Yes. Economic theory has proposed many plausible mechanisms that mean that large size should be associated with greater productivity and greater wealth. Further, when attempts are made to estimate the size of these effects, they turn out to be not insignificant. For example, see my own work which suggests that if the only change on Scottish independence were that it traded with the rest of the UK in the way that Ireland seems to trade with the UK, then this should be associated with a 5.5% fall in Scottish GDP.
However, these effects apply to all countries, not just Scotland, and if this were all that was going on then we should expect to see larger countries richer than smaller countries. As shown by Rose (2006), the economic literature on this generally finds no effect of size on growth or level of income (some papers even find a negative correlation e.g. Alouini & Hubert (2010)). This null result can be explained by supposing that there are non-GDP benefits of independence and richer and more productive regions, which can afford the trade-off, choose independence. This selection effect would mask the true relationship between size and GDP.
This selection effect however does not convince me. Given the persistence of national borders, then the randomising effect of technological change on productivity of different regions over time should mean that a small productive region which made the choice to be independent several hundred years ago is expected to be no more or less productive than another region that was poor several hundred years ago and made the choice to remain as part of a large country. Given random productivities, the benefits of size should be visible. They are not.
This either means that the benefits of size are wrong (I don't believe this) or that there are countervailing effects. Perhaps small countries are better run or function at a more appropriate scale (convex costs of complexity?). Perhaps there are spillover benefits to running a country rather than being a peripheral region of a larger country like the ability to attract talent (high status government employment, and many international firms want at least a small office presence in your region) which leads to a more diverse business ecology, which involves the provision of the full range of support services that new and growing businesses require.
In any case, if the correlation between size and income is approximately zero, then it suggests that the (GDP-related) costs and benefits of size roughly cancel out. This does not, itself, provide a case for independence or for union. It just suggests that if we value independence for other, non-GDP reasons, then there does not appear be any significant GDP cost/benefit to pay/gain in general. Of course, there may be issues specific to Scotland and the UK could lead to the expectation of GDP costs or benefits of independence.
If there is no relationship between country size and long run growth/wealth then surely this is bad for independence, given transition costs?
Usually, yes. But Scotland already has most of the infrastructure of a state. HMT's estimates of the transition costs were rubbished by the author whose research they relied upon. In any case, even if HMT's figures were appropriate, this is a one off cost which should be met by extra government borrowing and amortised over a very long period. If we, extremely pessimistically, assume £3bn cost at 5% borrowing rate, then this is an annual cost of £150m or 0.1% of GDP. This is not a big issue.
Lumping lots of disparate countries together produces this zero correlation between size and income. Would it not be more valid to consider subsets of reasonably similar polities? For example biggest is richest for Spanish-speaking Latin American countries (excluding Puerto Rico which is really part of the United States). And for English-speaking countries, the largest, the USA, stands out as the richest, in spite of the fact that it does not appear to have better institutions or national endowments per capita than Canada, Australia or New Zealand.
Interesting points. I'm glad you thought of making comparisons across countries which, other than size, have some similarities. I contend that a suitable comparison group for looking Scotland and the UK is the EU members of northern Europe which have never been communist. For these 11 countries (Ireland, UK, France, Belgium, Luxembourg, Netherlands, Germany, Austria, Denmark, Sweden, & Finland), there is a significantly negative correlation between size and income. Set against the Spanish speaking Latin American countries, or the worldwide English speaking countries, this isn't something that nails the argument - but it does show that your other two examples certainly don't nail the argument either.
More interestingly, looking at these countries allows us to make a specific point about Scotland and the UK rather than considering only the general size of countries issue. Eurostat has data that divides these countries up into 48 "NUTS1 regions" (*). These are shown in the graph below. I know of no reason to expect that 7 of the 12 UK regions should occupy the bottom 7 places in the ranking, with 11 of the 12 in the bottom half. The UK is not less fertile, it is not landlocked, nor is it lacking in natural resources (indeed it has the largest oil and gas reserves of any of these 11 countries). I contend that this is indicative of institutional problems in how the UK is run: perhaps to the benefit of London which is one of the richest regions in Europe, despite the poverty of the rest of the UK (indeed, the UK has the highest regional inequality in Europe). Are we to believe that it's luck that all the poorest regions are in the UK? Ireland had income per head of 70% of UK average when it gained independence in 1922, now it is in the top half of this ranking and would be the UK's second richest region if still in the UK. Escaping whatever causes the outcomes shown in this graph provides a clear expectation that Scotland can gain - in GDP terms - from independence. This is of course in addition to the non GDP benefits like electing political parties more closely aligned with preferences of the Scottish electorate.
(*) All NUTS1 regions of these 11 countries excluding 1 region from France: French overseas territories - not in northern Europe; and 6 regions from Germany: the East German Länder - formerly communist.
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