Choice of Parameter Values

sC, sS, sP,A^W_C A^W_P ,A^W_S

A^W_P

so that the productivity of P-type workers is given by

Ap =





(Y /N)/(K/N)^1−β Ω

s_C, s_S, s_P,^A_A^WCW P

,^A_A^WSW P





1/β

.

We then use equations equivalent to (33) to compute AC and AS.

5. We assume the frontier in yeartto be the maximum of observed productivity up to year t, i.e. A^W_it = max(A_ih|h≤t).

6. We and solve for the frontier by iteration on steps (3)-(6) to find the fixed point of the following problem

A^W_itn+1 = max(A_ih(A^W_itn,D)|h≤t)

where D stands for our data, A_ih is the vector of sector i productivity levels for all countries in our sample in year t computed using the BGP conditions of the model and our data as outlined below, and A^W_itn is the value of the frontier productivity level for sector i in yeart found in the n-th iteration of our algorithm.

7. We normalize the level of barriers to entry in the US to be equal to one and using the equation (35) we get

ζk

ζU S

= P_L,k^∗ P_{L,U S}^∗

!1/β

R^∗_k R^∗_{U S}

^β−1_β AL,U S

AL,k

φ sL,k

sL,U S

(39) which allows us, using the A’s computed previously as well as expressions (23) and the equations for intermediate good prices (see Appendix), to compute the (relative) level of barriers for each country.

4.2 Choice of Parameter Values

We have to pick values for the following parameters in our model: η’s, σ, φ, υ and β Unfortu-nately for many there is very little guidance in the existing literature. If this is the case, we make some judgment calls and experiment with several possible values. βis the labor’s income

share and we choose a value of 2/3, in agreement with Gollin (2002). We use a values of 1.4 for the markup based on work of Ramey and Nekarda (2013) and Jones and Williams (2000). The technology diffusion parameterφ is set equal to 0.5. We choose this value to match the speed of convergence to the steady state of about 2.5%, see Barro and Sala-i-Martin (2003).²¹ Lastly, we follow Gourinchas and Jeanne (2004) and choose the inter-temporal elasticity of substi-tution to be 1, the time discount rate to be 0.04, the depreciation rate to be 6% and finally the frontier productivity growth to be 1.2%. Together these choices produce the equilibrium world interest rate (in the absence of capital distortions) of 5.2%.

The choice ofσ turns out to be very important for some of our results. Based on estimates of Katz and Murphy (1992) and more recently Ciccone and Perri (2005) is about 1.4 or 1.6, but could be above 2.

In a seminal contribution, Katz and Murphy (1992) estimate σ using college/high school wage premium for the years 1963-87 and get an estimate of σ = 1.4. However, they observe that including a square and higher order polynomials oft (i.e. allowing for AH/AL to grow at variable rate) affects the estimate and they conclude that values as high as 2.6 are consistent with the data. More recently Ciccone and Peri (2005) use instrumental variables strategy (since H/Lresponds to shock to wages, OLS may be inconsistent) and data across US states. They findσclose to 1.5. Most recently however, Acemoglu and Autor (2011) argue that higher values ofσare also plausible. For example, using Katz and Murphy’s regression on updated data they findσ= 2.9. An additional concern, shared by Jonea (2014), is whether the existing US-basedl estimates are appropriate for a cross-country setting. In a companion paper Jermanowski and Tamura (2017), we estimate estimate σ using a EU KLEMS Growth and Productivity Accounts panel data set (O‘Mahony and Timmer, 2009). This is a detailed database of industry-level measures of output, inputs and productivity for 25 European countries, Japan and the US for the period from 1970 to 2005. We use the information on hours worked and wages in manufacturing broken down into three skill groups: low-skill (less than High School degree), medium-skill (High School degree) and high-skills (College). Generally, we estimate the elasticity to be considerably above 2 and, in some specifications, we are not able to reject the hypothesis that it is above 2.6, the value required for strong skill bias given our calibration of the other parameters. Since we want to explore the implications of the directed technology paradigm, including strong skill-bias, for the world income distribution, we compute and compare the results under two different values of elasticity: 1.6 and 2.6.²² Finally, we calculate the relative research efficiencies ηC/ηP and ηHS/ηP using the data from

21See the Appendix for the discussion of the model’s dynamics.

22Our Appendix briefly explains our approach and summarizes our estimates of σ using the EU KLEMS data.

Goldin and Katz (2008), who report relative wages and supplies of workers with different educational attainment for the US economy since 1910 based information from the censuses.²³.

Table 1: College and High School Premia from Goldin and Katz Year wC/wP wC/wHS wHS/wP

1915 2.74 1.89 1.45

1940 2.33 1.65 1.41

1950 1.69 1.37 1.24

1960 1.87 1.49 1.26

1970 2.00 1.59 1.26

1980 1.86 1.48 1.26

1990 2.26 1.73 1.31

2000 2.67 1.83 1.45

2005 2.62 1.81 1.44

Using the above data, the parameter values chosen above and our relative wage equation wH

w_L = ηH

η_L

_1+φσ^σ−1 H

L

^σ_1+φσ^−2−φ A^W_H A^W_L

^φ(σ−1)_1+φσ ,

we recover the relative η’s.²⁴

5 Results

We begin by presenting the skill-specific productivity levels, which we have computed and discussing how they differ across countries and what they imply about the evolution of the factor bias of technology during our sample period.²⁵ Next we present and discuss the measures

23We update the data to 2010 using Acemoglu and Autor (2011)

24This is a different approach than the one taken by Gancia et al. (2013). They arrive at an equation equivalent to the above formula (with the exception that they treat the U.S. as the frontier country, which by definition does not benefit from diffusion soφ= 0). They use observations on the skill premium and and relative supply of skills in 1970 and 2000 to solve for the intercept (^η_η^H_L) and the slope of this line defined by taking logs of the above equation. This gives the a value of about 2.3 for σ and a common value for the intercept. We instead back out (^η_η^H_L) by imposing a value for σ(either 2.6 or 1.6) and solving the above equation for each decade in our sample. The key difference is of course that in our approach, the relative productivity of different research directions are allowed to change over time.

25Recall that, in the two-skill version of the model, technological progress is said to be skilled-labor aug-menting if it increases AH and skill-biased if it increases AH/AL. In the empirical analysis we have three skill groups, so we obviously have more possible combinations of effects. To avoid confusion we will adopt the following terminology. We will say that technological progress, for example, favors college educated workers relative to high school educated worker when AC/AHS goes up, without any restriction on the concurrent change inAC/AP. We will only say that technological progress is college-biased, if it favors college educated

of barriers to technology adoption implied by our model. Finally, we evaluate the role of barriers and technology-bias in explaining cross-country income differences. We confine our analysis to the years 1910-2010, since this is the period for which we have the most reliable US skill premium data, a crucial ingredient into our calibration exercise.