# Monetary Policy Rule and Taylor Principle in Mongolia: GMM and DSGE Approaches

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Overview of Mongolian Monetary Policy

## 3. Literature Review and This Study’s Contributions

## 4. Empirical Analyses of Mongolian Monetary Policy Rule

#### 4.1. GMM Estimation

_{t}* = ř + β (E[π

_{t+n}|Ω

_{t}] − π*) + γ (E[y

_{t}|Ω

_{t}] − y*)

_{t}* is a target for the central bank’s policy rate in period t; ř is a natural rate of nominal interest rate; π

_{t+n}is an inflation rate between periods t and t + n; y

_{t}is a real output; π* and y* are respective optimal points for inflation rate and real output; E is an expectation operator; and Ω is the information available to the central bank at the time it sets a policy rate. Equation (1) is transformed into Equation (2) for an empirical estimation.

_{t}= (1 − ρ) (α + β π

_{t+n}+ γ x

_{t}) + ρ r

_{t−1}+ ε

_{t}

_{t}, actual policy rate, comes from r

_{t}= (1 − ρ) r

_{t}* + ρ r

_{t-1}with ρ ϵ [0, 1] being the degree of policy rate smoothing; the unobserved forecast variables, E[π

_{t+n}|Ω] and E[y

_{t}|Ω], are replaced by the realized variables, π

_{t+n}and y

_{t}; α and x

_{t}are defined as α ≡ ř − β π* and x

_{t}≡ y

_{t}− y* (output gap); and ε

_{t}is a combination of the central bank’s forecast errors of inflation and output, and exogenous disturbances.

_{t+n}in this study takes the values of 1, 0 and −1 to denote forward-, contemporaneous-, and backward-looking specifications, respectively.

_{t}= (1 − ρ) (α + δ e

_{t}) + ρ r

_{t−1}+ ε

_{t}

_{t}is a change in exchange rate in terms of local currency (tugriks) value per US dollar. In the case that the central bank prioritizes exchange-rate stabilization in its policy rule, the coefficient δ should take a significantly positive value.

_{t}), implying the conformity to the Taylor principle. The other coefficients including those of output gap are insignificant or weakly significant, otherwise impossible to calculate since the degree of smoothing ρ is over unity. As for Table 3, no meaningful coefficients are found in the estimation on the policy rate’ responses to exchange rate fluctuations.

#### 4.2. New Keynesian DSGE Estimation

_{t}= π

_{H, t}+ α Δs

_{t}

_{t}= ρ

_{a}a

_{t−1}+ ε

_{a}

_{t}

_{t}= ρ

_{e}e

_{t−1}+ ε

_{e}

_{t}

_{H,}and nominal interest rate $\tilde{\mathrm{r}}$. The data for the domestic inflation (the change in domestic goods prices) are calculated by a year-on-year change in the GDP deflator obtained by the division between nominal GDP and GDP at constant prices (retrieved from the National Statistics Office of Mongolia5). As for the data for output gap and nominal interest rate, the data of output gap x and policy rate r in Section 4.1 are applied, although the data of policy rate is processed into a detrended series by subtracting a Hodrick–Prescott-filter of that data, since the model is expressed by the deviation from the steady-state level.6 The sample period corresponds to the second-half one in Section 4.1.

_{r}, ϕ

_{π}, ϕ

_{x}], and thus the other parameters are treated as fixed. As shown in Table 5, the parameter on the degree of economic openness α is set to 0.58, which corresponds to the import/GDP ratio on the average in the sample period7. Second, the parameters [β, γ, η, θ, σ, φ, ρ

_{a}, ρ

_{e}, ρ

_{w}] are set according to various types of DSGE literature studies such as Smets and Wouters (2003, 2007), Gali and Monacelli (2005), Gali (2008). Finally, the parameters [κ

_{α}, λ, σ

_{α}, ω, Γ, Θ, Ψ] are set in the same way as Gali and Monacelli (2005). The prior means of [ϕ

_{r}, ϕ

_{π}, ϕ

_{x}] are set to the values estimated by the GMM in Section 4.1. Table 6 reports the prior-value settings in the left side of the column. The prior means of the parameters on the reaction to inflation ϕ

_{π}and the smoothing degree ϕ

_{r}correspond to the GMM-estimated parameters of the case π in the second half sample period (β = 1.172 and ρ = 0.905), which satisfy the Taylor principle. The prior-mean-value of the parameter on the reaction to output gap ϕ

_{x}is set to zero, however, as the GMM-estimated coefficient was insignificant in that case.

_{π}and the smoothing degree ϕ

_{r}have almost the same values as their prior means: in the reaction to inflation, 1.152 (posterior) versus 1.172 (prior); and in the smoothing degree, 0.891 (posterior) versus 0.905 (prior). Regarding the reaction to output gap, the posterior means turns out to be positive but still insignificant, judging from the Highest Posterior Density (HPD) Interval with its bottom line being negative.

#### 4.3. Discussions on Estimation Outcomes

## 5. Concluding Remarks

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | The data are retrieved from the website: http://www.imf.org/en/data. |

2 | The Mongolian economic size is 13.0 billion US dollars at current prices in terms of GDP in 2018, while the average size of Asian developing economies is 621.7 billion US dollars in the same year. The Mongolian ratio of “imports of goods and services” to GDP is 55.6 percent on the average during the period from 1995 to 2018, while the average ratio in Asian developing economies is 35.1 percent during the same period. The data of the GDP and the ratio of “imports of goods and services” to GDP are retrieved respectively from UNCTAD STAT: http://unctadstat.unctad.org/EN/. |

3 | The equations from (4) to (10) except (7) correspond to those in Gali and Monacelli (2005) as follows: Equations (4) and (5) to (37) in p. 719 of Gali and Monacelli (2005); (6) to (36) in p. 718; (8) to (14) in p. 712; (9) to (29) in p. 717; and (10) to (35) in p. 718. |

4 | For the Bayesian estimation, the study uses the software of Dynare and Matlab. |

5 | See the Mongolian Statistical Information Service at the website: https://www.en.nso.mn/. |

6 | The data of domestic inflation and output gap have no need to be processed under the assumption of zero-inflation steady-state. |

7 | The import/GDP ratio is the one that divides “Imports of Goods and Services” by GDP in Mongolia, using the data of International Financial Statistics of International Monetary Fund. |

**Figure 1.**Trend in Monetary Policy in Mongolia. Source: Author’s description based on the website of the Bank of Mongolia.

**Figure 3.**Impulse Responses to Monetary Policy Shock under the Dynamic Stochastic General Equilibrium (DSGE) Model. Source: Author’s estimation.

Variable | t-Statistic | Probability |
---|---|---|

r | −4.207 *** | 0.001 |

π | −3.535 ** | 0.011 |

x | −5.081 *** | 0.000 |

e | −3.643 *** | 0.008 |

[Total Period: 2007Q3–2019Q4] | |||

Coefficient | πt − 1 | π | πt + 1 |

(1 − ρ)*α | 4.861 (0.693) | −0.657 (−0.053) | 2.753 (0.391) |

(1 − ρ)*β | −0.001 (−0.021) | 0.038 (0.454) | 0.016 (0.255) |

(1 − ρ)*γ | 0.007 (0.455) | 0.013 (0.888) | 0.018 (1.318) |

ρ | 0.574 (1.009) | 1.031 (1.026) | 0.749 (1.323) |

J-statistics | 3.766 (0.287) | 0.707 (0.871) | 0.316 (0.956) |

Long-term Coefficients | |||

α | 11.414 | - | 11.001 |

β | -0.003 | - | 0.064 |

γ | 0.018 | - | 0.074 |

[First-half Period: 2007Q3–2011Q4] | |||

Coefficient | πt-1 | π | πt + 1 |

(1 − ρ)*α | 9.415 *** (9.284) | 0.804 (0.222) | 10.110 ** (2.565) |

(1 − ρ)*β | −0.066 *** (-5.538) | 0.016 (0.568) | −0.048 (−1.169) |

(1 − ρ)*γ | −0.008 * (−2.020) | 0.001 (0.123) | −0.005 (−0.522) |

ρ | 0.226 ** (2.670) | 0.940 ** (2.955) | 0.136 (0.419) |

J-statistics | 3.760 (0.288) | 1.238 (0.743) | 1.924 (0.588) |

Long-term Coefficients | |||

α | 12.174 *** | 13.429 | 11.706 ** |

β | −0.086 *** | 0.278 | −0.056 |

γ | −0.011 * | 0.017 | −0.006 |

[Second-half Period: 2012Q1–2019Q4] | |||

Coefficient | πt − 1 | π | πt + 1 |

(1 − ρ)*α | 2.461 (0.430) | 0.183 (0.074) | 0.125 (0.029) |

(1 − ρ)*β | 0.083 ** (2.362) | 0.110 *** (2.927) | 0.067 ** (2.351) |

(1 − ρ)*γ | 0.086 * (1.717) | 0.139 (1.066) | 0.002 (0.069) |

ρ | 0.736 (1.542) | 0.905 *** (4.007) | 0.923 ** (2.606) |

J-statistics | 3.040 (0.385) | 1.034 (0.793) | 3.631 (0.2C9) |

Long-term Coefficients | |||

α | 9.334 | 1.954 | 1.653 |

β | 0.316 ** | 1.172 *** | 0.885 ** |

γ | 0.327 * | 1.480 | 0.031 |

Coefficient | 2007q3–2019q4 | 2007q3–2011q4 | 2012q1–2019q4 |
---|---|---|---|

(1 − ρ)*α | −0.231 (−0.036) | 2.652 ** (2.905) | 9.574 (0.487) |

(1 − ρ)*δ | −0.039 (−0.939) | −0.051 * (−1.914) | 0.022 (0.448) |

ρ | 1.053 * (1.789) | 0.790 *** (6.874) | 0.167 (0.100) |

J-statistics | 0.158 (0.690) | 0.131 (0.716) | 0.588 (0.442) |

Long-term Coefficients | |||

α | - | 12.685 ** | 11.495 |

δ | - | −0.244 * | 0.027 |

[Endogenous Variables] | |

$\tilde{\mathrm{x}}$ | Output gap |

$\tilde{\mathrm{y}}$ | Output |

π | CPI inflation (the rate of change in consumer prices) |

π_{H} | Domestic inflation (the rate of change in domestic goods prices) |

$\tilde{\mathrm{r}}$ | Nominal interest rate |

$\stackrel{\u02c9}{\mathrm{r}}$$\stackrel{\u02c9}{\mathrm{r}}$ | Natural rate of interest rate |

s | Terms of trade |

E | Expectation operator |

[Exogenous Variables] | |

$\tilde{\mathrm{y}}$^{*} | World output that follows first-order autoregressive with i.i.d. shock, ε_{w} |

a | Productivity shock that follows first-order autoregressive with i.i.d. shock, ε_{a} |

e | Cost-push shock that follows first-order autoregressive with i.i.d. shock, ε_{e} |

ε_{r} | Monetary policy shock with i.i.d. |

[Fixed Parameters] | Descriptions | Assumption | Notes |
---|---|---|---|

α | Degree of economic openness | 0.58 | Import/GDP ratio in the sample average |

β | Discount factor for households | 0.99 | |

γ | Substitutability between goods produced in different foreign countries | 1.00 | |

η | Substitutability between domestic and foreign goods | 1.00 | |

θ | Probability a firm does not change its price | 0.75 | |

σ | Parameter on utility of consumption under constant relative risk aversion (CRRA) | 1.00 | Log utility of consumption |

φ | Parameter on disutility of labor | 0.00 | Linear disutility of labor |

ρ_{a} | Autoregressive parameter for productivity shock | 0.90 | |

ρ_{e} | Autoregressive parameter for cost-push shock | 0.90 | |

ρ_{w} | Autoregressive parameter for world GDP shock | 0.90 | |

[Definitional Identities] | |||

κ_{α} ≡ λ (σ_{α} + φ) | |||

λ ≡ {(1 – β θ) (1 – θ)}/θ | |||

σ_{α} ≡ σ/(1 – α) + α ω | |||

ω ≡ σ γ + (1 – α) (σ η – 1) | |||

Γ ≡ (1 + φ)/(σ_{α} + φ) | |||

Θ ≡ (σ γ – 1) + (1 – α) (σ η – 1) | |||

Ψ ≡ – Θ σ_{α}/(σ_{α} + φ) | |||

[Estimated Parameters: Monetary policy rule] | |||

ϕ_{r} | Smoothing degree of policy rate | ||

ϕ_{π} | Policy rate reaction to CPI inflation | ||

ϕ_{x} | Policy rate reaction to output gap |

Parameters | Priors | Posterior | ||||
---|---|---|---|---|---|---|

Dist. | Mean | Stdev. | Mean | 90% HPD Interval | ||

Monetary policy rule | – | – | – | – | – | |

Inflation | ϕ_{π} | norm | 1.172 | 0.050 | 1.152 | 1.071–1.232 |

GDP gap | ϕ_{x} | norm | 0.000 | 0.050 | 0.011 | −0.003–0.027 |

Smoothing | ϕ_{r} | norm | 0.905 | 0.050 | 0.891 | 0.854–0.928 |

Shocks | ||||||

Monetary Policy | ε_{r}_{t} | invg | 1.000 | 1.000 | 1.276 | 0.764–1.777 |

Productivity | ε_{a}_{t} | invg | 1.000 | 1.000 | 0.927 | 0.313–1.607 |

Cost-push | ε_{e}_{t} | invg | 1.000 | 1.000 | 2.124 | 1.658–2.567 |

World GDP | ε_{w}_{t} | invg | 1.000 | 1.000 | 17.176 | 13.101–22.539 |

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**MDPI and ACS Style**

Taguchi, H.; Gunbileg, G.
Monetary Policy Rule and Taylor Principle in Mongolia: GMM and DSGE Approaches. *Int. J. Financial Stud.* **2020**, *8*, 71.
https://doi.org/10.3390/ijfs8040071

**AMA Style**

Taguchi H, Gunbileg G.
Monetary Policy Rule and Taylor Principle in Mongolia: GMM and DSGE Approaches. *International Journal of Financial Studies*. 2020; 8(4):71.
https://doi.org/10.3390/ijfs8040071

**Chicago/Turabian Style**

Taguchi, Hiroyuki, and Ganbayar Gunbileg.
2020. "Monetary Policy Rule and Taylor Principle in Mongolia: GMM and DSGE Approaches" *International Journal of Financial Studies* 8, no. 4: 71.
https://doi.org/10.3390/ijfs8040071