## Abstract

Using Chilean data we present evidence about the relationship between job satisfaction, own wage, and reference group wage. We conducted a semi-nonparametric estimation of extended ordered probit models in order to identify the determinants of job satisfaction. Our main result indicates that a 10 % increase in the reference group wage would need to be compensated for by a 24.9 % increase in the own wage to give the same level of job satisfaction. This result shows the enormous importance of the reference group wage for job satisfaction.

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## Notes

- 1.
The disadvantage of parametric methods is that they impose a functional structure to the data without taking into account the nature of the data.

- 2.
See Appendix 1.

- 3.
See Appendix 2.

- 4.
It is easy to note that this approach (and the next one too) assumes that the reference group is exogenous, i.e. the econometrician decides on the relevant persons in order to construct the reference group. Obviously, this does not have to be carried out in such a way, but the information available for Chile does not allow us to endogenize the construction of the reference group. For instance, Clark and Senik (2009), using data from the European Social Survey, investigate who the individuals are with whom people compare themselves. They find that colleagues are the most frequently cited reference group. Incorporating this information represents a major source of improvement for job satisfaction estimates and the future research agenda should take this into consideration.

- 5.
The authors suggest constructing the rank as follows:

\(R_{ig} = \frac{{P_{ig} - 1}}{{N_{g} - 1}}\)

where

*P*_{ ig }is the position of individual*i*in group*g*and*N*_{ g }is the number of individuals in the group. - 6.
See Appendix 3.

- 7.
See Appendix 2.

- 8.
Our

*R*^{2}ranges from 0.0325 to 0.1022, which is not very different from that presented by Van Praag et al. (2003). - 9.
The critical value of a Chi squared distribution at 5 % is 7.81.

- 10.
Consider also the following. Figures 2, 3 and 4 show the estimated density for models (1), (2) and (3), respectively, using

*K*= 4. Clearly, the distribution exhibits important differences from normal (more leptokurtic) distribution. Given this background, it would be wrong to estimate the models assuming normality. - 11.
The standard error of this ratio is 1.061 (

*p*value = 0.019), which is calculated by the delta method using the STATA nlcom command.

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## Author information

### Affiliations

### Corresponding author

## Additional information

We are indebted to the comments of Enrique Calfucura, Alejandro Corvalán, Cristián Troncoso and Miguel Vargas.

## Appendices

### Appendix 1

As pointed out by Stewart (2004) the approximation of the density can be written as the product of a squared polynomial and a normal density. This results in a polynomial expansion with a Gaussian leading term. Choosing a normal distribution gives the result that the model nests the ordered probit and therefore we can use a likelihood ratio test in order to choose between these competing models. For *K* = 0, 1, 2, we obtain the ordered probit model. From *K* = 3, we obtain a generalization of the ordered probit model.

To perform the approximation, the following function is used:

where *ϕ*(*ɛ*) is the standard normal density function and where:

Normalization *γ*
_{0} = 1 is required. The distribution function is:

As Stewart (2004) remarks, this defines a family of semi-nonparametric distributions for increasing values of *K.*

### Appendix 2

Suppose we have *I* intervals and let *r*
_{1} < *r*
_{2} < ··· < *r*
_{
I−1} be the known limits of these intervals. Then, the model is:

where *w* is the individual wage (non-observable), *m* are variables affecting wages and \(u|m,r \sim N(0,\sigma^{2} )\). The econometrician observes the following:

The probabilities will be given for:

where ϕ is the cdf of a normal distribution. The log likelihood for the individual *l* will be:

Note that this log likelihood differs from the ordered probit because the thresholds are known. Finally, \(\widehat{\alpha },\,\widehat{\sigma }\) are parameters to estimate.

### Appendix 3

Supposing the existence of various domain satisfactions (for instance, *H* domains) in which job satisfaction is excluded, we model the determinants of these domains as follows:

for *h* = 1, …, *H* and where *q* are variables affecting the domain satisfaction and *z* represents other common unobservable variables. First, we estimate the *H* equations (one per domain) and calculate the residual vectors. The objective is to obtain the part *z* that is common to all the residuals, which could be defined as the first principal component of the *H* × *H* error covariance matrix. The resulting new variable would be the instrument for *z.* In this way, as pointed out by Van Praag et al. (2003), by adding *z* as an additional explanatory variable to Eq. (1), we could assume that we are correcting the endogeneity bias in estimating the model parameters.

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### Cite this article

Montero, R., Vásquez, D. Job Satisfaction and Reference Wages: Evidence for a Developing Country.
*J Happiness Stud* **16, **1493–1507 (2015). https://doi.org/10.1007/s10902-014-9571-y

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### Keywords

- Job satisfaction
- Reference wage
- Non-observables
- Semi-nonparametric

### JEL Classification

- C14
- I31
- J28