Model Structure

The illustrative model used to analyze the impact of technological change in the railroad sector in the US has a simple structure, which is summarized in Table 5.1. A single, representative agent with Cobb-Douglas preferences consumes three classes of goods: passenger rail services, agricultural goods and an aggregate residual good which is comprised o f all other goods, services and savings in the economy. This agent's income is derived from the endowments of capital, labour and land. Production occurs in three sectors; railway transport, agriculture and the aggregate sector. Output from the railway sector is assumed to be produced from capital and labour with a constant elasticity of substitution (CES) production technology.

The railway sector supplies passenger services and freight services using a constant elasticity of transformation technology with a high elasticity of transformation (2.0) to reflect the relative ease of shifting production between the two types of services. Freight services are intermediate inputs into the production of the agricultural and the aggregate goods, while passenger services are produced for final consumption.

The agricultural sector is assumed to employ land, labour and freight services using CES technology with a low elasticity of substitution (0.15). The choice of fixed coefficients technology in agriculture was rejected on the basis that farmers likely had some control over the destination of their outputs and the origin of inputs and thus could vary the proportion of transportation per unit output, and that a low degree of substitution between quantity of land and labour intensity in agricultural production seems reasonable.

Table 5.1

Production Structure

• Three production sectors - the railroad sector, the agricultural sector, and an aggregate residual sector - produce final consumption goods.

• The production of agricultural goods and the aggregate good use railroad services (freight) as an intermediate input.

• The railroad sector produces railroad services using CES technology and capital and labour inputs, allowing for the possibility of sector and factor specific technological change:

(J = c^nTx^A^y',),e> + (l-Tf)(*;'£')<t'lyt]l/<ll) where Q is the quantity o f railroad services produced,

Krand V are the capital and labour inputs to the railroad sector, x / and x / are the technological change parameters for capital and labour inputs for the sector, {'is a scale parameter, i f is the CES share parameter for capital in the railroad good sector and £ is the constant elasticity of substitution • Output from the railroad sector is allocated between passenger and freight services in a CET

transformation function, again allowing for sector and factor specific technical change:

Q = + ( I-a'X f//>)0t'ly<],,<1'11 where Q is the quantity of total railroad services produced,

Fand Pare the quantities of freight and passenger services, th’ and I,' are the technological change parameters for freight and passenger outputs for the sector, y ' is a scale parameter, o' is the share parameter for freight services, and x is the constant elasticity of transformation.

• The ai»i»rei>aie nnod sector produces output using a CES technology with freight services and value added as inputs, again allowing for sector and factor specific technological change:

O ' = y“(o" (l-a")(/|"f'')l*‘lv*)*,(*''>, where Q" is the output of the aggregate good sector,

F and V“ are the freight and value added inputs, and ty are the technological change parameters for freight and value added inputs for the sector, y" is a scale parameter, a“ is the share parameter for the freight input, and y is the constant elasticity of substitution.

• Value added in the ai’ereeate uood sector is produced using CES technology from capital and labour, and allowing for the possibility of sector and factor specific technological change:

V" = {" [nT'c/A'")'*'"'*’ + (I-h"Xt;"T")i* i>'*]*'<*'i> where P is the quantity of value added produced, K“

and ¿" are the capital and labour inputs to the aggregate good sector, x*“ and x," are the technological change parameters for capital and labour inputs for the sector, (“is a scale parameter and if' is the CES share parameter for capital in the aggregate good sector. The parameter <t> is the constant elasticity of substitution.

• flie agriculture sector produces agricultural output using CES technology and land, labour, and freight inputs, allowing for the possibility of sector and factor specific technological change:

= C/[X,/(x(/( // * 'l)'*) + + X ,/(x //^ )'-1’"]*"-" where { /is the quantity of agriculture produced, O', ¿'and ¿’'are the land, labour and freight inputs to the agriculture sector, x,/, x / and x / are the technological change parameters for land, labour and freight inputs to the sector, ( ' is a scale parameter, X,/ is the CES share parameter for land in the agriculture sector, X / is the CES share parameter for labour in the agriculture sector, X,/ is the CES share parameter for freight in the agriculture sector, and o is the constant elasticity of substitution.

Summary of the Model Structure Used to Illustrate Decomposition Analysis

Consumption Structure

• The single consumer has Cobb-Douglas preferences over agricultural goods, the aggregate good, and passenger rail services and maximizes the utility function:

U = * *’ where U is the level of utility, p is the consumer's expenditure share on the agricultural good, ft is the consumer's expenditure on the aggregate good, {/, (/', and P are quantities consumed of the agricultural good, the aggregate good and passenger services.

• The consumer is endowed with capital (K), labour (r,), and land (G).

Production of the aggregate good is undertaken from freight services and value added, again assuming CES technology with a low elasticity of substitution (0.25). As in agriculture, the producer is assumed to have some choice over the destination of output and, hence, over the quantity of freight services required per unit output. A large increase in fares, however, would be required for him or her to substitute away from transportation in production. Since the aggregate good is a residual good that encompasses all non-agricultural, non-railway goods and services in the economy, more substitutability between freight and value added input in production is assumed than in agricultural production. Value added in the production of the aggregate good is undertaken using capital and labour inputs with CES technology and an elasticity of 1.1. In equilibrium, the markets for all goods and factors identified in the model clear, each production sector makes zero profits and the consumer's budget is balanced.

The model uses a very strong closed economy assumption. Given the importance of trade (around 15 percent of GDP) and the increase in the trade between the US and Europe in the latter decades of the 19th century, this specification is clearly ahistorical, but it was chosen for transparency in presenting the decomposition analysis methodology.