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This paper applies the stochastic frontier production model to the lower 48 U.S. states over the period 1977–2000 to decompose the sources of total factor productivity (TFP) growth into technological progress, changes in technical efficiency, and changes in economies of scale. We find that technological progress comprises the majority of TFP growth but that differences in efficiency change explain cross-state differences in TFP growth. TFP growth was greater towards the end of the time period.

For decades, economists have been interested in measuring and identifying sources of productivity change. Fisher (1922) and Törnqvist (1936) provide early examples of constructing superlative productivity indices using price and quantity data. Researchers also measured productivity change by computing a Malmquist (1953) productivity index. Solow (1957) measured productivity growth for the U.S. economy using an aggregate production function. He computed total factor productivity (TFP) growth as the residual after subtracting labor and capital growth (i.e. growth in inputs) from output growth. His procedure, often denoted as “growth accounting” has been replicated for many other countries, time periods, and sets of inputs which Barro and Sala-I-Martin (1995, Chapter 10) summarizes. Such exercises are not merely academic but offer implications as to what extent output growth is sustainable in the future. Neoclassical growth models argue that economic growth (in terms of output per person) is not sustainable without continuous increases in TFP since factor accumulation exhibits diminishing returns that is eventually self defeating. Detailed decompositions along the lines of Solow (1957) have also changed perspectives regarding different growth episodes. Krugman (1994) argues that the East Asian Growth Miracle is not so miraculous once one accounts for increasing input levels. Young (1995) presents a more detailed account and reaches similar conclusions in that the East Asian Growth Miracle is better explained by rapid factor accumulation and not by increases in TFP. Therefore, measuring productivity growth and understanding why it does or does not occur becomes important for how we interpret various growth episodes. However, a disadvantage of using the approach in Solow (1957) is that it does not identify sources of TFP growth. For example, it does not indicate whether TFP growth stems from technological progress or from efficiency gains. An inefficiency in production exists when production takes place inside the technological (or production) frontier since output can be increased given the same technology and input levels. The farther one is below the frontier, the larger is the inefficiency and so measuring inefficiency is equivalent to measuring the distance from the production frontier. Efficiency gains occur as this distance decreases. Technological progress occurs when the frontier itself shifts. Distinctions between the two can be important. Efficiency gains are not sustainable without technological progress since they cannot recur once the frontier is reached. The issue then becomes how to decompose TFP growth into its components or, in other words, to find the sources of productivity change. Domazlicky and Weber (1997) use nonparametric techniques to create a Malmquist productivity index for the lower 48 U.S. states from 1977 to 1986.1 A disadvantage of their approach is that it is deterministic and so it labels any deviation from the frontier as an inefficiency. It does not allow for the possibility of random events or for other factors to affect output. Given the presence of random shocks affecting production, the use of a deterministic methodology is unwarranted.2 Only stochastic frontier models, which we use in our methodology, can account for the sources of TFP growth while also allowing for a stochastic environment. Stochastic frontier models consider both inefficiency and random disturbances as reasons why production is not at the technological frontier and distinguish between the two. Deterministic models do not consider random deviations and so attribute all of the discrepancy from the frontier to inefficiencies of production although this would not be appropriate in cases where random measurement errors are present, for example. Many applications of stochastic frontier estimation have examined the efficiency of firms or individual farmers. For example, Battese and Coelli, 1992 and Battese and Coelli, 1995 examine efficiency levels of paddy farmers in India. Piesse and Thirtle (2000) estimate efficiency gains in Hungarian agricultural and manufacturing firms during the transition away from communism. Other references are provided in Coelli, Rao, and Battese (1998) and Kumbhakar and Lovell (2000). Recent studies have also applied stochastic frontier estimation to compare efficiency differences across countries or across regions within a country. Wu (2000) examines Chinese regions so as to distinguish efficiency gains from technological progress and determine whether Chinese growth is sustainable. Gumbau-Albert (1998) measures inefficiency across Spanish regions and Gumbau-Albert (2000) considers to what extent efficiency gains can explain convergence within Spain after 1964. Osiewalski et al. (1998) claim that output growth in Poland was due to gains in efficiency as reform pushed production towards the frontier. Moroney and Lovell (1997) compare efficiency levels between market and planned economies in Europe. Adkins, Moomaw, and Savvides (2002) estimate technical efficiency across a wide sample of countries and examine its relationship with measures of institutions and political freedoms. Koop et al., 1999 and Koop et al., 2000 apply a stochastic frontier model to a cross-section of countries. Given the above applications, it seems natural to apply this methodology to U.S. states since production techniques are similar across states. But this does not imply that states do not differ across other dimensions such as policies, demographics, and geography. If efficiency levels do not differ across states, then these varied characteristics are not strong enough to cause inefficiency to vary across regions. On the other hand, varying efficiency levels would imply that these regional differences are not trivial and that even in a domain having a common national economic policy and similar institutions, regional differences in efficiency can still occur. This is not the first application of stochastic frontier estimation to U.S. states. Beeson and Husted (1989) examine manufacturing across U.S. states and what determines differences in this sector's efficiency. Of course, it is not clear to what extent their results can be extrapolated to other sectors. Puig-Junoy (2001) and Brock (2001) consider aggregate state output and so are more in line with our study. Both use stochastic frontier models to measure efficiency differences across U.S. states. However, neither Brock (2001) nor Puig-Junoy (2001) consider TFP growth and so do not answer more broad questions regarding changes in TFP, including what role efficiency change plays in determining TFP growth. A second advantage of this study is the use of a longer time period. Not only does this obviously provide for a larger sample, but use of a longer time period allows for a longer window so that temporary shocks play less of a role in driving the results of the paper. For example, the oil price shocks of the 1970's benefitted oil-producing states such as Texas. In Brock (2001), who examines the 10-year stretch from 1977 to 1986, Texas ranks near the top in efficiency. But to what extent is Texas's high ranking dependent on the oil price shocks of the 1970s and not on a deeper explanation? By looking at data through 2000, we can better answer this and similar questions because such states should fall in the rankings for later years if their high ranking mainly stemmed from being an oil producer when the price of oil was high. The same holds true for other temporary shocks whose relative benefits differ across states. More generally, by looking at changes in efficiency ranking over time, this study can point to potential reasons for such movements and help us better understand why some states improve efficiency levels at higher rates than do others, especially if states with similar movements contain similar industries. Consequently, such movements can also help explain differences in TFP growth over time. The paper is organized as follows. Section 2 presents the empirical methodology. It describes how we measure technical efficiency and how this methodology also allows us to estimate input elasticities as well as to decompose total factor productivity growth into its constituent parts. Section 3 describes the data and Section 4 presents the results. Inefficiency and TFP growth estimates are obtained for each state and for each year from 1977 to 2000. Our stochastic frontier model also allows us to examine how inefficiency is associated with various state characteristics. A conclusion follows.

This paper examined total factor productivity growth across U.S. states. Our findings are as follows: (1) TFP growth mainly stems from technological progress and this is encouraging because changes in efficiency can no longer be positive once the frontier is reached. However, differences in TFP growth across states mainly stem from differences in efficiency change. (2) Efficiency in the 48 contiguous states averaged 76% from 1977 to 2000. States undergoing the greatest declines in efficiency were oil and coal producing states. Those experiencing the greatest increases were those with larger financial sectors. (3) Human capital and urbanization are both associated with efficiency. Of the industries, agriculture is negatively associated with efficiency whereas financial sectors are positively associated. (4) The biggest states had the higher labor elasticities and lowest capital elasticities. The assumption of constant returns to scale often employed when using aggregate production functions is supported here and so the economies of scale component is negligible with regards to TFP growth. In our estimation, we have attempted to control for price differences across states by use of regional dummies. However, this is not a perfect solution as states within the same region might also significantly differ across this dimension. Consider Vermont versus New York. One possible way to account for these differences is through our measure of urbanization as price levels are likely to be higher in cities and this might be what our urbanization variable is capturing. If so, then it is less clear that some aspect of agglomeration is leading to greater efficiency. Obviously, this is an avenue of future research although what is really needed are state GDP measures that are adjusted for purchasing power parity differences across states. We encourage that such measures be developed, not only to better measure differences in efficiency across states but to compute TFP growth since changes in efficiency appear to be important in explaining differences in TFP growth across states.