[SPACE] World Trade

[tshiggins]

Originally Posted by Ulzgoroth

Hmm. Could it be coming from T(i, i) varying as V(i)^2? I'd overlooked that before. That will mean that the smaller the economy, the higher the fraction that goes to exports. Meanwhile, if V(i) << V(j), A(j, i) should be approximately linear in V(i). So a tiny colony gets imports proportional to its size but exports practically everything it produces.

...Does that agree with the direction of your imbalances?

I don't know the math, but I did study international political economies, and that's not right. In smaller (poorer) economies, locals consume a greater proportion of GDP, themselves, and export very little, most of the time. The populace also tends to perceive itself as relatively deprived, and consume as many imports as it can possibly afford (which usually isn't much, granted...).

Moreover, as the GNP of the poorer country increases, the amount of imported goods consumed increases, even more -- sometimes. As a result, trade imbalances can worsen at two or three times the percentage rate of GDP growth.

(That means consumption of imported goods is highly elastic to increases in GDP, right? Or do I have that backwards?)

That said, government policy and currency exchanges can skew this. In small countries that have policies oriented toward the development of export economies (Singapore and the other Asian Tigers), this can reverse itself, especially if the population is highly educated but the cost of living (and thus the cost of labor) is pretty low. Also, labor costs can stack nicely with large disparities in currency values, and make it attractive to relocate labor-intensive, low-skill industries to poorer nations.

That can cause the GDP of that poorer nation to spike upwards. However, that's usually followed by an even larger spike of the consumption of imports immediately thereafter, even though the country is still terribly poor, relatively speaking.

(Imbalances get even worse if technological sophistication in the large economy allows it to more cheaply manufacture some of the few products the poor economy can export. It gets worse, yet, if the larger economy can produce agricultural goods in demand in the poorer economy, much more cheaply than the local farmers can, and the trade regime allows them to dump surpluses on the international markets. That can devastate the livelihoods of nations.)

So, if your model shows an increasing trade imbalance to the detriment of small economies, I think it's probably right on, Agamegos (Brett).

[Ulzgoroth]

Originally Posted by tshiggins

I don't know the math, but I did study international political economies, and that's not right. In smaller (poorer) economies, locals consume a greater proportion of GDP, themselves, and export very little, most of the time. The populace also tends to perceive itself as relatively deprived, and consume as many imports as it can possibly afford (which usually isn't much, granted...).

It's important to note that 'smaller' and 'poorer' are not the same thing. Population isn't a component of the model at all. A world with a low V may be poor per capita, or it may just have few people. This may be a problematic limitation, but it probably isn't the reason the model produces imbalance of trade tied to size.

Originally Posted by tshiggins

(That means consumption of imported goods is highly elastic to increases in GDP, right? Or do I have that backwards?)

I think that's the right polarity, though I don't know whether that would be common usage.

[Agemegos]

Originally Posted by Ulzgoroth

Hmm. Could it be coming from T(i, i) varying as V(i)^2? I'd overlooked that before. That will mean that the smaller the economy, the higher the fraction that goes to exports. Meanwhile, if V(i) << V(j), A(j, i) should be approximately linear in V(i). So a tiny colony gets imports proportional to its size but exports practically everything it produces.

...Does that agree with the direction of your imbalances?

No. The results I'm getting are much more cracked than that. The split between exports and domestic consumption just isn't working at at, and it turns out that worlds have trade balance but don't meet their budget constraints. Worlds where transport is cheap both import and export more than the difference between their Vi and their Ti,i. The problem arises because the columns and rows involving worlds with Plenty of cheap tradev opportunities are reduced by the logistic function less than is average for the matrix, so reduction by costs followed by normalisation increases the total of row or column values to above the corresponding V. It's just garbage.

This is an assignment problem. The way I used to solve those back in the day was with the Simplex Algorithm, and I'm no longer convinced that there is an algebraic solution. If there is, I can't find it. Which means that I can't get the trick to work by which the model endogenously produces the split between export and consumption.

I'm not going to beat my head against it any more. not good for my head.

[Agemegos]

Originally Posted by tshiggins

(That means consumption of imported goods is highly elastic to increases in GDP, right? Or do I have that backwards)

It's an income-elasticity, so yes: it's price elasticities of demand that come out negative so that the elastic demands have actually small elasticities (large in absolute value but smaller than zero.

If you want to use it as to the manner born, the idiom is to speak of demand rather than consumption being elastic and use "with" rather than "to", or even more often to prefix the independent variable before "elasticity". But it really doesn't matter.

We have to be wary of making excuses for a bad model by attributing its anomalies to economic factors that were not built into it. That's a very common fault among my erstwhile colleagues. Wealth is not including in this model, nor development, nor exchange rate nor price-level effects, nor propensities to save or borrow, nor the qualities of prestige goods. So it can't be magically capturing any of those economic effects. I just fouled up, is all.

[Ulzgoroth]

Okay, some back-of-the-envelope here, I think there's a core problem with the earlier model. I may be coming quite late to that party, I'm not sure.

Even in a two-body problem with economic outputs v and V and a symmetric transport cost factor d, you generate vV/d/(V+v/d) imports to and vV/d/(v+V/d) exports from the 'v' economy. And 1/(v/d+V) > 1/(v+V/d).

Originally Posted by Agemegos

Now, random utility theory suggests that transport costs will tend to suppress consumption proportionately to a logistic function of the increase of price. So if we multiply each Ti,j by a logistic function of the generalised cost of transport from i to j the resulting T'i,j will be in the right ratios, and bilateral balance will be preserved if transport costs are symmetric — but consumers will not be consuming or investing their entire budgets. We can preserve the symmetries and the ratios between different T values by a scalar multiplication, and the appropriate factor is ∑V/∑T.

I'm going to try that out in a spreadsheet. Someone please check my logic.

I think I more or less follow up to here, and assume you know what you're about with the random utility theory. Assuming you mean that the actual T is T(i,j) = T'(i,j) * ∑V/∑T' your correction factor should make the sum of all transfers (including self-transfers) equal the sum of all economic activity, and the symmetry seems to ensure that trade balances are okay, but I think as a result you're not guaranteeing that ∑T(I,j) < V(I).

It seems that for any world X, T(X,X) = V(X)^2/∑T'. Regardless of how or if the world participates in the trade network.

[Agemegos]

Originally Posted by Ulzgoroth

I think I more or less follow up to here, and assume you know what you're about with the random utility theory. Assuming you mean that the actual T is T(i,j) = T'(i,j) * ∑V/∑T' your correction factor should make the sum of all transfers (including self-transfers) equal the sum of all economic activity, and the symmetry seems to ensure that trade balances are okay, but I think as a result you're not guaranteeing that ∑T(I,j) < V(I).

Yep, that's the problem.

It seems that for any world X, T(X,X) = V(X)^2/∑T'. Regardless of how or if the world participates in the trade network.

The T' values are measures of how it participates in trade: each is trade volume with a specific consumer. Their total, ∑T', ought to capture the world's overall participation in trade. It doesn't because of the normalisation problem you mentioned above.

[Ulzgoroth]

Originally Posted by Agemegos

Yep, that's the problem.



The T' values are measures of how it participates in trade: each is trade volume with a specific consumer. Their total, ∑T', ought to capture the world's overall participation in trade. It doesn't because of the normalisation problem you mentioned above.

That's the ∑T' from the universal normalization factor, which I presume must be across all (i,j), so it's the same for a world deeply enmeshed in a close trade network and one infinitely far from everything else.

[Agemegos]

Originally Posted by Ulzgoroth

That's the ∑T' from the universal normalization factor, which I presume must be across all (i,j), so it's the same for a world deeply enmeshed in a close trade network and one infinitely far from everything else.

Ah, true. But this statement isn't right

It seems that for any world X, T(X,X) = V(X)^2/∑T'. Regardless of how or if the world participates in the trade network.

because (1 + e^(Gi,i - k)) is by no means necessarily equal to 1 even though Gi,i is zero.

[Ulzgoroth]

Originally Posted by Agemegos

Ah, true. But this statement isn't right



because (1 + e^(Gi,i - k)) is by no means necessarily equal to 1 even though Gi,i is zero.

True, I was neglecting the factor 1/(1+e^-k) there.

I don't think having another constant factor between 0 and 1 in that formula is going to change the problem with it, though.

[Agemegos]

Originally Posted by Ulzgoroth

True, I was neglecting the factor 1/(1+e^-k) there.

I don't think having another constant factor between 0 and 1 in that formula is going to change the problem with it, though.

It doesn't, no.

I'm going to drop this now, because I'm starting to remember what "idempotent" means. I'll be having flashbacks next.