Two perspectives on preferences and structural transformation

TL;DR: This article assess the empirical importance of changes in income and relative prices for structural transformation in the postwar United States and find that with final expenditure income effects are the dominant force behind structural transformation, whereas with value-added categories price effects are more important.

Abstract: We assess the empirical importance of changes in income and relative prices for structural transformation in the postwar United States. We explain two natural approaches to the data: sectors may be categories of final expenditure or value added; e.g., the service sector may be the final expenditure on services or the value added from service industries. We estimate preferences for each approach and find that with final expenditure income effects are the dominant force behind structural transformation, whereas with value-added categories price effects are more important. We show how the inputoutput structure of the United States can reconcile these findings. (JEL E21, L16)

Summary

Introduction

• The authors explain two natural approaches to the data: sectors may be categories of "nal expenditure or value added; e.g., the service sector may be the "nal expenditure on services or the value added from service industries.
• In the data, both income and relative prices have changed signi_cantly.
• On the one hand, if the income elasticity of services is larger than one and if services are complements to the other consumption goods, then the economy is continually reallocating economic activity towards a sector with low productivity growth.
• The authors second contribution is to estimate utility functions for each of these two approaches and assess their implications for the driving forces behind structural transformation.

II. Final Consumption Expenditure

• The _nal consumption expenditure method originated in the literature on expenditure systems and associates the arguments of the utility function with _nal expenditure of households over different categories of goods and services.
• While expenditure shares do not depend on how one splits total expenditures into their price and quantity components, the series for prices do.
• For the period 1947–2010 and for the available commodities, the authors obtain annual data on _nal consumption expenditure, chain-weighted _nal consumption quantities, and chain-weighted prices from the BEA.
• Turning next to Figure 2, which shows the evolution of prices (with prices in 1947 normalized to 1), the authors see that while all three prices have increased, the price of services has increased relative to both manufacturing and agriculture, and the price of agriculture has increased relative to manufacturing.

B. Results with Final Consumption Expenditure

• In this section the authors estimate the parameters of the demand system (4) by using iterated feasible generalized nonlinear least square estimation.
• For further discussion on the econometric issues related to the estimation of demand systems, see the review article by Barnett and Serletis (2008).
• Instead, the authors report the Akaike information criterion and the root mean squared errors.
• Most notably, rows three and four show that in both 1947 and 2009, each of the nonhomotheticity terms are sizable compared to the actual consumption quantities of agriculture and services, suggesting that income effects could play an important role in shaping the shares of _nal consumption expenditure.
• 15 Given the nonhomotheticity terms, their model does not have a balanced growth path in the usual sense of the word.

III. Consumption Value Added

• As noted in the introduction, many multisector general equilibrium models represent the sectoral production functions in value-added form, in which case the arguments of the utility function necessarily represent the value-added components of _nal expenditure.
• The authors explore the mapping between these two speci_cations in more detail in a later section.
• 16 Having broken _nal consumption expenditure into its value-added components, the authors obtain data on consumption value-added expenditure shares and chain-weighted prices and quantities, which are displayed in Figures 9–11.
• Given that relative prices changed substantially, the near constancy of relative quantities, particularly of manufacturing relative to services, suggests a very low degree of substitutability between the different components of consumption value added.

B. Results with Consumption Value Added

• The authors follow the same procedure as was described previously in the context of estimating parameters using data on _nal consumption expenditure.
• The authors conclude that the econometrically preferred speci_cation implies an economically signi_cant role for both income and price effects in accounting for changes in expenditure shares.
• Notably, the preferred value of σ is not statistically different from zero.
• In particular, since the categories are quite broad, having σ = 0 does not in any sense imply that there is no substitutability between all the different goods and services that individuals consume.
• It seems reasonable to think that the key dimensions of substitution are within these two value-added categories, i.e., that the key substitution is between the uses of buildings or the uses of athletes’ and entertainers’ time, rather than between goods and services per se.

D. Related Literature

• In independent research, Buera and Kaboski (2009) asked whether there are parameters for which a canonical model of structural transformation can match the time series for sector shares in the United States.
• While this question is closely related to their work, there are several important differences between the two papers.
• First, Buera and Kaboski considered a longer time period than the authors do, 1870 to 2000.
• This problem arises because the sectoral composition of investment in the post-1947 period has changed dramatically: while in 1947 the shares of value added from manufacturing and services in value added of investment were roughly two-thirds and one-third, respectively, as of 2010 they are roughly one-half and one-half.
• Figure 16 shows this by comparing their consumption value added shares with the consumption value added shares that one gets by subtracting total investment value added as reported by the BEA data from the series of manufacturing value added used by Buera and Kaboski.

A. Comparing the Results

• The speci_cations have very different implications for the relative importance of changes in relative prices and income in accounting for changes in expenditure shares.
• Before delving into the details, it might be instructive to build some intuition.
• This reasoning does not apply to the consumption value-added speci_cation, since the category labeled agriculture now contains the agricultural inputs that went into both the production of “necessary” food and “luxury” restaurant meals.
• Because their empirical strategy was to uncover preference parameters by estimating the expenditure systems, their approach will emphasize how the expenditure system for consumption value added is derived from the expenditure system for _nal consumption expenditure.
• The authors conclude that the _rst condition in (9) is approximately borne out in the data.

B. Additional Measurement Issues

• In this section the authors note several measurement concerns and carry out some robustness exercises motivated by these concerns.
• Estimation results for this case are provided in Table 6.
• Intuitively, the quality adjustment implies that the relative price of services increases less than in their benchmark speci_cation, so that for a given value of σ there is less need for _ cs to offset the substitution away from services due to the higher relative price.
• More generally, as long as time is the key input into those market activities which are good substitutes for home production, it is reasonable to think that home production will enter symmetrically into the two different speci_cations.
• To stay with the example of the car manufacturer, all that matters with _nal consumption expenditure is how much is spent on purchases of cars.

V. Conclusion

• In answering this question, their analysis offers three contributions.
• A key step in achieving this is to develop and execute a procedure for producing time series data on consumption value added.
• A priori there is little guidance as to how different (or similar) the two answers might be.
• Changing the de_nition of what is meant, for example, by the label “services” has implications not only on the household side for what form of utility function is appropriate, but also on the production side for such things as the measurement of productivity growth.

Figures

Figure 17. Fit of Column 3

Figure 10. Price Indices (1947 = 1)

Figure 9. Expenditure Shares

Table 1—Results with Final Consumption Expenditure

Table 1—Results with Final Consumption Expenditure

Figure 8. Fit of Homothetic Specification in Column 3

Figure 7. Fit of Column 1 with Income Fixed at 1947 Values

Table 4—Nonhomotheticity Terms Relative to Final Consumption from the Data

Figure 18. Fit of Column 4

Table 6—Results for Final Consumption Expenditure and Different Specifications of Government Expenditures

Figure 15. Fit of Column 2 with Income Fixed at 1947 Value

Figure 3. Quantity Indices (2005 chained dollars, 1947 = 1)

Table 9—Decomposition of Increase in Expenditure Share of Services in Value Added (accumulated 1947–2010)

Table 5—Results for the Estimation of (7)

Figure 11. Quantity Indices (2005 chained dollars, 1947 = 1)

Table 3—Results with Consumption Value Added

Table 8—Results for Final Consumption Expenditures with Quality Adjustment

Figure 4. Fit of Column 1

Figure 5. Fit of Column 2

Figure 16. Shares in Consumption Value Added with Different Ways of Treating Investment

Figure 1. Expenditure Shares

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This document is published in:
American Economic Review, 2013, v. 103, n. 7, pp. 2752-2789
DOI: dx.doi.org/10.1257/aer.103.7.2752
© American Economic Association

Two Perspectives on Preferences and
Structural Transformation
†
By B H, R R,  Á V*
We assess the empirical importance of changes in income and
relative prices for structural transformation in the postwar United
States. We explain two natural approaches to the data: sectors may
be categories of nal expenditure or value added; e.g., the service
sector may be the nal expenditure on services or the value added
from service industries. We estimate preferences for each approach
and nd that with nal expenditure income effects are the dominant
force behind structural transformation, whereas with value-added
categories price effects are more important. We show how the input-
output structure of the United States can reconcile these ndings.
(JEL E21, L16)
Structural transformation—i.e., the reallocation of resources across the broad eco-
nomic sectors agriculture, manufacturing, and services—is a prominent feature of eco-
nomic development. Kuznets (1966) included it as one of the main stylized facts of
development, and recent work shows that extending the standard one-sector growth
model to incorporate structural transformation is important for a variety of substan-
tive issues.
1
However, there remains no consensus on the economic forces that drive
the process of structural transformation. Recent theories stress two distinct economic
1
See, for example, Laitner (2000) and Gollin, Parente, and Rogerson (2002) for an application to early devel-
opment, Messina (2006), Rogerson (2008), and Ngai and Pissarides (2008) for the evolutions of hours worked in
Europe and the United States, Duarte and Restuccia (2010) for productivity evolutions in the OECD, Caselli and
Coleman (2001) and Herrendorf, Schmitz Jr., and Teixeira (2012) for regional convergence, and Bah (2008) and
Herrendorf and Valentinyi (2012) for identifying problem sectors in poor countries. Other contributions to the
literature on structural transformation include Echevarria (1997); Kongsamut, Rebelo, and Xie (2001); Ngai and
Pissarides (2007); Acemoglu and Guerrieri (2008); and Foellmi and Zwei müller (2008). Herrendorf, Rogerson, and
Valentinyi (forthcoming) provide a review of this literature.
* Herrendorf: Department of Economics, W.P. Carey School of Business, Arizona State University, 350 East Lemon
Street, Tempe, AZ 85287 (e-mail: Berthold Herrendorf@asu.edu); Rogerson: Woodrow Wilson School, Princeton
University, Princeton, NJ 08544, and NBER (e-mail: rdr@Princeton.edu); Valentinyi: Cardiff Business School,
Cardiff University, Aberconway Building, Colum Drive, Cardiff, Wales, UK, and Institute of Economics HAS and
CEPR (e-mail: valentinyi.a@gmail.com). The authors thank Stuart Low and Ed Prescott for many helpful conversa-
tions about the topic of this paper. For comments and suggestions, the authors thank Paco Buera, Joe Kaboski, Todd
Schoellman, and the conference participants at the SED meetings in Prague (2007) and Istanbul (2009), the conference
of the Society for the Advancement of Economic Theory in Kos (2007), the RMM conference in Toronto (2008),
the conference on Developments in Macroeconomics at Yonsei University (2009), as well as seminar participants at
ASU, Autonoma de Barcelona, Bonn, the Deutsche Bundesbank, Frankfurt, Humboldt University, Köln, Luxembourg,
Mannheim, the San Francisco FED, Southampton, Toronto, UCLA, University of Pennsylvania, Western Ontario, and
York (Toronto). For nancial support, Herrendorf thanks the Spanish Ministry of Education (Grants SEJ2006–05710/
ECON and ECO2009-11165), Rogerson thanks both the NSF and the Korea Science Foundation (WCU–R33–10005),
and Valentinyi thanks the Hungarian Scientic Research Fund (OTKA) (Project K–105660–ny). Hubert Janicki, Loris
Rubini, and Paul Schreck provided able research assistance.
†
Go to http://dx.doi.org/10.1257/aer.103.7.2752 to visit the article page for additional materials and author
disclosure statement(s).
1

mechanisms that can explain why households reallocate expenditures across broad
economic sectors: one emphasizes changes in aggregate income, whereas the other
emphasizes changes in relative sectoral prices. For example, Kongsamut, Rebelo, and
Xie (2001) assume that only income changes matter, whereas Baumol (1967) and Ngai
and Pissarides (2007) assume that only relative price changes matter. In the data, both
income and relative prices have changed signicantly. We ask: how important is each
of these changes as a source of structural transformation?
2
In addition to being crucial for understanding the driving forces behind structural
transformation, the answer to this question has important implications. For example,
the decline of the manufacturing sector gures prominently in public policy discus-
sions, and a recurring issue is what public policies could slow or even reverse it. This
depends crucially on the forces that lead to the decline, and in particular on the rela-
tive strengths and on the directions of income and price effects. Another example
where the answer to this question has important implications is the future path of
economic growth. In a classic contribution, Baumol (1967) suggested that the secu-
lar increase in the expenditures on many labor-intensive services is largely due to
an increase in their relative prices, reecting the fact that there is little technological
progress in labor-intensive services. This so-called Baumol disease is of concern
because it slows down growth of real aggregate GDP. The extent to which this hap-
pens critically depends on the nature of income and price effects. On the one hand,
if the income elasticity of services is larger than one and if services are complements
to the other consumption goods, then the economy is continually reallocating eco-
nomic activity towards a sector with low productivity growth. On the other hand, if
the income elasticity of services is smaller than one and if services are substitutes
to the other consumption goods, then the economy is continually reallocating eco-
nomic activity away from a sector with low productivity growth.
We seek to assess the relative importance of changes in income and in relative
prices as driving forces for structural transformation in the US economy over the
period 1947–2010. Because these two mechanisms ultimately reect different
features of preferences, our objective amounts to answering the question, what
is an empirically reasonable specication of preferences in models of structural
transformation?
3
In answering this question, our analysis offers three contributions.
First, we point out a fundamental ambiguity regarding the conceptual denition
of commodities that arises when one seeks to connect a multisector model to the
data. To see the ambiguity, consider a static stand-in household model with util-
ity function u( c
a
, c
m
, c
s
), where c
a
, c
m
, and c
s
are consumption of agriculture,
manufacturing, and services, respectively, and three sectoral production functions,
c
i
= f
i
( h
i
) for i = a, m, s where h denotes labor input. Even conditional on giv-
ing specic labels to the sectors, there are still two very different interpretations of
what a sector is. If one interprets the sectoral production functions as value-added
production functions, consistency dictates that the arguments of the utility functions
2
We will refer to these effects as income effects and price effects. Our terminology differs somewhat from that
in microeconomics where the effects of changes in relative prices are decomposed into income and substitution
effects. In our terminology, the price effect comprises both the income and substitution effect of this decomposition,
whereas the income effect is the result of any change in income.
3
A companion paper, Herrendorf, Herrington, and Valentinyi (2012), focuses on the related question, what is an
empirically reasonable specication for sectoral technology in models of structural transformation?
2

are necessarily the value-added components of nal consumption. We will call this
the consumption value-added approach. To illustrate the signicance of this obser-
vation, consider the example of a cotton shirt. With the value-added interpretation, a
cotton shirt represents consumption of all three commodities: raw cotton from agri-
culture, processing from manufacturing, and retail services from the services sector.
Alternatively, one could interpret the commodities in the utility function as the
nal consumption purchases of the household. In this case the entire expenditure on
the cotton shirt represents consumption of manufactured goods, while a service such
as health care, for example, would be entirely counted as consumption of services.
We call this the nal consumption expenditure approach. Consistency now requires
that the sectoral production functions be nal consumption production functions
rather than value-added production functions. Each of these two approaches is inter-
nally consistent, but for a given model, the empirically reasonable choices for the
parameters of utility and production functions will potentially differ.
A separate question is whether one of these specications is more reasonable.
Following Lancaster (1966), a reasonable starting position is that households value a
large set of characteristics that are bundled in various combinations in different goods.
The two approaches we describe reect two different attempts to “aggregate” these
preferences using a utility function with a small set of arguments. Any attempt to
capture this complex ordering using a utility function with few arguments will lead to
some undesirable implications in specic contexts. For example, it may seem undesir-
able that the value-added approach implies that individuals worry about the intermedi-
ate inputs that go into the production of a given nal good (though we note that there
certainly are examples for which this is the case, such as organic vegetables or canned
tuna that is produced using methods that do not endanger dolphins). But, it is undesir-
able that in the nal-expenditure approach the utility that one obtains from eating an
apple is bundled with the services that are offered at the supermarket where the apple
is bought, as opposed to separately considering utility from the apple and utility from
the services offered at the supermarket. We think that the point here is not that one
approach is better, but that any specication that aggregates underlying characteristics
into a small number of categories is going to have its individual strengths and weak-
nesses in terms of capturing relevant aspects of preferences.
Our second contribution is to estimate utility functions for each of these two
approaches and assess their implications for the driving forces behind structural
transformation.
4
In each case we nd that a relatively simple utility function pro-
vides a good t to the relevant data. Importantly, the two specications have funda-
mentally different properties, thereby emphasizing the empirical signicance of the
ambiguity noted above. For the nal consumption expenditure approach, a speci-
cation close to the Stone-Geary utility function provides a good t to these data,
implying that changes in income rather than changes in relative prices are the domi-
nant force behind changes in expenditure shares. For the consumption value-added
approach, changes in income are much less important and changes in relative prices
4
Whereas the relevant data for the nal-expenditure approach is readily available, this is not true for the con-
sumption value-added approach. To be sure, data on total value added by sector are readily available, but these data
are not sufcient because not all of total value added is consumed. One of the byproducts of this article is to lay
out and implement a procedure for extracting the consumption component of total value added, and to produce an
annual time series for US consumption value added by sector between 1947 and 2010.
3

are much more important than for nal expenditure. In particular, a specication
close to a Leontief utility function now provides a good t to the data. In other
words, our ndings provide some measure of support for each of the specications
emphasized by Kongsamut, Rebelo, and Xie (2001) and Ngai and Pissarides (2007),
with the appropriate choice being dictated by how one interprets the arguments in the
utility function: under the nal consumption expenditure approach, the Stone-Geary
specication of Kongsamut, Rebelo, and Xie (2001) is a reasonable approximation,
whereas under the consumption value-added approach, the homothetic specication
of Ngai and Pissarides (2007) is a reasonable approximation.
We emphasize that our two estimated utility functions are based on two different
representations of the same underlying data. In particular, the nal consumption
expenditure data are linked to the consumption value-added data through intricate
input-output relationships, which implicitly translate part of the income effects
that dominate with nal consumption expenditure into relative price effects that
are much more important with consumption value added, and vice versa. Our third
contribution is to explore how the input-output structure inuences the mapping
between the two different representations and to derive conditions under which a
specication close to Stone-Geary for nal consumption expenditure is consistent
with a specication close to Leontief representation for consumption value added.
While our analysis is motivated by a desire to build empirically reasonable mod-
els of structural transformation, some of our basic messages are relevant for any
applied analysis in the context of multisector models. Specically, researchers must
be careful to apply consistent denitions of commodities on both the household and
production sides when connecting multisector models with data. Changing what is
meant by the label “services,” for example, has implications not only on the house-
hold side for what form of utility function is appropriate, but also on the production
side for such things as the measurement of productivity growth. This has important
implications for comparing results across studies and for the practice of import-
ing parameter values across studies. For example, it is not appropriate in general
to use the utility function that was estimated from nal consumption expenditure
together with value-added production functions at the sector level. If one wants to
use a utility function that was estimated from nal consumption expenditure, then
one either needs to write down a production structure that captures the complexi-
ties of the input-output relationships at the sector level, or nd a representation of
production that isolates the contribution of capital and labor to the production of
nal-expenditure categories. While this can be done, it is much more difcult than
working directly with sectoral value-added production functions.
5
An outline of the article follows. In the next section we describe the model and
the method that we use to calibrate preference parameters. In Section II we describe
the nal consumption expenditure method, and we report the estimation results for
this method. In Section III, we turn to consumption value added. We explain in some
detail how to construct the relevant time series of variables from existing data, and
we report the estimation results. Section IV links the results of both methods and
5
Valentinyi and Herrendorf (2008) showed how to construct sectoral production functions that use only capital
and labor to produce nal expenditure by broad category.
4

Frequently asked questions

Q1. What are the contributions in this paper?

This paper examined the behavior of household expenditure shares for the US economy over the period 1947 to 2010 and provided an answer to the simple question: what utility function should one use in applied work on structural transformation and related issues ? 

Q2. What are the future works in this paper?

There are several dimensions along which it will be important to extend the analysis carried out here. It is also of interest to extend this analysis to a larger set of countries, in particular to situations which feature a larger range of real incomes. This will be useful in assessing the extent to which one can account for the process of structural transformation with stable preferences. 

Q3. What is the next step in the derivation of the consumption value added system?

The next step in the derivation of the demand system for consumption value added is to aggregate the demands for c jit VA to the demand for c jt VA . 

Q4. Why is the classi_cation process done at the establishment level?

The main reason is that industry classi_cations are done at the establishment level, implying that all in-house services provided at a central administrative of_ce (headquarters) or a separate service-providing unit are classi_ed as service industries. 

Q5. What is the first step in converting _nal consumption expenditure into its valueadded?

The _rst step in breaking down _nal consumption expenditure into its valueadded components is therefore to convert _nal consumption expenditure measured in purchaser’s prices into those measured in producer’s prices. 

Q6. What is the effect of assuming that all of investment represents value added from the manufacturing sector?

Neglecting this change in the composition of investment while assuming that all of investment represents value added from the manufacturing sector leads to a spurious increase in the growth rate of the share of services in total consumption value added and a spurious decrease in the growth rate of the share of manufacturing in total consumption value added toward the end of the sample. 

Q7. What is the second way to judge the importance of income versus relative prices?

A second way to judge the importance of income versus relative prices is to assess the extent to which a homothetic speci_cation can _t the data, since such a speci_cation necessarily implies that total expenditure has no effect on expenditure shares. 

Q8. What is the main reason for the reabeling of activity?

The second issue concerns the possibility that reallocation of resources across sectors re|ects a relabeling of activity due to outsourcing, as opposed to fundamental shifts of economic activity across sectors. 

Q9. What is the prominent example of durables?

For housing, which is by far the most prominent example of durables, the BEA takes account of this and imputes the rents for owner-occupied houses. 

Q10. Does the reduction in time spent in home production mean a decrease in the quantity of output?

To the extent that technological progress has lessened the amount of time required to produce output at home, the reduction in time spent in home production need not imply a decrease in the quantity of home produced output. 

Q11. What is the main issue when examining time series changes in prices and quantities?

—An important issue when examining time series changes in prices and quantities is the extent to which the data take proper account of quality improvements. 

Q12. What is the first step in calculating the value added component of a sector?

Once this is done, the second step is to use the input-output tables to determine the sectoral inputs in terms of value added that are required to deliver the _nal consumption expenditure. 

Q13. What is the key difference between the two categories of consumption value-added?

It seems reasonable to think that the key dimensions of substitution are within these two value-added categories, i.e., that the key substitution is between the uses of buildings or the uses of athletes’ and entertainers’ time, rather than between goods and services per se.