innovation and inequality gilles saint-paul gerzensee, august 20-24 2007
TRANSCRIPT
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