Re: st: computing elasticities after using lpoly

[Nick Cox <njcoxstata@gmail.com>]

Although I don't usually recommend this, it's possible that your data
could be fitted well over the observed range by a low-order
polynomial, say a quadratic or cubic. If that's true, then varying
slopes can just be obtained by differentiating the polynomial
analytically.

Nick

On Sat, Oct 6, 2012 at 11:21 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> 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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