Estimate parameters of an indicator* that* minimize the difference between current GDP and potential GDP.

[Giorgio Di Stefano]

Dear all,

I am having a macro panel for a larger period of years and for a number of countries with the solid macro variables, dummies and some custom quality indicators, expressed in percentage, that I created as part of the project, A sample is provided below. According to my model indicators definitely determine macro variables.

I am looking for a way that will allow me to estimate the cost (or benefit) of each specific indicator, calculated as the cost of the percentage of GDP that has been given up due to each of the indicators not being at their optimal values. Determination is by taking the cost of lost output and dividing it by percentage change in the indicator of their optimal values to the actual.

In a simple formula that will be
Δgdp/Δindicator

Where :
Δ gdp is the variation (loss) of the GDP from the value of what output would have been if the indicator was at their optimal values

And

Δindicator the variation of their optimal values to the actual ones.

My first thought was an ML program with a Newton Raphson optimization or another way that could fit into the case as long as it is able to generate the required values and to estimate the cost.


In a detailed analysis I am looking for a way that will allow me to create stochastically a new variable that is continuous and discrete for each one of the indicator values separately and for each period that subject to the indicator, GDP (output) will minimize losses from their trend or to put in another way the cyclical trend will be minimized as much as possible


In a nutshell, in simple methodical words, find the stochastic optimized value in every period for each one of the indicators (i.e indicator1 in the sample data) 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 an hp filter. To estimate the parameters of the indicator that minimize the difference between current GDP and potential GDP and consequently the cost. My model is a panel var, but not so important is this step if the exercise. .

I would be grateful to you if you could be of my help or to suggest a way to perform this part.


* Example generated by -dataex-. To install: ssc install dataex
clear
input float id int ts str48 country double gdp float GDP_g double gdp_real float(indicator dummy gdp_cyclical gdp_trend gpd_gain gdp_a)
1 1990 "Australia" 310777222008.465 1.5 612845441833.156 -12.242857 1 2639502848 308137721856 .0394041 .28559932
1 1991 "Australia" 325310415195.04 -1.01 610411025719.071 -14.9 0 10349180928 314961231872 .3865072 .57119864
1 1992 "Australia" 324878874105.975 2.52 612929148885.66 -14.9 0 2671803648 322207055872 .7486191 .856798
1 1993 "Australia" 311544406970.208 3.83 637626569147.174 -3.484423 1 -20409010176 3.319534e+11 .8952165 1.1423973
1 1994 "Australia" 322211691456.244 4.77 663021292194.679 -.165 0 -24494258176 3.46706e+11 .9484286 1.4279966
1 1995 "Australia" 367216364716.365 2.8 688455180927.3 -.165 0 1511457536 3.657049e+11 .9702576 1.713596
1 1996 "Australia" 400302731411.229 4.08 715157730675.842 18.228453 1 16031287296 384271450112 .9804248 1.9991953
1 1997 "Australia" 434568007512.913 4.45 743524438064.517 22.593 0 36599459840 3.979685e+11 .985604 2.2847946
1 1998 "Australia" 398899138574.239 4.61 777553274793.62 27.6381 1 -6025076224 4.049242e+11 .9883389 2.570394
1 1999 "Australia" 388608221581.652 4.36 817003103115.573 48.458 0 -20514129920 4.091223e+11 .9896897 2.855993
1 2000 "Australia" 415222633925.768 3 849136627866.895 48.458 0 1639782144 4.135829e+11 .990099 3.141593
2 1990 "United Kingdom" 1093169389204.55 .74 1625140143652.04 30.468 0 12594491392 1.0805749e+12 .0394041 .28559932
2 1991 "United Kingdom" 1142797178130.51 -1.09 1607460266236.66 30.468 0 38082850816 1.1047143e+12 .3865072 .57119864
2 1992 "United Kingdom" 1179659529659.53 .37 1613424360275.27 28.6106 1 48790659072 1.1308689e+12 .7486191 .856798
2 1993 "United Kingdom" 1061388722255.55 2.49 1654185057671.47 27.9 0 -105758187520 1.1671469e+12 .8952165 1.1423973
2 1994 "United Kingdom" 1140489745944.29 3.82 1718614879651.65 27.9 0 -88973582336 1.2294634e+12 .9484286 1.4279966
2 1995 "United Kingdom" 1341584345905 2.43 1779996976908.1 27.9 0 24772661248 1.3168117e+12 .9702576 1.713596
2 1996 "United Kingdom" 1415358814352.57 2.5 1824346191893.82 27.9 0 1409031680 1.41395e+12 .9804248 1.9991953
2 1997 "United Kingdom" 1559078258022.27 4.2 1894671635328.74 14.663176 1 49479213056 1.509599e+12 .985604 2.2847946
2 1998 "United Kingdom" 1650172242464.39 3.29 1963729638937.01 8.072 0 5.74659e+10 1.5927063e+12 .9883389 2.570394
2 1999 "United Kingdom" 1682399288141.08 3.16 2031050676959.34 8.072 0 22264080384 1.660135e+12 .9896897 2.855993
2 2000 "United Kingdom" 1657816613708.58 3.4 2100867467607.3 8.072 0 -60127121408 1.7179438e+12 .990099 3.141593
end
format %ty ts
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[Giorgio Di Stefano]

I though just to bring it up again seeking for help. I am simply asking for help in order to estimate what GDP_g "would have been" if the indicator was at their optimal values.
For optimal I assume values that maximize GDP_g. To identify what GDP_g would be from the variables shown means minimize the difference between GDP_g and gdp_trend or their gdp_cyclical.

Also, I need to create both the values of optimal GDP_g and optimal indicator.


Variable indicator is a quality indicator expressed in percent that according to the model has an impact on GDP_g

The key question is how the indicator influences the GDP and under which values of the variable indicator in the data, GDP_g is maximized. Or achieves their maximum possible values and which are those for both GDP_g and indicator

I hope have clarified enough which of the variables are the variables I am interested and the information about how one thinks of their relationships to GDP_g so one might figure out what "optimal" values of those might be.


I would appreciate any help you could provide!

[Weiwen Ng]

Unfortunately, your original version of the question is still not clear.

The key question is how the indicator influences the GDP and under which values of the variable indicator in the data, GDP_g is maximized. Or achieves their maximum possible values and which are those for both GDP_g and indicator

This restatement seems clearer. The question is, was this your original intent?

You asked this on a general forum for a statistical software package. Some of us here are probably macroeconomists, but I don't know exactly who is. This might be more a macroecon question.

From the data sample you provided, you have observed values for GDP_g and your indicators. If you fit an OLS model or some variant of that model and you add squared terms for both indicators (or more complex polynomials), and then you use margins, you could probably find some sort of maximum value of GDP_g. You're basically asking the regression model what's the average effect of each indicator on GDP_g. You should be able to find the values of the indicators that maximize the average GDP_g. The main question is: because you keep asking and you keep distinguishing between potential and observed GDP, is this what you want to do? Alternatively, are you asking how would macroeconomists estimate a country's potential GDP at a given time? That type of question might be better asked on a macroecon forum, but someone might help here.

A secondary question is: your sample data have GDP, GDP_g, real GDP, and a few other variables. Which is it that you want to maximize?