How influential are COVID–19 data points? A fresh look at an estimated small scale DSGE model for the Philippines
5. Concluding remarks
The main objective of the paper is to empirically ascertain how influential or extreme observations affect key parameters estimates and shock contributions (via Kalman smoother) in an estimated small–scale New Keynesian DSGE model.
Expectedly, extreme observations have their own way of influencing results, some of which render the NKDSGE model inadequate. As expected, deep parameters that pertain to the discount factor have been affected minimally. In contrast, habit persistence declined after including pandemic quarters. Relative to base–
sample estimates, we find tremendous increase in IES estimates after using the full sample. Key parameters from the Taylor rule have changed minimally as well, plausibly indicating monetary authority efficiency in mitigating adverse shocks propagated by the pandemic. It turns out that one way to account for such extreme observations is to appropriately scale (via Bayesian estimation) demand, supply, and monetary policy shocks.
There are obvious model shortcomings. First, the model does not integrate formal structures that identify how COVID-19 related processes could influence labor supply, consumption, and production decisions. Differences in parameter estimates may be signaling either robust behavior or limited or weak parameter identification. Second, some exogenous shocks have been excluded. This may explain why historical decomposition estimates associated with the base sample fail to track the trajectory of output growth when extreme observations have been admitted. Third, while the parameters were all identified at the posterior median, results also indicate that there is tremendous model uncertainty.
For future work, the model will be refined to properly reflect how the current pandemic has affected macroeconomic outcomes. The labor bloc is envisioned to reflect labor market dynamics in the formal and informal sectors, since the pandemic has affected these sectors differently. We will also strengthen the fiscal bloc of the model by considering the integration of non-Ricardian households and by focusing on endogenous fiscal policy (spending, transfers, and deficits), complementarities between private and public capital, and labor market outcomes–key structures/features that played important roles in shaping Philippine macroeconomic dynamics during the pandemic period.
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Appendix
TABLE 2. Prior distribution and estimates of structural parameters:
2002Q1 – 2020Q1 Prior
type Prior
Mean Prior
Std Dev Post.
Mean Post.
Median 95% HPD Households
Discount factor (β) Beta 0.90 0.05 0.79 0.90 0.79 0.98 Habit persistence (θh) Beta 0.80 0.05 0.89 0.93 0.89 0.97 Inverse of the Intertemporal
Elasticity of substitution (σ) Gamma 1.00 1.20 0.29 0.56 0.29 0.93 Frisch labor supply elasticity (φ) Gamma 2.00 0.50 1.33 2.22 1.33 3.32 Firms
Calvo prices (ζ) Beta 0.80 0.10 0.55 0.68 0.55 0.80
Price indexation (ι) Beta 0.70 0.20 0.22 0.60 0.22 0.99 Central Bank
Interest rate smoothing (ρ) Uniform 0.00 1.00 0.78 0.83 0.78 0.88 Inflation response (γπ) Gamma 1.50 0.05 1.45 1.55 1.45 1.65 Output growth response (γΔy) Gamma 0.13 0.05 0.05 0.13 0.05 0.25 Persistence
Persistence parameter
Demand (ρD ) Uniform 0.00 1.00 0.73 0.94 0.73 0.99
Persistence parameter Supply
(ρS ) Uniform 0.00 1.00 0.51 0.73 0.51 0.90
Shocks
Monetary shock std (σM ) Inverse
Gamma 0.50 Inf 0.31 0.38 0.31 0.48 Demand shock Std (σD ) Inverse
Gamma 3.00 Inf 1.81 3.60 1.81 10.19 Supply shock Std (σS ) Inverse
Gamma 3.00 Inf 1.40 2.53 1.40 4.26 Intercepts
Mean inflation (μπ) Gamma 1.00 0.20 0.56 0.87 0.56 1.23
Mean Tbill rate (μR) Gamma 1.00 1.00 0.26 0.96 0.26 1.67 Mean output growth (μΔy) Normal 0.03 0.09 0.00 0.07 0.00 0.14
TABLE 3. Prior distribution and estimates of structural parameters:
2002Q1 – 2020Q2 Prior
type Prior
Mean Prior
Std Dev Post.
Mean Post.
Median 95% HPD Households
Discount factor (β) Beta 0.90 0.05 0.89 0.90 0.78 0.98 Habit persistence (θh) Beta 0.80 0.05 0.93 0.93 0.87 0.97 Inverse of the Intertemporal
Elasticity of substitution (σ) Gamma 1.00 1.20 0.49 0.46 0.22 0.83 Frisch labor supply elasticity (φ) Gamma 2.00 0.50 2.22 2.18 1.30 3.16 Firms
Calvo prices (ζ) Beta 0.80 0.10 0.55 0.68 0.55 0.80
Price indexation (ι) Beta 0.70 0.20 0.22 0.60 0.22 0.99 Central Bank
Interest rate smoothing (ρ) Uniform 0.00 1.00 0.82 0.82 0.77 0.88 Inflation response (γπ) Gamma 1.50 0.05 1.55 1.55 1.45 1.65 Output growth response (γΔy) Gamma 0.13 0.05 0.16 0.15 0.05 0.28 Persistence
Persistence parameter
Demand (ρD ) Uniform 0.00 1.00 0.92 0.96 0.75 0.99
Persistence parameter Supply
(ρS ) Uniform 0.00 1.00 0.71 0.73 0.41 0.92
Shocks
Monetary shock std (σM ) Inverse
Gamma 0.50 Inf 0.40 0.39 0.31 0.49 Demand shock Std (σD ) Inverse
Gamma 3.00 Inf 4.45 4.21 1.79 7.80 Supply shock Std (σS ) Inverse
Gamma 3.00 Inf 3.98 3.78 2.01 6.34 Intercepts
Mean inflation (μπ) Gamma 1.00 0.20 0.89 0.88 0.56 1.24
Mean Tbill rate (μR) Gamma 1.00 1.00 0.92 0.91 0.19 1.62 Mean output growth (μΔy) Normal 0.03 0.09 0.15 0.15 0.04 0.26
TABLE 4. Prior distribution and estimates of structural parameters:
2002Q1 – 2020Q3 Prior
type Prior
Mean Prior
Std Dev Post.
Mean Post.
Median 95% HPD Households
Discount factor (β) Beta 0.90 0.05 0.89 0.90 0.79 0.98 Habit persistence (θh) Beta 0.80 0.05 0.82 0.83 0.74 0.90 Inverse of the Intertemporal
Elasticity of substitution (σ) Gamma 1.00 1.20 0.30 0.28 0.13 0.48 Frisch labor supply elasticity (φ) Gamma 2.00 0.50 2.06 2.02 1.17 3.05 Firms
Calvo prices (ζ) Beta 0.80 0.10 0.65 0.65 0.51 0.79
Price indexation (ι) Beta 0.70 0.20 0.48 0.47 0.12 0.90 Central Bank
Interest rate smoothing (ρ) Uniform 0.00 1.00 0.80 0.80 0.72 0.86 Inflation response (γπ) Gamma 1.50 0.05 1.55 1.55 1.45 1.65 Output growth response (γΔy) Gamma 0.13 0.05 0.16 0.15 0.05 0.27 Persistence
Persistence parameter
Demand (ρD ) Uniform 0.00 1.00 0.96 0.96 0.92 0.99
Persistence parameter Supply
(ρS ) Uniform 0.00 1.00 0.73 0.73 0.52 0.92
Shocks
Monetary shock std (σM ) Inverse
Gamma 0.50 Inf 0.44 0.43 0.34 0.56 Demand shock Std (σD ) Inverse
Gamma 3.00 Inf 4.59 3.98 1.90 9.52 Supply shock Std (σS ) Inverse
Gamma 3.00 Inf 2.16 2.08 1.25 3.35 Intercepts
Mean inflation (μπ) Gamma 1.00 0.20 0.90 0.88 0.57 1.24
Mean Tbill rate (μR) Gamma 1.00 1.00 1.00 0.99 0.30 1.73 Mean output growth (μΔy) Normal 0.03 0.09 0.08 0.08 0.00 0.17
TABLE 5. Prior distribution and estimates of structural parameters:
full sample Prior
type Prior
Mean Prior
Std Dev Post.
Mean Post.
Median 95% HPD Households
Discount factor (β) Beta 0.90 0.05 0.89 0.90 0.79 0.98 Habit persistence (θh) Beta 0.80 0.05 0.84 0.84 0.76 0.91 Inverse of the Intertemporal
Elasticity of substitution (σ) Gamma 1.00 1.20 0.27 0.26 0.11 0.46 Frisch labor supply elasticity (φ) Gamma 2.00 0.50 2.09 2.05 1.21 3.08 Firms
Calvo prices (ζ) Beta 0.80 0.10 0.66 0.66 0.52 0.79
Price indexation (ι) Beta 0.70 0.20 0.47 0.44 0.12 0.90 Central Bank
Interest rate smoothing (ρ) Uniform 0.00 1.00 0.80 0.81 0.73 0.87 Inflation response (γπ) Gamma 1.50 0.05 1.55 1.55 1.46 1.65 Output growth response (γΔy) Gamma 0.13 0.05 0.15 0.15 0.05 0.27 Persistence
Persistence parameter
Demand (ρD ) Uniform 0.00 1.00 0.96 0.96 0.91 0.99
Persistence parameter Supply
(ρS ) Uniform 0.00 1.00 0.76 0.77 0.56 0.96
Shocks
Monetary shock std (σM ) Inverse
Gamma 0.50 Inf 0.44 0.43 0.33 0.56 Demand shock Std (σD ) Inverse
Gamma 3.00 Inf 4.28 3.97 1.85 7.31 Supply shock Std (σS ) Inverse
Gamma 3.00 Inf 2.22 2.12 1.22 3.48 Intercepts
Mean inflation (μπ) Gamma 1.00 0.20 0.89 0.88 0.56 1.22
Mean Tbill rate (μR) Gamma 1.00 1.00 0.96 0.96 0.27 1.66 Mean output growth (μΔy) Normal 0.03 0.09 0.08 0.08 -0.01 0.19