I would like to test whether the general relationship between the number of years of education and the wage is linear, exponential, etc. Or in other words, does going from 1 year to 2 years of education have the same impact on wages as going from 10 to 11. I want a general assessment for the world and not for a specific country.
I got standardized data from surveys on several countries and multiple times (since 2000). My idea is to build a multilevel mixed-effects model, with a fixed effect for the number of years of education and random effects for the country, the year of the survey and other covariates (age, sex, etc.). I’m not so used to this type of model: do you think it makes sense? Is this the most appropriate specification of the model for my needs?
I would assume a simple OLS or conditional correlation with fixed year, country, and individual fixed effects might be good start. Not sure if you can have some form of instruments for endogeneity problems that might arise as this depends on your dataset and model.
I would begin with the simplest methods (diagtams, correlations) to analyse the education-wage-relation for not more than a handful of countries separately (because, I think, the variation between countries is much higher than for differences in years of eduction. I doubt that you can find out an effect of an additional year of eduction for low numbers of years (your example: increase of 1 to 2 years), because most countries have a minimum of 8-9 years. Another problem is that bad pupils may need longer to get a degree. The wage is likely dpendent on the development between end of education (beginning to work? and the time when the wage was measured. Therefore, one should include the developmet of an average wage (as a sort of control variable) or take the relation to aveage wage as dependent variable. In any case, you should put much effort in finding a good specification before going into more "refined" estimations.
There are several statistical models for pooling data from multiple surveys in multiple countries and years. Some commonly used models include:
Hierarchical Linear Modeling (HLM): This model is commonly used in the social sciences to analyze data from multiple sources, such as surveys conducted in different countries and years. HLM is an extension of regression analysis that allows for the modeling of hierarchical data structures, such as individuals nested within countries and years. HLM is useful because it allows for the estimation of both fixed and random effects and can accommodate missing data.
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