| Change in TFP 1/y |
CTFP |
RTA TFPEE5TA |
|
TFPEE5TA |
|
\(\mathtt{CTFP}\left(t\right)=\mathtt{RTA}\left(t\right)\cdot\mathtt{TFPEE5TA}\left(t\right)\) |
| Domestic Rate of Technological Advance 1/y |
DRTA |
SC |
SCROTA SC1980 DROTA1980 EDROTA2022 |
RTA |
|
\(\mathtt{DRTA}\left(t\right)=\mathtt{DROTA1980}+\left(1+\mathtt{SCROTA}\cdot\left(-1+\frac{\mathtt{SC}\left(t\right)}{\mathtt{SC1980}}\right)\right)\cdot\mathtt{ifelse}\left(\left(t>2000\right),\mathtt{EDROTA2022},0\right)\) |
| Extra Cost of TAs From 2022 GDollar/y |
ECTAF2022 |
CTA |
CTA2022 |
ETTAF2022 ECTAGDP |
|
\(\mathtt{ECTAF2022}\left(t\right)=\mathtt{max}\left(0,-\mathtt{CTA2022}+\mathtt{CTA}\left(t\right)\right)\) |
| Extra Cost of TAs as share of GDP (1) |
ECTAGDP |
ECTAF2022 GDP |
|
PLUA |
|
\(\mathtt{ECTAGDP}\left(t\right)=\frac{\mathtt{ECTAF2022}\left(t\right)}{\mathtt{GDP}\left(t\right)}\) |
| Govmnt Spending as Share of GDP |
GSSGDP |
GDP GS |
|
|
|
\(\mathtt{GSSGDP}\left(t\right)=\frac{\mathtt{GS}\left(t\right)}{\mathtt{GDP}\left(t\right)}\) |
| Infrastructure Purchases Ratio y |
IPR |
CPUS GPU |
|
PPP |
|
\(\mathtt{IPR}\left(t\right)=\frac{\mathtt{CPUS}\left(t\right)}{\mathtt{GPU}\left(t\right)}\) |
| Imported ROTA 1/y |
IROTA |
GDPP |
GDPTL MIROTA2022 |
RTA |
|
\(\mathtt{IROTA}\left(t\right)=\mathtt{ifelse}\left(\left(t>2000\right),\mathtt{max}\left(0,\mathtt{MIROTA2022}\cdot\left(2+\frac{-\mathtt{GDPP}\left(t\right)}{\mathtt{GDPTL}}\right)\right),0\right)\) |
| Indicated TFP (1) |
ITFP |
OWTFP TFPEE5TA |
|
ECR |
|
\(\mathtt{ITFP}\left(t\right)=\mathtt{OWTFP}\left(t\right)\cdot\mathtt{TFPEE5TA}\left(t\right)\) |
| OWeoTFP |
OWTFP |
OW |
OWETFP OW2022 |
ITFP |
|
\(\mathtt{OWTFP}\left(t\right)=\mathtt{ifelse}\left(\left(t>2000\right),1+\mathtt{OWETFP}\cdot\left(-1+\frac{\mathtt{OW}\left(t\right)}{\mathtt{OW2022}}\right),1\right)\) |
| Productivity Loss from Unprofitable Activity (1) |
PLUA |
ECTAGDP |
FUATA |
RTFPUA |
|
\(\mathtt{PLUA}\left(t\right)=\mathtt{FUATA}\cdot\mathtt{ECTAGDP}\left(t\right)\) |
| Productivity of Public Purchases (1) |
PPP |
IPR |
IPRVPSS IPR1980 |
VPSS |
|
\(\mathtt{PPP}\left(t\right)=\mathtt{max}\left(0,1+\mathtt{IPRVPSS}\cdot\log\left(\frac{\mathtt{IPR}\left(t\right)}{\mathtt{IPR1980}}\right)\right)\) |
| Public SErvices per Person kdollar/p/y |
PSEP |
POP VPSS |
|
|
|
\(\mathtt{PSEP}\left(t\right)=\frac{\mathtt{VPSS}\left(t\right)}{\mathtt{POP}\left(t\right)}\) |
| Public Spending per Person kDollar/p/y |
PSP |
POP GS |
|
AWBPS PSSGDP |
|
\(\mathtt{PSP}\left(t\right)=\frac{\mathtt{GS}\left(t\right)}{\mathtt{POP}\left(t\right)}\) |
| Reduction in ROTA from Inequality 1/y |
RROTAI |
INEQI |
IIEEROTA |
RTA |
|
\(\mathtt{RROTAI}\left(t\right)=\mathtt{min}\left(1,1+\mathtt{IIEEROTA}\cdot\left(-1+\mathtt{INEQI}\left(t\right)\right)\right)\) |
| Rate of Technological Advance 1/y |
RTA |
DRTA IROTA RROTAI |
|
CTFP |
|
\(\mathtt{RTA}\left(t\right)=\mathtt{DRTA}\left(t\right)\cdot\mathtt{RROTAI}\left(t\right)+\mathtt{IROTA}\left(t\right)\) |
| Reduction in TFP from Unprofitable Activity (1) |
RTFPUA |
RTFPUA PLUA |
CTPIS IPT |
RTFPUA TFPIE5TA |
0.0 |
\(\frac{\mathrm{d}\mathtt{RTFPUA}\left(t\right)}{\mathrm{d}t}=\frac{-\mathtt{RTFPUA}\left(t\right)+\mathtt{PLUA}\left(t\right)}{\mathtt{CTPIS}+\mathtt{IPT}}\) |
| State Capacity (fraction of GDP) |
SC |
GDP VPSS |
|
DRTA |
|
\(\mathtt{SC}\left(t\right)=\frac{\mathtt{VPSS}\left(t\right)}{\mathtt{GDP}\left(t\right)}\) |
| TFP Excluding Effect of 5TAs (1) |
TFPEE5TA |
CTFP |
|
CTFP ITFP TFPIE5TA |
1.0 |
\(\frac{\mathrm{d}\mathtt{TFPEE5TA}\left(t\right)}{\mathrm{d}t}=\mathtt{CTFP}\left(t\right)\) |
| TFP Including Effect of 5TAs (1) |
TFPIE5TA |
RTFPUA TFPEE5TA |
|
|
|
\(\mathtt{TFPIE5TA}\left(t\right)=\left(1-\mathtt{RTFPUA}\left(t\right)\right)\cdot\mathtt{TFPEE5TA}\left(t\right)\) |
| Value of Public Services Supplied GDollar/y |
VPSS |
PPP GPU |
|
PSEP SC |
|
\(\mathtt{VPSS}\left(t\right)=\mathtt{GPU}\left(t\right)\cdot\mathtt{PPP}\left(t\right)\) |