Thesis
Reference
Contributions to the theory and practice of latent variable modelling and causal inference
FALCIOLA, Justine
Abstract
Unobservable concepts are frequent in economics: utility, expectations, beliefs, competitiveness of firms, productivity of a worker can all be viewed as latent variables.
Although not directly observable, each of these concepts can be indirectly measured by some related observable indicators. The first two chapters of this thesis provide a deeper understanding of the tools available to empirical researchers to measure latent variables. In the first chapter, we use factor analysis to measure decent work which was originally conceptualized by the International Labour Organization. In the second chapter, we investigate bias correction methods when factor scores are used as regressors. Focusing on nonlinear regression including covariates, we propose two bias-corrected estimators. Finally, in the third chapter, we show the detrimental effect of small amounts of contaminated data on the estimated causal impact of treatment and propose robust version of standard causal inference estimators.
FALCIOLA, Justine. Contributions to the theory and practice of latent variable modelling and causal inference. Thèse de doctorat : Univ. Genève, 2021, no. GSEM 96
DOI : 10.13097/archive-ouverte/unige:150268 URN : urn:nbn:ch:unige-1502689
Available at:
http://archive-ouverte.unige.ch/unige:150268
Disclaimer: layout of this document may differ from the published version.
1 / 1
modelling and causal inference
by
Justine Falciola
A thesis submitted to the
Geneva School of Economics and Management, University of Geneva, Switzerland,
in fulfillment of the requirements for the degree of PhD in Econometrics
Members of the thesis committee:
Prof. Eva Cantoni, Chair, University of Geneva Prof. Jaya Krishakumar, Supervisor, University of Geneva
Prof. Blaise Melly, University of Bern Prof. AlekseyTetenov, University of Geneva
Thesis No. 96 February 2021
Gen`eve, le 24 f´evrier 2021
Dean Marcelo OLARREAGA
I would like to thank the many people that supported me both academically and personally during the Ph.D. adventure. First of all, I would like to express my gratitude to Marco for introducing me to research and for all his support throughout this journey. I would also like to thank my supervisor Jaya Krishnakumar and the members of the jury, Eva Cantoni, Aleksey Tetenov, and Blaise Melly for accepting being part of the thesis committee, for their careful reading of this dissertation, and very helpful discussions.
I am grateful to my professors, colleagues, and friends at the Geneva School of Eco- nomics and Management and in particular to Angela, Fede, Chen, and Ingrid. I also want to thank my great friends Karelle, Ingrid, and Kristina for their caring presence.
Finally, a special thought goes to my family for their inestimable support and uncon- ditional love.
Unobservable concepts are frequent in economics: utility, expectations, beliefs, competi- tiveness of firms, productivity of a worker can all be viewed as latent variables. Although not directly observable, each of these concepts can be indirectly measured by some related observable indicators. The first two chapters of this thesis provide a deeper understand- ing of the tools available to empirical researchers to measure latent variables. In the first chapter, we use factor analysis to measure decent work which was originally conceptu- alized by the International Labour Organization. In the second chapter, we investigate bias correction methods when factor scores are used as regressors. We propose a unified framework that deals with the use of factor scores as explanatory variables both in linear as well as nonlinear regression. Focusing on nonlinear regression including covariates, we suggest a first bias-corrected estimator. Then, we propose a modified IV estimator to tackle situations with endogeneity and factor scores in the covariates. Finally, in the third chapter, we explore the role that robust statistics can play in causal inference. We show the detrimental effect of small amounts of contaminated data on the estimated causal impact of treatment and propose robust version of standard causal inference estimators.
Acknowledgements i
Abstract iii
Introduction 1
1 Towards a Work Wellbeing Index: A Model-Based Approach 3
1.1 Introduction . . . 4
1.2 Econometric model . . . 6
1.3 Confirmatory Factor Analysis . . . 7
1.3.1 Data . . . 7
1.3.2 Empirical strategy . . . 7
1.3.3 CFA estimation results . . . 9
1.3.4 Goodness of fit statistics . . . 10
1.4 Sensitivity analyses . . . 12
1.4.1 Estimation of the whole model . . . 12
1.4.2 Continuous versus categorical indicators . . . 12
1.4.3 Assessing normality . . . 13
1.4.4 Handling missing data . . . 13
1.5 Work Wellbeing Index . . . 13
1.6 Concluding remarks . . . 21
2 Bias-corrected Nonlinear Regression when using estimated factor scores as regressors 39 2.1 Introduction . . . 40
2.2 Model specification . . . 41
2.2.1 Nonlinear regression . . . 41
2.2.2 Factor model . . . 43
2.2.3 Bias of naive plug-in estimator . . . 43
2.3 Bias correction . . . 44
2.3.1 Unbiased estimating equations . . . 45
2.3.2 Sufficiency-IV estimator . . . 46
2.4 Asymptotics . . . 47
2.4.1 Statistical properties of the sufficiency estimator . . . 47
2.4.2 Statistical properties of the sufficiency-IV estimator . . . 48
2.5 Simulation study . . . 49
2.5.1 No endogeneity . . . 50
2.5.2 Endogeneity . . . 53
2.6 Empirical illustration . . . 60
2.7 Concluding remarks . . . 65
2.8 Proofs . . . 66
2.9 Appendix . . . 69
3 A robust statistics perspective of causal inference 75 3.1 Introduction . . . 76
3.2 Background . . . 77
3.2.1 Potential outcomes framework for causal inference . . . 77
3.2.2 Robust statistics framework . . . 77
3.2.3 M-estimators . . . 78
3.3 Randomized experiments and covariate adjustments . . . 79
3.3.1 Randomized experiments, a gold standard . . . 79
3.3.2 Covariate adjustments for randomized experiments . . . 80
3.3.3 Bounded influence approach . . . 81
3.4 Observational studies . . . 83
3.4.1 Inverse probability weighted estimators . . . 83
3.4.2 Robust IPW estimator . . . 84
3.4.3 Robust AIPW estimator . . . 89
3.5 Simulation study . . . 91
3.5.1 Randomized experiments estimator . . . 91
3.5.2 IPW estimators . . . 99
3.6 Empirical application . . . 102
3.7 Concluding remarks . . . 114
tiveness of firms, productivity of a worker can all be viewed as latent variables. Although not directly observable, each of these concepts can be indirectly measured by some related observable indicators. Structural equation models (SEM) provide a suitable tool to make inference on latent concepts using the information on the observed indicators. They con- sistently estimates the latent variables by combing the relationship between indicators and the latent factors, i.e. the measurement model, with the structural relationships among the factors and other covariates (Bentler and Chou,1987;Werts et al.,1973). Factor score regression provides an intuitive alternative to SEM by decomposing the estimation of the model in two steps. First, a factor analysis model is performed to estimate and predict the latent variables, i.e. derive factor scores. These factor scores are then typically used as observed explanatory variables in a regression analysis. Factor scores can be calculated using different methodologies and contain errors that should be accounted for in the en- suing regression analysis. Failing to consider the uncertainty associated with factor scores causes regression coefficients to be biased and inconsistent (Bollen, 1989; Hoshino and Bentler, 2011). However, factor score regression is still widely used in empirical research (DiStefano et al., 2009).
The first two chapters of this thesis provide a deeper understanding of the tools available to empirical researchers to measure latent variables.
In the first chapter, we use factor analysis to measure an unobserved concept: decent work. In 1999, the International Labour Organization (ILO) introduces the concept of decent work which rests on four pillars: employment, social protection, workers’ rights and social dialogue. Since then, the ILO has committed to promote full and productive employment as well as decent work as also attested by Goal 8 of the Sustainable Develop- ment Goals (SDGs). In any effort to reach this goal and allow for efficient monitoring of progress, adequate measurement of the latent decent work is crucial. Based on the four main concepts of decent work proposed by the ILO, we develop a Work Wellbeing Index offering a comprehensive picture of the employment dimension. Our index ambitions to go beyond productive work as the sole focus of employment by considering other aspects such as vulnerability in employment and social protection. The Work Wellbeing Index also aims to capture the extent to which the legal framework and the social dialogue of a country promote or hinder decent work. We use a factor analysis with multiple dimen- sions (i.e. factors) and several indicators for each factor to construct a framework and measure decent work. This data-driven technique allows for an objective estimation of the weights used in the aggregation of the different indicators as well as dimensions of the Work Wellbeing Index. Finally, our study analyses the evolution of this index over time, by region and income classes. We propose country profiles using radar plots to follow the evolution of decent work in its four dimensions. We also examine bivariate relationships between this index and other socio-economic factors such as human development, income and education.
In the second chapter, we propose to investigate bias correction methods when factor scores are used as regressors in nonlinear models. It is widely acknowledged that re- gressions with factor scores in the covariates produce biased and inconsistent estimators (Bollen, 1989; Hoshino and Bentler, 2011). Literature has proposed methods to reduce or correct bias in factor score regression although the focus was primarily on linear re- gression (Bollen,1989; Hoshino and Bentler,2011; Skrondal and Laake,2001;Gon¸calves, 2015). In this second chapter, we expand the existing literature to consider factor score regression in Generalized Linear Models (GLM). We link the issue of bias when using predicted latent scores in regression to the literature on measurement error. This allows us to build on the seminal work of Fuller (1987) and subsequent authors (Stefanski and Carroll, 1985, 1987; Carroll et al., 2006; Cook and Stefanski, 1994; Huang and Wang, 2001; Rabe-Hesketh et al., 2003; Schennach, 2004; Schofield, 2015) to propose a unified framework which deals with the use of factor scores as explanatory variables both in linear as well as nonlinear regression. Focusing on nonlinear regression including covariates, we suggest a first bias-corrected estimator. Then, we propose a modified IV estimator to tackle situations with endogeneity and factor scores in the covariates.
In the third chapter, we explore the role that robust statistics could play in causal in- ference. Robust statistics considers models as idealized approximations of reality and acknowledges that they rest on specific distributional assumptions. It provides methods that are robust to small deviations from the stochastic assumptions of the model. Book- length references on the topic include (Huber,1981; Huber and Ronchetti,2009;Hampel et al.,1986; Maronna et al.,2019). We show the effect of small amounts of contaminated data on the estimated causal impact of treatment on the outcome of interest. We pro- pose robust version of standard causal inference estimators. We consider methods such as covariate adjustments in randomized experiments and propensity score weighting in observational studies. We show in simulation studies that the proposed estimators have better robustness properties both in contaminated or regular scenarios.
Towards a Work Wellbeing Index: A
Model-Based Approach
1.1 Introduction
Measuring the “human development” of a country in order to monitor its progress is cen- tral to development debates. Since the first Human Development Report in 1990, three major dimensions have been recurrently analysed in the literature: material well-being, health and education. The Human Development Index (HDI) opened the door to many other indices ranging from quantitative aspects at their core to the inclusion of more sub- jective measures of well-being. Adherent to the idea that GDP and economic statistics do not give a complete picture of well-being across countries, the OECD proposed a Better Life-Index based on 11 topics in the areas of material living conditions and quality of life.
While a lot of focus has been put on education and health as the main components of human development, it seems that the employment has received comparatively less consideration in the literature on human development. The International Labour Organ- isation (ILO) drew the attention of the international community on the importance of addressing people’s well-being at work. The Director-General of ILO, Juan Somav´ıa was the first to introduce the concept of decent work in 1999, described as “opportunities for women and men to obtain decent and productive work in conditions of freedom, equity, security and human dignity” (Somavia,1999). The concept rests on four pillars: workers’
rights, employment, social protection and social dialogue. The first one is concerned with fundamental principles and rights at work. At its center, one finds the promotion of the Declaration on Fundamental Principles and Rights at work adopted in June 1998. The attention is set on the recognition of the right to freely associate and bargain, the abolition of forced labour -particularly child labour- as well as the elimination of all sorts of dis- crimination at work. The second and third goals of the Decent Work Agenda (ILO,2019) are respectively promoting employment and incomes for men and women and strength- ening social protection and social security. In its very definition of decent work, the ILO strives to promote the creation of employment indissolubly of its inherent quality. These two objectives encompass many aspects notably promoting widespread access to adequate employment, reducing gender inequalities in the work space, strengthening social protec- tion and expanding social security to only name a few. Finally, the ILO emphasises the relevance of strengthening social dialogue and tripartism to enhance decent work.
The importance of decent work is nowadays well recognized. Since the UN General As- sembly in September 2015, decent work and the four pillars of the Decent Work Agenda are essential components of the 2030 Agenda for Sustainable Development (SDGs,2015).
As highlighted by the 8th goal of the Sustainable Development Goals (SDGs), promoting full and productive employment as well as decent work has become a key area of engage- ment for the ILO and its constituents.
Since the first conceptualization of decent work by the ILO in its ground-breaking 1999 report (Somavia,1999), literature has put a strong focus on the measurement issue. Anker et al. (2003) identify a wide range of indicators readily available to materialize, measure and monitor decent work. In their view, it is the only way for countries to effectively gauge progress and enhance decent work. Ghai (2003) develops a first index of decent work for 22 OECD countries.1 His study considers quantitative aspects only. Bescond et al. (2003) present a composite index of decent work deficits (DWDs) for 40 countries
1The countries were mostly chosen for their comparable institutions and employment structure.
(2003) establish three distinct levels - the aggregated, the workplace and the individual one - on which decent work should be explored. At the macro level, decent work indices are computed for 84 countries and their relation to other key indicators (i.e. the HDI, in- come inequalities and GDP per capita) is analysed. Ahmed(2003) investigates the impact of promoting decent work on economic growth as well as development. He studies three existing indicators: the Human Development Index, the Decent Work Deficits (DWDs) and the per capita gross domestic product.
This chapter develops a Work Wellbeing Index (or a Decent Work index3) in an attempt to offer a comprehensive picture of the employment covering all the four pillars. Our Work Wellbeing Index explicitly acknowledges that qualitative measures of employment are equally important as the quantitative ones. The index summarizes complex multi- faceted realities of the work dimension by going beyond productive work as the sole focus of employment. Rather it is concerned with ”(...) security in the workplace and social protection for families, better prospects for personal development and social integration, freedom for people to express their concerns, organize and participate in the decisions that affect their lives and equality of opportunity and treatment for all women and men.” (ILO, 2019).
This chapter extends the existing literature on decent work measurement on the fol- lowing aspects. First, rights at work are explicitly taken into account in the construction and the measurement of the index. We try to capture the extent to which the legal frame- work promotes or hinders decent work by including information on the ratification of ILO conventions and protocols as well as measures of actual rights of workers. Second, this chapter proposes to measure decent work using statistical tools. We use a suitable sta- tistical method namely factor analysis to construct a framework to measure decent work.
This data-driven technique also allows for an objective estimation of the weights used in the aggregation of the different indicators as well as dimensions of the Work Wellbeing Index. Third, our Work Wellbeing Index includes an extensive list of indicators from various data sources to capture multiple aspects within each dimension. It is also com- puted for a variety of countries and adds perspective by spanning over several time periods.
The rest of the chapter is structured as follows. Section 1.2 briefly introduces the econo- metric model used in this chapter. Section1.3presents the empirical factor model adopted to measure decent work, the estimation results as well as a set of goodness of fit statistics.
Section 1.4 provides alternative robustness scenarios. Section 1.5 presents and analyses the final measure of decent work: the Work Wellbeing Index. Section 1.6 ends with some concluding remarks.
2The indicators chosen are earnings measured by hourly pay, hours worked, unemployment, male- female gap in the labour force participation and pension for old age.
3We use the term Work Wellbeing Index and Decent Work index in an inter-changeable manner throughout this chapter.
1.2 Econometric model
The econometric model is specified as a Confirmatory Factor Analysis (CFA) as described inBollen(1989) andMuth´en(1984). The general measurement model is defined as follows:
xi =ν+h(ξi) +δi i= 1, ..., n (1.1) where i denotes the country, ν is a (p×1) vector of intercepts, xi is a (p×1) vector of indicators, ξi is a (m×1) vector of latent factors and δi is a (p×1) measurement error vector. We specify a function h(·) to link the vector of observed indicators xi to the vec- tor latent factorsξias the model may include continuous as well as dichotomous indicators.
In the case of continuous indicators, the relation between the vector of observed indi- cators xi to the vector latent factors ξi is linear. Then equation 1.1 becomes
xi =ν+ Λξi+δi i= 1, ..., n (1.2) where Λ is a (p×m) matrix of factor loadings.
Ensuing from this specification, each particular λj contained in Λ can either be inter- preted as a factor loading or as the regression coefficient of xij =νj+λjξi+δij, where j denotes the indicator. In the latter, λj stands for the expected change inxij for one unit of change in ξi considering the other latent factors as constant.
In the case of binary indicators (i.e. the conventions ratified or the worker’s rights in our empirical model), the relationship described in (1.1) by the function h(·) is non lin- ear. The measurement model for one particular indicator, for instance the jth one, can be written as follows
xij =
1, if ˜xij ≥0 0, if ˜xij <0
˜
xij =νj+λjξi +δij
(1.3)
The variable xij is a dichotomous indicator taking the value 1 when a certain convention is adopted by a country and 0 otherwise and ˜xij is a continuous latent response variable.
We specify the stochastic assumptions of the model as:
E(ξi) = 0, E(δi) = 0 (1.4)
var(ξi) = Φ (1.5)
var(δi) = Θ (1.6)
cov(ξi, δi) = 0 (1.7)
The covariance matrix of the latent variables, Φ, is constrained to be identity whereas the covariance matrix of the measurement errors, Θ, is not. For the latter, the errors are allowed to be correlated whenever the correlation if found to be significant4.
4We tested the significance of each covariance between the measurement errorscov(δij, δik). Only the covariances significant at 5% level were kept in the model.
1.3.1 Data
Table 1.3 describes the list of indicators that we could collect to conceptualize and mea- sure the four pillars of decent work namely Rights at work, Employment Opportunities, Social Protection & Vulnerable Employment and Social Dialogue. These indicators come from several datasets. We build upon an initial database by Krishnakumar and Sarti (2013). The final dataset is a collection of various data sources including Kilm 8th (ILO KILM, 2015), ILOStat (ILOStat, 2015a), Laborsta (ILO Laborsta, 2015), ILO Social Se- curity Database (ILOStat, 2015b), OECD.StatExtracts (OECD, 2015), the World Bank (World Bank, 2015) and Rama (Rama and Artecona, 2002) that contain information on various aspects of employment as well as social protection. More qualitative measures on rights protection were obtained from the ILO Normlex database (ILO Normlex, 2015) as well as the Cingranelli-Richards Human Rights database (CIRI, 2014). Finally, the variables measuring social dialogue are taken from Vissier Version 5.0 (Visser, 2015) as well as ILOStat (ILOStat, 2015a).
Our analysis spans over the time period 1990-2015 and analyses information for 1’092 observations across 42 countries. Since we do not wish to restrict our analysis to only European countries, we try to achieve the best comprise between including as many key indicators as possible and retaining countries representing all the regions of the world.
Table 1.4 in Appendix reports information on country coverage by world regions and in- come levels as defined by the World Bank. We see that about 70% of the sample are high income OECD countries and mostly from Europe. The remaining 30% include countries from other income classes or regions of the world such as East Asia, Middle East & North Africa, Latin America or North America.
Due to substantial amount of missing values on key indicators, we turn to imputation methods to handle missing information. We rely on linear interpolation for replacing missing values. This appears to be a reasonable choice as the indicators exhibit little to almost constant changes over time which can be modelled using a linear trend. The issue of missing information is further assessed in section 1.4 of the chapter.
1.3.2 Empirical strategy
We build our theoretical model to measure decent work as proposed in Figure 1.1. As usual in the social science literature, observed variables are represented by rectangles whereas latent variables are indicated by ellipses. To render the path diagram more ev- ident, we omit the measurement errors in the figure. However, note that measurement errors are allowed to correlate whenever the added path is significant at the 5 percent level.
We estimate the model presented in Figure 1.1 following a two-step procedure. In the first step, each pillar of decent work is estimated separately through linear factor analysis.
We use Thomson factor scores (Thomson,1935) and obtain predicted values for our four latent pillars: Rights at work, Employment Opportunities, Social Protection & Vulnera- ble Employment and Social Dialogue. The estimation results are available in subsection 1.3.3. The second step that we perform is an aggregation step. We aggregate the four dimensions measuring decent work into our Work Wellbeing Index in several ways. One
proposition is to aggregate the four dimensions through second order factor analysis. Af- ter having estimated our model in a first stage, we use the predicted values for each pillar as indicators of the latent concept of Decent Work. Another proposition is to aggregate the predicted values through an arithmetic mean.5 Further details about the aggregation and construction of the Work Wellbeing Index will be presented in section 1.5. We es- timate the unknown parameters (loadings and variance-covariances) of the FA model by maximum likelihood. To provide a scale for the latent factor, the factor loading of one observed indicator is constrained to 1 for each latent variable. This implies that one unit of change in the latent variable leads to one unit of change in the constrained observed indicator.
Figure 1.1: Path diagram of Decent Work. Observed variables are represented by rect- angles whereas latent variables are indicated by ellipses. Measurement errors are omitted on the figure.
Rights at work Rights at work
Employment opp.
Employment opp.
Social protection Social protection
Social dialogue Social dialogue Decent Work
Fundamental conv.
Emp. policy conv.
Social security conv.
Worker's rights Occup. safety conv.
Women's eco. rights
Emp. services Emp. agriculture Female paid emp.
Minimum wage Wage industry Paid employment
Excessive hours
Social security Contrib. fam. worker
Rate fatal inj.
Old age pension Self employment Collective bargaining
Freedom of assoc.
FoA, CB & indu. rel.
Trade union density
Empowerment rights
We begin our empirical analysis by investigating the correlation structure of the different indicators. They measure different aspects of decent work such as employment oppor- tunities, adequate earnings, decent working time, stability and security of work, equal opportunity and treatment in employment, safe work environment, social security and social dialogue.
Figure1.10in Appendix presents correlation matrix of potential indicators to measure de- cent work. We see along the diagonal four interesting clusters. The first one is composed by variables measuring rights at work. ConvFund groups eight fundamental conventions regarding forced labour and its abolition, freedom of association and collective bargaining, equal remuneration, discrimination (in employment and occupation), minimum working age as well as the worst forms of child labour. ConvEmp is based on conventions regarding employment policy and promotion while ConvSafety includes conventions regarding occu- pational safety and health. Finally, ConvSocSecu is constructed using conventions about social security. Another cluster shows variables measuring employment (e.g. PaidEmp, EmplServ, EmplAgri and FemalePaidEmp). The variables measuring vulnerability in employment (e.g. ExcessHrs, SelfEmp, and ContribFamWorker) and the variables repre- senting various aspects of social protection (e.g. TU density and CBcoverage) also form
5The mean aggregation recognizes the fact that all four dimensions composing our Work Wellbeing Index are equally important and gives equal weights to each pillar.
Performing an Exploratory Factor Analysis (EFA) on our indicators, we retain four fac- tors with eigenvalues greater than 1 which explain a cumulative amount of variance by more than 85 %. The first factor is associated with an eigenvalue of almost 7 and suggests that the variables are well suited to measure one single concept: decent work. Looking at the second factor, we see a cluster of the variables measuring rights at work and social protection. The third and fourth factor show some overlap between the variables measur- ing employment opportunities and social dialogue. Table 1.5 reports these findings and is differed to the Appendix.
1.3.3 CFA estimation results
In this section, we report and analyse the results of the factor analysis as specified in Figure 1.1. To allow for comparison and whenever possible, the coefficients are reported in their standardized form with their respective standard error in parenthesis.
Our baseline model is estimated through linear factor analysis and the estimation is per- formed separately for each dimension. The results are displayed in Table 1.1. The first column shows the coefficients of various work conventions and labour rights indicators.
All the coefficients are positive and significant at the 1% level enabling us to identify this first latent variable as the Rights at work. The variable Fundamental conventions, Em- ployment policy and promotion, Occupational safety and Social Security represent diverse aspects of labour protection and were built using information on the ratification of the ILO conventions and protocols. Although the conventions are not legally binding, they provide relevant information on the potential work stability and security in each country.
By ratifying conventions on diverse aspects of labour protection, a country manifests its desire to move towards better rights at work. Moreover, associated international pressure is more likely to have an impact on signatory countries to apply the regulations previously adopted. The indicator Worker’s rights is a composite index that gives information on the actual rights of workers. It covers various aspects such as the right to freely associate and bargain, the abolition of forced labour, notably child labour. It pledges safe working conditions, minimum wage, adequate pay and decent hours of work. Finally, the variable Women’s economic rights is a measure of internationally recognized women rights such as for instance equality in pay, promotion practises and hiring.
The second column of Table 1.1 gathers indicators measuring employment opportunities.
All the coefficients are significant and of expected signs. Namely, all the variables mea- suring enhanced employment capability such as paid employment, women employment as well as adequate earnings captured by minimum wages and wages in the industry sector are positively loading on the latent variable. Considering disaggregated employment into sectors (agriculture, services and industry), we see that the share of employment into the service sector is positively associated with employment opportunities whereas the opposite is true for the share of employment in the agricultural sector. The negative association between employment in the agriculture and our latent variable is not surprising as agri- culture jobs are generally associated with vulnerability in employment, thus hindering decent work.
The third factor identified is Social Protection & Vulnerable Employment. The two first indicators, the social expenditures as a percentage of GDP and the share of active contrib- utors to the old-age pension schemes in percentage of the labour force, measure enhanced
social protection associated with a reduction of vulnerability in employment. The last four indicators (i.e. Self-employment, Contributing family workers, Rate of fatal injuries and Excessive hours) negatively load on the latent dimension as they measure vulnera- bility in employment. The loadings of all the indicators suggest that the latent factor identified is measuring social protection on one hand and employment vulnerability on the other hand.
Finally, the last column of Table 1.1 summarizes the results of the estimation of the latent factor Social Dialogue. The indicators Trade union density and Collective bargain- ing coverage measure the actual level of social dialogue within a country. Trade union density is measured by the share of net union membership as a proportion of the total number of wage and salary earners in employment. Collective bargaining coverage is a rate calculated by looking at the numbers of employees covered by collective bargaining as a share of the number of employees with the right to collective bargaining. The last three indicators in column four of Table 1.1 indicate the extent to which the rights to social dialogue are guaranteed within a country. These variables measure the level of legal protection with respect to distinct aspects of social dialogue such as for instance the right of citizens to associate and assembly freely, the right to bargain collectively over wages or the right of freedom of speech. We also compute robust standard errors to allow for heteroscedasticity, results are reported in Table 1.7 in Appendix. As for our baseline model, all the coefficients remain significant at the 1% level.
1.3.4 Goodness of fit statistics
This section presents some goodness of fit statistics of the baseline model presented in the previous section. Table 1.6 reports these various measures of fit.
The likelihood ratio test performed measures how well the model postulated reproduces the sample covariance. We would like to find a model that does not reject the null hypothesis that the modelled covariance matrix is equal to the one obtained from the saturated model that perfectly fits the data. Since the likelihood ratio test tends to be very sensitive to sample size, other popular fit statistics are also provided. Among them, the Root Mean Square Error of Approximation (RMSEA) that not only accounts for the sample size but also favours more parsimonious models. Browne et al. (1993) suggested that values below 0.08 correspond to an acceptable fit whereas values lower than 0.05 indicate a good fit. The Comparative Fit Index (CFI) belongs to the category of incremental fit indices that assesses the improvement of the model fit relatively to the baseline model. Generally, an accepted ground rule of good fit is a value of 0.90 or higher. The Tucker-Lewis index can be interpreted in the same manner as the CFI. The Standardized Root Mean Square Residual (SRMSR) is a popular absolute fit indicator that measures the mean absolute value of the residuals covariance. Hu and Bentler (1999) suggested that a value of 0.08 or smaller signals a good fit. Finally, the Coefficient of Determination (CD) is somewhat similar in its interpretation to a R-squared estimate in an OLS regression.
In light of preceding guidelines, the linear factor analyses measuring the four dimension Rights at work, Employment Opportunities, Social Protection & Vulnerable Employment and Social Dialogue fit well the data.
Table1.1:LinearFactorAnalysisoninterpolateddataset.EachpillarofDecentWork-Rightsatwork,EmploymentOpportunities, SocialProtection&VulnerableEmploymentandSocialDialogue-isestimatedseparately. Components of Decent Work - Estimation by pillars Rights at workEmployment Opportunities Social Protection & Vulnerable Employment Social Dialogue Fundamental conventions 0.372*** (0.0303)Paid employment 0.526*** (0.0320)Social security0.723*** (0.0325)Trade union density0.515*** (0.0694) Conv: Employment policy and promotion0.497*** (0.0281)Employment service 0.838*** (0.0248)Active contributors to old age pension scheme0.435*** (0.0285)Collective bargaining coverage 0.892*** (0.1106) Conv: Occupational safety 0.902*** (0.0301)Employment agriculture-0.717*** (0.0294)Self-employment -0.698*** (0.0267)Freedom of assembly and association
0.357*** (0.0524) Conv: Social Security0.656*** (0.0275)Female paid employment 0.351*** (0.0329)Contributing family workers-0.662*** (0.0282)Conv: FoA, CB and industrial relations
0.400*** (0.0590) Worker's rights0.067** (0.0334)Minimum wage0.474*** (0.0274)Rate of fatal injuries-0.340*** (0.0305)Empowerment Rights 0.309*** (0.0496) Women's economic rights0.133*** (0.0330)Wage industry 0.743*** (0.0253)Excessive hours-0.776*** (0.0294) Observations 1092 1092 1092 1092 Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
1.4 Sensitivity analyses
In this section, we present some alternative model estimation of our baseline model pre- sented in Figure1.1. We seek to check the “robustness” of assumptions implicitly made in the estimation of the baseline model. We wish to assess whether simplifying assumption such as treating binary indicators as continuous or assuming multivariate normality im- pact the estimation of the factor loadings presented in subsection 1.3.3. We also provide some further discussion on the handling of missing observations. All the tables and figures of this section are differed to the Appendix.
1.4.1 Estimation of the whole model
In section1.3.3, each dimension of decent work was separately estimated by linear factor analysis in order to simplify the estimation procedure. We now estimate the whole model in one step and present the results in Table 1.8. They are in line with those obtained previously. We also allow the different dimensions of decent work to correlate with each other and estimate their correlation. The results are reported in the bottom of the table.
All the estimated covariances are positive and significant at the 1% level. The greatest synergies occur between the concepts of employment opportunities and social protection.
This was already highlighted in the exploratory factor analysis reported earlier where em- ployment and social protection were greatly overlapping. Moreover, the legal framework represented by the latent variable Rights at work and the Social dialogue dimension seem to complement one another as shown by their high positive correlation.
1.4.2 Continuous versus categorical indicators
In the previous section, we assumed all indicators to be continuous and normally dis- tributed. To investigate whether this simplifying assumption affects the estimated coef- ficients, we propose to transform the categorical variables into continuous measures by expressing them as shares. For example, Fundamental conventions (%) is calculated as the share of conventions signed by a country out of the total number of fundamental conventions available (C087 C098 C029 C105 C138 C182 C100 C111). Table 1.9 reports the results when using only continuous variables in the linear factor analysis. The esti- mated coefficients are all significant and of same magnitude as in the estimation of our baseline model. Table 1.10and Table 1.11show the estimation results of nonlinear factor analysis to account for the categorical nature of some indicators. We propose to estimate a generalized factor analysis model fitting an ordered logit and results are shown in Table 1.10. Another proposition that simplifies the estimation of the model is to create dummy variables out of the categorical variables and fit a logit model. We display the results of the latter model in Table 1.11. Although the comparison with linear factor analysis is more complex due to the impossibility to standardize the coefficients in the case of nonlinear models, we do not see any strong qualitative differences in these last two esti- mations compared to our baseline specification. The next section further investigates the assumption of multivariate normally distributed data.
We estimate our baseline model using maximum likelihood which assumes multivariate normality of the data. Figure 1.11 presents the scatter plots of the data. We can clearly identify data that are binary or counts and hence not normally distributed.
To assess whether deviations from normality affect the estimation of the factor loadings presented in Table 1.1, we propose to estimate the factor analysis using Asymptotic Distribution Free (ADF) method. Table 1.12 displays the estimation results of a linear factor analysis estimating each dimension separately using the ADF method. The ADF function was developed by Browne (Browne, 1982; Browne, 1984) and has the advantage to relax the assumption of multivariate normality of the data in estimating the model.
All coefficients are of expected sign and significant. Their magnitude is almost identical to our baseline model presented in Table 1.1.
1.4.4 Handling missing data
We dealt with missing values by linear interpolation and used the interpolated dataset in the baseline analysis. To make sure that the results are not dependent on how we handled missing values, we also propose to run linear factor analysis on the original dataset, i.e.
before the replacement of missing values by linear interpolation. The corresponding results can be found in Table1.13. We see that the results of this factor analysis on the original dataset are extremely similar to those obtained on the interpolated dataset presented in Table 1.1.
To further investigate the robustness of our analysis on the linearly interpolated dataset, we run the same factor analysis using the method MLMV offered by Stata as an option to its sem command. The method MLMV is especially targeted at handling missing values and does not delete listwise any information as would other estimation methods. To deal with missing information, the method assumes joint normality of all variables as well as missing at random patterns and estimate the model using maximum likelihood. The data are grouped according to their missing patterns and summary statistics for each missing- value pattern are computed. The loglikelihood is then computed using the summary data.
The results of this estimation strategy are presented in Table 1.14. Again, the results are qualitatively identical to those obtained in our baseline specification in Table 1.1.
Both these checks give us confidence that the replacement of missing values by linear interpolation did not seem to have altered the main statistical associations of the dataset.
Finally, the results for multiple imputation procedures either though joint modelling or chained equations are not reported. Due to the relatively large proportion of missing values and convergence issues, multiple imputation procedures did not appear to be a suitable option.
1.5 Work Wellbeing Index
In section 1.3 we estimated the weights (i.e. factor loadings) for each indicator and used Thomson factor scores to obtain predicted values for our four latent pillars: Rights at work, Employment Opportunities, Social Protection & Vulnerable Employment and So- cial Dialogue. In this section, we turn to the final aggregation of the Work Wellbeing Index.
Recall that we had proposed two distinct ways to construct the final index of Work Wellbeing: using a second order CFA to aggregate the dimensions of decent work or as- signing them equal weights through an arithmetic mean. Table 1.15 displays the results of running a second factor analysis on the predicted values of the four dimensions of de- cent work. All the coefficients are significant and have a positive sign meaning that, as we expected, a better legal framework as well as more social protection, social dialogue and enhanced employment opportunities all contribute to improving decent work. An- other thing to notice is the different magnitude of the weights assigned to each dimension.
Namely, the dimensions of Social Protection and of Social Dialogue are associated with decent work with high coefficients, 0.752 and 0.671 respectively. Meanwhile, Rights at work and Employment opportunities only contribute for about 50% to the index. As before, Table 1.16 provides a range of goodness of fit statistics. Tables1.15 and 1.16 can be found in Appendix.
The Work Wellbeing Index with equal weights is constructed by aggregating the four dimensions of decent work through an arithmetic mean on previously rescaled data. Al- though the two aggregation methods yield slightly different results by favoring one or the other dimension, they are highly associated and they provide a similar picture of decent work.
Figure1.2 presents some information about the distribution of the indices for the four di- mensions of decent work and the two measures of Work Wellbeing. Looking the first violin plot of Rights at work, we see that the distribution is right skewed which suggests that most of the countries in our sample do not achieve high values in this dimension. On the opposite, the distribution of Social Protection & Vulnerable Employment is left skewed:
economies tend to achieve high level in this dimension. This fact might seem surprising but recall that about 70% of the sample is made of high income European countries.
There are however a few outliers (Turkey, Philippines and Malaysia) that perform poorly in this dimension as shown by the lower part of the violin plot. Interestingly, the density of Employment opportunities is bimodal: some countries perform well in this dimension as indicated by a 75th percentile at 78 whereas others do not (the 25th percentile is below 13). Finally, looking at the distribution of the two measure of decent work, we notice that the aggregation through the mean produces a rather symmetric and centered measure of decent work while the aggregation through second order CFA is more left skewed (as greater weights is given to the dimension of social protection in this aggregation scheme).
Figure1.2 gives additional information on the association between the different aspect of decent work and the two indices of Work Wellbeing. Scatter plots are displayed on the lower triangular of Figure 1.2 with red ellipses around the mean (the axis length equal to one standard deviation of the x and y variables). The upper triangular of Figure1.2shows correlation coefficients and their significance. We see that all the concepts are positively and significantly associated. Not surprisingly, the two indices of Work Wellbeing (2nd order and mean aggregated) are highly correlated with a significant correlation coefficient of 0.92. This corroborates our earlier finding that both measures of decent work produce similar qualitative results.
at work, Employment Opportunities, Social Protection & Vulnerable Employment and Social Dialogue.
Table1.2:ThelowertriangularandthediagonalshowscatterplotsandhistogramsofDecentWorkanditspillars:Rightsatwork,EmploymentOpportunities,SocialProtection&VulnerableEmploymentandSocialDialogue.Theuppertriangularpresentscorrelationcoefficientsandassociatedsignificancestars.
regions where the boxplots are order from low to high medians. Unsurprisingly countries from Europe & Central Asia have the highest median and a wide spectrum of decent work values as shown by the widespread distribution of the last boxplot. In fact this region includes a large share of the sample (about 70 %) and very different countries, e.g.
Sweden and Turkey. On the contrary, Latin America (LAC) has the lowest median with some variability around it: Brazil performs much better than Mexico and almost as well as Japan or Australia in the East Asia & Pacific region. Israel and Malta in the Middle East & North Africa region achieve higher values of decent work than most of the LAC countries. Finally, North America obtains decent work scores that are lower than the Eu- ropean median. In particular Canada and the United States suffer from low ratification of the ILO conventions and protocols which translates into poor scores for the dimension Rights at work and for the overall Work Wellbeing Index.
We see from the boxplots in Figure 1.4 that high income OECD economies have higher levels of decent work compared to non OECD and Upper middle income countries. Among OECD countries, Nordic economies such as Sweden, Finland or Denmark are in the top 90th percentile whereas Greece, Israel or Chile are below the 25th percentile and obtain decent work scores close to those from non OECD economies. Concerning upper middle income economies, the boxplot to the right shows that the dispersion around the median is high: Bulgaria and Brazil achieve scores similar to those of non OECD countries whereas Malaysia and Turkey perform relatively badly.
Figure 1.3: Boxplots of the Work Wellbeing Index across regions of the world.
Figure 1.4: Boxplots of the Work Wellbeing Index across income groups.
We analyse the evolution of the Work Wellbeing Index over the period 1990-2004 for a selection of countries. Figure 1.5 shows that decent work over these 10 years has been fairly constant for some countries (i.e. Sweden, Germany and Turkey), increasing for others (i.e. Finland and Portugal) and even decreasing for some (i.e Czech Republic).
Nordic and OECD countries have had high level of decent work since the nineties and do not show much progression. While we can appreciate a catch-up from several economies, others seem to be trapped in low levels of decent work although poor data availability does not allow much comparisons.
Figure 1.5: The Work Wellbeing Index over time for selected countries.
dimensions: Rights at work, Employment Opportunities, Social Protection & Vulnerable Employment and Social Dialogue. Figure 1.6 proposes radar plots of selected countries.
These countries’ profiles allow us to identify which dimensions are driving the changes that we observe in the Work Wellbeing Index. It helps understand which dimensions of the Work Wellbeing Index promote or hinder decent work in specific cases. Subfigure 1.6a shows that Sweden enjoys a high level of decent work (as shown by the large surface) which is well balanced across all four dimensions. In comparison, Subfigure 1.6b reveals that Portugal has a lower level of decent work and that it is more imbalanced (e.g. the employment opportunities are relatively smaller than social dialogue over the period).
Interestingly, Portugal had improved its scores in the Work Wellbeing Index over the period 1990-2004 as shown previously in Figure 1.5. A closer look at Subfigure 1.6b shows that Portugal actually suffers from a decrease in the Social Dialogue dimension which is overcompensated by an increase in both dimensions of Rights at work and Social Protection. The Employment dimension score appears almost constant over the period.
Lastly, Turkey gives a very distinct picture: it appears to be trapped in low levels of decent work with little progression over the period in all four dimensions of Work Wellbeing.
Radar plots are informative as they go beyond the aggregate measure of Work Wellbeing and give a more nuanced picture of the evolution of decent work within countries over time.
Figure 1.6: Radar plots of the four dimensions of the Work Wellbeing - Rights at work, Employment Opportunities, Social Protection & Vulnerable Employment and Social Di- alogue - for selected countries.
(a) Sweden (b) Portugal
(c) Turkey
Figure 1.7: The Work Wellbeing Index against the Gross National Income (GNI) per capita in thousands (2011 PPP $). The green line represents the 45◦ line.
Finally, to provide further insights, we propose to compare the Work Wellbeing Index to commonly used indicators in the human development literature. Figure 1.7 plots our decent work measure against Gross National Income (GNI) of some selected countries over about 10 years.6 Except for Turkey, Luxembourg and Switzerland, countries do not lie on the 45◦ line which suggests that higher income does not automatically associate with higher decent work. Therefore, GNI should not be used as a proxy of Work Wellbeing within a country. Although the relationship between the two variables is positive, there is a greater variability in the levels achieved in terms of decent work than in terms of income.
Consider for instance Sweden, France, Italy and Japan which all belong to a similar range of GNI per capita (all between 30’000 and 40’000 (2011 PPP $)) but differ greatly in terms of Work Wellbeing. This shows that there is a great range for improvement of decent work levels even for countries enjoying a relatively high income.
Since much of the literature on measuring the human development has focused on the Human Development Index, we compare this index to our Work Wellbeing Index. As shown by Figure 1.8, the general trend is that better scores in human development (i.e.
HDI) are positively associated with decent work. Although the relationship appears to be quasi-linear, the slope (represented by the red line) is steeper than the green 45◦ line.
While most of the countries achieve high values of human development as measured by the HDI, more disparities are present in terms of decent work. Moreover, the cloud of points is moving away from the 45◦ line over the period 1995-2004 while conserving approximately the same slope. This suggests that while countries achieve higher values of HDI over the years, the progress is rather slow in terms of decent work.
Looking at one dimension of the HDI, we compare our Work Wellbeing Index is to the education dimension. The results are reported in Figure 1.9. The Education Index is an average of mean years of schooling (of adults) and expected years of schooling (of children), both expressed as an index obtained by scaling with the corresponding maxima.
This time, we see that the pattern is closer to the green 45◦ line.
6To maximize the number of countries under analysis, we choose to focus on the years 1995, 2000 and 2004.
selected countries. The green line represents the 45◦ line.
Figure 1.9: The Work Wellbeing Index against the Education Index (dimension of the HDI) of selected countries. The green line represents the 45◦ line.
1.6 Concluding remarks
This chapter constructs and analyses a Work Wellbeing Index using a factor analysis model. We hypothesize the concept of decent work as a latent variable describing a mul- tifaceted reality. We suggest that decent work is composed by many dimensions and is only observable through the lens of multiple indicators. To remain as objective as possi- ble in the construction of the index, we determine the structure of our model through an exploratory factor analysis first and then estimate it using a confirmatory factor analysis.
The goodness of fit statistics bear out that the indicators chosen reproduce the model accurately. In line with the Decent Work Agenda formulated by the ILO, we identify four main latent aspects influencing Decent Work: Rights at work, Employment Opportuni- ties, Social Protection & Vulnerable Employment and Social Dialogue. On the conceptual level, we try to combine quantitative and qualitative measures as indicators of decent work.
The final model (Figure 1.1) is estimated for a sample composed of 42 countries over the time period 1990-2015. The picture is clear, as expected, all dimensions have positive association with the latent concept of decent work. We briefly discussed two aggregation schemes for the final index of Work Wellbeing (through a second order FA or arithmetic mean) and study the distribution of the two measures of Work Wellbeing and their four dimensions using violin plots. We provide some information about the association of our two measures of Work Wellbeing and conclude that they are are strongly correlated and produce similar results. We analyse the disparities in the Work Wellbeing Index classified by income groups or world regions. Graphical representation of the distribution of the Work Wellbeing Index across regions and income classes shows that Nordic and European
economies have the highest median scores of decent work. Interestingly, comparing our Work Wellbeing Index to GNI per capita reveals that high income does not automatically associate with high decent work. Comparing the Work Wellbeing Index to other com- monly used measures in the human development literature such as the HDI shows strong positive and quasi-linear association. Finally, we provide a deeper understanding of de- cent work by looking at the evolution of the Work Wellbeing Index over time and draw some countries’ specific profiles to analyse which dimensions promote or hinder decent work.
An interesting improvement of the Work Wellbeing Index would seek to include exogenous causes of decent work. Anker et al.(2003) have put forward the importance to consider the socio-economic context surrounding decent work. Following their proposition, an appeal- ing way forward would be to attempt to include measures of macroeconomic/monetary stability (i.e. inflation rate, external debt sustainability), labour productivity growth (i.e.
output per employed person (PPP level), growth of output per employed person) or edu- cation attainment (i.e. combined primary, secondary and tertiary gross enrollment ratio) as exogenous causes of decent work. The latter would allow to identify some possible feedback mechanisms from education to better employability and would be particularly insightful in terms of policy making.
The most important message is that decent work is a multidimensional concept and should be quantified as so. This chapter insists on the need to acknowledge the qualita- tive measures of employment as equally important as the quantitative ones. In addition, the relation of the Work Wellbeing Index to other key socio-economic measures as for example the HDI or the GNI per capita is found to be strong and positive. This suggest that decent work should not be looked at in an isolated manner but rather by considering the circumstances in which it occurs. The call for incorporating decent work into a highly integrated framework is well understood. To attest it, consider the 8th goal of the Sus- tainable Development Goals (SDGs,2015) defined as topromote inclusive and sustainable economic growth, employment and decent work for all.
Figures
Figure 1.10: Correlation matrix of the variables retained for the baseline model.
Figure 1.11: Scatter plots of the variables retained for the baseline model.
