Product and process innovation in the product life cycle: estimates for U.S. manufacturing industries.

• Author: Lee, Hyun-Hoon

1. Introduction

   Many theoretical analyses of international trade focus on the effects and endogenous determination of product innovation, technology transfer, and product obsolescence.(1) Despite these theoretical innovations, few direct tests of the empirical power of product-cycle models have been conducted, although a number of studies have examined general relationships between trade and innovation (usually measured by expenditures on research and development, R&D).(2) Such studies typically find a significant link between innovation and trade, but Finger |8~ suggests that this link may be due to the effects of process innovation on the cost of producing existing products, rather than to the introduction of new products.(3) In this study, we distinguish product- and process-oriented innovations, permitting estimates of their separate effects. We begin with a simple product-cycle model that predicts the impact of product- and process-oriented innovations on prices, wages, sales, and exports; and then estimate these predictions using data for eleven two-digit manufacturing industries in the United States during the period from 1974 to 1988. The distinction between product- and process-oriented technological change is important because it yields predictions that aid in assessing the power of the product-cycle models. Most empirical studies aggregate product- and process-oriented technological change, with the notable exceptions of the studies of productivity growth by Link |22~ and Terlecky |31~.

2. A Simple Model

   Our model is a version of the familiar Krugman |20~ model of North-South trade, extended to incorporate more than one domestic industry. For current purposes, we abstract from the dynamic structure of model, as well as from the endogenous determination of the rates of innovation, technology transfer, and obsolescence, which has been the focus of recent work in this area. Instead, we rely upon the model solely to illustrate the qualitative impact effects of product- and process-innovations (and, indirectly, the underlying investments in research and development |R&D~).

   Overview

   Assume that the world has two regions, North and South. New goods are recently developed goods that can only be produced in the North; old goods can be produced in both regions.(4) When the North produces only new goods, as we assume, the relative price of new and old goods is greater than one and demand determined. Consumers are identical and goods are all valued equally. Each region has m different industries. Processes are industry specific, so that a process for the production of goods in one industry cannot be used for the production of goods in another industry. Thus, industries are identified by the process employed, rather than by differences in demand characteristics.

   Each industry has only one factor of production, labor, which is homogenous in each industry. The total amount of labor in the world is fixed. Labor is immobile between industries and regions, yet freely mobile among products within each industry of each region. Thus, the model has the attributes characteristic of specific-factor models, which are most relevant to short- to intermediate-run periods. Labor productivities may differ across regions and industries due to differing process-oriented technologies.

   Demand

   As in Krugman |20~, the utility function held by all individuals in both regions is:

   |Mathematical Expression Omitted~

   where

   n(= |summation of~ |n.sub.Nj~ |where~ j=1 to m + |summation of~ |n.sub.Sj~ |where~ j=1 to m)

   is the total number of goods produced in the two regions, |C.sub.f~ is the consumption of the fth good, and |Theta~ is the demand parameter. Therefore, for a given income, a consumer's utility will improve if the number of available products increases. The utility function also implies that any two goods with the same price will be consumed in the same quantity by all consumers.(5)

   Thus, this specific form of utility function implies that the demand for a northern industry good relative to the demand for a southern industry good will depend only on the relative price in that industry. Arbitrarily choosing the first southern industry good as the numeraire, so that |P.sub.S1~ equals one, we may express the demand for a representative j-industry northern good relative to demand for the numeraire as:

   |Mathematical Expression Omitted~, j = 1 ... m (2)

   where |C.sub.Nj~ is total consumption of a representative j-industry northern good, |C.sub.S1~ is total consumption of the numeraire, and |P.sub.Nj~ is the price of a representative j-industry northern good (in terms of the numeraire). Production and Prices

   The technology of producing goods in each industry of each region is represented by a neoclassical production function exhibiting constant returns to scale. Perfect competition in each industry (and linearly homogenous production functions) yields the following labor requirements:

   |L.sub.ij~ = |a.sub.ij~|C.sub.ij~|n.sub.ij~, i = N,S; j = 1 ... m (3)

   where |L.sub.ij~ are the supplies of labor in industry j of region i and |a.sub.ij~ is the corresponding labor requirement per unit of output.

   Free entry into each industry assures that profits are driven to zero, so that prices equal average cost:

   |P.sub.ij~ = |a.sub.ij~|W.sub.ij~, i = N, S, j = 1 ... m (4)

   where |W.sub.ij~ is the wage rate for industry i in region j.

   Static Equilibrium

   From eqs. (2) and (3), relative demand for labor for a new (Northern) good in industry j relative to demand for labor for the numeraire can be written as:

   |Mathematical Expression Omitted~, j = 1 ... m. (5)

   Eq. (5) can then be rewritten for price:

   |P.sub.Nj~ = |(|a.sub.Nj~/|a.sub.S1~).sup.1-|Theta~~ |(|L.sub.Nj~/|L.sub.S1~).sup.(1-|Theta~)~ |(|n.sub.Nj~/|n.sub.S1~).sup.1-|Theta~~, j = 1 ... m. (6)

   Eqs. (4) and (6) yield the following expression for wages:

   |W.sub.Nj~ = |(|a.sub.Nj~/|a.sub.S1~).sup.-|Theta~~ |(|L.sub.Nj~/|L.sub.S1~).sup.(1-|Theta~)~ |(|n.sub.Nj~/|n.sub.S1~).sup.1-|Theta~~, j = 1 ... m, (7)

   and eqs. (3) and (6) yield the following expression for sales (note that sales, |S.sub.ij~, equal |P.sub.ij~|C.sub.ij~|n.sub.ij~):

   |S.sub.Nj~ = |(|a.sub.Nj~/|a.sub.S1~).sup.-|Theta~~ |(|L.sub.Nj~/|L.sub.S1~).sup.|Theta~~ |(|n.sub.Nj~/|n.sub.S1~).sup.1-|Theta~~...