The Production Life Cycle

• DOI: http://doi.org/10.1111/sjoe.12255
• Published date: 01 October 2018
• Date: 01 October 2018
• Author: Yibei Liu,Ben G. Li

Scand. J. of Economics 120(4), 1139–1170, 2018

DOI: 10.1111/sjoe.12255

The Production Life Cycle*

Ben G. Li†

Boston College, Chestnut Hill, MA 02467, USA

ben.li@bc.edu

Yibe i Liu

Yale-NUSCollege, Singapore 138610

yibei.liu@yale-nus.edu.sg

Abstract

Tasks in production have different dynamics from individuals products. We build a general

equilibrium model where three forces (i.e., offshoring, learning, and wage) interact to determine

how production fragmentation evolvesover time. We showthat the production process follows a

life cycle: its fragmentation emerges,deepens, and converges. Our model is stylized and versatile,

and it can be used to tractably characterize the loci of global output, productivity, welfare, and

value-added distribution as production fragmentation progresses.

Keywords: Industrialization; learning-by-doing; offshoring; product cycle

JEL classification:F63; O14

I. Introduction

When the current round of globalization began half a century ago, Vernon

(1966) hypothesized that industrial products have a life cycle: they originate

and are first produced in the industrialized North, and then are imitated

and produced in the less industrialized South. Vernon proved to be right, as

the following 50 years have witnessed the continual Southern takeover of

Northern products. However, Vernon’s product life cycle was not the only

ongoing cycle. During the same period, many Northern products retained

their Northern identities, although their production was progressively

fragmented and gradually moved to the South. This phenomenon, which

we refer to as the “production life cycle”, unraveled the era of global

manufacturing, including offshoring by the North, industrialization of the

†Also affiliated with Deakin Business School, Victoria3125, Australia.

*Wethank Jim Anderson, Davin Chor, Paola Conconi,Thibault Fally, Gita Gopinath, Juan Carlos

Hallak, Wolfgang Keller, Hideo Konishi, Jim Markusen, Keith Maskus, Larry Qiu, John Ries,

HeiwaiTang,Jon Vogel,StephenYeaple,and Kei-MuYi, as well as the two anonymousreferees, for

their valuable comments during different stages of the paper.We also thank seminar/conference

participants at various places.Any remaining errors are our own.

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1140 The production life cycle

South, global output increments, income redistribution, and the formation

of value chains.

A theoretical model of the production life cycle is needed, one that

should feature general equilibrium to consolidate input and output markets,

that should be dynamic to generate time-varying patterns, and that should

be tractable so that future studies can easily extend it. In this paper, we

endeavor to build such a model. In our model, production fragments (tasks)

of an industrial product have different levels of sophistication and the South

has weaker technologies than the North for sophisticated tasks. Cheaper

Southern labor incentivizes the North to offshore tasks for which Southern

technologies are either as efficient as, or moderately less efficient than, their

Northern counterparts. Offshored tasks of both types benefit the North by

lowering costs, while only those of the second type provide the South with

opportunities to improve its technologies. Through learning-by-doing, the

South has its wage rates elevated and its scope of tasks expanded.

Our model provides a uniform framework for rationalizing the

production life cycle: what it means, how it looks, why it happens, and

where it starts and ends. It predicts convergence as a unique characteristic

of the production life cycle, which does not occur in Vernon’s product

life cycle. There is a steady state at which tasks are allocated across

countries in proportion to their sizes. Before the steady state is reached,

income converges across countries through offshoring, even though there

exist perpetual technological gaps across countries. The South improves

its productivity, and thus its income, until the steady state is reached.

Intuitively, as all tasks are needed for making a product, within-product

comparative advantage causes specialization in tasks and learning-by-doing

eliminates technological gaps on offshored tasks. This is a new channel

through which global income converges rather than diverges.

Our model also provides five other findings. First, the output of global

production can be sufficiently characterized using a production function

with three elements: Northern labor, Southern labor, and a total task

productivity (TTP) term. Specifically, the productivity gains for the South

through learning-by-doing and those for the North through offshoring are

aggregable into a single TTP that increases and converges to its steady-state

level. This remarkably simplifies the analysis of global production, whose

major working forces can be showcased separately without recounting every

dynamic general equilibrium effect.

Second, we use the task type of average labor to measure a country’s

position along the global chain of tasks, and find that the North moves up

the chain by specializing in high-end tasks at which it excels. The South

also moves up, but as a net outcome of two effects: an up-effect due to

learning-by-doing, and a down-effect resulting from the sophisticated tasks

it conducts as a semi-qualifier. The two effects counteract each other and the

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B. G. Li andY. Liu 1141

up-effect dominates, owing to the Southern wage increments that exhaust

the Southern cost advantage and thus limit the scope of offshoring in every

period.

Third, along the course of convergence, the South is better off while

the North experiences a period of worsening welfare prior to the steady

state. This is because tasks that are more sophisticated do not generate

more employment and thus offshoring reduces the demand for Northern

labor. Our model also sheds light on the relationships between offshoring

and other global trends. As offshoring expands, Southern net imports rise,

Northward migration tends to decline, and technology payments can be paid

in either direction.

Fourth, the value added by the South to a given product increases at a

decreasing rate. As the South improves productivity and receives more tasks,

its wage rate rises and thus offshoring slows down. During this process, the

South still adds more value to the product but those value increments shrink

gradually.

Lastly, our model provides another mechanism that explains why having

a small country size is disadvantageous in economic development.1It is

difficult to identify, in retrospect, which Southern countries in the 1960s

were destined to prosper. If any similarity existed among those countries

that later became prosperous, it was a relatively large (rather than absolute)

population size.2In our model, if a Southern country is so small that its

initially assigned tasks match or exceed its share of the world labor force,

it would not have learning potential later.

Our paper is related to both the bodies of literature on international

trade and economic growth. The related body of literature on international

trade can be divided into two groups. The first group models industrial

cycles but does not have offshoring involved. Their industrial cycles are

product life cycles in Vernon’s style (Krugman, 1979; Dollar, 1986; Jensen

and Thursby, 1986, 1987; Segerstrom et al., 1990; Grossman and Helpman,

1991a,b).3These studies built on the new trade theory and thus relied

on product (variety) as the unit of analysis. The second group models

offshoring but does not generate industrial cycles (Kremer, 1993; Feenstra

1For discussions on the small-country disadvantage, see Alesina and Spolaore (1997), Easterly

and Rebelo (1993), and Commonwealth Consultative Group (1997).

2On the basis of our calculation, present emerging market economies accounted for 22 percent

of the world population (China and India excluded) in the year 1966. Their average population

(26.5 million) ranked as the 26th largest country in the world at that time. In comparison, present

Organisation for Economic Co-operation and Development countries accounted for 32 percent,

with their average population ranked 20th (32.7 million), at that time. Details are available on

request.

3For recent empirical studies on product cycles, see Feenstraand Rose (2000), Xiang (2014) and

Zhu (2005).

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