On the Substitution of Private and Public Capital in Production

IMF Working Papers, November 1, 2019

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Canonical URL: On the Substitution of Private and Public Capital in Production

Most macroeconomic models implicitly assume private and public capital stocks are perfect substitutes in the production function.
This paper tests that assumption by estimating a nested-CES production function where private capital, public capital, and labor are considered separately.
The estimation is based on a newly developed dataset on public and private capital stocks for 151 countries over a period of 1960-2014 consistent with Penn World Table version 9.
Key empirical result: evidence against perfect substitutability between public and private capital, especially for emerging and LIDCs, with the point estimate of the elasticity of substitution estimated closely around 3.

Dataset: public and private capital stocks for 151 countries, 1960-2014, consistent with Penn World Table version 9.
Model: nested-CES production function treating public capital and private capital separately alongside labor as inputs.
Estimation approach: test whether private and public capital are perfect substitutes by estimating the elasticity of substitution parameter (substitution parameter).

Findings:
- Evidence rejects perfect substitutability between public and private capital.
- Rejection of perfect substitutability is particularly pronounced for emerging markets and LIDCs.
- Point estimate of elasticity of substitution is reported as closely around 3.
Implications for modeling and policy:
- Aggregating public and private capital into a single total capital input may misrepresent production dynamics.
- Policies and models should account for limited substitutability between public and private capital, especially in emerging and low-income developing countries.

Subjects: Expenditure, Financial institutions, Human capital, Labor, National accounts, Private investment, Public investment and public-private partnerships (PPP), Stocks.
Keywords: approximation method, coefficient estimate, confidence interval, elasticity of substitution, estimation result, Global, Human capital, point estimate, private capital, Private investment, production function, public capital, Public investment and public-private partnerships (PPP), Stocks, substitution parameter, WP.

IMF Working Paper No. 2019/232.