When regional comparisons mix direct effects with economy-wide feedback

How much does government spending raise regional output? How strongly do stock-market gains affect local jobs? Economists often investigate these questions by comparing places with different exposure to the same national shock. A new preprint by Endong Wang and Ren Zhang examines why those comparisons can mix the effect researchers want with other economic responses—and proposes a correction.

The target is a dynamic partial-equilibrium effect: how an outcome responds over time to a treatment, such as spending, while specified other economy-wide variables follow an unchanged path. It is not the total effect after all economic feedback has played out.

A common shock need not have common consequences

Regional studies often include fixed effects: statistical adjustments for persistent differences between places and for influences shared at each date. The difficulty is that a shared influence can affect places differently.

Consider defense spending and interest rates. If places receiving more defense spending are also less sensitive to monetary tightening, their relatively strong output response may partly reflect that lower sensitivity—not spending alone. A time adjustment cannot remove this uneven response.

The authors distinguish two sources of what the paper calls HEDGE bias. One is correlation between exposure to the treatment and exposure to another aggregate variable. The other is feedback: shocks to that other variable can change the treatment itself. Holding interest rates fixed, for example, may change the spending path as well as output.

Under the paper’s model, either mechanism can make the conventional estimate miss the desired effect. The bias need not always point upward; its direction changes across response horizons in some simulations.

Holding a path fixed statistically

The proposed framework, heterogeneous-exposure local-projection instrumental variables, or HELP-IV, estimates responses at successive horizons. Its benchmark version adds the confounder’s entire path through the response horizon, interacted with treatment exposure.

Simply adding these variables as ordinary controls is insufficient in the authors’ analysis. Their realized values also reflect other shocks that affect outcomes. HELP-IV instead instruments both the treatment and the path controls using exposure-weighted proxies for the relevant shocks.

An instrument supplies variation intended to isolate a particular causal disturbance. Here, the identifying logic combines treatment and confounder shocks so their effects on the confounder path cancel. The resulting outcome response is divided by the treatment response under that same controlled experiment.

The identification proof requires valid, relevant instruments and the paper’s model assumptions. It does not establish that any available shock measure automatically satisfies them.

A composite version constructs the offsetting instrument separately, avoiding a large regression with many instrumented path controls. An extension addresses expectations, but when available shocks cannot fully offset the expected path, it estimates an explicitly different, information-constrained effect.

Smaller estimates in two applications

The fiscal application uses annual defense-spending and output data for 46 US states over 1969–2007. A cumulative multiplier compares accumulated output responses with accumulated spending responses.

At the two-year horizon, the conventional shift-share estimate is 1.45. Backward-looking HELP-IV, treating the interest rate as the only confounder, gives 1.00, with a standard error of 0.40. The expectations-aware version gives 0.90, but leaves part of the interest-rate response unabsorbed, so it is not a fully fixed-path estimate.

A further specification uses state characteristics to adjust exposure and accommodate additional one-way confounders. Its two-year estimate is 0.35. That result requires additional exposure-balancing assumptions. Its reported standard error excludes a cross-sectional uncertainty component that the authors cannot estimate without information about omitted exposures and their effects.

The stock-wealth application revisits county employment and payroll over 1991Q3–2015Q2. Composite HELP-IV addresses four aggregate confounders, including housing returns and income measures. The estimated two-year nontradable-payroll response falls from 3.24 to 0.83 basis points, for a stock-wealth increase equal to one percent of local annual labor income. The corrected estimate’s standard error is 0.74 basis points, indicating substantial uncertainty.

Feeding that coefficient into the earlier study’s model lowers implied annual consumption out of an additional dollar of stock wealth from 3.2 to 0.8 cents. This is a model-dependent implication, not a direct measurement of household spending.

What the correction cannot guarantee

Simulations support the framework under the tested assumptions, but noisy instruments and many path controls sometimes produce extreme estimates. Some confidence intervals also cover their targets less often than intended. The empirical applications rely on identified aggregate models; the stock-wealth comparison changes shock and exposure measures as well as confounder handling.

This preprint therefore offers a conditional identification framework, not a universal downward adjustment. Its central lesson is that regional comparisons must specify which economic paths they intend to hold fixed—and show why their instruments can isolate that experiment.