<p> Solow on the Decomposition of Growth</p><p>Y F(K, L) (CRS)</p><p>Y A(t)F(K, L)</p><p>Differentiate with respect to time: dY dA F dK F dL FK, L A dt dt K dt L dt </p><p>Divide by Y:</p><p>Y˙ A˙ F K˙ F L˙ A A Y A K Y L Y</p><p>Y K Y L Define wk and wL , where w w 1, and substitute into the K Y L Y L K equation above.</p><p>Y˙ A˙ K˙ L˙ (1) w w Y A K K L L</p><p>Put variables in intensive form:</p><p>Y K y , k . L L</p><p>We now need to use the following result: y˙ Y˙ L˙ y Y L</p><p>We will show that this is true:</p><p> Y dY dL d L Y L y˙ dt dt dt L2</p><p>1 dY 1 Y dL y˙ L dt L L dt y˙ L 1 dY L 1 Y dL y Y L dt Y L L dt</p><p> y˙ Y˙ L˙ y Y L</p><p>Similarly:</p><p> k˙ K˙ L˙ k K L</p><p>Using these results, we can rewrite (1) as y˙ L˙ A˙ k˙ L˙ L˙ w w y L A K k L L L</p><p>Recall that wL wK 1, so: y˙ L˙ A˙ k˙ L˙ w y L A K k L</p><p>Finally, y˙ A˙ k˙ w . y A K k</p><p> y˙ k˙ A˙ In this equation, , wK , and are measurable, so can be inferred (and we can y k A account for sources of growth. We use the preceding equation to decompose growth of per capita output into a component due to technical change and that due to growth of capital per worker. Results</p><p>1909-29: Technical change accounts for 0.90 percentage points of per capita growth per year.</p><p>1930-1949: Technical change accounts for 2.25 percentage points of per capita growth per year.</p><p>Technical change accounts for 7/8 of per capita growth; increased capital per worker accounts for just 1/8.</p><p>Technical change appears to be highly variable from year to year.</p><p>Technical change is neutral (the assumption about the specification of technical change in the production function seems to be appropriate).</p><p>Question: Is the neutrality of technical change (as assumed here) consistent with the assumption of labor augmenting technical change (required to make Solow’s growth theory fit the facts) ?</p>
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