development: new (?) themeskrugman [1999] on east asian crisis or cooper [1999] on busi-ness cycle...

/papers/talks/cea/slides.tex 1

Development: New (?) Themes

Debraj Ray

New York University

State of the Art Lecture, Canadian Economics AssociationMeetings, Vancouver, 2000.

2002 warning: these lectures are old so there will be someupdating. Don’t follow literally but only as a rough guide.


Convergence

Open almost any book on development and it will begin with theusual litany of woes.

Low physical capital per person,Undernutrition,Under-par educational attainments,Limited access to sanitation, safe water and housing,High population growth rates,High infant mortality rates,

and so on. Notice that some of these indicators may be regarded asdefining features of underdevelopment. Others are at least one stepremoved. And indeed, that is how it should be.

After all, we make a list of features to search for explanations, notjust to define the term.


Convergence, continued

Enormous empirical literature spawned on these “explanations”. Ex-amples of standard approach: regress per-capita income on a bunchof (provisionally) exogenous factors: the rate of savings (or invest-ment) or population growth rates (see, e.g., Mankiw, Romer and Weil[1992]), subsequent income growth on initial income, initial educa-tional attainments (e.g., Barro [1991]).

Much (though not all) of these studies are after some notion of con-vergence. Based on celebrated Solow model (1956), or the turnpiketheorems for optimal growth theory.

Basic idea: suppose output produced by capital and labor; constantsavings ratio. Then countries with a low relative capital endowmenthas high marginal return to capital (the “Law” of diminishing re-turns). Thus, controlling for savings rates, poorer countries will tendto grow faster and hence will catch up, converge.

Savings rate not the only control. Control for anything that system-atically affects marginal addition to per-capita income. Include sharpquantifiables such as population growth rates or looser concepts suchas “political climate” or “corruption”.

Thus the convergence hypothesis, properly interpreted, does not re-ally mean that all countries do actually converge. But it does meanthat a failure to observe convergence must be traced to one or anotherof some so-called exogenous factors.


The Influence of Convergence

The theory of convergence has two important — and unfortunate —implications for the way we think about development.

First, it limits our search for deep explanations. “Explain” inter-country variation by stating that

one country is more corrupt than another,or more democratic,or is imbued with some particularly hardworking cultural ethic.

Or one might even hang one’s hat on the following sort of theory:different societies have some intrinsic difference in their willingness— or ability — to save, or to procreate.

At some level these “explanations” are perfectly valid. But they arenot very deep. We wouldn’t like to stop there. We would like toknow, for instance, whether

low incomes provoke, in turn, low savings rates?

might underdevelopment be a cause of high population growth rates?

Is corruption just as much an outcome as a cause?

These are well-known circularities. Simply asserting that “nothing istruly exogenous” doesn’t take us very far. The question is whetherone can glean new insights.


Influence of Convergence, contd.

The second problem with the convergence approach is that it gener-ates a particular set of attitudes towards economic policy.

Stresses the role of factors (e.g., savings or population growth) thatmight be symptoms rather than causes. May be hard to change thesethrough simple-minded policy (e.g., more contraceptives, setting uppostal savings schemes, and so on).

Even if the policies are effective, possible misjudgment on requiredduration of necessary interventions.

More generally, promotes what Hoff and Stiglitz [2000] call shallowversus deep interventions. Examples:

privatization and regulatory policy (sequencing)

credit policy (social capital)

land or asset reform

In what follows, I outline theories in which societies that are funda-mentally similar might behave differently, and persistently so.

The phrase “fundamental similarity” must be understood contextu-ally. (e.g., not interested in theories that use culture, corruption,impatience or reproductive irresponsibility as explanations).


What I’d like to talk about...

Two sorts of theories

[1] Underdevelopment as a self-fulfilling failure of expectations.

[2] Underdevelopment as a persistent outcome of certain historicalconfigurations. Particular focus on differences in initial economicinequality.

[3] ... and some broad policy implications.


Underdevelopment and Expectations

Economic underdevelopment as coordination failure.

View stems from Paul Rosenstein-Rodan [1943], Myrdal [1944, 1957]and Albert Hirschman [1958].

For later developments, see Murphy, Shleifer and Vishny [1991],Krugman [1991], Matsuyama [1991, 1996], Ciccone and Matsuyama[1996], Rodriguez [1996], Journal of Development Economics [1996],Adsera and Ray [1998], Gans [1998]... and many others.

Game: n agents, action sets A1, A2, . . . , An. Payoff functions π1, π2, . . . , πn.Game exhibits a complementarity if there exists an ordering of theaction sets �i, i = 1, . . . , n such that if a−i �−i a′

−i, then

arg maxa∈Ai

πi(a, a−i) �i arg maxa∈Ai

πi(a, a′−i).

[Note: can define �−i in a variety of ways.]

Game with complementarities may exhibit Pareto-ordered multipleequilibria.

Complementarities may coexist both with “positive” or “negative”externalities. These terms are not robust to relabeling of payoff func-tions.


Looking for Complementarities

Basic recipe: Look for “equilibrium map” from some observable vari-able to itself, check for monotonicity.

1. Growth with Externalities (Romer [1986]). Economy-wideinvestment raises return to individual investment.

2. Financial Deepening (Acemoglu and Zilibotti [1997]). Greaterfinancial deepening encourages greater financial savings.

3. Corruption. Economy with limited auditing capacity in whichonly a fraction of “corrupt” people can be investigated.

4. Capital Deepening (Ciccone and Matsuyama [1996]). Greaterroundaboutness in production increases productivity of capital, and(under some conditions) increases the demand for individual machinevarieties.

5. Social Capital (Ghosh and Ray [1996], Banerjee and Newman[1997], Berman [1999]). Mobility destroys traditional social networks.All sorts of effects including a mobility feedback.

6. Norms (Munshi [1998], Ray [1998]). Percentage of populationshifting to new crop, entering small businesses, using contraceptives,joining the revolution ...

7. Currency Crises (Morris and Shin [1998]). Herding versus thefundamentals.

8. Discrimination and Group Reputations (Myrdal [1944],Arrow [1972], Tirole [1996]). Groups discriminated against may not“invest”, perpetuating discrimination.


Two Economy-Wide Coordination Failures

Can apply this idea in two distinct ways to economy-wide coordina-tion failures.

1. Inter-Industry Links (Hirschman [1958])

Steel

Iron

Coal

Mining

MachineryConsumer

Goods

Shipping

Railways

Exports

Figure 1: Inter-Industry Links.

Supply versus demand links.

Direct versus indirect links.


Two Economy-Wide Coordination Failures, contd.

2. Demand Complementarities (Rosenstein-Rodan [1943])

Expansion in some industries may raise income, and so generate de-mand for other industries.

Implies a potential complementarity across producers of non-inferiorgoods.

By the way: such “indirect” complementarities do not need to workthrough demand alone. E.g., creation of a skilled workforce.

Several qualifications needed for multiplicity to appear. Chief amongthem is some form of limited competition (special case of this: lim-ited international trade). See Murphy, Shleifer and Vishny [1989] orRodriguez [1996].

These models lay a (limited) foundation for policy debates, such asthe famous debate on “balanced versus unbalanced growth” (Rosenstein-Rodan [1943, 1961], Nurkse [1952, 1953], Hirschman [1958], Streeten[1956, 1963]...)


Implications

1. Complementarities may or may not result in multiple equilib-ria. When they do (e.g., Rosenstein-Rodan [1943]), the equilibria aretypically Pareto-ranked. When they don’t (e.g., Acemoglu-Zilibotti[1997]), the type of inefficiency can be typically pinned down.

2. Change in the way we think about policy. In convergence lit-erature, policy amounts to a sustained tweaking of parameters. Incontrast, the multiple equilibria context views policy as a way ofpulling the economy out of one equilibrium into another.

3. Temporary policies may have permanent effects: E.g.,

amnesties (Kahhat [1999]), minimum wage legislation (Basu, Geni-cot and Stiglitz [2000]), family planning programs (Phillips et al[1988], Munshi amd Myaux [1999]), certain affirmative action pro-grams (Gans [2000])...

4. Warning: Implementing equilibrium-tipping policies may be adelicate task. Small informational errors may generate new stableequilibria that are worse than the old ones (e.g., Bond and Pande[1999]). Especially true when policies can only be conditioned onobservables such as income, capital gains, and so on.


Other Policy Questions and the Role of History

Unfortunately, models of multiple equilibria don’t take us far enoughto even address certain important questions: E.g.,

• Why is QWERTY stickier than fashion?

• Why do the breakdown of norms follow a logistic path?

• How do we shed light on the balanced-versus-unbalanced growthdebate? The whole debate is clearly about equilibrium transi-tions.

Complementarities lead to a view of the world that is essentiallynon-deterministic. Too non-deterministic?

• Repeat a situation with multiple equilibria again and again. Howdoes a history of “bad play” affect the future? [Both Rosenstein-Rodan and Hirschman started with the presumption that itdoes.]

• One answer is that this approach is too “light” on state vari-ables. There are fundamentals that only permit one equilibriumor another (except perhaps for intermediate values). See, e.g.,Krugman [1999] on East Asian crisis or Cooper [1999] on busi-ness cycle theory.

• Still does not get around the multiple equilibrium problem! Alsofollowing phenomena (and others like them) cannot be properlyaddressed:


Equilibrium Transitions

Two regions, A and B. Endowment of K is split at date 0 betweenthe two regions.

Capital in B — call it K — has a rate of return that depends on K:r = f(K), where f is increasing. Capital in A (K − K) has fixedrate of return, normalized to zero.

NewOld

Number of PeopleNumber of People OA BA' B'

Per

Cap

ita S

ecto

ral R

etur

n

Figure 2: Canonical Model of Complementarities


Equilibrium Transitions, contd.

Can embed static coordination game into a dynamic model of tran-sitions.

Continuum of identical agents. Each owns one unit of capital. Cap-ital free to move between regions, perhaps at some cost.

Let γ ≡ {r(t), cA(t), cB(t)}∞t=0 be (perfect foresight) timepath of re-

turns and relocation costs. Let V (γ, i, t) be optimal value to an agentin region i, i = A, B, beginning at time t under this path.

By standard arguments, an agent in region i will switch (stay) attime t if V (γ, i, t) < (>)V (γ, j, t) − cj(t), and will be indifferent ifequality holds.

A path γ is an equilibrium if it is generated by the optimal decisionsof agents in response to γ.

Huge multiplicity of equilibria. Mirrors the multiple equilibriumpaths of repeated coordination games.

What role does history play in all of this?


Introducing History, Minimally

Several approaches to this problem. We discuss one.

Assume that there is some lag in the generation of external effects:r(0) is precisely f(K(0)), but thereafter,

r(t) = g(f(K(t)) − r(t)).

That is, r at any date “chases” the “appropriate” r at that date.

Several economic situations conform to this specification:

models of search or matching (e.g., Diamond [1982]),

models of variety-expansion driven by population (Krugman [1991a]),

models of learning skills or ideas from others (Adsera-Ray [1998]),

and so on. Note that existing literature (e.g., Cooper and John [1988],Matsuyama [1991], Krugman [1991b]) effectively assumes that g is“infinitely sensitive”; i.e., r(t) always equals f(K(t)) (but see Gale[1993], Chamley and Gale [1994], or Gans [1998] where lags also playa role).

Say that an intertemporal equilibrium is exclusively history dependentif the long-run outcome either equals the initial allocation, or entailsmigration only to the sector that is initially profitable. E.g. myopictatonnement.


Minimal History creates Strong History-Dependence

Proposition (Adsera and Ray [1998]). Assume f(K(0)) �= 0. Un-less the cost of relocation exhibits congestion, every equilibrium mustbe exclusively history dependent, irrespective of the discount rate.

Comments on:

The role of the externality lag

Fashion: the role of mavericks

What happens with congestion?

Interactions: is there no role for self-fulfilling beliefs?

rethinking equilibrium transitions (balanced versus unbalanced growth,and other matters).


Underdevelopment and History

History dictates much more than expectation-formation.

It may pin down the values of certain tangible variables and influencefuture developments.

Historical legacies may consist of

initial capital stocks

initial distributions of income or wealth

legal or social structure

group reputations

and so on.

Variations in historical legacies — or initial conditions — are notto be thought of as variations in the fundamental makeup of theeconomy.

Put this way, the approach replaces a belief in fundamental differ-ences with a study of path-dependence.


Modeling History

Two fundamental ways in which the history of initial endowmentspersistently matter:

Nonconvexities (at the level of the individual)

Interaction (across individuals)

In absence of these consult Loury [1981], which have several individ-uals independently solving a Ramsey optimal growth problem. Ingeneral, rates of return to investment will differ across individuals(this is the postulate of a missing credit market, which Loury ex-plores).

All the same, in the Loury model there is ergodicity. Persistent in-equality only driven by uncertainty (also see Champernowne [1953]).

Now a large literature that relies either on nonconvexities or inter-action or both. Especially concerned with the functional aspects ofinitial inequality in the distribution of income or wealth: Dasguptaand Ray [1986, 1987], Banerjee and Newman [1993], Eswaran andKotwal [1986], Galor and Zeira [1993], Lundqvist [1993], Ray andStreufert [1993], Bowles and Gintis [1994, 1995], Hoff [1994], Hoffand Lyon [1995], Legros and Newman [1996], Aghion and Bolton[1997], Mookherjee [1997], Piketty [1997] and others.

Also a political economy literature that describes how initial inequal-ities may affect political demands for redistribution, thus affectinggrowth (Alesina and Rodrik [1993], Benhabib and Rustichini [1997],Benabou [1996, 2000] and several others). Won’t go into that here.


A General Framework, with Applications

What follows based on Mookherjee and Ray [2000].

Population of unit size. H: a list of occupations. λ: populationdistribution over occupations. Date t indexes generation t.

For each λ, λ′, to be interpreted later as adjacent population distri-butions, a wage function w = {w(h)}h∈H is defined on H.

For each wage function w on H, a cost function x = {x(h)}h∈H isdefined on H. This is to be interpreted as the cost, payable in thecurrent period, of acquiring the occupation h in the next period.

Thus given a sequence {λt}∞t=0 of population distributions on H, we

obtain a sequence {wt, xt}∞t=0 of wage and cost functions defined on

H, where each wt comes from (λt, λt+1), and each xt comes from wt.In this case say that {wt, xt}∞

t=0 is generated by {λt}∞t=0.

Individuals only foresee the wage-cost sequence (the actual genera-tion of this sequence is of little import to them).


Framework, Contd.

For an individual i with h0(i) given:

max∞∑

t=0βtu(ct)

subject to the constraints

yt = wt(ht)

andyt = ct + xt(ht+1)

for all t. Implies a sequence of occupational choices {ht(i)}∞t=0.

Note 1: like a Ramsey problem with endogenous production functions

Note 2: capital market imperfections

Aggregate occupational choices: for each t, define λt(h) ≡ µ{i :ht(i) = h}. Such a sequence {λt}∞

t=0 is an aggregate response to{wt, xt}∞

t=0 (for given λ0).

An equilibrium (for given λ0) is a sequence {λt, wt, xt}∞t=0 such that

(a) {wt, xt}∞t=0 is generated by {λt}∞

t=0, and (b) {λt}∞t=0 is an aggregate

response to {wt, xt}∞t=0.


Examples

[1] Optimal Growth. H is set of all capital stocks or educationallevels (as in Loury [1981]). w(h) is an exogenous function — theproduction function; x(h) also exogenous: x(h) = −h.

[2] Nonconvex models (as in Galor and Zeira [1993]). H is adiscrete set of occupations. w(h) again exogenous, represents returnto occupation h. x(h) also exogenous, represents cost of acquiring h.

[3] Entrepreneurship (as in Banerjee and Newman [1993]). H ={1, 2}. 1 = worker; 2 = employer. x(h) = 0 if h = 1, and S if h = 2.

Production function F on employment L. w(1) given by

F ′λ(2)

λ(1)

= w(1),

while w(2) is just profit:

w(2) = F

λ(2)

λ(1)

− F ′

λ(2)

λ(1)

λ(2)

λ(1).

[4] Labor Skills (as in Lundqvist [1993]). H = {1, 2}. 1 = un-skilled worker; 2 = skilled worker. x(h) as in example [3].Production function F defined on unskilled and skilled labor.

w(h) = Fh (λ(1), λ(2))

for h = 1, 2.


Examples, contd.

[5] Demand (as in Mani [1998] and Ray [1998]). H a finite set ofcommodities. Person with occupation h produces one unit of goodh. x(h) exogenous. p = {p(h)}h∈H is a price vector on H. Givenincome y, consumer demand vector is c(p, y).Equilibrium price vector equates supply and demand:

∑

h∈H

c(p, p(h))λ(h) = λ.

Note that p(h) = w(h) for all h.

[6] Teaching. [Explains why wages might have to be taken as a func-tion of both the population distribution at the current and the nextdate.] H = {1, 2}. 1 = unskilled worker; 2 = skilled worker. Pro-duction function F defined on unskilled and skilled labor (a(1), a(2)).a(h) now to be distinguished from λ(h).x(h) = 0 if h = 1, and αw(2) if h = 2. Note dependence on w. Pre-sumably α < 1. To determine w, note that if λ and λ′ are “adjacent”population distributions,

a(1) = λ(1), while

a(2) = λ(2) − αλ′(2), so that

w(h) = Fh (λ(1), λ(2) − αλ′(2))

for h = 1, 2.


Emergence of Inequality

Consider (λ, x, w) such that (a) (x, w) in every period is generated bythe stationary λ in each period, and (b) given λ0 = λ, the stationarysequence λ aggregates optimal responses to the stationary (x, w).Then (λ, x, w) is a steady state or a stationary equilibrium.

Say that two occupations h and h′ are indistinguishable under (λ, x, w)if w(h) = w(h′) and x(h) = x(h′). Otherwise, they are distinct.

Proposition 1 Let (λ, x, w) be a stationary equilibrium. Then nopositive measure of individuals will switch from some occupation toanother occupation distinct from it.

Remark. Analogous to single-crossing/supermodularity.

Now we are in a position to establish

Proposition 2 [Inequality of Steady States.] Suppose h and h′ aredistinct with x(h) > x(h′). Then

u (w(h) − x(h)) > u (w(h′) − x(h′))

In standard convex growth model, no two distinct “occupations” insteady state. In interactive models, however, distinct occupied steadystates exist under very general conditions. For example, imagine thatwhenever an occupation is not occupied, its return goes to infinity.

In such cases, inequality emerges even if society were to start from aperfectly equal distribution of wealth.


Two Notions of History Dependence

Note: even if there is perfect equality to start with, the subsequentevolution of inequality is inevitable.

Nonergodic individuals and nonergodic societies. Former correspondsto individual fates that depend on ancestral choices. Latter corre-sponds to multiple steady states.

Proposition 2 shows that nonergodicity at the individual level is per-vasive in interactive models. What about “social nonergodicities”?

In general, multiple steady states are possible. E.g., in the two-skillexample, a fraction λ of skilled workers is a steady state if and onlyif

u(w) − u(w − S) ≤ δ

1 − δ[u(w − S) − u(w)] ≤ u(w) − u(w − S)

where w = F1(λ, 1 − λ) and w = F2(λ, 1 − λ).

Easy to check that there is a multiplicity of λs satisfying this condi-tion (though not necessarily lying in some connected interval).

However, as Mookherjee and Ray [2000] show, with a very large num-ber of occupations the multiplicity tends to disappear. Get backsocial ergodicity.


History-Dependence: Summary

To summarize: all sorts of mixtures are possible:

ergodic individuals and societies (Loury [1981], Aghion and Bolton[1997])

nonergodic individuals and nonergodic societies (Galor and Zeira[1993], Banerjee and Newman [1993])

ergodic individuals and nonergodic societies (Piketty [1997])

and nonergodic individuals in ergodic societies (Mookherjee and Ray[2000]).

In addition to this classification:while inequality, in turn, leads to a lack of efficiency, this does not nec-essarily imply that there are other equilibria that are Pareto-superior.

The combination of these two sets of observations has importantpolicy implications.


Policy Implications

Policy implications of history-dependence have sharper political edgesthan the ones implied by multiple equilibria.

If multiple equilibria are Pareto-ranked, then an equilibrium-tippingpolicy will — at least in the long run — benefit all the agents in theeconomy.

These conditions are significantly harder to meet in situations ofhistory-dependence, especially those in which the relevant historicalvariable is asset inequality.

Example: model of inequality and undernutrition studied in Das-gupta and Ray [1986]. Every competitive equilibrium in that modelis Pareto-efficient, even though they may display undernutrition, lowoutput (compared to other equilibria), and involuntary unemploy-ment.

It follows that — in the Dasgupta-Ray model — every policy designedto reduce undernutrition and unemployment must hurt some segmentof the population.

Admittedly, the Dasgupta-Ray model is an extreme illustration. In-efficiency appears as soon as we turn to a dynamic formulation. Buthere too, we must step carefully.


Nonergodic Societies

In line with multiple equilibrium story, policy need only be tempo-rary. But

Political Opposition. Inefficiency of equilibrium does not implyPareto-domination by other equilibria.

Equality and Efficiency. Models often have the property thatsteady state equilibria in which the distribution of wealth is rela-tively equal are “better” from the point of view of (productive andallocative) efficiency, output and employment, and possibly the rateof growth.

This suggests that redistribution is (functionally) a good policy. Butto clinch this, we need to study more carefully — and in more detail— the subtle and often complex connections between initial condi-tions and final steady states.

Inequality and Efficiency. In addition, sometimes inequalitymay be positively correlated with efficiency. More likely to be trueof extremely poor societies. (See, e.g., Ray [1998, Chapters 7 and 8],Esteban and Ray [1999], Matsuyama [1999], or Banerjee and Duflo[2000]). Then caught in a genuine tradeoff.

Half-Hearted Policies. A more complex phenomenon is thepossibility of “wrong” responses to small or half-hearted changes, asdiscussed for employment in Dasgupta and Ray [1987].


Ergodic Societies

Are we back to the usual “convergence” story when societies areergodic? No, because the individuals in them are not.

One important interpretation: the world economy as an ergodic soci-ety in which individual countries take up nonergodic positions. Thismay be identified with the point of view advocated by Quah [1997],among others.

Then the “persistent inequality” result shows that nonconvergencemay be endemic once an interactive approach is taken to study theseproblems.


Concluding Remarks

Goal in this talk has been particular rather than comprehensive. Fo-cus on development (or underdevelopment) as an interacting “equi-librium” that hangs together, precipitated by expectational inertiaor by historical conditions.

Why is this view an important one? Three reasons:

[1] It leads naturally to a theory of persistent differences rather thanconvergence.

[2] These theories do not rely on “fundamental” differences acrosspeoples or cultures.Of course, culture — like conditional convergence — plays a role.But all are part of some broader interactive theory in which “firstcause” is to be found — if at all — in historical legacies.

[3] These theories create a very different role for policy. Specifically,they place a much greater weight on one-time, or temporary, inter-ventions than theories that are based on “fundamentals”.This is not to say that once-and-for-all policies are the only correctones, but to appreciate that the interactive theories that we havediscussed have very different implications from the traditional ones.

Of course, even the practitioners of traditional convergence thoriesare aware of the viewpoints expressed here, and many are even sym-pathetic to it. But one hopes that future researchers will embracethis methodology not just from a distance, but in the essential wayin which their models are constructed.

development: new (?) themeskrugman [1999] on east asian crisis or cooper [1999] on busi-ness cycle...

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