Month: April 2025

Tariff dumbnamics in the penguin island autarky

The formula behind the recent tariffs has spawned a lot of analysis, presumably because there’s plenty of foolishness to go around. Stand Up Maths has a good one:

I want to offer a slightly different take.

What the tariff formula is proposing is really a feedback control system. The goal of the control loop is to extinguish trade deficits (which the administration mischaracterized as “tariffs other countries charge us”). The key loop is the purple one, which establishes the tariff required to achieve balance:

The Tariff here is a stock, because it’s part of the state of the system – a posted price that changes in response to an adjustment process. That process isn’t instantaneous, though it seems that the implementation time is extremely short recently.

In this simple model, delta tariff required is the now-famous formula. There’s an old saw, that economics is the search for an objective function that makes revealed behavior optimal. There’s something similar here, which is discovering the demand function for imports m that makes the delta tariff required correct. There is one:

Imports m = Initial Imports*(1-Tariff*Pass Through*Price Elasticity)

With that, the loop works exactly as intended: the tariff rises to the level predicted by the initial delta, and the trade imbalance is extinguished:

So in this case, the model produces the desired behavior, given the assumptions. It just so happens that the assumptions are really dumb.

You could quibble with the functional form and choice of parameters (which the calculation note sources from papers that don’t say what they’re purported to say). But I think the primary problem is omitted structure.

First, in the original model, exports are invariant. That’s obviously not the case, because (a) the tariff increases domestic costs, and therefore export prices, and (b) it’s naive to expect that other countries won’t retaliate. The escalation with China is a good example of the latter.

Second, the prevailing mindset seems to be that trade imbalances can adjust quickly. That’s bonkers. The roots of imbalances are structural, and baked in to the capacity of industries to produce and transport particular mixes of goods (pink below). Turning over the capital stocks behind those capacities takes years. Changing the technology and human capital involved might take even longer. A whole industrial ecosystem can’t just spring up overnight.

Third, in theory exchange rates are already supposed to be equilibrating trade imbalances, but they’re not. I think this is because they’re tied up with monetary and physical capital flows that aren’t in the kind of simple Ricardian barter model the administration is assuming. Those are potentially big issues, for which there isn’t good agreement about the structure.

I think the problem definition, boundary and goal of the system also need to be questioned. If we succeed in balancing trade, other countries won’t be accumulating dollars and plowing them back into treasuries to finance our debt. What will the bond vigilantes do then? Perhaps we should be looking to get our own fiscal house in order first.

Lately I’ve been arguing for a degree of predictability in some systems. However, I’ve also been arguing that one should attempt to measure the potential predictability of the system. In this case, I think the uncertainties are pretty profound, the proposed model has zero credibility, and better models are elusive, so the tariff formula is not predictive in any useful way. We should be treading carefully, not swinging wildly at a pinata where the candy is primarily trading opportunities for insiders.

Communicating uncertainty and policy sensitivity

This video is a quick attempt to run through some ways to look at how policy effects are contingent on an uncertain landscape.

I used a simple infection model in Ventity for convenience, though you could do this with many tools.

To paraphrase Mark Twain (or was it …), “If I had more time, I would have made a shorter video.” But that’s really part of the challenge: it’s hard to do a good job of explaining the dynamics of a system contingent on a wide variety of parameter choices in a short time.

One possible response is Forrester’s: we simply can’t teach everything about a nonlinear dynamic system if we have to start from scratch and the listener has a short attention span. So we need to build up systems literacy for the long haul. But I’d be interested in your thoughts on how to pack the essentials into a YouTube short.

Sources of Uncertainty

The confidence bounds I showed in my previous post have some interesting features. The following plots show three sources of the uncertainty in simulated surveillance for Chronic Wasting Disease in deer.

  • Parameter uncertainty
  • Sampling error in the measurement process
  • Driving noise from random interactions in the population

You could add external disturbances like weather to this list, though we don’t simulate it here.

By way of background, this come from a fairly big model that combines the dynamics of the host (deer) with an SIR-like model of disease transmission and progression. There’s quite a bit of disaggregation (regions, ages, sexes). The model is driven by historic harvest and sample sizes, and generates deer population, vegetation, and disease dynamics endogenously. The parameters used here represent a Bayesian posterior, from MCMC with literature priors and a lot of data. The parameter sample from the posterior is a joint distribution that captures both individual parameter variation and covariation (though with only a few exceptions things seem to be relatively independent).

Here’s the effect of parameter uncertainty on the disease trajectory:

Each of the 10,000 runs making up this ensemble is deterministic. It’s surprisingly tight, because it is well-determined by the data.

However, parameter uncertainty is not the only issue. Even if you know the actual state of the disease perfectly, there’s still uncertainty in the reported outcome due to sampling variation. You might stray from the “true” prevalence of the disease because of chance in the selection of which deer are actually tested. Making sampling stochastic broadens the bounds:

That’s still not the whole picture, because deer aren’t really deterministic. They come in integer quanta and they have random interactions. Thus a standard SD formulation like:

births = birth rate * doe population

becomes

births = Poisson( birth rate * doe population )

For stock outflows, like the transition from healthy to infected, the Binomial distribution may be the appropriate choice. This means there’s additional variance around the deterministic course, and the model can explore a wider set of trajectories.

There’s one other interesting feature, particularly evident in this last graph: uncertainty around the mean (i.e. the geometric standard deviation) varies quite a bit. Initially, uncertainty increases with time – as Yogi Berra said, “It’s tough to make predictions, especially about the future.” In the early stages of the disese (2003-2008 say), numbers are small and random events affect the timing of takeoff of the disease, amplified by future positive feedback. A deterministic disease model with reproduction ratio R0>1 can only grow, but in a stochastic model luck can cause the disease to go extinct or bumble around 0 prevalence for a while before emerging into growth. Towards the end of this simulation, the confidence bounds narrow. There are two reasons for this: negative feedback is starting to dominate as the disease approaches saturation prevalence, and at the same time the normalized standard deviation of the sampling errors and randomness in deer dynamics is decreasing as the numbers become larger (essentially with 1/sqrt(n)).

This is not uncommon in real systems. For example, you may be unsure where a chaotic pendulum will be in it’s swing a minute from now. But you can be pretty sure that after an hour or a day it will be hanging idle at dead center. However, this might not remain true when you broaden the boundary of the system to include additional feedbacks or disturbances. In this CWD model, for example, there’s some additional feedback from human behavior (not in the statistical model, but in the full version) that conditions the eventual saturation point, perhaps preventing convergence of uncertainty.

 

Understanding Prediction

I posted my recent blogs on Forrester and forecasting uncertainty over at LinkedIn, and there’s been some good discussion. I want to highlight a few things.

First, a colleague pointed out that the way terms are understood is in the eye of the beholder. When you say “forecast” or “prediction” or “projection” the listener (client, stakeholder) may not hear what you mean. So regardless of whether your intention is correct when you say you’re going to “predict” something, you’d better be sure that your choice of language communicates to the end user with some fidelity.

Second, Samuel Allen asked a great question, which I haven’t answered to my satisfaction, “what are some good ways of preventing consumers of our conditional predictions from misunderstanding them?”

One piece of the puzzle is in Alan Graham’s comment:

an explanation that has communicated well starts from the distinction between behavior sensitivity (does the simulation change?) versus outcome or policy sensitivity (does the size or direction of the policy impact change?). Two different sets of experiments are needed to answer the two different questions, which are visually distinct:

This is basically a cleaner explanation of what’s going on in my post on Forecasting Uncertainty. I think what I did there is too complex (too many competing lines), so I’m going to break it down into simpler parts in a followup.

Another piece of the puzzle is visualization. Here’s a pair of scenarios from our CWD model. These are basically nowcasts showing uncertainty about historic conditions, subject to actual historic actions or a counterfactual “high harvest” scenario:

Note that I’m just grabbing raw stuff out of Vensim; for presentation these graphics could be cleaner. Also note the different scales.

On each of these charts, the spread indicates uncertainty from parameters and sampling error in disease surveillance. Comparing the two tells you how the behavior – including the uncertainty – is sensitive to the policy change.

In my experience, this works, but it’s cumbersome. There’s just too much information. You can put the two confidence bands on the same chart, using different colors, but then you have fuzzy things overlapping and it’s potentially hard to read.

Another option is to use histograms that slice the outcome (here, at the endpoint):

Again, this is just a quick capture that could be improved with minimal effort. The spread for each color shows the distribution of possibilities, given the uncertainty from parameters and sampling. The spread between the colors shows the policy impact. You can see that the counterfactual policy (red) both improves the mean outcome (shift left) and reduces the variance (narrower). I actually like this view of things. Unfortunately, I haven’t had much luck with such things in general audiences, who tend to wonder what the axes represent.

I think one answer may be that you simply have to go back to basics and explore the sensitivity of the policy to individual parameter changes, in paired trials per Alan Graham’s diagram above, in order to build understanding of how this works.

I think the challenge of this task – and time required to address it – should not be underestimated. I think there’s often a hope that an SD model can be used to extract an insight about some key leverage point or feedback loop that solves a problem. With the new understanding in hand, the model can be discarded. I can think of some examples where this worked, but they’re mostly simple systems and one-off decisions. In complex situations with a lot of uncertainty, I think it may be necessary to keep the model in the loop. Otherwise, a year down the road, arrival of confounding results is likely to drive people back to erroneous heuristics and unravel the solution.

I’d be interested to hear success stories about communicating model uncertainty.