lecture 4: interpreting productivity differences

Lecture 4:

Interpreting Productivity Differences

Cross-Country Income Differences

Quantitative fit of Solow model

04/20/23 Pasha, Macro Theory II 3

The relation between Y/L and s, n, e in steady state1Y K (EH) y k

* *i i i is y (n g )k

*i i*i i

k s

y (n g )

1* ii

i

sy

n g

i

ii

1i

i

YG E

L g

se

nt

Taking the prediction to data


is about 1/3, = ½. g + ≈ 0.06

Plug in values for saving rates, population growth rates, and e: get predicted Y/L

1i i

ii i

Y sG e E t

L n g

i iEvidence: G(e ) exp e

Assume piecewise linear, declining in e

Taking the prediction to data


Solves problem that we don’t see E

i i

US US

Y L depends only on observables

Y L

For any country i,

Present actual and predicted values relativeto U.S.

Predicted y doesn’t vary enough


Problem with the Solow model or ?


determines how differences in s and n map to Y/L

If were higher, differences in s and nwould be magnified

Reasons why might be higher

• Increasing returns to scale• Externalities to physical capital

1i i

ii i

Y sG e E t

L n g

III. Productivity Differences

Development accounting


Assume a Cobb-Douglas production functionfor every country

1i i i i

i i i i

Y K (EH )

ln(Y ) ln(K ) (1 )ln(E ) (1 )ln(H )

Then, for any country i:

Development Accounting


US US US US

i i i i

E Y K H1ln ln ln 1 ln

E 1 Y K H

US US US US

i i i i

ln(Y ) ln(K ) (1 )ln(E ) (1 )ln(H )

ln(Y ) ln(K ) (1 )ln(E ) (1 )ln(H )

Thus, relative to the U.S., productivity in i is given by

Then we can write output in any two countries—say, theU.S. and country i, as:

E & Y/L: Hall-Jones (1999)


What do we conclude?• Productivity differences are a big reason for

differences in per-capita income– The R2 is about 0.8, so productivity explains the lion’s

share of the variation

• Explains major puzzles– Why high-human-capital people leave poor countries– Why relatively little physical capital flows to truly poor

countries

• But the Solow model says nothing about why productivity might vary across countries


Caveats

• Estimated E is a residual: All errors /mis-specifications end up there

• Everything is being done under the twin assumptions of CRS and competition

• These allow us to set as 1/3 from capital’s share

• If true is higher, then much less need(or evidence) for productivity differences


Reminder: EstimatingProductivity Differences

Basu, Macro 750 Lecture 5 Fall 2005 15

Development Accounting

US US US US

i i i i

E Y K H1ln ln ln 1 ln

E 1 Y K H

US US US US

i i i i

ln(Y ) ln(K ) (1 )ln(E ) (1 )ln(H )

ln(Y ) ln(K ) (1 )ln(E ) (1 )ln(H )

Thus, relative to the U.S., productivity in i is given by

Then we can write output in any two countries—say, theU.S. and country i, as:


Why Y/L varies: Hall-Jones (1999)


What is “productivity”?• Cross-country productivity differences may

mean several different things• Might be “real” or measurement error• Measurement error in input “efficiency” or

“quality” exaggerates measured E• Example: Labor input in poor countries less

efficient because of lack of nutrition and medical care in poor countries

• Taken into account, implies smaller productivity differences


What might cause “real” productivity differences?

• Higher prevalence of diseases and pests in tropical countries

• Technology differences across countries– What are these? How do they come about?

• Institutional differences more broadly• Anything that leads to less efficient allocation of

resources would be lower “productivity”– Wrong ‘industrial policy,’ lots of corruption, inefficient

credit markets, high level of distortionary taxation, etc.

I. Health


Does health explain Eis?• There are significant differences in the

Adult Mortality Rate (AMR) across countries– Latest UN Human Development Report:

A citizen of Zambia today has a lower chance of living to age 30 than someone born in Britain in 1840

• Among other things, means that workers in poor countries have lower effective labor input than workers in rich countries

• Weil (2005) looks at micro data on how health affects wages, then uses cross-country data on health to calculate “direct effect” of health on Y/L

• Direct effect might account for as much as 35 percent of the variation in Y/L across countries


Indirect effects of health• Recall your problem set: Lower expected

lifetime leads to optimal choice of fewer years of schooling– What’s the intuition?

• Other indirect effects?• Very hard to guess size of indirect effects• Even for high end of plausible magnitudes,

direct effect still leaves at least 30-40 percent Y/L differences unexplained


Proximate vs. causal effects• Clearly, accounting for health differences

reduces size of cross-country productivity differences

• But is health an exogenous reason for poverty, or is poor health due to poverty?

• Is there a parallel with the discussion of growth accounting?

II. Geography


Strong correlation

Source: McArthur-Sachs (2001, NBER wp 8114)


(Mis-)Fortunes of location

• Strong negative correlation between low Y/L and living closer to the equator

• One way to interpret this: Geography is critical determinant of development

• View of Landes (1998) and Sachs andco-authors (2000, 2001, 2002, 2003, etc)

• Diamond (1997) has a different argument


Why?• Diamond (1997) claims gains from living in

continents that are long East-West instead of North-South: transmission of useful ideas

• Landes/Sachs et al. stress diseases/pests• In tropics, no hard winter to kill pests that destroy

crops• Several tropical diseases highly virulent, and need

warm ambient temperature (e.g., malaria)• Sachs argues this is the major reason why malaria

was easy to destroy in the U.S. South, but still persists in the tropics


Should we be sceptical?

• Possible that malaria was destroyed in U.S. because U.S. is rich, not because its latitude is higher

• Again, argument of reverse causation:Is disease prevalence due to poverty?

• Sachs (2005) argues this direction too• But to explain correlation in data, need some

other reason why tropics are poor

III. Institutions


Institutional quality• Indexes of corruption, effective legal systems,

vote-buying, etc. show a strong tendency for poor countries to have bad institutions

• These worsen resource allocation,for example via cronyism or outright theft

• Suggests that good institutions may be part of higher productivity of rich countries

• Note: Some “bad” institutions may be good for Y/L—e.g., “liberal dictatorship,” as in Chile– Democracy uncorrelated with growth (Barro)


How to investigate?

• Correlation does not establish causation• Being poor due to low productivity may make

institutional quality worse, not the other way around

• So we need to find cases where institutions vary for reasons unrelated to (current) income

• In econometrics terminology, we need to find an instrument


The IV strategy

i i i iY L const Inst Xln( / ) ( )

Thus, we look for some variable Z that is correlated withInst but uncorrelated with , and use Z as an instrument:

We can express per-capita income as a regression:

where Inst is institutional quality, X is all other variablesthat affect income, and is an error term

Our concern is that might be correlated with Inst

i i iInst const Z


New proposed instrument

• Mortality rate of early colonialists (Acemoglu-Johnson-Robinson in a series of papers)

• Historical argument: Institutions “better” where settlers meant to live; more “extractive” where they just wanted to plunder and leave

• Settler mortality found to be a good predictor of institutional quality today (Z is relevant)

• Settler mortality not influenced by today’s wealth/poverty (Z is exogenous)


Correlation between 19th century settler mortality and current Y/L

Source: McArthur-Sachs (2001, NBER wp 8114)


Results, attacks, rebuttals• AJR: Exogenous variation in institutions explains a lot

of productivity and Y/L differences across countries• Sachs and others: Settler mortality just proxy for

diseases today• AJR: Include current disease rate as a control

(in X ). Disease insignificant; Inst significant• Sachs (2003, NBER wp 9490): Regresses Y/L on Inst,

instrumented with LMORT, but put in malaria as X variable (also instrumented)

• Finds malaria is significant (as is Inst)


What do we conclude?

• Institutions seem important• Debate is whether institutional quality

accounts for all differences in income• Not clear that “institutions rule”

(Rodrik et al., 2004, NBER wp)• This is the research frontier• Note: Debate is driven by ideas and insights,

not technique

lecture 4: interpreting productivity differences

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