposed a more flexible Gaussian model, enabling more precise quantification of the uncertainty in terms of the posterior probability of each timefrequency coefficient. However, their studies relied on specific source separation algorithms designed for mixtures of one prominent source plus background noise. In this paper, we address the problem of individual source feature extraction from under-determined mixtures involving several sources of interest, such as e.g. polyphonic music recordings. As a preliminary study, we concentrate on the local Gaussian model-based separation [START_REF] Vincent | Probabilistic modeling paradigms for audio source separation[END_REF], and extract the Mel Frequency Cepstral Coefficients (MFCCs) [START_REF] Logan | Mel frequency cepstral coefficients for music modeling[END_REF] of each source, which are the most popular features for AIR. Figure 1 shows the structure of the proposed approach. We estimate the posterior distribution of the source time-frequency coefficients either by Gibbs sampling or variational Bayes and subsequently derive the expectation of the features either by sampling or by moment matching.

Except for the latter, these techniques have not previously been used in this context to our knowledge. Cemgil et al. [START_REF] Cemgil | Variational and stochastic inference for Bayesian source separation[END_REF] applied Gibbs sampling and variational Bayes to source separation, but focused on evaluating performance on instantaneous mixtures and did not consider feature extraction nor convolutive mixtures. Also, somewhat surprisingly, they did not compare performance with Maximum Likelihood (ML) inference. Kolossa et al. [START_REF] Kolossa | Independent component analysis and timefrequency masking for speech recognition in multitalker conditions[END_REF] used moment matching to propagate uncertainty for MFCC extraction, but more powerful sampling techniques have not been exploited so far.

This paper is organized as follows. Section 2 introduces the source separation framework and the two inference algorithms for the estimation of the posterior distribution of the sources. Section 3 presents the feature extraction and uncertainty propagation algorithms. In Section 4, we evaluate these algorithms in combination with each other over instantaneous or convolutive mixtures. We conclude in Section 5.

UNCERTAINTY ESTIMATION IN SOURCE SEPARATION

Classically, we adress the source separation problem in the time-frequency domain by means of the Short-Time Fourier Transform (STFT). The mixing equation is given by

x f t = A f s f t + ε f t , (1)
where

x f t = [x 1, f t , . . . , x I, f t ] T denotes the mixture STFT co- efficients, s f t = [s 1, f t , . . . , s J, f t ] T the source STFT coeffi- cients, A f = [a i j f ] i j ∈
C I×J the mixing system and ε f t the noise. In this formulation, f = 1, . . . , F is the fequency index, t = 1, . . . , T the time frame index, i = 1, . . . , I the channel index and j = 1, . . . , J the source index. We focus on the under-determined scenario, for which I < J.

In this preliminary study, we assume that the mixing system A f is known and adopt a local Gaussian model [START_REF] Vincent | Probabilistic modeling paradigms for audio source separation[END_REF] for the source coefficients. As a consequence, the source coefficients can be separately estimated in each time-frequency bin. Therefore, we omit the indices f , t in the rest of this section for the sake of readability.

We set a zero-mean Gaussian prior over the source coefficients s with variance v: s ∼ N (0, v).

(

) 2
We assume independence between the sources so that the covariance matrix takes the diagonal form

v = diag([v j ] j=1•••J ).
We then set an inverse-gamma prior over each source variance v j with shape parameter α j and scale parameter β j = 0:

v j ∼ I G (α j , 0). ( 3
)
This prior is conjugate to the Gaussian likelihood and governs the shape of the variance, where α j = 0 corresponds to the scale-invariant Jeffreys prior. Finally, we assume that the noise ε f t is Gaussian with fixed covariance matrix E.

Maximum Likelihood

The state-of-the-art ML approach consists of estimating the source variances by means of the Expectation-Maximization (EM) algorithm in [START_REF] Duong | Underdetermined reverberant audio source separation using a full-rank spatial covariance model[END_REF] then deriving the source coefficients by multichannel Wiener filtering. Defining the complete data for each time-frequency bin to be {x f n , s f n } yields the following updates:

ŝ = Wx, (4)
Σ = (I -WA)v, (5)
v j = |ŝ| 2 -Σ j j , (6)
where

W = vA H (AvA H + E) -1 (7)
is the Wiener filter and I is the identity matrix. This approach basically gives a point estimate ŝ of the source coefficients. We aim to estimate the posterior probability of the source coefficients, which is given by

p(s|x) ∝ p(x|s, v)p(s|v)p(v)dv. (8)
In order to approximate this integral, which is intractable, we now consider two state-of-the-art Bayesian approximation techniques, namely Gibbs sampling and variational Bayes.

Gibbs Sampling

Gibbs sampling [START_REF] Bishop | Pattern Recognition and Machine Learning[END_REF] aims to approximate the joint posterior p(s, v|x) by a collection of R samples (s (r) , v (r) ) obtained by alternatingly sampling from the conditional distributions of the variables. It has been shown that these samples converge to the joint distribution, provided that the resulting Markov chain is reversible. The marginal distribution p(s|x) is then represented by the samples s (r) . The conditional distribution of the source coefficients boils down to the Wiener filter again

p(s|x, v) = N (s; Wx, (I -WA)v), (9)
where W is given in [START_REF] Ellis | Crosscorrelation of beat-synchronous representations for music similarity[END_REF].

Due to conjugacy rules, the conditional distribution of the variance of each source is again an inverse-Gamma distribution:

p(v j |s j ) = I G (v j ; α j + 1, |s j | 2 ). (10)
Consequently, in order to approximate p(s, v|x), each iteration r of our Gibbs sampling scheme consists in:

1. Sampling the source variance v (r)

j for j = 1 . . . J from p(v (r) j |s (r-1) j ),
2. Sampling the source coefficients s (r) from p(s (r) |x, v (r) ).

Variational Bayes

Variational Bayes [START_REF] Bishop | Pattern Recognition and Machine Learning[END_REF] is an alternative inference approach, which minimizes the Kullback-Leibler (KL) divergence between the true posterior distribution p(s, v|x) and some approximation q(s, v), which is typically specified by assuming some factorization. We assume the following factorization:

q(s, v) = q(s) J ∏ j=1 q(v j ). (11)
The factor distributions minimizing the KL divergence can be obtained by taking the expectation of the joint logdistribution of all variables over the other factors [START_REF] Bishop | Pattern Recognition and Machine Learning[END_REF].

Skipping the necessary maths due to space limitations, we obtain the following optimal factors:

q * (s) ∼ N c (s; µ, Σ), ( 12
) q * (v j ) ∼ I G (v j ; α j + 1, β j ), (13)
where

µ = Wx, (14)
Σ = (I -WA)β , (15)
β j = |µ j | 2 + Σ j j . (16)
β is given by β = diag([β j ] j=1...J ), µ j is the j th element of µ, I is the identity matrix and the Wiener filter W writes

W = β A H (Aβ A H + E) -1 .
(17) ( 14), (15), ( 16) and (17) depend on each other. After proper initialization of the factors, they are an iterative optimized by cycling through these equations and by replacing the dependent values with their new estimates.

To our surprize, even though the ML approach and our variational Bayes solution optimize different criteria, the update equations for the mean of the source coefficients of both methods are identical up to the change of variables v = β and ŝ = µ. However our approach also provides the covariance of the source coefficients.

Note also that, despite the similarity between the update equations of Gibbs sampling and variational Bayes, these two inference methods provide different results. In particular, Gibbs sampling better approximates multimodal posteriors, while variational Bayes is computationally faster.

UNCERTAINTY PROPAGATION FOR FEATURE EXTRACTION

Once the posterior distribution of the source coefficients s j f t in each time-frequency bin has been computed, we calculate the expectation of the MFCCs separately for each source as

µ MFCC jt = MFCC(S jt )P(S jt ) dS jt ( 18
)
where S jt = [s j f t ] f =1...F are the STFT coefficients of source j in time frame t. For ML, this boils down to MFCC( Ŝ jt ).

The calculation of the MFCCs for a given complexvalued spectrum S jt consists of taking the magnitude |S jt | of the spectrum, filtering it by a set of triangular filters spanning the Mel frequency scale and taking the discrete cosine transform (DCT) of the filtered spectrum [START_REF] Logan | Mel frequency cepstral coefficients for music modeling[END_REF]:

MFCC(S jt ) = 20 D log 10 (M|S jt |). (19)
In this formulation, D is the DCT matrix and M is the matrix containing the mel filter coefficients. Note that we chose the scaling so that the MFCCs are expressed in decibels (dB).

We now present two methods to propagate the uncertainty over the source coefficients to the MFCCs based on sampling and moment matching. Each method is applicable both to the output of Gibbs sampling and variational Bayes.

MFCC Estimation by Sampling

For each source j and time frame t, we sample L complexvalued source spectra S (l) jt and calculate the MFCCs using (19). Then, we compute the mean of these MFCCs as

µ MFCC jt = 1 L L ∑ l=1 MFCC(S (l) jt ). (20)
For the Gibbs sampling, the sample spectra S (l)

jt are obtained by randomly selecting one sample s (r) j f t for each frequency bin f , which we have saved during the Gibbs sampling. For the variational Bayes, we sample from the estimated posterior of the source coefficients shown in [START_REF] Vincent | BSS Oracle Toolbox[END_REF].

MFCC Estimation by Moment Matching

The moment matching approach propagates the uncertainty expressed by the means and variances of the posterior distributions of the estimated source coefficients through the calculation of the MFCCs. These means and variances are readily given when using variational Bayes or can be estimated from the source samples when using Gibbs sampling.

The absolute value of a complex Gaussian random variable, hence the magnitude spectrum of the estimated source coefficients follows a Rice distribution. For source j in time frame t, the mean and variance of the magnitude spectrum is given by the first and second raw moments of the Rice distribution as:

µ |s| = E[|S j,t |] and Σ |s| = E[|S j,t | 2 ] -(µ |s| ) 2 [9].
The mel-filtering of the magnitude spectrum is a linear transformation. So, we can simply match the moments:

µ MEL = M µ |s| , (21)
Σ MEL = M Σ |s| M T . ( 22
)
The logarithm in the calculation of the MFCCs is not a linear transformation. Here, we assume the log-normality of the MEL features. Incorporating the log-normal transformation proposed by Gales [START_REF] Gales | Model-Based Techniques for Noise Robust Speech Recognition[END_REF], the i-th coefficient is given by:

µ log i = 20 log 10 (µ MEL i ) -10 log 10 Σ MEL ii (µ MEL i ) 2 + 1 . ( 23
)
The final step, the DCT, is another linear transform. Hence, we apply moment matching again:

µ MFCC jt = D µ log .
(24)

EXPERIMENTAL EVALUATION

We now evaluate the uncertainty estimation and propagation algorithms proposed above in combination with each other.

Data

We considered a dataset of 20 stereo mixtures of 3 sources of 10 s duration, including 10 instantaneous mixtures and 10 convolutive mixtures with 250 ms reverberation time. Both types of mixtures were generated from the same 30 source signals, including 15 music and 15 speech signals. The source signals and the mixing filters were taken from the BSS Oracle toolbox [START_REF] Vincent | BSS Oracle Toolbox[END_REF]. No noise was added. The mixing system A f in each frequency bin f was either given by the mixing matrix in the instantaneous case or by the Fourier transform of the mixing filters in the convolutive case.

Algorithmic Settings

For the variational Bayes method, we used the noninformative Jeffreys prior for the source variances by setting the shape α j to zero. Furthermore, we assigned the noise covariance E to zero. These settings are natural given that the mixture does not include any noise and that no prior information is available about the source variances. We iterated the algorithm 50 times at maximum. These settings cannot be used for Gibbs sampling, otherwise the resulting Markov chain becomes irreversible. If v j = 0, the chain remains stuck in v j = 0 for subsequent iterations. Therefore we resorted to the noisy setting by assigning the noise covariance to 3 × 10 -6 I. Furthermore, we observed better mixing properties when setting the shape value α of the prior to a negative value. Preliminary experiments with different shape values led us to set the optimal shape value in terms of mean MFCC error to α = -0.13. Note that this yields a proper inverse-gamma posterior with a shape value α = 0.87.

In the instantaneous case, we generated 100 burn-in samples followed by R = 400 samples, which we used for feature extraction. In the convolutive case, we generated 200 burn-in samples followed by R = 800 samples.

In the feature extraction step, we calculated the first 20 MFCCs. For MFCC estimation by sampling, we generated L = 2000 sample spectra for each time frame t.

Evaluation Criteria

In order to assess the impact of source separation on feature extraction, we evaluate the proposed algorithms according to both tasks. Source separation quality is evaluated in terms of the Signal-to-Distortion Ratio (SDR) in [START_REF] Vincent | Performance measures in blind audio source separation[END_REF] between the mean of the estimated and the true source signals.

Feature extraction accuracy is evaluated in terms of the error between the estimated µ MFCC jt and the true MFCCs MFCC(S jt ). This evaluation method enables us to assess the performance of the feature extraction without running costly classification experiments with these features. Information retrieval techniques typically do not process the MFCCs on each time frame but average them over longer time intervals [START_REF] Ellis | Crosscorrelation of beat-synchronous representations for music similarity[END_REF]. Hence, unless otherwise specified, we average the estimated MFCCs over 1 s intervals. The raw error for source j in time interval t is given by

d jt = µ MFCC jt -MFCC(S jt ). ( 25
)
This error function ignores the energy of the corresponding time interval. However, errors in silent time intervals are not crucial for information retrieval and can be ignored. Therefore, we weight the error considering the energy levels. We first calculate the Root Mean Square (RMS) amplitude of the true source in each time interval t as e jt = 1

F ∑ F f =1 |s j f t | 2 .
We then define the weights as

e jt = 1 if e jt ≥ 0.1 × max t e jt , 0 if e jt < 0.1 × max t e jt (26)
Denoting the error over the n-th MFCC coefficient of source j in time frame t by d n jt , the total weighted RMS error over all sources is defined as 1 N

∑ n ∑ j ∑ t d 2 n jt e jt ∑ j ∑ t e jt . (27)
In this equation and in the following, we assume that the source signals have been concatenated so that t spans all time frames of all mixtures in the test dataset. We decompose this total error into a bias term and a standard deviation term. The bias over the n-th coefficient is given by b n j =

∑ t e n jt d n jt

∑ t e jt . We define the total bias for source j in the RMS sense by

b j = 1 N ∑ n b 2 n j . (28)
where the summation over n spans a certain subset of coefficients and N is the size of this subset. The standard deviation of the error over MFCC coefficient n of source j is given by

σ bn j = ∑ t e jt (d n jt -b n j ) 2 ∑ t e jt
. Hence we compute the total standard deviation as

σ j = 1 N ∑ n σ 2 bn j . (29)

Results

Table 1 shows the source separation performance of Gibbs sampling and variational Bayes compared to that of the stateof-the-art ML method. Recall that the mean source coefficients estimated by variational Bayes and by ML provide the same performance. ML and variational Bayes increase SDR Table 2 shows the total RMS error in dBs of the three above source separation methods in combination with sampling-based and moment-matching based MFCC estimation. In addition, we show the RMS error of deterministic MFCC computation, that uses only the mean estimates of the source STFT coefficients. As one can see, the first MFCC coefficient is significantly misestimated by all methods. This coefficient reflects the energy level of the signal. Source separation methods often fail to estimate this quantity: for instance, ML promotes sparsity and, as a consequence, typically under-estimates the energy of the sources [START_REF] Vincent | Probabilistic modeling paradigms for audio source separation[END_REF]. For the other MFCC coefficients, the error values are on the order of 2 to 5 dB. ML and variational Bayes followed by any of the feature extraction algorithms appear to outperform Gibbs sampling both on instantaneous and on convolutive mixtures. ML and deterministic MFCC computation perform slightly better on instantaneous mixtures, while variational Bayes followed by either sampling-based or moment matching-based MFCC computation performs slightly better on convolutive mixtures. Overall, moment matching does not significantly decrease feature extraction accuracy compared to sampling, while the former is on the order of 1000 times faster.

Interestingly, the fact that Gibbs sampling outperforms ML or variational Bayes in terms of source separation performance over convolutive mixtures does not translate into more accurate feature extraction. Instead, ML and variational Bayes lead to more accurate feature extraction over all mixtures, while they are on the order of 100 times faster. It is possible that Gibbs sampling could yield better results with a larger number of samples, however the computation overhead, which is already high would be infeasible.

Table 3 shows the bias and standard deviation of the MFCCs 2 to 20 achieved by variational Bayes followed by moment matching on convolutive mixtures, where the length of the time intervals over which MFCCs are averaged is equal either to 1 s as above or to one single time frame. Time aver- Finally, Table 4 presents the bias and standard deviation of the MFCCs 2 to 20 for the best algorithms in Table 2. ML leads to smaller bias than variational Bayes on instantaneous mixtures and vice-versa on convolutive mixtures. However, ML followed by deterministic MFCC computation smaller standard deviation on all mixtures types. This suggests that the ML approach might provide the best results in terms of information retrieval, since classifiers are typically insensitive to bias. Care must be taken however that the bias over each source depends on the other sources and on the mixing setup. Further experiments are needed to validate this observation by determining the average bias and standard deviation for a given source, e.g. a given musical instrument, over a variety of mixtures.

CONCLUSION

In this paper, we presented two Bayesian source separation algorithms and two uncertainty propagation algorithms for the computation of the expectation of the MFCCs of individual sources within an under-determined mixture.

Surprisingly, the standard ML source separation algorithm followed by deterministic MFCC computation appears to provide the best feature extraction performance on instantaneous mixtures. However, variational Bayes followed by either sampling-based or moment matching-based MFCC computation provides slightly better results on convolutive mixtures. Gibbs sampling performs worse in both mixing cases despite being 100 times slower for the chosen number of samples.

In the future, we will adapt these methods to more realistic scenarios, where the mixing system is unknown, and to more complex source separation models as in [START_REF] Vincent | Probabilistic modeling paradigms for audio source separation[END_REF]. We will also investigate the classification performance resulting from the estimated features.

  This work was supported by the Quaero Program funded by Oseo.

Figure 1 :

 1 Figure 1: Flow of the proposed probabilistic source separation and feature extraction approach.

Table 1 :

 1 SDR in dB achieved by Gibbs sampling (Sam) and by ML or variational Bayes (ML/Var) source separation on instantaneous (Inst) and convolutive (Conv) mixtures.

			s 1	s 2			s 3
		Sam ML/Var	Sam ML/Var	Sam ML/Var
	Inst	12.6	14.7	3.6	5.7	16.8	19.2
	Conv	6.8	6.3	7.6	6.6	6.2	5.9
	Source		Feature	MFCC 1	MFCCs 2 to 20
	separation	extraction	Inst	Conv	Inst	Conv
	ML		Determin.	19.4	34.7	2.4	4.7
			Determin.	30.2	29.1	4.2	4.9
	Gibbs Sam.	Sampling	43.0	38.4	5.9	4.7
			Moment	57.1	47.0	6.3	5.0
	Var. Bayes	Sampling Moment	27.7 28.2	45.7 46.1	2.8 2.8	4.6 4.6

Table 2 :

 2 Total RMS error in dB for the first MFCC and for MFCCs 2 to 20 obtained by ML, Gibbs sampling or variational Bayes-based source separation followed by deterministic, sampling-based or moment matching-based feature extraction over instantaneous and convolutive mixtures. by 2.2 dB on average compared to Gibbs sampling for instantaneous mixtures, but decrease it by 0.6 dB for convolutive mixtures.

Table 3 :

 3 Bias and standard deviation in dB of the MFCCs 2 to 20 calculated framewise or averaged over 1 s using variational Bayes and moment matching on convolutive mixtures.

				ML	Variational Bayes
			Determin.	Sampling	Moment
			bias std	bias std bias std
	Inst	s 1 s 2	0.2 1.3 1.0 3.1	0.4 0.8 3.5 0.8 3.5 1.4 0.4 1.6
		s 3	0.7 2.3	0.9	2.7	0.9	2.8
	Conv	s 1 s 2 s 3	1.7 1.9 2.9	3.7 3.9 4.7	1.2 3.8 1.2 3.8 1.5 4.1 1.5 4.1 2.1 4.9 2.1 5.0

Table 4 :

 4 Bias and standard deviation in dB over the MFCCs 2 to 20 obtained by the best algorithms in Table2over instantaneous and convolutive mixtures. aging of the MFCCs slightly affects the bias due to energybased error weighting but, more importantly, it reduces the standard deviation by 1.8 dB. More generally, we could observe this behavior for all feature extraction methods and for all mixtures types.


Arup Mitra
email: arupmitra7@gmail.com

Chandan Sharma
email: chandanieg@gmail.com

Marie-Ange Véganzonès
email: veganzones@aol.com

R Di

Bd F Mitterrand

Marie-Ange Véganzonès -Varoudakis

Patrick Plane

Catherine Araujo Bonjean

Total Factor Productivity and Technical Efficiency of Indian Manufacturing: The Role of Infrastructure and Information & Communication Technology

Keywords: India, Manufacturing Industry, Infrastructure, Information and Communication Technology, Total Factor Productivity, Technical Efficiency JEL classification: L60, H54, O53, O3

Les commentaires et analyses développés n'engagent que leurs auteurs qui restent seuls responsables des erreurs et insuffisances.

Introduction

The importance of infrastructure in the context of growth has been felt intensely both, by the researchers and policy makers, as it is considered to be one of the prime productivity stimulators.

The planning commission of India has recognized infrastructure inadequacies in both rural and urban areas as a major factor constraining country's growth. The government decided to increase expenditure on infrastructure from 4.6% of GDP to a figure between 7 and 8% in the eleventh plan period (2007-08 to 2011-12) (Planning Commission 2006).

On the other hand, manufacturing is an important sector in the Indian economy, comprising about 31 percent of the non-agricultural GDP [START_REF] Natarajan | Efficiency and productivity in the Indian unorganized manufacturing sector: did reforms matter?[END_REF]. This sector has gained in strength in many ways over the past twenty years, as a consequence of a liberalization of industrial controls and a gradual integration with the world economy. Important industries, for instance automobile components, pharmaceuticals, special chemicals, textiles are recording exceptional growth in terms of overall output, as well as in export in the reform period (since 1991). The average output growth rate of the manufacturing is around 8% in the last decade and now it is targeted to grow at around 12% in the eleventh plan (see Planning Commission 2006). However, despite a moderate increase in the last two decades, TFP growth of this sector declined to less than 2% in the 1990s, from above 5% in the 1980s (e.g., see Trivedi et al. 2000;[START_REF] Goldar | Import liberalization and productivity growth in Indian manufacturing industries in the 1990s[END_REF]. Recent estimates as well, found only a marginal improvement of TFP growth in the 2000s [START_REF] Sharma | Impact of infrastructure on output, productivity and efficiency: Evidence from the Indian manufacturing industry[END_REF][START_REF] Kathuria | Organised versus Unorganised Manufacturing Performance in the Post-Reform Period[END_REF]. 1 Recent related research, as well as government institutions (Planning Commission 2006), recognizes the infrastructure deficit as the most critical short-term obstacle to growth of the manufacturing sector.

In the theoretical literature, public infrastructure is considered to be a crucial factor of productivity and efficiency enhancement through external economies (e.g. [START_REF] Romer | Increasing returns and long-run growth[END_REF][START_REF] Lucas | On the mechanics of economic development planning[END_REF][START_REF] Barro | Economic Growth, International Editions[END_REF][START_REF] Anwar | An impure public input as a determinant of trade[END_REF]. Empirical findings on this issue, however, are inconsistent and often contrary to each other. Over the last two decades a large number of studies have focused on this issue. Most have noted that public infrastructure positively and sizably affects economic performance [START_REF] Aschauer | Is public expenditure productive[END_REF]Munnel 1990a and b;Eisner 1991;Ford and Poret 1991). Some others, for example Evans and Karras (1994) and [START_REF] Holtz-Eakin | Public-Sector Capital and the Productivity Puzzle[END_REF], challenged these findings on methodological ground and showed insignificant or minimal impact of public infrastructure. Nevertheless, with improvement in empirical methodologies, some recent studies again estimated large effects [START_REF] Stephan | Assessing the Contribution of Public Capital to Private Production: Evidence from the German Manufacturing Sector[END_REF][START_REF] Everaert | Public Capital and Long-Term Labour Market Performance in Belgium[END_REF][START_REF] Kamps | New Estimates of Government Net Capital Stocks for 22 OECD Countries 1960-2001[END_REF]). In the case of India, [START_REF] Mitra | Productivity and technical efficiency in Indian States' manufacturing: the role of infrastructure[END_REF], [START_REF] Hulten | Infrastructure, externalities, and economic development: a study of the Indian manufacturing industry[END_REF] and [START_REF] Sharma | Impact of infrastructure on output, productivity and efficiency: Evidence from the Indian manufacturing industry[END_REF] found moderate to large impact of infrastructure on the manufacturing performance. 2 This wide range of estimates made these findings almost unemployable in the policy formulation. In this backdrop, the present study attempts to answer this question by investigating the effect of core infrastructure and of Information & Communication Technology (ICT) on the performances of the Indian manufacturing.

In this paper, we introduce six main novelties from the empirical standpoint. First, while the previous studies in India mainly focused on the impact of infrastructure on Total Factor Productivity (TFP) growth or output, we move a step forward by analyzing the impact on another crucial indicator of industrial growth namely Technical Efficiency (TE). Second, the inclusion of too many infrastructure variables separately in a regression analysis may lead to multicollinearity problem. In order to avoid this, we construct two composite indicators of infrastructure (G) and Information & Communication Technology (ICT) by using Principal Component Analysis (PCA). Third, in most of the previous studies in this area, information was mainly taken from the annual survey of industry (ASI) database. We utilize a new manufacturing database, Prowess, which includes eight important industries and allows us to extend the time horizon of the study up to 2008. This dataset is rich and provides heterogeneity in terms of trade and R&D across industries and over time as well. Fourth, since in the recent years the ICT sector has grown at an unprecedented rate, we investigate the role of this sector separately on the performance of the Indian manufacturing sector. Fifth, most of the previous studies have directly applied OLS and have not paid serious attention to the stationarity of the variables. As it is a well-known fact that non-stationarity of data series causes various estimation problems, we utilize unit root test and cointegration techniques to test the integration between variables in the panel context. For the estimation, we use Fully Modified OLS (FMOLS) and System GMM, which are likely to produce better results than traditional estimators by taking care of endogeneity problem in the estimation analysis. It also allows us to use the variables at the level form in the analysis rather than their growth rates. This is important because some information is lost when first difference forms are used. Finally, the recent trends suggest that the government has been putting in some serious efforts to enhance the infrastructure services by liberalizing the related policies 3 , encouraging and engaging the private sector in infrastructure projects through public private partnership (PPP), and directly also investing in the infrastructure sector. The ongoing economic crisis has also provided this opportunity incidentally by enhancing public capital expenditure as part of fiscal stimulus and by encouraging higher private sector participation. The negative effect of this expansion is in terms of higher fiscal deficit (e.g., see [START_REF] Narayan | Trade-Off Between Government Deficit and Expenditure on Social Infrastructure[END_REF]) and therefore, it becomes extremely relevant to estimate the magnitude of the effects of infrastructure on the industrial performance.

The paper is organized as follows. The second section presents the data and its sources to be used in the empirical analysis. Section three discusses the methodological aspects linked to the computation of Total Factor Productivity (TFP) and Technical Efficiency (TE). The forth section describes our empirical models of investigation, as well as the econometric issues related to their estimation. The fifth section estimates these models and illustrates the impact of core infrastructure and ICT on TFP and TE. The last section concludes and presents some policy recommendations.

The Data on Infrastructure, ICT and the Manufacturing Sector

In this study, we have utilized data of two-digit industry groups in the Indian manufacturing sector. The data have been gathered from the Prowess database 4 provided by the Center for Monitoring Indian Economy (CMIE). Annual financial statements of firms belonging to eight industry groups, namely Food and Beverages, Textiles, Chemicals, Non-metallic Minerals, Metal and Metal Products, Machinery, Transport Equipments and Miscellaneous Manufacturing, have been used. Subsequently, firm-level data are transformed into industry-level data by aggregation. This is done for each year over the sample period, 1994-2008. The prime reason for taking 1994 as the initial year is that the Indian economy underwent structural reforms in the early 1990s, which have subsequently brought in vast changes in the manufacturing sector. Another practical reason is that the data on price indices and deflators for all variables are available from this year onwards.

We use net sales and gross value added of the industries as the measures of nominal output which is deflated by industry specific wholesale price indices (WPI) to obtain output in real terms 5 . The deflator is obtained from the Office of the Economic Adviser (OEA), Ministry of Commerce & Industry, Government of India (http://eaindustry.nic.in/). The series on real capital stock is constructed using the perpetual inventory capital adjustment Method.

Specifically, we compute it as:

t t t I K K + - = -1 ) 1 ( δ ………….. (1)
where, K is the capital stock, I is deflated gross investment, δ is the rate of depreciation taken at 7%, consistent with similar studies for India [START_REF] Unel | Productivity trends in India's manufacturing sectors in the last two decades[END_REF][START_REF] Ghosh | Do productivity and ownership really matter for growth? Firm-level evidence[END_REF]

3-Measuring Total Factor Productivity (TFP) and Technical Efficiency (TE)

We start our empirical analysis by computing TFP for each industry. For this purpose, we follow a two-stage procedure. In the first stage, a panel of the eight industries is constructed and following [START_REF] Mitra | Productivity and technical efficiency in Indian States' manufacturing: the role of infrastructure[END_REF], a basic production function in Cobb-Douglas form is specified:

where Q, K, and N are the value added, the capital input and the labor input, respectively for industry i for period t. T i is the time trend specified for each industry i and 1 1. This result also confirms a significant role of capital and a small role that labor plays. We have utilized the results of column 3 for calculating TFP of the sample industries, which is computed as follows:

where 1 α and 2 α are the estimated parameters of capital and labor, respectively.

To measure the Technical Efficiency (TE) of the Indian manufacturing sector, we utilize the Maximum Likelihood (ML) estimates of stochastic frontier production functions, developed by [START_REF] Battese | Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India[END_REF] for panel data. In this model, industry effects are assumed to be distributed as a truncated normal variable, which allows it to vary systemically with time. 6 Specifically, we employ time-varying efficiency model of the stochastic frontier as developed by [START_REF] Battese | Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India[END_REF]. The model may be specified as:

) ( it it it it V X Q µ α - + = ……………………. (4)
where it Q and it X are output and inputs in log-form of i-th industry at time t.

Disturbance term is composed of independent elements, it V and it µ . The former is assumed to be independently and identically distributed as

) , 0 ( 2 v N σ . The element it µ is a
nonnegative random variable, associated with technical inefficiency in production, assumed to be independent and identically distributed with truncation (at zero) of the distribution ) , (

2 µ σ µ it N .
The parameters α s can be obtained by estimating the stochastic production function (4) using a ML technique.

Coelli (1996) utilizes the parameterization of [START_REF] Battese | Estimation of a production frontier model: with application to the Pastoral zone of Eastern Australia[END_REF] to replace

v 2 σ and µ σ 2 with µ σ σ σ 2 2 2 + = v and µ µ σ σ σ γ 2 2 2 + = v
in the context of ML estimation. The term γ lies between 0 and 1 and this range provides a good initial value for use in an iterative maximization process. Subsequently, the relative Technical Efficiencies of each industry can be predicated from the production frontier as follows:

) exp( )) ; ( ( exp it it it X f Q TE µ α - = = ……………(5)
Since it µ is, by definition, a nonnegative random variable, TE is bounded between zero and unity, where unity indicates that the industry is technically most efficient. Our model measuring the efficiency is:

) ( ln , 2 , 1 0 , it it t t t t i t i t i u v D LnN LnK Q - + + + + = ∑ λ α α α ……………(6)
Here D t is a dummy variable having a value of one for th t time period and zero otherwise and t λ s are parameters to be estimated. The dummy variable is introduced in the model for the technical change; this is in line with the general index approach of Baltagi and Griffin (1988).

The change in t λ between successive periods becomes a measure of rate of technical change.

t t t t TC λ λ - = + + 1 1 ,

…… …………(7)

This implies that the hypothesis of no technical change is:

t k t ∀ = λ
. Using the above model, we estimate the TE of the industries. Our dataset for the panel of industries is same as that used earlier for TFP estimation.

Finally, as discussed above, a Cobb-Douglas production is postulated for the purpose of TE estimation. The results are presented in column 4 of Table 1. The estimated coefficients of capital and labour are very similar to the results of column 3 and both variables are positive and statistically significant at the conventional level. On the basis of these results, TE of the industries is estimated for further analysis. 8). TFP computed on the basis of results of column (3). TE computed on the basis of results of column (4).

Results of TFP and TE calculations clearly indicate substantial differences across industries (see

The Empirical Models of Manufacturing Performance and Estimation Issues

After estimating the TFP and TE of industries, we turn to assessing the impact of core infrastructure (G) and of Information & Communication Technology (ICT) on the performance indicators of the industries. For this purpose, we specify four models as follows:

it it it it e X TFP + + + = δ β α ) G ln( ) ln( …… …… (8) it it it it e X TFP + + + = δ β α ) ICT ln( ) ln( … ……. (9) it it it it e X TE + + + = δ β α ) G ln( ) ln( …… ………. (10) it it it it e X TE + + + = δ β α ) ICT ln( ) ln( … ……… (11)
where TFP, TE, G and ICT are estimated Total Factor Productivity, Technical Efficiency, Core

Infrastructure index and ICT index of industry i at period t in the models. Further, we also include a set of additional control variables (X) which may affect productivity. The set of additional control variables include R&D intensity 7 , trade intensity 8 and the size of the industry (Size). 9

In the related literature a number of issues arise relating to application of estimators.

These include spurious correlation due to non-stationary data, omitted variables, endogeneity and reverse causality, which may lead to biased estimation of coefficients. Therefore, we attempt to overcome these problems. To tackle the issue of non-stationary, [START_REF] Hulten | Public capital formation and the growth of regional manufacturing industries[END_REF] estimate the inter-relation between TFP and infrastructure using first differences. However, using the first difference of the series could be costly as this may remove the long-run characteristics of the variables of interest. Moreover, it is highly likely that the short-term properties are quite different from the long-term ones. Some researchers, for example [START_REF] Holtz-Eakin | Public-Sector Capital and the Productivity Puzzle[END_REF], have used the Fixed-effects (FE)

estimator for the analysis. The advantage of the FE estimator is that it can handle the issue of omitted variables that may be correlated with infrastructure. Somewhat FE also helps in alleviating the adverse consequences of endogeneity bias. Furthermore, to some extent, this estimation method addresses non-stationarity as well because in the 'within form', deviations from the mean are used in the estimation. Another method which could be useful in the presence of heterogeneity and contemporaneous correlation is system GMM (henceforth Sys-GMM). This estimator uses appropriate lags of variables in level form as instruments for equations in first difference form and conversely for equations in level form, all of which are combined into a system of equations with options to treat any of the variables in the system as endogenous. [START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF] proposed the use of extra moment conditions that rely on certain stationarity conditions of the initial observation, as suggested by [START_REF] Arellano | Another look at the instrumental variable estimation of errorcomponents models[END_REF].

When these conditions are satisfied, the resulting system sys-Sys-GMM estimator has been shown in Monte Carlo studies by [START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF] and [START_REF] Blundell | Estimation in Dynamic Panel Data Models: Improving on the Performance of the Standard GMM Estimator[END_REF] to have much better finite sample properties in terms of bias and root mean squared error.

Another option is to retain the long-run properties of the series, which is to follow [START_REF] Canning | Infrastructure, Long-Run Economic Growth And Causality Tests For Cointegrated Panels[END_REF], Fedderke and Bogetić (2009) and [START_REF] Sharma | Impact of infrastructure on output, productivity and efficiency: Evidence from the Indian manufacturing industry[END_REF], which apply panel co-integration techniques and establish a long-run relation between infrastructure and industrial performance. We are, therefore, set to apply aforementioned methodologies in this study alternatively for checking consistency and robustness of the estimates.

A preliminary step in our approach involves the testing for the stationarity of the series used in equations 8, 9, 10 and 11. This has been done using the cross-sectional Im-Pesaran-Shin (CIPS) panel unit-root test, which is based on the simple averages of the individual crosssectional augmented Dickey-Fuller statistics. The main advantages of this approach are that it incorporates potential cross-sectional dependence and it does not pool directly the autoregressive parameter in the unit root regression; thus it allows for the possibility of heterogeneous coefficients of the autoregressive parameters under the alternative hypothesis that the process does not contain a unit root. The results of the unit root test are reported in Table 2. For all individual series the hypothesis of unit root cannot be rejected at the level form; however it is rejected convincingly in the first difference form. If the data generating process for the variables is characterized by panel unit roots, it is crucial to test for cointegration in a panel perspective. We apply [START_REF] Pedroni | Critical values for cointegration tests in heterogeneous panels with multiple regressors[END_REF] test, an extension of the Engle-Granger construction to test the existing cointegration relationship. Two types of tests have been suggested by Pedroni. The first is based on the 'within dimension' approach, which includes four statistics: panel ν -statistic, panel ρ statistic, panel PP-statistic, and panel ADF-statistic. These statistics pool the autoregressive coefficients across different members for the unit root tests on the estimated residuals. The second test is based on the 'between-dimension' approach, which includes three statistics: group ρ -statistic, group PP- statistic, and group ADF-statistic. These statistics are based on estimators that simply average the individually estimated coefficients for each member. We calculate heterogeneous panel cointegration as well as heterogeneous group mean panel cointegration statistics and results are reported in Table .A.5 of the Appendix 5. The rows labeled 'within-dimension' approach contain the computed value of the statistics based on estimators that pool the autoregressive coefficient across different industries for the unit root tests on the estimated residuals. The rows labeled between-dimension report the computed value of the statistics based on estimators which average individually the estimated coefficients for each industry. Overall these results provide support for cointegrating relationship for all our models.

Estimating the Effects of Infrastructure and ICT on the Manufacturing Performance

Having established that there is a linear combination between variables that keeps the pooled variables in proportion to one another in the long run, we set to generate individual long-run estimates for all the models. Considering that the OLS estimators are biased and inconsistent when applied to cointegrated panels, we utilize the "group-mean" panel Fully Modified OLS (FMOLS) estimator developed by [START_REF] Pedroni | Critical values for cointegration tests in heterogeneous panels with multiple regressors[END_REF][START_REF] Pedroni | Purchasing power parity in cointegrated panels[END_REF]. 10 We first estimate equation 8, in which the impact of core infrastructure (G) on TFP is tested for the eight industries. Results are reported in Table 3. Surprisingly, estimated coefficients of the core infrastructure variable are found to be sizably large in several sectors, as well as on the overall manufacturing. The estimated effect indicates that infrastructure explains 65% of TFP growth in Transport Equipments, 32% in Metal & Metal Products and 30% in Textile. In other industries, it varies from being large to moderate (except in the case of Chemical, where it is found to be statistically insignificant 11 ). In average, results suggest that the impact on overall manufacturing is around 0.32, which means that 1% increase in infrastructure leads to a 0.32% TFP growth. Results regarding other control variables are rather mixed. Trade intensity is found to be positive and significant in Metal & Metal Products, Non Metallic Mineral Products, and Transport Equipments, which are sectors relatively exposed to foreign competition. The impact is estimated to be 5%-10% on these industries 12 . However the effect on the overall manufacturing is found to be around 2%, which is lower than expected. Furthermore, the R&D variable explains only 1.4% of TFP growth, which is not very surprising as Indian manufacturing is known for its low R&D intensity. Nonetheless, in research intensive industries, i.e. Chemical and Machinery, effect is found to be 6% and 5% respectively, which is quite encouraging, knowing that these sectors are also the most productive of our sample (see section 3). As for the size, impact is noticeable in Food & Beverage and Non Metallic Mineral Products, which are sectors characterized by small low productive firms. This result means that a policy of concentration would generate high productivity gains in these sectors. Keeping in mind the dramatic development of the ICT sector in the recent years in India, we separately examine the effect of this sector on TFP growth by estimating equation 9. Results indicate that ICT is closely linked to manufacturing productivity as well. Its impact for some industries is substantially large too (see Table 4). In Textile, Transport Equipments, and Metal & Metal Products industry, it has a positive and statistically significant effect of 18% to 22% on TFP. The effect on the overall manufacturing is also estimated to be positive and sizable (12%).

Results regarding other control variables are not found to be very diverse from that in equation 8.

Next, we shift to the impact of infrastructure on Technical Efficiency (TE). We first estimate equation 10 and test the effect of core infrastructure by industry (see Table 5). The overall results for TE are not very different from those for TFP. Interestingly, it is still Transport Equipments (which is also the most efficient industry of our sample, see table A.1.2 in Annex 1), which appears more dependent on infrastructure endowment (elasticity of 0.40). In the other industries, the estimated elasticity varies from 0.13 to 0.20 in Chemical and Textile products. 13 The estimated effect regarding the overall manufacturing (0.17) also confirm that TE is closely related to core infrastructure. Results regarding other control variables suggest that trade and research related activities do not have a really sizable impact on the efficiency of industries, contrarily to results for TFP 14 , while the variable Size appears as a more constant factor of efficiency growth, especially in Food and Non Metallic Mineral Products. Next, we test the effect of ICT on TE by estimating equation 11. Estimation results suggest that ICT has positive, statistically significant and sizable impact on all industries (see Table 6). The impact still varies among the sectors. It is still Transport Equipments, followed by Textile, which show the highest sensibility to ICT limitations (with an elasticity of 0.16 and 0.12 respectively). The overall elasticity is also estimated to be 0.08. As for the size, it still plays a role in the efficiency of the Food industry in particular, as seen previously 15 . On the whole, while the coefficients estimated vary, both in terms of magnitude and statistical significance, various constant effects are perceivable across the industries. Transport Equipments, Metal & Metal products and Textile are found to be highly associated with infrastructure provisions, including ICT, as far as their productive performances are concerned. This is also the case of the Chemical industry (which is the most productive sector in India, both in terms of TFP and TE, along with Transport and Machinery) for Technical Efficiency. This may be due to the fact that these sectors are relatively more exposed to foreign competition and need a more supportive environment in terms of infrastructure to be able to compete efficiently. This fragility justify that a special attention needs to be paid when taking decisions that may affect the quality and availability of infrastructure needed by these sectors. This also means that the pay off of an improvement of core and ICT infrastructure would be more substantial in these industries, which could play a leading role in the industrial development and the export capacity of the country. This conclusion is all the more important in the Indian context of infrastructure bottlenecks and economic reforms. It may also explain why some industries (Textile and Metal) have register less satisfying performance in term of TFP and TE. This could be the case of more productive ones (Chemical, Machinery) in the future, if infrastructure is not adequately improved in India.

Another finding relates to the ICT, which is pertinent, as earlier studies generally could not acknowledge its role in enhancing productivity gains. Launder (1995) and [START_REF] Hu | An Empirical Study of the Causal Relationship between IT Investment and Firm Performance[END_REF], for instance, found little evidence in favor of ICT contributing to productivity in the USA. [START_REF] Parham | Information Technology and Australia's Productivity Surge[END_REF] showed that the adoption of ICT only contributed to a 1.1% improvement in productivity surge in the 1990s in the case of Australia. In the recent years, it seems that the Indian manufacturing has gained considerably from ICT, not only in terms of production of equipments, but more because of the use of ICT in the production process. This has perhaps generated substantial technological advances for the Indian industry and we believe it is widely reflected in our results.

Our findings relating to core and ICT infrastructure are estimated to be pretty large in magnitude and therefore, we intend to examine the consistency of the results by an alternative estimator of GMM of [START_REF] Blundell | Initial conditions and moment restrictions in dynamic panel data models[END_REF]. The Blundell and Bond estimator, also called Sys-GMM estimator, combines the regression expressed in first difference forms (lagged values of the variables in the level forms are used as instruments) with the original equation expressed in level forms (this equation is instrumented with lagged differences of the variables) and allows to include some additional instrumental variables. We prefer this option to a fixed-effect estimator for two reasons. First, it allows us to take into account the unobserved time-invariant bilateral specific effects. Second, it can deal with the potential endogeneity arising from the inclusion of the lagged dependent variables and other potentially endogenous variables.

Results of the analysis using Sys-GMM are presented in Table 7. In column 1, findings pertaining to equation 8 validate that core infrastructure has been an important source of TFP growth in the Indian manufacturing. The estimated elasticity (around 0.18) is substantially large, however, lower than in the case of the FMOLS estimate (0.315). Results for equations 9, 10 and 11 show similarities in this respect (see columns 2, 3 and 4 of the table). The elasticity of TFP regarding ICT (0.09) is found to be also relatively lower than that provided by FMOLS (0.12).

The elasticity of TE with respect to core infrastructure and ICT (0.07 and 0.02 respectively) is even below half of the estimate of FMOLS (0.18 and 0.08). Findings regarding R&D and Trade intensity on both TFP and TE also show a smaller magnitude, below 1% impact on the productivity and efficiency of the Indian manufacturing sector. Our results advocate that the selection of estimator is crucial in this field of research, as the magnitude of elasticity varies drastically from one estimator to another. Keeping in mind the complications relating to the endogeneity of the infrastructure variable, this study therefore goes to considerable lengths to address identification and spurious correlation problems, by using FMOLS and Sys-GMM techniques.

Our results however still support the earlier findings of [START_REF] Mitra | Productivity and technical efficiency in Indian States' manufacturing: the role of infrastructure[END_REF], [START_REF] Hulten | Infrastructure, externalities, and economic development: a study of the Indian manufacturing industry[END_REF] and [START_REF] Sharma | Impact of infrastructure on output, productivity and efficiency: Evidence from the Indian manufacturing industry[END_REF], which found that infrastructure is an important channel of productivity growth in the Indian manufacturing sector. It seems, though, that over the period the role of public infrastructure has been increasing, as the magnitude of the TFP elasticity in this study is higher than that of the others. Nonetheless, if we compare our results with important international studies, it is somewhat the same: for instance, Aschauer (1989a), Munnell (1990a,b), Eisner (1991) and Duggall et al. (1999) for USA, [START_REF] Everaert | Public Capital and Long-Term Labour Market Performance in Belgium[END_REF] for Belgian regions, [START_REF] Kamps | New Estimates of Government Net Capital Stocks for 22 OECD Countries 1960-2001[END_REF] for 22 OECD countries, [START_REF] Stephan | Assessing the Contribution of Public Capital to Private Production: Evidence from the German Manufacturing Sector[END_REF] for West German regions and [START_REF] Demetriades | Intertemporal Output and Employment Effects of Public Infrastructure Capital: Evidence from12 OECD Economies[END_REF] for 12 OECD countries found the output elasticity with respect to infrastructure to be much higher (up to around 60 per cent). 16 It is noteworthy that the above mentioned previous studies have not necessarily tested the impact on TFP and TE specifically.

In contrast, results regarding other control variables are more mitigated. It seems that increased globalization and higher level of trade intensity has still not become an important source of productivity growth, except for a few sectors more exposed to foreign competition.

Perhaps, the learning by trade process is relatively slow in India, due to a long period of industrial protection and a high number of SMEs in the economy: therefore, it might take some more time in realizing its impact on productivity. Also, the size of the firms don't seem to be a significant source of productivity and efficiency in the Indian manufacturing, although concentration could play a certain role in some industries, such as Food,. As for R&D, low intensity remains a serious concern in India and requires the attention of the policy makers, as our results show that research intensive industries, such as Chemical and Machinery, tend to be more productive than other.

Conclusion and Policy recommendations

Using a recent dataset on the Indian manufacturing industry for 1994 to 2008, this paper presents evidence on the impact of core infrastructure (G) and of Information & Communication Technology (ICT) on the Total Factor Productivity (TFP) and Technical Efficiency (TE) of eight manufacturing industries in India. In the literature, a number of issues arise relating to application of estimators. These include spurious correlation due to non-stationary data, omitted variables, endogeneity and reverse causality, which may lead to biased estimation of coefficients.

In this study, we overcome these problems by utilizing a range of advanced estimation techniques, such as Sys-GMM, panel cointegration and FMOLS. Furthermore, the inclusion of too many infrastructure variables separately in a regression analysis often leads to serious multicollinearity problem. In order to avoid this, we construct composite indices for infrastructure and ICT by using the Principal Component Analysis (PCA) methodology.

Estimation results clearly bring out the key role played by core and ICT infrastructure in the context of the Indian manufacturing. Findings suggest an elasticity with respect to core infrastructure of around 0.32 for TFP, what is pretty high. Our results regarding TE are smaller, at around 0.12, but still sizeable. The evidence also highlights that the dramatic growth of ICT in India had a significant effect on the manufacturing productive performance, both at the TFP and TE level. This constitutes an interesting result still not acknowledged by the literature.

Considering the fact that our estimates with respect to infrastructure are pretty large in magnitude, we have examined the consistency of the results by an alternative estimator of Sys-GMM. The estimated elasticity using this estimator, although smaller, turned out to be still large.

Our results show as well that some industries, such as Transport Equipments, Metal & Metal Products and Textile for TFP and TE, and Chemical products for TE display a higher sensitivity to infrastructure endowment. Interestingly, these industries are somewhat more exposed to international competition. These results are of particular importance in the Indian context of infrastructure bottlenecks. It means that improving infrastructure and ICT endowment would particularly help these sectors to resist the strong international competition and reinforce the industrial export capacity of the country. This result constitutes an important mean of appreciation of the positive impact of a policy in favor of core and ICT infrastructure, since India manufacturing suffers from a deficient integration into the world economy, as well as a high competition in the world market.

In the analysis, we have also used three important control variables namely, trade and R&D intensity, as well as the size of the firms. The findings are mitigated and suggest a weak impact of these variables on the Indian manufacturing performance. Low in-house R&D remains a serious concern in India and requires a special attention of the policy makers. Actually, our estimations show that it is in Chemical and Machinery, which are more research intensive industries, that the impact of R&D is sizeable. Interestingly, these two industries are also the most productive ones, what constitutes an encouraging result. As for Trade intensity, our findings exhibit a higher sensitivity to this variables of sectors more exposed to international competition (Textile, Transport, and Metal, as well as Chemical in the case of TE), what means that trade liberalization have more impact in terms of productivity gains in these sectors. As for the size, a policy of concentration of firms would be advisable in sectors like Food and Non Metal products, which are characterized by a higher elasticity and a lower productivity of firms.

Results of this study are somewhat in the line of earlier findings of [START_REF] Mitra | Productivity and technical efficiency in Indian States' manufacturing: the role of infrastructure[END_REF], [START_REF] Hulten | Infrastructure, externalities, and economic development: a study of the Indian manufacturing industry[END_REF] and [START_REF] Sharma | Impact of infrastructure on output, productivity and efficiency: Evidence from the Indian manufacturing industry[END_REF]. However, it seems that over the period the role of public infrastructure has been increasing as the magnitude of the TFP elasticity in this study is estimated to be comparatively larger than that in others. In the light of the above findings, this study further supports the argument of [START_REF] Mitra | Productivity and technical efficiency in Indian States' manufacturing: the role of infrastructure[END_REF] that lack of infrastructure can bring a halt to growth in developing economies. As per our results, enhancing core and ICT infrastructures, especially in the sectors more sensitive to infrastructure deficiency, can constitute a powerful engine of competitiveness and industrial growth, with these sectors playing a leading role in India. Actually, like other developing countries, India is also increasingly concerned about improving productivity, as the country face the intensifying pressure of globalization. In this context, infrastructure deficiencies have to be taken into consideration, if the country wants to further diversify in an increasing competitive world. strong support to Griliches's view. To capture the R&D activities of industry, this study considers the ratio of R&D expenditure to industry's total sales. This variable is a measure of R&D intensity of industries and it is expected to have a positive impact on industries' productivity and efficiency growth.

  Tables A.1.1 and A.1.2 of Annex 1). It is the most productive industries in terms of TFP: Chemical, Transport Equipments and Machinery, which also show the fastest rate of TFP growth. Among the less productive are Textile and Non Metal products, which TFP growth is comparatively less satisfactory. As for TE, Transport Equipments and Chemical industries are still the most efficient, with a substantial rate of improvement of their efficiency over the period studied.

  and t indicates the year.

	The initial capital stock equals the net book value of capital stock for the year 1994. Data on
	other control variables such as trade (export and import) and R&D have also been extracted from
	the same database. A summary statistics of the variables is reported in Table A.4. of Appendix 4.
	For infrastructure, this study considers physical infrastructure for the period 1994-2008.
	It covers transportation (road, rail and air), Information & Communication Technology (ICT)
	and energy sectors. The data sources for these variables are World Development Indicators
	(WDI) online (2011), and Infrastructure (2009) publications of CMIE. Instead of using all
	infrastructure variables separately, which is likely lead to multicollinearity (see correlation
	between infrastructure variables in Table A.2.3. of Appendix 2), we construct a core and an ICT
	infrastructure index for India by using Principal Component Analysis (PCA). For details of the
	indicators and methodologies of construction of both these indices see Appendix 3.

Table 1 . Cobb-Douglas Production Function Estimation, 1994-2008

 1 Standard errors are in parentheses. In model 4, Log likelihood: 174.54228, Wald

	Variables	Coefficients (1)	Coefficients (2)	Coefficients (3)	Coefficients (4)
	ln (K)	1.1244 (0.0585)	0.3284 (0.0674)	0.40264 (0.0694)	0.4244 (0.0681)
	ln (N)	-0.04527 (0.0585)	0.03493 (0.0351)	0.06544 (0.0342)	0.0444 (0.0332)
	Trend		0.02643 (0.0018)	0.02426 (0.0019)	0.02348 (0.0019)
	Const	-0.41482 (0.3002)	2.5133 (0.2712)	2.2192 (0.2818)	2.61173 (0.3202)
		0.754	0.5918	0.6477
	Year-dummy	No	No	Yes	Yes
	Estimator	Fixed	Fixed	Fixed	Time-invariant inefficiency model
	Notes:

(Dependent Variable: ln(GVA)) :1296.01, Number of observations (panel):120(

Table 2 . Test for panel unit root applying Im, Pesaran and Shin W-statistics

 2

	Variables	At Level	At 1 st Difference
	Ln (TFP)	0.12202	-3.04503**
	Ln (TE)	1.92950	-4.91739**
	Ln (R&D intensity)	1.01247	-2.39198**
	Size ln (K)	-1.22424	-2.73512**
	Ln (Trade intensity)	2.14169	-2.45611**
	Core Infra Index ln (G)	1.54134	-5.63417**
	ICT Infra Index ln (ICT)	4.44407	-5.10710**
	Notes: ** denotes significance at 5%

Table 3 . FMOLS Result: Effects of Core Infrastructure on ln (TFP), 1994-2008

 3

	Industry	Core Infra Index ln (G)	Ln (Trade intensity)	Ln (R&D intensity)	Size ln (K)
	Chemical	-0.0787 (-0.572)	0.0018 (0.083)	0.0629** (3.825)	-0.0144 (-0.6395)
	Food and Beverage	0.2423** (3.259)	0.0413 (1.021)	0.006 (1.2705)	0.0056 (0.19668)
	Machinery	0.1779** (2.049)	0.0402 (0.976)	0.0492** (2.055)	0.0219 (0.4401)
	Metal & metal products	0.3291** (6.727)	0.1015** (4.467)	0.0045 (0.423)	-0.0931 (-3.003)
	Non metallic mineral	0.2622**	0.0552**	0.0058**	0.0129
	products	(3.668)	(2.725)	(2.725)	(0.5726)
	Textile	0.3079** (11.382)	-0.0371 (-1.215)	0.0023** (0.629)	0.00432 (0.2081)
	Transport equipments	0.6544** (11.478)	0.0913** (6.337)	-0.0114 (-1.547)	-0.1031** (-14.778)
	Miscellaneous	0.56603*	-0.1239*	-0.0061	-0.0329
	manufacturing	(1.909)	(-1.744)	(-0.1531)	(-0.2839)
	Overall	0.315** (14.108)	0.0214** (4.4727)	0.0142** (2.9503)	-0.0248** (-6.1121)
	Notes: ** and * denote significant at 5% and 10% critical level respectively. t-statistics are in parentheses.

Table 4 . FMOLS Result: Effects of ICT Infrastructure on TFP, 1994-2008

 4

		Core Infra
	Industry	Index	ln (Trade intensity)	ln (R&D intensity)	Size ln (K)
		ln (ICT)
	Chemical	-0.0111 (-0.265)	-0.0067 (-0.346)	0.0678** (7.891)	0.0063 (0.348)
	Food and Beverage	0.0781** (1.7958)	0.0794* (1.7467)	0.0059 (0.989)	0.0515** (2.003)
	Machinery	0.0095 (0.205)	0.065225* (1.777)	0.0708** (3.413)	0.051530 (1.060855)
	Metal & metal products	0.1778** (4.014)	0.1341** (4.434)	0.0074 (0.4867)	-0.0832** (-1.9258)
	Non metallic mineral	0.05662**	0.1037**	0.0031	0.0372**
	products	(1.7452)	(7.069)	(1.0361)	(1.7921)
	Textile	0.2237** (26.435)	0.0017 (0.1311)	0.0011 (0.60934)	-0.0008 (-0.087)
	Transport equipments	0.2174** (3.603)	0.0681* (1.761)	0.0194 (1.252)	-0.0963** (-4.976)
	Miscellaneous	0.2032	-0.0759	0.0209	0.0222*
	manufacturing	(1.217)	(-1.112)	(0.565)	(0.189)
	Overall	0.1244** (12.941)	0.0462** (5.431)	0.0245** (5.743)	-0.001482 (-0.584)
	Notes: ** and * denote significant at 5% and 10% critical level respectively. t-statistics are in parentheses.

Table 5 : FMOLS Result: Effects of Core Infrastructure on Ln (TE), 1994-2008

 5

	Industry	Core Infra Index ln (G)	ln (Trade intensity)	ln (R&D intensity)	Size ln (K)
	Chemical	0.1974** (9.146)	0.0183** (5.1496)	-0.00216 (-0.8359)	0.0136 (0.0136)
	Food and Beverage	0.1518** (4.808)	0.0148 (0.863)	0.0002 (0.0912)	0.0471** (3.874)
	Machinery	0.14989** (10.441)	0.0101 (1.491)	0.0111** (2.799)	0.0163** (1.979)
	Metal & metal products	0.1514** (21.081)	0.0178** (5.341)	0.0025 (1.584)	0.0188** (4.149)
	Non metallic mineral	0.1391**	0.02353**	-0.0005	0.0195**
	products	(13.042)	(7.686)	(-1.204)	(5.799)
	Textile	0.2033** (26.155)	0.0211** (2.406)	0.004** (3.687)	0.0162** (2.721)
	Transport equipments	0.4056** (15.049)	-0.0183** (7.783)	-0.0183** (-6.841)	0.0191** (7.563)
	Miscellaneous	0.1673**	0.0053	0.0036	0.0331**
	manufacturing	(6.383)	(1.0028)	(1.226)	(3.851)
	Overall	0.1757** (37.514)	0.0189** (11.215)	0.00004 (0.179)	0.0231** (11.945)
	Notes: ** and * denote significant at 5% and 10% critical level respectively. t-statistics are in parentheses.

Table 6 . FMOLS Result: Effects of ICT Infrastructure on ln (TE), 1994-2008

 6

	Industry	Core Infra Index ln (ICT)	ln (Trade intensity)	ln (R&D intensity)	Size ln (K)
	Chemical	0.0781** (4.106)	0.0161** (2.118)	0.0098** (2.944)	0.0176** (2.511)
	Food and Beverage	0.0662** (3.074)	0.0257 (1.143)	0.0004 (0.147)	0.0691** (5.603)
	Machinery	0.0763** (5.484)	0.0115 (0.794)	0.0204** (3.289)	0.0115 (0.794)
	Metal & metal products	0.0941** (9.287)	0.0301** (4.351)	0.0019 (0.568)	0.0223** (2.263)
	Non metallic mineral	0.0786**	0.0364**	-0.0016**	0.0192**
	products	(15.769)	(17.141)	(-3.712)	(6.167)
	Textile	0.1241** (10.789)	0.0547** (2.731)	0.0018 (0.722)	0.0189 (1.329)
	Transport equipments	0.1641** (4.133)	0.0318** (1.935)	-0.0047 (-0.705)	0.0213** (2.557)
	Miscellaneous	0.0886**	0.0166**	0.0088**	0.0353**
	manufacturing	(6.439)	(3.241)	(3.1911)	(4.012)
	Overall	0.0827** (20.889)	0.0046** (2.278)	0.0289** (12.176)	0.0269** (8.923)
	Notes: ** and * denote significant at 5% and 10% critical level respectively. t-statistics are in parentheses.

Table 7 : Sys-GMM Results: Determinants of ln (TFP) and ln (TE), 1994-2008

 7

	Variables	Coefficients (1)	Coefficients (2)	Coefficients (3)	Coefficients (4)
		Dependent variable-ln (TFP)	Dependent variable-ln (TE)
	ln (TFP) t-1	0.59927** (0.0709)	0.68144** (0.0699)
	ln (TE) t-1			0.5881052** (.05539)	0.74239** (0.0577)
	ln (R&D intensity)	0.00971** (0.0028)	0.00927** (0.00771)	0.002621** (.0008)	0.00195** (0.0008)
	Size ln (K)	-0.01885** (0.0074)	-0.01511** (0.00771)	0.00449** (0.0022)	0.0058 ** (0.0023)
	ln (Trade intensity)	0.00046** (0.01226)	0.0124523** (0.01245)	0.00641** (.00314)	0.0121** (0.0031)
	Core Infra Index ln (G)	0.1778** (0.0333)		0.07478** (.01468)
	Core Infra Index ln (G)		0.08963** (0.02209)		0.02006** (0.0098)
	Const	0.3899 (0.0938)	0.42987** (0.1055)	0.0064** (0.0735)	0.43261** (0.0862)
	Sargan (P-value)	108.6914 (0.0363)	108.8529 (0.0355)	188.8037 (0.000)	189.9978 (0.000)

Notes: Standard errors are in parentheses. *, ** indicate statistical significance at the 10% and 5%, respectively. Sargan is the

[START_REF] Sargan | The Estimation of Economic Relationships Using Instrumental Variables[END_REF]

test of over-identifying restrictions.

Table A .1.1. Estimated TFP of the Indian Manufacturing Industries, 1994-2008

 A

						Non metallic
			Food and		Metal & Metal	Mineral		Transport	Miscellaneous
		Chemical	Beverage	Machinery	Products	Products	Textile	Equipments	Manufacturing
	1994	2.61	2.23	2.32	2.09	1.99	2.06	2.11	1.7
	1995	2.64	2.21	2.31	2.13	1.95	2.04	2.23	1.72
	1996	2.65	2.21	2.33	2.15	2	2.08	2.23	1.8
	1997	2.67	2.2	2.36	2.12	1.96	2.14	2.25	1.72
	1998	2.66	2.25	2.37	2.1	1.99	2.15	2.22	1.7
	1999	2.7	2.26	2.4	2.11	2.02	2.16	2.19	1.67
	2000	2.75	2.25	2.46	2.19	2.02	2.2	2.3	1.86
	2001	2.73	2.29	2.44	2.24	2.04	2.24	2.26	1.92
	2002	2.71	2.32	2.45	2.22	2.08	2.23	2.3	1.9
	2003	2.74	2.35	2.47	2.29	2.1	2.24	2.42	1.93
	2004	2.88	2.36	2.52	2.31	2.16	2.25	2.49	1.82
	2005	2.91	2.41	2.56	2.37	2.15	2.28	2.53	1.78
	2006	2.9	2.4	2.6	2.36	2.16	2.28	2.54	1.78
	2007	2.93	2.39	2.69	2.44	2.18	2.29	2.57	1.88
	2008	2.94	2.41	2.72	2.4	2.25	2.31	2.55	1.92
	Average	2.76	2.3	2.47	2.23	2.07	2.2	2.35	1.81

Table A .1.2. Estimated TE of the Indian Manufacturing Industries, 1994-2008

 A

		Chemical	Food and	Machinery	Metal & metal	Non metallic	Textile	Transport	Miscellaneous
			Beverage		products	mineral		equipments	manufacturing
						products
	1994	87.55	87.55	87.55	87.55	87.55	87.55	87.55	87.55
	1995	88.68	88.73	88.42	88.23	88.74	88.91	88.37	88.79
	1996	90.03	89.63	89.65	89.17	89.96	90.22	89.95	90.38
	1997	90.95	89.96	90.33	89.82	90.75	90.86	91.38	91.1
	1998	91.34	89.93	90.28	89.7	91	90.89	91.72	91.05
	1999	91.98	90.61	90.62	90.03	91.41	91.24	92.81	91.55
	2000	93.37	92.09	91.95	91.18	92.67	92.24	94.66	93.53
	2001	93.81	92.47	92.33	91.47	93.08	92.55	94.89	94.01
	2002	93.87	92.41	92.34	91.29	92.89	92.42	94.55	93.91
	2003	94.7	93.73	93.39	92.13	93.78	93.35	95.17	94.73
	2004	94.76	94.29	93.59	92.38	94.63	93.5	95.82	95.06
	2005	95.38	94.77	93.98	92.94	95.1	94.04	96.34	95.92
	2006	96.21	95.65	94.79	93.81	95.6	94.78	97.15	96.58
	2007	96.99	96.66	95.46	94.46	96.13	96.17	98.78	97.29
	2008	97.55	97.4	96.1	95.28	97	96.94	100	98.18

Table A .2.1 Infrastructure and ICT Variables: Sources of Data

 A

	Variable	Sector	Indicator	Data sources
	Air	Transportation	Air transport, passengers carried	WDI
	Electricity	Electricity	Electricity production (kWh/per-capita)	WDI
	Internet	Information and Communication Internet users (per 100 people)	WDI
	Mobile	Information and Communication Mobile cellular subscriptions (per 100 people)	WDI
	Mobile_Tele	Information and Communication Mobile and fixed-line telephone subscribers (per 100 people)	WDI
	Port	Transportation	port(commodity wise traffic ,000 tones)	CMIE
	Rail_goods	Transportation	Railways, goods transported (million ton-km)	WDI
	Rail_pass	Transportation	Railways, passengers carried (million passenger-km)	WDI
	Roads	Transportation	Roads, total network (km/1000people)	WDI
	Tele	Information and Communication Telephone lines (per 100 people)	WDI

Table A .2.2. Correlation between Infrastructure Variables

 A

	Variable	Air	Internet	Rail-goods	Rail-pass	Roads	Electricity	Mobile	Port
								tele
	Air	1.0000
	Internet	0.94436	1.0000
		(11.120)
	Rail-goods	(12.455) 0.95490	(26.195) 0.98924	1.0000
	Rail-pass	0.92500	0.97362	0.98821	1.0000
		(9.4285)	(16.526)	(24.988)
	Roads	0.44718	0.59462	0.63232	0.71497	1.0000
		(1.9363)	(2.864)	(3.161)	(3.9606)
	Electricity	0.86329	0.91276	0.94132	0.96968	0.79114	1.0000
		(6.624)	(8.654)	(10.802)	(15.367)	(5.009)
	Mobiletele	0.96660	0.96579	0.96958	0.94285	0.49967	0.84824	1.0000
		(14.607)	(14.424)	(15.342)	(10.958)	(2.234)	(6.203)
	Port	0.84629	0.92715	0.94871	0.96885	0.77283	0.98565	0.85021	1.0000
		(6.1528)	(9.5834)	(11.622)	(15.151)	(4.716)	(22.615)	(6.254)

Table A .3.3. Principle Component Analysis: ICT Infrastructure (ICT) (1994 to 2008)

 A

						Eigenvalue			Proportion
		P1				2.8351**				0.9451
		P2				0.15522				0.0517
		P3				0.00959				0.0032
		Table A.3.4. Factor loadings: ICT Infrastructure (ICT) (Eigenvectors)
										P1
			Internet							0.5908
			Mobile							0.5762
			Tele							0.5647
						Appendix 4
					Table A.4. Summary statistics
		ICT	Core	ln	ln	ln (R&D	ln (Trade	ln	ln	ln	ln (Q)	ln	ln
		Infra Index ln	Infra	(TE)	(K)	intensity)	intensity)	(N)	(Q)	(TFP)	(real	(M)	(F)
		(ICT)	Index ln						(GV		output)
			(G)						A)
	Mean	2.89	2.71	2.02	4.33	1.93	0.3	3.8	4.28	2.03	4.64 4.29	3.2
								5					2
		2.94	2.74	2.02	4.23	1.81	0.27	3.9	4.25	2.03	4.65 4.30	3.1
	Media							4					6
	n
	Maxim	3.01	2.82	2.06	5.15	3.29	0.77	4.3	5.34	2.08	5.65 5.32	3.7
	um							5					9
		2.15	2.23	2	3.58	0.69	0.14	3.0	3.35	1.99	3.76 3.43	2.6
	Minim							2					4
	um
	Std.	0.21	0.14	0.01	0.35	0.65	0.11	0.2	0.41	0.02	0.39 0.04	0.3
	Dev.							9					5
		-2.96	-2.87	-0.02 0.56	0.25	1.76	-0.9	0.33	0.36	0.11 0.03	-
	Skewn												1.5
	ess												2
		10.8	10.47	2.23	2.66	2.01	6.62	3.2	3.29	2.21	0.22 0.15	0.2
	Kurtos							8					2
	is

For detailed survey of the related literature, seeSturm et al. (1998) andRomp and Haan (2007).

Under the recent the stimulus packages, many steps have been taken to ensure more flows of fund for infrastructure construction which includes the permission given to Indian Infrastructure Finance Corporation Limited (IIFCL) to borrow INR 3000 million from market by issuing tax free bonds.

Prowess Database is online database provided by the Centre for Monitoring Indian Economy (CMIE). The database covers financial data for over 23000 companies operating in India. Most of the companies covered in the database are listed on stock exchanges, and the financial data includes all those information that operating companies are required to disclose in their annual reports. The accepted disclosure norms under the Indian Companies Act, 1956, makes compulsory for companies to report all heads of income and expenditure, which account for more than 1% of their turnover.

We prefer gross value added as a measure of output in computing TFP, as it is widely used in the Indian manufacturing sector literature[START_REF] Kumar | A decomposition of total productivity growth: a regional analysis of Indian industrial manufacturing growth[END_REF][START_REF] Goldar | Indian manufacturing: productivity trends in pre-and post-reform periods[END_REF][START_REF] Unel | Productivity trends in India's manufacturing sectors in the last two decades[END_REF][START_REF] Ahluwalia | Productivity and Growth in Indian Manufacturing[END_REF][START_REF] Balakrishnan | Total factor-productivity growth in manufacturing industry: a fresh look[END_REF][START_REF] Goldar | Productivity Growth in Indian Industry[END_REF]. There are many advantages of using gross value added over output. Firstly, it allows us a comparison between the firms that use different raw materials. Secondly, if gross output is used as a measure of output, it adds the necessity of including raw materials, which may obscure the role of labor and capital in the productivity growth[START_REF] Hossain | Trade liberalization and technical efficiency: evidence from Bangladesh manufacturing industries[END_REF] Karunaratne 2004, Kumar 2006).

The original model of[START_REF] Battese | Frontier production functions, technical efficiency and panel data: with application to paddy farmers in India[END_REF] is for firm level data, whereas we employ the model on industry data. Our working hypothesis is that some industries operate more efficiently than others.

It is well established in the related literature that Research and Development (R&D) intensity is an important determinant of productivity and export performance of firms. The pioneering study of[START_REF] Griliches | Issues in Assessing the Contribution of R&D to Productivity[END_REF] has shown in the 'R&D Capital Stock Model' that this factor has a direct effect on the performance of firms. Empirical evidence reported by[START_REF] Cuneo | Productivity and R&D at the firm level in French manufacturing[END_REF],[START_REF] Lichtenberg | The Impact of R&D Investment on Productivity. New Evidence using linked R&D-LR&D Data[END_REF] and[START_REF] Hall | Exploring the relationship between R&D and productivity in French manufacturing firms[END_REF] also provides

Trade intensive firms transfer technology through exporting and importing output material and other inputs, which can potentially help firms to enhance their productivity (see[START_REF]Equalizing exchange: trade liberalization and income convergence[END_REF][START_REF] Sachs | Economic Reform and the Process of Global Integration[END_REF]. Therefore, on this account, we include this variable in our TFP and TE equations. The Trade intensity of the industry is captured by the ratio of total export plus import to the value of total sales of the industry.

Theoretically, because of economies of scale, a larger size and increasing output should have a positive influence on the productivity of industry. Capital (K) is taken as a proxy of the size of the industry in the model and it is expected to have a positive influence on productivity, as well as on efficiency.

We have applied 'group-mean FMOLS', because we have a small sample for the analysis.[START_REF] Pedroni | Fully modified OLS for heterogeneous cointegrated panels[END_REF][START_REF] Pedroni | Purchasing power parity in cointegrated panels[END_REF] has shown that the 'group-FMOLS' has relatively lower small sample distortions and more flexibility in terms of hypothesis testing than other three versions of FMOLS (see also[START_REF] Basher | PPP tests in cointegrated panels: evidence from Asian developing countries[END_REF].

We will see that it is not the case anymore for TE.

In Miscellaneous Manufacturing also the variable is estimated to be statistically significant, however, the sign of the coefficient is negative.

It is noteworthy that Chemical, in which TFP and infrastructure are uncorrelated, is responsive to infrastructure in terms of TE.

Trade intensity is now a factor of efficiency in the Chemical and Textile industry, in addition to Non Metal and Metal sectors as in the case of TFP, with much smaller elasticities however.

Appendix 3 Composite Infrastructure and ICT indicators

In order to construct a composite core infrastructure index for India, we apply Principal Component Analysis (PCA). In this exercise, normalized values of nine important infrastructure indicators are used. The results bring out one significant component and this component explains 90% of variance in the underlying individual indicators. In the next stage, on the basis of the results of PCA, factor loadings of variables are used as weights of respective variables in constructing the composite infrastructure index.