Bénédicte Grandon
email: b_grandon@yahoo.fr

Hiyon Yoo
email: yoo@linguist.univ-paris-diderot.fr

Does prosodic similarity matter in L2 production? The case of Korean learners of French

Keywords: Second Language, prosody, rhythm, intonation, French, Korean, Speech production

French and Korean share similar prosodic characteristics as far as rhythm and intonation are concerned. In order to determine how this prosodic similarity affects the second language production, we propose in this paper to examine these prosodic parameters in read productions by Korean learners of French as a second language compared to French native speakers. We show that the productions of Korean learners and French native speakers present minor differences: concerning rhythm, Korean learners are less systematic in lengthening the last vowel at a phrase-final position while the overall pitch contour is similar for both groups of speakers, especially for the subject and object phrases. We argue that these minor differences are not sufficient enough for the detection of a "foreign accent" only with prosodic cues.

Introduction

In the last years, several studies have shown that the types of errors made by second language (L2) speakers depended on whether phonological categories were similar or different in both First (L1) and Second (L2) languages (see [START_REF] Best | A Direct Realist Perspective on Cross-Language Speech Perception[END_REF][START_REF] Flege | Second Language Speech Learning: Theory, Findings, and Problems[END_REF] among others for the segmental component). As far as the prosodic level is concerned, studies on intonation [START_REF] Jilka | Different Manifestations and Perceptions of Foreign Accent in Intonation[END_REF][START_REF] Martin | Phonological and Phonetic Influences in Nonnative Intonation[END_REF] and rhythm [START_REF] Barry | Rhythm as an L2 Problem: How prosodic is it?[END_REF] have shown that when the intonational contour or rhythmic pattern exists in both languages, if the distinct features are minor, speakers are more prone to making mistakes. The present study focuses on the prosodic components of production in French by Korean native speakers. French and Korean are both described as "syllable-timed" languages [START_REF] Di Cristo | Intonation in French[END_REF][START_REF] Jun | The Phonetics and Phonology of Korean Prosody[END_REF], with common prosodic features: (1) Primary stress, realized through syllabic lengthening, is located on the last syllable of the last lexical word of a phrase (among others [START_REF] Martin | Phonological and Phonetic Influences in Nonnative Intonation[END_REF][START_REF] Di Cristo | Intonation in French[END_REF][START_REF] Jun | The Phonetics and Phonology of Korean Prosody[END_REF], (2) non-stressed syllables have a constant duration [START_REF] Di Cristo | Intonation in French[END_REF], Lee 1993), and (3) declarative sentences have a descending pitch contour beginning on the first accented syllable in French (Di Cristo 1999) and on the sentence's second syllable in Korean [START_REF] Lee | The structure of Korean Prosody[END_REF]) and continuing through the end of the sentence. Furthermore, the intonation of modality is seen as the result of F0 realization at IP-final level both in French [START_REF] Delattre | Les dix Intonations de Base du Français[END_REF][START_REF] Martin | Phonological and Phonetic Influences in Nonnative Intonation[END_REF] and Korean [START_REF] Jun | The Phonetics and Phonology of Korean Prosody[END_REF]. This quick comparison of the prosodic structure of the two languages reveals their prosodic similarity. In this paper, we present the results of a production experiment which aims at understanding how rhythm and intonation of native Korean speakers translate into French, and examining if there are enough cues in L2 realizations to consider the existence of a Korean foreign accent in French based on rhythm and intonation only.

Production experiment

In this section, we present the experimental protocol of our production experiment, followed by the results we obtained.

Method

Participants

All speakers were students living in Seoul at the time of the recordings: Two female native speakers of Standard Parisian French (19 and 20 years old) and three female (23, 23 and 26 years old) and one male (23 years old) native speakers of Standard Seoul Korean, with variable proficiency levels in French.

Corpus

Since our aim was to compare the prosodic characteristics of two groups of speakers, we chose to work on a read corpus, which allowed keeping the same segmental information for both groups while avoiding differences due to hesitations or lexicon and syntax. Declarative sentences were designed in French following the pattern "NP Subj -VP-NP Obj ". All sentences are balanced: in each sentence, the three phrases (NP Subj , VP and NP Obj ) have an identical number of syllables, varying from 1 to 10 syllables: there are two sentences of 3 times 1 syllables, two sentences of 3 times 2 syllables, two sentences of 3 times 3 syllables, etc. up to 3 times 10 syllables. Our corpus contains a total of 20 sentences. ( 1

Recordings

Recordings were made with the Audacity software (Audacity Version 2.0), in mono, using a sampling frequency of 22050 Hertz and 32bits. All recordings were done on a laptop, using an external microphone, in a quiet room. The twenty sentences of the corpus were read five times in a random order. The order was different for each series of sentences. All speakers read the five series of sentences in the same order, with pauses between each series. The recordings were made without any time constraint. Speakers read the sentences before the recording session, and could ask for explanation if they had trouble understanding the meaning of the sentences. They were allowed to take breaks whenever they wished and to re-read sentences if they faced difficulties.

Data analyses

The corpus was segmented and annotated using Praat [START_REF] Boersma | Praat: doing phonetics by computer[END_REF]. The annotation was first made automatically using the Easyalign software [START_REF] Goldman | EasyAlign: an automatic phonetic alignment tool under Praat[END_REF]) and verified manually. Segment durations and F0 values of vowels in phrase-final syllables were automatically extracted using a Praat script. For rhythm, we chose the vowel over the syllable as the unit of analysis. Vocalic durations were normalized in order to put aside "inter-speaker" and "intra-speaker" variations: instead of comparing raw durations, we used a ratio of the duration of each occurrence produced by the speaker divided by the mean duration of this type vowel in this speaker's corpus. F0 values were measured at three points per vowel: at the beginning, middle and end. In order to avoid "inter-speaker" variation, the data were normalized in semi-tones calculated using each speaker's mean F0, using the following formula (1) from [START_REF] Martin | Phonological and Phonetic Influences in Nonnative Intonation[END_REF]): F0(ST) = 12*(Log(F0/speaker's_meanF0))/Log(2.00)

(1).

We ran ANOVA tests in order to compare phrase-final vocalic durations and phrase-final F0 modulations of the two groups (L1 and L2). We used regression tests to study the difference in realization of the declination line over sentences by the two groups. Statistics were run on the R software (R Development Core Team 2012).

Results

Rhythm

The study of rhythm consisted in measuring the presence or absence of vocalic lengthening in a given position. For the final vowel of each phrase (subject, verb and object), we set that a vowel can be considered as l e n g t h e n e d w h e n i t s normalized duration is above the threshold of 1.2 (mean + 20%). We considered that choosing the mean duration value was not sufficient enough to determine a lengthening compared to the threshold of 1.2, above which lengthening can clearly be perceived. ANOVA tests were conducted for every sentence, but because of limits of space, we show the results for three sentences only, illustrating our purpose. Figure 1 shows the variation of mean vocalic durations for the two groups of speakers (French L1 and Korean L2) for three sentences (3x2=6, 3x4=12 and 3x9=27 syllables).

In most cases, both French L1 speakers and Korean L2 learners lengthen the last vowel of the subject phrase. French speakers almost never lengthen the end of a verb, which shows that they tend to group the verb with its object and to place lengthening only at the end of the sentence. Korean speakers present more diverse results, with vocalic lengthening found in six cases out of ten (sentences with 3x4, 3x5, 3x6, 3x7, 3x8, 3x10 syllables), which might correspond to a more frequent segmentation of the sentence f o r l e a r n e r s t h a n f o r n a t i v e speakers. Vowels at the end of object phrases ( which represents also the end of sentences) are systematically longer for French speakers while Korean learners do not produce this expected lengthening (vocalic lengthening of 1,2 can be seen only for sentences with 3x2, 3x4 and 3x10 syllables). We ran ANOVA tests to compare the realizations of vowels at the end of phrases for the two groups of speakers. Thus, for 3x2 syllable sentences, durations are similar for both groups of speakers, with a lengthening of the 2nd vowel (Subject-final syllable), of the 4th vowel (verb-final syllable) and of the 6th vowel (Object and sentence final syllable). The difference of lengthening is significant for both groups for each position (for the 2nd vowel, (F(1,57) = 4,380 p=.0408), for the 4th syllable (F(1,55) = 1,113 p=.0001) and the 6th vowel (F(1,55) = 17,378 p=.0001)). For 3x4 syllable sentences, the two groups have a different realization of lengthening: no lengthening of the 4 th and 8 th vowels (subject-final and verb-final syllables) but lengthening of the 12 th v o w e l ( sentence-final syllable) for the French speakers an moderate l e n g t h e n i n g o f t h e 4 th , 8 th a n d 1 2 th vowels for the Korean speakers. The ANOVA tests show significant differences between the two groups for the three vowels: for the 4 th vowel F(1,54) = 9,863 p=.0027, for the 8 th vowel F(1,54) = 16,118 p=.0002 and for the 12 th v o w e l F(1,54) = 14,353 p=.0004. However these results differ from the predicted results, since the group of Korean speakers and not the group of French speakers shows a systematic vocalic lengthening in phrase-final syllables for each phrase (subject, verb and object).

For the 3x9 syllable sentences, there is a lengthening of only the 9 th vowel by French speakers and of the 9 th and 11 th vowels by the Korean speakers. The differences between the two groups for the 9 th and 18 th vowels are not significant, contrarily to the difference between the two groups on the sentence-final vowel which is significant (F(1,48) = 18,292 p<.0001).

Figure 1: Mean vocalic duration of the two groups for 3x2, 3x4 and 3x9 syllable sentences.

Intonational patterns at phrase-final level

For intonation, the F0 values for the last vowel of each phrase (subject, verb and object) were compared for the two groups of speakers. Results show that the two groups (French native speakers and Korean learners of French) produce very close patterns. Figure 2 illustrates the differences and similarities of the F0 measures for the two groups of speakers (French L1 and Korean L2 speakers) for three sentences (3x2=6, 3x4=12 and 3x9=27 syllables).

Figure 2: Mean F0 of the two groups for3x2, 3x4 and 3x9 syllable sentences.

Thus, at the end of sentences (i.e. at the end of object phrases), both French and Korean speakers produce massively a falling pattern (sentences 3x2, 3x3, 3x6, 3x8, 3x9, 3x10), which can be followed by a small rising (sentences 3x2, 3x6, 3x8). Korean learners have more random productions with more final risings, and even a rising pattern for sentence 3 x 7 . However, the ANOVA test reveals a non-significant difference for F0 realizations of the two groups of speakers on the last vowel of the sentence. The F0 realization on the last vowel of the subject is also similar for both groups. However, the type of pattern can vary, with a fall-rise pattern for sentence 3x1, a rising pattern for 3x5, 3x6 and 3x10 syllable sentences, and a falling pattern for the 3x7 syllable sentence. The realizations of the two groups of speakers differ for sentences with 3x2, 3x3, 3x8 and 3x9 syllables. Within the group of French speakers, the last vowel at this position is produced as a flat pattern in short sentences (3x1 and 3x2 syllables), a rising pattern in sentences with 3x3, 3x7 and 3x9 syllables, a rise-fall pattern in sentences 3x5 and 3x10 and a falling pattern in sentences 3x4, 3x6 and 3x8. Korean learners realize also the same patterns but not for the same sentences: rising pattern is found in sentences 3x3, 3x5 and 3x7, a flat pattern in sentences 3x1 and 3x8, a rise-fall pattern in sentences 3x2, 3x9 and 3x10, a falling pattern in sentence 3x4, and a falling pattern followed by a rise in sentences 3x6.

For 3x2 syllable sentences, the realizations of the two groups are very close, with significant differences at only two points

Declination line

The analyses of declination line (Table 2, Figure 3) show that all slopes are negative, which means t h a t t h e g l o b a l F 0 progressively declines for all sentences. F o r all s e n t e n c e s, slopes of Korean L2 speakers of French are systematically lower than those of the French L1 speakers, which indicates that the declination is systematically stronger for French native speakers.

Table 1: Slopes of declination lines for the two groups of speakers.

Furthermore, for both groups, the longer the sentence is, the more the slope in absolute value decreases. This fact points out a diminution of the declination depending on the F0 target at the end of sentences, which is approximately constant. The Korean L2 speakers however seem to have a greater F0 amplitude around the declination line than the French speakers, which could be explained by differences in group size or a greater F0 modulation by Korean speakers. Further experimentation and more speakers could help understand these particular results.

Conclusion

For both French and Korean speakers, results of the present study reveal a s y s t e m a t i c a n d s t r o n g l e n g t h e n i n g o f t h e subject-final vowels and the object-final vowels (i.e. sentencefinal vowels) but not o f t h e v e r b -final vowels a s f a r t h e rhythmic component is concerned. In L2 productions however, systematic lengthening occurs at almost every final position. This vowel lengthening can also be observed in other positions in longer sentences, which reveals a different segmentation strategy in L2 speakers. The analyses of phrase-final contours (subject, verb and object) show that French and Korean speakers have a similar subject and object-final realization of F0. However for L2 speakers, modulation of F0 appears to have a more random shape and height than for L1 speakers. Comparative analyses of declination lines through regression tests show a progressive decrease of F0 for both groups, with L1 speakers' declination being steeper than L2 speakers' declination. These differences in the production of L1 and L2 speakers in French are consistent with [START_REF] Jilka | Different Manifestations and Perceptions of Foreign Accent in Intonation[END_REF] but are not sufficiently pronounced to precisely identify which of the four types of errors they represent. The prosodic similarity of the two languages in contact seems to be a criterion to consider in determining the types of errors. This result is confirmed by a perception study we conducted [START_REF] Grandon | Do Korean L2 learners have a "foreign accent" when they speak French? Production and perception experiments on rhythm and intonation[END_REF] with native speakers of French, since these minor differences were not sufficient to allow the listeners perceiving a foreign accent in productions of French by Korean speakers.

  Results are less h o m o g e n e o u s a t t h e e n d o f v e r b g r o u p s .

  (F(1,55) = 12,056 p=.0010) at subject-onset point and vowel mid-point at verb-final level (F(1,57) = 19,818 p<.0001). For 3x4 syllable sentences, the two groups have a different realization of F0 patterns: flat F0 declination for French L1 speakers and peak pattern for Korean learners on the subject final vowel with significant differences on F0 values on the subject final vowel (F(1,36) = 6,306 p=.0168) at vowel-onset, (F(1,54) = 7,740 p=.0074) at mid-point and (F(1,36) = 4,514 p=.0405) at end-point) and at end-point of the verb-final vowel (F(1,12) = 4,890 p=.0472). For 3x9 syllable sentences, both groups have similar realization of F0 patterns at verb and object level, but different at subject level: French L1 speakers have a rising pattern and Korean learners have a rising-falling pattern, with a significant difference at end-point of the subject-final vowel (F(1,22) = 9,172 p=.0062). At verb-final level, the group of French speakers have a rising F0 pattern whereas the Korean learners have a rising-falling pattern, with a significant difference between both groups at mid-point (F(1,47) = 5,895 p=.0191) and at end-point (F(1,29) = 5,582 p=.0251). Both groups have a falling F0 pattern at object-final level, but the Korean learners have a stronger, earlier fall, with a significant difference between groups at mid-point (F(1,42) = 4,229 p=.0460).

Figure 3 :

 3 Figure 3: Declination lines of the two groups for 3x2, 3x4 and 3x9 syllable sentences.

  Schmid, C. Gendrot, C., & M. Adda-Decker. 2012. Une comparaison de la déclinaison de F0 entre le français et l'allemand journalistiques. Actes des 28èmes Journée d'Etude sur la Parole, Grenoble, France, 4-8th June 2012, pp. 329-336.

), (2) and (3) and sample examples of the corpus, in French, with English translation: (1) 3x2 (6 syllables) sentence (le chat) SUBJ (a bu) VP (le lait) OBJ

	(the cat) SUBJ (drank)VP (the milk)OBJ
	(2) 3x4 (12 syllables) sentence
	(Les deux garçons) SUBJ (ont rencontré) VP (un vieil ami) OBJ
	(The two boys)SUBJ (met)VP (an old friend)OBJ
	(3) 3x9 (27 syllables) sentence
	(Le voyageur perdu en Corée) SUBJ (a eu l'occasion d'utiliser) VP
	(son dictionnaire français-coréen) OBJ
	(The lost traveler in Korea)SUBJ (was able to use)VP (his French-
	Korean dictionary)OBJ

Acknowledgements

This work is supported by a public grant as part of the "Investissements d'Avenir"-Labex EFL program (reference: ANR-10-LABX-0083).


Bénédicte Grandon
email: b_grandon@yahoo.fr

Hiyon Yoo
email: yoo@linguist.univ-paris-diderot.fr

Do Korean L2 learners have a "foreign accent" when they speak French? Production and perception experiments on rhythm and intonation

Keywords: L2 prosody, intonation, rhythm, production, perception, Korean, French

French and Korean are two languages with similar prosodic characteristics as far as rhythm and intonation are concerned. In this paper, we present the results of production and perception tests where we describe the prosodic characteristics of Korean L2 learners of French. Our aim is to analyze the impression of "foreign accent" for two prosodic components (intonation and rhythm) of speech produced by Korean L2 learners of French and the perception of this "accent" by native listeners of French (L1). We show that the productions of Korean learners and French native speakers present minor differences but that they do no translate into cues for determining clearly the presence of a "foreign accent".

Introduction

Through the past decades, several second language (L2) acquisition models have shown that similarity is more problematic than difference for the L2 learner. Researchers, among others [START_REF] Flege | Second Language Speech Learning: Theory, Findings, and Problems[END_REF], in his Speech Learning Model but also [START_REF] Mennen | Phonological and Phonetic Influences in Non-native Intonation[END_REF] and [START_REF] Jilka | Different Manifestations and Perceptions of Foreign Accent in Intonation[END_REF] for intonation and [START_REF] Barry | Rhythm as an L2 Problem: How prosodic is it?[END_REF] for rhythm, posit that L2 acquisition is more difficult for sounds and prosodic units where the contrast with L1 is poor. What happens then when L1 and L2 share most prosodic characteristics? In this paper, we investigate the impression of "foreign accent" (i.e. nonnative production, see among others [START_REF] Piske | Factors affecting degree of foreign accent in an L2: a review?[END_REF] and [START_REF] Vaissière | Identifying a language or an accent: from segment to prosody[END_REF]) for two prosodic components (intonation and rhythm) in speech produced by Korean L2 learners of French and the perception of this "accent" by native listeners of French (L1). French and Korean are both described as "syllable-timed" languages ( [START_REF] Di Cristo | Intonation in French[END_REF] for French, [START_REF] Jun | The Phonetics and Phonology of Korean Prosody[END_REF] for Korean), with common prosodic features: (1) Primary stress, realized through syllabic lengthening, is located on the last syllable of the last lexical word of a phrase (among others [START_REF] Martin | Intonation du Français[END_REF] and ( [START_REF] Di Cristo | Intonation in French[END_REF] for French, [START_REF] Jun | The Phonetics and Phonology of Korean Prosody[END_REF] for Korean), (2) non-stressed syllables have a constant duration ( [START_REF] Di Cristo | Intonation in French[END_REF] for French, [START_REF] Lee | The structure of Korean Prosody[END_REF] for Korean), and (3) declarative utterances have a falling pitch contour beginning on the first accented syllable in French [START_REF] Di Cristo | Intonation in French[END_REF] and on the utterance's second syllable in Korean [START_REF] Lee | The structure of Korean Prosody[END_REF] and continuing through the end of the sentence. Furthermore, the intonation of modality is seen as the result of the realization of the fundamental frequency (F0) at the end of utterances both in French ( [START_REF] Delattre | Les dix Intonations de Base du Français[END_REF], [START_REF] Martin | Intonation du Français[END_REF]) and Korean ( [START_REF] Jun | The Phonetics and Phonology of Korean Prosody[END_REF]). Finally, the declination slope is steadily declining in both languages, no matter the length of the utterances ( [START_REF] Ko | Declarative Intonation in Korean: An Acoustical Study of F(o) Declination[END_REF] for Korean and [START_REF] Schmid | Une comparaison de la déclinaison de F0 entre le français et l'allemand journalistiques[END_REF] for French). Since French and Korean share these prosodic characteristics, we expect that (1) French native speakers and Korean learners of French (L2) produce overall similar intonational and durational patterns of vowels at the end of chunks and (2) that these similarities, along with minor differences in the production of Korean speakers cannot be perceived as the manifestations of a "foreign accent". In the next sections, we present the production and perception analyses we conducted to test these hypotheses.

Rhythm and intonation in L2 Korean productions of French utterances

In order to determine the prosodic proximity between French L1 and L2 productions, we built a comparative reading experiment with L2 learners of French and French native speakers. The aim of this experiment is to locate the prosodic differences concerning intonational patterns and rhythmic organization that can be seen in L2 productions and to measure variation from native L1 productions.

Corpus and experimental procedure

The corpus consisted in declarative utterances following the pattern "NP subject -V-NP Object ", where each chunk has an identical number of syllables (varying from 1 to 10 syllables). Three examples (from the shorter to the longest utterance) are given below in French, with English translation:

(1) utterance 1x3 (9 syllables) Two female native speakers of Standard French and four native speakers of Standard Seoul Korean (three female and one male), with variable proficiency levels in French were asked to read the sentences that were presented to them. All speakers were students in their twenties living in Seoul at the time of the recordings. The corpus gathers a total of 20 utterances presented five times in a random order and mixed with distractors that were not taken into account (a total of 600 utterances were analyzed).

The recordings took place in a quiet room, using the Audacity software [START_REF]Audacity Version2.0[END_REF] (in mono, using a sampling frequency of 22050 Hz ad 32bits) on a laptop, with an external microphone. Annotations of the sentences and extraction of durations and F0 values were done first automatically with the Easyalign software [START_REF] Goldman | EasyAlign: an automatic phonetic alignment tool under Praat[END_REF] and Praat scripts [START_REF] Boersma | Praat: doing phonetics by computer[END_REF], and then checked manually. Three acoustic parameters were analyzed: rhythm, intonation patterns and declination. For better objectivity in the normalization of the data, we chose the vowel over the syllable as the unit of analysis; thus for rhythm, we used a ratio of the duration of each occurrence produced by the speaker divided by the mean duration of the corresponding vowel in all her/his productions, which allowed us to eliminate both "interspeaker" (resulting from speakers' different speech rates) and "intra-speaker" (resulting from different intrinsic vocalic duration) variations, as well as variation resulting from different syllabic structures. For intonation, F0 raw values (three measures per vowel) were converted into semi-tones relative to each speaker's mean F0 1 . The R software [START_REF]R: A language and environment for statistical computing[END_REF] was used to run the ANOVA tests.

Results and discussion 2

Rhythm

For the final vowel of each chunk (subject, verb and object), we considered that a vowel is lengthened when its normalized duration is 1.2 or above (mean + 20%). We considered that choosing the mean value was not sufficient enough to determine a lengthening compared to the threshold of 1.2, above which lengthening can clearly be perceived Figure 1 shows the variation of mean vocalic durations for the two groups of speakers (French L1 and Korean L2) for three sentences (3x3=9, 3x5=15 and 3x10=30 syllables).

In most cases, both French L1 speakers and Korean L2 learners lengthen the last vowel of the subject chunk. French speakers almost never lengthen the end of a verb, which shows that they tend to group the verb with its object and to place lengthening only at the end of the sentence. Korean speakers present more diverse results, with vocalic lengthening found in six cases out of ten (sentences with 3x4, 3x5, 3x6, 3x7, 3x8, 3x10 syllables), which might correspond to a more frequent segmentation of the utterance for learners than for native speakers. Vowels at the end of object chunks ( which represents also the end of utterances) are systematically longer for French speakers while Korean learners do not produce this expected lengthening (vocalic lengthening of 1,2 can be seen only for sentences with 3x2, 3x4 and 3x10 syllables). We ran ANOVA tests to compare the realizations of vowels at the end of chunks for the two groups of speakers. Thus, for sentence 3x3 syllables, it appears that the third and the ninth vowels produced by French speakers is longer than the adjacent vowels, even though the normalized values never cross the threshold of 1,2. Results of ANOVA tests show a significant difference for both groups, except for the utterancefinal vowel (F(1,56) = 5,737 p=.0199).

The durations of 3x5 syllable utterances, are similar for both groups of speakers: both groups lengthen the 5 th and the 15 th vowels (for this last vowel, the lengthening is much more important for French speakers than for Korean learners), while the 10 th vowel is lengthened only by Korean speakers. Notice that the ANOVA test is significant between the two groups only for the 10 th syllable (F(1,50) = 14,657 p=.0004).

For the 3x10 syllable utterances, there is a lengthening of the 10 th , 15 th and 30 th vowels for French speakers and of the 3 rd , 10 th , 16 th , 20 th and 30 th vowels for Korean speakers. The differences between the two groups are significant for the 10 th vowel (F(1,51) = 5,666 p=.0211) and for the 30 th vowel (F(1,51) = 9,16 p=.0039) but not for the 20 th vowel (F(1,51) = 0,866, p=.3565).

Figure 1: Mean vocalic duration of the two groups for 3x3, 3x5 and 3x10 syllable utterances. Results show a main difference between the two groups for the final vowel of the utterance, which is lengthened systematically by French speakers while Korean speakers present less homogeneous results for vocalic durations at this position. The findings correspond to what is expected for French rhythm ( [START_REF] Di Cristo | Intonation in French[END_REF], [START_REF] Martin | Intonation du Français[END_REF]) where lengthening of the last syllable of an accentual group is a main rhythmic characteristic in French. Lengthening at subject-final level seems to indicate the presence of an accentual group boundary on this position, while the absence of lengthening at verb-final level indicate a grouping of the verb and its object, putting the two chunks into a unique group with only a final lengthening. Korean learners produce vocalic lengthening less systematically but more frequently. Rhythm is organized in terms of group weight: They have a tendency to re-segment the utterances in order to obtain a maximum of six/seven syllables per group ( [START_REF] Martin | Intonation du Français[END_REF] among others posit that accentual groups in French contain seven syllables), and to lengthen the end of these new groups, no matter the syntactic description. Moreover, lengthening is less marked for Korean learners than for French speakers.

Intonation

For intonation, we compared the F0 values for the last vowel of each chunk (subject, verb and object). Results show that the two groups (French native speakers and Korean learners of French) produce very close patterns. Thus, at the end of utterances (i.e. at the end of object phrases), both French and Korean speakers produce massively a HL pattern (utterances 3x2, 3x3, 3x6, 3x8, 3x9, 3x10), which can be followed by a small rising (utterances 3x2, 3x6, 3x8). Korean learners have more random productions with more final risings, and even a rising pattern for utterance 3x7. However, the ANOVA test reveals a non-significant difference for F0 realizations of the two groups of speakers on the last vowel of the utterance. The F0 realization on the last vowel of the subject is also similar for both groups. However, the type of pattern can vary, with a fall-rise pattern for utterance 3x1, a rising pattern for utterances 3x5, 3x6 and 3x10, and a falling pattern for utterance 3x7. The realizations of the two groups of speakers differ for utterances 3x2, 3x3, 3x8 and 3x9 syllables Results are less homogeneous at the end of verbs. Within the group of French speakers, the last vowel at this position is produced as a flat pattern in short sentences (3x1 and 3x2 syllables), a rising pattern in utterances 3x3, 3x7 et 3x9 syllables, a rise-fall pattern in utterances 3x5 and 3x10 and a falling pattern in utterances 3x4, 3x6 et 3x8. Korean learners realize also the same patterns but not for the same utterances: rising pattern is found in utterances 3x3, 3x5 and 3x7, a flat pattern in utterances 3x1 and 3x8, a rise-fall pattern in utterances 3x2, 3x9 and 3x10, a falling pattern in utterance 3x4, and a falling pattern followed by a rise in utterances 3x6. Figure 2 illustrates the differences and similarities of the F0 measures for the two groups of speakers (French L1 and Korean L2 speakers) for three utterances (3x3=9, 3x5=15 and 3x10=30 syllables). Thus, for utterances 3x3, even though the main shape of the F0 curve is similar for the two groups, the ANOVA test reveal significant results for: For intonation, it appears that overall F0 shape is similar for both Korean learners and French native speakers, but statistical analysis show significant differences in some positions of contour, especially at the end of the verb and at the end of utterances. The F0 contours produced by Korean learners are less systematic and present more variety than those produced by French speakers.

F0 declination slope

We used a regression-analysis in order to measure the overall declination slope of the F0 ( [START_REF] Lieberman | Measures of the sentence intonation of read and spontaneous speech in American English[END_REF] and [START_REF] Schmid | Une comparaison de la déclinaison de F0 entre le français et l'allemand journalistiques[END_REF]). The slopes of the regression line were calculated by taking into account the three F0 values (converted in semi-tones) on the last vowel of each group. Results given in Table 1 show that the two groups have the same attitude in regards to this prosodic characteristic, with an overall progressing F0 declination from the beginning to the end of utterances. However, results show that the declination slope is slightly more important for French native speakers than Korean learners (the slopes of regression line are always negative, and have a higher absolute value for the French speakers than for the Korean speakers). This observation can also be seen in the study of [START_REF] Mennen | Phonological and Phonetic Influences in Non-native Intonation[END_REF] who noticed that declination slope is less marked in L2 speakers than L1 speakers. Finally, contrarily to what has been observed by [START_REF] Ko | Declarative Intonation in Korean: An Acoustical Study of F(o) Declination[END_REF] for Korean, there is a correlation between the length of the utterances and the declination slope: when the utterance is longer, the declination slope is less steep, but the highest F0 point at the beginning of the utterance and the lowest point and the end of the utterance remain the same, no matter the length of the utterance. Since the production analyses revealed slight but statistically significant differences between French native speakers and Korean learners, the next step of our procedure was to test if these differences are perceived, and if they represent sufficient cues to identify a foreign accent. We present the results of the perception experiment in the next section.

Table 1: Slopes of regression line for all utterances and for the two groups of speakers (French an Korean)

Perception

Since the production experiment showed only slight differences in production in French by French and Korean speakers both for rhythm (vocalic durations) and intonation (F0 contours and declination lines), we expect that these differences in the Korean speakers' production at a prosodic level are not sufficient enough to be perceived by naive French listeners as a « foreign accent » in comparison to the French speakers' production. In this section we present the results of a pilot experiment built to test the perception of this "accent".

Experimental procedure

The perception experiment is built in three different conditions. First, we neutralized segmental information: we synthesized the intonation and rhythm of two French and two Korean speakers who participated at the production experiment with the voice of a French native speaker, which allowed us keeping segmental information but changing the prosodic profile of the utterances (we thus obtained synthesized sentences with different prosodic profiles on a same French voice). Second, segmental and rhythmic information have been neutralized: thus, we coupled a long /a/ sound with the intonational tier of the four speakers used in the first condition while rhythm is neutralized for all syllables: in this test, we chose to keep only part of the initial stimuli (3x4, 3x6 and 3x8 syllables were not used) since the listening task of utterances with no segmental information is quite difficult to perform for naïve listeners. The third test is the control condition: stimuli remain unmodified productions of the same speakers, without any manipulation of segmental information, rhythm and intonation. The perception experiment is created and run on Praat [START_REF] Boersma | Praat: doing phonetics by computer[END_REF]. Eight native speakers of French took part in the experiment which was conducted on a laptop and using headphones. The experiment is a forced choice task in which they are asked to judge if the stimulus is pronounced by a speaker with a foreign accent or by a French native speaker.

Results and discussion

When segmental information has been neutralized and only rhythm and intonation remain (test 1 of Tables 2 and3), answers for "foreign accent" are only slightly above chance (62.5 to 67.2%) for shorter sentences (1 to 3 syllables per group). Results gradually improve for longer sentences (4 to 9 syllables per group) and reach 87.5% for "foreign accent".

When only the parameter of intonation is kept as the only cue, results for shorter sentences are low (42.2 to 54.7% for "foreign accent"), improve when sentences are longer (5 and 7 syllables per group) but remain around average for the longest tested sentences (9 syllables per group). The analyses of answers chosen per stimulus show that listeners identify the stimuli of native speakers of French correctly in only 42.7% of cases, which indicate that in this test, choices are made randomly. In the control condition (Test 3 of Tables 2 and3), results are as expected for all types of sentences (above 95.3%): segmental variation has not been analyzed in this study, yet it seems to be strong enough for the listeners to identify a foreign accent.

Conclusion

The production experiment showed that as far as rhythm is concerned, Korean learners of French tend to change boundaries and to lengthen the end of these groups, no matter the syntactic structure. Otherwise, strategies for intonation and declination slope are quite similar for both language groups. This pilot perception experiment gives a first indication of the difficulty for native listeners to clearly perceive slight, randomly distributed differences in the production of L2 learners of French. It also reveals that the identification of "foreign accent" is easier when utterances are longer. This result is consistent with [START_REF] Jilka | Different Manifestations and Perceptions of Foreign Accent in Intonation[END_REF]'s results on German and US-English production and perception. It appears that the perception of a "foreign accent" is linked to prosodic proximity of the two tested languages. Ongoing work includes more listeners but also the dissociation between the two main parameters, rhythm and intonation. Moreover, a further production and perception study with the same material in French with speakers of a typologically different language could help understanding and confirming our findings.

Figure 2 :

 2 Figure 2: Mean F0 of the two groups for 3x3, 3x5 and 3x10 syllable utterances.

  1) the last vowel of the verb (at onset (F(1,39) = 11,479 p=.0016), at mid-point (F(1,56) = 10,045 p=.0025) and at end-point (F(1,44) = 9,303 p=.0039) of the vowel) and 2) at end-point of the vowel of the object (F(1,33) = 5,883 p=.0209). For utterances 3x5, the ANOVA test shows that there is a significant difference for the verb (at mid-point (F(1,51) = 14,255 p=.0004) and at end-point of the final vowel of the verb (F(1,40) = 13,974 p=.0006)) and the object (at midpoint of the final vowel of the object F(1,43) = 5,453 p=.0243). The ANOVA test is not significant at subject-final level.For utterances 3x10, the main F0 shapes are similar for both groups. However, the ANOVA test reveals a significant difference at the subject position (at mid-point (F(1,52) = 11,827 p=.0012) and at end-point (F(1,35) = 36,713 p<.0001) on the last vowel of the subject ), mainly because of the more important rise produced by the Korean learners.

Table 2 :

 2 Percent of answers for "foreign accent" for the three conditions for each utterance (1/L2 rhythm and intonation, 2/Intonation only, 3/ no modification)

Table 3 :

 3 Results sorted by types of stimuli (produced by French or Korean speaker)

We used the following formula taken in[START_REF] Martin | Intonation du Français[END_REF] for the computation of semi tones: F0(ST) = 12*(Log(F0/speaker's_meanF0))/Log(2.00)

ANOVA tests were conducted for every type of sentences, but because of limits of space, we show the results for three utterances, illustrating our purpose.

i This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the "Investissements d'Avenir"-Labex EFL program (reference: ANR-10-LABX-0083)


Alessandra Colombelli

Naciba Haned

Christian Le Bas
email: christian.lebas@univ-lyon2.fr

Digep

Christian Le
email: christian.lebas@univ-lyon.fr

On Firm Growth and Innovation: Some new empirical perspectives using French CIS (1992-2004)

Keywords: Innovation, process and product innovator, firm growth, CIS. JEL classification: D22, L20, L60, O31, O33

The aim of this paper is to examine whether firms that innovate, experience higher rates of growth than firms that do not. Our analysis is based on different models and econometric methodologies applied to several waves the Community Innovation Surveys (CIS) for French industry, during 1992-2004. Our main findings are that innovative firms grow more than noninnovative ones. The estimation techniques give results that are quite robust to the effects of different types of innovation on firm growth. In particular, the quantile regression results

show that the coefficient of innovation is higher for firms with the highest growth rates, a result that is robust to different measures of the dependent variable.

Introduction

A major argument supporting innovation policy is that more innovation generates more growth which promotes higher levels of employment and job creation. Innovation is viewed as a means by which new knowledge is transformed into economic growth. So the notion that innovation results in more growth is a commonly accepted rationale for implementing innovation policy in both Europe and America.

While the theoretical literature provides excellent explanations for why innovation is a determinant of firm growth, empirical studies find it more difficult to identify a strong link between them, and the process of firm growth and its relationship with innovation has for long intrigued economists. Following the pioneering work of [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF], evolutionary economics has maintained that innovation is crucially important for firm growth. More recently, analysis of firm growth and innovation has gained momentum [START_REF] Ernst | Patent applications and subsequent changes of performance: evidence from time-series cross-section analyses on the firm level[END_REF][START_REF] Coad | Innovation and firm growth in high-tech sectors: A quantile regression approach[END_REF][START_REF] Corsino | Product Innovation and Firm Growth: Evidence from the Integrated Circuits Industry[END_REF]. However, investigation of this relationship is not straightforward, it is difficult also to find empirical regularities with respect to the type of innovation, innovation proxies and methodologies used in the empirical literature. Thus, our main objective here is to explore this relation empirically using data from the Community Innovation Surveys (hereafter, CIS) of French firms during the period 1992 to 2004. We focus on a panel of 1,074 firms obtained by merging three waves of the CIS with the French annual enterprise survey from 1992. The CIS makes it possible to analyse the impact of different types of innovation (product versus process) on firm growth and to use both qualitative and quantitative proxies for innovation. For the empirical analysis, we adopt a Gibrat-like model and exploit different specifications and estimation techniques to check the consistency and robustness of our results.

Our findings confirm that innovation has a positive effect on the rate of firm growth. In particular, our results show that if the effects of product innovation and process innovation are disentangled, the relationship with firm growth remains strong and positive. We find also that innovation is of crucial importance for high-growth firms. Our results are robust to different specifications of growth dynamics.

The paper is organised as follows. Section 1 provides a survey of the literature and defines our research questions; Section 2 presents the data and variables used; Section 3 describes the methodology; Section 4 comments on the results;, and Section 5 concludes the paper.

Survey of the literature and research questions

A natural starting point for an investigation of the determinants of firm growth is the wellknown Gibrat's Law framework. The 'law of proportionate effects', proposed by [START_REF] Gibrat | Les inégalités économiques[END_REF], argues that the firm size distribution is highly skewed, presumably following a lognormal function. Gibrat's framework assumes that firm size follows 'random walk': there are no determining factors that explain differences in firm growth. It has been shown that the rates of growth of large and/or old firms are very often erratic and, consequently, unpredictable (see [START_REF] Geroski | The Growth of Firms in Theory and in Practice[END_REF]. This means, for instance, that for large firms, there is no deterministic impact of innovation activity on their growth. It has been acknowledged that Gibrat's Law cannot be considered a general law, but rather a dynamic rule that is valid for large and mature firms [START_REF] Sutton | Gibrat's legacy[END_REF]. Thus, its validity cannot be taken for granted ex ante [START_REF] Lotti | Defending Gibrat's Law as a long-run regularity[END_REF]. There is a large recent literature that deals with the theoretical coherence and empirical relevance of Gibrat's Law [START_REF] Cefis | Testing Gibrat's legacy: A Bayesian approach to study the growth of firms[END_REF][START_REF] Coad | The Growth of Firms: A Survey of Theories and Empirical Evidence[END_REF]. Suffice to say that Gibrat's law is at odds with most of the latest empirical studies on the existence and persistence of heterogeneity in firms, including in their performance [START_REF] Colombelli | The persistence of innovation and path dependence[END_REF]. 2 [START_REF] Bottazzi | Corporate growth and industrial dynamics: evidence from French manufacturing[END_REF] discuss the properties of the growth rate distributions in French manufacturing industry data and find significant differences in firm sizes across industries.

Among the studies that deal explicitly with innovation/growth links at firm level, many are inspired by [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF]. Mansfield's work was the first rigorous empirical assessment of the complex relationship between growth and innovation at the firm level. [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF]Mansfield : 1042) ) asks 'How much of an impact does a successful innovation have on a firm's growth rate?' He first observed that firms that had achieved significant innovations grew more rapidly, and at rates of average growth that were twice as fast as in other firms. He noted also that the estimated effect depended on the industry under consideration and argued that innovation has a bigger impact on the growth rates of small firms. Mansfield's paper, which deals with the 'processes of firm formation, growth and decline' [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF](Mansfield, : 1043)), is the first empirical evolutionary approach to the determinants of firm growth. While many firms decline and exitin some cases soon after entry -others grow, innovate and build a capital of basic competencies (or capabilities) necessary to survive and succeed. These positive links are confirmed by [START_REF] Scherer | Corporate Inventive Output, Profits, and Growth[END_REF], [START_REF] Mowery | Industrial Research and Firm Size, Survival, and Growth in American Manufacturing, 1921 -1946: An Assessment[END_REF][START_REF] Geroski | The Growth of Firms in Theory and in Practice[END_REF][START_REF] Geroski | Do Innovating Firms Outperform Non-innovators?[END_REF] and are the core of the evolutionary approach [START_REF] Dosi | Statistical Regularities in the Evolution of Industries. A Guide through some Evidence and Challenges for the Theory[END_REF][START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF][START_REF] Winter | Schumpeterian competition in alternative technological regimes[END_REF]. Innovation is assumed to be 'good' for growth and survival, but only under certain conditions. Firms need to capture the value from innovation [START_REF] Teece | Profiting from technological innovation: Implications for integration, collaboration, licensing and public policy[END_REF] and, in some sectors, to implement methods to improve performance (e.g. economies of scale or scope). Innovation creates firm advantage over competitors, which results in increased market share, the mechanism that transforms innovation into growth. Some authors argue that technical innovation promotes firm growth through a second (although less important) way.

They argue that the process of technological innovation transforms the firm's core competencies [START_REF] Geroski | The profitability of innovating firms[END_REF][START_REF] Lee | A theory of firm growth: Learning capability, knowledge threshold, and patterns of growth[END_REF], making the firm more able to innovate and/or cope with the selection environment. In a sense, the study addresses the two faces of research and development (R&D): innovation and learning (an idea that stems from the famous analysis by [START_REF] Cohen | Innovation and Learning: The Two Faces of R&D[END_REF].

A recent strand of studies on different types of firms provides new empirical insights into the effects of innovation on firm performance. For example, [START_REF] Audretsch | Innovation, growth and survival[END_REF] looks at the postentry performance of new firms. He proves that in industries where innovative activity is important, the probability of a new entrant surviving is lower than in industries where innovation is less important. He finds also that entrants that survive show higher growth rates. 3 [START_REF] Cefis | A matter of life and death: innovation and firm survival[END_REF] examine the effects of innovation on survival using data on Dutch manufacturing firms. They show that firms benefit from an innovation premium that extends their life in the industry, independent of firm age or size. Process innovation seems to have a particularly distinctive effect on survival. [START_REF] Cainelli | Innovation and economic performance in services: a firm-level analysis[END_REF], using CIS data on Italian service sectors, confirm that innovation activities have a positive impact on firm growth and productivity. [START_REF] Coad | Innovation and firm growth in high-tech sectors: A quantile regression approach[END_REF] use a large sample of high-tech firms and find that growth may or may not be related to innovation activity (as measured by firm patenting activity). They employ quantile regression techniques and note that innovation is more crucial for growth in 'rapid-growth' firms. Along the same lines, [START_REF] Cassia | Firms'growth: Does the innovation system matter?[END_REF] and [START_REF] Cassia | Do universities knowledge spillovers impact on new firm's growth? Empirical evidence from UK[END_REF] provide evidence that university knowledge inputs and outputs are important determinants of UK entrepreneurial firms' growth. [START_REF] Ernst | Patent applications and subsequent changes of performance: evidence from time-series cross-section analyses on the firm level[END_REF], in his study of growth in German firms, conducts a quantitative analysis and finds that, after a lag of some two to three years following patent application to a specific patent system (national or European), sales increase . This would seem to underline that the effects of invention on a firm's growth performance are not immediate, but rather emerge soon after the invention has been implemented (note that mere application for a patent does not mean the invention is implemented). [START_REF] Corsino | Product Innovation and Firm Growth: Evidence from the Integrated Circuits Industry[END_REF] uses new (and unique) types of data. He gathered information on new semiconductor devices commercialised during the period of [1998][1999][2000][2001][2002][2003][2004] from producers around the world. He carried out a corporate level econometric analysis and found that the most recent innovations have a more significant effect on firm growth. When he conducted the estimations at the business-unit level, the influence of product innovation on business-unit growth is higher than found at the corporate level. Therefore, he stresses the importance of the level of observation in trying to identify an association between growth and innovation.

This literature survey provides some general findings. The studies reviewed mostly provide evidence in favour of a positive and significant relation between firm innovation and firm growth. This finding is consistent across the use of different proxies for innovation. As a consequence, it is tempting to consider this finding a stylised fact. Only a few studies found results mitigating the relationship between innovation and growth. 4 Of course, innovation is only one factor among several explanatory variables and there are some important issues that remain unaddressed or neglected by the current literature. 5First, the type of innovation (product versus process) is only infrequently taken account of in the literature. Some studies note that new products have an impact [START_REF] Roper | Product Innovation and Small Business Growth: A Comparison of the Strategies of German, UK and Irish Companies[END_REF]; others consider each type of innovation [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF]. Thus, it might be interesting to assess the effect of each type of innovation within the same framework. In this context, CIS data are useful in providing a great deal of information on the types of invention, and differentiate between product and process innovation. The paper by [START_REF] Mairesse | Using Innovations Surveys of Econometric Analysis[END_REF] demonstrated the richness of the data collected through the CIS.

Second, the literature uses different specifications for product and process innovation, and innovation proxies (R&D, patents). To cope with this problem, one of the original contributions of the present paper is that we use additional and complementary indicators based on CIS. This enables us to test the robustness of the innovation effect on growth by changing the definition of the innovation variables. For instance, we use qualitative as well as quantitative variables for innovation (e.g. share of innovative products and marginally modified products in turnover). Also, [START_REF] Coad | Innovation and firm growth in high-tech sectors: A quantile regression approach[END_REF] raise an interesting issue. They note that innovation is more crucial for 'rapid-growth' firms. Given this perspective, quantile regression is essential to test the effects of innovation on firms' growth rates.

Finally, as some scholars have noted (in particular [START_REF] Geroski | Corporate Growth and Protability[END_REF], the specification of the dependent variable is important and may be crucial. Many studies seem not to attach much importance to their choice of index of performance, citing value-added rate of growth, sales growth, or other factors. This choice would seem to matter for testing the sensitivity of the results to the definition of the growth variable. 6 In our view, these issues have been inadequately explored and documented in the literature dealing with the relation between innovation and firm growth, and summarized in Table 0, but should be considered critical for an accurate understanding of how this relation works. The present paper contributes to the literature by providing new means to deal with these issues. It focuses on French industry in the period 1992-2004. Our contribution lies in the use of different waves of the CIS for the French industries, and the application of different econometric methods to this research question. In particular, the use of quantile regression should capture the crucial important of innovation for high-growth firms.

INSERT TABLE 0 ABOUT HERE

Data description

This empirical study focuses mainly on the long-term, post-innovation growth performance of innovative firms, differentiated by type of innovation, compared with non-innovative firms.

The sample used for the econometric analysis was constructed from CIS7 data and 6 Another difficult question that is not dealt with here, but warrants more attention is that the timing of the innovation effects (noted in particular by [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF][START_REF] Geroski | The Growth of Firms in Theory and in Practice[END_REF][START_REF] Geroski | Do Innovating Firms Outperform Non-innovators?[END_REF] is extremely important for explaining the effects on growth (see [START_REF] Coad | Firm Growth: A Survey[END_REF]. Are these effects relevant in the short or medium/long term? [START_REF] Geroski | Do Innovating Firms Outperform Non-innovators?[END_REF] show that the effects of innovation on firm performance are realised vey soon after the firm innovates.

complemented by data from the 1992 annual enterprise survey. 8 We obtained an unbalanced panel of 1,074 firms covering four time periods. 9 Below, we discuss how we dealt with the data sources and sampling issues and describe sample and the variables derived.

Sources and sampling

Our analysis is based on a data set obtained from merging three waves of the CIS: CIS2 (1994)(1995)(1996), CIS3 (1998CIS3 ( -2000) ) and CIS4 (2002CIS4 ( -2004)). We collected information that enables us to construct variables measuring the firm growth rates over our study period, and their innovation activities during the same time period. We used CIS information on firm turnover, number of employees, and activity (identified with NACE codes). 10 This information is available every second year, for each of three year time periods covered by the CIS. To capture innovation activity, the surveys include a set of questions asking whether the firm innovated or not in the three years prior to the survey. Thus, we can access information on product and process innovators for the periods 1994-1996, 1998-2000 and 2002-2004. We merged the datasets by identifying each statistical unit according to its enterprise code (the enterprise is the legal unit), and retaining it in the final data set of firms that responded to all three CIS. We restrict our analysis to the sample that resulted from the merger.

Because some information on turnover and size is missing in the CIS for 1992, another set of data is used to provide more information about the firms obtained from merging the three waves of the CIS. We use the annual enterprise surveys to complete this missing 1992 information, notably for turnover, size and industrial activity.

We obtained a total of 1,074 manufacturing firms, with 20 or more employees, for the three time periods: t1, 1994 to 1996; t2, 1998 to 2000 and t3, 2002 to 2004 (see Table 1 for the structure of the dataset).

INSERT TABLE 1 ABOUT HERE

It should be noted that the raw data from the three waves of the CIS that we use, have a very different construction. These surveys are not conducted at regular intervals and do not cover the same sample of firms; the samples are constructed using stratified sampling methods in which firm size and industry are key parameters; and the sampling methodology differs from one wave to another. This implies that the firms surveyed in successive waves may not be the same.

As a result, it is difficult to detect which firm entries and exits are due to economic causes and which are caused by random sampling. We are not able to evaluate the general characteristics of firms that exit and enter in our sample (i.e. we cannot analyse attrition). For example, in CIS2 and CIS3, census data are used to identify firms with at least 500 employees and a stratified random sample (by size and economic activity) is applied for firms with less than 500 employees. The same rules are used for CIS4, but a cut-off point of 250 employees is applied. In addition, some CIS waves use a minimum of 10 employees as the criterion for inclusion, while others include apply the criterion of 20 employees. CIS2 systematically includes firms with more than 20 employees, while CIS4 includes firms with at least 10 employees. In CIS3, stratification by size differs: for manufacturing sectors the firms surveyed have a minimum of 20 employees, but in the services sector firms with a minimum of 10 employees are included. Moreover, while the first and the last waves of the CIS apply exclusively to firms in the manufacturing industry, CIS3 and CIS4 include services (services in the widest sense are included in CIS4; CIS3 includes only selected services fields).

Given these limitations, we think that our sample of 1,074 firms is a good approximation of CIS firms. Table 2 provides information on the distribution of the data by sector. Given that we use CIS data which provide information only on industrial firms, our final dataset includes industrial activities. This is in line with previous work on firm growth and innovation [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF]Evans, 1987aEvans, , 1987b)). Electrical engineering, wood, paper and printing, chemical, metal and machinery activities account for more than 10% each, with the remaining economic activities represented in our sample accounting for less than 10% of the observations. A similar distribution characterises the CIS, with the exception of textile that is less represented in our sample.

INSERT TABLE 2 ABOUT HERE

Table 3 shows the sample and CIS distribution by size in the period under scrutiny. Our sample comprises mainly large firms with more than 250 employees (approximately 75.76 %). Medium-sized firms represent about 19 % of the sample, with small firms with less than 50 employees accounting for 5.34 %. The distribution by size of CIS firms is similar: large firms with more than 250 employees account for 80.34 %, medium-sized firms represent about 10.96 %, and small firms with less than 50 employees represent about 8% of the total.

INSERT TABLE 3 ABOUT HERE

Table 4 compares the proportion of innovative firms in CIS and in our sample. It shows that firms in our sample are in general less innovative than the firms surveyed in CIS. In particular, 43.2 % of the companies of our sample are product or process innovators; for the total manufacturing firms surveyed in CIS, this percentage is 52.3 %.

INSERT TABLE 4 ABOUT HERE

Definition of the variables

Growth rates

For each year, starting from 1994, we compute firm growth rates following two different methods.

We first define a firm's rate of growth as the log-difference of size:

) ln( ) ln( 1 , , ,    t i t i t i S S Growth
, where S i,t is firm turnover at time t, deflated using the French GDP deflator (base year 2000)

drawn by Thomson Datastream, and S i,t-1 is its lagged value 11 .

Second, we compute the compound average growth rate (CAGR), which provides a theoretical growth rate, assuming steady growth over the period t 0 -t n, and hence takes into account that each time period covers more than one year.12 1 0 ,

, 0 1 ,            t i Turn tn i Turn CAGR t tn t i
11 Firm growth can be measured using various indicators, such as sales, employment or assets. However, as Table 0 suggests, the stream of literature related to this paper analysing the effects of innovation on firms' growth adopts sales as a proxy for size. Also, while the links between innovation and employment, and between innovation and assets, undoubtedly are important, they refer to rather different theoretical backgrounds aimed at capturing different dynamics, which are not the focus of this paper.

Figure 1 shows the distribution of firm growth rates. It shows that the empirical distribution of growth rates in our sample is more Laplacian than Gaussian. This is in line with work that analyses the distribution of firm growth rates [START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF][START_REF] Bottazzi | Why are distributions of firm growth rates tent-shaped?[END_REF][START_REF] Castaldi | The patterns of output growth of firms and countries: Scale invariances and scale specificities[END_REF]. In particular, the mean growth rate for the whole period is approximately 20% for both measures used, but their standard deviations show wide variations because of the large time span (1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004). Consequently, it is useful to analyse the distribution of growth rates as a function of innovation distribution. We expect innovation to have a positive impact on firm growth.

Innovation

The goal of our analysis is not an extensive overview of the corporate growth of the firms in the CIS samples, but observation of the interactions between innovation and growth.

Consequently, the definition of our innovation variables is crucial.

We employ two main variables: the first measures product innovation; the second measures process innovation. In the CIS, a firm is considered to be 'innovative' if, over a given period of time (the previous three years), it introduced a new product or a new process. This information is gathered through a set of:

(1) dichotomous variables that reveal whether or not the firm produced an innovation during the period covered by the survey;

(2) quantitative variables based on firms' responses to a question about the percentage of sales due to the commercialization of new products (new goods and services). 13 Since these variables can be used to proxy for the commercial success of innovations, they are being used increasingly in the empirical literature [START_REF] Mairesse | Using Innovations Surveys of Econometric Analysis[END_REF].

While product innovations are associated with more radical technologies and are expected to result in higher growth rates because of their higher economic returns, process innovations are based on more defensive technological strategies. However, the effects of product and process innovations are linked indirectly and lead to new types of products [START_REF] Barras | Interactive innovation in financial and business services: The vanguard of the service revolution[END_REF]). We constructed a set of dichotomous variables: Ino, taking the value 1 if the firm has introduced either a product or a process innovation; 13 CIS questionnaire.

Inop, taking the value 1 if the firm has introduced a product innovation; Inoc, taking the value 1 if the firm has introduced a process innovation.

A second set of information on innovation provided by CIS is quantitative and estimates the share of innovative products and marginally modified products in turnover (respectively Inoprod and Inoproc). However, while firms generally are able to quite easily quantify the share of turnover from product innovation, they are often less able to give the same information for process innovation. For this reason we use only Inoprod and drop Inoproc.

Descriptive statistics are presented in Table 5.

INSERT TABLE 5 ABOUT HERE

Methodology

We start our empirical analysis by comparing the growth rate distribution among different firm types -innovative vs non-innovative firms. To this end, we perform a two-sample Fligner-Policello robust rank order test. This test is a useful alternative to the Mann-Whitney-Wilcoxon test as in the Fligner-Policello test the assumption of the underlying sample distributions being the same is dropped. 14 This test confirms the null hypothesis that the two groups of firms, innovating and non-innovating, are sampled from the same population. We define innovating firms as those firms that introduced either a product or a process innovation during the period under scrutiny. As we are also interested in differentiating between the roles of product and process innovation, we also distinguish between product and process innovating firms. The results of the Fligner-Policello test are presented in Table 6. The test rejects the null hypothesis of an equal distribution between innovators and non-innovators.

The same null hypothesis is also rejected for product innovators and non-innovators, and process innovators and non-innovators. These results suggest that innovating firms generally perform better than non-innovators.

INSERT TABLE 6 ABOUT HERE

After testing for whether innovation can be considered a source of growth differentials, we analyse the effects of innovative activities on firm growth. Studying the determinants of firm growth poses some methodological issues, in particular, with respect to how they relate to the distributional properties of growth rates, and their persistence over time. Below, we discuss how we address these methodological issues.

In the empirical analysis, we use a Gibrat-like model that includes firm size as an explanatory variable. The empirical literature uses two different specifications for testing Gibrat's Law.

Since our objective is not to test the validity of the law, but to verify the impact of innovation on firm growth, we use both specifications in order to check the consistency and robustness of our results to the use of different specifications and estimations techniques.

The first specification to model growth in firms' turnover as a function of firm innovation follows the original logarithmic representation in Gibrat's Law:

    t i t j t i t i t i Ino S S , 1 , 3 1 , 2 1 , ln ln                 (1)
where S i,t and S i,t-1 represent turnover (deflated) for firm i at time t and t-1, respectively, Ino i,t-1 is product or process innovation for firm i at time t-1. ω j and ψ t represent a set of industry 15 and time dummies, controlling respectively, for macroeconomic and time fluctuations. The inclusion of the lagged dependent variable in the model requires dynamic estimation techniques. We have a large N and small T panel data set. Following the literature on dynamic panel estimators [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations[END_REF][START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF][START_REF] Bond | Dynamic panel data models: a guide to micro data methods and practice[END_REF], equation (1) is estimated using the Generalised Method of Moments (GMM) methodology. In particular, to increase efficiency, we use the GMM-System (GMM-SYS) estimator developed by [START_REF] Blundell | Initial Conditions and Moment Restrictions in Dynamic Panel Data Models[END_REF]. Blundell and Bond demonstrate dramatic improvement in the performance of the system estimator compared to the usual first-difference GMM estimator developed by [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations[END_REF]. By using instrumental variables in levels with lagged first-differenced terms, this approach, allows us to control for endogeneity of the innovation variables.

Transforming Equation (1), we obtain an alternative specification of Gibrat's Law as follows:

  t i t i t i t i t i Ino S Growth , 1 , 3 1 , 2 1 , ln                .
(2) Equation ( 2) can be estimated using traditional panel data techniques implementing the fixed effects estimator. As a robustness check, we also estimate the model using Ordinary Least Squares (OLS). Finally, to provide further evidence on the relationship between firm growth and innovation, we estimate Equation ( 2) by means of quantile regressions. This approach is 15 The industrial context is important because innovation is 'industry context specific' [START_REF] Dosi | Sources, Procedures, and Microeconomic Effects of Innovation[END_REF]. Thus, we need to control for industry effects.

relevant for our analysis since growth rate distributions appear to be fat-tailed (see Figure 1).

In the OLS and quantile regressions we also include a set of industry dummies in order to control for sectoral specificities.

A second methodological issue that needs to be taken into account in our analysis is related to serial correlation in firms' annual growth rates. While debate on this issue remains ongoing, previous works have found evidence of persistence in growth rates [START_REF] Chesher | Testing the Law of Proportionate Effect[END_REF][START_REF] Geroski | Corporate Growth and Protability[END_REF][START_REF] Bottazzi | Explaining the Distribution of Firms Growth Rates[END_REF][START_REF] Coad | Firm Growth: A Survey[END_REF][START_REF] Coad | Firms growth: empirical analysis[END_REF]. To control for any growth autocorrelation, we test an additional specification that includes the lagged growth rates as an explanatory variable. Thus, an alternative specification of our model can be written as:

  t i t j t i t i t i t i Ino S Growth Growth , 1 , 4 1 , 3 1 , 2 1 , ln                   
(3) Since Equation (3) includes the lagged dependent variable among the explanatory variables, it is estimated using the GMM-SYS methodology discussed above.

Results

The results of the econometric estimations are presented in Tables 789101112, which show the results for different equations, estimation techniques and variables.

General results

We start by commenting on the results of the estimations related to equation (1), which represents Gibrat's Law in its classical form (Table 7). Our basic results confirm that innovation has a positive and significant impact on the rate of firm growth. The variable Ino, which takes the value 1 if the firm has introduced either a product or a process innovation, is positively and significantly (p<0.05) related to the rate of firm growth. We also wanted to figure out the nature of the impact of innovation on firm growth. If we consider product (Inop) and process innovation (Inoc) separately, we find that both types of innovation have a positive and significant impact on firm growth (p<0.05 and p<0.01, respectively). We also test the sensitivity of the impact of product innovation on firm growth to the definition of the innovation variable. If innovation is expressed as a quantitative variable (Inoprod), we observe that the coefficient remains positive and significant (p<0.10).

Our results also confirm that small companies grow more than large ones, as shown by the coefficient of Ln(S ,t-1 ), which is found to be less than 1 and significant at the 1% level.

In order to shed further light on the relationship between innovation and growth, Equation ( 2) analyses an alternative specification of . This can be estimated by means of quantile regressions, which allow us to analyse the heterogeneity in the returns to innovation. Table 8 shows the results obtained by using Ino as a proxy for innovation activities. Let us recall that this variable is related to both product and process innovation. The evidence obtained by applying the quantile regression suggests that, although innovation exert a positive effect on firms' growth, this effect is stronger for firms in the uppermost quantile than for firms in the lower quantiles. This means that, for high-growth firms, innovative activity makes an important contribution to their superior growth performance (in line with the findings in [START_REF] Coad | Innovation and firm growth in high-tech sectors: A quantile regression approach[END_REF].

In Tables 9 -11 we disentangle the differential impact of product and process innovation from the general effect. Actually, as it is showed in Table 9, product innovation appears to have a stronger impact for firms in the uppermost quantile. This evidence is also confirmed when we use as an explanatory variable an alternative definition of product innovation (Table 10), although the results are less marked when we use the quantitative variable (Inoprod). The difference with the previous estimation clearly is due to the differences in the nature of the variables (quantitative versus categorical). Indeed, Inoprod represents an estimation of the percentage of sales due to the commercialisation of new products. As Mairesse and Mohnen (2010) note, 16 this variable is less reliable than qualitative variables since firms may encounter difficulties in quantifying the share of their turnover due to the commercialisation of product innovations. Nevertheless, the significant coefficients in Table 10 suggest that the results are in line with the previous estimations.

When one focuses on the specific effect of process innovation (Table 11), the results of the quantile regression suggest instead that the impact is stronger for firms at the 25 th percentile than for the other ones. All in all, these results provide further support to the well known framework linking innovation to firms' lifecycles (Abernathy and Utterback, 1978). 16 These two authors analyse the quality of CIS data noting that: 'Many of the variables, qualitative and quantitative as well, are of a subjective nature, being largely based on the personal appreciation and judgment of the respondents. One of the most interesting variables and that is relatively well known, the share in total sales due to new products, has, for example, values that tend to be rounded (10%, 15%, 20%, …), attesting to its subjective nature and suggesting that perhaps we should treat it as a categorical variable and not make too much out of its continuous variations' (Mairesse and Mohnen, 2010: 9).

According to this frame of analysis, firms in the fast growing stages of their lifecycle are mostly focused on the introduction of product innovations which make it possible to gain further market shares and sustain the growth process. On the contrary, firms in the maturity stage characterized by decreasing growth rates are more interested in the introduction of process innovations which allows for preserving competitiveness by lowering production costs.

Robustness checks

To check for the robustness of our results we propose a number of different estimations. First of all, all the estimations presented in Tables 7 through 12 have been run by using an alternative measure of firm growth rates (CAGR).

All the results are robust to the different measures of firm growth rates, but the coefficients when Growth is the dependent variable are higher than when CAGR is the dependent variable. This can be interpreted using the descriptive statistics reported in Table 6. Since CAGR is calculated on the basis of the assumption of steady growth, it provides a relatively smooth picture of the growth process versus that obtained using the log-difference indicator.

The average value of CAGR is lower than the value of Growth, and for this reason, the effects of innovation on CAGR also appear quite smooth.

It is also important to check the robustness of our analysis by estimating Equation (2) using alternative estimation techniques other than quantile regression. In particular we show the results obtained by implementing OLS, fixed and random effects (Tables 891011). We find again that small companies grow more than large ones, shown by the negative and significant coefficient of Ln(S i,t-1 ). More important, our results confirm that innovation has a positive and significant impact on firms' growth rates in all the estimations, a result that is robust to the use of alternative estimators. For product innovation (Tables 9 and10) and process innovation (Table 11), we find similar and even more robust results. When we test the sensitivity of the impact of product innovation on a firm's growth, to the definition of the innovation variable, we find that the results are less robust if we use the quantitative variable (Inoprod).

Finally, we test an additional specification (see Equation 3) in order to control for autocorrelation among growth rates (Table 12). While we do not find any serial correlation in annual growth rates for the firms in our sample, our basic results related to the relationship between innovation and growth are confirmed when we use this alternative specification.17

INSERT TABLE 7 to 12 ABOUT HERE

Conclusion

Our empirical study based on French CIS data for the period 1992-2004 enables us to complement the literature on firm growth and to respond to the issues noted in the introduction. Our main findings can be summarised as follows.

First, innovative firms (whatever the type of innovation) produce more growth than noninnovative firms.

Second, the estimation techniques mostly yield quite robust results for the qualitative innovation variables. The exception is the Inoprod variable which is the quantitative innovation variable. The use of a quantitative variable for product innovators sometimes results in non-significant outcomes due to the peculiarity of this variable.

Third, we use two indicators for firm growth. Our study shows that the results obtained are definitively robust to the dependent variable measurement method. In general, the coefficients are higher with Growth than with CAGR.

Fourth, the results of the quantile regressions are in line with other studies [START_REF] Coad | Innovation and firm growth in high-tech sectors: A quantile regression approach[END_REF]: the effects of innovation on growth are stronger on firms with the highest growth rates.

The results of our analysis have clear implications for innovation policy. First, since our analysis consider the output of innovation activities rather than the typical input measure such as R&D investments, we would propose that innovation policies should care not only about the support to R&D investments (like tax credits policies), but they should also care about the output of the innovation process, and in particular about the differential impacts of product and process innovation.

Moreover, the effects of innovation appears to be different also across different quantiles. In particular, when considering innovation outputs as a whole, this variable shows the higher coefficient for firms in the uppermost quantile. However, when distinguishing between process and product innovation, our results suggest that product innovation exert a stronger impact for firms in the uppermost quantile, while process innovation shows a higher coefficients for firms in the lowermost quantile. This would suggest that targeted innovation policies should care about the firms' idiosyncratic features, and in particular about their relative position in the firm lifecycle.

Our analysis also leaves some interesting questions unanswered, which would open some avenues for future research. For example, it might be interesting were policy makers to experiment with policy tools in order to analyse their effectiveness. With this objective in mind, we would add other variables to our panel model (e.g. whether firms receive tax credits, and among those that do whether they experience higher growth). Within the framework proposed, it is possible to provide a more accurate assessment of public technology support.

While the present study provides new insight on the impact of innovation on firm performance in terms of growth, it would be interesting in future research to analyse the persistence of innovation. For example, in the present study we do not examine whether some firms innovate persistently while others do not. Our longitudinal data would allow us to determine whether firms that persistently innovate grow more than sporadic innovators.

Appendix. Table 0. Empirical studies on the relation between firm growth and innovation

Study

Country and time period

Measure for firm size and growth rate (Type of data)

Measure for innovation activity

Main results [START_REF] Mansfield | Entry, Gibrat's law, innovation and the growth of firms[END_REF] USA, 10 enterprises and 10 aggregated industries

(

Figure

  Figure 1. Growth rates distribution

Table 1 . The structure of the final panel

 1

		1916-1954)	Minimum efficient size, relative size variation (Individual data)	Successful innovations determine if a firm is an innovator or not	The firms that carried out significant innovations grew more rapidly than the others
	Geroski et al.(1993)	U-K large quoted firms (1976-1982)	Profit margins and indirect measure of size: market concentration (Panel of 721 firms)	Number of innovations produced by each innovating firm	The number of innovations (number of patents) has no impact on corporate growth
					Patent
	Ernst (2001)	German machine tool manufacturers (1984-1992)	Sales (panel of 50 firms)	applications (German and European patent	Patents increase sales with a 2 or 3 years lag
					system)
	Del Monte and Papagni (2003)	Italian manufacturing firms (1989-1997)	Return on sales (panel of 500 firms)	Research Intensity	Correlation between Growth rate and Research Intensity
					The introduction
	Cefis and Marsili (2005)	Netherland manufacturing firms (1996-2003)	Survival time (panel of 3 275 manufacturing firms)	of an innovation on the market and innovation	The innovating firms extend their life in the industry
					type
	Coad and Rao (2008)	Large sample (world) of high-tech firms (1963-1998)	Total sales (panel of 4012 firms in high-tech sectors)	Innovativeness expenditures) index (measure of patent activity and R&D	Innovation more crucial for the growth of 'rapid-growth firms'
	Cassia et al. (2009)	U-K public companies (1995-2006)	Total sales (Panel of 200 firms)	Universities, Outputs Knowledge, Inputs and	Effects on firm growth
	Corsino and Gabriele (2010)	Worldwide firms from (1998-2004) semiconductors	Total sales (panel of 95 firms)	Innovations counts	Product innovations affect firm growth
	year	Time	Growth t	Growth t-1	Inno t	Inno t-1
	1992-1994	T0	G 0	.	.	.
	1994-1996	T1	G 1	G 0	Inno 1	.
	1998-2000	T2	G 2	G 1	Inno 2	Inno 1
	2002-2004	T3	G 3	G 2	Inno 3	Inno 2

Table 2 . Sample distribution by industry

 2

	Nace Rev 1.1	Sample	CIS
		%	%

Table 3 . Sample distribution by size

 3

	Size class	Sample	CIS
		%	%
	20 -49	5.34	8.69
	50-249	18.90	10.96
	>250	75.76	80.34
	Obs	100	100

Table 4 . Proportion of innovative firms in CISs and in the sample used in the empirical analysis (%)

 4

	Sample	CIS
	%	%

Table 5 . Summary statistics

 5

	Variable	Obs.	Mean	Std. Dev.	Min	Max
	ln(S i,,t )	3222	7.417175	1.756326	1.410513	14.49669
	ln(S i,t-1 )	2822	7.591357	1.600403	2.633156	14.48141
	Growth	2822	0.0854136	0.2754607	-1.516976	2.377159
	Lag_growth	2750	0.1577891	1.512188	-3.521861	10.91398
	CAGR	2822	0.0545427	0.1733176	-0.531626	2.282415
	Ino	2390	0.6355649	0.4813721	0	1
	Inop i,t-1	2380	0.4331933	0.4956209	0	1
	Inoc i,t-1	2397	0.5127242	0.4999424	0	1
	Inoprod i,t-1	1025	-2.490742	1.123468	-4.61512	0

Table 6 . Two-Sample Fligner-Policello Robust Rank Order Test

 6

	Growth	Obs.	Average	Index of	u	2-tailed p-
			placement	variability		value
	Non-innovators	610	2.1e+02	1.1e+07	-3.117	0.0018
	Innovators	463	3.4e+02	1.3e+07
	Non-innovators	610	1.8e+02	8.7e+06	-2.770	0.0056
	Product Innovators	402	3.4e+02	1.1e+07
	Non-innovators	610	1.9e+02	9.8e+06	-2.981	0.0029
	Process Innovators	423	3.4e+02	1.2e+07
	CAGR	Obs.	Avarage	Index of	u	2-tailed p-
			placement	variability		value
	Non-innovators	610	2.0e+02	1.1e+07	-3.290	0.0010
	Innovators	463	3.4e+02	1.3e+07
	Non-innovators	610	1.8e+02	8.8e+06	-2.953	0.0031
	Product Innovators	402	3.4e+02	1.1e+07
	Non-innovators	610	1.9e+02	9.9e+06	-3.160	0.0016
	Process Innovators	423	3.4e+02	1.2e+07

Table 7 . Estimates of the growth of firms' turnover (equa. 1).

 7

		(1)	(2)	(3)	(4)	(5)
	VARIABLES	GMM-SYS	GMM-SYS	GMM-SYS	GMM-SYS	GMM-SYS
	Ln(S ,t-1 )	0.986***	0.976***	0.977***	0.975***	0.927***
		(0.0155)	(0.0150)	(0.0148)	(0.0146)	(0.0328)
	Ino i,t-1		0.0352**
			(0.0154)
	Inop i,t-1			0.0307**
				(0.0136)
	Inoc i,t-1				0.0394***
					(0.0136)
	Inoprod i,t-1					0.0138*
						(0.00793)
	Constant	0.0694	0.113	0.250**	0.117	0.565**
		(0.0942)	(0.104)	(0.114)	(0.0878)	(0.235)
	D_Industry	yes	yes	yes	yes	yes
	D_Year	yes	yes	yes	yes	yes
	Observations	2822	2367	2357	2374	1015
	Number of ID	1073	1070	1070	1072	600
	Notes:*** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses.

Table 8 . Estimates of the growth rate (equa. 2).

 8

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
		OLS	FE		RE				Quantile
		Growth	CAGR Growth CAGR Growth	CAGR		Growth			CAGR
	VARIABLES							q25	q50	q75	q25	q50	q75
	Ln(S ,t-1 )	-0.0211*** -0.0123*** -0.430*** -0.264*** -0.0284*** -0.0189*** -0.00674*** -0.00879*** -0.0163*** -0.00311** -0.00453*** -0.00870***
		(0.00371) (0.00222) (0.0203) (0.0117) (0.00435) (0.00275) (0.00241) (0.00226) (0.00380) (0.00154) (0.00119) (0.00225)
	Ino i,t-1	0.0451*** 0.0253*** 0.0317** 0.0148* 0.0481*** 0.0270*** 0.0312*** 0.0252*** 0.0389*** 0.0150*** 0.0130*** 0.0208***
		(0.0114) (0.00684) (0.0148) (0.00848) (0.0118) (0.00708) (0.00613) (0.00783) (0.00682) (0.00450) (0.00450) (0.00670)
	Constant	0.0927** 0.0545** 3.680*** 2.264*** 0.137*** 0.0960*** -0.0234	0.0450** 0.131*** -0.0126 0.0231** 0.0683***
		(0.0377) (0.0226) (0.169) (0.0968) (0.0454) (0.0289) (0.0261)	(0.0203) (0.0278) (0.0128) (0.0104)	(0.0183)
	D_Industry	yes	yes	no	no	yes	yes	yes	yes	yes	yes	yes	Yes
	D_Year	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	Yes
	Observations	2367	2367	2367	2367	2367	2367	2367	2367	2367	2367	2367	2367
	R-squared/pseudo 0.073	0.065	0.329	0.347	0.1274	0.124	0.0296	0.0422	0.0664	0.0322	0.0457	0.0711
	Number of ID			1070	1070	1070	1070

Ino i,t-1 is a dummy variable taking the value 1 if the company has introduced either a new product or a new process on the market. Notes: *** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses.

Table 9 . Estimates of firm growth rate (measured by growth and GAGR)

 9 is a dummy variable taking the value 1 if the company has introduced a new product on the market. Where Growth is measured using the first difference equation Notes:*** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses.

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
		OLS	FE		RE				Quantile
		Growth	CAGR	Growth	CAGR	Growth	CAGR		Growth			CAGR
	VARIABLES							q25	q50	q75	q25	q50	q75
	Ln(S ,t-1 )	-0.0204*** -0.0117*** -0.430*** -0.264*** -0.0273*** -0.0179*** -0.00468 -0.00991*** -0.0144*** -0.00228 -0.00498*** -0.00782***
		(0.00366) (0.00220) (0.0204) (0.0117) (0.00431) (0.00273) (0.00329)	(0.00281) (0.00376) (0.00190) (0.00146)	(0.00158)
	Inop i,t-1	0.0413*** 0.0212*** 0.0329** 0.0124 0.0424*** 0.0211*** 0.0312*** 0.0325*** 0.0367*** 0.0153*** 0.0163*** 0.0202***
		(0.0109) (0.00654) (0.0139) (0.00797) (0.0113) (0.00678) (0.00945)	(0.00882)	(0.0110) (0.00580) (0.00344)	(0.00493)
	Constant	0.0957** 0.0553** 2.803*** 1.734*** 0.281*** 0.181***	-0.0611	0.128***	0.258***	-0.0298	0.0646***	0.137***
		(0.0378)	(0.0227)	(0.134) (0.0770) (0.0770)	(0.0490)	(0.0731)	(0.0302)	(0.0686)	(0.0420)	(0.0190)	(0.0270)
	D_Industry	yes	yes	no	no	yes	yes	yes	yes	yes	yes	yes	yes
	D_Year	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes
	Observations	2357	2357	2357	2357	2357	2357	2357	2357	2357	2357	2357	2357
	R-squared/pseudo	0.072	0.064	0.329	0.346	0.126	0.121	0.0290	0.0445	0.0668	0.0315	0.0479	0.0717
	Number of ID			1070	1070	1070	1070
	Inop i,t-1

Table 10 . Estimates of firm growth rate (measured by growth and GAGR)

 10 is the share of product innovation on turnover, where Growth is measured using the first difference equation. Notes:*** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses.

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
		OLS	FE		RE				Quantile
		Growth	CAGR	Growth	CAGR	Growth	CAGR		Growth			CAGR
	VARIABLES							q25	q50	q75	q25	q50	q75
	Ln(S ,t-1 )	-0.0224*** -0.0133*** -0.365*** -0.218*** -0.0271*** -0.0197*** -0.00731	-0.0132*** -0.0197*** -0.00373 -0.00663** -0.0106***
		(0.00579) (0.00345) (0.0344) (0.0187) (0.00629) (0.00407) (0.00844)	(0.00402) (0.00644) (0.00440) (0.00258)	(0.00236)
	Inoprod i,t-1	0.0136** 0.00984** 0.0130	0.00667	0.0129* 0.00843** -0.00263	0.00784** 0.0141** -0.00131 0.00391*** 0.00757**
		(0.00672) (0.00401) (0.0104) (0.00567) (0.00682) (0.00408) (0.00670)	(0.00317) (0.00585) (0.00380) (0.00147)	(0.00383)
	Constant	0.332*** 0.205*** 3.400*** 2.022***	0.244*	0.176**	0.0459	0.112	0.293***	0.0236	0.0537	0.154**
		(0.0944)	(0.0563)	(0.304)	(0.165)	(0.136)	(0.0867)	(0.195)	(0.146)	(0.0887)	(0.0841)	(0.0745)	(0.0697)
	D_Industry	yes	yes	no	no	yes	yes	yes	yes	yes	yes	yes	yes
	D_Year	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes
	Observations	1015	1015	1015	1015	1015	1015	1015	1015	1015	1015	1015	1015
	R-squared/pseudo	0.096	0.093	0.298	0.327	0.133	0.145	0.0344	0.0616	0.1008	0.0302	0.0572	0.0946
	Number of ID			600	600	600	600
	Inoprod i,t-1

Table 11 . Estimates of firms growth rate (measured by growth and GAGR)

 11 -0.0203*** -0.0119*** -0.430*** -0.265*** -0.0276*** -0.0185*** -0.00659* -0.00825*** -0.0148*** -0.00313** -0.00442*** -0.00775*** (0.00365) (0.00218) (0.0203) (0.0116) (0.00428) (0.00271) (0.00375) (0.00195) (0.00297) (0.00144) (0.00106) (0.00255) Inoc i,t-1 0.0421*** 0.0233*** 0.0301** 0.0158** 0.0453*** 0.0257*** 0.0310*** 0.0220*** 0.0252** 0.0151*** 0.0115*** 0.0127*** (0.0108) (0.00648) (0.0132) (0.00758) (0.0110) (0.00660) (0.00742) (0.00797) (0.0114) (0.00304) (0.00399) (0.00490) Where Inoc is a dummy variable taking the value 1 if the company has introduced a new process on the market. Notes:*** p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses.

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
		OLS	FE		RE				Quantile
		Growth	CAGR Growth CAGR Growth	CAGR		Growth			CAGR
	VARIABLES							q25	q50	q75	q25	q50	q75
	Ln(S ,t-1 )
	Constant	0.203*** 0.120*** 3.684*** 2.266*** 0.140* 0.0973** -0.0921	0.0615	0.164	-0.0455 0.0325**	0.0849*
		(0.0637) (0.0382) (0.169) (0.0967) (0.0738) (0.0471) (0.0935)	(0.0631)	(0.109) (0.0493) (0.0140)	(0.0439)
	D_Industry	yes	yes	no	no	yes	yes	yes	yes	yes	yes	yes	yes
	D_Year	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes	yes
	Observations	2374	2374	2374	2374	2374	2374	2374	2374	2374	2374	2374	2374
	R-squared/pseudo 0.072	0.065	0.328	0.347	0.126	0.124	0.0297	0.0414	0.0645	0.0326	0.0451	0.0694
	Number of ID			1072	1072	1072	1072

Table 12 . Estimates of the firms' growth rate measured by growth and GAGR (equa. 3)

 12 p<0.01, ** p<0.05, * p<0.1. Standard errors in parentheses.

		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
	VARIABLES	GMM-SYS	GMM-SYS	GMM-SYS	GMM-SYS	GMM-SYS
		Growth	CAGR	Growth	CAGR	Growth	CAGR	Growth	CAGR	Growth	CAGR
	growth t-1	0.0315	0.00288***	0.0566	0.00315***	0.0565	0.00311***	0.0587	0.00314***	0.159*	0.0425
		(0.0355)	(0.000216)	(0.0358)	(0.000170)	(0.0360)	(0.000162)	(0.0357)	(0.000163)	(0.0942)	(0.0613)
	Ln(S ,t-1 )	-0.0332*** -0.0196*** -0.0326*** -0.0183*** -0.0319*** -0.0177*** -0.0321*** -0.0180*** -0.0329*** -0.0207***
		(0.00458)	(0.00326)	(0.00495)	(0.00319)	(0.00466)	(0.00292)	(0.00482)	(0.00309)	(0.00794)	(0.00473)
	Ino i,t-1			0.0438*** 0.0240***
				(0.0122)	(0.00720)
	Inop i,t-1					0.0399*** 0.0196***
						(0.0115)	(0.00668)
	Inoc i,t-1							0.0444*** 0.0241***
								(0.0113)	(0.00653)
	Inoprod i,t-1									0.0149**	0.00827**
										(0.00754)	(0.00421)
	Constant	0.256***	0.121***	0.278***	0.101***	0.267***	0.0987***	0.267***	0.162***	-0.0141	0.142**
		(0.0716)	(0.0227)	(0.0724)	(0.0211)	(0.0747)	(0.0240)	(0.0729)	(0.0294)	(0.198)	(0.0612)
	Observations	2750	2750	2334	2334	2324	2324	2341	2341	1001	1001
	Number of ID	1073	1073	1070	1070	1069	1069.	1072	1072	598	598
	Notes:***

An exception is DelMonte and Papagni (2001). Based on a sample of 500 firms in the period 1989-1997 (drawn from the Mediocredito survey of Italian manufacturing) they confirm Gibrat's Law. They show that the growth rate of firms is positively correlated with their research intensity (considered as a proxy for firm innovation activity).

[START_REF] Baldwin | Innovation Capabilities: The Knowledge Capital Behind the Survival and Growth of Firms[END_REF] provide a rich analysis of an evolutionary approach, but deal only with small Canadian firms.

E.g., Bottazi et al. (2001), in a study of worldwide firms in the drug sector, find no relation between innovation and growth. These results would seem to be an exception, which might be due to the economic conditions in that sector.

Table 0 provides a summary of the main studies.

The CIS databank was made available to Naciba Haned under the mandatory condition of censorship of any individual information.

The 'enquête annuelle enterprises' are French surveys conducted by Sessi, the Ministry of Agriculture (for IAA) and INSEE (the French public Institute of Statistics). These longitudinal datasets provide yearly information on French firms' balance sheets for firms that have 20 employees or more.10 The European Union's industrial classification of economic activities, recognized by the Accounting Economic System (National Institute of Statistics).

The log-difference is the most widespread measure of sales growth used in the literature. However, in our case, it may have some drawbacks due to the fact that the firm observations do not corresdpond to consecutive years. For this reason we also use the CAGR index, which also provides a measure that assumes a steady growth rate, but we think that both are worth including.

The two-sample Fligner-Policello robust rank order test assumes neither normality nor equal variance, nor equal shape.

Overall, the coefficients of product/process innovation are consistent with the previous estimations. The differences between CAGR and Growth remain due to the different specifications of the two variables.

1 Alessandra Colombelli would like to thank University Lumière Lyon 2 (France) for awarding her a postdoc fellowship in 2010. Christian Le Bas is grateful to the International Centre for Economic Research (ICER) in Turin, where, as a Visiting Fellow, he completed this paper.