Question 10.89

10.89 Agricultural productivity.

Few sectors of the economy have increased their productivity as rapidly as agriculture. Let’s describe this increase. Productivity is defined as output per unit input. “Total factor productivity” (TFP) takes all inputs (labor, capital, fuels, and so on) into account. The data set AGPROD contains TFP for the years 1948–2011.24 The TFP entries are index numbers. That is, they give each year’s TFP as a percent of the value for 1948.

agprod

  1. Plot TFP against year. It appears that around 1980 the rate of increase in TFP changed. How is this apparent from the plot? What was the nature of the change?
  2. Regress TFP on year using only the data for the years 1948–1980. Add the least-squares line to your scatterplot. The line makes the finding in part (a) clearer.
  3. Give a 95% confidence interval for the annual rate of change in TFP during the period 1948–1980.
  4. Regress TFP on year for the years 1981–2011. Add this line to your plot. Give a 95% confidence interval for the annual rate of improvement in TFP during these years.
  5. Write a brief report on trends in U.S. farm productivity since 1948, making use of your analysis in parts (a) to (d).

10.89

(a) The rise from 1948 from 1980 is fairly consistent then shifts and increases at a much faster rate from 1981 to 2011. (b) . (c) (1.55206, 1.78825). (d) (2.93208, 3.53961). (e) Overall, there has been rapid growth in agricultural productivity since 1948. But there was a significant shift in that productivity around 1980. Before that, the growth, on average, was between 155% and 179% each year; after 1980, the growth was between 293% and 353% each year. These results are at 95% confidence.