Public administration labor cost forecasting and wage distribution. An exploratory analysis.

ABSTRACT

The Maastricht Treaty constraints imply a continuous control of the Public Administration (PA) deficit: so there has been an increasing demand for an efficient and effective public expenditure management, especially regarding PA wages (about 12% of Italy's GDP). The Ministry of Economy and Finances (MEF). PA Model forecasts wage dynamics on the basis of economic and normative hypotheses. The labor cost higher increments correspond to the wage settlement years, there is however a background dynamic pattern--more evident in the no wage settlement years--arising from decentralized wage bargaining, personnel seniority, promotions and professional qualifications changes. A homogeneous balanced panel extracted from the PA personnel yearly survey allows an in-depth study on wage distribution levels and dynamics. An important feature of such a study is the information synthesis on each observation average wage by two index numbers--a quantity index of Laspeyres type and a price or wage index of Paasche type--so defined as to jointly measure levels and dynamics of two observation-specific effects. a share, based on the personnel qualifications structure (weighed with a given average national wage), a shift, based on average wages dynamic (weighed with observation-specific personnel qualifications structure).

1. INTRODUCTION

Since the Maastricht Treaty constraints imply a continuous control of the Public Administration (PA) deficit, there has been an increasing demand for an efficient and effective public expenditure management, especially regarding PA wages (about 12% of the GDP). The PA model developed at the Ragioneria Generale dello Stato (RGS; Ministero dell'Economia e Finanze) simulates wage dynamics on the basis of the last realized levels and a set of economic and normative hypotheses (expected inflation, wage settlements, etc.; Venanzoni e Zaghini, 1992). The narrow model dimensions do not permit subnational forecasts; local wage dynamics, not always checked by the Central Government, may however vary over time and influence the General public deficit, which is a Central Government's competence. Moreover the model is mainly based on institutional factors and relations; it is therefore difficult to identify the effects of systematic forecasting errors by model's past performance. The likely clash between centralized constraints and decentralized dynamics is doomed to grow as a consequence of fiscal federalism and public functions decentralization.

Such features are especially relevant for the National Health Service (NHS), due to its intrinsic institutional complexity (Venanzoni, 1994) and the sub-national segmentation of the operational units (local health authorities, hospitals, etc.). The importance of the NHS labor costs (19% of the total Public Sector and over 2,2% of the GDP) requires monitoring and forecasting models, in order to process the mass of accounting and administrative informations brought forth by the system itself.

The NHS labor cost higher increments correspond to the wage settlement years: 1990-91, 1996-97, 2000-01 (Fig. 1). It is however possible to observe a background dynamic pattern--more evident in the years with no wage settlement effects (e.g. 1992-95)--which arises from various sources: decentralized wage bargaining, personnel seniority and promotions, professional qualifications changes, etc. Such factors affect average wages in a locally differentiated way: they can only be identified by a disaggregated data analysis. However, in order to be useful for the national monitoring and forecasting purposes, such analysis results have to be synthesized by means of a limited number of indicators. This approach can be applied to the RGS data set SICO (SIstema COnoscitivo del personale dipendente delle Amministrazioni Pubbliche) which collects from 1997 data on employees, monthly installments and wages paid in each public board. This set contains very disaggregated NHS data (more than 100 different contractual entries for roughly 80 different professional qualifications), although not for individual employees; so a true analysis of the wages size distribution is not possible, unlike the case of the PA departments (e.g. Ministries) for which SICO collects individual informations.

[FIGURE 1 OMITTED]

2. PANEL CONSTRUCTION AND ANALYSIS

A homogeneous balanced panel (323 units over the period 1998-2000, for 969 observations overall) can be extracted from the SICO data set (344 autonomous boards in 1997, 324 in 2000); gross data errors have been corrected in a preliminary analysis, so that the ultimate panel allows us to make a reliable in-depth study. The boards high turn-over--particularly marked in Lombardia due to the NHS reorganization--and their final migration from financial to economic accounting, suggested us to discard 1997 data. Such a short time span restricts the panel analysis; it will be next extended with the 2001-02 data. The survey has no data processing quality control. The preliminary analysis--carried on with a view to the possible administrative and collection errors--found 20 outliers (out of 323 boards) with anomalous standard deviations of monthly per-capita mean wages (total wages divided by total installments); 16 boards have subsequently rectified their original data. To such effect, let's observe the three 1998-2000 non parametric interpolations (histogram with Epanechnikov kernel; Silverman, 1986) of the logarithm of the average per-capita wage (Fig. 2). The distribution, shaped like the normal one (corresponding to a lognormal distribution of the original variable), is rather stable over the three years, apart from a natural translation to the right. However, one could observe a sensible asymmetry, non random irregularities in the tails and a possible multimodality, which suggests the presence of mixtures of distributions.

[FIGURE 2 OMITTED]

Two research strategies are possible. The first consists of a non parametric test on the shape and translations of the distribution over the three years (Pittau-Zelli, 2002); such an approach is not however useful for the essential forecasting purposes stressed in the introduction We should not forget the parallel necessity of an in-depth quality control of the survey itself, in order to identify wrong data, like the ones already checked in the preliminary analysis, but not so large to affect the distribution shape. Such a long and difficult analysis--the first step alone took over a month--would be greatly increased by a parametric search for outliers. One can alternatively assume that the Fig. 2 distributions are indeed mixtures of standard parametric distributions that can be distinguished by the presence of specific factors. The estimation both of the original distribution parameters and the mixtures factors would easily allow us to construct a model in order to monitor and forecast the NHS labor costs.

3. MODEL AND RESULTS

In order to formulate the model, the log-normal distribution is chosen as an approximation to the true distribution. The specific translations factors considered are: region, year (mainly due to wage settlements), category (hospitals, local health authorities, etc.) and scale effects. The sample size allows us to test first-order interactions among the main factors (none is significant). The limited time frame of the panel (3 years for level variables, 2 for differences) only enables us to formulate the model and to test that data do not plainly reject its basic hypotheses. A deeper analysis, related both to the factors and to more general distribution shapes (Mc Donald, 1984), will be possible only with the availability of new panel waves.

The model consists of one identity and four stochastic equations, to be estimated on the pooled data set, with fixed effects panel analysis on residuals. An important feature is that the information contained in the 969 observations on average wages is synthesized by two index numbers: a quantity index Iq (Laspeyres type, 1998 base year) and a price or wage index Iw (Paasche type). They are so defined to jointly measure levels and dynamics of two observation-specific effects: a 'share', based on the personnel qualifications structure (weighed with a given average national wage); a 'shift', based on average wages dynamic (weighed with observation-specific personnel qualifications structure):

ln ([W.sub.i,t]) = ln ([N.sub.i,t]) + ln ([w.sub.i,t])

(1) [??] ln ([N.sub.i,t]) = [a.sub.1] + [[??].sub.r][b.sub.1r][R.sub.r] + [[??].sub.t][t.sub.1t][T.sub.t] + [[??].sub.c][c.sub.1c][C.sub.c] + [[??].sub.1i,t]

(2) ln ([w.sub.i,t]) = [a.sub.2] + [[??].sub.r][b.sub.2r][R.sub.r] + [[??].sub.t][t.sub.2t][T.sub.t] + [[??].sub.c][c.sub.2c][C.sub.c] + [n.sub.2] ln ([N.sub.i,t]) + [q.sub.2] [Iq.sub.i,t] + [w.sub.2] [Iw.sub.i,t] + [[??].sub.2i,t]

(3) [lq.sub.i,t] = [a.sub.3] + [[??].sub.r][b.sub.3r][R.sub.r] + [[??].sub.t][t.sub.3t][T.sub.t] + [[??].sub.c][c.sub.3c][C.sub.c] + [n.sub.3] ln ([N.sub.i,t]) + [[??].sub.3i,t]

(4) [lw.sub.i,t] = [a.sub.4] + [[??].sub.r][b.sub.4r][R.sub.r] + [[??].sub.t][t.sub.4t][T.sub.t] + [[??].sub.c][c.sub.4c][C.sub.c] + [n.sub.4] ln ([N.sub.i,t]) + [[??].sub.4i,t]

Where:

W: total wages; N: monthly installments; t = 1998, 1999, 2000; i = 1, 2, ... l: boards; j = 1, 2, ... J: professional qualifications; [R.sub.r], [T.sub.t], [C.sub.c]: regional, yearly and category vectors of dummies.

[Iq.sub.i,t] = [k.summation over j = 1][n.sub.i,j,t][w.sub..,j,98]/[k.summation over j = 1][n.sub..,j,.][w.sub..,j,98]

[Iw.sub.i,t] = [k.summation over j = 1][w.sub.i,j,t][n.sub.i,j,t]/[k.summation over j = 1][w.sub..,j,98][n.sub.i,j,t]

[n.sub..,j,.] = [T.summation over t = 1][I.summation over i = 1][N.sub.i,j,t]/[T.summation over t = 1][I.summation over i = 1][J.summation over j = 1][N.sub.i,j,t]

[w.sub..,j,98] = [I.summation over i = 1][W.sub.i,j,98]/[I.summation over i = 1][N.sub.i,j,98]

The use of a mean of the relative frequencies over time at the denominator of lq eliminates a downward bias of the index that is due to the presence of numerous zeros because of the introduction of new professional qualifications (a zero for each new one in the base year, and each old one in current years).

The estimation of eq. 1 shows an employees' yearly growth trend of about 0.6%, with no specific factor present. Eq. 2 shows a mean wage yearly growth trend of about 0.4%, lq e lw being equal, with some specific factor present (board category). Eq. 3 shows a quantity index yearly growth trend of about 0.4%, with many specific factors present (regions and board category). Eq. 4 shows a wage index yearly growth trend of about 2%, with many specific factors present, and particularly a growth of 8% in 2000 (wage settlement year). Scale effects are generally absent. The residual panel analysis shows no fixed effects in eqs. 1 and 2; fixed effects are instead found in eqs. 3 and 4, with single boards heterogeneity and residuals autocorrelation. So the analysis shows a NHS labor costs overall yearly growth trend of about 3.4%, without considering wage settlements.

Eq. 2--with high goodness-of-fit ([R.sup.2]C = 0.88) and white noise residuals--is already useful for forecasting purposes, starting from given values of Iq and Iw. The use of Iw, which summarizes each board average wages dynamics, may look a redundancy. As a matter of fact such an index, build from a selection of employees rolls and wages categories, synthetizes and brings to acceptable dimensions all the relevant normative and economic informations about NHS manpower (see note 3). It would so be possible to translate wage settlements hypotheses into Iw values for each board, and to get consistent estimates of total wage bills, at the local regional and national levels. A sample of current information would so allow to monitor NHS labor costs (both expenditure dynamics and data quality): eqs. 1-4, and errors [[??].sub.1i,t]-[[??].sub.4i,t], would swiftly point out significative anomalous dynamics by board, region or overall.

REFERENCES

Mc Donald, J. B., "Some Generalized Functions for the Size Distributions of Income", Econometrica, 52. 1984.

Pittau, M. G. and Zelli, R., "Income Distribution in Italy: a Nonparametric Analysis", Statistical Methods and Applications, 9, 2002.

Silverman, B. W., "Density Estimation for Statistics and Data Analysis", Chapman and Hall, London, 1986.

Venanzoni, G., "Evoluzione e costo del servizio sanitario nazionale", Rivista di Politica Economica, anno LXXXIV, s. III, n. X, Roma, 1994.

Venanzoni, G. and Zaghini, E., "Caratteristiche di un modello disaggregato a breve-medio termine del Settore Pubblico e della Pubblica Amministrazione", Ricerche applicate e modelli per la politica economica, Banca d' Italia, Perugia, 1992.

Dr. Felici Francesco earned his Ph.D. at the University of Rome "La Sapienza" in 2003. Currently he is a Public Finance Econometric Researcher at Consip Spa.

Dr. Bartolucci Tiziana earned his degree in Economic Statistics at the University of Rome "La Sapienza" in 1988. Currently he is a Public Finance Econometric Researcher at Consip Spa.

Dr. Venanzoni Giuseppe earned his degree at the University of Rome "La Sapienza" in 1972. Currently he is Full Professor of Economics and Statistics at the University of Rome "La Sapienza".