Donald M. Waldman

A Monte Carlo study of estimators of stochastic frontier production functions

1. Introduction In recent papers which appeared almost simultaneously, Aigner, Love11 and Schmidt (ALS) (1977) and Meeusen and van den Broeck (1977) proposed a new error specification for frontier production function models. The specification is that the error term is the sum of two components ~ one normal with zero mean, and the other non-positive. ALS refer to a model with this error specification as a ‘stochastic frontier’, since the non-positive component of the disturbance represents the shortfall of actual output from the frontier, while the frontier contains the normal component of the disturbance, and is therefore stochastic. This specification avoids the serious statistical difficulties [discussed by Schmidt (1976) and Greene (1980)] which are encountered in the estimation of full frontiers - that is, in the presence of a purely non-positive error term. Any number of one-sided distributions exist which could plausibly be assumed to represent the distribution of the shortfall of output from the frontier. ALS consider (negative) half-normal and exponential distributions, while Meeusen and van den Broeck consider exponential only. Other possibilities include Gamma [Richmond (1974)] and lognormal [Greene (1980)]. ALS find very little difference in the fit of half-normal and exponential, in two empirical applications. In this paper we will restrict our attention to the half-normal case, which is the case considered in most detail by ALS.

A stationary point for the stochastic frontier likelihood

The likelihood function for the stochastic frontier model is shown to possess an unusual stationary point which may or may not be a maximum. A condition is given to determine if the point is a maximum, and the result is interpreted in the context of specification and estimation. The specification and estimation of frontier or envelope functions has been a concern of econometricians for some time. The subject became of widespread interest with the introduction of a particularly attractive formulation of the model, the stochastic frontier of Aigner, Love11 and Schmidt (ALS) (1977) and Meeusen and Van den Broeck (1977). In that model, the random disturbance is composed of the sum of a symmetric and a one-sided random variable. This specification avoids the statistical problems of earlier formulations, while providing a convenient measure of the relative inefficiency. A recent survey may be found in F@sund et al. (1980). The distributional assumptions most commonly made are the zero-mean normal distribution for the symmetric component and the same distribution truncated above zero for the one-sized component.’ With this assumption, the likelihood equation is well defined, and ALS propose maximum likelihood estimation. This method has been widely applied [for examples, see (3), (4) and (5)]. However, recent experience with simulating the properties of competing estimators for this model has indicated that the likelihood function is not entirely well behaved.* We show that the likelihood function always has a stationary point at one particular set of parameter values.3 A condition is given when this point is a local maximum and when it is a

Quality-adjusted Cost Functions and Policy Evaluation in the Nursing Home Industry

Proper evaluation of cost-quality trade-offs inherent in regulatory policy requires identifying the structure of production from the behavioral response of quality to the policy change. However, estimating the structure of production with endogenous quality is difficult because of both measurement problems and data availability. We develop a simple method for identifying and estimating cost functions in the presence of endogenous and unobserved quality. Using this method, we estimate that a quality-adjusted cost function for nursing homes treating quality as exogenous yields seriously misleading estimates of marginal cost and economies of scale. We then used the parameter estimates to evaluate the cost-quality trade-off in nursing home regulatory policy.

Tax Credits, Labor Supply, and Child Care

We explore the impact of the child care tax credit in the U.S. income tax system on the labor supply decisions of married women with young children by incorporating the cost of child care into a structural labor supply model. Using data from the 1986 NLSY, we find that government subsidies to child care increase labor supply substantially. Our policy simulations show that an increase in the value of the child care tax credit (i.e., percent of expenditures subsidized) would have a much larger effect on labor supply than an increase in the annual expenditure limits of the subsidy or making the subsidy refundable.

U.S. Economic Sensitivity to Weather Variability

To estimate the economic effects of weather variability in the United States, the authors define and measure weather sensitivity as the variability in economic output that is attributable to weather variability, accounting for changes in technology and changes in levels of economic inputs (i.e., capital, labor, and energy). Using 24 yr of economic data and weather observations, quantitative models of the relationship between state-level sectoral economic output and weather variability are developed for the 11 nongovernmental sectors of the U.S. economy; temperature and precipitation measures were used as proxies for all weather impacts. All 11 sectors are found to have statistically significant sensitivity to weather variability. Economic inputs were then constant and economic output was estimated in the 11 estimated sector models, varying the weather inputs only using 70 yr of historic weather observations. It was found that U.S. economic output varies by up to

Household Evacuation Decision Making and the Benefits of Improved Hurricane Forecasting: Developing a Framework for Assessment

485 billion year − 1 of 2008 gross domestic product, about 3.4%, owing to weather variability. U.S. states that are more sensitive to weather variability are identified and sectors are ranked by their degree of weather sensitivity. This work illustrates a valid approach to measuring the economic impact of weather variability, gives baseline information and methods for more detailed studies of the sensitivity of each sector to weather variability, and lays the groundwork for assessing the value of current or improved weather forecast information given the economic impacts of weather variability.

United States Demand for Internet Access

Hurricane warnings are the primary sources of information that enable the public to assess the risk and develop responses to threats from hurricanes. These warnings have significantly reduced the number of hurricane-related fatalities in the last several decades. Further investment in the science and implementation of the warning system is a primary mission of the National Weather Service and its partners. It is important that the weather community understand the public’s preferences and values for such investments; yet, there is little empirical information on the use of forecasts in evacuation decision making, the economic value of current forecasts, or the potential use or value for improvements in hurricane forecasts. Such information is needed to evaluate whether improved forecast provision and dissemination offer more benefit to society than alternative public investments. Fundamental aspects of households’ perceptions of hurricane forecasts and warnings and their potential uses of and values for improved hurricane forecast information are examined. The study was designed in part to examine the viability of survey research methods for exploring evacuation decision making and for eliciting values for improved hurricane forecasts and warnings. First, aspects that affect households’ stated likelihood of evacuation are explored, because informing such decisions is one of the primary purposes of hurricane forecasts and warnings. Then, stated-choice valuation methods are used to analyze choices between potential forecast-improvement programs and the accuracy of existing forecasts. From this, the willingness to pay (WTP) for improved forecasts is derived from survey respondents.

Household demand for broadband internet service

This study uses survey data from 2003 to empirically assess United States residential demand for Internet access. Econometric results indicate that service reliability, speed, and the ability to share music and video files are highly valued Internet access attributes. The latter finding suggests commercial development of online file sharing services has potential to generate substantive network effects for access providers, hardware manufacturers, software and content providers. Legal and reimbursement issues need to be resolved between interested telecommunications parties and the entertainment industry to realize these gains in the future.

Household Demand for Broadband Internet in 2010

How much are consumers willing to pay for broadband service?

Properties of technical efficiency estimators in the stochastic frontier model

Abstract This paper uses data from a nationwide survey administered during late 2009 and early 2010 to estimate a random utility model of household preferences for broadband Internet service. Reliability and speed are important service characteristics: the representative household is willing to pay