University of Wisconsin-Madison
Department of Agricultural and Applied Economics
Development Economics Preliminary Examination
February 14-18, 2005
Answer any three questions. All questions have equal weight. Please type your answers. Your
answers must be submitted to Ian Coxhead, Development Prelim Chair, 413 Taylor Hall no later
than 5 pm on Friday, February 18
1. Poverty rates are disproportionately high in rural areas of most world regions. This
observation has led some to advocate policies that will improve the access of poor rural
households to land. Others argue that such policies will be ineffective. This question asks
you to consider the debate between these two positions both theoretically and empirically.
a. Define total income for a rural family as:
Y  P.Q( LQ , A )  w( L f  LQf )  wLQh  r A ,
where the agricultural commodity, Q, is produced with a constant returns to scale
technology using labor ( LQ ) and land (A). Farm labor is the sum of family and hired
labor ( LQ  LQf  LQh ). To keep things simple, assume that the land to which the
family has access is fixed at A . The family has a total labor stock of labor ( L f ) that
can be allocated to farm and non-farm activities. Some of the labor allocated offfarm may be used up in searching for jobs, and the number of days employed as a
function of time allocated to off-farm activities is ( L f  LQF ) , where
0    1;   0;   0 . P is the price of the commodity Q, w is the wage rate, and r
is the land rental rate.
Assuming that families allocate resources in order to maximize income, under what
circumstances will a policy that enhances land access (i.e., increases A ) for a poor
family actually make them better off in income terms? When will improved land
access have no effect on family income? In answering this question, you should
define a poor family as one for whom LQH=0 and LQf< L f . You may find the
analysis easier if you note that under constant returns to scale, the income of a poor
family can be written as:


y  PAq(lq )  w L f  lq A  rA ,
where the lower case letters denote values per-unit of land.
b. Suppose that you now want to use the model above to empirically determine whether
or not policies designed to improve land access are good anti-poverty measures.
Using the model, please explain what empirical proposition you would test.
c. Finally, assume that you had data on a random sample of rural households (rich and
poor, landed and landless). Econometrically, how would you undertake the task of
estimating the test statistic you identified in part (b) above.
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2. In their article, “Does natural resource abundance increase Latin American income
inequality,” Journal of Development Economics, Volume 59 (1999): 3-42, Leamer, Maul,
Rodriguez, and Schott argue that natural resource abundance and export orientation are
fundamentally related to Latin America’s high levels of income inequality as well as to their
weak growth performance.
a. Evaluate their empirical argument concerning the impacts of natural resource
booms on inequality and growth. Then, comment more broadly on the empirical
issue of whether specialization in natural-resource exports has proven to be
problematic for inequality and growth elsewhere in the world, emphasizing both
trends and potential explanations of these trends.
b. Develop or borrow an endogenous growth model that explicitly links inequality
and slow growth to natural resource specialization. Try to be clear about what
assumptions drive the inequality and the growth results and how they are linked.
Do the results depend on the ownership structure of the resource sector? If so,
how? If not, why not?
c. Choose a policy intervention that might be used to improve growth and inequality
outcomes associated with your model. Comment on the potential tradeoffs
associated with the policy intervention you choose.
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3. Consider the following theoretical model of aggregate economic growth:
Y = AK + BKL1–
(1)
where A > 0, B > 0 are productivity parameters, and 0 <  < 1.
(a) Assume that the savings rate is exogenously fixed at s, population grows at an
exogenous rate n, and capital depreciates at a constant rate d. Show that this model is
capable of generating the following two “stylized facts” of economic growth, namely (i)
conditional convergence across similar economies, and (ii) a rate of per-capita income
growth that is positive in the long run (i.e. in the steady state).
(b) Provide a critical commentary on this model as a tool for understanding economic
growth processes. Are there other “stylized facts” of growth that it can or should
generate? List each of these and provide some empirical motivation for your choices.
(c) The Chicago economist Robert Lucas once famously asked why, if models of the
above type are correct, it should be that when labor is internationally mobile, migration
takes place not from rich countries where human capital is abundant to poor countries
where it is scarce, but in the other direction: “why do all the Ph.D.s go to Boston and
Silicon Valley instead of India?” Identify and briefly describe at least one aggregate
growth model in which incentives for the migration pattern observed by Lucas would
exist. Is this class of model also consistent with conditional convergence and positive
growth rates in the steady state?
(d) The main mechanism of most growth models is an increase in the ratio of capital to
labor. The Rybczinski theorem of international trade theory predicts that in a two-sector,
two-factor economy with constant prices, unequal rates of factor endowment growth will
drive a process of change in the structure of production. Can you adapt or extend any of
the above models to provide a simultaneous explanation of aggregate growth and
structural change in a stylized developing country model?
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4. Imagine that a major environmental organization requests your help in designing a project
aimed at identifying types of agricultural technologies that can promote conservation and
development in tropical forest areas. Specifically, they want agricultural technologies that
raise incomes of farmers and reduce deforestation at the same time. Suppose further that
they include in their request help for two distinct types of tropical forest locations: (a.)
Frontier areas with significant recent migration (colonist) inflows, and (b.) Settled areas with
established communities, fragmented peasant households, and surrounding tropical forest
mountains (the environmental area of concern). Propose a household-level model (or a
second with variations on the first) that can be used to explore the impacts of the agricultural
technologies listed below in these situations. Be specific about your choice of key
assumptions in the design of the model (i.e, the characteristics of the technology, the
completeness of markets). Also, be clear on your assumptions regarding what might be
considered immediate effects and longer-term effects of these technologies. After you have
explored the predicted impacts of the technologies, briefly discuss their implications for the
basic type of empirical design you would suggest for testing the hypotheses predicted by the
models.
Agricultural technologies under exploration:




Improved pasture for cattle
High yielding grain varieties (e.g., corn or rice)
Permanent tree crops (e.g., cocoa, coffee, coca, citrus)
Organic vegetables
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5. Formal insurance contracts are rarely available to permit agricultural households to protect
themselves against variation in income resulting from weather or price shocks. In contrast,
informal or mutual insurance arrangements are commonly observed in many parts of the
world. For purposes of this question, assume that an informal insurance arrangement is one
in which terms of the arrangement cannot be enforced through legal means.
(a) What are the incentive compatibility conditions that limit or constrain the formation of
mutual insurance arrangements? To answer this question, you may want to devise a
simple 2-person model of mutual insurance that can be used to illustrate the factors that
shape incentive compatibility. Please reflect on part (b) below before devising your
model.
(b) Imagine that agents are heterogeneous (e.g. they differ by wealth, social or ethnic group,
etc.). Are some types of agents likely to be excluded from mutual insurance
arrangements, or unable to gain as much insurance as other agents? In answering this
question, please rely on the model that you developed in part (a). How do the
implications of your model compare with results from the empirical literature that has
estimated the effectiveness of mutual insurance?
(c) What are the long-run implications of differential access to mutual insurance? In
answering this question, you do not need to do any additional modeling. However,
please draw on relevant literature to help frame your thinking on this question.
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