1. Assessing Long Run Structural Change in Multi-Sector General Equilibrium Models
Roberto Roson
Dept. Economics, Ca’Foscari University, Venice and IEFE Bocconi University, Milan

2. Intro and Motivation
CGE models are often used to assess policies and impacts occurring at some distant future (e.g., climate change)
But they are calibrated on the basis of some past input-output or SAM tables, meaning that they mirror an economic structure quite different from the one we could possibly observe in the future

3. Two Sources of Structural Change
consumption patterns may change, because of diverse income elasticities, possibly associated with varying income distributions (endogenous in CGEs)
industrial productivity may change at various speeds, or factor productivity could do so (exogenous in CGEs)

4. Generalized Engel's Law
the evolution over time of industrial shares, in terms of employment, value added or expenditure, is non monotonic
for instance, the share of manufacturing is typically hump shaped
to replicate this characteristic into a model, a sufficiently sophisticated demand system must be adopted

5. Some Alternative Demand Systems
Hierarchical Demand System (HDS)
Linear Demand System (LES), Stone-Geary and other CES generalizations
Quadratic Almost Ideal Demand System (QUAIDS)
An Implicitly, Directly Additive Demand System (AIDADS)

6. AIDADS (1)

7. AIDADS (2)

8. Estimation of AIDADS is difficult
it is not possible to get a closed form solution for the utility level u, which must then be estimated numerically, alongside other parameters
a number of constraints must also be taken into account, to ensure regularity conditions for the system
how to get future values for utility levels?

9. Estimation Strategy
ICP (2015) provides data on real and nominal consumption expenditure for 180 countries at the year 2011, in 14 categories, which are further aggregated here in 11 consumption classes
For the estimation of AIDADS parameters, we closely follow Cranfield (1999), by formulating the equations in terms of budget shares, and adding a stochastic error term
We performed a non-linear maximum likelihood procedure

10. Parameter Values
Remember: gamma = basic consumption, alpha and beta = initial and final bounds for shares in non-basic consumption

11. Linking Utility to Income

12. Consumption Patterns

13. Differential Productivity Growth
Empirical literature is scant
It focuses on (a) structure and aggregate growth, (b) productivity convergence
The Groeningen GGDC Centre provides an unbalanced panel of value added labor productivity (40 countries, )
Fixed effects panel regression on annual labor productivity variations (%)
Pieceways linear interpolation with variable time break

14. Last Estimated Value
2.61
Last Estimated Value
1.50

15. Last Estimated Value
2.85
Last Estimated Value
0.44

16. Test Simulations
Scenario SSP2 provides projections of (1) Real GDP and (2) population
Simulation A: shocking value added productivity in each region according to the SSP2 GDP growth at 2050
Simulation B: same as above, but industrial labor productivity is differentiated and corresponds to estimated growth only in the aggregate (weighted average)

17. Gross Output Structure, North America
2011
2050a
2050b
Agriculture
4.9%
4.6%
4.8%
Mining
2.0%
1.0%
1.2%
Manufact
23.7%
19.4%
21.1%
Utilities
2.2%
2.3%
Construction
6.6%
7.2%
7.9%
TradeRH
11.3%
12.0%
TransComm
5.9%
6.1%
6.4%
Finance
13.0%
14.4%
13.3%
Government
17.5%
19.5%
16.8%
Services
12.9%
13.6%
14.1%

18. Country-level Fixed Effects
The fixed effects estimated at the country level account for some specific characteristics of the different economies, influencing the labor productivity growth in each sector, in addition to the general worldwide tendency. Therefore, it is a way of indirectly considering factors like the institutional setting, natural conditions, but also the internal composition of the sectors.
Since the fixed effects regression estimates one parameter for all regions in the 10 panels, each country is characterized by a vector of 10 parameter values, expressing its specific “productivity profile”. These profiles have been the subject of a cluster analysis, aimed at finding similarities in groups of countries.
In this way, three major clusters have been identified. In one cluster, for illustrative purposes labeled “Rising”, there are several high growth countries of the Far East (including China and South Korea) and Botswana. In the second cluster (“Steady”) there are all European countries, Mauritius, Nigeria, Egypt, India, Indonesia, Japan and other Asian countries. In the remaining group (“Lagging”) we can find the U.S. (suggesting the existence of a global convergence, at least in part), all Latin America and most of the African countries.

20. Next Steps
Keeping together demand and supply drivers of structural change into a unified modeling framework
Suggestions are welcome

21. Thank You this is a work in progress! roson@unive.it