Theory of Skill Premia

1. Theory of Skill Premia Lent Term Lecture 2 Dr. Radha Iyengar

2. Last Week… • Facts about inequality • Grew in US, UK, not so much other places • Gap in Earnings between HS and College grads grew • Doesn’t seem to be a simple cohort effect • Doesn’t seem to be all earnings volatility

3. This week…Skill Premia • Why do returns to different skills differ? • What happens when production technologies change? • How is this related to observed facts from last week?

4. The set-up… • We begin with a simple closed economy, aggregate production framework: • factors are paid their marginal products • the economy operates on its supply and demand curves. • Two types of workers: H and L • Can be high and low skilled, college and HS grads, etc.

5. Workers • Workers are imperfect substitutes: • If workers were instead perfect substitutes, their wages would always move together up to multiplicative constant (reflecting relative efficiency units) • Perfect substitution implies relative wages, only on the return to the single factor of skill NOT relative supplies

6. Labor Supply • At time t, there are L(t) type L and H(t) type H workers supplying labor • We’ll make labor supply inelastic for ease of exposition • The production function for the aggregate economy takes the constant elasticity of substitution (CES) form(with ρ≤1):

7. Elasticity of Substitution • elasticity of substitution between skilled and unskilled workers • Skilled and unskilled workers are .gross substitutes. when the elasticity of substitution σ > 1 (or ρ > 0) and gross complements when σ < 1 (or ρ < 0). • In the CES framework, the value of σ plays a critical role because it determines how changes in either technology (given by the A’s) or supplies (L’s) affects demand and wages.

8. 3 Special Cases in CES framework • σ→ 0 (or ρ→∞ ). In this case, skilled and unskilled workers are Leontief, and output can only be produced using skilled and unskilled workers in fixed proportions. This is a case of perfect complements. • σ →∞ (or ρ→ 1). Skilled and unskilled workers are perfect substitutes (and so relative supplies of each do not affect relative wages .though chances in aggregate supplies will affect relative wages by affecting the price of skill overall). • σ→ 1 (or ρ→ 0). The production function is Cobb Douglas, with fixed shares paid to each factor

9. Wage Setting • Given competitive labor markets, the unskilled wage is given by: • And skilled wage is given by:

10. Two Labor Market Results: • ∂WH/ ∂(H/L) < 0, i.e. the own labor demand curve is downward sloping. • ∂ WL/∂(H=L) > 0, i.e. Everything else equal, as the fraction of skilled workers in the labor force increases, the wages of unskilled workers should increase. • Hence, skilled and unskilled workers are Q-complements a greater quantity of the one increases the marginal product of the other. • This seems more natural if you think of the two inputs as capital and labor; more intensive use of capital raises the marginal productivity of labor and vice versa

11. Skill Premia! • Combine two equations and we get: • We can write this in log form for ease of interpretation

12. The RELATIVE demand curve • Taking derivatives of this: • the relative demand curve for high versus low skilled workers is downward sloping. • For given skill bias, Ah/Al, an increase in relative supplies H/L lowers relative wages with elasticity σ

13. Why Does Increased H/L Decreases Relative Wages? • Two potential ways this happens: • Suppose there’s only 1 good: an increase in the relative supply of high skilled worker will cause firms to reassign some tasks performed by low skilled workers to high skilled, thereby lowering the marginal productivity and hence the wages of high skilled. • Suppose there are multiple goods: Output of the high-skilled good will rise, increasing consumption of this good but lowering consumers marginal utility of consuming it and hence its price.

14. What happens if relative efficiency (A’s) changes? • What if we change the skill bias, i.e. Ah/Al • Depends on whether σ is bigger or smaller than 1 • Hard to measure σbut it’s though to be bigger than 1

15. How could increase Ah/Al not increase High Skilled wages? • An intuitive way to see this is to consider a Leontif production function where high and low skilled workers are used in constant proportions in a competitive market. • An increase in the supply of high skilled workers in this setting effectively creates “excess supply: for a given number of unskilled workers. • The extra skilled workers will either bid down wages of other skilled workers or will become unemployed (lowering average wages for skilled workers if zeros are counted). • Not considered likely based on what we know about σ

16. Average Wages • Average wages should increase: • When the skill composition of the labor force rises, wages increase. • Intuitively: When the wages of skilled are below unskilled, this effectively implies that unskilled are scarcer than skilled; additional skilled workers effectively lower the skill composition of the labor force

17. Societal Wealth • If Ah or Al rises with σ > 1, wages should rise for all workers, both skilled and unskilled (though inequality may increase). • Factor augmenting technical change always raises societal wealth since we can get more output for a given set of inputs. • Keep this in mind as an explanation for observed Trends • male wages below the median fell substantially in real terms in the U.S. during the 1980s • Not true in other countries

18. Summary from our Simple Model In response to an increase in H=L (and assuming the skill premium is positive): 1. The skill premium w = WH/WL falls. 2. Wages of unskilled workers rise. 3. Wages of skilled workers decrease. 4. Average wages rise. These results can readily be generalized to a case with capital, i.e., F(AlL;AhH;K); and they will generally go through.

19. Long-term skill bias technical change • The key result from the above is that as H/L increases, w falls. • But in every advanced country the supply of educatedworkers has risen dramatically in the past 6 decades but relative wages of better educated workers have remained consistently above those of less educated, though the degree to which they have done so has varied by decade. • Hence, the relativedemand for skilled workers must have risen practically everywhere.

20. Technology vs. Skill Supply Growth • We observe increased relative supply of skill and increased wages so we think technical change may be “skill-biased” (favoring high skilled) • Not necessary that technical change has outstripped growth in supply of educated workers. • Rate of technical change is not always fixed • Tinbergen (1975) point: “The two preponderant forces at work are technological development, which made for a relative increase in demand and hence in the income ratio... and increased access to schooling, which made for a relative decrease.”

21. Evolution of Inequality • Long term trend increases towards greater relative demand and greater supply of skilled workers • Bursts of supply and/or technologically-induced demand accelerations/ decelerations that cause demand to temporarily move out more rapidly than supply or vice versa in some eras.

22. Katz-Murphy (1992) Model • Insight: if you know (or assume) σ, can back out the implied change in relative demand for high versus low-skilled worker • Let’s go back to our wage skill premium from the CES model

23. Estimating changes in Relative Demand • Get some time series data • Estimate changes over time • A’s vary by year, as do the supplies of skilled and unskilled workers and the skilled/unskilled wage ratio • Fixed σ • We observe supplies and we can estimate the wage premium.

24. Unknowns: • Ah/AL • σ • Our hypothesis is that ∂ln(Ah/AL)/ ∂t > 0 so we estimate Time fixed constant

25. Results • there has been a trend increase in the relative demand for skilled workers • the elasticity of substitution between them σ = -1/0.709 = 1.41. • Caveat: K-M regression has only 25 data points, and they are highly serially correlated.

27. Is it steady or accelerating demand • KM: Steady demand and fluctuations in supply are drivers of inequality • Natural question: Could this be due to accelerating/changing demand • Define a demand index

28. How to test for accelerating demand • Is there an acceleration in the rate of change in Dt? • Specific test: ΔD70-99>ΔD45-69 • How to estimate? • A consistent series for wages and employment • Estimates of wagebill shares (wHH;wLL) • Estimate of wH/wL

30. Concerns… • One concern in implementing this framework is that the wagebill shares may confound changes in prices (wH/wL) with changes in the composition labor if the quality of high and low skill workers varies with time. • That is: Supply change Price change

31. Isolating true change in supply • Subtract of the component of wagebill share change due to pure price changes (estimated from a regression) and hence calculates the effective supply change as a residual.

32. AKK (2004) Results

33. Conclusions from AKK • There is evidence of growing relative demand for skilled workers in every decade except the 1940s • it is believed war-era industrialization dramatically raised relative demand for less-skilled workers

34. AKK (2004): Demand Shifts

35. More Conclusions AKK • Whether demand accelerated in the 1970s or 1980s relative to the prior decades depends sensitively on the assumed elasticity • a demand acceleration in the 1970s may have been masked by a simultaneous supply acceleration. • If this inference is correct, inequality would have grown in the 1970s had supply not suddenly jumped.

36. AKK (2004) Changes in Wage Supply

37. Takeaways from AKK (2004) • There is clear evidence that net demand changes were larger over 1970 - 2000 (i.e., the most recent three decades relative to the prior three). • This is evidence of acceleration • depends heavily on including the 1940s. • There appears to be demand deceleration in the 1990s. • key fact: necessity of demand shifts, with some evidence of their acceleration in the 1970s or 1980s.

38. Theories for Explaining Inequality: • Steady demand. • One possibility motivated by the Tinbergen framework (and partly affirmed for the 1960s - 1980s by Katz-Murphy) is that for unspecified (and perhaps exogenous) reasons, there has been a steady rise in demand for skills throughout the century. • Hence, movements in the wage premium reflect changes in the trend growth of supply. when supply lags demand, the premium rises (and vice versa). • Simple but plausible one, and it may explain much of the data if not all of it. Richer versions of the K-M model (e.g., Card and Lemieux 2001) may do a better job of explaining the data using this hypothesis than does the original K-M paper.

39. Theories of Inequality II 2. Accelerating demand • This hypothesis posits a discontinuous increase in the trend rate of demand growth, perhaps occurring in the 1970s or 1980s, that, coupled with the slowdown in supply, caused inequality to rise. • This is also a reasonable hypothesis a priori: why should the rate of movement of the relative demand curve be steady across periods? What gives this hypothesis added plausibility to many economists is the simultaneity of the computer revolution with the rise in inequality in advanced countries. • Generally, hypotheses in this vein (accelerating demand) will specify a variety of reasons why demand will have accelerated, and provide evidence for these causes.

40. Theories of Inequality III 3. International trade. • There was substantial growth in world trade flows, especially in the United States. • The most rapid growth is during the 1970s, not the 1980s. • Trade between countries with different factor endowments will change relative prices and will therefore raise or lower inequality among owners of those factors

41. Theories of inequality IV 4. International outsourcing. • This is subtly different from trade. Rather than opening factor markets to trade, you simply purchase certain factor-intensive inputs from overseas and turn them into final products in your own country. 5. Institutional changes. Declining union penetration and falling minimum wages are a major feature of the U.S. and U.K. labor markets during the period of inequality growth. In other countries, these institutional changes have been far more moderate. A number of authors have argued that these institutional changes explain the observed changes in wage setting rather than the forces of supply and demand.

42. Next 3 Weeks… • Theories on why higher skills maybe more productive • Returns to Education • Education Production • Signaling Models