Ram Natarajan

Evaluating Contextual Variables Affecting Productivity Using Data Envelopment Analysis

A DEA-based stochastic frontier estimation framework is presented to evaluate contextual variables affecting productivity that allows for both one-sided inefficiency deviations as well as two-sided random noise. Conditions are identified under which a two-stage procedure consisting of DEA followed by ordinary least squares (OLS) regression analysis yields consistent estimators of the impact of contextual variables. Conditions are also identified under which DEA in the first stage followed by maximum likelihood estimation (MLE) in the second stage yields consistent estimators of the impact of contextual variables. This requires the contextual variables to be independent of the input variables, but the contextual variables may be correlated with each other. Monte Carlo simulations are carried out to compare the performance of our two-stage approach with one-stage and two-stage parametric approaches. Simulation results indicate that DEA-based procedures with OLS, maximum likelihood, or even Tobit estimation in the second stage perform as well as the best of the parametric methods in the estimation of the impact of contextual variables on productivity. Simulation results also indicate that DEA-based procedures perform better than parametric methods in the estimation of individual decision-making unit (DMU) productivity. Overall, the results establish DEA as a nonparametric stochastic frontier estimation (SFE) methodology.

Productivity Change, Technical Progress, and Relative Efficiency Change in the Public Accounting Industry

We present evidence on components of productivity change in the public accounting industry toward the end of the 20th century. Using revenue and human resource data from 64 of the 100 largest public accounting firms in the United States for the 1995-1999 period, we analyze productivity change, technical progress, and relative efficiency change over time. The average public accounting firm experienced a productivity growth of 9.5% between 1995 and 1999. We find support for the hypothesis that technical progress rather than an improvement in relative efficiency was the reason for this productivity growth. Firms that were early movers into management advisory services (MAS) and those that emphasized growth in MAS over growth in the traditional audit and tax services enjoyed significantly higher productivity growth than their peers. These firms also contributed significantly more to the industrys technical progress.

Analysis of trends in technical and allocative efficiency: An application to Texas public school districts

Abstract We present a new DEA based method to analyze efficiency trends over time and differences across subgroups in a panel data setting. We employ a result that the aggregate technical and allocative inefficiency score equals the technical inefficiency when input quantities are aggregated into a single total input cost variable, and develop test procedures to evaluate the presence of allocative inefficiency. We apply these methods to test for the presence of allocative inefficiency in Texas school districts over 1993–99, and analyze shifts and trends in both technical and allocative inefficiencies over time for different regions. Our empirical results indicate the existence of statistically significant allocative inefficiencies. While technical inefficiency increased over the six year sample period, allocative inefficiency remained relatively stable during this period. These results for the full sample obtain also when we repeat the analysis for different regions.

DEA-based hypothesis tests for comparing two groups of decision making units

In this paper, we develop five statistical tests to compare the efficiencies of different groups of DMUs. We consider a data generating process (DGP) that models the deviation of the output from the best practice frontier as the sum of two components, a one-sided inefficiency term and a two-sided random noise term. We use simulation to evaluate the performance of the five tests against the Banker tests (Banker, 1993) that were designed for DGPs containing a single one-sided error term. It is found that while the Banker tests are very effective when efficiency dominates noise, the tests developed in this paper perform better than the Banker tests when noise levels are significant.

Evaluating the Adequacy of Parametric Functional Forms in Estimating Monotone and Concave Production Functions

We consider situations where the a priori guidance provided by theoretical considerations indicates only that the function linking the endogenous and exogenous variables is monotone and concave (or convex). We present methods to evaluate the adequacy of a parametric functional form to represent the relationship given the minimal maintained assumption of monotonicity and concavity (or convexity). We evaluate the adequacy of an assumed parametric form by comparing the deviations of the fitted parametric form from the observed data with the corresponding deviations estimated under DEA. We illustrate the application of our proposed methods using data collected from school districts in Texas. Specifically, we examine whether the Cobb–Douglas and translog specifications commonly employed in studies of education production are appropriate characterizations. Our tests reject the hypotheses that either the Cobb–Douglas or the translog specification is an adequate approximation to the general monotone and concave production function for the Texas school districts.

Technological progress and productivity growth in the U.S. mobile telecommunications industry

The fast growing U.S. mobile wireless industry has been experiencing dramatic technological change and substantial competition. As a result of these catalysts, we argue that wireless firms have experienced significant productivity improvement and provide new evidence that technological progress almost exclusively contributed to productivity improvements in the wireless industry by significantly expanding the production possibilities set. We employ nonparametric estimation procedures based on Data Envelopment Analysis (DEA) that utilize input-output data from a representative sample of 16 firms in the mobile wireless industry to estimate productivity change, technological change, and relative efficiency change for the period spanning the years from 2000 to 2002. Our findings show that the industry experienced a significant growth of 13% in productivity, which was primarily due to an average technological progress of 9.9% in the industry. Additionally, we find that national wireless operators experienced significantly higher productivity growth and contributed more to technological progress than regional providers. Firms that were industry pioneers as evidenced by high market share at the beginning of our sample period experienced higher productivity growth and greater technological progress compared to firms with lower initial market share. Moreover, the industry experienced significantly higher productivity growth and technical progress in the later sample period between 2001 and 2002 than in the early period between 2000 and 2001.

Executive compensation contracts and voluntary disclosure to security analysts

We hypothesize that a CEO’s responsiveness to security analysts’ demands for information about the firm is influenced by the structure of the CEO’s compensation package. Our analysis is based on a sample of 469 CEO presentations to security analyst societies by 149 firms during the period 1984‐1988. Consistent with the argu ments of Nagar (1999; 1998) that CEO shareholdings and golden parachutes reduce the cost to the CEO of disclosing proprietary information, we find that CEO share holdings and the presence of golden parachutes are positively associated with the total amount of information that a CEO discloses at an analyst society presentation. Consistent with the argument that CEOs whose cash compensation is sensitive to firm performance have incentives to release bad news so as to lower expectations about future performance and, hence, bonus targets, CEO cash compensation performance sensitivities are positively associated with the CEO’s willingness to disclose bad news.

Recent Advances in Data Envelopment Analysis: An Illustrative Application to the U.S. Public Accounting Industry

In this paper we present some recent methodological innovations in Data Envelopment Analysis and empirical results from the application of these innovations to the U.S. public accounting industry. This paper draws on three different working papers: Banker, Chang and Cunningham (1999), Banker, Chang and Natarajan (1999) and Banker and Natarajan (1999). We describe how a consistent estimator of aggregate technical and allocative inefficiency can be obtained using DEA models and how it can be used to derive firm-specific estimates of allocative inefficiency. We also provide a statistical foundation for the various two-stage methods used in the prior DEA literature to estimate the impact of contextual variables on productivity. Finally, we document the presence of significant technical and allocative inefficiencies in the U.S. public accounting industry and explain the variation in productivity across firms through a set of contextual variables.