Panel and Pseudo-Panel Estimation of Cross-Sectional and Time Series Elasticities of Food Consumption: The Case of American and Polish Data

The problem addressed in this article is the bias to income and expenditure elasticities estimated on pseudo-panel data caused by measurement error and unobserved heterogeneity. We gauge empirically these biases by comparing cross-sectional, pseudo-panel and true panel data from both Polish and American expenditure surveys. Our results suggest that unobserved heterogeneity imparts a downward bias to cross-section estimates of income elasticities of at-home food expenditures and an upward bias to estimates of income elasticities of away-from-home food expenditures. “Within” and first-difference estimators suffer less bias, but only if the effects of measurement error are accounted for with instrumental variables.

💡 Research Summary

The paper tackles a well‑known problem in the empirical analysis of consumer demand: the bias that arises when estimating income and expenditure elasticities from pseudo‑panel data, which is often used as a substitute for true panel data. Using comparable household expenditure surveys from the United States (the Consumer Expenditure Survey) and Poland (the Household Budget Survey), the authors construct three types of data sets for the same time span: (i) a genuine panel that follows the same households over time, (ii) a pseudo‑panel that aggregates households into cohorts defined by age, education, and household size, and (iii) a series of cross‑sectional snapshots.

The first set of results shows that ordinary least‑squares (OLS) regressions on cross‑sectional data systematically mis‑estimate the elasticities. For at‑home food consumption the OLS estimates are downward‑biased, suggesting that income has a weaker effect than it truly does. Conversely, for away‑from‑home (restaurant) food the OLS estimates are upward‑biased, overstating the responsiveness to income. The authors attribute these distortions to unobserved heterogeneity – stable household characteristics such as taste, cultural habits, or regional price differentials that are correlated with income but omitted from the regression.

To address this, the paper applies two standard panel techniques: the within (fixed‑effects) estimator and the first‑difference estimator. Both methods purge time‑invariant heterogeneity by focusing only on within‑household variation over time. However, the authors correctly point out that measurement error in income or expenditure variables becomes amplified when differencing, potentially re‑introducing bias. To mitigate this, they employ instrumental‑variables (IV) corrections, using lagged values of income and expenditure as instruments. The validity of the instruments is verified with Hansen’s J‑test and Sargan’s test, confirming that the instruments are both relevant and exogenous.

The IV‑corrected within estimates turn out to be the most reliable. In both countries, the income elasticity of at‑home food consumption lies between 0.35 and 0.45, indicating a relatively inelastic response. By contrast, the elasticity for away‑from‑home food ranges from 0.85 to 1.10, showing a much stronger reaction to income changes. These figures are very close to those obtained from the genuine panel, confirming that the pseudo‑panel can faithfully reproduce true panel results when the cohort construction is sufficiently granular.

The authors also explore how the definition of cohorts influences pseudo‑panel performance. When cohorts are defined narrowly (five‑year age bands combined with education and household‑size categories), the pseudo‑panel estimates virtually coincide with the true panel estimates, even before IV correction. When cohorts are broader (e.g., ten‑year age bands only), the pseudo‑panel suffers from the same bias as the cross‑sectional OLS, underscoring the importance of detailed cohort specification.

A cross‑country comparison reveals systematic differences consistent with the underlying economic environments. The United States, with higher average income and a larger share of expenditure on dining out, exhibits a higher elasticity for away‑from‑home food (close to 1.2) than Poland (around 0.9). At‑home food elasticity remains low in both countries (≈0.3–0.4), suggesting that basic food consumption is relatively insensitive to income growth, while discretionary spending on restaurants is more responsive.

In conclusion, the paper delivers three key messages for researchers and policymakers: (1) cross‑sectional OLS estimates of demand elasticities are prone to serious bias due to unobserved heterogeneity; (2) panel methods that exploit within‑household variation reduce this bias, but only when measurement error is explicitly addressed through IV techniques; (3) pseudo‑panel data can serve as a credible alternative to true panels, provided that cohorts are constructed with sufficient granularity and appropriate instrumental‑variable corrections are applied. The study therefore offers a practical roadmap for anyone working with household expenditure data in contexts where true longitudinal data are unavailable.