I want to find how the number of COVID-19 cases, deaths and lockdown affect each sector in Sri Lankan economy. Hausman test suggested me fixed effect model as the most suitable model. I need to fit the fixed effect model for each sector separately including the sector as a dummy variable to the model. but I get the error 'Near singular matrix'. Why is that? Is it impossible to fit fixed effect model for each sector separately when the sector was included as a dummy variable?
It may be that columns of your columns of your x matrix are not independent. Start by checking what happens if you remove the sector dummy variable. Best wishes David Booth
David Eugene Booth but this problem doesn't occur when I fit random effect model
But you said that the random effects model is not appropriate so why does it matter? Further you seem to be treating sector differently in the two models. So how can. You compare them directly? David Booth
It sounds as if you wish to estimate a model like
sectorit = ai + b1 covid + b2 deaths + .......
where i refers to sector and t to time period.
I would have difficulty estimating this equation for individual sectors as I do not see how you could have enough data.
Fixed effects panel estimation assumes that b1 b2 etc are constant across sectors. I would think that this is unreasonable. Perhaps I have not understood but I think that you need to reconsider your model.
Panel data would also require that you have separate measurements for covid, deaths, etc. for each sector.
Before you start your econometrics you should have a model based on economic theory/common sense. This model will contain various unknown parameters. The econometric model (and data) determine the econometrics to be used. In this case, the model needs to be reconsidered and then one could decide or seek advise on the econometrics to be used.
In panel data, it is possible to fit fixed effect models separately for each dummy variable, but this approach is not recommended because it can lead to biased estimates and inefficient inference.
Fixed effect models in panel data are typically used to control for unobserved heterogeneity that is time-invariant. This is accomplished by including a set of dummy variables for each individual in the data. The inclusion of these individual-specific dummy variables absorbs the time-invariant heterogeneity, allowing for unbiased estimation of the remaining time-varying effects.
Fitting fixed effect models separately for each dummy variable would essentially be the same as estimating a separate model for each individual. This approach would fail to account for the time-invariant unobserved heterogeneity that is common to all individuals. As a result, the estimates would be biased and inefficient.
Therefore, it is recommended to include all the dummy variables in the model together as a set of fixed effects. This allows for a more efficient estimation and unbiased inference of the time-varying effects.
@Randimal Herath
Fixed-effects filter (FEF) model could be a possible solution here. Please visit original paper on FEF:Article Estimation of Time-invariant Effects in Static Panel Data Models
and its application here:Article Estimating the effect of time‐invariant characteristics in p...
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