trade, unemployment and inequality

Index Ricardo HOS HOV Technology & Human Capital Melitz meets Pissarides Inequality & Unemployment

University of Washington

Trade, Unemployment and InequalityA quick review

Jorge Rojas-Vallejos

2015

Jorge Rojas-Vallejos (UW) Trade, Unemployment & Inequality 2015 1 / 89


Content

Ricardo

HOS HOV

Technology

Human Capital

Melitz meets Pissarides

Inequality & Unemp.

Detour



Content

Ricardo

HOS

HOV

Technology

Human Capital


Inequality & Unemp.

Detour



Content

Ricardo

HOS HOV

Technology

Human Capital


Inequality & Unemp.

Detour



Trade

International Trade

1 Allocation of resources across economic activities,

2 Distribution of incomes across factors of production.



Ricardian Model

The Ricardian Assumptions:1 Two countries, two goods, one factor (labor),

2 Labor is immobile across countries and mobile across sectors,3 Constant returns to scale (CRS) production,4 Identical and homothetic preferences,5 Perfect Competition (all agents are price takers).

RemarkThe basic idea applied is opportunity cost. In a two-goods economya country will produce the one that requires less unit labour.



Ricardian Model

The Ricardian Assumptions:1 Two countries, two goods, one factor (labor),2 Labor is immobile across countries and mobile across sectors,

3 Constant returns to scale (CRS) production,4 Identical and homothetic preferences,5 Perfect Competition (all agents are price takers).




Ricardian Model

The Ricardian Assumptions:1 Two countries, two goods, one factor (labor),2 Labor is immobile across countries and mobile across sectors,3 Constant returns to scale (CRS) production,

4 Identical and homothetic preferences,5 Perfect Competition (all agents are price takers).




Ricardian Model

The Ricardian Assumptions:1 Two countries, two goods, one factor (labor),2 Labor is immobile across countries and mobile across sectors,3 Constant returns to scale (CRS) production,4 Identical and homothetic preferences,

5 Perfect Competition (all agents are price takers).




Ricardian Model

The Ricardian Assumptions:1 Two countries, two goods, one factor (labor),2 Labor is immobile across countries and mobile across sectors,3 Constant returns to scale (CRS) production,4 Identical and homothetic preferences,5 Perfect Competition (all agents are price takers).




Qwine

Qmeat

LChileaChilew

LChileaChilem

CChilem = QChilem

CChilew = QChilew

What do we know its true in Autarky? PPF = BC



Qwine

Qmeat

LChileaChilew

LChileaChilem

CChilem = QChilem

CChilew = QChilew

What do we know its true in Autarky?

PPF = BC



Qwine

Qmeat

LChileaChilew

LChileaChilem

CChilem = QChilem

CChilew = QChilew

What do we know its true in Autarky? PPF = BCJorge Rojas-Vallejos (UW) Trade, Unemployment & Inequality 2015 5 / 89


In a trading equilibrium, assume PmeatPwine >aChmeataChwine

Qwine

Qmeat

LChaChw

LChaChm

uaut

slope= PmeatPwine

utrade

CChm

CChw



Ricardian Model

QuestionSome argue that high relative wages in the North relative to theSouth are evidence of Northern exploitation of Southern workers.What can we say about it in this framework?

Yes, in this model wages are larger in the trading equilibrium thanin the autarky one.

multi-goods extension continuum of goods



A Continuum of Goods

The Dornbusch, Fischer, and Samuelson model (1977).

1 A continuous of goods index by j [0,1],

2 ac(j) is the amount of labour required in country c to produceone unit of good j,

3 A(j) = aB(j)

aA(j) is a downward slope monotonic function represen-ting the ratio of these ac(j) in the two countries of the model.

This model facilitates the analysis of the range of goods that a coun-try will export and import.



DFS modelRemarkAn expansion of the labour endowment of one country relative toother will cause it to expand its exports, NOT JUST by exportingmore of what it already exported, BUT ALSO by exporting goodsthat it previously imported.

=wA

wB

aA(j)wA < aB(j)wB good j is produce in A and exported to B

So, we have:

A(j) > good j is produce in A and exported to BA(j) < good j is produce in B and imported by A



DFS modelPutting everything together gives:



DFS model

With this framework many comparative statics can be done. DFSalso include transport costs explaining non-traded goods. Thus,

RemarkEach country has a fraction of goods that it will be able to produceas long as they cost less than imported goods including the transportcost.



Many countries and Ricardo

Please see:Eaton and Kortum (2002) Technology, Geography, and Trade,Econometrica, pp: 1741-1779.



Heckscher-Ohlin-Samuelson Model

We just saw in the Ricardian model that:1 everyone wins from trade,2 there is only one factor of production (labour),3 outcome is complete specialization,4 differences in technology are the underlying mechanism.

Too simple right?!

In HOS, we assume:1 2 2 2 Model: 2 Countries, 2 Goods (Outputs), 2 Factors

(Inputs),2 No productivity differences. All countries share the same

technology.



Heckscher-Ohlin-Samuelson Model

3 Output can be produced with different input mixes,4 Factors are mobile across sectors but not across countries,5 Countries differ in their relative abundance of factors.

Assumption (5) is the source of comparative advantages in the HOSmodel1.

1AKA Factor proportions theory



Rybczynski Theorem

An expansion in one factor (input) leads to an absolute decline inthe output of the commodity that uses the other factor more inten-sively.

Assuming that:

aLMaTM

>aLFaTF

M is more labour intensive than F

If L increases, then F will decrease.



Stolper-Samuelson Theorem

Assume M is more labour intensive than F, and pF is constant. Anincrease in pM raises the return to the factor used intensively in theproduction of M by an even greater relative amount2.

M is labour intensive and pM increases = dww >dpMpM

2Jones (1965), Journal of Political Economy. Great paper!



Generalization

Input endowment magnification effect. General Rybczynski theo-rem.(aLF

aTF>

aLMaTM

) (dLL

>dTT)

= dFF

>dLL

>dTT

>dMM

Output price magnification effect. General Stolper-Samuelson theo-rem.(aLF

aTF>

aLMaTM

) (dpFpF

>dpMpM

)= dw

w>

dpFpF

>dpMpM

>drr



PPF in HOS

QT

QC

Why the PPF is not a straight-line?

Exactly! Imperfect substitutability across sectors.



Open to trade



Factor Price Equalization

This model leads to:

Relative factor prices converge across countries eventhough factors are immobile across countries!

Factors of production are immobile across countries but goods aremobile. Trade in goods is enough to lead to factor price convergence.



Heckscher-Ohlin-Vanek Model

The setup is as follows:1 Many countries, indexed by i {1, . . . ,C},2 Many sectors, indexed by j {1, . . . ,N},3 Many factors, indexed by k {1, . . . ,M},4 Technologies and preferences are identical across countries,5 FPE prevails under free and frictionless trade.



Empirical Evidence

How does HOV model perform?

Quoting Davis et al. (NBER 5625). Empirically... it is a flop.

Quoting Davis again ... relaxing the assumption of FPE yields adramatic improvement...



Technology, Human Capital And Unemployment

In this section we discuss some of the ideas in:

Davis (1998) Technology, unemployment, and relative wagesin a global economy, European Economic Review, and

Davis et al. (2000) Human capital, unemployment, and rela-tive wages in a global economy, Federal Reserve.



Technology, Human Capital And Unemployment

So far, we have always assumed full employment of factors and non-market rigidities. However, there are two factor market develop-ments of interest that we would like to understand.

1 The growing skilled-to-unskilled wage gap in the UnitedStates,

2 The rise and persistence of unemployment in Europe.

To understand this the usual approach was looking at each regionseparately, but Davis (1998) had the idea of looking at the problemin a unified model of a trading world. We are in a global economyand hence the dynamic system is integrated more than ever before.



Technology and Unemployment

The structure of this economy is the HOS model, except that em-ployment of unskilled labour will be subject to a binding minimumwage. We (they) assume that skilled labour is fully employed. Thus,

HX + HY = H (1)

while the unskilled labour factor market constraint due to the min-imum wage regulation is,

NX + NY + U = N + U = L (2)



Technology and UnemploymentDefine the relative goods price as P pX/pY and the relative worldendowment as h H/L. So,



Technology and UnemploymentFor the United States (flexible wage),

LUSX + LUSY = L

US (3)

For Europe (regulation min. wage),

NEX + NEY + U = N

E + U = LE (4)

Figure: Trading equilibrium



Neutral technical progress in X at fixed prices



American labour(unskilled) saving technicalprogress in X



Human Capital and Unemployment




Firm Heterogeneity, search unemployment and tradeliberalization

by Felbermayr, Prat, and Schmerer.Working paper at The European Trade Study Group (2007).

In this paper, they introduce unemployment a` la Pissarides (2000)into Melitz (2003).



The Model

Assumptions:I HHs utility follows U = ln C + U,I Perfect financial markets,I r is exogenous,I Labour only factor of production,I Labour is inelastically supplied,I Perfect competition for final consumption good,I Monopolistic competition, at the intermediate inputs level,

firms produce each a unique variety.

They focus in the long-run, excluding the short-run dynamics.



The Model

Production function:

Y =[M

1

q()1 d

] 1

, > 1 (5)

where is the elasticity of substitution between any two varietiesand is the mass M of intermediate inputs.

The price index dual is:

P =[

1M

p()d]1/(1)

(6)

where p() is the price of input .



The Model

Quantities of intermediates inputs are:

q() =YM

p() (7)

Total production costs are:

c() = w()q()()

+ f (8)



The Model

The labour market is characterized by search frictions. The aggre-gate matching function exhibits CRS.

Firms

Workers

Some definitions: = v/u: vacancy-unemployment ratio,c: cost of posting vacancies



Pricing Behaviour

The market value of an intermediate producer with productivity is:

J(l, ) = Maxv

11 + r

{p(q)qw(l, )l cv + (1 )J(l, )}

subject to

p(q) =(

YM

) 1

q1 (9)

q = ll = (1 )l + m()v

some firms will exit, and some worker-firm matches will be de-stroyed (probabilities).



Pricing Behaviour

The market value of an intermediate producer with productivity is:

J(l, ) = Maxv

11 + r

{p(q)qw(l, )l cv + (1 )J(l, )}

subject to

p(q) =(

YM

) 1

q1 demand

q = l firm production functionl = (1 )l + m()v law of motion

some firms will exit, and some worker-firm matches will be des-troyed (probabilities).



Pricing Rule

After some algebra:

p(l, ) =1

(

1)[

w(l, ) +w(l, )

ll +

cm()

(r + s1

)](10)

Second term is the over-employment effect, and third term is therecruitment cost.s + + is the rate of job destruction.

Melitz (2003) was:

p(l, ) =1

(

1)

w(l, ) =w



Wage BargainingThe bargaining process is summarized in an exogenous parameter .However, this could endogenized.

Combining the Nash-bargainingcondition and using the envelope theorem for the pricing problemleads to:

Job Creation equation:

w(l, ) = p(l, )( 1

)(

r + s1

)c

m()(11)

Wage Curve equation:

w(l, ) = rU +(

1 )(

r + s1

)c

m()(12)

(12) strikingly shows that wages are constant across firms! Why?Firms exploit their monopsony power till workers are paid their out-side option.



Wage BargainingThe bargaining process is summarized in an exogenous parameter .However, this could endogenized. Combining the Nash-bargainingcondition and using the envelope theorem for the pricing problemleads to:


w(l, ) = p(l, )( 1

)(

r + s1

)c

m()(11)


w(l, ) = rU +(

1 )(

r + s1

)c

m()(12)






w(l, ) = p(l, )( 1

)(

r + s1

)c

m()(11)


w(l, ) = rU +(

1 )(

r + s1

)c

m()(12)

(12) strikingly shows that wages are constant across firms! Why?

Firms exploit their monopsony power till workers are paid their out-side option.





w(l, ) = p(l, )( 1

)(

r + s1

)c

m()(11)


w(l, ) = rU +(

1 )(

r + s1

)c

m()(12)




Entry, Exit And Autarky Equilibrium

As in Melitz (2003), the entry process is in two stages.1 Develop new variety. Sunk cost fE, fixed costs f .2 Firm learns its productivity and decides {stay, exit}

Similar math to the one in Melitz leads to the next to graphical re-lations.



Equilibrium Threshold Productivity



Equilibrium Labour Market Tightness



Trade Liberalization

Next, we study the effects of trade liberalization on productivityand unemployment. They run the following comparative statics:

1 Falling transport costs,

2 Rising number of trade relations,

3 Rising fixed costs for export.



Fall in Transport Costs



Rise Trade Relations



Rise Fixed Costs for Export



Inequality: The famous Gini index



A Quick Look at Inequality

Since 1947, when the General Agreement on Tariffs and Trade (GATT)was created, the world trading system has benefited from multilateraltrade liberalization (IMF website)



Gini World Today

Source: World Bank



Poverty $2 a day (PPP) Today

Source: World Bank



Inequality and Unemployment

In this section we look at the model developed in:

Helpman, Elhanan, Oleg Itskhoki, and Stephen Redding. (2010).Inequality And Unemployment In A Global Economy,

Econometrica, 78(4), pp: 1239-1283.

This model introduces search and matching frictions into a Melitz(2003) framework.



Inequality and Unemployment

We will study the determinants of wage distributions, namely:

1 Within-industry reallocation,

2 Labour market frictions,

3 Differences in workforce composition across firms.



Preview

I The opening of trade enhances wage inequality, but can eitherraise or reduce unemployment,

I Wage inequality is higher in a trade equilibrium than in au-tarky. BUT, gradual trade liberalization first increases and laterdecreases inequality.



Preview

A trade friction can either raise or reduce wage inequality dependingupon the initial condition.



What is new here?

In this paper the new key feature is that they allow for an endoge-nous measure of matched workers for each firm rather than as-suming one-to-one matching between firms and workers.



The Model

Assumptions:1 Two countries, Home and Foreign (*),

2 Continuous of workers ex-ante identical,

3 Workers are risk-neutral (later they extend this to risk-averseones),

4 Demand within the sector is defined over the consumption of acontinuum of horizontally differentiated varieties + CES.



The ModelReal consumption index for the sector is:

Q =[

jJq(j)dj

]1/, (0,1) (13)

controls for the elasticity of substitution between varieties.

Demand function for a given variety j is,

q(j) = A1/(1)p(j)1/(1), A is a demand shifter (14)

The equilibrium revenue of a firm is,

r(j) = p(j)q(j) = Aq(j) (15)



Firms actions

fe > 0

ac

Exit

Domestic

D&E markets

Bargaining over surplus



Firms actionsWhere:fe: fixed entry cost (sunk) is i.d. following a Pareto Distribution

G() = 1(min

)z, min > 0, z > 1

ac: screening threshold

Tractable and a good approximation to observed data.Jorge Rojas-Vallejos (UW) Trade, Unemployment & Inequality 2015 59 / 89


Other costs in the model

1 fd > 0: fixed cost of production,

2 fx > 0: fixed cost of exporting,

3 > 1: iceberg variable trade cost, basically, we need to ship so the foreign market gets 1 unit of our good.



Production Technology

y = (h a) , (0,1) (16)

where:y: output of each variety,: firms productivity,h: workers hired,a: average ability of these workers.

Also, a Ga(a) with parameter k > 1. A key feature here is com-plementarity in worker ability. The productivity of a worker isincreasing in the abilities of other workers employed by the firm.



Screening Technology

We (they) assume that all firms have the same screening technol-ogy. Worker ability cannot be costlessly observed when firms andworkers are matched.

Screening imprecise signal about a

Screening cost is assumed to be:

sc(ac) = cac, c, > 0 (17)

Intuitive sense that higher ability higher cost of screening.



Workers hired

a ac

h = n(

aminac

)k a = k

k 1ac

This average ability into the production function yields,

y = yna1kc , y =k

k 1akc (18)

The knife-edge condition such that firms screen is k (0,1)



Workers hired

a ac h = n(

aminac

)k

a = kk 1ac


y = yna1kc , y =k

k 1akc (18)




Workers hired

a ac h = n(

aminac

)k a = k

k 1ac


y = yna1kc , y =k

k 1akc (18)




Firms revenues

r() rd() + rx()

r() Y()1Ay()

where Y() is the firms market access.

Y() 1 + Ix()/(1)(

A

A

)1/(1)where Ix() is an indicator function for exporting.



Bargaining problem

The outcome is:I Firms fraction is

1(1 + )

I Each worker gets1 1

(1 + )

The firm can perfectly anticipate this while maximizing profits.



The Firms optimization problem

Max pi()

s.t. Production technology

Total Revenue

Firms market access

or,

pi() = Maxn,ac,Ix

11 +

[1 + Ix/(1)

(A

A

)1/(1)]1

A(yna1kc ) bn c

ac fd Ixfx



Access Market

The presence of fixed production costs imply a zero-profit cutoff suchthat:

Y() ={

1 if d < < xYx if x



FOCs firm

h

n(a) Measure of workers sampled

h

ac(b) Screening a threshold



Revenues and Wages

The higher the productivity, the larger the revenues and the largerthe size of the firm. This depends on > k. We now that the shareof workers is /(1 + ). Hence,

w() =

1 + r()h()

=subs.

b[

ac()amin

]k(19)

In addition, the expected wage conditional on being sample is thesame across all firms, so

w()h()n()

= b = search cost (20)

Thus, workers have no incentive to direct their search.



Revenues and Wages

Combining the above with FOCs, we get:

ln w() = Constant +k

k ln h() (21)

If > k, then there is an employer-size wage premium.



Revenues and Productivity

Using the FOCs into the revenue function, we get:

r() = r[c(1k)/bY()A

]1/(22)

From (22) we see that relative revenues of any two firms depend onlyon:

1 relative productivities,2 relative market access.

r(i)r(j)

=

(ij

)/(Y(i)Y(j)

)/



Labour market tightness

Search cost is assumed to be increasing in labour market tightness(x),

b = 0x1 , 0 > 1, 1 > 0

labour market tightness is,

x =NL

where N is workers sampled and L is workers searching for employ-ment in the sector. Thus, expected income in the sector is,

= Expected wage prob. being sampled = bx (23)

(23) uses risk-neutrality of workers.



Wages as a function of firm productivity

So, more productive firms NOT only have higher revenues, profitsand employment, as in the benchmark model of firm heterogeneityof Melitz (2003), BUT ALSO pay higher wages.



Wage Inequality in the Closed Economy

w Gw(w) = 1(wmin

w

)1+1/

PropositionIn the closed economy, is a sufficient statistic for sectoral wageinequality. In particular,

i. the coefficient of variation of wages is /

1 2ii. the Lorenz curve is represented by sw = 1 (1 sh)1/(1+), where

sh is the fraction of workers and sw is the fraction of their wageswhen workers are ordered from low-to-high-wage earners,

iii. the Gini coefficient is /(2 + ),iv. the Theil index is ln(1 + ).



Wage Inequality in the Closed Economy

PropositionIn the closed economy, inequality in the sectoral distribution of wagesis increasing in firm productivity dispersion (lower z) and increasingin worker ability dispersion (lower k) if and only if

z1 + 1 + > 1



Open versus Closed Economy

Figure: Cumulative distribution function of wages

Propositioni. Sectoral wage inequality in the open economy when some but

not all firms export is strictly greater than in the closed economy,Jorge Rojas-Vallejos (UW) Trade, Unemployment & Inequality 2015 76 / 89



Propositionii. Sectoral wage inequality in the open economy when all firms

export is the same as in the closed economy.

This proposition highlights a new mechanism for wage inequalitydue to trade that is not present in HOS...

Participation of some but not all firms in exporting



Open versus Closed EconomyCorollaryAn increase in the fraction of exporting firms,I raises sectoral wage inequality when the fraction of export-

ing firms is sufficiently small,I reduces sectoral wage inequality when the fraction of export-

ing firms is sufficiently large.




PropositionThe opening of the closed economy to trade amplifies differences inworkforce composition across firms.



Sectoral UnemploymentWorkers may be unemployed mainly for two reasons,

1 They are not matched with a firm,

2 Their match-specific ability draw a < ac(1) and (2) are frictional elements since workers cannot immediatelyachieve another match or another ability level.

Sectoral unemployment rate u is defined as,

u =LH

L= 1 H

N

NL

= 1 x (24)

where H is the measure of hired workers, N matched workers, Lworkers seeking for employment in the sector, and is the sectoralhiring rate.



Sectoral Unemployment

They smartly derived,

= (,Yx)aut (25)

then they analyze the () function,(0,Yx) = 10 < (,Yx) < 1, (0,1] since Yx > 1 > k

Thus, they get the next proposition.



Sectoral Unemployment

PropositionThe opening of the closed economy to trade has an ambiguousoverall effect on the sectoral unemployment rate:

i. The tightness of the labour market can either remain constantor rise following the opening of trade, which leaves unchangedor reduces the rate of unemployment,

ii. The hiring rate is strictly lower in the open economy than in theclosed economy, which raises the rate of unemployment.



Extensions of this model

1 Heterogenous workers ex-ante The results on within-group wage inequality hold,

Wage inequality between different groups may increase or de-crease,

The rise of within-group inequality dominates, hence trade liber-alization raises overall wage inequality.

2 Risk-averse workers Predictions for wage inequality are the same as for risk-neutral

workers, The opening of trade has two effects,

increases expected worker income (),increases labour market tightness (x) and search costs (b).




1 Heterogenous workers ex-ante The results on within-group wage inequality hold, Wage inequality between different groups may increase or de-

crease,

The rise of within-group inequality dominates, hence trade liber-alization raises overall wage inequality.








crease, The rise of within-group inequality dominates, hence trade liber-

alization raises overall wage inequality.









alization raises overall wage inequality.2 Risk-averse workers

Predictions for wage inequality are the same as for risk-neutralworkers,

The opening of trade has two effects,increases expected worker income (),increases labour market tightness (x) and search costs (b).








The opening of trade has two effects,increases expected worker income (),

increases labour market tightness (x) and search costs (b).








The opening of trade has two effects,increases expected worker income (),increases labour market tightness (x) and search costs (b).



THANKS!



Why do we care?

Figure: President Salvador Allende (1971) with Chilean workers



Why do we care?

Figure: Coup detat (1973) in Chile. A democratic government wasoverthrown!



Why do we care?

Figure: Some of us were lucky. Others still do not know where theirrelatives are!



Why do we care?

Figure: Some advised the new government.

Without Equality of Opportunity, Freedom is the privileged of a fewand Oppression the reality of everyone else.


IndexRicardoHOSHOVTechnology & Human CapitalMelitz meets PissaridesInequality & Unemployment

trade, unemployment and inequality

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