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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: RE: st: string functions on the name of a variable |

Date |
Sun, 27 Nov 2005 17:55:38 -0000 |

Wow! How many data points? How many parameters? How much collinearity? The correct name is Fourier, as already pointed out. Apart from that pedantic correction, I regret that this is too complex a question for me in the time available. Nick n.j.cox@durham.ac.uk Dev Vencappa > Nick, thanks for the solution you provided. I have tried it > but got stuck and on second thoughts I realised it may be > better to explain more clearly what I want exactly. > > Suppose I have the following equation to estimate: > > to=f(clli, clnl, ca, te, re) > > We want to estimate a flexible fourier representation of the > above. The final equation will have the first five terms, > translog terms and trigonometric terms, as follows: > > to= clli + clnl + ca + te + re + Translog terms + Fourier terms > where Translog terms are: (0.5*clli^2)+(0.5*clnl^2) + > (0.5*ca^2)+(0.5*te^2)+(0.5*ro^2)+ (clli * clnl) + (clli * > ca)+ (clli * te) + (clli * ro) + (clnl * ca)+ (clnl * te) + > (clnl * ro)+ (ca*te) + (ca*ro) + (te*ro) > > where Fourier terms are > > sin(clli) + cos (clli)+ sin (clnl) + cos (clnl) + sin(ca) + > cos (ca) + sin (te) + cos (te) + sin (ro) + cos (ro) > > By flexible fourrier I mean that one can have more layers of > trigonometric terms that combine these variables in different > ways, eg. combining two variables as follows: > > sin(clli+ clnl) + cos (clli+clnl)+ sin (clli+ca) + cos > (cli+ca) + sin (clli+te) + cos (clli+te) + sin (clli+ro) + > cos (clli+ro) + sin (clnl+ca) + cos (clnl+ca) + sin (clnl+te) > + cos (clnl +te) + sin(clnl+ro) + cos (clnl + ro) + sin > (ca+te) + cos (ca+te) + sin (ca+ro) + cos (ca+ro) + sin > (te+ro) + cos (te+ro) > > Another layer of this function would be combining three > variables in the same way, four variables and five variables > (five would be the highest combination of variables one can > create because there are only five right hand side variables) > > Now, each of these right hand side variables is rescaled > using a particular formulae (e.g. see paper by A. Kasnan > (2002) Central Bank Review 1, pp. 1-20). I have copied below > how I created the variables and the rescaling used. > > gen to=lntoen > gen pro=lnprof > gen clli=lnclli > gen clnl=lnclnl > gen ca=lnca > gen te=lntech > gen ro=lnroin > gen pril=lnpril > gen prinl=lnprinl > > local var "to pro clli clnl ca te ro" > foreach j of local var{ > sum `j' > gen x=(1.6*_pi)/(r(max)-r(min)) > gen z=(0.2*_pi)-(x*r(min))+(x*`j') > *z is the rescaling to be applied to each variable > gen R`j'=z > *create trigonometric terms for these rescaled variables > gen sin`j'=sin(R`j') > gen cos`j'=cos(R`j') > *create squared terms of the rescaled variable > gen `j'sqr=0.5*R`j'^2 > drop x z > } > > local z "clnl ca te ro" > foreach x of local z{ > gen clli`x'=Rclli*R`x' > gen sinclli`x'=sin(Rclli+R`x') > gen cosclli`x'=cos(Rclli+R`x') > } > > local z "ca te ro" > foreach x of local z{ > gen clnl`x'=Rclnl*R`x' > } > > gen cate=Rca*Rte > gen caro=Rca*Rro > gen tero=Rte*Rro > > local z "prinl ca te ro" > foreach x of local z{ > gen pril`x'=Rpril*R`x' > gen sinpril`x'=sin(Rpril+R`x') > gen cospril`x'=cos(Rpril+R`x') > } > > local z "ca te ro" > foreach x of local z{ > gen prinl`x'=Rprinl*R`x' > gen sinprinl`x'=sin(Rprinl+R`x') > gen cosprinl`x'=cos(Rprinl+R`x') > } > > *create third layer of FF function > local z "sin cos" > foreach x of local z{ > gen `x'clliclnlca=`x'(Rclli+Rclnl+Rca) > gen `x'clliclnlte=`x'(Rclli+Rclnl+Rte) > gen `x'clliclnlro=`x'(Rclli+Rclnl+Rro) > gen `x'cllicate=`x'(Rclli+Rca+Rte) > gen `x'cllicaro=`x'(Rclli+Rca+Rro) > gen `x'clnlcate=`x'(Rclnl+Rca+Rte) > gen `x'clnlcaro=`x'(Rclnl+Rca+Rro) > gen `x'clnltero=`x'(Rclnl+Rte+Rro) > gen `x'catero=`x'(Rca+Rte+Rro) > gen `x'prilprinlca=`x'(Rpril+Rprinl+Rca) > gen `x'prilprinlte=`x'(Rpril+Rprinl+Rte) > gen `x'prilprinlro=`x'(Rpril+Rprinl+Rro) > gen `x'prilcate=`x'(Rpril+Rca+Rte) > gen `x'prilcaro=`x'(Rpril+Rca+Rro) > gen `x'prinlcate=`x'(Rprinl+Rca+Rte) > gen `x'prinlcaro=`x'(Rprinl+Rca+Rro) > gen `x'prinltero=`x'(Rprinl+Rte+Rro) > *create fourth layer of FF function > gen `x'clliclnlcate=`x'(Rclli+Rclnl+Rca+Rte) > gen `x'clliclnlcaro=`x'(Rclli+Rclnl+Rca+Rro) > gen `x'clliclnltero=`x'(Rclli+Rclnl+Rte+Rro) > gen `x'cllicatero=`x'(Rclli+Rca+Rte+Rro) > gen `x'clnlcatero=`x'(Rclnl+Rca+Rte+Rro) > *fifth layer > gen `x'clliclnlcatero=`x'(Rclli+Rclnl+Rca+Rte+Rro) > } > > To make it easier for estimation, I store the Translog terms > in a global macro, and same for each of the layers of the > fourier terms (i.e. first layer, second layer, etc) > > My first question is how I find a shortcut way of creating > these different combinations of fourier terms? > Clearly, somehow, Stata will need to be told that if two > variables are combined once through a sine and cosine of > their additions, then they cannot be combined a second time. > > Second, suppose I have estimated an equation. Suppose I want > to differentiate the above with respect to all variables that > have clli in their names and add all these partial > derivatives. This would be the addition of all these terms > retrieved from the estimated coefficients. When there are > interaction of terms,I am not too sure how to handle this in > an automated function in Stata. > > Suppose I have a translog term cllica which is the product of > clli and ca. differentiating lntoen with respect to clli will > be the coefficient of cllica multiplied by ca (I will > evaluate this at mean values of the variables). Any thoughts > on how I would go about doing this automatically please? > > It gets a little bit more complicated for me when I try with > the fourrier terms. Suppose my variable is > > sincllica =sin (Rclli+Rca). The derivative with respect to > clli is _b[sincllica]*cos(clli+ca) > > or if > > coscllica =cos (Rclli+Rca). The derivative with respect to > clli is _b[coscllica]* - sin(Rclli+Rca) > > How would I tell Stata to automatically deal with that (i.e > recognise where there are sin and cosine variables (I guess > wildcards will provide the solution here but I can't figure > out how to write this)? The solution to this will be the > solution for the third layers, fourth layers and fifth layers as well. > > Apologies for this long email, but I would really be grateful > if a shortcut solution to this problem were available as I am > finding myself writing a very long do file to work this out. > Many thanks in advance. > > Dev > > >>> n.j.cox@durham.ac.uk 11/21/05 11:14 am >>> > I don't see that you need a function here. > > The set of variables with "clli" as part of > their names is given by the wildcard *clli* > and so can be put into a macro by > > unab clli : *clli* > > Presumably you know what variables appear > on the RHS of your regression and can manufacture > a local macro containing them, say rhs. > > The intersection is then > > local cllirhs : list clli & rhs > > and you can cycle over these with > > foreach v of local cllirhs { > ... = ... + _b[`v'] > } > > Assuming that by Fourrier you mean Fourier, I don't see why > handling a set of Fourier terms need be messy. The utility > -fourier- from -circular- on SSC provides one way of getting > a bunch of them. > > Alternatively, in one recent program I needed to generate a bunch > of them on the fly. Here is the code generalised mildly: > > // regression in terms of sin j theta, cos j theta > local sc > local terms = <plug in your own> > > forval j = 1/`terms' { > tempvar S C > gen `S' = sin(`j' * `theta') > gen `C' = cos(`j' * `theta') > local sc `sc' `S' `C' > } > > // regression will fail if data points too few > // or response missing > // assumes a `touse' marking observations to be used > > capture regress <response to be plugged in> `sc' if `touse' > if _rc gen `sm' = . if `touse' > else predict `sm' if `touse' > > drop `sc' > > On the other hand, quite what a "Flexible" Fourier analysis > is I don't know. > > Nick > n.j.cox@durham.ac.uk > > Dev Vencappa > > > I have the following problem and would be grateful if you > > could provide some help: > > > > Suppose I have a regression equation with lntoen as my > > dependent variable and a lot of right hand side variables > > called lncllisqr lncllica lncllite lncaclli (and there are > > more variables like these which contain the word "clli" in > > their name as well as other variables named differently). > > After estimation, I am trying to add the coefficients of all > > variables in an estimation that have "clli" in their names. > > While I can do this manually by using _b[variablename], I am > > faced with a problem as I am estimating a Flexible Fourrier > > function, which tends to be very messy in terms of the > > addition of trigonometric terms. > > > > I am trying to differentiate lntoen with respect to all > > variables that contain "clli" in their names. I am trying to > > automate this process by asking stata to add the coefficients > > of all variables that contain "clli" in their names. > > > > Does anybody know if there is an equivalent to one of the > > list of string functions (such as e.g. substr) that can allow > > me to write some condition to check if the variable contains > > the characters "clli" in its name and then add their > > coefficients please? > > > > Apologies if a similar posting has been up on the list before > > and escaped my attention. > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > This message has been checked for viruses but the contents of > an attachment > may still contain software viruses, which could damage your > computer system: > you are advised to perform your own checks. Email > communications with the > University of Nottingham may be monitored as permitted by UK > legislation. > > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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