Information, the Dual Economy and Development
Abhijit V. Banerjee and Andrew F.
Newman
Question
• Economic development leads to modernization.
• But modernization is more than rise in living standards.
• Social, political, commercial relations change.
What is the relation between the
institutional changes and economic change in a modernizing economy?
In this paper, we look at…
• Tradeoff between credit availability in
traditional sector and higher productivity in modern sector-affects level of migration.
• Characterize the economies where inefficient level of migration will be observed.
• Look at dynamics, two way interaction
between process of growth and process of institutional change.
• Comment on robustness of Kuznet’s curve.
Some crucial assumptions
• Modern sector has greater productivity as compared to traditional sector.
• Traditional sector has a relatively low level of
information asymmetry. It is supported by many
evidences related to role of villages in providing loans for consumption smoothing, Grameen banks use this;
• Dasgupta(1987): finds that access to informal security mechanisms such as consumption loans is the main reason why people do not move.
• Once people move to city, they are completely cut off from the traditional sector.
The model
• One period
• Two locations: village and city
• Perfectly storable good and continuum of agents.
• Initial wealth a for each individual.
• Labor is freely mobile.
• Chance of consuming an indivisible good before entering productive phase, yields s, costs m units.
• vNM preferences:
U=y+u
y=income, u=utility from youth consumption
First best
• Assume, wages are higher in city, λw, λ>1 where w is wage in village.
• Normalize no. of people to 1.
• R(a):Measure of people in village with wealth less than a.
• U(a): Measure of people in city with wealth less than a.
• First best: No information problems.
• First best requires everyone is in city. How?
• r*= s/m (One possible case)
• Supply: 𝑎 for r ≥1, 0 otherwise
• Surplus=λ𝑤+[(s/m)-1]𝑎
• Now assume free mobility of capital, but information is not mobile.
• A borrower born either in village or city can chose to be on an agreed location (with moneylender) while borrowing the loan.
• Let ρ denote probability of fleeing upon agreed location successfully before income y is realized.
• If detected, punished maximally by having his consumption held to 0.
• Let π denote probability of successfully escaping repayment after income is realized. If detected, same punishment is imposed.
• Assume ρ=π=0 for person who is born in village and choses to remain in village.
• Assume π=ρ>0 otherwise.
• Assume λ(1-π)<1
• For city guy:
– If he agrees to stay in city:
Ex post and ex ante Incentive compatible constraint: 𝑎 ≥ 𝑚 − 1−π λ
𝑟
• For village guy,
– If he agrees to locate in city
Ex post IC: 𝑎 ≥ 𝑚 − λ𝑤 1−π
𝑟
Ex ante IC: 𝑎 ≥ 𝑚 − λ𝑤 1−π
𝑟
– If he agrees to locate in village
Ex post IC: 𝑎 ≥ 𝑚 − 𝑤
𝑟
Ex ante IC: 𝑎 ≥ 𝑚 − 𝑤
𝑟
We see…
• The above conditions imply that a city guy will never chose to locate in village. (Show.)
• He consumes the youth good only if his wealth level is greater than ac=m-(1-π)λ𝑤
𝑟
• The villagers with wealth levels a>=ac=𝑚 − (1 − π) λ𝑤
𝑟 and a<=av=m-𝑤
𝑟 will chose to migrate.
• People with wealth levels in between migrate if r≥𝑟 (w)
Note.
• Threshold values (all of them!) are:
– Increasing in interest rate – Decreasing in income
– Increasing in ρ and π
• Proposition 1: An agent born in the village
with wealth a and who earns w there migrates to the city when the interest rate is r only if
a)a≥ac(w,r) b)r≥𝑟 (w) c)a≤av(w,r)
Demand of loans
• For r>s/m, demand=0.
• For r=s/m, r>𝑟 everyone migrates to city. People are indifferent between consuming and not
consuming. (Why?). Demand lies in [0, m[1- R(ac(s/m))-U(ac(s/m))]
• For 𝑟 <r<s/m, demand=m[1-R(ac(r))-U(ac(r))]
• At r=𝑟 people with aє[ac,av] are indifferent
between migrating and not migrating, =>demand lies in [m(1-R(ac(𝑟 ))-U(ac(𝑟 )), m(1-R(av(𝑟 )-U(ac(𝑟 ))]
• For r<𝑟 demand is m[1-R(av(r))-U(ac(r))]
Under what conditions inefficient level of migration will be observed?
• We say, a given level of migration is inefficient if social surplus can be increased relative to its equilibrium level by forcing agents to chose
locations in some way other than that occurs in equilibrium.
• We should expect the situation where some remain in rural sector is candidate for
inefficiency. (Why?)
Necessary condition
• 𝑟 ≥1 (Show.)
• This implies:
(s-m) ≥ (λ-1)w …condition 1
• Proposition 2: Suppose condition 1 holds and R(.) and U(.) are continuous. Then the level of migration is inefficient if and only if
a)1-R(av(1))-U(ac(1))>𝑎 /m b)1-R(ac(r’))-U(ac(r’))<𝑎 /m
Implications of the model
• First result shows that wealthiest, most productive or poorest and least productive have greater incentive to leave.
• Second result shows that more people will move to modern sector when interest rate is very low or very high.
• Rural credit institution creates inefficiency by allowing the interest rate to be set too high relative to second best level.
• Since it facilitates borrowing, some people chose to remain in traditional sector. If they were moved, wealth would be put to more productive use.
• If economy is sufficiently wealthy, 𝑎 ≥m, migration is always efficient. [Since (a) of previous proposition is always
violated.]
• Rich and poor economies will tend to have
efficient migration. 1-R(ac(r)) and R(av(r)) will be higher for r<𝑟 respectively.
• Middling economies are more likely to face the problem of under migration. Why?
• Falling interest rate due to migration will hurt
lenders. Surplus increase not necessarily a pareto improvement.
• If urban sector is suddenly opened to a very poor economy, there should be full migration.
• Both average wealth levels and distribution of wealth level will determine the degree of under migration.
Level of Migration
Why study dynamics?
• Is under-migration still a possibility if wealth
distribution is endogenous and in more generality can under-migration be a long-run phenomenon ( under-migration trap)
• Is Kuznets’s inverted U hypothesis validated by this story of migration?
• We start with a purely rural economy and examine the level of migration and the distribution of labor earnings over time after the urban sector is opened
The model
• Economy lasts for infinite number of periods and population is constant
• In every period, an individual receives a
bequest from his parent that in turn becomes his initial wealth for the next period
• Consumption and earnings occur twice at dates 1 and 2 within the period
The model
• Utility is of the form
• Location choice, borrowing and youthful
consumption occur before date 1; uncertainty (if any) about skill level is resolved at date 1, and the wage earned at date 2 is the same as that earned at date 1
• The agent's date 1 consumption occurs after repaying any loans
• Agents who are caught after reneging on loans are subject only to having their date- 1 income
confiscated; date-2 income is inappropriable.
• We focus on the case when each agent consuming date 1 earnings net of loan repayments at date 1, and splitting date-2 earnings between date-2
consumption and the bequest
• Bequest is therefore if income is y
• Agents learn their skill level after choosing the location
Model
Assumptions
• Multitude of skill levels w (corresponding to village labor earnings)
– Distribution – Support
– Density
– Mean and Variance
• Corresponding cdf for city is
Assumptions
• To ensure loans are repaid out of period 1 income, we need
• But this would mean that fraction of villagers
born with wealth level less than is always zero
• To ensure average wealth level is less than m , we need
Assumptions
• Coefficient of variation is used as an inequality measure, (Standard deviation/Mean)
• The rural population at the beginning of the period is
• Since is the bequest , fraction of rural population
at the beginning of period t with wealth less than x is
• Rural wealth distribution is
• Urban wealth distribution is
Inverted U
• Distribution of wages in the economy in period t is given by
• To validate the inverted U hypothesis, we need to show
– Monotonic decline in rural population
– Economy fully modernizes ( rural population converges to 0)
– It does so in more than one period
Inverted U
• First requirement is ensured as nobody moves from the city to the village
• For the second, we need to have a lower bound on the number of people who leave the village in every period
• For the third, we need to ensure that the first period equilibrium rate of interest is less than
Full Modernization
Under-migration in the long run
• We drop the assumption to ensure that there is no full modernization
• This implies
Under-migration in the long run
Under-migration in the long run
Different patterns of migration
Different patterns of migration
Different patterns of migration
Alternative modeling assumptions
• Possibility of violations of inverted U hypothesis
• Over-migration???
• Capital is not mobile between the two locations
