## SUR estimation for shares that sum up to 1

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jacarandas
Posts: 20
Joined: Tue Feb 10, 2015 10:11 pm

### SUR estimation for shares that sum up to 1

Hi,

I am trying to estimate and forecast a system of market shares equations (J) with the same RHS exogenous regressors. As the market shares sum up to 1, I will be dropping one equation and estimating J-1 equations instead.

The EViews help manual says that "since the system of equations may contain cross-equation restrictions on parameters."

So, I am wondering if a constraint stating that all market shares sum up to 1 needs to be imposed. And, if so, how should this constraint be written out?

I am using EViews 10.

Any help would be much appreciated.

Thanks!

EViews Gareth
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Joined: Tue Sep 16, 2008 5:38 pm

### Re: SUR estimation for shares that sum up to 1

If you have alpha, beta and gamma and you want to impose that they sum to 1, just rewrite them as alpha, beta and (1-alpha-beta).

jacarandas
Posts: 20
Joined: Tue Feb 10, 2015 10:11 pm

### Re: SUR estimation for shares that sum up to 1

Thanks Gareth!

Do I have to drop the Gamma equation as alpha, beta and gamma sums up to 1 in my SUR estimation?

So, is this what I end up estimating?

model.append alpha = my usual regressors
model.append beta = my usual regressors
model.append @identity gamma = 1-alpha-beta

Won’t gamma be an identity then, which SUR won’t allow?

OR

model.append alpha = my usual regressors
model.append beta = my usual regressors
model.append 1-alpha-beta = my usual regressors

Thanks!

EViews Gareth
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### Re: SUR estimation for shares that sum up to 1

Ah, sorry, I thought you wanted the coefficients to sum to one, not the variables. I’m now not sure I understand what you are trying to do

jacarandas
Posts: 20
Joined: Tue Feb 10, 2015 10:11 pm

### Re: SUR estimation for shares that sum up to 1

Hi!

I’m trying to estimate a SUR system of market shares. But, as they sum up to 1, I know I’ve to drop an equation to avoid singularity. But, in doing so,
- should I impose a constraint in the system such that the shares still add up to 1, even though I’ve dropped an equation out.
- I’ve tried dropping different shares equations out. To get the remaining share that’s dropped out, I’ve just used 1- sun(shares forecasts from system). But, the remaining share forecast is always different depending on what’s dropped out. I’ve thought it’ll be the same as I’ve the same regressors.

jacarandas
Posts: 20
Joined: Tue Feb 10, 2015 10:11 pm

### Re: SUR estimation for shares that sum up to 1

EViews Gareth wrote:Ah, sorry, I thought you wanted the coefficients to sum to one, not the variables. I’m now not sure I understand what you are trying to do

Hi! Just wondering it’ll be able to get some help on this:

- I’ve Alpha, beta and gamma shares that add up to 1. I have the same explanatory variables for all of them plus one variable specific to each of the shares.
- to avoid the singularity issue, I dropped one equation. But I realise my results change depending on which equation I drop. Why? When I drop alpha, what I did to get the forecast alpha share is 1- beta - gamma.
- are there restrictions I should place in a SUR system like this to estimate these equations? And how can I do that? I’ve read a few articles on electrical parties and goods market shares where authors have excluded one equation to avoid singularity but no mention of restrictions to be placed.

Any help will be great. Thanks.

jacarandas
Posts: 20
Joined: Tue Feb 10, 2015 10:11 pm

### Re: SUR estimation for shares that sum up to 1

EViews Gareth wrote:Ah, sorry, I thought you wanted the coefficients to sum to one, not the variables. I’m now not sure I understand what you are trying to do

Hi Gareth,

Just wondering if you understand what I am trying to do now. See posts below?

Thanks!

EViews Gareth
Fe ddaethom, fe welon, fe amcangyfrifon
Posts: 11848
Joined: Tue Sep 16, 2008 5:38 pm

### Re: SUR estimation for shares that sum up to 1

I do not. But someone might.