How to estimate cluster robust errors in the presence of fixed effects for groups within cross sectional data?

Question

I am dealing with cross sectional data that has groups within the observations. For example, the dataset of an online firm registered in one country that allows multiple banks from different countries to sell the loans originated on their platforms. Each row in the dataset is one observation (one loan) with several characteristics, the start date, the interest rate, if it has been paid back, etc. Hence, each observation is unique as it represent different loans originated by multiple banks. There are also several observations by the same bank, but each observation represent different loans. I use data of 4 months in 2022. I do not regard the data as time series as Time-series would be the same loans on several observations over time, daily, monthly, or so. I do not consider the data as panel as well, because I am assessing the performance of one online business (there is only one wave of data). Am I correct in my inference?

Secondly, since different banks sell their loans from different countries, I need to control for their fixed effects. Hence, I included some characteristics of the banks such as size, age, etc. of each bank as control variables. I also control for the location of the banks. I have over 40 banks in the data spanning from 20 countries. Instead of including countries, I classified them based on geographical region such as asia, africa, etc. I have 4 regions in my data and I did this because inclusion of country as factor variable instead of geographical location causes specification errors. I want to control for serial correlation by including cluster robust errors. I usually see people adding geography as cluster variable. Is it okay to choose any other bank characteristic variable that you controlled for, for example size in my case? Size is a numeric variable and is different for all banks forming 46 clusters. Is it necessary to cluster based on countries? As I have mentioned earlier, inclusion of country variable causes specification errors, which is why I stuck to geographic region which is only 4 groups. I have read that we need at least 10 groups to cluster errors.

My dataset is of an online platform that allows multiple banks to sell the loans they have originated. This online platform is a registered company, they do not issue loans but they allow other banks to sell already issued loans on their platform. Say Bank A sells originates loans from different customers. The loans are now represented on their balance sheet. To increase their liquidity and to issue more new loans, they sell these loans at a lower interest rate. For example, if the loan was issued to customer at 10% interest rate they would sell it for 8% interest rate on the platform, generating a profit margin from the difference. The banks not only get a profit margin by selling loans, but also liquidity. This motivates banks to participate on the platform by selling their loans. Origination date is the date the bank issues the loan to a customer, selling date is the date the bank sells the loan on the platform. Banks may choose to sell the loan on the same day it was originated. But they can also sell older loans that they issued months back. It is not necessary that they have to sell newly originated loans.

Furthermore, banks can also choose whether or not to sell loans in a particular month. There are banks in my sample period(4 months), that didnt sell any loans in the first month, but sold in the rest three. There are banks that sold loans in all 4 months.

Answer 1

1. I'm assuming the loans that are included in your 4 month sampling frame originated in that time frame. In that case, this is an, albeit brief, longitudinal study. The assumption of whether or not to adjust or control for time, even in the relatively brief span that data are collected, is somewhat stronger than stationarity. The need for such an assumption, of course, is so that results generalize (or apply) to different settings - like the present. A nice interpretation of "controlling" for an effect is that you make no assumption about its causal relation to other factors except that it is not a collider nor a mediator. So, even if time has no effect and you can afford the "degrees of freedom" to control for it, then there is no harm to the analysis. Chances are there is some effect, in much the same way that regressions in the social sciences often adjust for age and for sex without much thought - it's just done.

2. Again depending on the sample size (say you have 10,000s of loans), it's not unheard of to control for country using a fixed effect, i.e. 19 coefficient terms contrasting with a referent term. But even if not, the addition of a random effect could reduce the residual correlation between observations and thus improve inference. Region, then, is obviously an ideal candidate for fixed effect adjustment. People often forget that random intercepts - the most common form of random effect - do little more than assign intercept terms based on a projection of randomness. How much better then to use a fixed effect (when possible) to do the same thing more precisely and facilitate statistical inference! Even if you made maximal use of all measured factors to reduce residual correlation between error terms, there is still potential value of using robust, sandwich-based errors, to control for unmeasured correlation.