Growth Accounting, 1865-1929

Growth Accounting, 1865-1929: The Great Traverse J. Bradford DeLong Professor of Economics, U.C. Berkeley Research Associate, NBER [email protected] September 30, 2008

In 1869 the United States had 35 million people in it, at an average measured economic standard of living of some $1,600 year-2008 dollars per year, at least two-thirds farmers or other small-town rural dwellers. By 1929 farming and other small-town rural dwellers were down to oneeighth of the population, the United States had 122 million people in it, and the average measured economic standard of living was some $6,000 year-2008 dollars per year. These give us growth rates of 1.9% per year for the population of the country and of 2.1% per year for output per capita. (Contrast with growth rates of 2.9% per year for population—from 4 to 35 million—and 1.4% per year—another near-tripling—in measured economic output per capita.) The continuation—nay, the acceleration—of growth in output per worker alongside continued population growth is especially remarkable given that the frontier had closed in the immediate aftermath of the Civil War: the natural resources the United States had then conquered were all that there were. Yet growth continued: the focus shifted from expansion and resources to industrialization. America became an industrial economy. Even farming became an industrial occupation: no longer muscle, ox, and horsepower but automatic reapers, harvesters, pumps, stationary gasoline engines, tractors.

1

So we shift the production function we work with away from the resourcefocused “Malthusian” one we have been dealing with up to now to a different rule-of-thumb for economic growth: 1 1 g(Y ) =  g(K ) +  (g(L) + g(E)) 2 2

where g(Y) is the proportional growth rate of total output, g(L) the growth rate of the population or labor force, and g(E) the growth rate of the € efficiency of labor. Subtract off the growth rate of the labor force from both sides to get: 1 1 g(y) =  g(k) +  g(E) 2 2

where now g(y) and g(k) are the growth rates of output per capita and the capital stock per capita, respectively. Subtract off half of the growth rate € of output per capita from both sides: 1 1 1 1 g(y) −  g(y) =  g(y) =  (g(k) − g(y)) +  g(E) 2 2 2 2

Multiply by two: €

g(y) = (g(k) − g(y)) + g(E)

And let’s give the difference between the growth rates of the capital stock and the growth rate of output per worker a name: d, for capital € deepening—the extent to which the economy becomes “more industrial” in the sense that each unit of output made is backed by and in fact requires an increasing number of units of capital behind it: g(y) = d + g(E)

This is a very simple equation. In an industrializing economy, the growth rate of output per worker will be equal to the growth rate of the efficiency € of labor E plus the amount of capital deepening d.

2

What determines the rate of capital deepening? Let’s write down an equation for the growth rate of the capital stock per worker k, with s being the share of national output saved and invested in capital and pk being the price of capital goods in terms of output as a whole:  s  Y  g(k) =    − δ − g(L)  p k  K 

where δ is the rate of depreciation—the rate at which the capital stock wears out, rusts away, needs to be replaced. And let’s look before and € after an episode of capital deepening. Both before the capital deepening starts and after it ends: g(y) = d + g(E) = 0 + g(E) = g(E)

€

And because there is no capital deepening y and k are growing at the same rate. This tells us that both in 1865 and in 1929: g(y) = g(k)  s  Y  g(E) =    − δ − g(L)  p k  K   s  Y  g(L) + g(E) + δ =     p k  K  K (s / p k ) = Y g(L) + g(E) + δ

Now let’s plug in some numbers. In 1865 the rate of population growth is 3% per year, the rate of growth of the efficiency of labor is this 0.9% per € year we got from the British Industrial Revolution, the rate of depreciation δ is some 4% per year, the rate of national savings s is some 20% per year and the price of capital goods pk we set at 1 in 1865. Thus our equation becomes:

3

K  .20 (s / p k ) (.20 /1) = = = 2.5   =  Y 1865 g(L) + g(E) + δ .03 + .009 + .04 .08 By 1929 our rate of population growth has dropped to 2% per year. The price of capital goods has dropped to 2/3. And the national savings rate € has increased by one-quarter to some 25%. So our equation becomes:

K  (.25 /(2 / 3)) = .37 = 5.3 (s / p k ) =   =  Y 1929 g(L) + g(E) + δ .02 + .009 + .04 .07 The jump from 2.5 to 5.3 in the capital-output ratio (measured at 1865 prices) gives us an annual rate of capital deepening of 1.2% per year. Plug € this back into our industrializing-America equation for the growth rate of output per worker: g(y) = d + g(E) = 1.2% + 0.9% = 2.1%

And it fits. Between 1865 and 1929 some 4/7 of American economic growth in measured economic output per capita came from capital € deepening—more capital, more produced means of production, more machines backing up each worker. And 3/7 of American economic growth in measured economic output per capita came from improvements in the efficiency of labor—working smarter made possible by more education, organizational improvements, and other improvements in technology not directly related to those that made capital goods cheaper.

4