Lecture 5. Total Factor Productivity and Dual Theory (Total Factor Productivity and Dual Theory)
Recommended reading: 【Economic History】 Economic History Table of Contents
1. National Income Determination Equation
2. Dual Approach to TFP
1. National Income Determination Equation
⑴ Formalization
[ Y = rK + wL + iT ]
① Y: National income
② K: Units of capital (units of physical capital)
③ L: Number of workers (units of human capital)
④ T: Units of land
⑤ r: Profit per unit of capital
⑥ w: Wage per worker
⑦ i: Land rent per unit of land
⑵ Malthusian theory: No increasing-returns effect
[ r,\; w,\; i = \text{constant} ]
2. Dual Approach to TFP
⑴ Overview
① Growth accounting: the relative contributions of the rate of technical progress, capital growth, and labor growth to economic growth
② In the pre-industrial era, it is difficult to obtain (or to obtain accurately) information on capital, labor, and land
③ The dual approach is a convenient indirect method: it infers growth by checking increases in factor payments per unit of input and increases in output
⑵ Derivation
① The aggregate production function of the macroeconomy is represented under constant returns to scale (CRS, constant returns to scale)
○ Y: Total output
○ z: Technology level
○ K: Capital input
○ L: Labor input
○ T: Land input
○ α: Capital income share
○ β: Labor income share
○ 1 − α − β: Land income share
○ Tip. Solving with the Lagrange multiplier method yields: (\alpha = rK / Y), (\beta = wL / Y)
② Take ln on both sides and then take the differential (instantaneous growth rate)
③ Total factor productivity (TFP): the rate of technical progress
○ The improvement in productivity (or the portion of economic growth) that cannot be explained by increases in land, human capital, and physical capital (which grow arithmetically in this setting)
○ Limitation 1. Economic growth itself can have an uplifting effect (e.g., Adam Smith’s idea of the division of labor)
○ Limitation 2. Increases in output due to weather, etc., can be mistaken for technical progress
○ Nevertheless, TFP is still widely accepted as a useful tool
○ Example: The following example includes the contribution of land as well
○ Output growth rate = 5% (real value)
○ Labor: growth rate of labor hours = 5%, weight = 0.5
○ Capital: capital growth rate = 5%, weight = 0.3
○ Land: land growth rate = 1%, weight = 0.2
○ Conclusion: (\text{TFP} = 5\% - (0.5 \times 5\% + 0.3 \times 5\% + 0.2 \times 1\%) = 0.8\%)
⑶ Empirical studies on TFP
① Philip Hoffman studied French agriculture from 1522 to 1789
○ He argued that external shocks such as the Wars of Religion and disorder resulted in a low long-run average for French agriculture
○ Even in the pre-industrial era, if resources and opportunities are developed rationally, agricultural TFP growth can reach 0.1–0.2%
○ Developing resources and opportunities well requires inter-regional trade and proximity to major urban areas
② According to D. L. Farmer, even just before the Black Death, resources in England were being used efficiently
③ Growth accounting for major countries
Table 1. Growth accounting for major countries
Posted: 2019-07-11 22:46
Updated: 2020-09-14 11:47