NONSURVEY INPUT-OUTPUT ESTIMATION TECHNIQUES: EVIDENCE ON THE STRUCTURE OF ERRORS

ABSTRACT This paper concerns the nature and extent of error introduced to regional input-output multipliers by errors associated with the estimation of regional purchase coefficients (rpc's). Using the Washington State input-output model and computer simulations, estimates of multiplier error are generated for two distinct sources of rpc error. The results indicate that multiplier error from both rpc sources may be significant and support the findings of previous studies which highlight the importance of error introduced to the household purchases column for multiplier accuracy.     

The Net Effects of Large Plant Locations and Expansions on County Employment*

This paper argues that the net economic impact of new firm locations or expansions is determined by a multitude of opposing forces. Using a unique database, I set out to evaluate the net effects of these opposing forces by looking at the net change in local employment and population arising from large (greater than 300 new jobs) firm locations or expansions in the State of Georgia. The analysis suggests that the employment multipliers associated with new firm locations are much less than one; that is, the net employment effect of a large firm opening is smaller than the gross employment impact. This result is consistent with other empirical economic impact studies, which find multipliers much smaller than those of typical input–output models, often less than unity, and a previous study showing little net effect of large plant openings. Expansions of existing establishments are shown to have substantial multiplicative effects, however, with an average employment multiplier of 2.0. I discuss possible reasons for differential impacts across new and expanding firms, focusing on the nature of the firms. Differences in net impact across industries and high‐tech versus low‐tech firms also is evaluated. I find that the impact of large firm locations or expansions on population in the resident county generally is negative, but positive for the broader region encompassing the county of location and its contiguous neighbors.     

THE ROLE OF ERROR STRUCTURE IN SIMULATIONS ON REGIONAL INPUT-OUTPUT ANALYSIS*

Previous simulation experiments on regional input-output analysis have concluded that regional purchase coefficients are more important than technical coefficients in contributing to multiplier accuracy. This paper shows that the multiplicative error structure used in those experiments may have biased the results. A new error structure, combining a multiplicative and an additive component is introduced, and simulations are conducted on randomly generated models. The analysis shows that the results are sensitive to the relative magnitudes of the two error components, as well as to the closure of the model.     

An approximate form for the Chapman grazing incidence function

Numerical modelling of the ionosphere requires repeated evaluation of the Chapman function Ch(x, χ). This normally involves a numerical integration of the Chapman expression. Approximate values can be obtained using accurate tables of the error function integral, but large numerical errors make this approach unusable for values of χ less than about 80°. Algebraic expressions are obtained for the rapid, direct calculation of the Chapman function, at any zenith angle and for scale heights from 6 to 120 km. The maximum errors in this calculation correspond to an error of about 0.03° in the zenith angle, while the rms error is half this amount.     

NoteAbout the Concept of "Net Multipliers"

Net multipliers, as introduced by Oosterhaven and Stelder (2002) accept outputs as entries instead of final demand. They are found by multiplying ordinary multipliers by the final demand ratio over the sector's output. This pragmatic solution suffers from ratio instability over time. The alternative net multipliers proposed here are based on the interpretation of the Leontief inverse matrix for the effects generated at each round. The new solution is not sensitive to the size of impacts. Now net multiplier is equal to the corresponding ordinary multiplier minus one, and the ordering of multipliers is unchanged.     

IMPLAN's Induced Effects Identified Through Multiplier Decomposition

An analysis of regional multipliers is developed to reveal a structural flaw in how IMPLAN computes induced effects. This analysis reveals a fixed ratio across sectors between total and Type I employment multipliers, and that IMPLAN's "Type III" income multipliers are inversely related to the average wages in the direct and indirect sectors, and that "Type III" output multipliers are not affected by wages. A multiplier decomposition is developed that separates direct and indirect effects from the induced and further separates the induced impact into relative wage and regional income retention effects. The decomposition is useful in making comparisons among impact models.     

The accumulation of stochastic copying errors causes drift in culturally transmitted technologies: Quantifying Clovis evolutionary dynamics

The archaeological record is the empirical record of human cultural evolution. By measuring rates of change in archaeological data through time and space it is possible to estimate both the various evolutionary mechanisms that contribute to the generation of archaeological variation, and the social learning rules involved in the transmission of cultural information. Here we show that the recently proposed accumulated copying error model [Eerkens, J.W., Lipo, C.P., 2005. Cultural transmission, copying errors, and the generation of variation in material culture and the archaeological record. Journal of Anthropology archaeology 24, 316–334.] provides a rich, quantitative framework with which to model the cultural transmission of quantitative data. Using analytical arguments, we find that the accumulated copying error model predicts negative drift in quantitative data due to the proportional nature of compounded copying errors (i.e., neutral mutations), and the multiplicative process of cultural transmission. Further, we find that the theoretically predicted rate of drift in long-lived technologies is remarkably close to the observed reduction of Clovis projectile point size through time and space across North America.     

A Map Overlay Error Model Based on Boundary Geometry

An error model for quantifying the magnitudes and variability of errors generated in the areas of polygons during spatial overlay of vector geographic information system layers is presented. Numerical simulation of polygon boundary displacements was used to propagate coordinate errors to spatial overlays. The model departs from most previous error models in that it incorporates spatial dependence of coordinate errors at the scale of the boundary segment. It can be readily adapted to match the scale of error–boundary interactions responsible for error generation on a given overlay. The area of error generated by overlay depends on the sinuosity of polygon boundaries, as well as the magnitude of the coordinate errors on the input layers. Asymmetry in boundary shape has relatively little effect on error generation. Overlay errors are affected by real differences in boundary positions on the input layers, as well as errors in the boundary positions. Real differences between input layers tend to compensate for much of the error generated by coordinate errors. Thus, the area of change measured on an overlay layer produced by the XOR overlay operation will be more accurate if the area of real change depicted on the overlay is large. The model presented here considers these interactions, making it especially useful for estimating errors studies of landscape change over time.     

Errors Caused by Rounded Data in Two Simple Facility Location Problems

As a rule, data to be used in locational analysis are either rounded up or rounded down. Therefore, error is incurred if such location data are used. The objective of this paper is to examine location error and cost error due to rounding in unweighted minisum and minimax problems in one-dimensional continuous space. Several conclusions on rounding effects are obtained by examining the respective mean-squared errors. First, rounding tends to exert more serious influence on the minisum problem than on the minimax problem. Second, in both location problems, the location error shows a pattern that is the inverse of that of the cost error.     

Statistical errors in the determination of wind velocities by the spaced antenna technique

This paper is concerned with the statistical errors which are present when wind velocities in the atmosphere are determined by the radar method known as the spaced antenna technique. It is assumed that the (complex) data is processed by the method known as full correlation analysis (FCA). A theory is first developed to give the error in the determination of the position of the maximum of a cross-correlation function and the value of lag such that the auto-correlation falls to a value equal to that of the crosscorrelation at zero lag. These are the basic quantities needed for the application of FCA. These error estimates are tested with a variety of numerically simulated data and shown to be realistic. The results are applied to real data and, using the standard techniques for the propagation of errors, they lead to estimates of the errors in the derived wind velocities. In order to test these estimates, an experiment was carried out in which two independent wind determinations were made simultaneously. The differences were used to obtain experimental estimates of the errors. It was found that the theory overestimates the error in the wind velocities by about 50%. Possible reasons for this are discussed.     

Accuracy of obsidian hydration dating based on obsidian–radiocarbon association and optical microscopy

Most archaeologists using obsidian hydration dating (OHD) in the United States develop hydration rates from association of obsidian hydration rims with dates based on radiocarbon, subsequently using the rate for chronometric analysis. The overall accuracy of the process has never been quantified. This paper reports an accuracy analysis in which sources of uncertainty are defined and modeled and their effects quantified. A Monte Carlo simulation is used to quantify errors from rate development, while uncertainties in age resulting from chronometric analysis are calculated analytically. For typical ranges of error values, hydration rate errors of ∼5% or less are achievable in the absence of systematic errors, with errors of chronometric age estimates ∼20–30% or less.     

ON THE BIAS OF MULTIPLIER ESTIMATES*

ABSTRACT. This paper considers the bias of the matrix of multipliers when the underlying data are random. The traditional approach is to specify the stochastic nature of the input coefficients directly. It is shown that this approach implies a transactions table which is biased in a most unbalanced way. Next the practitioner's point of view, i.e., taking the transactions table as the source of random errors, is adopted. One of the results states that, within each row of the multiplier matrix, either the biases are zero, or positive biases are canceled out by negative biases in the sense that their weighted average is zero. The conditions are based on the idea that information on aggregates is more exact than information on their details. The usual asumptions of independence and unbiasedness of the individual errors are avoided. The results are shown to have a direct interpretation in connection with the RAS-updating procedure.     

Archaeofaunal Relative Abundance,Sample Size,and Statistical Methods

Tests for correlations between sample size and taxonomic relative abundance are commonly used in zooarchaeological analyses to determine whether observed trends in relative abundance might simply be the result of sampling error. Monte Carlo simulations designed to evaluate the utility of this method indicate that it is inadequate as a means of detecting errors resulting from the incorporation of small samples in an analysis. Among simulated sets of sample assemblages, significant correlatoins between sample size and relative abundance are distributed randomly with respect to whether or not Type II errors concerning trends in relative abundance are present, and are underrepresented in cases in which Type I errors are present. This is because the conditions that are most conducive to correlations between sample size and relative abundance are quite different from the conditions that will lead to erroneous conclusions about the presence or absence of a trend in relative abundance. An alternative chi-square-based statistical method for evaluating trends in sample relative abundance, Cochran's test of linear trend, results in lower rates of both Type I and Type II errors than is the case with previously used correlation-based methods.     

The Encoding-Error Model of Pathway Completion without Vision

We present a model that accounts for errors in short-cutting to complete a triangular pathway by individuals deprived of visual input. The model assumes that systematic error arises from components of navigation concerned with encoding an internal representation of the pathway, rather than the computation of a homeward trajectory or motor output per se. Subjects' tendency to compress the range of actually produced turns and distances, in comparison to the range of correct values, is attributed to regression toward the mean of encoded values during encoding of segments and turns, in the face of uncertainty about the actual values. Individual-subject variations are attributed to differences in the encoding-function parameters, not to variations in the processes themselves. The model provides excellent accounts of data obtained with triangular pathways but fares less well when pathway complexity increases, at which point errors do not appear to be solely attributable to encoding processes. The sources of error identified by the model are likely to play a role in navigation more generally.     

Heterogeneity of Attribute Sampling Error in Spatial Data Sets

This paper considers the standard error of the estimate of the mean of a spatially correlated variable in the case where data are obtained by a process of random sampling. Two distinct mean estimation problems are identified: estimating the area mean and estimating the population mean. Methods are described for obtaining standard error estimates in the two cases and, within the limits of publicly available information, the methods are implemented on average household income data at the census tract scale for Syracuse, New York. The purpose of the paper is to draw attention to issues of data precision in relation to sampled geographic information on averages and in particular to consider the problems of estimating standard errors using such data. The paper also examines the extent to which standard errors vary between census tracts.     

Reducing Errors in Rainfall Estimates through Rain Gauge Location

Facility location models are examined as a framework for generating rain gauge networks designed to reduce errors in mean areal precipitation (MAP) estimation. Errors in estimating MAP may be divided into two types: (i) capture error, not observing a storm which occurs in a gauged area, and (ii) extrapolation error, using a rain gauge measurement to represent a heterogeneous area. In this paper, five rain gauge location models are developed to minimize these errors. The models include adaptations of the maximal covering location problem, the p-median model, and three models derived from multicriteria cluster analysis. The models are tested using precipitation data from an experimental watershed maintained by the U.S. Department of Agriculture in Arizona. Analysis of the results reveals, for the particular watershed, that (1) in sparse networks, location of rain gauges can play a larger role than number of rain gauges in reducing errors in MAP estimates; (2) models based on mean hydrologic data provide nearly as good networks as models based on spatially correlated data; and (3) models yielding the best networks for estimating precipitation for flood predictions are different from the models providing the best precipitation estimates for low flow forecasts.     

A Multivariate Model for Spatio‐temporal Health Outcomes with an Application to Suicide Mortality

This article considers models for multivariate mortality outcomes (e.g., bivariate, trivariate, or higher dimensional) observed over a set of areas and through time. The model outlined here allows for spatially structured and white noise errors and for their intercorrelation. It also includes possible temporal continuity in such types of error via structured temporal effects. An extension to spatially varying regression effects is considered, as well as the option of nonparametric specification of priors for spatial residuals and regression effects. Allowing for spatially correlated intercepts or regression effects may alter inferences regarding the changing impact on mortality of socioeconomic or environmental predictors. The modeling framework is illustrated by an application to male and female suicide mortality in London, focusing on the impact on suicide of deprivation and social fragmentation (“anomie”) in the 33 London boroughs during three periods: 1979–83, 1984–88 and 1989–93. Suicide trends by age group are also considered and show considerable differences in the trends in impacts of deprivation and social fragmentation.     

Quantifying Interpolation Errors in Urban Airborne Laser Scanning Models

Airborne laser scanning (ALS) is becoming an increasingly popular data capture technique for a variety of applications in urban surface modeling. Raw ALS data are captured and supplied as a 3D point cloud. Many applications require that these data are interpolated onto a regular grid in order that they may be processed. In this article, we identify and analyze the magnitudes and spatial patterning of residuals from ALS models of urban surfaces, at a range of different scales. Previous research has demonstrated the effects of interpolation method and scale upon the nature of error in digital surface models (DSMs), but the size and spatial patterning of such errors have not hitherto been investigated for urban surfaces. The contribution of this analysis is thus to investigate the ways in which different methods may introduce error, and to understand the uncertainty that characterizes urban surface models that are devised for a wide range of applications. The importance of the research is shown using examples of how the different methods may introduce different amounts of error and how the uncertainty information may benefit users of ALS height models. Our analysis uses a range of validation techniques, including split-sample, cross-validation, and jackknifing, to estimate the error created in DSMs of urban areas.     

Spatial Interpolation and Disaggregation of Multipliers

Most non-survey methods of estimating single-region multipliers have been shown to produce a systematic upward bias, unless a considerable amount of "superior" data is added. Here it is argued that this conclusion does not need to apply to the case of a non-survey, spatial disaggregation of multipliers. The method proposed consists of four steps with two substantive formulas. The first secures the non-survey interpolation of the lacking intra-regional multipliers for the smaller regions by means of regression. The second secures the non-survey spatial disaggregation of the inter-regional spillovers by means of second-order distance decays. The method is illustrated numerically by means of the interpolation and disaggregation of the 2 × 14 Type II biregional employment multipliers for aggregate Dutch regions into one 40 × 40 inter-regional employment multiplier matrix for the Netherlands as a whole.     

Poverty Reduction and SAM Multipliers: An Evaluation of Public Policies in a Regional Framework

The objective of this paper is to obtain several poverty reduction effects by using multipliers based on social accounting matrices. Expressions relating them to Foster, Greer and Thorbecke poverty measures were derived, and two simulations were carried out for the Spanish region of Extremadura. In the first, we posited a per capita transfer equivalent to certain social policy instruments already existing in this region. Structural path analysis is also used to determine the paths by which poverty reduction effects are transmitted. In the second, we calculate the minimum government expenditure in transfers needed to reduce the regional poverty indices to the national values. The results confirmed that the main feature of poverty in Extremadura is incidence.