Malthus to Solow Hansen and Prescott

AER, 2002

Google Citations: 349

The Puzzle: Why Did Income Per Capita Start Growing?

Their answer: shift from land-intensive (non-constant returns in labor and capital) to solow growth.

Two Production Functions: Each Produces the Same Final Good

Technology Grows Exogenously:

Capital fully depreciates. So:

Firm Maximization

Individuals live two periods and maximize the following utility function:

Each individual supplies one unit of labor in period 1 and zero labor in period two.

Utility Maximization

Markets clear:

Population grows according to:

Two Propositions

Calibrated Parameters

Simulated Growth Path

“Our Simulated Growth Path has several features in common with the historical data shown in Figure 1 and Tables 1 and 2. During the periods when only Malthus technology is being used, population grows at the same rate as output, and the wage stays constant. After period 0, population growth increases, and the real wage increases as well … The value of land relative to output decreases after the Solow technology is adopted. This is roughly consistent with the pattern seen in Table 2.”

Praise

• Transition from Malthus to Solow usually assumed; this shows how it could happen endogenously; it gives us various estimated parameters and follow-up researchers can see whether these parameters (i.e. technological growth and fertility) are reasonable.

Criticisms• Their showing how this shift can happen endogenously is not all that

remarkable (If Solow technology grows fast enough and starts low enough, it will not be used at first and will relatively quickly be used almost exclusively.)

• Why assume technological growth constant? -- Solow technology grows at same rate whether economy is not using it at

all or using it almost exclusively.• Assumptions vs. tests not made explicit.• Ratio of assumptions to tests high: no fertility in utility function; exogenous

technology.• Doesn’t do that well on tests. a) Economy shifts from no-Solow to almost-completely-Solow too fast. b) Wages do not grow fast enough in relation to population.