1.1 Cross-linguistic differences in auxiliary selection

Some languages make use of two auxiliaries with intransitive verbs to express past perfective: be and have, as in (1). Auxiliary selection refers to the language-specific processes governing the choice of auxiliary. Languages that have this split include Germanic languages such as Dutch and German, Romance languages such as French and Italian as well as minority languages such as Occitan, Sardinian and Corsican. Other languages such as English and Spanish only have one perfective auxiliary (have), as in (2)¹ (Zaenen 1993; Hoekstra 1999; Legendre 2007; McFadden 2007; Rosemeyer 2014; Gillmann 2015; Kailuweit 2015).

Intransitive verbs can be classified as unaccusatives, as in (1a, 2a), syntactically having a single internal argument, and unergatives, as in (1b, 2b), having a single external argument, as originally proposed by Perlmutter (1978) and Burzio (1986). The single (internal) argument of unaccusatives is initially assumed to take the same position as the object of transitive verbs, while the single (external) argument of unergatives is in the same initial position as the subject of transitives. With intransitives, the selection of be is a marker of unaccusativity. Unergatives (1b, 2b) and transitive verbs (3) select have.

In addition to intransitive verbs, reflexive (pronominal) verbs in French (4) and Italian (5) select be (Manzini 1986; Zribi-Hertz 1987).

There are important cross-linguistic differences in auxiliary selection rules. Languages differ in the number of intransitive verbs that select be. French be-selecting intransitives are considered a subset of Italian unaccusatives (Sorace 2000; Legendre 2007), with approximately 90 in Italian and 20 in French (Schwarze 1996; Heidinger 2015). However, this generalization may obscure other patterns. For instance, ‘appear’, ‘happen’ and ‘be’ select be in Italian, but form a mixed group in German, Dutch and French (Aranovich 2007). Specifically, the equivalent of unaccusative ‘happen’ selects be in both French (arriver) and Italian (succedere), while some stative verbs such as ‘be’ select have in French, but be in Italian. Also, semantically similar verbs may not select the same auxiliary, such as ‘disappear’ and ‘appear’, which select different auxiliaries in French (disparaître ‘disappear’ selects have while apparaître ‘appear’ typically selects be). Both select be in Italian (scomparire/aparire).

In contrast to intransitives, reflexive verbs show limited cross-linguistic differences. As mentioned above, these verbs all select be in both Italian and French. Semantic reflexives in German and Dutch, which take a reflexive pronoun such as 3SG ‘zich’ (Dutch) / ‘sich’ (German) select have similarly to transitive verbs, as in (6) (McFadden 2007: 691).

Table 1 summarizes these auxiliary selection rules.

Theoretical accounts generally differ on whether auxiliary selection is governed by lexical semantics or syntax. For lexical semantics-based proposals, determining factors include categorisations based on change of state, stativity or telicity (Bentley & Eythórsson 2004; Randall 2007). For instance, Bentley and Eythórsson (2004) propose that have is a default (elsewhere) auxiliary while be is produced as a morphological marker when semantic conditions are met. An influential framework for intransitive verbs is the Auxiliary Selection Hierarchy (ASH), first proposed by Sorace (Sorace 2000; Legendre & Sorace 2010), which divides intransitives into separate groups along agentive-aspectual lines going from categorical be-selecting (change of location, e.g. ‘arrive’) to categorical have-selecting (controlled processes, e.g. ‘work’) verbs, one key aim being to account for cross-linguistic differences such as in the case of ‘existence of state’ verbs (e.g. ‘exist’ which takes be in Italian and have in French).

Alternatively, syntax-based accounts argue that auxiliary selection with intransitives is not determined by the projection of argument structure (internal or external argument) but by the specific syntactic frame the verb is inserted in (Borer 1994; Folli 2001), which may better account for ‘variable behaviour’ verbs such as correre (run), as in (7) (van Valin 1990: 233).

Variability thus appears to the extent that these verbs occur in different syntactic frames. Other syntax-based proposals view auxiliary selection as the product of a local Agree (probe-goal) relation with a functional head (Bjorkman 2011; Amato 2023). According to Amato’s (2023) proposal, whether auxiliary be or have is spelled out depends on specific features of the functional head Perf. The place of reflexives is also a matter of debate within syntactic approaches, though most authors view the reflexive clitic as a valency reducing element rather than a true pronoun (see for instance McGinnis 2022). Some accounts analyse Romance reflexives as essentially unaccusative, with a single internal argument and reduction of the external argument (Grimshaw 1992; Embick 2004), therefore accounting for the selection of be. However, others argue that the external argument is preserved and it is the internal argument that is reduced, at least for agent arguments such as in (4) and (5) above. Be-selection in this case is proposed to be the result of either the missing theta-role or the missing accusative case assignment (Reinhart & Siloni 2005).

In the following section, we show that there is additional intra-dialectal variation that must be taken into account by studies of auxiliary selection.

1.2 Synchronic variation

Varieties of French that have been shown to have greater use of have with be-selecting intransitive and reflexive verbs include North American regions: Montreal French, Vermont French, Acadian French as well as other French minority regions in Canada (Sankoff & Thibault 1977; Russo & Roberts 1999; Willis 2000; King & Nadasdi 2005; Rea 2020).

Studies of variation in Montreal French using corpora generated from recorded participant interviews have found significant rates of have with be-selecting intransitive verbs (Sankoff & Thibault 1977; Rea 2020), ranging from less than 10% (e.g. aller ‘go’, venir ‘come’, partir ‘leave’) to 90% have productions (e.g. tomber ‘fall’, passer ‘pass’).² There was some degree of variation for all participants in these studies, although the speaker’s level of education correlated with a generally lower rate of have use. Item frequency was inversely correlated with have use, i.e. be was more likely with higher frequency items. These studies also show that variation is not evenly distributed: some speakers (almost) never produce non-standard auxiliaries, while others do so frequently, and intra-speaker variability is observed for some speakers. This was true for both intransitive and reflexive verbs. For instance, in Rea (2020) non-standard have use with reflexives was at a low frequency (1.3% of total) and restricted to a minority of participants, with individual rates ranging from approximately 2% to 38%.

Other North American varieties show even greater variability. Acadian French (Eastern Canada) has been found to have near-categorical use of have with intransitive and reflexive verbs in some of the French-speaking regions studied (King & Nadasdi 2005; Balcom 2008). King and Nadasdi (2005) for instance find that in one region the only verbs displaying some variability are mourir ‘die’ and naître ‘be born’, where auxiliary use can be linked to the contrast between eventive and resultative uses, as in (8) (King & Nadasdi 2005: 106).³

A study of Vermont French (Russo & Roberts 1999) showed similar results overall to the Montreal study by Sankoff and Thibault (1977), with significant differences in auxiliary use by verb.

One possible factor for the increased rate of have production with be-selecting verbs is contact with English as these varieties of French occur in areas that are likely to have a high level of bilingualism. This is supported by studies that found have use to be correlated with a lower French proficiency in English-French bilinguals (Canale et al. 1978; Mougeon & Beniak 1986). It is therefore possible that non-standard have auxiliary uses are in part evidence for change through contact with English. If so, European varieties may show more limited variation due to generally lower levels of bilingualism. However, it is also possible that the dominant factors responsible for this variability are socio-economic, and in this case we could expect to find similar variability in European varieties of French.

Relatively less is known about variation in Italian. The Auxiliary Selection Hierarchy makes explicit the prediction that societal variation is likely to be observed in the variable classes of verbs, such as ‘existence of state’ and ‘continuation of a preexisting state’, but not for categorical verb classes. In support of this, some experimental studies based on acceptability judgments (Bard et al. 1996) or eye-tracking (Vernice & Sorace 2018) are consistent with the view that speakers’ preferences for either auxiliary is stronger for categorical than variable verb groups. However, Rastelli (2023) points out that corpus data do not necessarily match these predictions. For instance, have use with unaccusative past participles durato ‘last’, rimasto ‘remain’, bastato ‘suffice’, appartenuto ‘belong’ and intervenuto ‘intervene’ is negligible (Rastelli 2023: 73–74). An experimental study with university students in Northern Italy (Rastelli 2023) found that participants’ choice of auxiliary could be considered ‘variable’ for only a subset of the expected verbs (approximately 60% of verbs considered variable based on the ASH). Additionally, participants’ auxiliary preferences were generally better predicted by item frequency in the corpus than semantics (including the effect of telicity or classification into separate ASH categories for states and processes).

In summary, specific varieties are likely to present more variability in auxiliary production than what has been described for standard French and Italian. Despite considerable differences between speakers, factors associated with an increased rate of have auxiliaries include: contact with English, socio-economic factors representing a lower awareness of normative usage, and lower item frequency. This shows that variability in participants’ auxiliary use must be taken into consideration. For studies of acquisition in particular this underscores the need to consider potential input variability as children’s productions (or comprehension) would be different in the presence of variable linguistic input.

1.3 Acquisition of auxiliary selection

Prior studies on the acquisition of auxiliary selection in French and Italian have analysed child error⁴ rates in production of auxiliaries with different verb types but reach different conclusions (Snyder et al. 1995; Boyce et al. 2017). Firstly, their results differ on whether child errors occur with both auxiliaries or preferentially represent the overuse of have with be-selecting verbs. Secondly, the studies disagree on the overall rate of error and whether the same error patterns are seen with reflexives and intransitives. Furthermore, the studies did not include an analysis of language input which, as argued above, is crucial for this investigation.

1.4 Aims of the present study

The current study aims to address the conflicting findings that prior research has reported. This means analysing rates of error with be- and have-selecting intransitives in order to better understand how auxiliary selection is acquired. As detailed above, if errors are only observed for be-intransitives, this would suggest that children acquire have-selection before be-selection. On the other hand, if both error patterns are observed (as in Boyce et al. 2017), this would suggest that both be- and have-selection are acquired simultaneously.

Secondly, we compare the acquisition of auxiliaries in French and Italian. Specifically, we aim to determine if overall error frequencies are similar in both languages. This is relevant as we could expect the same basic processes to determine the acquisition of auxiliary selection in Italian. If there are significant differences, we should ask whether there are potential causes that are independent of auxiliary selection.

We also analyse the role of input in auxiliary selection to determine if there is any variation. If there is some degree of non-standard use in parental speech, we would have to consider whether child errors are merely the result of reproducing this variable input and not due to grammar-internal factors.

Finally, by comparing child error patterns with intransitives and reflexives we can determine whether the acquisition of be-selection involves the same processes with both verb types. We therefore consider errors in relation to person/number forms for both reflexives and intransitives to determine if the reported person/number asymmetry (Boyce et al. 2017) is limited to reflexive constructions. If this also occurs with be-selecting intransitives, we could rule out the syncretism of clitic forms as a cause for such errors and look for other potential factors.

2.1 Selection of corpora

This study used monolingual French corpora from CHILDES (MacWhinney 2000). We selected all the available corpora that spanned at least the period of approximately age 2 to 3 years, when auxiliaries are first produced. Corpora were also chosen for the availability of parental speech. The selected French corpora (and children) were: Champaud (Grégoire) (Champaud 2004), Geneva (Marie) (Hamann et al. 2003), Leveillé (Philippe) (Suppes et al. 1973), Lyon (Anaïs, Marie, Marilyn, Nathan, Théotime) (Demuth & Tremblay 2008), Paris (Anaé, Antoine, Julie, Léonard, Madeleine, Théophile) (Morgenstern & Parisse 2007), Yamaguchi (Adrien) (Yamaguchi 2012) and York (Anne, Léa and Max) (Plunkett 2002) (Table 2).

Most of the French-speaking children are from France, with the exception of Léa (Belgium), Max (Canada) and G-Marie (Geneva, Switzerland).

2.2 Searches, coding procedures and exclusions

Searches were conducted using the CLAN program (MacWhinney 2000). Different search procedures were used depending on verb type (be-selecting intransitive, have-selecting intransitive, reflexive).⁵ The first series of searches were conducted on the Leveillé corpus and aimed to replicate the number of be and have auxiliaries with reflexive verbs from Snyder et al. (1995).

2.3 Coding and data analysis

Each selected utterance was coded for the individual child, language, speaker (child/adult), verb category (reflexive, be-selecting intransitive and have-selecting intransitive), specific verb, tense of the auxiliary (present or other), person/number (1SG, 2SG, 3SG, 1PL, 2PL, 3PL), the auxiliary produced in the utterance (be or have), and the selected auxiliary (according to language-specific auxiliary selection criteria). Each utterance was coded as ‘adultlike’ if the auxiliary produced matched the auxiliary selected, or ‘non-adultlike’ if there was a mismatch. Non-adultlike auxiliary uses were checked against the phonological tier (%pho) if available and/or the recording, where available.¹⁰

Data analysis was carried out in R (R Core Team 2023).

3.1 Auxiliary use in French and Italian input

As discussed above, we aim to determine if children’s non-adultlike auxiliary uses in French are true errors or can be attributed to variability in the input. As a first step, we therefore analyse auxiliaries produced in parental speech to determine the degree of variability that is present, if any, for each verb type: reflexive, be-selecting intransitive and have-selecting intransitive.

If child errors are the result of input variability, we can expect to see non-standard uses in both child and adult data. On the other hand, if children’s non-adultlike auxiliary uses are innovations we would expect to find greater rates of such auxiliary productions in child speech than in the associated parental speech. Variability in this context is represented by a significant percentage of non-standard have auxiliaries with be-selecting intransitive and reflexive verbs as we would not expect any be auxiliaries with have-selecting intransitives in adult speech.

Auxiliaries in parental speech are shown in Figure 1 as total counts of be and have auxiliaries by verb type for French (left) and Italian (right).

Figure 1: Auxiliary productions in French (left) and Italian (right) parental speech.

As this figure shows, in French there are no non-standard uses of have with reflexives (out of a total of 873 auxiliary–participle pairs) or of be with have-intransitives (out of a total of 1246 pairs). There are 3 counts of have with be-selecting intransitives (out of a total of 1741 auxiliary–participle pairs). These utterances are shown in (12).

In the case of (12a) the transcript reveals that the mother is repeating the child’s utterance and auxiliary choice. For (12b) the verb descendre ‘go down’ is used transitively in a previous utterance (go down the slope) while for (12c) this is referring to the child’s temperature rather than physical movement, usage which typically selects have (Manente 2008).

It is clear from these results that there is no real variability in the French language input. This means that any child errors must be child innovations as they cannot be the result of non-standard uses of have in the input.

For Italian (Figure 1, right), be is used with all be-selecting intransitive and reflexive verbs, while have is produced with all have-selecting intransitive verbs. This confirms that there is also no variability in the Italian input: as seen for French, parents produce auxiliaries according to auxiliary selection rules of standard Italian.

In the following section, we provide an analysis of auxiliaries produced by children, comparing productions of be and have for reflexive, be-selecting intransitive and have-selecting intransitive verbs.

3.2 Auxiliary use in child speech

We analyse the auxiliaries produced with intransitive and reflexive verbs in child data. Non-standard uses include the production of have with be-selecting intransitives and reflexive verbs, or that of be with have-selecting intransitives. Recall that previous studies (section 1.3.1) differed on whether children make errors with both auxiliaries or only overuse have with be-selecting verbs. We therefore aim to determine if child errors are dependent on verb type. This is shown in Figure 2 as total counts of be and have auxiliaries by verb type for French (left) and Italian (right).

Figure 2: Auxiliary productions in child French (left) and Italian (right).

In French, the error frequencies are much higher for both be-selecting verb types, at 10% of auxiliaries with be-selecting intransitives (90 out of 878 counts) and 20% of auxiliaries with reflexives (50 out of 250 counts), than with have-selecting intransitives, where the frequency is less than 1% (2 out of 656 counts).

Examples of non-adult-like auxiliary uses are given below for French be-selecting intransitive (13a) (Anaé 2;06) and (13b) (Anaïs 2;09), and reflexive verbs (13c) (Grégoire 2;05).

To determine whether this pattern in French represents a significant deviation from the input, we ran a mixed effects logistic regression using R Statistical Software (R Core Team 2023) and the lme4 package (Bates et al. 2015) with production of auxiliary have as a binary dependent variable i.e. production of have was coded as 1, and production of be was coded as 0. Fixed effects included ‘verb type’ (reflexive, be-selecting and have-selecting intransitives) and ‘speaker’ (child/adult) with the individual child as a random intercept.

As the dependent variable is the production of have, we would expect to see a difference between have-selecting intransitives and reflexive or be-selecting intransitives as a main effect. More importantly, an interaction between ‘speaker’ and ‘verb type’ is indicative of a difference in have use across the different verb types between children and adults. If so, post-hoc tests can tell which verb type shows a significant difference between children and adults.

The model terms are shown in Table 5. As expected, this shows a significant contrast for have-selecting intransitive as a main effect (β = 43.23, z = 2.87, p = 0.004). There is also a significant main effect for ‘child’ relative to ‘adult’ (β = 20.31, z = 2.17, p = 0.030) and a significant interaction for speaker (child) and verb type (have-selecting) (β = –35.87, z = –2.38, p = 0.017).

In order to determine which verb type was responsible for this effect, we ran posthoc tests using the emmeans package (Lenth 2023), shown in Table 6. This shows that there is a significant difference in have productions between child and adult speakers for the reflexive (F = 4.71, p = 0.030) and be-selecting intransitive (F = 54.25, p < 0.001) categories, while children and adults do not differ significantly for have-selecting intransitives.

Turning to Italian child speech (Figure 2, right), there are a small number of errors, with error rates of 3% for be-selecting intransitive verbs (4 errors out of a total of 120 auxiliary–participle pairs), 2% for reflexives (1 error out of 56 pairs), and 1% for have-selecting intransitives (1 error out of 100 pairs). See the relevant child utterances in (14). (14a) to (14c) are auxiliary errors with be-selecting intransitive verbs produced by Diana (all at 2;05). (14d) is a production of have with a reflexive, also for Diana (2;06). (14e) uses have with a be-selecting intransitive (fall), (Raffaello, 2;01)¹¹ while (14f) is the only instance of be with a have-selecting intransitive (or null-object transitive) (Marco, 2;01).¹²

It is worth noting that 4 of the 6 errors in Italian were produced by one child (Diana) and most children only produced adultlike auxiliaries. In contrast, in child French we measured at least one auxiliary error for each of the 18 French-speaking children though there were considerable differences in error rates by child, as well as differences between intransitives and reflexives for instance for many of the children. See supplementary files for counts by individual child.

To determine whether these error frequencies are different to those seen in French, we ran a mixed effects logistic regression model comparing auxiliary productions in child French and child Italian. This analysis takes have production as a binary dependent variable, with language (French/Italian) and verb type (be-selecting intransitive, reflexive, have-selecting intransitive) as fixed effects. Individual child and lexical verb were added as random intercepts.¹³

As have-production is the dependent variable, we expect to see a main effect of verb type (have-selecting intransitive). A main effect of language is also likely and would reflect different proportions of be-selecting verbs. More importantly, an interaction of verb type and language for any of the three verb categories would indicate a significant difference between the two languages for that verb category. Therefore, if the rate of error is higher in child French for be-selection alone, we would expect to see an interaction for be-selecting intransitive and/or reflexive, but not have-selecting intransitive, as French-speaking children do not produce significant errors with the latter.

The model is shown in Table 7. As predicted, there is a significant contrast for verb type (have-selecting) as a main effect (β = 10.05, z = 7.63, p < 0.001) and language (Italian) (β = –2.53, z = –2.11, p = 0.035).

We ran posthoc tests to determine if there are significant contrasts between languages for each of the three verb types. This is shown in Table 8. The analysis shows a significant interaction for reflexive (f = 4.43, p = 0.035) and be-selecting intransitive (f = 4.39, p = 0.036) categories, but not for have-selecting intransitives (f = 0.43, p = 0.510), which is consistent with a difference between French and Italian children’s use of auxiliaries with the two be-selecting verb categories, but not for have-selecting intransitives.

The results show that French-speaking children produce significantly more auxiliary errors with the be-selecting verb categories, confirming that the much higher error frequency in French be-selecting verbs (10% to 20%) compared to Italian (2%–3%) is a significant difference between languages.

In the following section we examine the French auxiliary errors produced in more detail. As discussed above (section 1.3.1), a prior study reported different rates of error for reflexives by person/number: highest for 1SG, lower for 2SG, and at zero for 3SG. We therefore compare the distribution of person/number forms in both be-selecting verb types to better understand this effect and determine if it applies to be-selecting intransitives in addition to reflexives.

3.3 Auxiliary productions by person/number

Further analyses are needed to better understand auxiliary error patterns in child French. For instance, though all French children produce non-adultlike auxiliaries to some degree, there are considerable differences across individuals, and error rates are not necessarily similar between be-selecting intransitive and reflexive verbs. Also, it is noteworthy that there are significant errors with verbs that have shown very limited variability in the literature, such as aller ‘go’.¹⁴

3.3.1 Auxiliary productions in French child speech

To gain a better understanding of the reasons children are producing such errors we analysed the specific adultlike (be) and non-adultlike (have) auxiliary forms used by each of the French-speaking children for the be-selecting verb categories. We focus on present tense auxiliaries (equivalent to present perfect verbs) as these make up the vast majority of perfect auxiliaries in the corpora (at 94% of be-selecting verbs in parental speech, and 96% in child speech) and start being produced by children before other auxiliary forms.

It is necessary to consider the verbal paradigm for present tense be, shown in Table 9. For both auxiliaries, 2SG and 3SG forms are identical single vowels, with distinct forms for 1SG and 3PL. 1PL ‘nous’ is not typically used in colloquial and child-directed speech, and 2PL ‘vous’ is infrequent.¹⁵

Table 9: French be and have paradigms.

	person/number	subject auxiliary
be	1st-SG	je suis
	2nd-SG	tu es [e]
	3rd-SG	il est [e]
	3rd-PL	ils sont
have	1st-SG	j’ai [e]
	2nd-SG	tu as [a]
	3rd-SG	il a [a]
	3rd-PL	ils ont
refl-be	1st-SG	je me suis
	2nd-SG	tu t’es [te]
	3rd-SG	il s’est [se]
	3rd-PL	ils se sont

We first analyse the distribution of person-number forms in relation to child errors. Figure 3 shows the total counts of each of these person/number auxiliary forms for be-selecting intransitive and reflexive verbs, comparing adultlike (blue) to non-adultlike (orange).¹⁶

Figure 3: Person/number distribution of present tense auxiliaries in BE-selecting verbs in child French.

It is clear from the relative proportions that there is an increased rate of error with 1SG. In the case of reflexives it is the only error observed. With be-selecting intransitives, while 3SG and 3PL errors are present, the relative rate of error is much higher for 1SG than 3SG. Specifically, for this verb type the rate of error for 1SG auxiliaries is 42% (42 errors out of 100 counts) while for 3SG auxiliaries it is 5.3% (35 out of 664 counts). No errors were observed for 2SG (out of 11 counts for be-selecting intransitives and 14 for reflexives). These results differ from those of Boyce et al. (2017), as we show that the increased rate of 1SG errors is not limited to reflexives but rather is a characteristic of both be-selecting verb types.

In order to determine if this asymmetry in error frequencies is significant, we ran a mixed effects regression model on the data for child productions of be-selecting verbs, with production of auxiliary have as the binary dependent variable, fixed effect for ‘person’ (1SG, 2/3SG and 3PL), and both ‘child’ and ‘verb’ as random intercepts. For this analysis 2SG auxiliaries were recoded as 3SG to reflect the syncretism and homophony. A main effect of ‘person’ in this model would reflect a difference between any of the 1SG, 2/3SG and 3PL factors. The model terms are shown in Table 10. This shows an effect of the variable ‘person’ for 3PL (β = 1.93, z = 8.49, p < 0.001).

Table 10: Mixed effects logistic regression for have production by person/number form in child French.

Fixed effect	β	se	z	p
(Intercept)	–1.94	0.45	–4.33	<0.001
person (3PL)	1.93	0.23	8.49	<0.001
person (2/3SG)	0.14	0.29	0.50	0.621

As we aim to determine if the asymmetry is significant between the three person/number forms, we ran pairwise tests on this model using the ‘emmeans’ command from the emmeans package (Lenth 2023), in order to analyse the contrasts for each pair, shown in Table 11.

Table 11: Pairwise comparisons of person/number levels in the child French have-model.

contrast	β	se	z	p
1SG–3PL	1.78	0.46	3.83	<0.001
1SG–2/3SG	3.99	0.34	11.56	<0.001
3PL–2/3SG	2.21	0.46	4.83	<0.001

Importantly, this shows that there is a significantly higher production of have with 1SG than 2/3SG auxiliaries (β = 3.99, z = 11.56, p < 0.001). Have productions are also significantly higher with 1SG than 3PL (β = 1.78, z = 3.83, p < 0.001) and greater with 3PL compared to 2/3SG (β = 2.21, z = 4.83, p < 0.001).

In summary, this analysis shows that auxiliary errors are not evenly distributed among person/number forms. Instead, errors are more common for 1SG than other forms of be, with a much higher percentage of adultlike auxiliaries produced for 3SG. Furthermore, in contrast to Boyce et al. (2017) we found no errors with 2SG auxiliaries, showing that this increased error rate is specific to 1SG.

In the following sections, we consider a potential explanation for these errors due to the homophony between 1SG have and 3SG be in spoken French. Specifically, since both are realised as [e], it is possible that 1SG be errors are not true auxiliary selection errors (i.e. not 1SG have) but represent instead the extension of 3SG be where 1SG is required. In the following section, we analyse the frequencies of the different be auxiliaries in parental speech, as a high proportion of 2/3SG be could be a potential factor responsible for these over-productions.

3.3.2 Auxiliary use by person/number in parental speech

As there are significantly higher rates of error in child auxiliary productions for 1SG compared to other person/number forms, we analyse the distribution of these person/number forms in parental speech as a potential source of error. Importantly, as 2/3SG be (es/est) and 1SG have (ai) are both realised as [e] in spoken French, there are two potential sources for child errors with 1SG be: children may be selecting the wrong 1SG auxiliary (have) or they may be selecting the expected auxiliary (be), but using a 3SG ‘est’ instead of 1SG ‘suis’ (see Table 9 above). For consistency we will refer to the former as auxiliary selection errors and the latter as 3SG extensions.

We analyse parental speech in order to determine the relative frequencies of 2/3SG [e] compared to the other forms in the be paradigm. If there is a significantly higher frequency of one form relative to others in the language input this could be a factor explaining why children over-produce a 3SG instead of a 1SG be auxiliary. As both 2SG and 3SG are realized as [e] we have combined them in this analysis.

The total counts by person/number category for reflexive and be-selecting intransitive verbs in French parental speech are shown in Figure 4.

Figure 4: Person/number distribution of present tense auxiliaries in BE-selecting verbs in French parental speech (2SG and 3SG are both [e]).

In both verb types, 2SG/3SG [e] make up the vast majority of auxiliaries, at 88% of total auxiliaries for be-selecting intransitives (1430 out of 1617 counts) and 86% for reflexives (699 out of 816 counts), with 1SG and 3PL forms together accounting for the remaining 12% of be-selecting intransitive auxiliaries (57 counts for 1SG and 122 counts for 3PL out of a total of 1617) and 14% for reflexive auxiliaries (87 counts for 1SG and 26 counts for 3PL out of a total of 816).¹⁷

To analyse these distributions we ran a mixed effects regression model with ‘counts’ as a continuous dependent variable, fixed effect for ‘person’ (1SG, 2SG/3SG, 3PL), and both ‘child’ and ‘verb’ as random intercept terms.¹⁸ In this case, a main effect of ‘person’ would be consistent with significant differences between counts for the different person/number forms.

The model terms are shown in Table 12. This shows a significant effect of the variable ‘person’ for 2SG/3SG (β = 4.01, t = 6.34, p < 0.001) but not for 3PL.

Table 12: Mixed effects regression for counts by person/number form in adult French.

Fixed effect	β	se	t	p
(Intercept)	–1.60	0.73	–2.20	0.030
person (3PL)	–0.52	0.82	–0.64	0.526
person (2SG/3SG)	4.01	0.63	6.34	<0.001

As for the child data, we ran pairwise tests on this model in order to analyse the contrasts for each pair, shown in Table 13. The contrasts show significantly lower counts of 1SG be compared to 2SG/3SG (β = –4.01, t = –6.33, p < 0.001) and significantly lower counts of 3PL be compared to 2SG/3SG (β = –4.54, t = –7.32, p < 0.001), while the contrast between 1SG and 3PL was not significant.

Table 13: Pairwise comparisons of person/number levels in adult French.

contrast	β	se	t	p
1SG–3PL	0.52	0.82	0.63	0.802
1SG–2SG/3SG	–4.01	0.63	–6.33	<0.001
3PL–2SG/3SG	–4.54	0.62	–7.32	<0.001

In summary, there is a significant asymmetry in the distribution of person/number be auxiliaries in parental speech, with much higher frequencies of 2SG/3SG [e]. This confirms the skewed nature of the input, which could therefore be a factor explaining children’s over-production of 3SG auxiliaries in the early stages of acquisition.

3.3.3 Auxiliary use in Italian by person/number

This section analyses the relative frequencies of person/number forms in the Italian data for child and parental speech. Mainly, if there is a similar asymmetry between the different person/number forms in the parent’s speech as was found in French, this could suggest that the relative frequencies of person/number forms are not a significant factor responsible for the 1SG errors in child French, since this error type is specific to French (Italian auxiliary errors included one 2SG error with be, four 3SG errors with be, and one 1SG error with have, section 3.2).

The Italian paradigm for present tense be and have is shown in Table 14. The only syncretism is in the be forms for 1SG and 3PL.¹⁹ There is no homophony between any of the have and be forms, in contrast to French (section 3.3.1).

Table 14: Italian be and have paradigms.

	person/number	auxiliary
be	1SG	sono
	2SG	sei
	3SG	è
	1PL	siamo
	2PL	siete
	3PL	sono
have	1SG	ho
	2SG	hai
	3SG	ha
	1PL	abbiamo
	2PL	avete
	3PL	hanno
refl-be	1SG	mi sono
	2SG	ti sei
	3SG	si è
	1PL	ci siamo
	2PL	vi siete
	3PL	si sono

Figure 5 shows the relative proportion of each be auxiliary by verb type for child and adult Italian.

Figure 5: Person/number distribution of present tense BE auxiliaries in Italian parent and child speech (1SG and 3PL are both ‘sono’).

As for French, we only consider present tense auxiliaries. In the parents’ speech, the relative proportions are similar for both verb types (reflexive and be-selecting intransitives), with the majority of auxiliaries as 3SG forms, which account for 65% of be-selecting intransitives (555 out of a total of 849 counts) and 63% (164 out of a total of 262 counts) of reflexive verb counts respectively. In contrast, 1SG/3PL ‘sono’ accounts for 7% of be-selecting intransitives (60 out of 849) and 10% (27 out of 262) of reflexive verb counts, while 2SG ‘sei’ auxiliaries make up 18% of be-selecting intransitive pairs (150 out of 849 counts) and 27% of reflexive pairs (71 out of 262 counts). There are also 82 counts of 1PL ‘siamo’ with be-selecting intransitive verbs, representing 10% of total be-selecting intransitive auxiliaries.²⁰ On the whole these frequencies show that there is a marked asymmetry in relative frequencies in parental speech, though possibly not to the same extent as was seen for French.

In child speech in comparison, there is a higher proportion of 1SG/3SG auxiliary ‘sono’ and a lower proportion of 2SG auxiliaries with both verb types. There is also a somewhat higher percentage of 3SG forms with reflexives.

To determine if the asymmetry in parental speech is significant, we conducted a mixed-effects regression model with total counts as a continuous dependent variable, person (1SG/3PL, 2SG, 3SG, 1PL) as fixed effect, and both ‘child’ and ‘verb’ as random intercepts. A main effect of ‘person’ would be consistent with significant differences between counts for the different person/number forms.

The model terms are shown in Table 15. This shows a significant effect of the variable ‘person’ for 2SG (β = –1.44, t = –2.49, p = 0.013).

Table 15: Mixed effects regression for counts by person/number forms in adult Italian.

Fixed effect	β	se	t	p
(Intercept)	1.00	0.61	1.64	0.118
person (1SG/3PL)	–0.13	0.86	–0.15	0.881
person (2SG)	–1.44	0.58	–2.49	0.013
person (3SG)	–0.21	0.47	–0.41	0.684

We also conducted pairwise comparisons in order to analyse each of the person/number contrasts. The analysis of the French data showed that there was a significant contrast between the counts of 2SG/3SG and the other two auxiliary forms (1SG and 3PL) (section 3.3.2). If the distribution of person/number auxiliaries is essentially the same in the two languages, we would expect to see similar contrasts between 3SG and the other person/number categories in Italian.²¹

The result of this analysis is shown in Table 16. The contrasts show significantly lower counts for 1SG/3PL be compared to 3SG (β = –3.22, t = –4.31, p < 0.001) and significantly lower counts of 2SG be compared to 3SG (β = –1.99, t = –3.03, p = 0.014). Other contrasts were not significant.

Table 16: Pairwise comparisons of person/number levels in adult Italian.

contrast	β	se	t	p
1PL–(1SG/3PL)	1.31	1.29	1.02	0.738
1PL–2SG	0.08	1.23	0.07	0.999
1PL–3SG	–1.91	1.18	–1.62	0.369
(1SG/3PL)–2SG	–1.23	0.84	–1.46	0.461
(1SG/3PL)–3SG	–3.22	0.75	–4.31	<0.001
2SG–3SG	–1.99	0.66	–3.03	0.014

In summary, the analysis of the distribution of person/number forms in Italian parental speech shows a similar pattern to what was found for French. Although the asymmetry is more pronounced in French, with somewhat higher overall percentages of 2SG/3SG in that language compared to 3SG in Italian, in both languages there is a contrast between 3SG and the other forms of the be paradigm. Since Italian children do not replace 1SG be ‘sono’ with 3SG ‘è’, the results obtained for Italian parental speech suggest by extension that this is not likely to be the main reason French-speaking children produce non-adultlike 1SG be forms and therefore other underlying reasons must be responsible for these productions.

If child errors with be auxiliaries are extensions of 3SG forms due for instance to a delayed acquisition of 1SG be ‘suis’, instead of auxiliary selection errors, we would expect this delay to apply to any production of 1SG be, i.e. including instances of be as a copula. In the following section we consider this possibility by comparing the earliest occurrences of be as auxiliary and copula.

3.4 Children’s first productions of 1SG ‘suis’ as auxiliary and copula

As child error rates for French auxiliaries with be-selecting intransitive verbs are significantly higher for 1SG be ‘(je) suis’ compared to 3SG ‘(il/elle) est’ (section 3.3.1), it is possible that this represents a more general difficulty in the acquisition of the be inflectional paradigm, which would not be limited to be as an auxiliary. In other words, if the issue is with acquisition of the paradigm we should find a similar effect with production of ‘suis’ in copular constructions.

To test this hypothesis, we searched for the first occurrences of 3SG and 1SG forms for each of the children, comparing be and have for uses as both auxiliaries and copula/main verb, as a measure of the relative delay in production of 1SG compared to 3SG forms.²² If the difficulty in acquisition is limited to be as an auxiliary (and the errors with 1SG be are due to auxiliary selection), we would expect to see a delay in the first occurrences of ‘(je) suis’ as an auxiliary compared to ‘(je) suis’ as copula, relative to first occurrences of 3SG ‘(il/elle) est’. If on the other hand the difficulty is due to the acquisition of the be paradigm (and the errors with 1SG be are due to extensions of 3SG be) we would expect to find a similar delay in production of 1SG be independently of type (auxiliary or copula), relative to first productions of 3SG be. We also measured first occurrences of 1SG and 3SG have as auxiliary and main verb to determine if this possible 1SG delay is limited to be.

The results of this analysis are shown in Figure 6 for be (left) and have (right), comparing 1SG and 3SG as auxiliary or copula/main verb, plotted by age in months. Comparing the median age of first occurrence for be, there is a general delay between 1SG and 3SG forms which does not appear to depend on whether this is an auxiliary or copula i.e. there is a similar delay for 1SG relative to 3SG in both types. In comparison, for have there appears to be no relative delay (1SG vs. 3SG) for the auxiliary and a slight delay for the main verb.

Figure 6: First occurrence of 1SG and 3SG BE and HAVE as auxiliary and main verb in child speech.

To test the significance of these results we conducted a mixed effects regression model with age in months as the dependent (continuous) variable and the three independent variables as fixed effects: verb (be/have), type (auxiliary/main verb), person (1SG/3SG). ‘Child’ and ‘verb’ were fitted as random intercepts. For either verb (be and have), a main effect of ‘person’ would indicate a significant delay in the occurrence of 1SG compared to 3SG, independently of ‘type’, while a main effect of ‘type’ (auxiliary/main verb) would reflect a delay in the first occurrence of either (independently of ‘person’). An interaction between ‘person’ and ‘type’ would indicate a greater delay in the production of the 1SG in either type (auxiliary or main verb). Crucially, if the difficulty in the acquisition of 1SG be is due to auxiliary selection, we would expect an increased delay with 1SG auxiliaries compared to 1SG copulas, i.e. an interaction between ‘type’ and ‘person’ for be. If on the other hand it is related to an inherent difficulty in acquiring the full be paradigm, we would expect a similar delay for 1SG relative to 3SG independently of ‘type’ i.e. no interaction between these variables. We make no specific predictions for have, though the absence of 1SG errors with auxiliary have would be consistent with a different pattern for this verb reflecting the absence of a similar delay.

The model fixed effects are shown in Table 17. There is a significant effect of person (3SG) (β = –8.90, t = –9.52, p < 0.001) reflecting on average earlier production of 3SG forms (by approximately 9 months), a significant main effect of verb have (β = –7.48, t = –8.01, p < 0.001) reflecting an average earlier production of this verb (by approximately 7.5 months), and a significant effect of type (main verb) (β = –3.09, t = –3.16, p = 0.002) consistent with an earlier production of main verb forms (by approximately 3 months). There is also a significant interaction of person (3SG) with verb (have) (β = 9.07, t = 7.14, p < 0.001), and an interaction between verb (have) and type (main verb) (β = 4.74, t = 3.63, p < 0.001).

We ran posthoc tests by verb (be/have) on this model, shown in Table 18 for be and Table 19 for have. For be there is a main effect of ‘person’ (1SG/3SG) (f = 204.57, p < 0.001) and ‘type’ (auxiliary/main verb) (f = 29.53, p < 0.001) but no interaction between these variables. These results show that there is a general delay for 1SG (relative to 3SG) be and a general delay of be as an auxiliary (independently of person/number), but importantly, no increased delay for 1SG be as an auxiliary. This analysis is therefore consistent with a general delay for 1SG be, supporting the hypothesis that 1SG errors represent a difficulty in the acquisition of the be paradigm, rather than a difficulty specific to the acquisition of be-auxiliary selection.

For have first occurrences there is a main effect of person (f = 8.39, p = 0.005), reflecting a somewhat later occurrence of 1SG overall, but no main effect of type (auxiliary/main verb). The interaction between these two variables is significant (f = 10.15, p = 0.002), which can be interpreted as an increase in the delay for the first occurrence of 1SG with one of the two types (main verb as shown in Figure 6).

To summarize our results for French, there are significant errors in child French be-selecting intransitives and reflexive verbs. These are not due to input variability given that there are no non-standard uses in French parental speech. Furthermore, these errors occur preferentially with 1SG be. Although there are two possible sources of error for 1SG be, our results show that the errors are likely to represent the delayed acquisition of the 1SG form of the be paradigm and are not limited to auxiliary uses. The asymmetric nature of the input by person/number, with a much greater frequency of 2SG/3SG be in parental speech may be a factor though other factors are likely to be responsible as similar errors do not occur in child Italian.