A Simulation Study of Joint Uses of Data Envelopment Analysis and Statistical Regressions for Production Function Estimation and Efficiency Evaluation

A previous paper by Arnold, Bardhan, Cooper and Kumbhakar (1996) introduced a very simple method to estimate a production frontier by proceeding in two stages as follows: Data Envelopment Analysis (DEA) is used in the first stage to identify efficient and inefficient decision-making units (DMUs). In the second stage the thus identified DMUs are incorporated as dummy variables in OLS (ordinary least squares) regressions. This gave very satisfactory results for both the efficient and inefficient DMUs. Here a simulation study provides additional evidence. Using this same two-stage approach with Cobb-Douglas and CES (constant elasticity-of-substitution) production functions, the estimated values for the coefficients associated with efficient DMUs are found to be not significantly different from the true parameter values for the (known) production functions whereas the parameter estimates for the inefficient DMUs are significantly different. A separate section of the present paper is devoted to explanations of these results. Other sections describe methods for estimating input-specific inefficiencies from the first stage use of DEA in the two-stage approaches. A concluding section provides further directions for research and use.     

The effects of the gender of children on expenditure patterns in rural China: a semiparametric analysis

We analyse expenditure patterns for rural China, focusing on differences between families with boys and girls. The sample includes more than 5000 nuclear families from 19 Chinese provinces. Following the existing literature, we estimate Engel curves for food and for alcohol, a typical adult good. We use a flexible, partially linear specification and allow for endogeneity of total expenditures. The results are similar to those of other studies, not providing much evidence of gender differentials. We then focus on the decision to send a child to school and on the budget share spent on educational goods. Using both parametric and semiparametric estimates, we find evidence that boys are more often sent to school and that expenditures on a boy that goes to school are larger than for a school‐going girl of the same age. Copyright © 2005 John Wiley & Sons, Ltd.     

Allowing for inefficiency in parametric estimation of production functions for urban transit firms

Efficient versus inefficient observations are first identified and evaluated numerically by the nonparametric free disposal hull (FDH) method. Next, parametric production frontiers are obtained by means of estimating translog production functions through OLS applied to the subset of efficient observations only. Technical progress is included at both stages. Monthly data from three urban transit firms in Belgium, to which this two-stage technique is applied, show widely varying degrees of efficiency over time and across firms, and much less technical progress than standard (i.e., non frontier) econometric estimates suggest.     

School district quality and property values: Examining differences along school district boundaries

Examining differences across school district boundaries rather than school attendance zone boundaries has several advantages. These advantages include being applicable when attendance zones are not available or less relevant to educational outcomes as arises with within district school choice and for examining the effect of factors like school spending or property taxes that do not vary within districts. However, school district boundaries have often been in place for many years allowing households to sort based on school quality and potentially creating distinct neighborhoods on either side of boundaries. We estimate models of housing prices using repeated cross-sections of housing transactions near school district boundaries in Connecticut. These models exploit changes over time to control for across boundary differences in neighborhood quality. We find significant effects of test scores on property values, but those effects are notably smaller than both OLS and traditional boundary fixed effects estimates.     

The effect of environmental regulation on environmental innovation

Environmental expenditure estimates resulting from US environmental policy are based on current technology which may overstate policy's true costs. Existing evidence shows that ex ante cost estimates are greater than realized costs due to unexpected technological progress. This research programme asks whether innovation is a response to environmental regulation or whether the true regulatory compliance costs are overestimated ex ante when technological advancement is ignored? The author conducts an empirical study of the US manufacturing industry's environmental patent activities and environmental regulation as measured by pollution abatement and control expenditure (PACE) data. She finds a statistically significant positive relationship between environmental regulation and innovation when estimated by ordinary least squares (OLS). However, the OLS coefficient of pollution abatement costs is inconsistent because of a correlation between the explanatory variable and unobservable variables. Two-staged least squares addresses the inconsistency problem, resulting in positive and significant PACE coefficients. Thus, there is evidence that innovation is a response to environmental regulation. © 1998 John Wiley & Sons, Ltd and ERP Environment.     

A model of local demand for education

A careful modeling of the spending behavior of local school districts in New Jersey is presented. The theoretical model relies on the common hypothesis of political competition leading to a median outcome as well as the assumption that school superintendents act as budget maximizers. The model is estimated for a sample of 177 school districts under three different aid formulas. Pooling of the cross sections suggests that the response of school expenditures to changes in variables other than those associated with school aid parameters has remained constant over time. The results are discussed in the context of recent theories regarding the effect of intergovernmental aid on the level of public expenditure.     

Growth and government: Is there a difference between developed and developing countries?

I examine the role of government in the growth of 64 industrialized and developing countries, considering both expenditure and financing aspects of government. Recognizing that there may be differences between the two country groups, I estimate both standard OLS and dummy variable regressions. The general conclusion is that although most fiscal variables are not significantly related to economic growth, the means of financing matters more than government spending. I find that seigniorage and the budget surplus are important for growth, but the LDCs is the group that drive the results in all regressions.     

Indirect inference in structural econometric models

This paper considers parametric inference in a wide range of structural econometric models. It illustrates how the indirect inference principle can be used in the inference of these models. Specifically, we show that an ordinary least squares (OLS) estimation can be used as an auxiliary model, which leads to a method that is similar in spirit to a two-stage least squares (2SLS) estimator. Monte Carlo studies and an empirical analysis of timber sale auctions held in Oregon illustrate the usefulness and feasibility of our approach.     

The economic returns to schooling for Italian men. An evaluation based on instrumental variables

We study the relationship between (log) hourly earnings and schooling for male household heads in Italy, using cross-sectional data from the 1993 and 1995 waves of the Bank of Italy (BI) survey on the income and wealth of Italian households. In line with international evidence, we find that OLS under-estimate the return to schooling. When the endogeneity of schooling is taken into account, the return to an additional year in school increases from 4.8% to 5.6%. This estimate is lower than the estimates tabulated by Card [Card, D., 1994. Earnings, Schooling and Ability Revisited. NBER Working Paper no. 4832.] for the United States. We also find evidence that this return increases with higher levels of educational attainment.     

Returns to education in Portugal

This paper compares OLS and IV estimates of the returns to education for male workers in Portugal. The results suggest that OLS estimates of the return to education are broadly in line with results for other western economies, although they are marginally at the upper end of the scale. IV estimates of the return to education are as high or lower than those obtained with OLS. Apparently, OLS estimates provide an upper-bound of the return to education. However, due to the nature of the identifying strategy, a generalisation of the results to the entire population may be premature.     

Estimating a public school expenditure model under binding spending limitations

A model explaining desired expenditure on education is estimated for a sample of New Jersey school districts. Because the limit on annual increases in school spending is binding for a subsample of jurisdictions, the Tobit estimation procedure is used. We test for equality of the pre- and postlimitation structures and find substantial similarity. The cap on expenditure increases was part of a court-ordered reform of New Jersey school finance law. The results can be used to explain the failure of the existing school finance laws in lessening expenditure disparities at the lower end of the distribution.     

Poverty and crime in 19th century Germany

We estimate the impact of poverty on crime in 19th century Bavaria, Germany. Rainfall is used as an instrumental variable for grain (rye) prices to address econometric identification problems in the existing literature. The rye price was a major determinant of living standards during this period. The rye price has a positive effect on property crime: a one standard deviation increased property crime by 8%. OLS estimates are twice as large as instrumental variable estimates, highlighting the value of our empirical approach. Higher rye prices lead to significantly less violent crime, though, and we argue that higher beer prices, caused by the higher rye prices, are a likely explanation.     

Quantile models and estimators for data analysis

Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate than the regression quantiles.     

Matching and semi-parametric IV estimation, a distance-based measure of migration, and the wages of young men

Our paper estimates the effect of US internal migration on wage growth for young men between their first and second job. Our analysis of migration extends previous research by: (i) exploiting the distance-based measures of migration in the National Longitudinal Surveys of Youth 1979 (NLSY79); (ii) allowing the effect of migration to differ by schooling level and (iii) using propensity score matching to estimate the average treatment effect on the treated (ATET) for movers and (iv) using local average treatment effect (LATE) estimators with covariates to estimate the average treatment effect (ATE) and ATET for compliers.We believe the Conditional Independence Assumption (CIA) is reasonable for our matching estimators since the NLSY79 provides a relatively rich array of variables on which to match. Our matching methods are based on local linear, local cubic, and local linear ridge regressions. Local linear and local ridge regression matching produce relatively similar point estimates and standard errors, while local cubic regression matching badly over-fits the data and provides very noisy estimates.We use the bootstrap to calculate standard errors. Since the validity of the bootstrap has not been investigated for the matching estimators we use, and has been shown to be invalid for nearest neighbor matching estimators, we conduct a Monte Carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching. The data generating processes in our Monte Carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values. The estimated standard errors from the bootstrap are very close to those from the Monte Carlo experiments, which lends support to our using the bootstrap to calculate standard errors in our setting.From the matching estimators we find a significant positive effect of migration on the wage growth of college graduates, and a marginally significant negative effect for high school dropouts. We do not find any significant effects for other educational groups or for the overall sample. Our results are generally robust to changes in the model specification and changes in our distance-based measure of migration. We find that better data matters; if we use a measure of migration based on moving across county lines, we overstate the number of moves, while if we use a measure based on moving across state lines, we understate the number of moves. Further, using either the county or state measures leads to much less precise estimates.We also consider semi-parametric LATE estimators with covariates (Frölich 2007), using two sets of instrumental variables. We precisely estimate the proportion of compliers in our data, but because we have a small number of compliers, we cannot obtain precise LATE estimates.     

TECHNOLOGICAL INNOVATION AND EMPLOYMENT IN DERIVED LABOUR DEMAND MODELS: A HIERARCHICAL META‐REGRESSION ANALYSIS

The effect of technological innovation on employment is of major concern for workers and their unions, policy makers and academic researchers. We meta‐analyse 570 estimates from 35 primary studies that estimate a derived labour demand model. We contribute to existing attempts at evidence synthesis by addressing the risks of selection bias and that of data dependence in observational studies. Our findings indicate that: (i) hierarchical meta‐regression models are sufficiently versatile for addressing both selection bias and data dependence in observational data; (ii) innovation's effect on employment is positive but small and highly heterogeneous; (iii) only a small part of residual heterogeneity is explained by moderating factors; (iv) selection bias tends to reflect preference for upholding prevalent hypotheses on the employment effects of process and product innovations; (v) country‐specific effect‐size estimates are related to labour market and product market regulation in six OECD countries in a U‐shaped fashion; and (vi) OLS estimates reflect upward bias whereas those based on time‐differenced or within estimators reflect a downward bias. Our findings point out to a range of data quality and modelling issues that should be addressed in future research.     

A note on “estimating school district expenditure functions under conditions of closed-end matching aid”: Closed-end matching aid in the context of a two-part tariff

An alternative approach to estimating school district expenditure functions when the budget constraint is kinked is offered. Proper parameterization of the budget constraint permits one to estimate the expenditure function without using a censored sample procedure.     

The Hiring Function Reconsidered: on Closing the Circle

This paper investigates the matching of job searchers with vacant jobs: a key component of the dynamics of worker reallocation in the labour market. The job searchers may be unemployed, employed or not in the labour force and we estimate matching or hiring functions including all three groups. We show that previous studies, which ignore both employed job seekers and unemployed job seekers who are considered to be out of the labour force, produce biased estimates of the coefficients of interest. By considering only unemployment outflows into jobs and ignoring interdependencies with other flows, these studies overlook an important aspect of job matching. Our estimates on Australian data support a more general approach and produce models that dominate those proposed previously. We find that concentrating on the aggregate matching function alone does not reveal the full extent of the interaction across job searchers. Indeed, we find that job searchers from the three groups do not receive a fair share of hires: there appears to be segmentation of hiring opportunities which may be explained by a form of ranking of applicants. Together these results demonstrate that the disaggregate worker flows and their interdependence are key features on the labour market and should be included in studies of the hiring process.     

Estimation of data measured with error and subject to linear restrictions

Variables are often measured subject to error, whether they are collected as part of an experiment or by sample surveys. A consequence of this is that there will be different estimates of the same variable, or, more generally, linear restrictions which the observations should satisfy but fail to. With knowledge of the variances of the various observations, it has been shown elsewhere that maximum-likelihood estimates of the observations can be produced. This paper shows how, given a sequence of such observations, estimates can be produced without knowledge of data reliabilities. The method is applied to estimates of constant price US GNP. It suggests that 64 per cent of the discrepancy should be attributed to the expenditure estimate, with only 36 per cent going to the income/output estimate. The current method of presentation, on the other hand, places the whole of the error in the income/output estimate.     

Inconsistency of the OLS estimator of the partial adjustment-adaptive expectations model

Following elimination of unobservable quantities it is assumed that the disturbance in the partial adjustment-adaptive expectations model follows a first-order moving average. The inconsistency of OLS is derived and calculated for different parameter values. The results indicate that the inconsistency in the estimate of the long-run elasticity is very small but that the short-run elasticity is likely to be seriously overestimated. Also, if OLS is used, it is quite probable that the model will be incorrectly rejected in favour of the partial adjustment (or the adaptive expectations) model by itself.     

Self-selection bias and cost-of-living estimates

Due to continued interest in geographic living-cost differentials, some researchers have used data from the ACCRA Cost of Living Index. This paper explores further the potential for using ACCRA data for cost-of-living research. In particular, it investigates the possibility of self-selection bias affecting OLS estimates using ACCRA data. The findings indicate that self-selection bias is a concern that researchers using ACCRA data should be aware of. Results using Heckman’s two-step procedure to estimate a cost-of-living model indicate promise for using ACCRA data to update and expand upon previous cost-of-living research. The author wishes to acknowledge Keith Ihlanfeldt and Cynthia Rogers for constructive comments on an earlier version of this paper presented at the 35th Meeting of the Southern Regional Science Association and also wishes to thank the two anonymous referees for their suggestions on improving the paper.