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# SV: st: Transition matrices and probabilities.

 From Andreas Dall Frøseth To "statalist@hsphsun2.harvard.edu" Subject SV: st: Transition matrices and probabilities. Date Thu, 2 May 2013 14:53:57 +0000

```I have a follow-up question on this topic.

I've managed to use the -svy:tab- command to create the transition matrix, and now wish to use the proportions to test my hypothesis.

So, my hypotheses are equal to those in the article I posted earlier, and as follows:
H1: "Firms that show high profitability at low growth (value 3 in the variable I used in the transition matrix) are more likely to reach a state of high growth and high profitability (value 4 in the same variable) in subsequent periods than are firms that first show high growth at low profitability (value 2)."

H2: "Firms that show high growth at low profitability (value 2) are more likely to reach a state of low growth and low
profitability (value 1) in subsequent periods than are firms that first show high profitability at low growth (value 3)."

And here is my transition matrix:
(From: . svy:ta lkategorier kategorier, row)

-----------------------------------------------------------
lkategori |                   kategorier
er        |     1      2      3      4      5      6  Total
----------+------------------------------------------------
1 | .2062  .2447  .0428  .1634  .2156  .1275      1
2 | .2683  .1768  .0878  .1122  .2549     .1      1
3 | .1445  .0929  .1561  .2619  .2026  .1419      1
4 | .1634  .0305   .269  .2698  .1914  .0759      1
5 | .2076  .0735  .1006  .1792  .3636  .0754      1
|
Total | .1978  .1183  .1312  .1974  .2558  .0995      1
-----------------------------------------------------------

(lkategorier is the lagged variable to kategorier)

Any suggestions to how I proceed to test these hypotheses?

- Andreas
________________________________________
Fra: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] p&#229; vegne av Austin Nichols [austinnichols@gmail.com]
Sendt: 23. april 2013 20:16
Til: statalist@hsphsun2.harvard.edu
Emne: Re: st: Transition matrices and probabilities.

Nick and
Andreas Dall Frøseth--

3. -svyset- to enable testing after:
4. -svy:tab- to get column proportions for a standard transition matrix
http://www.stata.com/statalist/archive/2011-04/msg01110.html

There are a variety of other considerations, left for a possible
future SJ paper (?)...
but I recommend http://www.jstor.org/stable/1914306 to start thinking

I have not seen the cited paper, but
"four categories, based on growth and profits (above or below industry
average),"
sounds like a harebrained way to model firm growth.
Where is the q theory? Where is debt and equity finance? What are the
effects of foreign investment? Taxes?
http://www.brookings.edu/~/media/Projects/BPEA/1981%201/1981a_bpea_summers_bosworth_tobin_white.PDF

On Tue, Apr 23, 2013 at 12:37 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> Search the archives for "transition probabilities". Austin Nichols has
> often shown on this list that you just need
>
> 1. A categorical variable showing system state.
>
> 2. -tsset-, so that lagged variables can be defined.
>
> 3. -tabulate-.
>
> Here is a dopey example.
>
> . webuse grunfeld, clear
>
> . su invest , detail
>
>                            invest
> -------------------------------------------------------------
>       Percentiles      Smallest
>  1%         1.27            .93
>  5%        2.215           1.18
> 10%         9.73           1.36       Obs                 200
> 25%       33.405           1.81       Sum of Wgt.         200
>
> 50%       57.485                      Mean           145.9583
>                         Largest       Std. Dev.      216.8753
> 75%       140.36          755.9
> 90%       460.25          891.2       Variance       47034.89
> 95%       565.05         1304.4       Skewness       2.895513
> 99%       1097.8         1486.7       Kurtosis       13.90504
>
> . gen which = invest > r(p50)
>
> . tsset company year
>        panel variable:  company (strongly balanced)
>         time variable:  year, 1935 to 1954
>                 delta:  1 year
>
> . gen previous = L.which
> (10 missing values generated)
>
> . tab which previous
>
>            |       previous
>      which |         0          1 |     Total
> -----------+----------------------+----------
>          0 |        81         11 |        92
>          1 |        17         81 |        98
> -----------+----------------------+----------
>      Total |        98         92 |       190
>
>
> . tab which previous, col
>
> +-------------------+
> | Key               |
> |-------------------|
> |     frequency     |
> | column percentage |
> +-------------------+
>
>            |       previous
>      which |         0          1 |     Total
> -----------+----------------------+----------
>          0 |        81         11 |        92
>            |     82.65      11.96 |     48.42
> -----------+----------------------+----------
>          1 |        17         81 |        98
>            |     17.35      88.04 |     51.58
> -----------+----------------------+----------
>      Total |        98         92 |       190
>            |    100.00     100.00 |    100.00
>
> Nick
> njcoxstata@gmail.com
>
>
> On 23 April 2013 14:19, Andreas Dall Frøseth
> <Andreas.Froseth@stud.nhh.no> wrote:
>> Dear listers.
>>
>> I am currently experiencing some difficulties regarding the analysis in my research paper. I'm trying to replicate the method used in Davidsson, P., Steffens, P. & Fitzsimmons, J. (2009) "Growing profitable or growing from profits: putting the horse in front of the cart?" Journal of Business Venturing, 24(4).. 388-406. This study analysis the relationship between growth and profits, trying to find what determines the best basis for future profitable growth within their sample of swedish and australian firms. They define four categories, based on growth and profits (above or below industry average), and use state transition probabilities as a starting point of their analysis. Further they use standard z-tests to test the differences between the transition proportions. I'm sorry if this explanation is unclear, but hopefully you'll have access to the paper, for further explanations.
>>
>> My question on this matter is; is there a way to do this in Stata? I.e. a command allowing me to calculate the transition probabilities on 1 year transitions, as well as 3 or 5 year transitions. I'm working with a large set of (unbalanced) panel data, containing a large number of companies, identified with a company ID. The time variable is "year", being data from 1999 - 2010, but with gaps. At this point, I have calculated the needed variables, but have yet to place the companies in their respective categories, due to uncertainties on another point (a post I made to the list earlier).
>> If there is no good way to implement this in STATA, I would appreciated it if anyone have suggestions on software that can perform such analysis.
>>
>> All feedback will be appreciated.

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