The document discusses a study analyzing the relationship between monetary policy rates, credit risk measures, and commercial interest rates on business loans in Chile. It presents preliminary analysis showing no clear evidence of cointegrating relationships between the variables. The study then shifts to a univariate model allowing for asymmetric pass-through of policy rate changes and the role of monetary policy expectations. It notes some issues with autocorrelated residuals that are addressed by including MA terms in the residuals. The goal is to better quantify how credit risk changes impact the pass-through of policy rates to commercial lending rates.

1. BANCO CENTRAL DE CHILE 12 October 2017
Credit Risk and Monetary Pass-through.
Evidence from Chile
Michael Pedersen
Central Bank of Chile
Eesti Pank
Tallinn, 12 October 2017
* The opinions expressed are those of author and do not represent those of the Central Bank of Chile or
its board members.

2. 2
Analysis of commercial interest rates of
business loans
Policy
rate
Commercial
rate
• Cost of
financing
(interbank
rate)
• Client risk
• Etc.

3. 3
Analysis of commercial interest rates of
business loans
Policy
rate
Commercial
rate
• Cost of
financing
(interbank
rate)
• Client risk
• Etc.

4. 4
The monetary transmission mechanism

5. 5
The monetary transmission mechanism

6. 6
About this study
 Commercial interest rates are market rates and depend on several factors
such as the evaluation of the risk of the client.
 This analysis proposes the use of higher order moments of the interest rate
distribution to quantify changes in the credit risk.
 Fact: Different clients obtain loans in different months. In this context:
 How can we measure changes in client risks across months?
 When controlling for changes in these measures, how large is the pass-
through from changes in the monetary policy rate to the market rates?

7. 7
An illustrative example. ΔMPR = -0.50
Business lending rate. Histograms Dec-03 and Jan-04

8. 8
An illustrative example. ΔMPR = -0.50
Business lending rate. Histograms Dec-03 and Jan-04

9. 9
Inspired by the financial literature: Higher order
moments as measures of credit risk
 Variance: Higher variance, higher uncertainty
of the client portfolio, higher credit risk
premium, higher interest rate. Expected effect
on the rate: +
 Skewness: More negative skewness, the
distribution moves to the right, more higher-
risks clients, higher interest rate. Expected
effect on the rate: -
[High correlation with kurtosis]
 Observable: Interest rate, which includes
credit risk premium.

10. 10
An illustrative example. ΔMPR = -0.50
Business lending rate. Histograms Dec-03 and Jan-04
Weighted moments of the distribution
MPR ̅ 2 3
Dec. 2003 2.25 5.68 11.60 4.71
Jan. 2004 1.75 6.85 19.97 1.77

11. 11
An illustrative example. ΔMPR = -0.50
Business lending rate. Histograms Dec-03 and Jan-04
Weighted moments of the distribution
MPR ̅ 2 3
Dec. 2003 2.25 5.68 11.60 4.71
Jan. 2004 1.75 6.85 19.97 1.77

12. 12
Related literature: MPR pass-through in Chile
 Espinosa-Vega & Rebucci (2004, CBC book): Pass-through
in Chile is similar to those in other countries, but
incomplete in the long run.
 Econometric model: Error-Correction ADL. Interest rates of
consumption and business loans, in pesos and CPI-indexed
(UF).
 April 1993 – September 2002.
 Becerra et al. (2010, Chilean Economy): The lack of pass-
through during the financial crisis can be explained by
higher national and international risk.
 Econometric model: ADL. Nominal interest rates of
consumption and business loans.
 2005-2009, weekly observations.

13. 13
Related literature: The risk-taking Channel
 The risk-taking Channel: Low interest rates make
commercial banks take higher risk on loans.
 Adrian & Liang (2014, Staff Report FEDNY): Overview of
studies on the risk-taking channel.
 Jiménez et al. (2014, Econometrica): What do 23 millions
bank loans tell about the effect of the monetary policy on the
credit risk taken by commercial banks?
 Commercial banks take higher credit risks when the MPR is
low.
 A study of applications and loan contracts.
 This study: Is there an easier way to measure credit risk?

14. 14
A simple framework to illustrate the context
in which the empirical study is conducted
 Let r be the return on a 1 dollar loan.
 To simplify, assume perfect competition, risk neutral banks, zero recuperation
rate and no arbitrage in prices. Let p be the default probability and rf the risk-free
interest rate. Then:
(1 + r)(1 – p) + 0p = 1 + E(r) = 1 + rf
 1 + r = (1 + rf) / (1 – p)
 r ≈ rf + p
 Hence, with a one-to-one relationship between the MPR and the risk-free interest
rate, the pass-through is instantaneous and complete when adjusting by the credit
risk.
 In line with Merton (1974).

15. 15
The study is on nominal rates of business loans
(60% of the total lending market)
Structures of the Chilean lending and deposit markets (%, 2013)
Com. Cons. Mort. Dep.
Nominal 78.8 99.1 0.0 74.7
Real 10.0 0.9 100.0 6.0
USD 11.1 0.1 0.0 19.2
Distribution between lending horizons of business loans (%, 2013)
< 30 days 4.4
30 - 89 days 5.0
90 days - 1 year 29.9
1 - 3 years 26.2
> 3 years 34.4

16. 16
The study is on nominal rates of business loans
(60% of the total lending market)
Structures of the Chilean lending and deposit markets (%, 2013)
Com. Cons. Mort. Dep.
Nominal 78.8 99.1 0.0 74.7
Real 10.0 0.9 100.0 6.0
USD 11.1 0.1 0.0 19.2
Distribution between lending horizons of business loans (%, 2013)
< 30 days 4.4
30 - 89 days 5.0
90 days - 1 year 29.9
1 - 3 years 26.2
> 3 years 34.4

17. 17
Distribution by type of loan
Distribution of business loans by maturity (%, 2013)
< 1M 1-3M 3-12M 1-3Y >3Y
(4.4) (5.0) (29.9) (26.2) (34.4)
Amortizing loan 68.1 53.1 40.5 38.2 59.8
Approved overdraft current account 9.4 4.8 55.3 60.2 32.1
Approved overdraft other accounts and credit cards 3.6 0.0 3.8 0.1 0.0
Non-approved overdraft current account 18.9 41.9 0.0 0.0 0.0
Credit card purchases paid in fees 0.0 0.1 0.3 0.1 0.1
Revolving credit card debt 0.0 0.1 0.0 1.4 8.0

18. 18
Distribution by type of loan
< 1M 1-3M 3-12M 1-3Y >3Y
(4.4) (5.0) (29.9) (26.2) (34.4)
Amortizing loan 68.1 53.1 40.5 38.2 59.8
Approved overdraft current account 9.4 4.8 55.3 60.2 32.1
Approved overdraft other accounts and credit cards 3.6 0.0 3.8 0.1 0.0
Non-approved overdraft current account 18.9 41.9 0.0 0.0 0.0
Credit card purchases paid in fees 0.0 0.1 0.3 0.1 0.1
Revolving credit card debt 0.0 0.1 0.0 1.4 8.0
Distribution of business loans by maturity (%, 2013)

19. 19
Data: Commercial Interest rates and risk
measures
 Variable of interest: Monthly business interest rate: ijt (j = 0,1,2,3)
 Period: Jan.02 – Feb.17 (t = 1,…,182)
 Daily interest rates for each bank are utilized to calculate weighted moments for
intra policy meetings periods:
1
,
1
,
 j: loan type (0: total, 1: 3-12M, 2: 1-3Y, 3: >3Y)
 d: day of operation, d = 1,…,Djt
 b: bank: b = 1,…,Bjt
 ωj: Amount of the loan with interest rate ij
 σkw(ijt): weighted k’th moment of the distribution with weighted mean ijt.

20. 20
Interest rate and risk measures
σ2w
(ijt) σ3w
(ijt)
i0t
i1t
i2t
i3t
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
35
40
45
50
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: 0.70
0
1
2
3
4
5
6
7
8
9
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: -0.73
0
2
4
6
8
10
12
0
5
10
15
20
25
30
35
40
45
50
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: 0.55
0
2
4
6
8
10
12
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: -0.79
0
5
10
15
20
25
0
50
100
150
200
250
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: 0.73
0
5
10
15
20
25
-2
-1
0
1
2
3
4
5
6
7
8
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: -0.74
0
2
4
6
8
10
12
14
16
18
0
10
20
30
40
50
60
70
80
90
100
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: 0.10
0
2
4
6
8
10
12
14
16
18
-1
0
1
2
3
4
5
6
7
8
2002 2004 2006 2008 2010 2012 2014 2016
Correlation: -0.80
Risk measures (solid, LHS) and difference between commercial
and interbank interest rates (punctuated, RHS)

21. 21
Preliminary empirical analysis 1: Long-run
relations between commercial rate and interbank
market rate. Bivariate VAR models
 As in Lim (Economic Record, 2001) and Gambacorta & Iannotti (Applied
Economics, 2007).
 Step 1: Are interest rates I(1)? Mixed evidence from a battery of UR tests.
 Step 2: Assuming that they are, do they cointegrate? Johansen’s Trace test
(merely indicative): Rates are I(1), but do not cointegrate.
i0t i1t
i2t i3t
0
5
10
15
20
25
30
2007 2009 2011 2013 2015 2017
0
5
10
15
20
25
30
2007 2009 2011 2013 2015 2017
0
5
10
15
20
25
30
2007 2009 2011 2013 2015 2017
0
5
10
15
20
25
30
2007 2009 2011 2013 2015 2017
Rolling Trace tests (vertical line: 5% critical level)

22. 22
Preliminary empirical analysis 2: Long-run
relations between interest rates and risk measures.
4-dimensional VAR models
 Include risk measure in VAR models
 Step 1: Are risk measures I(1)? Mixed evidence from a battery of UR tests.
 Step 2: Assuming that they are, do they cointegrate with the interest rates?
Johansen’s Trace test (merely indicative): Variables are I(1), but do not
cointegrate.
Rolling Trace tests (vertical line: 5% critical level)
i0t i1t
i2t i3t
0
10
20
30
40
50
60
70
80
90
2007 2009 2011 2013 2015 2017
0
10
20
30
40
50
60
70
2007 2009 2011 2013 2015 2017
0
10
20
30
40
50
60
70
80
90
2007 2009 2011 2013 2015 2017
0
10
20
30
40
50
60
70
80
90
2007 2009 2011 2013 2015 2017

23. 23
No clear evidence… What to do??? Assume one CI
relation exists in each VAR. What are the
characteristics of the systems?
 3 out of the 4 models: one-to-one LR relation between commercial and interbank
rates -> complete pass-through in the long run.
 The last model (1-3Y): Less than complete LR pass-through.
 Not evident that commercial rate adjust to LR relation, only in one model (1-
3Y).
 Granger causality tests in the VECM model:
 Interbank rate causes commercial rate (all 4 models)
 Commercial rate does (almost always) not cause the interbank rate (only in
the 1-3Y model).
 Risk measures do not cause any of the interest rates
 The relations, if they exist, are contemporaneous
 Interest rates do (almost always) not cause risk measures.
 Apply an univariate framework

24. 24
Univariate model setup
 Models:
 Allow for asymmetric pass-through, and a role for monetary policy expectations:
1
1 if Δ 0
0 otherwise
, 2
1 if Δ 0
0 otherwise
,
1
1 if E Δ Δ 0
0 otherwise
, 2
1 if 0 E Δ Δ 0
0 otherwise
,
3
1 if 0 E Δ Δ 0
0 otherwise
, 4
1 if 0 E Δ Δ 0
0 otherwise
.
,
1
∆ ∆ ∆ , 0,1,2,3

25. 25
Univariate model setup (cont.)
 Deterministic terms: constant, seasonal and outlier dummies.
 Method: General-to-specific, i.e. based on inference.
 Problems:
 Auto correlated residuals:
 Solution: Include MA-terms in the residuals
 Relatively small sample (65 changes of the policy rate)
 Solution: Standard errors estimated with jackknife replications.
 Robustness estimations:
 Business cycle, inflation rate, national and international general risk measures
(EMBI and VIX), and a measure of non-conventional monetary policy are not
important variables.
 Credit risk and interest rate interaction terms are mostly not statistically
significant and do not affect the presented estimated coefficients.

26. 26
A side remark with respect to expectations
Monetary policy decisions and expectations (Jan.02 – Feb.17)
(numbers of meetings, percentage)
∆MPR = 0 117
(64.3%)
E(∆MPR) = ∆MPR 111
(94.9%)
E(∆MPR) > 0 6
(5.1%)
∆MPR > 0 37
(20.3%)
E(∆MPR) = ∆MPR 27
(73.0%)
E(∆MPR) = 0 6
(16.2%)
0 < E(∆MPR) < ∆MPR 4
(10.8%)
∆MPR < 0 28
(15.4%)
E(∆MPR) = ∆MPR 12
(42.9%)
E(∆MPR) = 0 11
(39.3%)
0 > E(∆MPR) > ∆MPR 5
(17.9%)

27. 27
Results of estimations
Estimations results. Dependent variable: Change in business lending rate
Δi0t Δi1t Δi2t Δi3t
Const. -0.01
(0.01)
-0.01*
(0.01)
-0.02
(0.02)
-0.02
(0.03)
-0.01
(0.05)
-0.05
(0.04)
0.05
(0.05)
-0.04
(0.05)
∆ 1 0.23***
(0.08)
0.24***
(0.08)
0.01
(0.37)
0.03
(0.23)
0.01
(0.06)
0.02
(0.04)
-0.03
(0.04)
0.04
(0.04)
∆ 1 1.01***
(0.38)
0.93***
(0.15)
2.10**
(1.00)
1.19**
(0.47)
1.76
(1.95)
1.25***
(0.41)
1.91
(1.28)
1.46**
(0.68)
∆ 2 0.73***
(0.24)
0.77***
(0.18)
0.47
(0.34)
0.82***
(0.27)
0.58
(0.91)
0.66
(0.78)
0.71
(0.52)
0.87**
(0.41)
∆ 1 1 2 -0.10
(0.59)
-0.96
(1.60)
0.27
(3.91)
-5.42
(3.28)
1 -0.01
(0.02)
-0.08
(0.15)
-0.09
(0.12)
-0.05*
(0.03)
∆ 2 0.07***
(0.005)
0.07***
(0.01)
0.06***
(0.01)
0.06***
(0.01)
0.05***
(0.005)
0.05***
(0.004)
-0.004
(0.007)
∆ 3 -0.47***
(0.08)
-0.47***
(0.09)
-0.59***
(0.21)
-0.56**
(0.23)
-1.69***
(0.13)
-1.68***
(0.15)
-2.75***
(0.14)
-2.61***
(0.11)
1 -0.04
(0.11)
-0.26*
(0.16)
-0.22
(0.59)
-0.25
(0.42)
2 -0.07
(0.24)
-0.61
(0.37)
-0.31
(1.34)
-0.31
(0.92)
3 0.02
(0.13)
-0.08
(0.48)
-0.25
(0.50)
-0.55
(0.41)
4 0.16
(0.13)
0.21
(0.26)
0.54
(0.70)
0.43
(0.52)
Observations 181 181 181 181 181 181 181 181
2
0.77 0.78 0.54 0.52 0.86 0.87 0.73 0.72
LogL 4.70 -0.64 -104.6 -112.1 -210.2 -212.2 -289.7 -296.4
Wald 0.93 0.15 0.98 0.09
LR 0.87 0.08 0.69 0.06
LM 0.02 0.06 0.04 0.99
Notes: Numbers in parentheses are jackknife estimated standard errors. */**/***: Statistically significant wh
applying a 10%/5%/1% confidence level. LogL: Value of maximized log likelihood function. Wald / LR / LM:
value of Wald / Lagrange ratio / Lagrange multiplier test for the restrictions imposed.

28. 28
Result 1: Expectations are not important
Estimations results. Dependent variable: Change in business lending rate
Δi0t Δi1t Δi2t Δi3t
Const. -0.01
(0.01)
-0.01*
(0.01)
-0.02
(0.02)
-0.02
(0.03)
-0.01
(0.05)
-0.05
(0.04)
0.05
(0.05)
-0.04
(0.05)
∆ 1 0.23***
(0.08)
0.24***
(0.08)
0.01
(0.37)
0.03
(0.23)
0.01
(0.06)
0.02
(0.04)
-0.03
(0.04)
0.04
(0.04)
∆ 1 1.01***
(0.38)
0.93***
(0.15)
2.10**
(1.00)
1.19**
(0.47)
1.76
(1.95)
1.25***
(0.41)
1.91
(1.28)
1.46**
(0.68)
∆ 2 0.73***
(0.24)
0.77***
(0.18)
0.47
(0.34)
0.82***
(0.27)
0.58
(0.91)
0.66
(0.78)
0.71
(0.52)
0.87**
(0.41)
∆ 1 1 2 -0.10
(0.59)
-0.96
(1.60)
0.27
(3.91)
-5.42
(3.28)
1 -0.01
(0.02)
-0.08
(0.15)
-0.09
(0.12)
-0.05*
(0.03)
∆ 2 0.07***
(0.005)
0.07***
(0.01)
0.06***
(0.01)
0.06***
(0.01)
0.05***
(0.005)
0.05***
(0.004)
-0.004
(0.007)
∆ 3 -0.47***
(0.08)
-0.47***
(0.09)
-0.59***
(0.21)
-0.56**
(0.23)
-1.69***
(0.13)
-1.68***
(0.15)
-2.75***
(0.14)
-2.61***
(0.11)
1 -0.04
(0.11)
-0.26*
(0.16)
-0.22
(0.59)
-0.25
(0.42)
2 -0.07
(0.24)
-0.61
(0.37)
-0.31
(1.34)
-0.31
(0.92)
3 0.02
(0.13)
-0.08
(0.48)
-0.25
(0.50)
-0.55
(0.41)
4 0.16
(0.13)
0.21
(0.26)
0.54
(0.70)
0.43
(0.52)
Observations 181 181 181 181 181 181 181 181
2
0.77 0.78 0.54 0.52 0.86 0.87 0.73 0.72
LogL 4.70 -0.64 -104.6 -112.1 -210.2 -212.2 -289.7 -296.4
Wald 0.93 0.15 0.98 0.09
LR 0.87 0.08 0.69 0.06
LM 0.02 0.06 0.04 0.99
Notes: Numbers in parentheses are jackknife estimated standard errors. */**/***: Statistically significant wh
applying a 10%/5%/1% confidence level. LogL: Value of maximized log likelihood function. Wald / LR / LM:
value of Wald / Lagrange ratio / Lagrange multiplier test for the restrictions imposed.

29. 29
Result 2: (a) Movements of interbank rates only
matter when MPR changes. (b) No adjustment
to long-run relations
Estimations results. Dependent variable: Change in business lending rate
Δi0t Δi1t Δi2t Δi3t
Const. -0.01
(0.01)
-0.01*
(0.01)
-0.02
(0.02)
-0.02
(0.03)
-0.01
(0.05)
-0.05
(0.04)
0.05
(0.05)
-0.04
(0.05)
∆ 1 0.23***
(0.08)
0.24***
(0.08)
0.01
(0.37)
0.03
(0.23)
0.01
(0.06)
0.02
(0.04)
-0.03
(0.04)
0.04
(0.04)
∆ 1 1.01***
(0.38)
0.93***
(0.15)
2.10**
(1.00)
1.19**
(0.47)
1.76
(1.95)
1.25***
(0.41)
1.91
(1.28)
1.46**
(0.68)
∆ 2 0.73***
(0.24)
0.77***
(0.18)
0.47
(0.34)
0.82***
(0.27)
0.58
(0.91)
0.66
(0.78)
0.71
(0.52)
0.87**
(0.41)
∆ 1 1 2 -0.10
(0.59)
-0.96
(1.60)
0.27
(3.91)
-5.42
(3.28)
1 -0.01
(0.02)
-0.08
(0.15)
-0.09
(0.12)
-0.05*
(0.03)
∆ 2 0.07***
(0.005)
0.07***
(0.01)
0.06***
(0.01)
0.06***
(0.01)
0.05***
(0.005)
0.05***
(0.004)
-0.004
(0.007)
∆ 3 -0.47***
(0.08)
-0.47***
(0.09)
-0.59***
(0.21)
-0.56**
(0.23)
-1.69***
(0.13)
-1.68***
(0.15)
-2.75***
(0.14)
-2.61***
(0.11)
1 -0.04
(0.11)
-0.26*
(0.16)
-0.22
(0.59)
-0.25
(0.42)
2 -0.07
(0.24)
-0.61
(0.37)
-0.31
(1.34)
-0.31
(0.92)
3 0.02
(0.13)
-0.08
(0.48)
-0.25
(0.50)
-0.55
(0.41)
4 0.16
(0.13)
0.21
(0.26)
0.54
(0.70)
0.43
(0.52)
Observations 181 181 181 181 181 181 181 181
2
0.77 0.78 0.54 0.52 0.86 0.87 0.73 0.72
LogL 4.70 -0.64 -104.6 -112.1 -210.2 -212.2 -289.7 -296.4
Wald 0.93 0.15 0.98 0.09
LR 0.87 0.08 0.69 0.06
LM 0.02 0.06 0.04 0.99
Notes: Numbers in parentheses are jackknife estimated standard errors. */**/***: Statistically significant wh
applying a 10%/5%/1% confidence level. LogL: Value of maximized log likelihood function. Wald / LR / LM:
value of Wald / Lagrange ratio / Lagrange multiplier test for the restrictions imposed.

30. 30
Result 3: Credit risk measures matter and with
the expected signs
Estimations results. Dependent variable: Change in business lending rate
Δi0t Δi1t Δi2t Δi3t
Const. -0.01
(0.01)
-0.01*
(0.01)
-0.02
(0.02)
-0.02
(0.03)
-0.01
(0.05)
-0.05
(0.04)
0.05
(0.05)
-0.04
(0.05)
∆ 1 0.23***
(0.08)
0.24***
(0.08)
0.01
(0.37)
0.03
(0.23)
0.01
(0.06)
0.02
(0.04)
-0.03
(0.04)
0.04
(0.04)
∆ 1 1.01***
(0.38)
0.93***
(0.15)
2.10**
(1.00)
1.19**
(0.47)
1.76
(1.95)
1.25***
(0.41)
1.91
(1.28)
1.46**
(0.68)
∆ 2 0.73***
(0.24)
0.77***
(0.18)
0.47
(0.34)
0.82***
(0.27)
0.58
(0.91)
0.66
(0.78)
0.71
(0.52)
0.87**
(0.41)
∆ 1 1 2 -0.10
(0.59)
-0.96
(1.60)
0.27
(3.91)
-5.42
(3.28)
1 -0.01
(0.02)
-0.08
(0.15)
-0.09
(0.12)
-0.05*
(0.03)
∆ 2 0.07***
(0.005)
0.07***
(0.01)
0.06***
(0.01)
0.06***
(0.01)
0.05***
(0.005)
0.05***
(0.004)
-0.004
(0.007)
∆ 3 -0.47***
(0.08)
-0.47***
(0.09)
-0.59***
(0.21)
-0.56**
(0.23)
-1.69***
(0.13)
-1.68***
(0.15)
-2.75***
(0.14)
-2.61***
(0.11)
1 -0.04
(0.11)
-0.26*
(0.16)
-0.22
(0.59)
-0.25
(0.42)
2 -0.07
(0.24)
-0.61
(0.37)
-0.31
(1.34)
-0.31
(0.92)
3 0.02
(0.13)
-0.08
(0.48)
-0.25
(0.50)
-0.55
(0.41)
4 0.16
(0.13)
0.21
(0.26)
0.54
(0.70)
0.43
(0.52)
Observations 181 181 181 181 181 181 181 181
2
0.77 0.78 0.54 0.52 0.86 0.87 0.73 0.72
LogL 4.70 -0.64 -104.6 -112.1 -210.2 -212.2 -289.7 -296.4
Wald 0.93 0.15 0.98 0.09
LR 0.87 0.08 0.69 0.06
LM 0.02 0.06 0.04 0.99
Notes: Numbers in parentheses are jackknife estimated standard errors. */**/***: Statistically significant wh
applying a 10%/5%/1% confidence level. LogL: Value of maximized log likelihood function. Wald / LR / LM:
value of Wald / Lagrange ratio / Lagrange multiplier test for the restrictions imposed.

31. 31
Result 4: When controlling for changes in the
credit risk, MPR pass-through cannot be rejected
to be symmetric and instantaneously complete
Estimations results. Dependent variable: Change in business lending rate
Δi0t Δi1t Δi2t Δi3t
Const. -0.01
(0.01)
-0.01*
(0.01)
-0.02
(0.02)
-0.02
(0.03)
-0.01
(0.05)
-0.05
(0.04)
0.05
(0.05)
-0.04
(0.05)
∆ 1 0.23***
(0.08)
0.24***
(0.08)
0.01
(0.37)
0.03
(0.23)
0.01
(0.06)
0.02
(0.04)
-0.03
(0.04)
0.04
(0.04)
∆ 1 1.01***
(0.38)
0.93***
(0.15)
2.10**
(1.00)
1.19**
(0.47)
1.76
(1.95)
1.25***
(0.41)
1.91
(1.28)
1.46**
(0.68)
∆ 2 0.73***
(0.24)
0.77***
(0.18)
0.47
(0.34)
0.82***
(0.27)
0.58
(0.91)
0.66
(0.78)
0.71
(0.52)
0.87**
(0.41)
∆ 1 1 2 -0.10
(0.59)
-0.96
(1.60)
0.27
(3.91)
-5.42
(3.28)
1 -0.01
(0.02)
-0.08
(0.15)
-0.09
(0.12)
-0.05*
(0.03)
∆ 2 0.07***
(0.005)
0.07***
(0.01)
0.06***
(0.01)
0.06***
(0.01)
0.05***
(0.005)
0.05***
(0.004)
-0.004
(0.007)
∆ 3 -0.47***
(0.08)
-0.47***
(0.09)
-0.59***
(0.21)
-0.56**
(0.23)
-1.69***
(0.13)
-1.68***
(0.15)
-2.75***
(0.14)
-2.61***
(0.11)
1 -0.04
(0.11)
-0.26*
(0.16)
-0.22
(0.59)
-0.25
(0.42)
2 -0.07
(0.24)
-0.61
(0.37)
-0.31
(1.34)
-0.31
(0.92)
3 0.02
(0.13)
-0.08
(0.48)
-0.25
(0.50)
-0.55
(0.41)
4 0.16
(0.13)
0.21
(0.26)
0.54
(0.70)
0.43
(0.52)
Observations 181 181 181 181 181 181 181 181
2
0.77 0.78 0.54 0.52 0.86 0.87 0.73 0.72
LogL 4.70 -0.64 -104.6 -112.1 -210.2 -212.2 -289.7 -296.4
Wald 0.93 0.15 0.98 0.09
LR 0.87 0.08 0.69 0.06
LM 0.02 0.06 0.04 0.99
Notes: Numbers in parentheses are jackknife estimated standard errors. */**/***: Statistically significant wh
applying a 10%/5%/1% confidence level. LogL: Value of maximized log likelihood function. Wald / LR / LM:
value of Wald / Lagrange ratio / Lagrange multiplier test for the restrictions imposed.

32. 32
Result 4: When controlling for changes in the
credit risk, MPR pass-through cannot be rejected
to be symmetric and instantaneously complete
Estimations results. Dependent variable: Change in business lending rate
Δi0t Δi1t Δi2t Δi3t
Const. -0.01
(0.01)
-0.01*
(0.01)
-0.02
(0.02)
-0.02
(0.03)
-0.01
(0.05)
-0.05
(0.04)
0.05
(0.05)
-0.04
(0.05)
∆ 1 0.23***
(0.08)
0.24***
(0.08)
0.01
(0.37)
0.03
(0.23)
0.01
(0.06)
0.02
(0.04)
-0.03
(0.04)
0.04
(0.04)
∆ 1 1.01***
(0.38)
0.93***
(0.15)
2.10**
(1.00)
1.19**
(0.47)
1.76
(1.95)
1.25***
(0.41)
1.91
(1.28)
1.46**
(0.68)
∆ 2 0.73***
(0.24)
0.77***
(0.18)
0.47
(0.34)
0.82***
(0.27)
0.58
(0.91)
0.66
(0.78)
0.71
(0.52)
0.87**
(0.41)
∆ 1 1 2 -0.10
(0.59)
-0.96
(1.60)
0.27
(3.91)
-5.42
(3.28)
1 -0.01
(0.02)
-0.08
(0.15)
-0.09
(0.12)
-0.05*
(0.03)
∆ 2 0.07***
(0.005)
0.07***
(0.01)
0.06***
(0.01)
0.06***
(0.01)
0.05***
(0.005)
0.05***
(0.004)
-0.004
(0.007)
∆ 3 -0.47***
(0.08)
-0.47***
(0.09)
-0.59***
(0.21)
-0.56**
(0.23)
-1.69***
(0.13)
-1.68***
(0.15)
-2.75***
(0.14)
-2.61***
(0.11)
1 -0.04
(0.11)
-0.26*
(0.16)
-0.22
(0.59)
-0.25
(0.42)
2 -0.07
(0.24)
-0.61
(0.37)
-0.31
(1.34)
-0.31
(0.92)
3 0.02
(0.13)
-0.08
(0.48)
-0.25
(0.50)
-0.55
(0.41)
4 0.16
(0.13)
0.21
(0.26)
0.54
(0.70)
0.43
(0.52)
Observations 181 181 181 181 181 181 181 181
2
0.77 0.78 0.54 0.52 0.86 0.87 0.73 0.72
LogL 4.70 -0.64 -104.6 -112.1 -210.2 -212.2 -289.7 -296.4
Wald 0.93 0.15 0.98 0.09
LR 0.87 0.08 0.69 0.06
LM 0.02 0.06 0.04 0.99
Notes: Numbers in parentheses are jackknife estimated standard errors. */**/***: Statistically significant wh
applying a 10%/5%/1% confidence level. LogL: Value of maximized log likelihood function. Wald / LR / LM:
value of Wald / Lagrange ratio / Lagrange multiplier test for the restrictions imposed.
p-values for the hypotheses of symmetric and
instantaneously complete pass-through:
0.42, 0.65, 0.75, 0.79.

33. 33
Conclusions and policy recommendations
 The information in the weighted average of a commercial interest rate may be
limited. Higher order moments help with a more complete vision.
 Changes in the higher order moments supply information about changes in the
risk associated with the portfolio of clients.
 In a theoretical illustrations it can be shown that with a one-to-one relation
between the risk-free interest rate and the monetary policy rate (MPR), the pass-
through of MPR changes is instantaneous and complete when correcting for
changes in the credit risk.
 Empirical estimations confirm this relation in Chile.
 Policy recommendations:
 To better understand changes in commercial interest rates, not only the
weighted averages of the rates should be monitored, but also the higher
order moments of the distribution. This is particularly important when
evaluating the effects of MPR changes.
 For transparency: Publish these higher order moments.