Innovation and InequalityGilles Saint-Paul

Gerzensee, August 20-24 2007

I. Introduction

What is this course about?

• Our aim is to analyze when technical progress can make some workers worse-off

• The “standard” view is that technical progress raises wages: workers produce more, and wages = productivity

• Historically, episodes of revolt against technical change

• Furthermore, rise in wage inequality since the 1970s

Why do we believe that wages increase with technical progress?

• Kaldor’s « stylized facts » of growth

• Output per capita grows, and share of wages is constant

• Therefore wage per capita grows

• And, according to Neo-classical models, technical progress is the ultimate engine of growth

Where do these stylized facts come from?

• Empirical approximation over the very long run

• Theoretical property of balanced growth paths in NC growth models

• But: – the economy is on a BGP only in the long run– BGP exists only under special conditions

A first research direction

• A natural route is to re-examine the conditions under which a BGP exists

• What happens in the short-run?• What happens if technical progress is not

multiplicative in labor and the production function is not Cobb-Douglas?

• By challenging these conditions, we may get that technical progress harms wages in general

Heterogeneity

• In growth models, labor is a homogeneous input

• Thus, all wages go up, or all wages go down

• One may extend this model by introducing heterogeneous labor

• Technical progress may them harm some workers and benefit others

Sources of heterogeneity

• Just different endowments won’t do it

• Multidimensional labor input

• Multisectors with costly reallocation

• Heterogeneity with respect to learning/reallocation costs

A second research direction

• Introduce different kinds of labor in the standard neoclassical model

• Presumably, the results will depend on whether technical progress is complement or substitute with a given kind of labor

Individuality

• In NC classical models, people own abstract quantities of factors of production which they sell.

• For the market for human time (= labor), that is problematic

• People can’t do two things at the same time

• They can’t be at two different places at the same time

Why does individuality matter?

• An individual’s contribution to a firm may be unique and not reducible to the sum of the contributions of homogeneous factors.

• Individuals may reap rents out of that uniqueness

• Individuals also cooperate, exerting spillovers over each other’s productivity

• And these effects are all affected by technical progress

Pricing

• The neo-classical model assumes competitive pricing

• But firms may have monopoly power, which reduces consumption wages

• And if all is not homothetic, that power may be affected by technical change

• Thus, pricing is another factor through which productivity may have unconventioonal effects on wages

II. Models of the distribution of income

• An individual’s labor income is the sum of the value of all the labor inputs he supplies to the market:

• But what he can supply to the market depends on time, space, and our modelling strategy…

• I can be beautiful and clever, but not a beauty model and a scientist at the same time.

• But if I’m a beautiful executive, that may help me in negotiating contracts…

Three basic models

• The unbundling model

• The specialization model

• The bundling model

The unbundling model

• Each characteristic is supplied anonymously to a single market

• Each characteristic has a unique price

• This price is equal to its marginal product

Example

• Two characteristics, raw labor l and human capital h

• Prices w = FL’ and ω = FH’

• z(l,h) = wl + ωh

• People may be ranked by skill s, dl/ds > 0, dh/ds > 0.

• The skill premium ω/w is « inegalitarian » if h is more elastic to skill than l

The specialization model

• Each characteristic is supplied anonymously to a single market

• But workers can only supply one characteristic

• They elect the one which maximizes their income

An interpretation

• Characteristics = productivity at different tasks

• Fixed time endowment• One may only perform one task at the

same time

Example

• Two characteristics, raw labor l and human capital h

• Prices w = FL’ and ω = FH’

• z(l,h) = max(wl,ωh)

• People may be ranked by skill s, dl/ds > 0, dh/ds > 0.

Example (ctd)

• People specialize according to their comparative advantage:

• That leads to sorting by skills

• The most skilled supply human capital

s

z(s)

z = wl(s)

z = ωh(s)

Figure 1.2: occupational choice and the wage schedule

Specialize in H

Specialize in L

An increase in the skill premium increases inequality

• We consider any pair of workers s, s’

• Assume s’ > s

• There are five possible cases depending on their specialization before and after the increase in the skill premium

The unbundling model

• People supply their whole vector of characteristic to a single employer

• Therefore, they cannot unbundle their characteristics and supply them to different employers

• Nor can they specialize in a single characteristic

• Each employer treats each characteristic as a homogeneous input

• While employers offer a single price for each characteristic, this price may differ across employers

• People elect the employer which yields the maximum income

• There exist results about whether or not prices are equalized across employers

• If not, we expect sorting by skills across employers

III. Productivity and wages in the standard neo-classical growth

model

The balanced growth path

• Output grows at a constant rate

• This rate is determined by the growth rate of total factor productivity

• The share of wages in total income is constant

• Therefore, wages grow at the same rate as output

• This rate goes up with that of TFP

A BGP exists and the economy converges to it if

• TFP is multiplicative in labor

• The production function has constant returns in labor and capital

• The utility function is isoelastic

Reconsidering the predictions

• We look at three possibilities:– Output-augmenting TP– Labor-augmenting TP– Capital-augmenting TP

• And at two time horizons:– The short-run, with fixed K– The Ramsey long run, such that

III.1. The short run

Output-augmenting TP

• With A multiplicative in F, the marginal product of labor goes up unambiguously with A

Capital-augmenting TP

• An increase in A is equivalent to an increase in K

• As F’’KL > 0, the marginal product of labor unambiguously goes up

Labor-augmenting TP

• Wages fall iff

Interpretation

• Each worker has more efficiency units wages go up

• But MP product of efficiency units fall wages go down

• Latter effect strong if capital/labor complementarity strong, i.e. F’’/F’ large in absolute value

Example

• With a CES production function

wages fall with A iff

III.2 The long-run

The adjustment of capital

• Output-augmenting: upon impact, MPK goes up, more capital in the LR, wages go up even more

• Capital-augmenting: MPK may fall, less capital in the LR, can this lead to falling wages?

• Labor-augmenting: MPK goes up, more capital in LR, can this overturn lower wages in the SR?

In the LR, wages cannot fall

• Otherwise, firms would face the same interest rate, lower labor costs, and would produce more

• That would lead to strictly positive profits, which cannot be in equilibrium

• In other words, the economy must lie on the factor-price frontier.

w

r

ρ

w

Figure 2.1: long-run determination of wages in the Ramsey model

FPF

w

r

ρ

w

Figure 2.2: long-run impact of technical progress on wages in the Ramsey model

FPFFPF’

w’

Other models of accumulation

• Technical progress may induce little more or less accumulation

• This may lead to higher ROR on capital in the LR

• Therefore, wages may fall in the LR

• But that rests on strong income effects in savings

w

r

r

w

Figure 2.3: wages may fall if the marginal product of capital goes up by a lot.

FPFFPF’

w’

r’

Wages can only fall in two cases

• In the short run, if TP is labor augmenting, and complementarities between K and L are strong

• In the long run, if income effects are so strong that the capital stock is reduced by enough.

IV. Heterogeneous labor

The 3-factor model

• There are now 3 factors, H,K,L• The Ramsey condition no longer

determines wages• It just pins down a partial factor-price

frontier• Technical change may twist that frontier so

that the wage of one kind of labor falls• If w falls we have skilled-biased technical

progress

Determination of factor prices

• Production function

• Factor-price frontier

• Ramsey condition

• Supply=demand

• These 3 conditions determine the 3 factor prices

Figure 3.1: The factor price frontier with 3 factors

w

ω

r

w

ω

Figure 3.2: The partial factor-price frontier: relationshipbetween w and ω for a given r.

slope = -L/H

Technical progress without conflict

• If the slope of the partial FPF does not change too much, then both H and L gain

• That means that TP has little impact on the MRS between H and L

• In other words, it is not particularly more complementary with one factor than the other

w

ω

Figure 3.3: Technical change with little bias: Both wages increase

Neutral technical progress

• The MRS between H and L is unaffected if they enter through a homogenous aggregate unaffected by A

• The slope ratio of the partial FPF is given by the derivatives of the cost function of the aggregate, independent of A

Skilled-biased technical progress

• The MRS between skilled and unskilled sharply falls

• The partial FPF flattens

• I can now use 1 skilled instead of many unskilled

• To maintain equilibrium in the labor market, the wage of the unskilled has to fall

w

ω

Figure 3.4: Technical progress with a strong bias againstUnskilled workers: w falls

Capital-skill complementarity

• Capital-augmenting TP harms the unskilled and benefits the skilled

• The same is true of capital accumulation

• Thus, an investment boom (in IT) triggered by a fall in the price of capital goods (e.g. computers) is inegalitarian

• In the long-run, w = r/A, wages fall proportionally to TP

Estimating KSC

• Krusell et al estimate the following:

• Their estimates are ε = -0.5 and σ = 0.4

• Their model does well at tracking the skill premium

Figure 3.5: Actual vs. Matched skill premium in the Krusell et al. model. Source: Krusell et al. (1999)

V. Unbalanced growth

The basic idea

• Several sectors

• Labor immobile between sectors in the short run

• Technical progress asymmetrical between sectors

• In the LR, technical progress benefits workers

• In the SR, wage dispersion goes up

The substitutability case

• If goods are substitute, demand increases a lot for the more productive sectors

• Labor needs to be reallocated to those sectors

• Wages go up in these sectors in the short run

The complementarity case

• If goods are complements, demand increases little in the more productive sectors

• Labor has to be reallocated away from these sectors

• Wages fall in the sectors where technical progress happens

A simple model

• Continuum of goods• Isoelastic utility• Linear production• In the short run,

allocation of labor frozen

• In the long run, it adjusts to equalize wages

The equilibrium conditions

• FOC for utility maximization

• Zero profits

• Relative labor demand

• Aggregate price level

The long run

• Labor adjusts so as to equalize wages

• Equilibrium wage necessarily goes up

The short run

• If technical change homothetic, all wages go up proportionally

• Assume TP takes place only in a few sectors

• Under substitutability, people gain from TP in their sector

• They lose under complementarity

• They always gain from TP in other sectors