A General Equilibrium Model of
Formalization in a Dualistic Economy
with Evidence from Indonesia
LIU Yuwei, FU Yuming, LIAO Wen-Chi
Department of Real Estate
National University of Singapore
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Stylized facts of a dualistic developing economy
La Porta & Shleifer (2014). Informality and Development. Journal
of Economic Perspectives, 28(3):





Informal sector is large
Informal entrepreneurs have low skill, low productivity,
hire few workers, and sell only to local customers
Informal entrepreneurs largely do not pay taxes, do not
have access to financial services and many public services,
and do not grow and become formal entrepreneurs
Informality decreases with economic development
Informality is lower in regions with more educated labor
force
1
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Size of the Informal Economy by Alternative Measures
La Porta & Shleifer (2008). The Unofficial Economy and Economic Development.
Brookings Papers on Economic Activity
2
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
To understand informality…




Why don’t informal entrepreneurs become formal to take
advantage of financial, legal, and other business and
public services, to be more productive?
Why don’t the more efficient formal firms absorb all the
informal employment?
What is the welfare implication of the co-existence of
formal and informal employment?
How can policies promote formalization and economic
development?
3
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The supply-side and demand-side determinants of
informality

Supply side:
o
o
Human capital of entrepreneurs
The cost of formalization: taxes and regulatory compliance
▪ Azuma & Grossman (2002). A Theory of the Informal Sector. NBER Working Paper
No. 8823.
▪ de Paula & Scheinkman (2007). The Informal Sector. NBER Working Paper No.
13486.

Demand side:
o
Market size for formal firms: local and external markets
▪ Murphy, Shleifer & Vishny (1989). Industrialization and the Big Push. Journal of
Political Economy 97(5)

Need to consider both the supply side and demand side
together in order to evaluate the impact of each exogenous
factors and policy interventions
4
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Our objectives



Formulating a general equilibrium model to account for
both demand-side and supply-side determinants of
formality
Account for geographic pattern of employment: multiple
regions with heterogeneous access to the global market
Numerical counterfactual analysis of economic
development, formalization, and welfare
5
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Additional stylized facts of informality and development from Indonesia
Export Growth, Education and Formal Employment Share
Formal sector share
of employment
Supply factor:
human capital
Demand factor:
External demand
Source: CEIC, Census data 2000-2010 and NLFS 1995, 2015
6
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Additional stylized facts of informality and development from Indonesia
Average Years of Schooling of Form and Informal Entrepreneurs,
Java vs Outside of Java
Java formal
entrepreneurs
Non-Java formal
entrepreneurs
Informal
entrepreneurs
Source: CEIC, Census data 2000-2010 and NLFS 1995, 2015
7
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Additional stylized facts of informality and development from Indonesia
High School Graduate Share of Entrepreneurs by firm size
in Indonesia
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
2005
2010
Small Firm
Large Firm
Source: NLFS 2005, 2010
8
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Additional stylized facts of informality and development from Indonesia
Zipf coefficient of employment size distribution across top 100 counties
County
Year
County urban area
Total
Formal
Informal
Total
Formal
Informal
employment employment employment employment employment employment
1995
-1.491
-1.135
-1.349
-0.990
-0.921
-1.040
2000
-2.073
-1.071
-1.688
-1.202
-1.095
-1.138
2005
-2.240
-1.293
-1.668
-1.267
-0.996
-1.384
2010
-1.423
-0.947
-1.301
-0.920
-0.807
-1.017
2015
-1.356
-0.977
-1.197
-0.874
-0.785
-0.941
Source: NLFS.
9
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model: the economy

The economy comprises with two open cities, indexed c = 1,2, each trading
with the rest of the world (ROW). The economy is endowed with 𝑁 workerconsumers, who have heterogeneous skills and are perfectly mobile
between the cities.
𝑁 worker-consumers, skill ∈ 𝜑𝑚𝑖𝑛 , 𝜑𝑚𝑎𝑥 ,
perfectly mobile between cities
City 1: amenity 𝐴1 , trade cost 𝑇1
Employees
Informal entrepreneurs
Formal entrepreneurs
City 2: amenity 𝐴2 , trade cost 𝑇2
Employees
Informal entrepreneurs
Formal entrepreneurs
Import &
Export
ROW
10
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model: the economy
A worker with skill 𝜑 (entrepreneur productive efficiency, as in Behrens, Duranton &
Robert-Nicoud, 2014) has three occupation choices in city 𝑐 :



To be a formal entrepreneur, incurring a fixed cost per period 𝜃𝑐 for
intermediate services to access the world market, and producing a
differentiated good 𝑗 with labor input 𝑙 𝑗 :
o
output 𝑋𝐹𝑐 (𝑗) = 𝜑(𝑗)𝑙(𝑗),
o
profit 𝜋𝐹𝑐 𝑗 = 𝑝𝑐 𝑗 𝑋 𝑗 − 𝑤𝑐 𝑙 𝑗 − 𝜃𝑐 .
To be an informal entrepreneur, incurring no fixed cost but selling only to
the local market a differentiated good:
o
output 𝑋𝐼𝑐 𝑗 = 𝜑 𝑗 𝑙 𝑗
o
profit 𝜋𝐼𝑐 𝑗 = 𝑝𝑐 𝑗 𝑋 𝑗 − 𝑤𝑐 𝑙 𝑗 .
To be an employee, earning a wage 𝑤𝑐 determined by the demand and
supply for labor in city 𝑐 in dependent of worker skill.
11
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
Consumption and utility

Differentiated goods sold in city c are produced by three sets of producers:
local informal firms 𝛺𝐼𝑐 , local formal firms 𝛺𝐹𝑐 , and formal firms in ROW 𝛺𝑂 :
𝑥 𝑗 , 𝑗 ∈ 𝛺𝐼𝑐 + 𝛺𝐹𝑐 + 𝛺𝑂

Worker-consumers with an income 𝑦𝑐 𝜑 in city c derive utility from local
amenity 𝐴𝑐 and the bundle of differentiated goods at a constant elasticity of
1
substitution 𝜎 = 1 + 𝜺 :
𝑢𝑐 (𝜑) = 𝐴𝑐
𝛺𝐼𝑐 +𝛺𝐹𝑐 +𝛺𝑂
subject to a budget constraint
o
𝑥(𝑗)
𝛺𝐼𝑐 +𝛺𝐹𝑐 +𝛺𝑂
1+𝜀
d𝑗
𝛺𝐼𝑐 +𝛺𝐹𝑐 +𝛺𝑂
Worker’s indirect utility is 𝑢𝑐 (𝜑) = 𝐴𝑐
,
𝑝(𝑗)𝑥(𝑗) 𝑑𝑗 = 𝑦𝑐 𝜑
Worker’s Marshallian demand for good j is 𝑥 𝑗
the price index in city c is ℙ𝑐 =
o
1
1+𝜀
𝑝𝑐 (𝑗) −𝜎 𝑦𝑐 (𝜑)
=
ℙ𝑐
ℙ𝑐
−𝜀
1
−𝜀
𝑝(𝑗)
, where
d𝑗
𝑦𝑐 (𝜑)
ℙ𝑐
12
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
Market demand and firm output

Profit maximizing price: 𝑝𝑐 𝜑 =

(1+𝜀)𝑤𝑐
𝛷𝑐𝜀
1+𝜀 𝑤𝑐
𝜑
=
𝛷𝑐𝜀
ℙ
𝜑 𝑐
1
Market price index: ℙ𝑐 =
𝛷𝐼𝑐 =
𝛺𝐼𝑐
1
𝜑(𝑗)𝜺
𝑑𝑗, 𝛷𝐹𝑐 =
𝛺𝐹𝑐
, where 𝛷𝑐 = 𝛷𝐼𝑐 + 𝛷𝐹𝑐 +
1
𝜑(𝑗)𝜺
𝑤𝑐 𝜺
𝑤𝑂 𝑇𝑐
𝛷𝑂 ,
𝑑𝑗, and 𝛷𝑂 represent, respectively, the aggregate
productive capacity of the city and the aggregate capacity of local informal firms, local
formal firms, and formal firms in ROW, and 𝑇𝑐 > 1 represents trade cost.

Price after trade cost: export 𝑝𝑐 𝜑 =

Market demand for formal firms:
𝑋𝐹𝑐 𝑗 = 𝑝𝑐 𝑗
where 𝑌𝑐 =
−𝜎
1
𝜀
ℙ𝑐 𝑌𝑐 +
𝜑𝑚𝑎𝑥
𝑦 (𝜑) 𝑑𝜑
𝜑𝑚𝑖𝑛 𝑐
1
𝜀
𝛺𝑐𝐹
import 𝑝𝑐 𝜑 =
1
𝑇𝑐−σ ℙ𝑂 𝑌𝑂
+ 𝜃𝑐
𝑇𝑐 𝛷𝑐𝜀
ℙ𝑐 ,
𝜑
= 𝑍𝑐 +
𝑤𝑂 𝜀 −σ
𝑇𝑐 𝑍𝑂
𝑤𝑐
𝜀
𝑇𝑐 𝛷𝑂
ℙ𝑂
𝜑
𝜑𝜎
,
(1+𝜀)𝑤𝑐
d 𝑗 is aggregate local income (expenditure), 𝑌𝑂 is
aggregate ROW income, 𝑍𝑐 ≡ 𝑌𝑐 𝛷𝑐 and 𝑍𝑂 ≡ 𝑌𝑂 𝛷𝑂 represent city productivity.
1

Market demand for informal firms: 𝑋𝐼𝑐 𝑗 = 𝑝𝑐 𝑗
−𝜎 ℙ𝜀
𝑐
1 − 𝜏𝑐 𝑌𝑐 =
𝑍𝑐 𝜑𝜎
.
(1+𝜀)𝑤𝑐
13
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
Occupation choice in city c

Profit
for formal firms: 𝜋𝐹𝑐 𝑗 =
𝑍𝑐 +
1
𝑤𝑂 𝜀
𝑤𝑐
𝑇𝑐−σ 𝑍𝑂
1
𝜑𝜀
σ
𝑝𝑐 𝑗 𝑋𝐹𝑐 𝑗
𝜎
− 𝜃𝑐 =
− 𝜃𝑐 ,
1
for informal firms: 𝜋𝐼𝑐 𝑗 =

𝑝𝑐 𝑗 𝑋𝐼𝑐 𝑗
𝜎
=
𝑍𝑐 𝜑 𝜀
,
𝜎
The skill cutoff for informal entrepreneurs,
𝜑𝑐 , is determined by 𝑢𝑊𝑐 = 𝑢𝐼𝑐 𝜑𝑐 , or 𝑤𝑐 =
𝜋𝐼𝑐 𝑗

1
𝜀
: 𝜑𝑐 =
𝜎𝑤𝑐
𝑍𝑐
The skill cutoff for formal entrepreneurs, 𝜑𝑐 ,
is determined by 𝑢𝐼𝑐 𝜑𝑐 = 𝑢𝐹𝑐 𝜑𝑐 , or 𝜋𝐹𝑐 𝑗 =
𝜋𝐼𝑐 𝑗
1
𝜀
: 𝜑𝑐 =
1
𝜎𝜃𝑐 𝑤𝑐 𝜀 𝜎
𝑇𝑐
𝑍𝑂 𝑤𝑂
14
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
Aggregate employment and income in city c

Employment (demand):
by formal firms 𝐿𝐹𝑐 =
𝝋
𝑋 𝜑
𝑁𝑐 𝜑 𝒎𝐚𝐱 𝐹𝑐𝜑
𝑐
by informal firms 𝐿𝐼𝑐 = 𝑁𝑐

d𝐺𝑐 𝜑 =
𝑤𝑐
𝑇𝑐−σ 𝑍𝑂
𝛷𝐹𝑐
1+𝜀 𝑤𝑐
𝑍𝑐 𝛷𝐼𝑐
1+𝜀 𝑤𝑐
Labor market clearing:
𝜑
𝑁𝑐 𝜑 𝑐 𝑑 𝐺𝑐
𝑚𝑖𝑛

𝜑𝑐 𝑋𝐼𝑐 𝜑
𝜑𝑐
𝜑
d𝐺𝑐 𝜑 = 𝑍𝑐 +
1
𝑤𝑂 𝜀
1
𝑍𝑐
1+𝜀 𝑤𝑐
𝜑 = 𝐿𝐹𝑐 + 𝐿𝐼𝑐 = 𝛷𝐼𝑐 + 𝛷𝐹𝑐
+
𝑤𝑂 𝜀 𝛷𝐹𝑐
𝑍𝑂
σ
𝑤𝑐
𝑇𝑐 1+𝜀 𝑤𝑐
Aggregate income
1
𝑌𝑐 = 1 + 𝜀
𝜑
𝑤𝑐 𝑁𝑐 𝜑 𝑐 𝑑 𝐺𝑐
𝑚𝑖𝑛
𝜑 =
𝛷𝐼𝑐 +𝛷𝐹𝑐
𝑌𝑐
𝛷𝑐
which gives trade balance equation:
or 𝑍𝑐 =

2
𝑤𝑂 𝜀
𝑤𝑐
𝛷𝐹𝑐
𝛷𝑂 𝑇𝑐
𝑍𝑂 =
𝑤𝑐
𝑤𝑂 𝑇𝑐
1
𝑤𝑂 𝜀
1
ℙ𝑂 𝜀
𝑤𝑐
ℙ𝑐
1
𝜺
𝛷𝐹𝑐 𝑍𝑂
𝛷𝑐 𝑇𝑐
+
𝑤𝑂 𝜀 𝛷𝐹𝑐
𝑌,
𝑤𝑐
𝛷𝑂 𝑇𝑐σ 𝑂
𝛷𝑂 𝑍𝑐 =
1
𝑤𝑂 𝜀
𝑤𝑐
𝛷𝐹𝑐
𝑍 ,
𝑇𝑐σ 𝑂
.
Result 1: Aggregate productivity in city 𝑐 increases with world productivity, local price
competitiveness, local wage competitiveness, formal productive capacity, but decreases
with trade cost.
15
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
Labor mobility and spatial equilibrium

Inter-city labor market clearing for employees
𝑤𝑐
ℙ𝑐
𝑢𝑊𝑐 = 𝐴𝑐
=
𝐴𝑐 Φ𝑐
1+𝜀
𝑢𝑊1 = 𝑢𝑊2 ⟹
,
Φ1 𝜀
Φ2
=
𝐴2
𝐴1
, Let 𝐴𝑐 = 𝑒 −𝑎𝑁𝑐 to reflect the congestion dis-
amenity, then aggregate producer productivity increases with city size:
Φ1 𝜀
Φ2

= 𝑒𝑎
𝑁1 −𝑁2
Inter-city labor market clearing for informal entrepreneurs
𝑢𝐼𝑐 𝜑 =
𝜋 𝜑
𝐴1 𝐼1
ℙ1
= 𝑢𝑊1
𝑢𝐼1 𝜑 = 𝑢𝐼2 𝜑 ⟹
𝑍1
𝑤1
1
𝑍𝑐 𝜑 𝜀
𝑤1 𝜎
=
𝑍2
𝑤2
1
=
𝜑 𝜀
𝜑1
𝑢𝑊 ,
or 𝜑1 = 𝜑2 .
16
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
Spatial sorting of formal entrepreneurs

Inter-city labor market clearing for
formal entrepreneurs
1
𝑢𝐹𝑐 𝜑
𝑢𝑊
𝑍𝑐
𝑤𝑐
=
=
𝜑
𝜑
+
1
𝜀
𝑤𝑂 𝜀 𝑍𝑂
𝑤𝑐 𝑇𝑐 σ
𝜑1 𝜀
σ
𝜃
1
𝜀
𝜑
𝑐 𝜑𝑐
+ 𝑤𝑐
𝜃
− 𝑤𝑐
𝑐
𝑢𝐼𝑐 𝜑 = 𝑢𝑊
𝜃
− 𝑤𝑐 ,
𝑐
𝑢𝑊 𝜑 =
𝑢𝐹1 𝜑 − 𝑢𝐹2 𝜑 increases with 𝜑 if and
only if 𝑤1 𝑇1 < 𝑤2𝑇2 ⟹ sorting of formal
entrepreneurs.

σ
1
𝜑0𝜀
𝜃1 𝜃2
=
−
𝑤1 𝑤2
1
𝜑2𝜀
1
1
−
𝑤1𝜎 𝑇1𝜎 𝑤2𝜎 𝑇2𝜎
𝜑0 increases with 𝑤1 and 𝑇1 , decreases
with 𝑤2 and 𝑇2 .
1
𝜀
𝐴𝑐 Φ𝑐
1+𝜀
1
𝜑1𝜀
Formal
Employee Informal
city 2
𝑢𝐹1 𝜑0 = 𝑢𝐹2 𝜑0 ⟹
1
𝑤𝑂 𝜀 𝑍𝑂
1
𝜑𝜀
𝜑
𝜑
Formal
city 1
−1
Lower skill cutoffs raise aggregate
productive capacity and 𝑢𝑊 , rotate
the equilibrium utility curves up
(greater incentive for HC upgrading)
17
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
The equilibrium

The equilibrium is an allocation of labor endowment—a
population 𝑁 and a probability distribution of skill 𝐺 𝜑 —to
cities 𝑐 ∈{1, 2} and to occupations {employee, informal
entrepreneur, form entrepreneur}, characterized by the set of
endogenous variables {𝛷𝐼𝑐 , 𝛷𝐹𝑐 , 𝜑𝑐 , 𝜑𝑐 , 𝜑0 }, so that utility 𝑢(𝜑) is
maximized given market clearing prices, wages, and
productivity {ℙ∗𝑐 , 𝑤𝑐∗ , 𝑍𝑐∗ }, the preference and urban congestion
parameters {𝜀, 𝑎}, location fundamentals {𝑇𝑐 , 𝜃𝑐 }, and world
market conditions {ℙ𝑂 ,𝑤𝑂 , 𝑍𝑂 }.
18
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
The equilibrium solution
Step 1: for a given informal skill cutoff 𝜑, 𝑤1 and 𝑤2 adjusts to achieve trade
balance in each city. Using the cutoff condition and trade balance equation, we
have 𝑍𝑐 = 𝜎𝑤𝑐 𝜑
2
+1
𝜀
𝑤1
1
𝜀
2
𝑤𝑂 𝜀 𝑍𝑂 𝛷𝐹𝑐
,
𝑤𝑐
𝛷𝑂 𝑇𝑐
=
=𝜑
2
+1
𝜀
𝑤2
1
−𝜀
2
1 𝑤𝜀 𝑍
𝑂 𝑂
𝜀
𝜎𝛷𝑂 𝑇1
=𝜑
1
𝜀
where 𝜑2 𝑤2↑ =



𝑁
2
𝜀𝑍
𝑤𝑂
𝑂
𝜎𝛷𝑂 𝑇2
which gives
𝜑𝑚𝑎𝑥 1
𝜑 𝜀 𝑑𝐺
𝜑0
𝜑0 1
𝜑 𝜀 𝑑𝐺
𝜑2
𝑁
1
𝜎𝜃2 𝑤2 𝜀 𝜎
𝑇2
𝑍𝑂 𝑤𝑂
𝜑
E1
𝜑
1
𝜀
and 𝜑0 𝑤1↑ , 𝑤2↓ =
E2
σ
1
𝑤𝑂 𝜀 𝑍𝑂
𝜃1
𝑤1
−
𝜃2
𝑤2
1
𝑤1𝜎 𝑇1𝜎
−
1
𝑤2𝜎 𝑇2𝜎
−1
A higher 𝜑 directly raises 𝑤1 and 𝑤2 , which then raises 𝜑0 and 𝜑2 ; 𝑤1 𝜑 and 𝑤2 𝜑
decrease.
A higher 𝑇1 lowers 𝑤1 and raises 𝜑0 directly, 𝑤1 𝑇1 will rise; 𝑤2 and 𝜑2 increase with 𝜑0 .
A higher 𝑇2 raises 𝜑2 and lowers 𝑤2 and 𝜑0 directly, raising 𝑤1 and 𝑤2 𝑇2 .
A proportional increase in 𝜃𝑐 raises 𝜑0 , thus lowering 𝑤1 but raising 𝑤2 and 𝜑2 .
19
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
The model:
The equilibrium solution
Step 2, 𝜑 adjusts to equalize aggregate supply of, and demand for, employee
workers.
𝜑
𝑑𝐺
𝜑𝑚𝑖𝑛
Aggregate supply: 𝑁
Aggregate demand:
𝑐=1,2
𝜑 ,
𝐿𝐼𝑐 + 𝐿𝐹𝑐 =
𝑐=1,2
𝛷𝐼𝑐 + 𝛷𝐹𝑐 +
1
1
𝑤1 𝜀
𝑇1 𝑤𝑂
𝑤2 𝜀
𝑇2 𝑤𝑂
𝛷𝑂
,
E3
𝛷𝑂 +
1
1
𝜀𝜑 𝜀
Which gives:
𝑁
𝜑
𝑑𝐺
𝜑𝑚𝑖𝑛
𝜑 =
𝑁
𝜑𝑚𝑎𝑥 1
𝜑 𝜀 𝑑𝐺
1 𝜑
𝜀𝜑 𝜀
1
𝜑 +
𝑤1 𝜀
𝑇1 𝜑
1
+
𝑤2 𝜀
𝑇2 𝜑
1
1+𝜀 𝜀 1
ℙ𝑂
𝜀

The supply side increases with 𝜑 and the demand side decreases with 𝜑 .

An increase in 𝑇1 or 𝑇2 reduces labor demand and thus 𝜑.

Normalize ℙ𝑂 = 1.
20
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis



Impact of preference for diversity—role of informal
entrepreneurs
Impact of external demand—role of market size for formal
firms
Impact of human capital endowment—role of entrepreneur
supply

Impact of fixed cost for formal firms—role of regulation

Impact of lower urban friction


The effect of better infrastructure in city 1 (lower 𝑇1 ) under
different entrepreneur supply and demand conditions
The effect of better infrastructure in city 1 (lower 𝜃1 ) under
different entrepreneur supply and demand conditions
21
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Numerical Simulation: Baseline Case


Pareto distribution for skill, with density 𝑔 𝜑 = 𝑘
𝑘
φ𝑘
𝑚𝑖𝑛 φ𝑚𝑎𝑥
𝑘
φ𝑘
𝑚𝑎𝑥 −φ𝑚𝑖𝑛
𝜑 −𝑘−1
Parameters set {𝑁 =100, 𝜎 = 3, 𝑎 = 0.03, 𝑘 = 4.5, 𝜑𝑚𝑖𝑛 = 1, 𝜑𝑚𝑎𝑥 = 30,
𝑌𝑂 = 7500, 𝑤𝑂 = 106.1, ℙ𝑂 = 1, 𝑇1 = 1.5, 𝑇2 = 2, 𝜃1 = 150, 𝜃2 = 100}
City 1
City 2
Total
Population 𝑁𝑐
51.1
48.9
100
Wage Rate 𝑤𝑐
10.5
8.2
-
1.285
Relative Wage Rate
City 1
City 2
Total
Productive Capacity Φ𝑐
50.4
44.2
94.6
Formal Capacity Φ𝐹𝑐
6.85
3.8
10.65
1.802
Relative Formal Capacity
Aggregate Income 𝑌𝑐
706.7
483
1189.7
Informal Capacity Φ𝐼𝑐
Export Income
308
81.7
389.7
Relative Informal Capacity
Price Index ℙ𝑐
2.23
1.85
-
Total Employment
44.7
39.2
83.9
Aggregate Utility
68.5
60.1
128.6
Formal Firm
0.281
0.339
0.62
Average Utility
1.34
1.23
1.29
Informal Firm
6.11
9.34
15.45
Formal Employment
25.6
13
38.6
Formal Employment Share
0.572
0.332
0.46
Informal E’s Utility Slope
Formal E’s Utility Slope
0.453
1.91
1.75
-
21.6
32.9
54.5
0.655
22
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis
Stronger preference for diversity: reduce 𝜎 from 3 to 2.7
City 1
City 2
Total
Population 𝑁𝑐
51.4
48.6
100
Wage Rate 𝑤𝑐
13.4
10.5
-
1.273
Relative Wage Rate
City 1
City 2
Total
Productive Capacity Φ𝑐
46
39.9
85.9
Formal Capacity Φ𝐹𝑐
5.52
3.33
8.85
1.657
Relative Formal Capacity
Aggregate Income 𝑌𝑐
906.6
619
1525.6
Informal Capacity Φ𝐼𝑐
Export Income
370.6
118.5
489.1
Relative Informal Capacity
Price Index ℙ𝑐
2.24
1.91
-
Total Employment
42.7
37.1
79.8
Aggregate Utility
86.8
75.4
162.2
Formal Firm
0.445
0.504
0.949
Average Utility
1.69
1.55
1.62
Informal Firm
8.25
11.03
19.28
Formal Employment
22.5
12.4
34.9
Formal Employment Share
0.528
0.333
0.438
Informal E’s Utility Slope
Formal E’s Utility Slope
0.7
3.08
2.8
-
21.7
29
50.6
0.748
Number of firms increases, but overall formal employment share decreases.
Population and wage dispersion across cities increase, but formal share
converges. Workers become more productive, and the utility slope increase.
23
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis
Greater external demand: raise 𝑌𝑂 from 7500 to 9000
City 1
City 2
Total
Population 𝑁𝑐
51.2
48.8
100
Wage Rate 𝑤𝑐
11.16
8.69
-
1.285
Relative Wage Rate
City 1
City 2
Total
Productive Capacity Φ𝑐
51.8
45
96.8
Formal Capacity Φ𝐹𝑐
7.47
4.14
11.61
1.803
Relative Formal Capacity
Aggregate Income 𝑌𝑐
757.6
511.3
1268.9
Informal Capacity Φ𝐼𝑐
Export Income
359.3
95.3
454.6
Relative Informal Capacity
Price Index ℙ𝑐
2.32
1.94
-
Total Employment
45.3
39.2
84.5
Aggregate Utility
70.2
60.8
131
Formal Firm
0.328
0.396
0.724
Average Utility
1.37
1.25
1.31
Informal Firm
5.59
9.17
14.76
Formal Employment
28
14.3
42.3
Formal Employment Share
0.619
0.364
0.501
Informal E’s Utility Slope
Formal E’s Utility Slope
0.451
1.94
1.78
-
19.8
32.4
52.2
0.61
Number of formal firms and formal employment share increases. Population and
wage dispersion increase somewhat, so does formal share. Workers become
more productive, and the utility slope for formal entrepreneurs increase.
24
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis
Greater supply of human capital: reduce 𝑘 from 4.5 to 4.0
City 1
City 2
Total
City 1
City 2
Total
51.2
48.8
100
60.4
52.5
112.9
11.87
9.2
-
10.58
5.8
16.38
1.289
Relative Wage Rate
1.824
Relative Formal Capacity
815
549.8
1364.8
375.5
98.6
474.1
Relative Informal Capacity
2.29
1.91
-
Total Employment
45.8
39.8
85.6
Aggregate Utility
76.7
66.7
143.4
Formal Firm
0.292
0.397
0.689
Average Utility
1.5
1.37
1.43
Informal Firm
5.08
8.62
13.7
Formal Employment
29.1
14.9
44
Formal Employment Share
0.636
0.373
0.514
Export Income
Informal E’s Utility Slope
Formal E’s Utility Slope
0.423
1.54
1.43
-
22
37.3
59.3
0.589
Number of formal firms and formal employment share increases. Population
and wage dispersion increase somewhat, so does formal share. Workers
become more productive, but utility slopes decrease.
25
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis
Joint changes: 𝜎 from 3 to 2.7, 𝑌𝑂 from 7500 to 9000, 𝑘 from 4.5 to 4
City 1
City 2
Total
City 1
City 2
Total
51.6
48.4
100
54.2
46
100.2
15.9
12.45
-
8.69
5.19
13.88
1.277
Relative Wage Rate
1.675
Relative Formal Capacity
1120.7
744.4
1865.1
521.2
165.2
686.4
Relative Informal Capacity
2.41
2.08
-
Total Employment
44.4
37.6
82
Aggregate Utility
98.8
83.8
182.6
Formal Firm
0.553
0.688
1.241
Average Utility
1.91
1.73
1.83
Informal Firm
6.67
10.05
16.72
Formal Employment
27.8
15.2
43
Formal Employment Share
0.625
0.404
0.524
Export Income
Informal E’s Utility Slope
Formal E’s Utility Slope
0.675
2.63
2.42
-
20.3
30.6
50.9
0.664
Number of firms and formal employment share increases. Population and wage
dispersion increase, but formal share converges. Workers become more
productive, and utility slopes rises.
26
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis
Lower urban friction: reduce 𝑎 from 0.03 to 0.025
City 1
City 2
Total
Population 𝑁𝑐
51.4
48.6
100
Wage Rate 𝑤𝑐
10.5
8.2
-
1.285
Relative Wage Rate
City 1
City 2
Total
Productive Capacity Φ𝑐
50.6
43.9
94.6
Formal Capacity Φ𝐹𝑐
6.85
3.8
10.65
1.802
Relative Formal Capacity
Aggregate Income 𝑌𝑐
710.7
479.8
1190.5
Informal Capacity Φ𝐼𝑐
Export Income
308
81.7
389.7
Relative Informal Capacity
Price Index ℙ𝑐
2.22
1.86
-
Total Employment
44.9
39
83.9
Aggregate Utility
88.4
76.7
165.1
Formal Firm
0.281
0.339
0.62
Average Utility
1.72
1.58
1.65
Informal Firm
6.19
9.26
15.45
Formal Employment
25.6
13
38.6
Formal Employment Share
0.569
0.335
0.46
Informal E’s Utility Slope
Formal E’s Utility Slope
0.582
2.45
2.25
-
21.9
32.6
54.4
0.669
Informal firms and employment become more concentrated, and formal
employment share converge somewhat. Wage rate remain unchanged, but
utility and utility slopes increase.
27
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis—lowering transport cost under different entrepreneur
supply and demand conditions
Simulation results for 𝑇1 =1.5 / 𝑇1 = 1.4
Parameter set
Baseline
σ=2.7
𝑌𝑂=9000
𝑘=4
σ=2.7, 𝑘=4
𝑌𝑂=9000
Wage Rate 1
10.54/ 11.12
13.37/ 14.21
11.16/ 11.78
11.87/ 12.48
15.9/ 16.9
Wage Rate 2
8.21/ 7.92
10.51/ 10.15
8.69/ 8.38
9.2/ 8.87
12.45/ 12.02
Aggregate Income 1
707/ 772
907/ 1000
758/ 830
815/ 887
1121/ 1237
Aggregate Income 2
483/ 458
619/ 586
511/ 484
550/ 520
744/ 702
Average Utility 1
1.34/ 1.40
1.69/ 1.76
1.37/ 1.44
1.50/ 1.57
1.91/ 2.01
Average Utility 2
1.23/ 1.24
1.55/ 1.56
1.25/ 1.26
1.37/ 1.38
1.73/ 1.75
Formal Capacity1
6.85/ 8.13
5.52/ 6.62
7.47/ 8.85
10.58/ 12.32
8.69/ 10.23
Formal Capacity 2
3.80/ 3.53
3.33/ 3.13
4.14/ 3.84
5.8/ 5.33
5.19/ 4.82
Formal Employment Share 1
0.572/ 0.675
0.528/ 0.619
0.619/ 0.727
0.636/ 0.740
0.625/ 0.719
Formal Employment Share 2
0.332/ 0.339
0.333/ 0.342
0.364/ 0.371
0.373/ 0.375
0.404/ 0.409
Lowering transport cost in city 1 raises wage rate in city 1 but depress it in city 2, with a bigger
effect under a stronger preference for diversity. ￮ Aggregate income increases in city 1, partially
offset by a decrease in city 2; the effect is stronger when the entrepreneur demand and supply are
greater. ￮ Formal share rise in both cities; the rise is little affected by economic conditions.
￮
28
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Counterfactual analysis—Lowering fixed cost under different entrepreneur supply and
demand conditions
Simulation results for 𝜃1 =150 / 𝜃1 = 140
Parameter Set
Baseline
σ=2.7
𝑌𝑂=9000
𝑘=4
σ=2.7, 𝑘=4
𝑌𝑂=9000
Wage Rate 1
10.54/ 10.66
13.37/ 13.58
11.16/ 11.28
11.87/ 11.98
15.9/ 16.11
Wage Rate 2
8.21/ 8.12
10.51/ 10.39
8.69/ 8.60
9.2/ 9.11
12.45/ 12.30
Aggregate Income 1
707/ 718
907/ 926
758/ 770
815/ 826
1121/ 1143
Aggregate Income 2
483/ 476
619/ 609
511/ 504
550/ 542
744/ 732
Average Utility 1
1.34/ 1.35
1.69/ 1.70
1.37/ 1.38
1.50/ 1.50
1.91/ 1.92
Average Utility 2
1.23/ 1.23
1.55/ 1.55
1.25/ 1.25
1.37/ 1.36
1.73/ 1.73
Formal Capacity 1
6.85/ 7.22
5.52/ 5.89
7.47/ 7.87
10.58/ 11.06
8.69/ 9.20
Formal Capacity 2
3.80/ 3.71
3.33/ 3.25
4.14/ 4.05
5.80/ 5.66
5.19/ 5.06
Formal Employment Share 1
0.572/ 0.585
0.528/ 0.543
0.619/ 0.633
0.636/ 0.649
0.625/ 0.641
Formal Employment Share 2
0.332/ 0.333
0.333/ 0.335
0.364/ 0.365
0.3731/ 0.3733
0.404/ 0.405
￮ Lowering fixed cost in city 1 raises wage rate in city 1 but depress it in city 2, with a bigger effect under a
stronger preference for diversity. ￮ Aggregate income increases moderately in city 1, partially offset by a decrease
in city 2; the effect is greater under a stronger preference for diversity. ￮ Formal share rise in both cities; the rise is
little affected by economic conditions.
29
Liu, Fu, and Liao: A General Equilibrium Model of Dualistic Economy
Concluding remarks




Informal sector contributes to the economy by supplying local diversity
o
Informal sector capacity rises relative to the formal sector, raising informal
sector share of employment, as preference for diversity increases.
o
Population diverges, but formal employment share converges, across cities
when preference for diversity rises or urban friction declines.
Formal sector share of employment rises as external demand increases or
human capital supply grows.
Lower urban friction allows greater concentration of informal employment
in the more productive city, raising total income and skill productivity.
Lowering transport cost, or fixed cost for formal firms, in city 1 raises wage
in city 1 and depress it somewhat in city 2. Formal share rises. Aggregate
income increases in city 1 but decrease somewhat in city 2. The effect is
much stronger by lowering transport cost, especially when entrepreneur
demand and supply are stronger.
o
Stronger entrepreneur demand and supply elevate city incentive to improve
transport infrastructure.
30