Poverty trap in a world of perfect markets: an efficiency wages

explanation

Giacomo RodanoLSE

(7th March 2005)

EC501 EOPP Workshop

Abstract

• There is a vast literature on poverty traps, that stresses the role of market imperfections as a necessary conditions for an individual poverty trap to emerge.

• I will show that a poverty trap may emerge even in a world where credit market are perfect.

• The main ingredient to generate a poverty trap is the assumption that productivity of the agents depends on the amount they consume (sort of “efficiency wage” idea).

• This has important policy implications: improving the working of credit market could not be enough to eliminate a poverty trap, while one-shot changes in the initial distribution of asset can lead to efficiency improvement.

Outline

• Poverty trap and related literature

• My suggested mechanism: “efficiency wages”

• A simple model

• Conclusions and directions for further research

• Comments (throughout the presentation, please!)

Individual poverty traps• Main idea: out of identical agents:

– Same preferences– Same technology

• some (the poor) are trapped in a low productivity equilibrium (also in the long run), due to the basic fact that they are poor:– Different (lower) endowment of wealth

• So what?– Efficiency: the poor do not exploit fully their capabilities,

they do not contribute as much as they can to the economic system

– Interesting dynamic evolution on wealth distribution (twin peaks/polarization with few agents that jumps from poor to rich rather than steady convergence) even in the case of ergodicity of welath distribution (see Benerjee 2002 and Mookerjee and Ray 2000).

Main mechanismTwo necessary conditions:• Credit market imperfections: if not whenever there is a profitable

opportunity, the poor agents will find someone to finance them and, given profitability, they are able to repay. Usual consideration of moral hazard, asymmetric information and voluntary default explain why they poor agents are not able to get credit and so are stuck in a poverty trap.

• Non-convexities in production: if not the agents are able to save little by little and so they will become richer and richer. If there is a threshold (fixed cost) the poor will never be able to overcome it– Some works weakens this assumption:

• Piketty (1997) poverty trap is driven by the equilibrium on the labor market equilibrium

• Moav (2002) bequest is a luxury good

• Nobody gets rid of the other: some form of market imperfections is needed to generate a poverty trap.

Literature

Individual poverty trap and credit market imperfections:– Loury 1981: not a poverty trap– Galor-Zeira 1993: investment in education– Banerjee-Newman 1993: occupational choice– Dasgupta-Ray 1996, and Ray-Streufert 1993: under nourishment

Also related literature:– Aghion-Bolton 1997, and Matsuyama 2000: endogenous credit

markets– Piketty 1997: endogenous wages

Poverty trap and lack of insurance market:– Siglitz 1969 (see Banerjee 2002, for a survey). Main idea: poor agents

are more risk averse so they will invest less than the rich agents and are trapped in a low equilibrium.

Are credit market imperfections necessary? Who cares? At this stage it is a purely theoretical exercise. It is also difficult to take to the data.

• Policy implication: the main policy implication of the poverty trap literature goes like “It is true that one shot redistribution can have permanent costs, but it is big, it is not pareto- improving. Let ‘s rather improve working of credit markets (legal system, property rights, microfinance, land titling…)”. My model points out that all these policy could be not enough(more heuristic)

• Wealth matters: my model points out that differences between poor and rich are relevant even in addition to the well know feature that poor are disadvantaged by markets imperfection. In the model in the end it is the budget constrain which has a bite. (Export somehow similar idea to explain social mobility patterns in US?)

Mechanism: “efficiency wages”

• Not new in theoretical literature: – Original efficiency wage models Leibenstein 1957 and Stiglitz

1976: at low level of wages, productivity is related to the income (wages). This may lead to involuntary unemployment.

– Dasgupta-Ray 1986: use this assumption to generate a poverty trap, through the equilibrium on the labor market. This is essentially static model (and the result hinges upon some non-convexities of the relation between consumption and productivity).

– Ray-Streufert 1993: extend the model to dynamic setting but assume borrowing constraints (i.e. credit market imperfections).

• There is a strong empirical support to the main assumption.– Strauss-Thomas 1995 and Ray 1998 (Ch. 8)

Main idea is that productivity of agents depends on the amount they consume. (Broadly defined consumption can include health services… not only a nutrition story)

Preview Results and Intuition• A poverty trap may emerge if there is a positive and concave

relation between consumption and productivity• The main mechanism has two basic ingredients:

– given the budget constraint, poor agents consume less than rich one

– when consumption is low, given decreasing return, the cost of leaving bequest in terms of consumption high (cost of bequest = R(1 - y’(c)).

– so poor agents leave less bequest than rich one and are trapped into poverty

• Under certain conditions this mechanism generates a poverty trap

• In this case one shot redistribution can improve (more efficiency unit of capital) the long run outcome of the system

Rest of the talk: the model

• Production side• Individual human wealth• Consumption and bequest decisions• Evolution of wealth in the long run

– The poverty trap• Policy implications• Conclusions and directions of further research

Model: production

• Taken from Galor-Zeira (1993) and Moav (2002)• Small open economy: interest rate (r) is given• Homogeneous good produced by a representative, perfectly

competitive, firm using capital (K) and efficiency unit of labor (H) as input according to a constant return to scale technology

• Individual decision are taken one period in advance: so stock of H is taken as given by the firm

• Given r the FOC of the firm with respect to capital uniquely determine K/H and FOC with respect to H uniquely determines the remuneration per unit of human capital (w)

Model: individual problem (short run)

• Individuals have identical preferences and have access to the same “investment” technology. They live one period and derive utility from consumption (c) and bequest (b) according to the following utility function

• They differ only according their inherited wealth (a) that determines their lifetime resources constraint, which is given by

The model: the human wealth

• In the morning the agents are subject to a transformation process that determines their productivity.

• In the spirit of (nutritional) efficiency wage models their productivity depends positively on how much they consume.

• For simplicity we assume the simplest concave formulation for this relation

• Where we assume < 1 and y0 can be zero.• Main mechanism/results should be there also with a

general increasing concave function y(c). This formulation is simpler.

The main assumption

cc1

y(c)

y0

The model: The consumer problem

c

b

c1

Graphically:

R

R(1-)

R(a+y0)

The lifetime resources constraint is given by the following:

The model: The consumer problem

c

b

Graphically:

The preferences are homothetic so the locus of the combinations of c and b such as MRS is constant is a straight line through the origin.

Formally

MRS=R(1-)

MRS=R

MRS > R

R>MRS>R(1-)

MRS<R(1-)

The model: the solution

The graph shows the wealth-expansion path of consumption and bequest:

The model: the intuition

• The result that higher wealth lead to higher consumption does not depend on the particular functional form of preferences or human wealth

• In a more general setting in which the human wealth is a generic function, increasing and concave over the relevant part we have that the main mechanism is still there: the rich find cheaper and cheaper to leave bequest in terms of consumption. Formally the FOC is

• And the mechanism is a c y’(c) b/c

The model: the poverty trap• In the long run (across generations) we have at+1 = bt

• So the evolution of wealth is represented by the following difference equation. Under certain conditions (next slide) by the following graph.

The Trap: conditions

a

bFirst I assume that: (to compare it with the convergence case if y’(c) = 0). If not true agents give such a big weight to bequest that wealth diverges in the long run.

b

aa a**a1 b

aaa2a*

A necessary condition for a trap is a1 < a which impliesIf not satisfied all agents will end up rich.

Another necessary condition for a trap is a2 < a which implies if is small, or simply if is big.

Policy implications

• Steady state distribution depends on initial distribution. All the dynasties with initial wealth below a will end up poor (with low wealth a*) and the others will end up rich (with high wealth a**).

• Notice that since a* < a1, we have that in steady state the poor consume less than c1 so their efficiency of labor is lower than rich agents.

• Given initial distribution G0(.) we have that:

• One shot redistribution that moves more agents above the critical threshold a without moving anybody below will increase the amount of efficiency of labor in the economy.

Conclusions and further research

• A poverty trap may emerge even in a world of perfect credit markets

• So poverty and persistence in poverty is not necessary the result of market imperfections

• Redistribution policy can improve• AND NOW?

– See if the theoretical result is empirically relevant/plausible. Have a look at data and check whether the conditions for the emergence of a trap are significantly

– Export the idea that poverty can be persistent even when market are perfect from development to macro and explain the pattern of inequality and social mobility in rich countries (e.g. US)

Alternative specifications

cc

y(c)

A c1

y(c)

A

y(c)

cc

y(c)

B C

Alternative specifications

c1c0 c

a4

b

c1

c0

c

a3

a2

c

y(c)

c1

Alternative specifications

a3

at +1

ata*0 a4aa2