[SPACE] World Trade

[Agemegos]

Hmm. Is that capturing triangle trades?

Or ought we to make T(i, j) = V(i)*V(j)/(1 + e^(k*G(i, j) - l)), normalise that, and produce trade volumes directly, dividing by the V(i) to get proportions?

[ericthered]

Originally Posted by Agemegos

And there I though I had missed out on triangle trades and wondered where I had gone wrong!

Normalisation makes each world consume only as much as it produces, imposing an assumption of overall trade balance. But it doesn't impose bilateral trade balance. You get triangle trades (and more complex patterns).

So do just keep the trade imbalances? so T(A,B) != T (B,A)?

Note: != means does not equal. Programmer syntax.

[Ulzgoroth]

Originally Posted by Agemegos

Yeah, the splat for multiplication goes back at least to FORTRAN in 1957. But the lecturers still used the dot in my maths classes 1982–1984 and my statistics/econometrics classes 1986–1989. Whereas a splat appears instead of an × on the multiplication keys of some calculators now. I think it was Excel that made it popular beyond the world of programming. At a guess, anyway.

I'm a cave-man, nevertheless.

If it was a middle-dot I wouldn't have questioned it, might not even have thought to explain it. That's the symbol I usually use for multiplication in handwritten material, and probably the one most of my math classes have used. But using a period as a typed stand-in for that I've never seen before.

[Agemegos]

Originally Posted by ericthered

So do just keep the trade imbalances? so T(A,B) != T (B,A)?

Note: != means does not equal. Programmer syntax.

I'm not sure. I'm used to applying this stuff to destination and mode choice on a commuter network, where there is no balance constraint, and most of the literature is about brand and model choice in marketing theory, where very naturally there is no individual brand and model constraint. I feel that I ought to be able to work this out easily, but I'm not well and my mind isn't working properly.

I think the normalisation method I outlined above guarantees that each world's consumption totals to 100%, but I might have made a mistake about what percentages I'm adding. If I'm summing at j the proportions that the trades make up of the outputs of the several i then normalising is nonsense. But if I'm summing the proportions that the trades make up of V(j) that's guaranteeing overall balance-of-trade.

Try this to be on the safe side. It's an extra calculation but meh! Computers do calculations.

1. Knowing the pair-wise distances between all the worlds in your set, and the freight rate (include insurance) as a function of distance for the interstellar technology you are using, and the loading-and-launch costs for the ground-to-orbit-and-back-to-ground technology you are using, calculate the cost of transporting goods from each world to each other world. Ignore interest costs and taxes for this exercise; those are elegant refinements. If you are using a spreadsheet (which would be very much the easy way to do this) make a special case that generalised cost is zero in shipping from a world to itself: you don't have to pay the fixed launch costs. Store these in a square array (it will have a string of '0's down the diagonal); in future I'm going to refer to the cost of transport from world i to world j as G(i, j)
   
2. Guess values for k and l, constants that relate to the unknown ways that imports fit into the production functions of the worlds, consumer preferences, the relationship of freight rates to cargo values, and all sorts of things.
   
3. Using the Economic Volume figures that GURPS Space's generation supplies, and where the Economic Volume of world i is V(i), go through all the pairs of possible origin with possible destination, including all the cases where the origin is the destination. For every origin-destination pair (i is the origin, j is the destination), calculate the following temporary value, which is an un-normalised propensity of product from i to end up at j:
   

   T(i, j) = V(i) * V(j) / (1 + e ^ ( k * G (i, j) + l))

   Store those in a square array.
   
4. For each possible origin i, calculate the total of the T(i, j), and call the result ∑(i). That is, sum the rows. That's the total propensity of product from i to be consumed anywhere, which has to be normalised to the actual output of i.
   
5. For each origin-destination pair i, j calculate the proportion P of the output produced on i that is consumed on j, which is P(i, j) = T(i, j)/∑(i).
   
6. If you don't like the look of the figures, adjust k and l and repeat steps 2 – 5. Increasing k will reduce trade, long-distance trade being more affected than short-distance. Increasing l will reduce all trade without affecting long-distance more than short distance.
   
7. When you are happy with the pattern of trade that results, take the actual value of exports from each origin i to each destination j as A(i, j) = P(i, j) * V(i).

Someone check my logic.

[Agemegos]

Originally Posted by Ulzgoroth

If it was a middle-dot I wouldn't have questioned it, might not even have thought to explain it. That's the symbol I usually use for multiplication in handwritten material, and probably the one most of my math classes have used. But using a period as a typed stand-in for that I've never seen before.

Okay. I promise not to do it any more.

[Anthony]

I wonder if you could do it via some sort of monte carlo method -- just generate a large number of (unnamed, generic, vanilla) random products (perhaps proportional to GDP, perhaps not) and create a function that determines the odds of that demand being satisfied at a given transport cost from a given source. Then run through them attempting each potential trade destination (in order of transport cost., starting with the local world) until the demand is satisfied (possibly keeping track of net trade, so a world that's running a trade surplus is less likely to satisfy a demand, a deficit is more likely). That guarantees a maximum trade volume, which will typically be a smaller fraction of GDP for a larger world (since the probability of a demand being satisfied locally will increase), though it's certainly possible for some demands to never be satisfied. On the other hand, that may not be a problem.

[Agemegos]

Originally Posted by Anthony

I wonder if you could do it via some sort of monte carlo method -- just generate a large number of (unnamed, generic, vanilla) random products (perhaps proportional to GDP, perhaps not) and create a function that determines the odds of that demand being satisfied at a given transport cost from a given source. Then run through them attempting each potential trade destination (in order of transport cost., starting with the local world) until the demand is satisfied (possibly keeping track of net trade, so a world that's running a trade surplus is less likely to satisfy a demand, a deficit is more likely). That guarantees a maximum trade volume, which will typically be a smaller fraction of GDP for a larger world (since the probability of a demand being satisfied locally will increase), though it's certainly possible for some demands to never be satisfied. On the other hand, that may not be a problem.

Yeah, I've known Monte Carlo methods to be used for similar problems, which is to say for destination and mode choice for commuters on congested traffic networks. Back when we had a peace dividend unemployed simulation programmers from the American DoE were using unemployed nineties supercomputers to do it. I think they all work for NSA now.

However, we know that random utility models converge to nested multinomial logit as the number of goods and consumers increases. Nested multinomial logit is not really a computationally intense problem: much easier than millions upon millions of Monte Carlo runs. Also (not that this matters for game settings), when you are trying to model the real world, estimating the multinomial nested logit regressors is a simple exercise in GLS regression, whereas calibrating the parameters of a model by trial and error tweaks with Monte Carlo runs in between is a very sucky way to spend a bunch of months. (I know a little about it, because I started out using models with crude demand modelling that depended on calibrating arbitrary parameters by tweaking and running until the model output matched observation. I wasn't using Monte Carlo, but I was using wholly inadequate computers so that modelling runs between parameter tweaks took about a day each anyway. It sucked.)

[RyanW]

Originally Posted by Agemegos

For trade in the opposite directions? They ought to come out the same unless transport costs are assymetric.

If I'm understanding it correctly, trade should be symmetrical, because everything is being traded at some sort of parity. If one world is runnng a trade deficit, it is effectively a net exporter of money, either in the form of some sort of credit, or in paying a premium for imported goods. Does that make sense?

[Agemegos]

Originally Posted by RyanW

If I'm understanding it correctly, trade should be symmetrical, because everything is being traded at some sort of parity.

That's not exactly right, since you can have triangle trades (and quadrilateral trades, etc.). The original Triangle Trade involved British merchants (from Bristol, mostly) investing their capital in manufactures from Birmingham, Manchester, and Sheffield (cloth, cutlery etc.) and taking that to West Africa, where they sold the Manchester and Birmingham ware and used the proceeds to buy slaves. They took the slaves to the Caribbean and the southern British colonies on the North American mainland, sold them, and bought sugar, molasses, rum, and tobacco (and maybe cotton, though perhaps that was later). Then they took the plantation products back to England and sold them, taking a profit and buying more Manchester and Brummagem.

In this case there was a bilateral trade imbalance on each side of the triangle. The slavelord kingdoms in Africa had a trade deficit with England and a trade surplus with the New World; the New World had a trade deficit with Africa and a surplus with England; England had a trade deficit with the sugar, tobacco, and cotton colonies and a trade surplus with the slaver kingdoms in Africa. But at each point the surpluses cancelled the deficits and the trade did not produce a net imbalance of trade anywhere. (There were imbalances of trade, but those were produced by capital movements, not the trade.)

The problem is that I don't think this model is producing triangle trades. It might be, because everything is included in everything and I'm not thinking clearly enough to trace the connections. But it seems to me that in the real world it takes real-exchange-rate effects to make this work out, and those are not in the model.

If one world is runnng a trade deficit, it is effectively a net exporter of money, either in the form of some sort of credit, or in paying a premium for imported goods. Does that make sense?

There are a few ways that worlds can run a balance of trade deficit. They can export money so long as they have money that other worlds want, they can borrow so long as others are prepared to lend, they can sell assets such as shares in their industry and resources, they can pay the balance out of the earnings of their foreign investments.

The normalisation I used in the method outlined above guarantees that each world's exports to specific other places plus its consumption of domestic output will be equal to its economic output, i.e. that all of its output will all be consumed or invested somewhere; therefore it guarantees that total consumption+investment will be equal to total production; which is good. What it doesn't do, or at least doesn't do that I can see, is guarantee that each world's exports are equal to its imports: that there is balance of trade.

Now, a world (or country) doesn't have to have balance of trade all the time. As you suggested, and as I discussed above, export of cash balances, financial investment (asset sales) and a few other things can give you an imbalance of trade. The problem for the model is that those things are mostly transient (you run out of hard currency to export, or run out of factories, farms, and mines to sell to foreign investors, or fill up with carpet-bagging immigrants), and the chief exception (drawing interest and dividends from overseas investment) depends on thrift and surplus income and having run a trade surplus in the past, not on your position in the trade network. The model seems to be predicting permanent trade deficits (and corresponding surpluses elsewhere) on the basis of the pattern of trade routes, and that doesn't make sense. So much the worse for the model.

I guess it's possible that the model is actually okay, that the combinations and the normalisations all work out to combine the variables in such a way that the bilateral imbalances cancel out through triangle trades. But I don't see how it happens if it does, so it would be unsound (for me) to count on it.

Long story short: trade imbalances can happen, but they happen for reasons that the model doesn't reflect, and therefore any trade imbalances predicted by the model do not correspond to those real possibilities.

[Ulzgoroth]

Originally Posted by Agemegos

I guess it's possible that the model is actually okay, that the combinations and the normalisations all work out to combine the variables in such a way that the bilateral imbalances cancel out through triangle trades. But I don't see how it happens if it does, so it would be unsound (for me) to count on it.

Long story short: trade imbalances can happen, but they happen for reasons that the model doesn't reflect, and therefore any trade imbalances predicted by the model do not correspond to those real possibilities.

Could it be that the model is okay, but over time trade imbalances will result in changes to V (about which this model makes no predictions) which will have the effect of eliminating the imbalance?

It looks like it should be possible for V(i) changing to have that effect. Lower V(i) should not change P(i, j) and decrease P(j, i) less than proportionately, so if a planetary economy contracts the balance of trade should shift toward them. I don't know whether long-term trade deficit would decrease V(i), but it seems plausible.