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# Re: st: computing elasticities after using lpoly

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: computing elasticities after using lpoly Date Sat, 6 Oct 2012 11:21:59 +0100

```That paper is not accessible to me at this time.

You can differentiate numerically using -dydx-.

But I wouldn't use -lpoly- for that purpose at all. I would use
-fracpoly- or a spline approach (e.g. -rcspline- (SSC)) to get smooths
before I tried to get slopes. The problem with all these approaches is
that estimates of slope are very sensitive to noise.

Nick

On Sat, Oct 6, 2012 at 11:07 AM, Arka Roy Chaudhuri <gabuisi@gmail.com> wrote:
> Thank you Nick for your advice. However my point in using lpoly is
> precisely its flexibility. But at the same time I want a measure of
> the slope of the curve that I get from using lpoly at different points
> of the curve-so I am not actually looking for one specific
> number.Rather I am trying to find the slope at different values of my
> independent variable-so that I can get an idea of the elasticities at
> different parts of the expenditure distribution. Basically I am trying
> to implement both Fig 2 and Fig 3 in the following paper (albeit in my
> context):Deaton, Angus S. and Subramanian, Shankar. "The Demand for
> Food  and Calories," Journal of Political Economy, Feb.  1996,104(1),
> pp. 133-62
>
> On Sat, Oct 6, 2012 at 2:19 AM, Nick Cox <njcoxstata@gmail.com> wrote:
>> It seems to me that the whole point of -lpoly- is to be flexible about
>> modelling a relationship. It has absolutely no sense of any idea of an
>> overall slope. If you want a number for the slope, -lpoly- is useless.
>> If you want an independent view of how far the relationship after some
>> smoothing really is (e.g.) linear or monotonic, then -lpoly- can be
>> useful, mostly by providing a graph. For what you want, any
>> appropriate regression method will be better, such as -regress- or
>> -qreg-.
>>
>> Nick
>>
>> On Sat, Oct 6, 2012 at 10:06 AM, Arka Roy Chaudhuri <gabuisi@gmail.com> wrote:
>>
>>> I am using Stata 11 on a Windows 7 machine. I am using lpoly to
>>> estimate nonparametric regressions of the form:
>>>
>>> log(y)=f(log(x)) + u
>>>
>>> where y= per capita expenditure on food
>>> x= total per capita expenditure
>>>
>>> Using lpoly, I can get a graph of per capita expenditure on food
>>> against total per capita expenditure. However I am also interested in
>>> obtaining expenditure elasticities of percapita expenditure on food at
>>> different levels of  total per capita expenditure i.e in my context
>>> d(log(y)/d(log(x)) where x and y are as earlier defined.The problem is
>>> that lpoly does not give estimates of any slope coefficients so I am
>>> at a loss on how to compute these elasticities. I would really
>>> appreciate if anybody could give me advice in this regard.
>>>
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