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Invention, Innovation, and Wage Inequality in Developed Countries

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Abstract

A growth model that endogenizes skill formation and the skill requirements of invention and innovation is used to analyze developed countries that must invent and innovate vs those that may specialize in innovation. Invention (innovation, respectively) is defined as the creation of (use of) new technologies with the potential to increase (that actually increases) total factor productivity. It is shown that a small innovation specialist will have a larger share of knowledge that is skill saving resulting in lower wage inequality, but with an equal economic growth rate as the invention leader. Specialization in innovation is preferred for all agents in the small country because growth rates of wages for high- and low-skilled workers are higher at the steady state. The large country cannot specialize in innovation, as it cannot rely on significant amounts of invention from abroad. The novel effect helps explain higher returns to skills and the larger increase in wage inequality in the arguably more inventive United States than in other advanced countries in recent decades. The results do not depend on international spillovers from the large to small country (yet still hold in their presence), thereby explaining the skill differential during the information technology revolution, which has been not been characterized by significant, costless spillovers.

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Notes

  1. Aghion et al. [1999] summarize inequality trends during the 1980s and early 1990s from sources that include Murphy and Welch [1992], Juhn, Murphy and Pierce [1993], Machin [1996], Atkinson [1996], and Rubinstein and Tsiddon [1999].

  2. Bowman [2008] presented a model for a closed economy that was the first to incorporate the three forces of technological change (invention, innovation, and adaptation) and two levels of skill. It extended Eicher [1996] to include the social learning assumption and help resolve a puzzle in the US growth and inequality experience of the 1963–2003 period. That closed economy model [of Bowman 2008] is used here as the large economy benchmark as we further develop the model to include a small, open economy that is affected by the large economy. See that paper for a discussion of how this approach differs from other endogenous growth models that have been developed to examine inequality and growth issues.

  3. There are problems in using patent data to distinguish invention from innovation because both activities may result in patents.

  4. The UK had the second highest share of the top 400 (11 percent). Of the top 16, the remaining 4 non-American universities (all within the top 7) were British. The UK is considered a mixed case for this model. It is interesting that the UK shared with the US the experience of rising inequality along several dimensions. Yet the UK had a lower relative wage than the US at the start and at the end of the 1980s and its initial income inequality was not particularly high in the early 1980s. Thus, it is potentially a mixed case empirically. Theoretically, the motivation of this paper may also suggest that it is a mixed case. Industrialization began in the UK, which may imply institutions that promote invention (as they could not rely on inventions from abroad as an industrial leader). But it is now much smaller economically relative to the US and may no longer need to rely on domestically created invention. Key data regarding the unexplained residual returns to high skills does not include the UK. For these reasons, we confine our analysis to the US vs the advanced countries previously mentioned.

  5. The pupil–teacher ratio is assumed to exceed 1; otherwise no high-skilled workers would be available for a production sector unless the percentage of the workforce that was high skilled was decreasing.

  6. The concluding section describes our expectation that the result of the model in terms of the direction of the effect of specialization on the relative wage would not change under the less restrictive assumptions that W may be affected by X or that X may be incompletely (rather than completely) specialized in innovation.

  7. Changes in the ratio of total to adaptive knowledge, (V/A), imply changes in the same direction for the ratio of frontier to adaptive knowledge, ((VA)/A).

  8. For the remaining parameters that affect wage inequality, we can easily show their effect. Increased wage inequality from an increase in μ I or λ will raise the relative wage in X by a lesser amount: X sss /=(αμ I /γμ D )<W ss /=[αμ I /(γ−1)μ D ]; and X sss / I =(αλ/γμ D )<W ss / I =[αλ/(γ−1)μ D ]. Increased wage inequality from a decrease in μ D or γ will raise the relative wage in X by a lesser amount. This is also to say that an increase in μ D or γ will result in a smaller decrease in the relative wage for X. So the negative change is a larger number for X: X sss / D =(−αλμ I /γμ D 2)>W ss / D =[−αλμ I /(γ−1)μ D 2]; and X sss /=(−αλμ I /γ2μ D )>W sss /=[−αλμ I /(γ−1)2μ D ].

  9. A spillover modeled as a higher productivity parameter in the inventive sector (μ I ) would not match the data. The small country would have a higher wage premium and grow faster while receiving spillovers whether or not it was specialized (from equations (34), (39), (35), and (36)). In addition to better matching the wage data, a higher student–teacher ratio represents partial specialization in innovation.

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APPENDIX

APPENDIX

Deriving steady-state growth rates

From MPLWD,t at ss and using the constancy of (V/A) ss W and ω ss W:

Total output in W in time t (denoted by QW t ) is equal to total income in W (wWH,tHW t +wWL,tLW t ). Making use of (2) and the fact that L ss W=1−P ss W, Q ss W becomes Q ss W=wWH,ssP ss W+wWL,ss(1−P ss W). Or for X, Q ss X=wXH,ssP ss X+wXL,ss(kP ss X). As P ss W is constant and %ΔwWH,ss=%ΔwWL,ss by (A1), we can see from the previous expression for Q ss W that %ΔQ ss W=%ΔwWH,ss=%ΔwWL,ss. The steady-state growth rate in total output in W (denoted g ss W) is the same as ss growth rate in income per capita in W (denoted by q ss W), as there is no population growth or changes in labor force participation in W (LFPW). Human capital investment expenditures at ss equal wWH,ssP ss W/γ. Therefore they also grow at a constant rate equal to the growth in total output. The only other component of total spending, total consumption expenditures, must also grow at the same rate. Per capita and aggregate consumption expenditures at ss (c ss W and C ss W, respectively), grow together as there are no changes in the population or LFPW:

Steady-state adaptive knowledge in W relative to X in the open case, (AW/AX) ss ∣(X open), is constant (as seen in (31)) as P ss X and (V/A) ss W are constant. From this and from (1) and (3) evaluated as ss, then g ss W∣(X open)=%ΔV ss W=%ΔA ss W=%ΔA ss X=μ I P ss W/γ and g ss X∣(X closed)=μ I P ss X/γ.

From versions of MPHWN,t, (3), (5), (9), and (11), the ratio of adaptive knowledge in W relative to X as open is:

From the previous expression evaluated at ss, we know that (VW/AX) ss ∣(X open) is constant, because it was shown that P ss W, P ss X, (V/A) ss W, (VW/AX) ss , and (AW/AX) ss are constant in that case. Thus, %ΔA ss X=%ΔV ss X can be added to the previous expression for W's steady-state growth rate examined for X as open: g ss W∣(X open)=%ΔV ss W=%ΔA ss W=%ΔA ss X=%ΔV ss X=μ I P ss W/γ. Constant P ss X and P ss W imply constant H I and H N in both countries at ss (under either case for X). With (V/A) ss X and (V/A) ss W constant (under either case for X), we see from (11) that H N , L N , and L D , must all be constant at ss as well. From the previous expression for g ss W, growth rates are equal in W and X as the rates of change in all technology stocks grow at the same constant rate. As A ss X grows at a constant rate, so does wXL,ss from MPLX evaluated at ss. Thus, wXH,ss also grows at the same rate as ωX is constant by (12) evaluated at ss. Adding these results to the previous expression for g ss W, and substituting (33a) into μ I P ss W/γ, the endogenous steady-state economic growth solely in terms of the model's parameters is found (while also making use of (A.2)):

For case of X as closed, plugging (33b) for P ss X into its growth rate of μ I PX t /γ:

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Bowman, K., Taengnoi, S. Invention, Innovation, and Wage Inequality in Developed Countries. Eastern Econ J 39, 511–529 (2013). https://doi.org/10.1057/eej.2012.20

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