Hello Cemre,

If you'll kindly elaborate your query, being sure to indicate what your variables are and how they are quantified, if not obvious (and whether you're looking at this as a multilevel model), as well as your specific research question(s), I suspect you would get more focused recommendations from the Rgate community.

Good luck with your work.

David Morse , firstly i would like to thank you for your comment. You're absolutely right.

I am working on economic impacts of artificial intelligence for my PhD dissertation. Now, i have two models. The first one is employment, the other one is growth model.

In employment model, dependent variable is employment rate independent variable is artificial intelligence index and control variables are wage, gdp, labor productivity, population. For this model, I used GMM and i got statistically significant model. However, in Thesis Monitoring Committee, they asked me that if i'm sure whether the model is true or not. Then, i doubted myself. I guess that i have to mount an argument about my model or must change econometric method.

I would like to know via within -between random effects the extent to which your dependent variable is time varying or time invariant. I would also fit a series of models to assess the extent to which your 'independent variables are time varying or essentially cross sectional - that is fit a RE model with each independent variables as the response. I would be more convinced that something is going on if the within effect holds up irrespective of between effect.

Article Fixed and Random effects models: making an informed choice

Article Explaining Fixed Effects: Random Effects Modeling of Time-Se...

Article Understanding and misunderstanding Group mean centering: a c...

Article Stylised fact or situated messiness? The diverse effects of ...

Given the relatively small number of observations ; I would think about using the quantitative results to inform causal process tracing to strengthen your arguments

Chapter Causal-Process Tracing

"In most small-N studies, the tracing of causal processes plays an important role. Very often, causal-process tracing (CPT) is used as a complementary technique to co-variational analysis (COV). Tracing the process that leads from a causal factor to an outcome makes it possible to enhance the internal validity of a causal claim that ‘x matters’ (Gerring 2007a: 173–84). This ‘added value’ is especially warranted when the compared cases are not as similar as they should be (to be ‘controlled’), when the co-variatonal analysis is indeterminate (because more than one independent variable co-varies with the dependent variable in a theoretically meaningful way), or when the measurement and classification of variables is not as clear-cut as it should be. "

Within-between random effects analysis will allow you to keep your eyes on the specific countries involved.

Kelvyn Jones thank you for your valuable comment. There is presence of cross sectional dependence for all variables. So, ı thought that ı cannot use random or fixed effect because of presence of cross sectional dependence. Maybe, ı am wrong.

I will read carefully the articles you shared. Thank you so much, again.

There is continuing controversy about random versus fixed effects which is covered by the Wikipedia entry

https://en.wikipedia.org/wiki/Kelvyn_Jones

"He (with colleagues) has challenged the 'gold standard' that fixed effects should be the standard approach to the analysis of Panel data and that a Hausman test is an appropriate way of choosing between a Fixed effects model and a Random effects model. Somewhat controversially they argue that a particular form of the random effects model (the within-between model or the similar Mundlak model) offers all that fixed effects can provide and more.[15][16][17] They also challenge the Fixed Effects Vector Decomposition (FEVD) model of Plumper and Troeger.[18] One reaction was: "This paper and the instructive controversial over FEVD have shown me that my econometrics training had not - as I once assumed - taught me all that there is to know about fixed effects estimation. In particular, the authors' treatment of 'heterogeneity bias' clarifies the importance of addressing both 'within' and 'between' variation in the data and they make a compelling case for considering both 'individual' and 'ecological' influences".[19] Another was: "Bizarre and often incorrect paper by two political scientists on the virtues of random-effects over fixed-effects".[20] to "You can and should use a well-specified random effects model. Always.".[21] These models shown algebraically in the table for a two-level panel model are discussed and illustrated with snippets of R code by Daniel Lüdecke,[22] and there is a R package (panelr) for panel data analysis by Jacob Long that facilitates their implementation.[23][24] An extensive review of the potential of this approach in economics concluded that it has been "unreasonably ignored" due in part to "disciplinary isolation" of the subject.[25] In the psychological literature, Hamaker and Muthén, (2020) [26] report that “The most elaborate and animated treatment of the connection [between FE versus RE models and centering in multilevel models] can be found in the recent paper of Bell and Jones (2015). They build a compelling case for multilevel modelling, arguing that, while the problem of endogeneity is very real, the point is that we should simply use the right multilevel model to tackle it (i.e., based on person mean centering the time-varying covariate and/or including these means as a predictor at the between-level)

• He and colleagues argue that group-mean centering in multilevel models can be a useful procedure in random coefficient models,[27] thereby disagreeing that it is a 'dangerous' procedure.[28] Reactions to this critique include "may the Saints & Angels protect us from ever having a paper this thoroughly dismantled"[29] and "Seriously though, if you are interested in multilevel modelling I highly recommend this short, instructive and frankly rather sassy paper."[30] The essence of the argument is that in a two-level model, the slope parameter associated with level-1 variable is a potentially uninterpretable mixture of within and between effects. The solution is to decentre the level-1 variable by subtracting the level 2 cluster mean and including these level 2 means in the model. The argument is made in terms of continuous variables and is extended to multicategory predictors by Yaremych et al (2021).[31] "

Kelvyn Jones I really appreciate you taking the time. You've broadened my horizons, sir. I am going to start working out these details. Thank you so much, again.