Dear all,
I am having a quadratic polynomial loss function of the form :
for a macro panel for a larger period of years and for numerous countries with the solid macro variables, dummies, categorical variables and some custom quality indicators, expressed in percentage, which you can see in the data example below for shorter time length and fewer countries.
where It and Xt are referred to an indicator and the output gap (gdp_hp in the sample data) in period t, respectively, I* is the indicator optimal target, and λ > 0
is the relative weight on output- gap stabilization. The intertemporal loss function in period t is
I am looking for a code/program that will allow me to find the stochastically optimized value in every year and every country for the indicator1 and its corresponding GDP output in the sample data, generated stochastically those two new variables in my real dataset that are continuous and discrete for the indicator and gdp values separately, for each country and year such that for those values can bring actual GDP close to steady state(potential output), or minimize at most the cyclical component of output estimated with a hp filter.
Output gap is Xt. : measure of the difference between the actual output and the output it could achieve when at full capacity. Present in the data with hp filter estimation.
δ, (0 <δ<1), is adiscount factor has also in some way the role of special capital. It is assumed to be high at the beginning of the period, lowering as times passes, reaching to lowest at the end of period. End of persiod is shown with dummy 1
I have used margins for the panel estimations as whole , but need to estimate each year and country separately by getting the optimal values of the indicator and country in each year and for each country.
I have seen also the optimization manual , was not able to solve though . Data sample is below:
I would appreciate any help you can provide
Thank you in advance
Best.
Mario Ferri! .
I am having a quadratic polynomial loss function of the form :
for a macro panel for a larger period of years and for numerous countries with the solid macro variables, dummies, categorical variables and some custom quality indicators, expressed in percentage, which you can see in the data example below for shorter time length and fewer countries.
where It and Xt are referred to an indicator and the output gap (gdp_hp in the sample data) in period t, respectively, I* is the indicator optimal target, and λ > 0
is the relative weight on output- gap stabilization. The intertemporal loss function in period t is
I am looking for a code/program that will allow me to find the stochastically optimized value in every year and every country for the indicator1 and its corresponding GDP output in the sample data, generated stochastically those two new variables in my real dataset that are continuous and discrete for the indicator and gdp values separately, for each country and year such that for those values can bring actual GDP close to steady state(potential output), or minimize at most the cyclical component of output estimated with a hp filter.
Output gap is Xt. : measure of the difference between the actual output and the output it could achieve when at full capacity. Present in the data with hp filter estimation.
δ, (0 <δ<1), is adiscount factor has also in some way the role of special capital. It is assumed to be high at the beginning of the period, lowering as times passes, reaching to lowest at the end of period. End of persiod is shown with dummy 1
I have used margins for the panel estimations as whole , but need to estimate each year and country separately by getting the optimal values of the indicator and country in each year and for each country.
I have seen also the optimization manual , was not able to solve though . Data sample is below:
I would appreciate any help you can provide
Thank you in advance
Best.
Mario Ferri! .
Code:
* Example generated by -dataex-. To install: ssc install dataex clear input float id int year str48 country double gdp float(indicator1 cpi u industry dummy1 dummy2 dummy3 gdp_cyclical gdp_trend gpd_gain gdp_a) 1 1990 "Australia" 310777222008.465 -12.242857 7.333022 6.926 . 1 1 1 2639502848 308137721856 .0394041 .28559932 1 1991 "Australia" 325310415195.04 -14.9 3.176675 9.5792 93713.09 0 0 0 10349180928 314961231872 .3865072 .57119864 1 1992 "Australia" 324878874105.975 -14.9 1.0122311 10.7288 92812.27 0 0 0 2671803648 322207055872 .7486191 .856798 1 1993 "Australia" 311544406970.208 -3.484423 1.7536534 10.8738 94994.95 1 1 1 -20409010176 3.319534e+11 .8952165 1.1423973 1 1994 "Australia" 322211691456.244 -.165 1.9696348 9.7187 96376.65 0 0 0 -24494258176 3.46706e+11 .9484286 1.4279966 1 1995 "Australia" 367216364716.365 -.165 4.6277666 8.4693 99077.38 0 0 0 1511457536 3.657049e+11 .9702576 1.713596 1 1996 "Australia" 400302731411.229 18.228453 2.6153846 8.5062 102631.7 1 1 1 16031287296 384271450112 .9804248 1.9991953 1 1997 "Australia" 434568007512.913 22.593 .22488755 8.3622 104749.55 0 0 0 36599459840 3.979685e+11 .985604 2.2847946 1 1998 "Australia" 398899138574.239 27.6381 .8601346 7.6756 109901.92 1 0 0 -6025076224 4.049242e+11 .9883389 2.570394 1 1999 "Australia" 388608221581.652 48.458 1.4831294 6.8723 114295.6 0 0 0 -20514129920 4.091223e+11 .9896897 2.855993 1 2000 "Australia" 415222633925.768 48.458 4.457435 6.2826 113996.52 0 0 0 1639782144 4.135829e+11 .990099 3.141593 2 1990 "France" 1269179616913.63 -13.6 3.1942835 9.36 . 0 0 0 12937712640 1.2562419e+12 .0394041 .28559932 2 1991 "France" 1269276828275.78 -13.6 3.213407 9.1341 57521.93 0 0 0 -34903797760 1.3041807e+12 .3865072 .57119864 2 1992 "France" 1401465923172.24 -13.6 2.3637605 10.2052 60116.48 0 0 0 47276544000 1.3541894e+12 .7486191 .856798 2 1993 "France" 1322815612694 -1.6244903 2.1044629 11.3213 59929.35 1 1 1 -79937978368 1.4027536e+12 .8952165 1.1423973 2 1994 "France" 1393982750472.59 2.136771 1.6555153 12.5928 62658.27 0 0 0 -59940192256 1.453923e+12 .9484286 1.4279966 2 1995 "France" 1601094756209.75 2.136771 1.7964814 11.8356 63422.89 0 0 0 102137733120 1.498957e+12 .9702576 1.713596 2 1996 "France" 1605675086549.56 2.136771 1.9828837 12.3673 63864.86 0 0 0 86150086656 1.519525e+12 .9804248 1.9991953 2 1997 "France" 1452884917959.09 -8.4159155 1.203943 12.5662 64603.23 1 1 1 -60753162240 1.513638e+12 .985604 2.2847946 2 1998 "France" 1503108739159.44 -16.154552 .6511269 12.0749 66943.195 0 0 0 10017265664 1.4930915e+12 .9883389 2.570394 2 1999 "France" 1492647560196.04 -16.154552 .5371416 11.9808 68686.82 0 0 0 32687667200 1.45996e+12 .9896897 2.855993 2 2000 "France" 1362248940482.77 -16.154552 1.67596 10.2172 70390.32 0 0 0 -55671873536 1.4179208e+12 .990099 3.141593 3 1990 "United Kingdom" 1093169389204.55 30.468 8.063461 6.9736 . 0 0 0 12594491392 1.0805749e+12 .0394041 .28559932 3 1991 "United Kingdom" 1142797178130.51 30.468 7.461783 8.5521 53880.47 0 0 0 38082850816 1.1047143e+12 .3865072 .57119864 3 1992 "United Kingdom" 1179659529659.53 28.6106 4.5915494 9.7772 55163.84 1 1 1 48790659072 1.1308689e+12 .7486191 .856798 3 1993 "United Kingdom" 1061388722255.55 27.9 2.558578 10.3482 57319.64 0 0 0 -105758187520 1.1671469e+12 .8952165 1.1423973 3 1994 "United Kingdom" 1140489745944.29 27.9 2.2190125 9.6502 62721.02 0 0 0 -88973582336 1.2294634e+12 .9484286 1.4279966 3 1995 "United Kingdom" 1341584345905 27.9 2.697495 8.6936 63936.54 0 0 0 24772661248 1.3168117e+12 .9702576 1.713596 3 1996 "United Kingdom" 1415358814352.57 27.9 2.851782 8.1916 64279.65 0 0 0 1409031680 1.41395e+12 .9804248 1.9991953 3 1997 "United Kingdom" 1559078258022.27 14.663176 2.201143 7.0722 65329.98 1 1 1 49479213056 1.509599e+12 .985604 2.2847946 3 1998 "United Kingdom" 1650172242464.39 8.072 1.8205616 6.2032 65680.11 0 0 0 5.74659e+10 1.5927063e+12 .9883389 2.570394 3 1999 "United Kingdom" 1682399288141.08 8.072 1.7529508 6.0429 67823.23 0 0 0 22264080384 1.660135e+12 .9896897 2.855993 3 2000 "United Kingdom" 1657816613708.58 8.072 1.1829562 5.5616 69648.87 0 0 0 -60127121408 1.7179438e+12 .990099 3.141593 4 1990 "United States" 5.963144e+12 29.4 5.397956 5.6 . 1 0 0 84337139712 5.878807e+12 .0394041 .28559932 4 1991 "United States" 6.158129e+12 29.4 4.234964 6.8 . 0 0 0 -39289442304 6.197419e+12 .3865072 .57119864 4 1992 "United States" 6.520327e+12 29.4 3.0288196 7.5 . 1 0 0 -9196966912 6.529524e+12 .7486191 .856798 4 1993 "United States" 6.858559e+12 13.382143 2.951657 6.9 . 0 0 0 -23772067840 6.882331e+12 .8952165 1.1423973 4 1994 "United States" 7.287236e+12 12.5 2.607442 6.1187 . 1 0 0 25660139520 7.261576e+12 .9484286 1.4279966 4 1995 "United States" 7.639749e+12 12.5 2.80542 5.6504 . 0 0 0 -29441933312 7.669191e+12 .9702576 1.713596 4 1996 "United States" 8.073122e+12 12.5 2.931204 5.4511 . 1 0 0 -38092492800 8.111215e+12 .9804248 1.9991953 4 1997 "United States" 8577554463000 8.977967 2.3376899 5.0003 74095.41 0 0 0 -11419578368 8.588974e+12 .985604 2.2847946 4 1998 "United States" 9062818211000 8.784 1.552279 4.5105 75984.69 1 0 0 -34884067328 9.097702e+12 .9883389 2.570394 4 1999 "United States" 9630664202000 8.784 2.1880271 4.2188 79374.63 0 0 0 -140565792 9.630805e+12 .9896897 2.855993 4 2000 "United States" 10252345464000 8.784 3.376857 3.992 81904.71 1 0 0 76239831040 1.0176106e+13 .990099 3.141593 end format %ty year
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