[Paper Review] Unbalanced Growth and Land Overvaluation

Tomohiro Hirano, Alexis Akira Toda|arXiv (Cornell University)|Jul 1, 2023

Economic theories and models4 citations

TL;DR

This paper establishes a theoretical link between unbalanced productivity growth, the elasticity of substitution between land and labor, and persistent land overvaluation in modern economies. Using a stochastic overlapping generations model with land as both a production factor and store of value, it proves that when labor productivity grows faster than land productivity and the elasticity of substitution exceeds 1, land prices systematically exceed their fundamental value—defined as the present value of future rents—leading to long-run overvaluation.

ABSTRACT

Historical trends suggest the decline in importance of land as a production factor but its continued importance as a store of value. Using an overlapping generations model with land and aggregate uncertainty, we theoretically study the long-run behavior of land prices and identify economic conditions under which land becomes overvalued on the long-run trend relative to the fundamentals defined by the present value of land rents. Unbalanced growth together with the elasticity of substitution between production factors plays a critical role. Around the trend, land prices exhibit recurrent stochastic fluctuations, with expansions and contractions in the size of land overvaluation.

Motivation & Objective

• To analyze the long-run behavior of land prices in modern economies where technological progress is faster in non-land sectors.
• To investigate why land prices may systematically exceed their fundamental value despite declining use in production.
• To identify the economic conditions under which land becomes overvalued relative to the present value of future land rents.
• To formalize the mechanism through which unbalanced growth and factor substitution elasticity drive persistent overvaluation.
• To establish a theoretical foundation—'Land Overvaluation Theorem'—for understanding recurrent fluctuations in land price deviations from fundamentals.

Proposed method

• Formulates a two-period overlapping generations (OLG) model with heterogeneous agents (young and old) and land as both a production input and financial asset.
• Employs a constant elasticity of substitution (CES) production function with factor-augmenting technological progress to model labor and land inputs.
• Applies a backward induction argument to show that land is always overvalued when productivity growth is unbalanced and elasticity of substitution exceeds 1.
• Uses stochastic discount factors derived from intertemporal marginal rates of substitution to model asset pricing under uncertainty.
• Establishes bounds on the fundamental value of land using wage and rent growth dynamics, showing that the ratio of fundamental value to price tends to zero over time.
• Proves the Land Overvaluation Theorem via a series of lemmas, demonstrating that $ P_t > V_t $ almost surely for all $ t $, given the stated conditions.

Experimental results

Research questions

• RQ1 Under what conditions does land become overvalued relative to its fundamental value in a growing economy?
• RQ2 How does unbalanced productivity growth—faster in non-land sectors—affect the long-run trend of land prices?
• RQ3 What role does the elasticity of substitution between labor and land play in determining land price deviations from fundamentals?
• RQ4 Why do land prices exhibit persistent overvaluation even when land's role in production diminishes?
• RQ5 Can a theoretical model with overlapping generations and stochastic discounting explain recurrent fluctuations in land overvaluation?

Key findings

• When the elasticity of substitution between labor and land exceeds 1 at high input levels, land prices grow faster than the present value of future land rents, leading to persistent overvaluation.
• In a two-sector model with faster productivity growth in the tech sector, land prices rise due to savings motives and capital gains expectations, even as land rents grow slowly.
• The fundamental value of land, defined as the expected discounted sum of future rents, grows more slowly than the market price of land, causing the price-to-fundamental-value ratio to rise over time.
• The Land Overvaluation Theorem proves that $ P_t > V_t $ almost surely for all $ t $, given that the elasticity of substitution exceeds 1 and productivity growth is unbalanced.
• The ratio $ V_t / P_t $ converges to zero almost surely as $ t \to \infty $, implying that overvaluation becomes increasingly pronounced in the long run.
• The model shows that land overvaluation is not a temporary mispricing but a structural feature of economies with unbalanced growth and high factor substitutability.