2.1. The atlas

The Scots Syntax Atlas (SCOSYA, Smith et al. Reference Smith, Adger, Aitken, Caroline Heycock and Thoms2019) is a fully searchable online atlas, mapping morphosyntactic variation across Scots varieties. The atlas contains data gathered from over 140 locations across Scotland (Figure 1), with four speakers – two aged 18–25 and two aged 65+ – per location. Participants were recruited following standard sociolinguistic criteria for identifying speakers local to the community under study (e.g. Feagin Reference Feagin, Chambers and Schilling2013), and data collection was conducted by field-workers who were also members of the community in order to mitigate effects of the Observer’s Paradox (Labov Reference Labov1972).

Figure 1.

Locations around Scotland where data have been collected in the Scots Syntax Atlas. Each dot represents one community.

Data were collected from each pair of participants in two ways. First, data were collected from sociolinguistic interviews (Labov Reference Labov, Baugh and Sherzer1984: 32), totalling ca. 275 hours of conversation. The interview recordings are text-to-sound transcribed using the open source software TranscriberAG (https://transag.sourceforge.net), creating a rich corpus of searchable spoken data from Scots varieties. Second, participants completed an acceptability judgment task on 200+ examples of morphosyntactic phenomena, administered following the ‘interview method’ for syntactic data collection (Barbiers & Bennis Reference Barbiers and Bennis2007). Participants judged each example on a Likert scale from 1 to 5 (e.g. Schütze Reference Schütze2016). Each point on the scale was labelled, with 5 described as ‘I would definitely say that’. At the other end of the scale, 1 was described as ‘I would never say that’. Each participant was asked to provide around 200 judgments, with a total of over 110,000 judgments overall. These data were fed into the online atlas and allowed us to visualise patterns of acceptability across geographic space (the different locations) and time (the different age groups). The full dataset and more details about the project are available through the online atlas at https://scotssyntaxatlas.ac.uk.

In what follows, we will focus on the judgment data for the following sentences in the questionnaire: one testing amn’t in an inversion environment (specifically a tag questionFootnote ¹), one testing amn’t in a declarative, and one testing amnae in a declarative.Footnote ²

We use these data to investigate three empirical issues. In Section 2.2, we consider whether the inversion asymmetry with respect to amn’t holds more broadly across our larger dataset. In Section 2.3, we examine the relationship between amn’t and amnae in declaratives, assessing the predictions of the proposal in Bresnan (Reference Bresnan, Baltin and Collins2001) regarding the inversion asymmetry. In Section 2.4, we take a closer look at declarative amn’t and identify some major regional differences in its acceptance.

Before moving onto the results, we should establish some methodological caveats regarding the data that we have gathered using these examples. One potential issue with the examples in (7)–(8) is that they both involve the use of negative contraction (I amn’t/amnae) rather than auxiliary contraction (I’m not/no) in a context which strongly favours the use of the auxiliary contraction – namely, present tense be and a pronominal subject. The usage preference for auxiliary contraction in these contexts is well-documented for a number of British varieties, including varieties of Scots (Tagliamonte & Smith Reference Tagliamonte and Smith2002), and this effect is visible in the SCOSYA corpus, which contains not a single example of amn’t and only one example of amnae, given in (9); this is out of 1,800 potential contexts where negation and am occurred together, in the whole 3,000,000-word corpus.

We should stress that low frequency in use does not necessarily entail low acceptance or ungrammaticality; for example, you aren’t is also vanishingly rare in our spoken corpus (there are only a handful of examples in the SCOSYA corpus), due to a preference for you’re not, yet it seems unlikely to us that it is ungrammatical in any varieties in the United Kingdom. Nevertheless, it is possible that when naive informants are asked to rate I amn’t/amnae (or indeed, you aren’t) for acceptability, they may occasionally give it a low rating because of this preference, despite the best efforts of field-workers to explain the task – even if the relevant form is grammatical for the speaker and may show up (albeit rarely) in their usage. This might, in turn, lead to depression of the rate of acceptance of examples such as (7)–(8) – in particular, relative to examples like (6). We will return to this caveat at a few points below. Also, we note that there is a general role for age in the acceptability of amn’t/amnae in the SCOSYA data, with younger speakers accepting both inverted and declarative amn’t and declarative amnae at a higher rate than older speakers. A small benchmarking study investigating differences in acceptability between the age groups for seven known Scots-wide features showed an average acceptance rate of 72.2% for the older speakers and 90.2% for the younger speakers. It may be that this difference between the age groups is due to younger speakers having greater perceptual linguistic awareness than older speakers, evidenced in their accuracy in metalinguistic tasks (Drager Reference Drager2011, Carrera-Sabaté Reference Carrera-Sabaté2014, Lawrence Reference Lawrence2017, though see Jamieson Reference Jamieson2020 for the opposite). It may also be the case that there is change in progress with amn’t, moving towards greater acceptability. As instances of amn’t and amnae are so rare in the SCOSYA corpus, we cannot use any additional existing data to test this hypothesis further. We therefore acknowledge that change may be a possibility, but we set it aside for future sociolinguistic investigation.

We will now present the geographical distribution of the amn’t and amnae data from SCOSYA and highlight where it supports or provides counterarguments to Bresnan and Yang’s proposals. Throughout, we report the acceptance rate: how many participants rated the example 4 or 5 in the judgment task. We use this as an operationalisation of acceptability, following, for example, Zanuttini et al. (Reference Zanuttini, Wood, Zentz and Horn2018), who use the same cut-off for similar types of acceptability judgment results in the Yale Grammatical Diversity Project, and Thoms et al. (Reference Thoms, Adger, Heycock and Smith2019), Jamieson et al. (Reference Jamieson, Adger, Heycock, Smith and Thomsto appear), who used these cutoffs when investigating other aspects of the SCOSYA data. We also report the mode throughout as a quick and clear way to establish how the majority of participants responded to a particular example or in a particular area.

2.2. Geographical distribution of amn’t and the inversion asymmetry

To begin with, we show that there is indeed a strong asymmetry between declaratives and inversions with respect to the acceptability of amn’t across Scots dialects. This broadly confirms one of the key empirical claims in Bresnan (Reference Bresnan, Baltin and Collins2001). We can see this with maps representing the scores for the examples in 6 and 7. Figures 2 and 3 show acceptability maps, in which dark spots represent locations where the example was given a score of 4 or 5 by two or more speakers.

Figure 2.

I’m coming with you, amn’t I?, accepted by $ \ge $ 2 speakers.

Figure 3.

I amn’t ready yet, accepted by $ \ge $ 2 speakers.

We can see from simply looking at the maps that amn’t is accepted much more widely, and indeed much more uniformly, in inversions than in declaratives.Footnote ³ This can also be seen in the descriptive statistics: the inversion example in (6) had a mode of 5, with the individual-level acceptance rate at 60%. The numbers for declarative amn’t are much lower: Example (7) had a mode of 1 and an acceptance rate of 34%.

Clearly, then, the example testing amn’t in a declarative was less well accepted in the SCOSYA data than the example testing amn’t in inversions, potentially indicating a difference in terms of the grammatical status of amn’t in these two environments, in line with what was proposed by Bresnan Reference Bresnan, Baltin and Collins2001. While it is possible that some portion of the difference in acceptability between the two examples could be attributable to the preference for auxiliary contraction over negative contraction in declarative contexts, it seems unlikely that this would account for the full extent of the difference in scores. An additional consideration, which we expand on more in Section 2.4, is that whereas the scores for (6) in the map in Figure 2 are high more or less uniformly across the country, the scores for (7) in Figure 3 vary much more by region. This would be unexpected if the difference between inversions and declarative was due solely to methodological issues.

2.3. Geographical correlation between amn’t and amnae

We have seen that Bresnan’s (Reference Bresnan, Baltin and Collins2001) proposed inversion asymmetry holds in the SCOSYA data. Now let us consider the second major claim of her argument: that the amn’t asymmetry is due to the fact that declarative amnae effectively blocks declarative amn’t. In her account, then, the two forms should be in complementary distribution, at least in regions where -nae forms are used productively.

To assess this claim, we provide map data for declarative amnae in Figure 4, which can be compared with declarative amn’t in Figure 3. In addition, to contextualise the results for amnae, we provide map data from another example of -nae negation: havenae, as tested in the sentence in (10).Footnote ⁴

Figure 4.

I amnae ready, accepted by $ \ge $ 2 speakers.

Figure 5.

I havenae been there before, accepted by $ \ge $ 2 speakers.

It is easy to see from Figure 5 that havenae is generally accepted across Scotland, with the exception of the Highlands and the Western Isles, which exhibit standard English forms (e.g. Shuken Reference Shuken and Trudgill1984).

Figure 6.

Labelled dialect regions of Scotland, corresponding to the regions in Table 1.

We can see in Figure 4 that amnae is also, unsurprisingly, rejected in these areas. However, what is surprising (in light of Bresnan Reference Bresnan, Baltin and Collins2001’s claim) is that acceptance of amnae is generally low outside of the Highlands, too, especially when compared to other -nae forms, like havenae. This can also be seen in the descriptive statistics: the example in (10) with havenae has a mode of 5 and an acceptance rate of 65%, whereas (8) (I amnae ready!) has a mode of 1 and an acceptance rate of 32% – very similar to what we saw for declarative amn’t. In fact, the maps for amnae and declarative amn’t are quite similar once the Highlands and Western Isles are ignored, with patches of lower acceptance in the Northeast and various places in the central part of the country.

Looking at the data at the individual level,Footnote ⁵ it is remarkable that scores for amnae and declarative amn’t are, in fact, moderately positively correlated (R = 0.52)– more so than amnae with other -nae forms such as havenae (R = 0.34). This is the opposite of what is expected on Bresnan (Reference Bresnan, Baltin and Collins2001)’s account, and we believe it tells us that that account cannot be right. We suggest that any account of the amn’t gap will have to also explain the fact that it tends to pattern together with amnae across Scots varieties, while still allowing them to come apart in some situations.

2.4. Geographical distribution of acceptability of declarative amn’t

We have seen that the SCOSYA data do not support Bresnan’s (Reference Bresnan, Baltin and Collins2001) claim that declarative amn’t is blocked by declarative amnae; instead, the presence of the two features is moderately positively correlated. We also saw in Figure 3 that there is regional variation in the patterns of acceptability of declarative amn’t. We explore that further below, showing that although it is not predicted by Bresnan’s (Reference Bresnan, Baltin and Collins2001) account, Yang’s (Reference Yang2016, Reference Yang, Bowern, Horn and Zanuttini2017) approach opens up the possibility of a different explanation for the distribution of the forms. As noted in Section 2, the SCOSYA data come from over 140 research sites across Scotland. In the atlas, these are grouped into broader geographic regions based on areas demarcated in traditional dialectological work (e.g. Grant Reference Grant1931, Aitken Reference Aitken and Trudgill1984, Johnston Reference Johnston and Jones1997, Millar Reference Millar2007), resulting in 15 broad regions. Table 1 provides an overview of the descriptive statistics for declarative amn’t for 11 of these dialect regions in the SCOSYA dataset.Footnote ⁶ The regions are labelled in Figure 6, which can be cross-referenced with Table 1.

Table 1.

Declarative amn’t across Scotland

The descriptive statistics clearly show regional variation in the scores for declarative amn’t. Scores are particularly high in Lothian, the Western Isles and Tayside & Angus and particularly low in Ayrshire, Glasgow, the Northeast and Stirling & Falkirk. For the remaining regions (Borders, Dumfries, Fife and the Highlands), the picture is more mixed: in most of these regions, the mode was 1, indicating high levels of rejection. However, the number of participants accepting it was between 30%–50%, suggesting a more complex picture.Footnote ⁷

There are two striking observations we can make from this data. The first is the high scores for declarative amn’t in the Western Isles. The second is the regional variation on the east coast of Scotland. Acceptance is high in Lothian in the south but lower to the immediate north in Fife. Then it rises again as we go yet farther north to Tayside and Angus before plunging in the Northeast.

We can summarise the generalisations about the amn’t gap and the inversion asymmetry that we have extracted from SCOSYA as follows:

In what follows, we account for these generalisations by leveraging a view of the syntax of negation, proposed in Thoms et al. (Reference Thoms, Adger, Caroline Heycock and Smith2023), which takes negation in inversion constructions to be distinct from negation in declaratives. We combine this with a slight extension to Yang’s Tolerance Principle to deal with cases of variation in exponence, and we show how the two together provide a way of understanding why amn’t distributes the way it does in Scots (and potentially in varieties of English more generally).

5.1. Accounting for amn’t in inversion contexts

In Section 3, we analysed negation in inversion versus declarative contexts as realisations of distinct morphosyntactic elements. That is, negation in declaratives is the realisation of a NegOP in Spec,NegP, which is just below T, and which cliticises to the finite auxiliary in T. Negation in inversion contexts, however, is the realisation of a NegOP in Spec,HighNegP, just below C in the left periphery. The realisation rules we posited above are repeated in (26):

Given that these are distinct realisation rules, it should be possible for each rule to be assessed separately with respect to Tolerance calculations. This provides the route to an account of the inversion asymmetry: if the inventories of negative auxiliary forms attested in declaratives and inversions are substantially different, then the outcome of the Tolerance calculations for (26a) and (26b) may differ, and with that come differences with respect to amn’t.

Let us consider in detail how the Tolerance calculation would work out for (26b), the spell-out rule for -n’t in inversion environments. Recall that the N for a given rule is the number of finite auxiliaries with reliably attested forms that correspond to an output of (26b), which would mean negated auxiliaries in the pre-subject position. Yang proposed the N for his general -n’t attachment rule to be 18, since there were 18 finite auxiliaries that had reliably attested forms in his COCA survey. We will assume that a similar N would apply for the rule in (26b).Footnote ¹⁸ This gives a threshold of six, as before.

What about the list of exceptions? In Scots, there are no ain’t forms, and the reduced form of don’t, [dɔ̃], does not occur in inversion contexts at all (Kaisse Reference Kaisse1985). Unlike in American English, aren’t and weren’t are not stored as exceptions since they are realised as bisyllabic forms in Scots, as predicted by the rule. Ultimately, then, the list of exceptions only includes can’t, won’t and don’t,Footnote ¹⁹ and, for some speakers, the use of aren’t for am in aren’t I? (See Section 3 above). This would amount to a minimum of four (maximally five) exceptions, below the threshold of six. In consequence, the theory predicts that (26b) will be productive, thus generating amn’t in inversions. This is summarised below:

The calculation above will work out similarly for most varieties of Scots since the inventories of negated auxiliaries in inversion contexts are largely uniform.Footnote ²⁰ The account, therefore, correctly predicts the fairly widespread acceptance of amn’t in inversions in Scotland.

5.2. Amn’t in declaratives: the impact of the variable rule analysis

What of amn’t in declaratives? For this, we must consider the variable realisation rule in (26a). At first blush, one might expect that this rule is doomed to fail to become productive because any rule that realises negation as -n’t would have the -nae forms as exceptions to contend with, and vice versa. However, it is essential to note that we are proposing that the different negative forms are generated by two distinct disjuncts of a single spell-out rule – a Labovian variable rule.

How can Yang’s Tolerance calculations apply to such Labovian rules? There is no reason to expect a difference in how we should calculate N (the number of items to which the rule is applicable). The question is how we should calculate e (the number of exceptions). We propose that all that has to be done to make sure that the Tolerance calculation generalises to this case is to take seriously the idea that a variable rule is just that – a single rule. Hence, any realisation that cannot be generated by the rule counts as an exception.

That is, if the rule is not a variable rule, exceptions will be counted just as before. If there are multiple disjunctive parts (i.e. if the rule is variable), the exception list for the rule is the union of the exceptions to all the disjuncts. Thus, following the principle proposed in (28), don’t and can’t would constitute exceptions to (26a), and so would daa and caa. By contrast, cannae, havenae and other regular forms would not constitute an exception to this particular rule since they are generated by one of the disjuncts.

It follows that in Scots varieties where -nae ‘contributes’ more irregular forms, the entire rule in (26a) would become less likely to be productive because the irregular -nae forms would increase the number of exceptions. Crucially for the case at hand, this variable rule is the one that, if productive, generates amn’t. That is, in a dialect where there are many irregular -nae forms, learners are less likely to retain a productive rule like (26a), and so they would be less likely to produce and accept amn’t.

Let us demonstrate by considering two varieties: Lothian Scots and Northeastern Scots. First, consider the Lothian Scots forms in Tables 3 and 4, where again the irregular forms are in boldface. Following the principle in (28), the range of exceptions to (26a) in this variety is the union of the the irregular forms listed in these two tables. As shown in Table 3, the irregular -n’t forms are can’t, don’t, mustn’t, won’t and the reduced don’t form [dɔ̃]; recall that aren’t and weren’t are regular as pronounced in Scots, and ain’t is absent altogether. In Table 4, we can see that there is only one irregular -nae form in Lothian Scots – dae for don’t (and this only for a subset of speakersFootnote ²¹). With this mix of forms, the rule in (26a) is below or at the Tolerance threshold, and so learners in that area ought to be likely to acquire (26a) as a productive rule.

Table 3.

Auxiliaries and their negated -n’t forms in Lothian Scots

Note: Irregular forms in bold.

Table 4.

Auxiliaries and their -nae-negated forms in Lothian Scots

Note: Irregular forms in bold.

As a result, the analysis predicts that amn’t would commonly be accepted by speakers of this variety. This prediction is borne in our data: amn’t was rated particularly highly in the Lothian region.

The calculation is quite different for Northeastern Scots, not because there are any differences in its -n’t inventory compared to what we have just seen for Lothian Scots, but because there are more irregular -nae forms – namely, caa ‘can’t’, winna ‘won’t’. This variety also has zero auxiliary forms for have and do when they are followed by negation (see Thoms et al. Reference Thoms, Adger, Caroline Heycock and Smith2023), in addition to daa (the local variant of dae) ‘don’t’. This inventory puts the exception list for this variety well above the threshold, and so (26a) is predicted to typically fail to become productive here.

Our analyses, therefore, predict that amn’t should be widely rejected in the Northeastern Scots varieties – again, the right result.

Let us now consider how this account extends to other varieties of Scots. Recall that one of the major results that we sought to account for was the variation up the east coast, whereby declarative amn’t is accepted very widely in Lothian, Tayside and Angus, very little in the Northeast, and to some degree in Fife. We have already shown that the account explains the substantial difference in scores between the Northeast and Lothian. The analysis extends readily to Tayside and Angus, which have the same inventory of negated auxiliary forms as Lothian (modulo some predictable vowel quality differences). Irregulars such as the winna(e) ‘won’t’ and caa ’can’t’ that are present in the Northeast seem not to be a feature of these varieties, and the zero auxiliary forms are not used there at all. The Tolerance calculation is thus the same as for Lothian, and amn’t is predicted to be productive in declaratives.

As for Fife, which occupies the peninsula between Lothian and Tayside & Angus, there are more irregular negative forms in the varieties spoken there, as caa and winnae are attested conservative features of the area, and dae is also widely used by young and old speakers. As a result, the number of irregulars in Fife is generally higher than in Lothian, Tayside and Angus, and almost as high among older or conservative varieties as in the Northeastern varieties. The picture with amn’t in Fife, however, is quite mixed; in particular, there is an especially strong difference between the generations, as the acceptance rate among the old participants was particularly low, just 4.5% (mode and median 1), whereas the acceptance rate among younger participants was 50%. This can be compared with the situation in the other areas with generally low scores (Northeast, Glasgow and Ayrshire), where the rates of acceptance were much closer between the age groups (10% and 24%, 12% and 25%, and 19% and 19%, respectively). We suggest, then, that there is a true generational difference in the use of amn’t in Fife, and we speculate that this could be related to change in the use of the irregular forms in this region. Although we cannot use corpus data to probe this analysis of the Fife data further, additional judgment data gathering in future work may be able to test it more rigorously. As it stands, we take this analysis to give us a plausible account of the Fife data, and thus a fairly complete understanding of the variation with amn’t on the east coast.

Finally, let us comment on how the analysis handles the data from the rest of the country. Putting the varieties without -nae to one side, the account predicts two broad kinds of varieties: those with a larger number of exceptions to (26a), which should pattern with Northeastern Scots in disfavouring amn’t, and those with fewer exceptions, which should pattern with Lothian Scots. Concerning the latter group, the analysis makes broadly the right predictions for varieties in Dumfries and the Borders, both of which have higher rates of acceptance of amn’t (see Table 1 above). These varieties typically have the same inventory of irregulars as Lothian Scots: although some speakers in these regions accept daa/dae (examples were attested in all areas), caa is largely unattested (except for in some varieties in the Borders), winna(e) is unattested, and the zero auxiliaries are completely unattested.

As for the remaining regions, the proposal’s predictions are unclear in the cases of Stirling and Falkirk, and the Highlands (which encompasses Inverness and the area around it). In the case of Stirling and Falkirk, this is a somewhat unusual region: there are only seven locations in this grouping, and it is in a transitional area in central Scotland between several other, better-defined dialect regions. We generally have lower information about the dialects of this region compared to others (for instance, concerning the use of irregular auxiliariesFootnote ²²). We therefore tentatively put this region to one side, pending further empirical data collection.

Similar remarks apply to the Highlands region, which contains just seven locations (23 ratings in total for (7), I amn’t ready yet!). Speakers in that region also gave amn’t in inversions relatively low ratings. This suggests there is more to understand about the status of the data from there, and again, we put this region aside.

What about Glasgow and Ayrshire? The proposal seems to make the wrong prediction for Glasgow and Ayrshire, where there is little to no irregularity in the -nae paradigm, but amn’t is rated quite low. However, the varieties of this region have at their disposal an additional form for the realisation of negated first-person singular present tense be – namely, amurnae:

Given the Elsewhere Principle, our account predicts that the availability of another, more specific form will result in blocking of the application of the general rule, and so amurnae will block application of (26a) to generate amn’t for the relevant speakers, just like won’t blocks generation of willn’t for all other English speakers. Thus, even if (26a) is productive for speakers of these varieties, they are not expected to produce and accept amn’t in declaratives if they have acquired amurnae. This accounts for the low acceptability of declarative amn’t in this region. It is possible that amurnae is used beyond these regions – for instance, in parts of Stirling and Falkirk – in which case, this might explain some of the uncertainties surrounding what is going on in this region, but information on this feature is very sparse. We also leave this for future investigation.

The results of our analysis are summarised in Table 5, which shows that the predictions of our account are largely confirmed.

Table 5.

Our predictions regarding declarative amn’t across Scotland

A final comment to make on the data from declarative amn’t is the extent of interspeaker variation: in no single area was declarative amn’t uniformly rejected or uniformly accepted, and in most areas there was a mix of responses. Thus, there was a degree of what we might call overacceptance, with some speakers accepting declarative amn’t in some areas where our analysis predicts it should be absent (e.g. the Northeast). Similarly, there was a degree of what we might call underacceptance, where a number of speakers reject declarative amn’t in areas where we would expect it to be accepted more uniformly (e.g. the Western Isles).

There may well be methodological reasons for this. It is, of course, reasonable to assume that some proportion of overacceptance and underacceptance can be attributed to the noisy nature of large-scale acceptability judgment data gathering. However, previous work has shown (Jamieson et al. Reference Jamieson, Adger, Heycock, Smith and Thoms2023) that the judgment data from the SCOSYA project largely lines up with patterns of production in the SCOSYA corpus – in particular, in the case of features that are not strongly stigmatisedFootnote ²³ and which are used commonly enough in the corpus for usage statistics to be observed.

We noted at the end of Section 2 that there might be some methodological issues with respect to gathering data on negative contraction examples specifically – speakers might rate negative contraction lower because of a preference for using auxiliary contraction I’m no/not – which would account for some amount of underacceptance of declarative amn’t. This could potentially be a factor in explaining the fact that declarative amn’t is rated lower than inversion amn’t in general, even in regions where the two are predicted by our analysis to be more or less the same. For instance, in the Western Isles, where there are no -nae forms in the mix, declarative amn’t is accepted 53% of the time, and inversion amn’t 72% of the time.

In addition to methodological issues, our analysis makes room for a certain degree of individual-level variation, in particular, with respect to overacceptance of amn’t in areas where the general -n’t-attachment rules fail to become productive. Recall from the discussion in Section 4 that forms that may be the output of a productive rule in one variety may be learned as irregular forms in another where there are more exceptions and hence no productive rule. Indeed, on our account – following Yang – this is the situation for North American speakers learning the form isn’t or hasn’t. Amn’t is likely to be extremely rare in the input to North American learners, so we would not expect it to be learned as an irregular in this way, but things could potentially be different in some Scots varieties. It is clear that amn’t is rare in production – recall there was not a single clear example in the 3,000,000-word SCOSYA corpus – and so usage of amn’t is unlikely to be driving the whole set of dialect differences we have seen above, but it is possible that there will be individuals who have learned amn’t on the basis of (scant) production data in neighbouring varieties, even in communities where the makeup of the negative auxiliary inventory is such that it would typically rule out a productive negative attachment rule.

Taken together, these factors give us a way to understand the variability in the amn’t data. However, it is highly unlikely that these factors combine to explain the extensive and systematic regional differences that we have laid out above.