The Role of Productivity Growth in U.S. Agriculture

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The rise in agricultural productivity has long been chronicled as the single most important source of economic growth in the U.S. farm sector. Though their methods differ in important ways, the major sectoral productivity studies by Kendrick and Grossman (1980) and Jorgenson, Gollop, and Fraumeni (1987) share this common conclusion. In a recent study, Jorgenson, Ho, and Stiroh (2005) find that productivity growth in agriculture averaged 1.9 percent over the 1977-2000 period. Output grew at a 3.4 percent average annual rate over this period. Thus productivity growth accounted for almost 80 percent of the growth of output in the farm sector. Moreover, only three of the forty-four sectors covered by the Jorgenson et al. (2005) study achieved higher rates of productivity growth than did agriculture.

The U.S. Department of Agriculture (USDA) has been monitoring agriculture's productivity performance for decades. In fact, in 1960, USDA was the first agency to introduce multifactor productivity measurement into the Federal statistical program. Today, the Department's Economic Research Service (ERS) routinely publishes total factor productivity (TFP) measures based on a sophisticated system of farm production accounts. Its TFP model is based on the transcendental logarithmic (translog) transformation frontier. It relates the growth rates of multiple outputs to the cost-share weighted growth rates of labor, capital, and intermediate inputs. See Ball et al. (1997, 1999) for a complete description of the USDA model.

The applied USDA model is quite detailed. The changing demographic character of the agricultural workforce is used to build a quality-adjusted index of labor input. Similarly, much asset-specific detail underlies the measure of capital input. The index of land input, for example, is constructed by aggregating county-level data. The contributions of feed, seed, energy, and agricultural chemicals are captured in the index of intermediate inputs. An important innovation is the use of hedonic price indexes in constructing measures of fertilizer and pesticide consumption. The result is a time series of total factor productivity indexes for the aggregate farm sector spanning the period 1948 to 2015 (table 1). State-specific measures are available for the 1960-2004 period. The State series provides estimates of both the growth and relative levels of total factor productivity (see tables 3-23).

National Agricultural Productivity

Input growth typically has been the dominant source of economic growth for the aggregate economy and for each of its producing sectors. Jorgenson, Gollop, and Fraumeni (1987) find this to be the case for the aggregate economy for every subperiod over 1948-79. Denison (1979) draws a similar conclusion for all but one subperiod, covering the longer period 1929-76. In their sectoral analysis, Jorgenson, Gollop, and Fraumeni find that output growth relies most heavily on input growth in 42 of 47 private business sectors in the 1948-79 period, and in a more aggregated study (Jorgenson and Gollop, 1992) that extends through 1985, in 8 of 9 sectors.

Agriculture turns out to be one of the few exceptions: productivity growth dominates input growth. This is confirmed in table 2 that reports the sources of output growth in the farm sector for the entire 1948-2015 period and 12 peak-to-peak subperiods. (The subperiods are not chosen arbitrarily, but are measured from cyclical peak to peak in aggregate economic activity. Since the data reported for each subperiod are average annual growth rates, the unequal lengths of the subperiods do not affect the comparisons across subperiods. This convention and these subperiods have been adopted by the major productivity studies). Applying the USDA model, output growth equals the sum of contributions of labor, capital, and materials inputs and TFP growth. The contribution of each input equals the product of the input's growth rate and its respective share in total cost.

The singularly important role of productivity growth in agriculture is made all the more remarkable by the dramatic contraction in labor input in the sector, a pattern that persists through every subperiod. Over the full 1948-2015 period, labor input declined at an average annual rate of 2.06 percent. When weighted by its 20-percent share in total costs, the contraction in labor input contributes an annual average -0.46 percentage point per year to output growth.

Capital input in the sector exhibits a different history. Its contribution to output growth alternates between positive and negative over the 1948-2015 period. On average, however, capital, like labor, contracts over the full period. Its negative growth contributes an annual -0.04 percentage point to output growth.

The negative contributions of both labor and capital are all the more notable given the positive contributions offered through improvements in both labor and capital quality, the recomposition of labor hours and capital stocks to higher marginal productivity sub-types. As revealed in table 2, farms have shifted to higher-quality labor. This is primarily due to a more highly educated labor force. (As discussed earlier, labor hours are cross-classified by sex, employment class, age, and education. Analysis of the changing composition of hours over the 1948-2015 period reveals that, among these four sources, education was the only dimension making a positive contribution to labor quality. As overall labor hours declined, demographic shifts in the sex, employment class, and age composition of workers left higher proportions of hours worked in cells representing lower marginal productivity sex, class, age cohorts. In contrast, the decline in labor hours was coincident with an increase in the proportion of more highly educated workers. This was sufficient to offset the negative effects of the changing sex, class, and age composition of hours and results in the persistent pattern of improving labor quality throughout the full 1948-2015 period.) Increased labor quality made a positive contribution to output growth in 11 of 12 subperiods, averaging 0.12 percentage points per year.

Material input's contribution was positive in 9 of the 12 subperiods, but averaged a substantial positive rate equal to 0.60 percent per year. Though large, this positive contribution just offsets the negative contributions through labor and capital. The net contribution of all three inputs was 0.1 percentage points per year, leaving responsibility for positive growth in farm sector output to productivity growth in all but 1948-1953 and 1973-79 subperiods.

Examining table 1 makes clear that the 1973-79 period is an outlier. Output, labor, and capital growth rates did not deviate much from trend. Materials input, however, exhibited significant positive growth at a rate far in excess of the incremental growth in output, accounting single-handedly for the measured decline in TFP growth. This anomaly appears to be due to rapid growth in export demand during this subperiod which resulted in both the increased consumption of intermediate inputs as well as a significant withdrawal of goods from inventory. Both led to a reduction in productivity growth.

The early 2000s saw the emergence of bio-fuels as a major source of demand for grains and oilseeds. Corn used in ethanol production in 2007 accounted for roughly one-quarter of total demand. The land area planted to corn increased some 15 million acres between 2006 and 2007, resulting in the cultivation of more marginal lands. Consumption of agricultural chemicals (i.e., fertilizer and pesticides) increased more than 10 percent. Yet yields per acre were largely unchanged.

In spite of these anomalous subperiods, over the 1948-2015 period, TFP grew an average of 1.38 percent annually. Cumulated over the full 65 year period, this average annual rate (compounded annually) implies that farm sector productivity in 2015 was 152 percent above its 1948 level. Given the cumulative 0.1 percent annual increase in total input growth between 1948 and 2015, productivity growth caused agricultural output to grow significantly in every subperiod so that by 2015, farm output was 170 percent above its level in 1948.

Measuring State Productivity

A properly constructed national measure of productivity growth for the aggregate farm sector provides a useful summary statistic indicating how economic welfare is being advanced through productivity gains in agriculture, but it may mask important State-specific or regional trends. For this reason, USDA has constructed estimates of the growth and relative levels of productivity for the 48 contiguous States for the 1960-2004 period (estimates are not made for Alaska and Hawaii). These indexes, expressed relative to the level of TFP in Alabama in 1996, are presented in table 19 along with their percentage rates of growth. In the tables 20, 21, and 22 we rank the States by their level and growth of farm output, input use, and TFP, in 1960 and 2004.

One remarkable similarity exists across all States for the full 1960-2004 period. Every State exhibited a positive and generally substantial average annual rate of TFP growth. There is considerable variance, however. The median TFP growth rate over the 1960-2004 period was 1.67 percent per year. However, 9 of the 48 States had productivity growth rates averaging more than 2 percent per year. Only Oklahoma and Wyoming had average annual rates of growth less than 1 percent per year. The reported average annual rates of growth ranged from 0.58 percent for Oklahoma to 2.58 percent for Oregon (see map above). Cumulated over the entire 45-year period, productivity growth in Oklahoma was responsible for only a 30-percent increase in that State's output. Over the same period, TFP growth in Oregon resulted in a 319-percent increase in the State's agricultural output.

A key question is whether States with lower levels of productivity tend to grow faster than the technology leaders: are there forces (e.g., the diffusion of technical knowledge from the leading States to the more backward ones) that lead to convergence over time in the levels of productivity?

A number of studies find evidence of convergence. McCunn and Huffman (2000) found evidence of "catching-up" in levels of TFP (i.e., β-convergence), although they rejected the hypothesis of declining cross-sectional dispersion (i.e., σ-convergence). Ball, Hallahan, and Nehring (2004) also found evidence of convergence in levels of productivity after controlling for differences in relative factor intensities (i.e., embodiment). (Their tests for convergence are conditional on these variables. In the literature on the empirics of growth (see Barro and Sala-i-Martin, 1992), this is referred to as conditional convergence.)

More recently, Ball, San Juan, and Ulloa (2014) examined the relation between the business cycle and convergence in levels of agricultural productivity. They found evidence of convergence in TFP levels across the different phases of the business cycle, but the speed of convergence was greater during periods of contraction in economic activity than during periods of expansion.

Finally, the expected pattern of convergence across the business cycle finds some empirical support. This pattern is the result of the pro-cyclical nature of innovation and the time lags in the diffusion of technical information. In contrast with, say the manufacturing sector, however, the magnitude of the effects of the business cycle through the rate of convergence appears to be smaller in the agricultural sector. The authors attribute this to public funding of R&D in the agricultural sector. Since innovations resulting from public R&D can be considered public goods that firms can adopt relatively quickly, the diffusion of technical information will be more rapid in agriculture and this points to a smaller impact of the business cycle on TFP convergence.