Estimating flexible functional forms using macroeconomic data

W. Erwin Diewert (), Koji Nomura and Chihiro Shimizu ()
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W. Erwin Diewert: University of British Columbia
Chihiro Shimizu: Hitotsubashi University

Empirical Economics, 2025, vol. 69, issue 5, No 6, 2697 pages

Abstract: Abstract The paper estimates a flexible functional form for a joint cost function using US aggregate data for the years 1970–2022. There are four outputs (consumption, government, investment and exports) and six inputs (imports, labour, machinery and equipment services, structure services, other capital services and land services). Curvature conditions on the joint cost function are imposed without destroying the flexibility of the functional form. Various elasticities of supply and demand are estimated along with technical progress bias terms for each input. When using aggregate time series data based on the System of National Accounts, the paper shows that it is probably better to estimate a joint cost function rather than a gross output function or a GDP function. The paper also shows that assuming that an aggregate production function has constant elasticities of substitution is not appropriate for the US. Finally, the importance of including land as an aggregate input is stressed.

Keywords: Production theory; Duality theory; Production functions; Joint cost functions; Gross output functions; GDP functions; Shephard’s Lemma; Hotelling’s Lemma; Samuelson’s Lemma; Flexible functional forms; Estimation of technical progress; User costs; Modeling monopolistic behavior; Land as a factor of production (search for similar items in EconPapers)
JEL-codes: C01 C02 C32 C43 C51 C82 D24 D42 E01 E23 F11 O47 (search for similar items in EconPapers)
Date: 2025
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Working Paper: Estimating Flexible Functional Forms using Macroeconomic Data (2024)
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DOI: 10.1007/s00181-025-02727-y

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