Back Matter
• 1 https://isni.org/isni/0000000404811396, International Monetary Fund

### Annex

#### A. Data Sources

##### Multivariate Filter—Technical Details

The structure of the MVF in section C follows Blagrave and Santoro (2016) very closely. It contains two blocks of equations modeling the dynamics of GDP and oil prices. The first block is as follows

$yt=Yt−Y¯t(1)$
$Y¯t=Y¯t−1+Gt+ɛtY¯(2)$
$Gt=θGSS+(1−θ)Gt−1+ɛtG(3)$
$yt=φyt−1+ɛtp+ɛty(4)$

Equation (1) states that the output gap yt is the log deviation of real GDP (Yt) from its potential level $Y¯t$. The stochastic process for output is described by equations (2)(4). The level of potential output evolves according to potential growth Gt and a level shock $ɛty¯$. Potential growth is also subject to shocks $ɛtG$ that fade gradually according to the parameter θ. The output gap is affected by demand shocks $ɛty$ and shocks to the price of oil $ɛty$. The block describing oil prices is as follows

$pt=Pt−P¯t(5)$
$pt=(1−ρ)pt−1+ɛtp(6)$
$P¯t=(1−μ)P¯t−1+PSS¯+ɛtP¯(7)$

Equations (5)(7) break down oil prices into changes due to cyclical and trend shocks. The oil price gap pt is the deviation of the actual oil price Pt from its trend or structural component $P¯t$. The price of oil is subject to temporary shocks $ɛtp$, which will affect the output gap, and permanent shocks $ɛtP¯$, which affect potential output. The model is estimated using Bayesian methods. Priors are chosen following the guidance in Blagrave and Santoro (2016) and Blagrave and others (2015). Table 1 lists the priors and posterior estimates.1

Table 1.

Priors and Posterior Estimates

## References

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• Blagrave, P. and M. Santoro, 2016, “Estimating Potential Output in Chile: A Multivariate Filter for Mining and Non-Mining Sectors,IMF Working Paper No. 16/201 (Washington: International Monetary Fund).

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In 2003, Colombia liberalized and restructured the oil sector, modifying the contract and taxation frameworks, as well as moving the regulatory function away from the major state-owned oil company (Ecopetrol) to an independent agency (ANH).

Specifically, L = WorkingAgePop * LFPR * (1 — U) * HumanK_Judex.

Reductions in labor informality show up as improvements in TFP in the accounting framework used in this paper since there is no informality data pre-2001 to adjust labor inputs throughout the sample.

See 2015 Colombia Selected Issues Paper Chapter 2.

TFP is obtained as a residual from the log version of equation (1), using actual GDP, the capital stock adjusted by utilization, and actual employment adjusted by human capital. Potential TFP is the result of applying an HP filter (λ=6.25) to the TFP residual.

See Cardenas and Rozo (2002) on the link between crime and productivity in Colombia.

The steady state log oil price Pss is set to the sample average and G_ss to 3.70.

Potential Growth in Colombia
Author: Mr. Sergi Lanau, Mr. Jorge Roldos, and Jose Daniel Rodríguez-Delgado