Let's say a bank has 5 different types of deposits. One type is certificates of deposits (CD), and the other 4 types are different checking and savings account products with various interest rates levels.

The deposit mix represents the sum of the % of deposits allocated to each of the 5 product types. That sum obviously equals 100%.

I want to figure how that deposit mix shifts in response to interest rate levels (proxy is probably the US Federal Funds rate). The hypothesis is that as interest rate level increases the deposit mix will shift more and more towards CDs and away from the other products and vice verse. It makes sense, but is it true?

I probably will work with a good time series of monthly observations in deposit mix for over 8 years or so.

I was thinking maybe this is a Discriminant Analysis (DA) problem. But, I fear DA may not handle % variables that are not categorical variables with binomial outcomes (1, 0). I was also thinking maybe this is a Logit Regression (LR) problem. But, there is also the issue of the variables not being categorical. And, can Logit handle more than one dependent variable? In this care there are essentially 5.

So, how would you handle this problem? Using what method? And what software? Could you do it long hand in Excel?


First, I think you need to have a clear definition of your dependent variable. How are you going to quantify the product mix?

For example, if you only wanted to compare CDs and another product, your dependent variable could be defined as the ratio of one to the other. I don't see how you could discuss the mix of all of the products at once.

Also, I think this is more of a time series problem, not a cross sectional logistic regression problem. You might want to look at vector autoregressive models (VAR) to model how the mix changes over time.

  • $\begingroup$ To further define the deposit variable, to keep it short let's say there are just 3 products: CDs, savings acct., checking acct. And, let's assume they have all equal share of the deposit mix: CDs 33.3%, savings 33.3%, checking 33.3%. And, we want to observe how that deposit mix changes over time using FF rate as the one independent variable. Could you really do that using VAR? What software do you need to do VAR? $\endgroup$
    – Sympa
    Sep 27 '12 at 17:42
  • 1
    $\begingroup$ Yeah, I think that's a great application of VAR - you want to know how the FF rate is correlated with those shares over time. I would certainly recommend R: function VAR() from package vars cran.r-project.org/web/packages/vars/vars.pdf $\endgroup$
    – wcampbell
    Sep 27 '12 at 18:15
  • $\begingroup$ I looked into VAR and with a colleague developed a VAR model for this problem. My conclusion is that it is really not a VAR application. Logically it does not make any sense. To predict any of the dependent variables you need future estimates of all the other dependent variables. That does not work. Can anyone come up with a sensical alternative? $\endgroup$
    – Sympa
    Oct 13 '12 at 15:56
  • $\begingroup$ Revisiting this question, the answer is actually rather poor. It does not address the problem at all that is well specified as is. I invite others to give it a shot. $\endgroup$
    – Sympa
    Jul 31 '16 at 16:25

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