Experiences with multiple propensity score matching Jan Hagemejer & Joanna Tyrowicz University of Warsaw & National Bank of Poland

Plan 1. Standard solutions to the automatisation challenge 2. Where they do not work? Example of propensity score matching  Using loops and global function together  Generating the resultssets for atypical estimations.  Difficulties with using bootstrap (and obtaining resultssets ) 3. Summary comments … and some (hard learned) advices SUGM London, Jan Hagemejer & Joanna Tyrowicz

The standard route  Problem: several estimations of similar form + need to compare results.  Three simple solutions:  Solution 1: brute force = sit & type (copy / paste from output)  Solution 2: use parmest (Roger Newson) if estimations on simple categories in data (limitations of „by” command)  Solution 3: use loops  outreg/outreg2  nicely formatted tables,  publication-ready,  in many formats, even directly to Word or LaTeX.  Note: if you need nice summary statistics, you can use outsum either with by or within loops SUGM London, Jan Hagemejer & Joanna Tyrowicz

Where the problems come from?  2nd and 3rd solution works only with regression-type estimations  However, some procedures are incompatible with pre-cooked solutions  Need to report:  output of the procedure  sample properties after matching  balancing properties of matching  Problem1: actually, none of these is in the typical output  Problem2: we need it for many estimations looped over many variables and each one of them takes a looooong time SUGM London, Jan Hagemejer & Joanna Tyrowicz

Detailed problem description  Analyse the effects of privatisation  Take two firms A and A’. Firm A gets privatized. Firm A’ does not get privatised (ever). Want to compare firms A and A’ each year before and after privatisation of firm A (in fact we are comparing private firms to privatized SOEs due to few SOEs left in the sample)  Observe what happens before and after the „event” of privatisation  E.g. firm A may be one year before privatisation in 1999 and firm B in 2006, so „event” is an anchor and time „runs” both ways.  Effects may be observed in many spheres:  E.g. profits, investments, international competitiveness, employment, productivity  Effects may be due to self-selection  E.g. only better firms are privatised, so difference in performance is not due to privatisation (there might be other effects why firms are privatised related to, for instance, budget presure).  Use propensity score matching to compare privatised firms to non- privatised firms SUGM London, Jan Hagemejer & Joanna Tyrowicz

What we want to get: SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 6

Detailed problem description  Thus, in our case:  Many time periods (for each „time-to-anchor” a separate estimation)  Many variables (for each variable separate outcomes, but within one „anchor” the same balancing properties)  Two ways of estimating: regular and bootstrapping (especially the latter made things complex)  Each estimation: roughly hours (big dataset)  Over a hundred estimations  To verify if matching is ok, need to check balancing properties  Additional pitfalls :  We needed some statistics for all estimations and they were not in the return list  More precisely: procedure computes them to be able to produce output, but they were not added to the return list by authors SUGM London, Jan Hagemejer & Joanna Tyrowicz

Summary of the problems SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 8 Our problem was quite specific… BUT consisted of many general problems: 1. Loops take a lot of time – need to find efficient ways 2. Some things cannot be obtained fast => even more reasons to run it automatically 3. Obtaining datasets of the results we need (so-called resultssets )  Getting visible data if they are not an output  Using invisible data 4. Getting around with bootstrap

The structure of our estimations SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 9 Specific loops Balancing properties Before and after matching statistics Loop for variables (15 variables) Run standard estimations Run bootstrap estimation Loop for time (12 periods)

How global function can be usefull?

Using the global function for estimations SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 11  Our application: observe the same firms back and forth from the moment of privatisation („anchor”)  „Anchors” happen in different years  But we can only match on one dimension: has or has not the „anchor”  Conceptual solution: use lags and forwards to get the time dimension  Technical problem: many outcome variables and de facto many loops  Technical solution: define separately matching variables and output variables global in=„capital roa export_status etc…” MATCHING VARS! global out=„productivity employment efficiency etc…” COMPARISON VARS! global outf=„forwards of $out”

Getting from results to „resultssets”

Why (and what) do we need (in) the resultssets? SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 13  Why?  Most importantly: without resultssets we cannot  analyse the changes over time  decompose the observed differentials  If we do not do it automatically, it would have to be copied manually from logs – many estimations, many variables, etc  What ? Step 1: Find out the reality 1. Size of each of the three groups: treated, total and control (= matched) 2. Averages in all three groups (medians, etc.) 3. Knowledge if in fact they are different (= test of the statistical significance based on difference and standard error of this difference)  What? Step 2: find out, how good the findings are statistically 1. Balancing properties!

Our solution to step 1 SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 14  Initialize the store for our resultsets using postfile. Index the result table with variable names, years and other things that the code loops around tempname memhold postfile memhold indices variable_names_for_results  Start the big loop (event) forvalues d=6(1)18 {  Run pscore (needed for bootstrap) and subsequently psmatch psmatch2 d`d' our_pscore_`d', out($out $outf $outl) some options

Our solution to step 1  Run pscore and psmatch psmatch2 d`d' our_pscore_`d', out($out $outf $outl) some options  Start the loop foreach out in $out $outf1 $outf2 {  Generate means and standard errors for treaded/matched/unmatched, using output from psmatch (some more about this later) local se_after=r(seatt_`out')  Post the `locals’ to the postfile using post command in each loop iteration SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 15

Our solution to step 2 SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 16  For balancing properties we need to use pstest over all the matching variables pstest $in  In order to produce nice tables, we need to loop over all the matching variables in $in and create some ‚locals’ in memory to later save them as separate variables: foreach in in $in { capture local bias_reduction=r(bired_`in') capture local pvalue_bef=r(pbef_`in') capture local pvalue_after=r(paft_`in') capture gen b_red_`in'=`bias_reduction' capture gen pval_ber_`in'=`pvalue_bef' capture gen pval_aft_`in'=`pvalue_after‚ }  Spit out everything to a spreadsheet (alternatively you can use postfile again): outsheet b_red* pval* using stats_priv_`d', replace  Make some graphs and clean up psgraph graph save priv_support_`d', replace drop b_red* pval*

„Missing statistics”

Solving problem of „missing” statistics  Psmatch produces nice tables with all the required statistics. However, they are only shown on the screen and vanish right after that  Look into the „ado” file you are using (procedure)  Throughout the file, there are commands return scalar x=`somelocal’  Sometimes – for clarity – scalars are dropped at the end of procedure  Your prefered statistic (if it is in the output, it has to be at least a local) would simply have to have a local like that too  If it does not – you can always generate it based on your preferences and available locals => Modify the original ado file SUGM London, Jan Hagemejer & Joanna Tyrowicz

Solving problem of „missing” statistics – example 1 Original ado file – line 380 Modified ado file – line 380 SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 19 qui foreach v of varlist `varlist' { replace _`v' =. if _support==0 tempname m1t m0t u0u u1u att dif0 sum `v' if _treated==1, mean scalar `u1u' = r(mean) sum `v' if _treated==0, mean scalar `u0u' = r(mean) sum `v' if _treated==1 & _support==1, mean scalar `m1t' = r(mean) local n1 = r(N) sum _`v' if _treated==1 & _support==1, mean scalar `m0t' = r(mean) scalar `att' = `m1t' - `m0t' scalar `dif0' = `u1u' - `u0u‘ return scalar att = `att' return scalar att_`v' = `att‚ /no „return” of needed scalars/ qui foreach v of varlist `varlist' { replace _`v' =. if _support==0 tempname m1t m0t u0u u1u att dif0 … /all the same as earlier plus / return scalar diff = `dif0' return scalar diff_`v' = `dif0‘ return scalar mean0 = `u0u' return scalar mean0_`v' = `u0u‘ return scalar mean1 = `u1u' return scalar mean1_`v' = `u1u'

Solving problem of „missing” statistics – example 2 return scalar seatt = `stderr' return scalar seatt_`v' = `stderr' qui regress `v' _treated scalar `ols' = _b[_treated] scalar `seols' = _se[_treated] return scalar seatt = `stderr' return scalar seatt_`v' = `stderr' qui regress `v' _treated scalar `ols' = _b[_treated] scalar `seols' = _se[_treated] return scalar seols = `seols‘ return scalar seols_`v' = `seols' SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 20 Original ado file – line 440 Modified ado file – line 440

Problems with bootstrap

 The psmatch procedure does not take into account when calculating se’s that the propensity score is estimated. A possible solution to this is to use bootstrap.  What problems with bootstrap ?  Need to run it separately for each variable (it bootstraps only one standard error at a time)  Output is given in a totally different form  It takes a looong time  New piece of code for just BS standard errors => new variable loops within each time loop SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 22

Problems with bootstrap SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 23  Again, create the postfile  Run the actual bootstrap in loops (post results in every iteration) foreach out in $out $outf1 $outf2 { use data, clear bootstrap r(att): psmatch2 d`d‘ $in, out(`out') some options matrix mat = e(b), e(se) /without this, no resultssets/ svmat mat /convert matrix to variables/ rename mat1 a`d'_diff_after_bs_`out‘ /create meaningful names/ rename mat2 a`d'_se_after_bs_`out‘ gen time_of_event=`d post `postfile’ indices (a`d'_diff_after_bs_`out‘) (a`d'_se_after_bs_`out‘) } postfile close

Final steps 1. Merge files obtained from bootstrap on „anchor” (to have a complete resultsset within each „anchor” period) 2. Organise the data 3. Produce tables and graphs (again in loops) 4. Write paper SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 24

The resulting graphs (1)  6 figures showing levels for 3 groups (15 matches each) SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 25

The resulting graphs (2)  6 figures showing the decomposition of the treated- unmatched difference (15 matches each) SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 26

The resulting graphs (3)  6xn figures showing the „balanced panel” version for all variables of the treated-unmatched difference SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 27

Some advices we did not take at the right time 1. Use „sample 10” for testing procedures - saves a lot of time 2. Leaving mess is not useful if we ever want to come back  Your memory lasts shorter than that of saved files – describing dofiles really helps  Loops are better than copy&paste – and less messy too 3. Beware of changes in STATA syntax (all the time…) SUGM London, 2012Jan Hagemejer & Joanna Tyrowicz 28

Thank you for your attention! Jan Hagemejer & Joanna Tyrowicz University of Warsaw and National Bank of Poland