Extending the Neural Phillips Curve to Smaller Economies with Limited Historical Data
More than three years ago, I introduced the Hemisphere Neural Network—or what I sometimes call the Neural Phillips Curve—in my paper now published in JBES. This model presents a new kind of interpretable neural network: it predicts inflation as a sum of four distinct components, echoing the traditional decomposition in standard Phillips curves. Specifically, it separates:
• Inflation expectations,
• Economic slack (or the output gap),
• Short-term effects of commodity prices,
• And other residual influences.
In that paper, I focused primarily on the United States, relying on quarterly data from the 1960s onward, drawing from well-established sources like the FRED-QD database.
However, after presenting the model at several central banks and discussing with researchers around the world over the past few years, it became clear that two major challenges arise when applying this framework beyond the U.S.:
1. Limited Historical Data
Unlike the United States, many countries lack long, consistent time series. In some cases, reliable data are available only from the 1990s onward. Even when earlier data exist, economic transformations—such as structural reforms, the adoption of inflation targeting, or major political shifts—often render historical series incompatible with contemporary conditions. Although the Hemisphere Neural Network is designed with structure in mind, it still requires a reasonable number of observations to estimate the contributions meaningfully.
2. Small Open Economy Dynamics
The U.S. economy is large and can be modeled, more or less, as if it were closed (in fact, when I added an international hemisphere in the original paper, the results changed only slightly). For small open economies, however, external shocks often play a much greater role in inflation dynamics. In such cases, a standard Phillips curve decomposition may overlook crucial drivers. Moreover, when the neural network constructs internal representations of slack and inflation expectations, omitting external factors can cause the model to force-fit endogenous components to account for what are, in reality, exogenous shocks—leading to counterintuitive interpretations.
Addressing the Challenges
Given these hurdles, how can we adapt the Hemisphere Neural Network to work in data-scarce, externally-sensitive economies? I propose two complementary strategies:
Addressing Challenge 1 by Statistical Nudging
One way to mitigate the lack of historical data is to regularize the estimation more heavily or to inject prior information about the expected behavior of the components. It is fair to say that central bankers typically hold fairly strong priors about what economic slack should plausibly look like. Thus, my suggestion is to use what I call “functional shrinkage.” The component-wise structure of the Hemisphere Neural Network is particularly useful here, as it allows for defining shrinkage constraints even in a highly nonparametric model where individual weights carry little interpretive meaning on their own. One can easily modify the HNN’s mean squared error loss function to add a penalty term of the form \xi * \sum{t=1}^T corr(g_t, g_t^*) where \xi is a tuning parameter controlling how much we nudge the estimated g_t toward the current in-house estimate g_t^*. Similar adjustments can be made, if necessary, for other components as well.
A more sophisticated avenue is transfer learning: pre-train the network’s structure on larger, similar economies, then fine-tune it on the smaller country’s data. Another possibility is pooling information by combining data across several small economies that share similar inflation dynamics (for example, within a regional bloc). Both strategies could potentially be implemented using the new World Macro Database. Still, I view them as more demanding and less likely to deliver immediate results.
Adressing Challenge 2 by Explicitly Capture External Shocks
For small open economies, it is crucial to explicitly model external drivers alongside domestic components. This could mean:
• Adding a fifth explicit component tied to import prices or terms-of-trade shocks.
• Allowing the commodity price component to capture broader external influences, beyond domestic commodity exposure.
• Introducing global inflation proxies as direct inputs to the network.
• Changing the target from headline inflation to core inflation or services inflation.
• Taking out with dummies things we do not expect the model to fit.
By explicitly accounting for external pressures, the network can better distinguish between domestic slack-driven inflation and imported inflation, preserving the meaningful decomposition that makes the Hemisphere Neural Network appealing in the first place. As for country-specific guidance, a natural starting point is to examine the specification of the usual in-house workhorse Phillips curve.
Conclusion
The Hemisphere Neural Network blends the interpretability of traditional macroeconomic models with the flexibility of modern machine learning. As with any model, however, careful adaptation is needed when moving beyond its original context. The approaches outlined above represent natural extensions of the design and offer a promising path for applying neural Phillips curves across a broader range of countries. Moreover, they are readily implementable with the current R and Python codes, requiring only minor adjustments.
