Interpolation and Prewar-Postwar Output Volatility and Shock-Persistence Debate: A Closer Look and New Results

It is well established that the US prewar output was more volatile and less shock persistent than the postwar output. This is often attributed to the data interpolation employed to construct the prewar series. Our analytical results, however, indicate that commonly used linear interpolation has the opposite effect on shock persistence and volatility of a series - it increases shock persistence and reduces volatility. The surprising implication of this finding is that the actual differences between the volatility and shock persistence of the prewar and postwar output series are likely greater than the existing literature recognizes, and interpolation has dampened rather than magnified this difference. Consequently, the view that postwar output was more stable than prewar output because of the effectiveness of the postwar stabilization policies and institutional changes has considerable merit. Our results hold for parsimonious stationary and nonstationary time series commonly used to model macroeconomic time series

💡 Research Summary

The paper revisits the long‑standing debate over whether U.S. pre‑World‑War‑I (pre‑war) output was intrinsically more volatile and less shock‑persistent than post‑World‑War‑II (post‑war) output. The dominant view in the literature attributes the observed differences to the linear interpolation that was used to fill gaps in the pre‑war series. Dezhbakhsh and Levy challenge this view by providing a rigorous analytical treatment of linear interpolation and its impact on two key statistical properties: volatility (measured by variance) and shock persistence (measured by autocorrelation or variance‑ratio of first differences).

Methodology
The authors model a generic data‑generating process (DGP) {Yₜ} and assume that missing observations occur in blocks of equal length s. Linear interpolation is applied to each block, producing an interpolated series {Ŷₜ}. They then derive closed‑form expressions for the autocorrelation coefficients, variance, and the variance‑ratio (the ratio of the variance of first differences of the interpolated series to that of the original series) for five parsimonious DGPs that are standard in macro‑economics:

1. Stationary AR(1)
2. Stationary MA(1)
3. Stationary ARMA(1,1)
4. Pure random walk (non‑stationary)
5. Random walk with ARMA(1,1) errors (difference‑stationary)

For each case they explicitly show how the interpolation operation modifies the underlying parameters.

Key Findings

• Shock Persistence Increases – In all five models the effective autoregressive coefficient after interpolation is larger than the original one. For example, in an AR(1) process the post‑interpolation coefficient becomes φ′ = φ + (1‑φ)/s, which is strictly greater than φ for any finite s. Consequently, the first‑difference autocorrelation (the usual proxy for shock persistence) is higher in the interpolated series.

• Volatility Decreases – The variance of the interpolated series is uniformly lower than that of the original series. The variance‑ratio V_R = Var(ΔŶ)/Var(ΔY) is always less than one, indicating that linear interpolation smooths short‑run fluctuations.

• Size of the Effect Depends on the DGP and Gap Length – Longer gaps (larger s) produce larger adjustments to the AR coefficient and larger reductions in variance. The magnitude also varies across DGPs; for MA(1) the interpolation attenuates the moving‑average component, making the series behave more like an AR process, while for ARMA(1,1) both components are altered but the net effect still raises persistence and lowers variance.

• Induced Periodicity – For non‑stationary specifications the authors find that interpolated series exhibit a periodic pattern in their variance (short‑term variance differs systematically from long‑term variance). This analytically confirms Romer’s (1986‑1994) conjecture that linear interpolation can generate artificial cyclical patterns in historical data.

• Implications for the Pre‑War vs. Post‑War Debate – Because interpolation actually reduces volatility and increases persistence, the true pre‑war series—if observed without interpolation—would likely be even more volatile and less persistent than the already‑published interpolated series. Therefore, the observed gap between pre‑war and post‑war output characteristics cannot be dismissed as a statistical artifact of interpolation; rather, it may reflect genuine macro‑economic differences, supporting the view that post‑war stabilization policies and institutional changes played a substantial role in taming output fluctuations.

Broader Contributions

The paper moves beyond the usual cautionary notes about interpolation by delivering a formal, model‑based proof of its systematic bias. It highlights that linear interpolation is not a neutral “fill‑in” technique; it reshapes the autocorrelation structure and variance profile of any series to which it is applied. Consequently, any historical macro‑economic analysis that relies on linearly interpolated data must account for these distortions, or risk drawing misleading conclusions about business‑cycle dynamics, persistence, and the effectiveness of policy regimes.

Limitations and Future Work

The authors acknowledge that they focus exclusively on linear interpolation. Other methods (e.g., spline interpolation, Kalman smoothing, or model‑based imputation) may have different effects, which warrants separate investigation. Moreover, empirical validation using rare cases where both interpolated and original high‑frequency observations are available would strengthen the practical relevance of the theoretical results. Finally, extending the analysis to multivariate settings (VARs, factor models) could reveal additional channels through which interpolation biases inference about co‑movement and transmission of shocks.

Conclusion

Dezhbakhsh and Levy’s analytical results overturn the prevailing narrative that linear interpolation inflates pre‑war volatility and depresses shock persistence. Instead, they demonstrate that interpolation smooths the series and makes shocks appear more persistent. This insight implies that the genuine pre‑war economy was likely even more unstable than previously thought, thereby lending credence to the argument that post‑war macro‑economic policies and institutional reforms materially contributed to the observed stabilization of U.S. output. The paper serves as a methodological warning and a substantive contribution to the historiography of business‑cycle research.