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st: How to calculate confidence interval of the long-run elasticity


From   San K <devank@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: How to calculate confidence interval of the long-run elasticity
Date   Fri, 3 Aug 2012 16:25:02 +1000

Hello,
I would like to check if I’m doing right to calculate to confidence
interval of the long-run elasticity estimates.

Here are the results from xtabond2.
----------------------------------------------------------------------------------
                 |              Corrected
    ConsDayAvgLN |      Coef.   Std. Err.      z    P>|z|     [95%
Conf. Interval]
-----------------+----------------------------------------------------------------
Lag4ConsDayAvgLN |   .2124323   .0607073     3.50   0.000     .0934483
   .3314164
  waitedAvgPrice |   .0000588   .0000306     1.92   0.055    -1.23e-06
   .0001189
waitedAvgPriceL1 |   .0007982   .0001699     4.70   0.000     .0004653
   .0011311
waitedAvgPriceL2 |  -.0005356   .0003933    -1.36   0.173    -.0013064
   .0002352
waitedAvgPriceL3 |  -.0003919     .00042    -0.93   0.351     -.001215
   .0004313
waitedAvgPriceL4 |  -.0013985   .0002538    -5.51   0.000     -.001896
   -.000901
          summer |  -.1151637   .0858191    -1.34   0.180     -.283366
   .0530386
          autumn |  -.1719444   .0863831    -1.99   0.047    -.3412522
  -.0026366
          winter |   -.181052   .0877778    -2.06   0.039    -.3530934
  -.0090106
          spring |  -.1314596   .0861975    -1.53   0.127    -.3004036
   .0374844
----------------------------------------------------------------------------------

This is what David (ddrukker@stata.com) suggests doing to calculate
the standard error.
http://www.stata.com/statalist/archive/2002-07/msg00028.html

Based on the above I did the following:
* calculate the long-run estimate
mat price_LR = (_b[waitedAvgPrice]+_b[waitedAvgPriceL1]+_b[waitedAvgPriceL2]+_b[waitedAvgPriceL3]+_b[waitedAvgPriceL4])/(1-_b
[Lag4ConsDayAvgLN])

* calculate Chi2
testnl 0 = (_b[waitedAvgPrice]+_b[waitedAvgPriceL1]+_b[waitedAvgPriceL2]+_b[waitedAvgPriceL3]+_b[waitedAvgPriceL4])/(1-_b[Lag
4ConsDayAvgLN])
  (1)  0 = (_b[waitedAvgPrice]+_b[waitedAvgPriceL1]+_b[waitedAvgPriceL2]+_b[waitedAvgPriceL3]+_b[waitedAvgPriceL4])/(1-_b[Lag4ConsDayAvgLN])
               chi2(1) =       31.19
           Prob > chi2 =        0.0000

* calculate the standard error
. mat stdError=price_LR/sqrt(r(chi2))

* Long-Run estimate at the price of $213
. mat price_LR_213=price_LR*213

Then finally using the Excel I calculated the 95% confidence level by
multiplying the stdError by 1.96 and add (or subtract) to the
price_LR_213.

Is this the correct way of doing it? Why I’m concern is that I’m
getting very tight confidence interval!

Any help is appreciated.

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