## 1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental Variables Estimates

## Source details

**Canonical URL:** [1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental Variables Estimates](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0586.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0586.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0586.pdf.json)

---

### Research question, approach, and headline findings
- Research question: Whether monetary policy affects the real economy, and how forward-looking central bank behavior biases simple estimates.
- Identification strategy: Instrumental variables (IV) estimates using German interest rates as the instrument for other European countries’ nominal short-term rates to control for endogenous, forward-looking policy responses.
- Rationale for instrument:
  - Germany often acted as an “anchor” country for many European countries during 1973–1998 (and particularly during the EMS/ERM period), making German interest rates highly predictive of other countries’ interest rates.
  - Using Germany as an instrument formalizes historical “narrative” identification and nests it within a dynamic regression/VAR framework.
- Key empirical summary results:
  - IV estimates: a 5 percentage point increase in interest rates → contraction in annual real growth of 2 to 3 percentage points.
  - Naïve OLS estimates: a 5 percentage point increase → slowdown of 0.5 to 1 percentage points.
  - Pooled IV (Row A of Table 3): -0.113 percentage points (quarterly effect per 1 percentage point increase).
  - Sample average OLS effect across countries: -0.043 percentage points (quarterly).
  - Sample median OLS effect: -0.039 percentage points (quarterly).
  - Pooled OLS (Row A, no covariates): -0.031 percentage points (quarterly).
  - Pooled OLS equally weighted [Pooled 1]: -0.0325 percentage points (quarterly).
- Interpretation:
  - Two-stage least squares reduces bias due to forward-looking policy and provides a complementary set of estimates to VAR and narrative approaches.
  - Heterogeneity: the degree of forward-looking behavior (and OLS bias) is larger for countries with higher monetary policy independence and weaker economic ties to Germany.

### Identification strategy, formal model, and bias characterization
- Forward-looking policy reaction function:
  - i_t = β_0 + β_1 ˆy_{t|t−1} + β_2 ˆπ_{t+1|t−1} + v_t
- Standard growth regression and OLS inconsistency condition:
  - y_t = α_0 + θ i_t + φ′_1 W_{t−1} + u_t
  - OLS consistency requires C[u_t, i_t | W_{t−1}] = 0; this fails if W_{t−1} ⊂ Ω_{t−1} (central bank’s information set).
- IV / “projection” approach and first stage:
  - Augmented policy reaction: i_t = β_0 + β_1 ˆy_{t|t−1} + β_2 ˆπ_{t+1|t−1} + β_3 z_t + ν_t, where z_t is an instrument.
  - First-stage regression: i_t = β_0 + φ′_2 W_{t−1} + β_3 z_t + η_t.
  - Valid IV requires cov[u_t, z_t | W_{t−1}] = 0.
- Relation to VAR identification:
  - The IV system leads to a non-recursive structural VAR that relaxes contemporaneous exclusion restrictions typical in classic VARs.
- Approximate bias characterization:
  - B_IV ≈ η β_3 B*_OLS.
  - IV has smaller approximate bias than OLS if η < β_3 / (1 − ρ^2).
  - Pooled magnitudes: β_3 is close to 0.8 and ρ is close to 0.4, making the right hand side of the inequality over 0.95.
  - Intuition: IV bias increases with correlation of output shocks and Bundesbank forward-looking bias, and decreases with strength of domestic–German interest rate correlation.
- Static IV parameter in dynamic contexts:
  - If true DGP includes lags y_t = α_0 + θ_0 i_t + θ_1 i_{t−1} + ... + θ_p i_{t−p} + φ′_1 W_{t−1} + u_t, then estimated θ summarizes θ_0 + θ_1 γ_1 + ... + θ_p γ_p with γ_j = C[i_t, i_{t−j} | W_{t−1}] / V[i_t | W_{t−1}].
  - The static IV identifies a reduced-form parameter measuring the effect of an episode of tight monetary policy.

### Data, sample, and implementation details
- Sample period and countries:
  - Quarterly data for eleven European countries, 1973–1998: Austria, Belgium, France, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom.
  - Denmark and Ireland omitted due to quarterly nominal interest rate data limitations.
- Key variables and sources:
  - Nominal GDP: IMF International Financial Statistics (IFS), deflated by each country’s real GDP deflator (1995=100).
  - Short-term interest rate: overnight lending or call money rate from the Global Financial Database, averaged end-of-month rates quarterly.
  - Main estimator equations: Equations (2) and (5) with the level of the quarterly German overnight rate as instrument for national call money rates.
  - Seasonality: quarterly dummies included in all specifications.
- Missing-data periods (reported):
  - GDP missing: Belgium 1973Q1–1980Q2; Netherlands 1973Q1–1977Q1; Portugal 1973Q1–1977Q1; Sweden 1973Q1–1980Q1.
  - Interest rates missing: Italy 1973Q1–1978Q2; Portugal 1973Q1–1975Q3.
- Alternative interest-rate measures tried: central bank discount rate, three-month treasury-bill rate (annualized); results robust.

### Main empirical results: country-level, pooled findings, and magnitudes
- Baseline OLS findings (no covariates):
  - Cross-country OLS: modest negative effects of a one percentage point increase on quarterly real growth; example country estimates:
    - Netherlands: -0.094 percentage points (quarterly per 1 percentage point increase).
    - France: -0.015 percentage points (quarterly per 1 percentage point increase).
  - Sample average OLS effect: -0.043 percentage points (quarterly).
  - Sample median OLS effect: -0.039 percentage points (quarterly).
- Pooled OLS and IV comparisons:
  - Pooled OLS (Row A, no covariates): -0.031 percentage points (quarterly).
  - Pooled OLS equally weighted [Pooled 1]: -0.0325 percentage points (quarterly).
  - Pooled IV (Row A of Table 3): -0.113 percentage points (quarterly).
  - The pooled IV estimate exceeds pooled OLS by about a factor of three in the baseline pooled specification.
  - Row (A) of Table 3 (averaged over four pooled estimates): reduction in real growth of 0.115 percentage points (quarterly).
  - Row (G) of Table 3: average reduction of 0.15 percentage points (quarterly).
- Annualized magnitude interpretation:
  - IV: a 5 percentage point increase → contraction in annual real growth of 2 to 3 percentage points.
  - Naïve OLS: same 5 percentage point increase → slowdown of 0.5 to 1 percentage points.
- First-stage strength:
  - Most countries have first-stage coefficient at least 0.8.
  - Pooled first-stage estimates range from 0.69 to 0.91, with most between 0.75 and 0.8.
  - Including lags of inflation and output growth generally reduces first-stage coefficient on average; lags of output growth tend to increase it, lags of inflation tend to reduce it.

### Heterogeneity, cross-country patterns, and interpretation of OLS–IV gap
- Cross-country heterogeneity:
  - OLS–IV difference larger for countries less tied to Germany economically and with greater scope for independent monetary policy (e.g., larger countries or those with wider exchange rate bands).
  - OLS–IV gap:
    - Positive and greater for larger countries.
    - Decreasing with trade-to-GDP ratio.
    - Increasing with exchange rate volatility vis-à-vis the deutsche mark.
    - Increasing with distance (proxy), though distance is imperfect.
  - Examples: small bias in France (closely following German policy); large biases in Norway and Switzerland.
- EMS effects (1979 onward):
  - EMS period strengthens Bundesbank leadership and constrains member countries’ policy.
  - EMS-era results confirm baseline: IV systematically more negative than OLS; differences small relative to full sample.
  - Pooled first-stage coefficients tend to increase under EMS (e.g., from about 0.85 to about 1 without controls; from about 0.7 to 0.82 for a conservative specification).

### Robustness checks, dynamics, and diagnostics
- Controls and lags:
  - Inclusion of first four lags of real output growth and inflation produces only small differences in OLS estimates; IV estimates change only modestly (strengthened on average except Spain and Austria).
  - If covariates fully controlled forward-looking policy bias, OLS would become more negative and the OLS–IV gap would shrink; results show the opposite.
- Dynamics and lagged interest rates:
  - Static estimators can be interpreted as weighted sums of current and lagged interest-rate effects.
  - Inclusion of lagged home interest rates in pooled OLS and IV affects estimates; lags of German rates are too persistent to serve as separate instruments (weak instrument problem).
  - IV estimates including lagged interest rates suggest past interest rates may be endogenous as well, consistent with policy horizons of several quarters.
- Leverage and influence diagnostics:
  - Leverage plots: leverage coefficients generally close to zero for most countries.
  - Exceptions with higher leverage: Austria, the Netherlands, and Sweden.
- Sensitivity to outliers and specification:
  - Results reported with robust (Eicker-White) standard errors and Newey-West corrections for 4th order serial correlation.
  - Inclusion of lags of real exchange rates does not materially change results.

### Analytical appendix results on imperfect instruments
- When instrument z_t is not purely exogenous, estimands:
  - θ̂OLSp = θ + (β3 a + C[ηt, ut | Wt−1]) / V[it | Wt−1]
  - θ̂IVp = θ + a / C[zt, it | Wt−1]
- Relationship between OLS and IV bias:
  - BOLS = ρ2 BIV + b, with b ≡ C[ηt, ut | Wt−1] / V[it | Wt−1].
  - Under (A.4): BOLS > BIV ⇐⇒ BIV < b / (1 − ρ2).
  - Approximation: BIV ≈ η β3 b.
  - Using pooled empirical magnitudes β3 ≈ 0.8 and ρ ≈ 0.4 → right-hand side of (A.7) over 0.95, producing expectation that IV estimates will be less biased than OLS in the settings considered.

### Main conclusion and methodological implication
- Empirical conclusion: Using quarterly German nominal interest rates as an instrument, the causal effect of a 5 percentage point increase in nominal interest rates is a contraction in annual real growth of 2 to 3 percentage points; naïve OLS implies 0.5 to 1 percentage point contraction.
- The OLS–IV difference is interpreted as measuring forward-looking policy endogeneity; the systematic positive bias in OLS is robust to inclusion of lagged GDP growth and inflation.
- Methodological implication: The IV approach, while not a panacea (limitations include instrument validity, dynamics, and weak instrument concerns), serves as a useful diagnostic to bound and complement VAR and narrative estimates of monetary policy effects.

*Source: _wp0586 - 1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental Variables Estimates (IMF PDF).*

### 1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental

### 1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental Variables Estimates

### Major sections
- 1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental Variables Estimates ................................................................................................ 25
- 2.    Summarizing Least Squares ............................................................................ 26
- 3.    Summarizing Least Squares ............................................................................ 27
- 4.    Comovements in European Nominal Interest Rates .............................................. 28
- 5.    Summarizing Least Squares ............................................................................ 29
- 6.    Baseline OLS and IV Estimates for the EMS Period ............................................. 30

### Appendix tables and figures
- Appendix Tables
  - A1. Country Summary Statistics  ........................................................................... 31
  - A2. Entry and Realignment dates into EMS.............................................................. 32
  - A3. Unit Root and Cointegration Tests For Quarterly Interest Rates ............................... 33
- Figure
  - 1.    IV and OLS-IV and Country Characteristics  ...................................................... 34
- Appendix Figures
  - A1. Leverage Plots for OLS Estimates (no lags)  ....................................................... 35
  - A2. Leverage Plots for IV Estimates (no lags)  .......................................................... 36

*Source: _wp0586 - 1.    The Effect of Interest Rates on the Real Economy: Least Squares and Instrumental Variables Estimates (IMF PDF).*

### References ........................................................................................................ 37

### _wp0586 - References ........................................................................................................ 37

### Introduction: question, approach, and summary findings
- Research question: Whether monetary policy affects the real economy, and how forward-looking central bank behavior biases simple estimates.
- Identification strategy: Instrumental variables (IV) estimates using German interest rates as the instrument for other European countries’ nominal short-term rates to control for endogenous, forward-looking policy responses.
- Rationale for instrument:
  - Germany often acted as an “anchor” country for many European countries during 1973–1998 (and particularly during the EMS/ERM period), making German interest rates highly predictive of other countries’ interest rates.
  - Using Germany as an instrument formalizes historical “narrative” identification (Friedman and Schwartz 1963; Romer and Romer 1989) and nests it within a dynamic regression/VAR framework.
- Key empirical summary results:
  - IV estimates suggest that the effect of a 5 percentage point increase in interest rates is a contraction in annual real growth of 2 to 3 percentage points.
  - Naïve OLS estimates suggest a slowdown of 0.5 to 1 percentage points for a 5 percentage point increase in interest rates.
  - IV estimates are substantially more negative than OLS for most countries, indicating forward-looking monetary policy induces an OLS bias.
- Interpretation:
  - Two-stage least squares reduces bias due to forward-looking policy and provides a complementary set of estimates to VAR and narrative approaches.
  - Heterogeneity: the degree of forward-looking behavior (and OLS bias) is larger for countries with higher monetary policy independence and weaker economic ties to Germany.

### Identification strategy: formal model and bias characterization
- Policy reaction function (forward-looking central bank):
  - i_t = β_0 + β_1 ˆy_{t|t−1} + β_2 ˆπ_{t+1|t−1} + v_t
  - ˆy_{t|t−1} = E[y_t | Ω_{t−1}], ˆπ_{t+1|t−1} = E[π_{t+1} | Ω_{t−1}]
- Standard growth regression specification:
  - y_t = α_0 + θ i_t + φ′_1 W_{t−1} + u_t
  - OLS consistency requires C[u_t, i_t | W_{t−1}] = 0, which fails if the researcher’s information set W_{t−1} is a strict subset of the central bank’s information set Ω_{t−1}.
- IV / “projection” approach:
  - Augmented policy reaction function: i_t = β_0 + β_1 ˆy_{t|t−1} + β_2 ˆπ_{t+1|t−1} + β_3 z_t + ν_t, where z_t is an instrument (e.g., foreign interest rate or exchange rate target) assumed orthogonal to short-run domestic output innovations.
  - First-stage regression: i_t = β_0 + φ′_2 W_{t−1} + β_3 z_t + η_t.
  - Valid IV requires cov[u_t, z_t | W_{t−1}] = 0.
- Relation to VAR identification:
  - IV system leads to a non-recursive structural VAR that relaxes contemporaneous exclusion restrictions typically imposed in classic VARs.
  - The IV approach can make explicit the identifying assumptions and expose limitations of conditioning-only approaches.
- Characterizing remaining bias of IV:
  - Let η denote coefficient on German output growth innovations in the population regression of home output innovations on German innovations.
  - Approximate bias of IV: B_IV ≈ η β_3 B*_OLS.
  - IV has smaller approximate bias than OLS if η < β_3 / (1 − ρ^2), where ρ is the conditional correlation of domestic and foreign interest rates.
  - Pooled magnitudes reported: β_3 is close to 0.8 and ρ is close to 0.4, leading the right hand side of the inequality to be over 0.95.
  - Intuition: IV bias increases with the correlation of output shocks and the Bundesbank’s forward-looking bias, and decreases with the strength of the domestic-base interest rate correlation.
- Interpretation of the static IV parameter in dynamic contexts:
  - If true DGP is y_t = α_0 + θ_0 i_t + θ_1 i_{t−1} + ... + θ_p i_{t−p} + φ′_1 W_{t−1} + u_t, then OLS and IV estimate summary parameter θ ≡ θ_0 + θ_1 γ_1 + ... + θ_p γ_p, with γ_j = C[i_t, i_{t−j} | W_{t−1}] / V[i_t | W_{t−1}].
  - The static θ summarizes the instantaneous effect θ_0 and the weighted historical effects θ_j; thus the static IV identifies a reduced-form parameter measuring the effect of an episode of tight monetary policy.
- Practical limitations noted:
  - Difficulty of using lagged foreign interest rates as separate instruments due to high persistence of interest rates (weak instrument problem).
  - Potential omitted-variable concerns if real exchange rate or terms-of-trade movements affect both German policy and domestic outcomes; authors included lags of real exchange rates as controls and found results unchanged.

### Data and empirical implementation
- Sample and countries:
  - Quarterly data for eleven European countries, 1973–1998: Austria, Belgium, France, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom.
  - Notable data limitations: Denmark and Ireland omitted due to quarterly nominal interest rate data limitations.
- Data sources and variables:
  - Nominal GDP: IMF International Financial Statistics (IFS), deflated by each country’s real GDP deflator (1995=100).
  - Short-term interest rate: overnight lending or call money rate from the Global Financial Database, averaged end-of-month rates quarterly.
  - Seasonality: quarterly dummies included in all specifications.
  - Missing quarterly GDP or interest rate data for some countries/periods:
    - GDP missing: Belgium 1973Q1–1980Q2; Netherlands 1973Q1–1977Q1; Portugal 1973Q1–1977Q1; Sweden 1973Q1–1980Q1.
    - Interest rates missing: Italy 1973Q1–1978Q2; Portugal 1973Q1–1975Q3.
  - Alternative interest rate measures tried: central bank discount rate, three-month treasury-bill rate (annualized); results robust.
- Main estimation equations: Equations (2) and (5) with the level of the quarterly German overnight rate as an instrument for national call money rates.

### Main empirical results: country-level and pooled findings
- Baseline OLS findings (no covariates):
  - Cross-country OLS estimates imply modest negative effects of a one percentage point increase in the interest rate on quarterly real growth; examples:
    - Netherlands: -0.094 percentage points.
    - France: -0.015 percentage points.
  - Sample average OLS effect across countries: -0.043 percentage points.
  - Sample median OLS effect: -0.039 percentage points.
- Pooled OLS summary statistics (Table 2; pooled by several weight schemes):
  - Pooled OLS estimate without control variables in Row (A): -0.031 percentage points.
  - Pooled OLS equally weighted [Pooled 1]: -0.0325 percentage points.
- IV vs OLS:
  - For most countries (except Austria and Belgium) IV estimates are more negative than OLS estimates, indicating endogenous forward-looking policy raises OLS bias.
  - Pooled IV estimate in Row (A) of Table 3: -0.113 percentage points (i.e., a one percentage point increase in interest rates causes a reduction in quarterly real output growth of 0.113 percentage points on average in pooled IV).
  - The pooled IV estimate exceeds the pooled OLS estimate by about a factor of three in the baseline pooled specification.
  - Differences between OLS and IV are statistically significant in pooled models; for single countries differences are reported in the tables.
- Magnitude interpretation in annualized terms (from summary statements):
  - A 5 percentage point increase in interest rates → contraction in annual real growth of 2 to 3 percentage points (IV).
  - OLS implication for same 5 percentage point increase → slowdown of 0.5 to 1 percentage points (naïve OLS).
- Heterogeneity and economic linkages:
  - OLS–IV difference (and extent of forward-looking policy) tends to be larger for countries less tied to Germany economically and with greater scope for independent monetary policy (e.g., larger countries or those with wider exchange rate bands).
  - Countries heavily dependent on trade with Germany or with high bilateral co-movement of shocks with Germany exhibit stronger correlation of domestic shocks with Bundesbank policy, making OLS versus IV differentiation more difficult.
  - Exchange rate volatility, exchange rate band width, trade dependence, and bilateral distance are discussed as factors influencing the relative biases of OLS and IV.
- Robustness and specification comments:
  - Inclusion of four lags of real output growth and inflation as controls reduces potential bias of OLS; reported results include robust (Eicker-White) standard errors and Newey-West standard errors correcting for 4th order serial correlation.
  - Authors experimented with including lags of real exchange rates; results were basically unchanged.
  - First-stage coefficients β_3 are large in pooled estimates (close to 0.8), supporting the predictive power of German rates for other countries’ rates.
  - Cointegration/unit-root considerations: authors treat the level first-stage relationships as potentially cointegrating and argue regressions in levels are appropriate for their sample and institutional context given partial capital controls and the EMS period.

### Key numeric magnitudes and parameter relationships (preserved exactly as in source)
- Sample period: 1973–1998.
- Countries: 11 European countries (Austria, Belgium, France, Italy, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom).
- Representative point estimates:
  - Effect of a 5 percentage point increase in interest rates (IV): contraction in annual real growth of 2 to 3 percentage points.
  - Effect of a 5 percentage point increase in interest rates (naïve OLS): slowdown of 0.5 to 1 percentage points.
  - Average OLS effect across countries: -0.043 percentage points (quarterly).
  - Median OLS effect: -0.039 percentage points (quarterly).
  - Pooled OLS (Row A, no covariates): -0.031 percentage points (quarterly).
  - Pooled OLS equally weighted [Pooled 1]: -0.0325 percentage points (quarterly).
  - Pooled IV (Row A of Table 3): -0.113 percentage points (quarterly).
- Bias relationships and pooled parameters:
  - Approximate IV bias: B_IV ≈ η β_3 B*_OLS.
  - IV has smaller approximate bias than OLS if η < β_3 / (1 − ρ^2).
  - Pooled magnitudes: β_3 is close to 0.8; ρ is close to 0.4; the right hand side of the inequality is over 0.95.

*Source: _wp0586 - References ........................................................................................................ 37*

### 1. It is generally significant and larger for bigger countries (e.g., France, Italy, Spain, and the

### _wp0586 - 1. It is generally significant and larger for bigger countries (e.g., France, Italy, Spain, and the

### Bias from omitted variables and inclusion of lags
- Baseline model without other regressors may be biased by confounders affecting both nominal interest rates and real output growth.
- Natural control variables: lags of growth and lagged inflation can capture persistence and some effects of past interest rates.
- Inclusion of the first four lags of real output growth and inflation (Columns (4) to (6) of Table 1) yields:
  - Only small differences in OLS estimates relative to baseline (Columns (1) to (3)), suggesting past output growth and inflation are not strongly correlated with current interest rates or output growth.
  - Differences between OLS results are never significant and do not follow a particular pattern across countries.
  - IV estimates show minor differences; inclusion of lags of output growth moderately strengthens the estimated IV effect on average for all countries but Spain and Austria.
- Standard errors in Columns (3) and (6) of Tables 1 and 6 are computed as square root of the differences in variance of IV and OLS estimates; this is an approximation for heteroscedasticity-robust or Newey-West standard errors.

### Pooled specifications and robustness checks
- Tables 2 and 3 present a wide range of pooled specifications using different weights and various combinations of lags of inflation and output growth (Rows (B) to (G)).
- Rows (H) and (I) allow for different lag coefficients for each country.
- Additional flexibility in lag structure affects the interest rate estimate only in very minor ways.
- Summary statistics across an extended set of specifications report mean, median, and standard deviation; in all specifications IV remains more negative than OLS.
- Specific pooled findings:
  - Row (A) of Table 3: reduction in real growth (averaged over the four pooled estimates) of 0.115 percentage points.
  - Row (G) of Table 3: average reduction of 0.15 percentage points.
- If covariates fully controlled bias from forward-looking monetary policy, OLS would become more negative and the OLS–IV gap would decline; results suggest the opposite.

### First-stage relationship with German interest rates
- IV estimates rely on a strong and significant first-stage relationship between national and German interest rates (Table 4).
- Most countries have a first-stage coefficient of at least 0.8.
- Several countries have first-stage coefficients significantly below unity:
  - Spain, Switzerland, and the United Kingdom: coefficients significantly below unity.
  - Norway, Spain, and Sweden: coefficients between 0.5 and 0.6.
- Including lags of inflation and output growth generally reduces the first-stage coefficient on average:
  - Lags of output growth tend to increase the first-stage coefficient.
  - Lags of inflation tend to reduce the first-stage coefficient.
- Pooled first-stage estimates (Table 5) range from 0.69 to 0.91, with most pooled coefficients between 0.75 and 0.8.
- Conclusion: German monetary policy appears to be a strong and robust determinant of interest rates for the countries in the sample.

### Cross-country heterogeneity and interpretation of OLS–IV gap
- Figure 1 and Figure 2 analyses (based on Table 1):
  - Fig. 2(a): IV estimates become less negative the larger the fraction of GDP due to trade with Germany.
    - Implied IV coefficient for a country with no economic ties to Germany is roughly -0.15.
  - Fig. 2(b): IV estimates are more negative for countries with more volatile currencies vis-à-vis the deutsche mark.
  - The OLS–IV difference:
    - Positive and greater for larger countries.
    - Increasing with distance (not shown).
    - Decreasing with the trade to GDP ratio [Fig. 2(c)].
    - Increasing with exchange rate volatility [Fig. 2(d)].
- Interpretation:
  - The OLS–IV gap reflects at least partially the degree of endogeneity in monetary policy arising from forward-looking behavior.
  - IV estimates are less biased than OLS estimates the less economically integrated a country is with Germany and the more flexible its exchange rate regime vis-à-vis the deutsche mark.
- Caveats:
  - Some heterogeneity in coefficient estimates is expected from sampling variation; occasional outliers should not be overweighted.
  - Distance is an imperfect proxy for trade; trade-to-GDP ratio is preferred as a measure of economic integration.

### Quantitative magnitudes and cross-country patterns
- Average effects:
  - OLS suggests a 5 percentage point increase in nominal interest rates leads to a decline in annual real GDP growth of 0.5 to 1 percentage points.
  - Using German interest rates as an instrument (IV), the effect rises to 2 to 3 percentage points (a threefold increase).
- Cross-country implications:
  - Larger countries should exhibit a greater inflationary bias since they were generally less dependent on Germany economically and had more discretion vis-à-vis their exchange rate regime.
  - Empirical findings:
    - Small bias in France (which followed German monetary policy closely during the EMS).
    - Large biases in Norway and Switzerland.
  - Overall consistency with the belief that smaller open countries may have less scope to conduct independent monetary policy.

### Sensitivity analysis: EMS period, outliers, dynamics
- EMS (European Monetary System) began in 1979 and committed countries to keep exchange rates within bands of the German rate; this should strengthen Bundesbank leadership and constrain member countries’ monetary policy.
- Table 6: EMS-era results (1979 to the present) confirm baseline findings:
  - IV estimates systematically more negative than OLS estimates, and more so for larger countries.
  - Differences between EMS period and full sample are small.
  - Most countries see:
    - Small increase in magnitude of OLS coefficients (exceptions: Austria and the United Kingdom for the specification with lags).
    - Slight reduction in size of IV estimates (exception: United Kingdom).
- Pooled changes (no control variables vs. with controls):
  - Pooled OLS estimate increases from -0.03 to -0.0413 percentage points for constant GDP weights (change not statistically significant).
  - Pooled IV estimate declines in magnitude from -0.1209 to -0.0939.
  - Including four lags of growth and inflation, results are:
    - OLS: -0.0346 vs. -0.0203.
    - IV: -0.1353 vs. 0.10.
- Germany-specific findings:
  - Coefficient on German nominal interest rate in a regression of quarterly GDP growth drops from -0.073 to -0.036, or from -0.064 to zero when lags are included (standard errors large).
- First-stage coefficients under EMS:
  - Tendency to increase for several countries.
  - Austria’s coefficient is no longer significantly different from one (reflecting effective surrendering of monetary policymaking during EMS).
  - Pooled first-stage coefficients increase on average from about 0.85 to about 1 without control variables, and from about 0.7 to 0.82 for a more conservative specification.
  - Increases are partly driven by convergence in growth and inflation.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0586.pdf*

### conclusion is robust to lags of output growth and inflation as controls. Thus, at least part of

### _wp0586 - conclusion is robust to lags of output growth and inflation as controls. Thus, at least part of

### Main conclusion on monetary policy effects
- Using quarterly German nominal interest rates as an instrument for other European countries’ nominal interest rates, the estimated causal effect of a 5 percentage point increase in nominal interest rates is a contraction in annual real growth of 2 to 3 percentage points.
- Naïve OLS estimates suggest a contraction of 0.5 to 1 percentage points for the same 5 percentage point increase.
- The OLS–IV difference is interpreted as a measure of the extent to which the monetary authority is forward-looking; the paper finds a systematic and positive bias in OLS estimates that is unaffected by inclusion of lagged values of GDP growth or inflation as control variables.
- The IV approach focuses on exogenous variations in interest rates and stresses transparent identifying assumptions; it is presented as a useful diagnostic and research tool though not without drawbacks (e.g., limited practicality for estimating dynamic policy impacts and dependence on appropriate instruments).

### Robustness checks and dynamics
- The static model estimators (Tables 1, 2, 3, and 6) can be interpreted as weighted sums of the impact of current and lagged interest rates when lagged effects exist (see equations (10) and (11)).
- Differences in point estimates across countries may reflect accumulation of differential effects over time and differences in the persistence of interest rates.
- A dynamic specification including lagged home country interest rates (assuming lagged rates predetermined) was estimated as a check:
  - Inclusion of lagged interest rates in pooled OLS leads to differences of unclear sign: if all countries are included OLS is more negative; if only countries with complete data are included OLS is less negative.
  - In the first-stage, including lagged own interest rates reduces the coefficient on the instrument considerably, consistent with a positive correlation of current and lagged interest rates within and across countries.
  - IV estimates that include lagged interest rates produce significantly positive effects of past interest rates on output growth and stronger negative effects of current rates — suggesting lagged interest rates may be endogenous as well, consistent with monetary policy actions with a horizon of several quarters.
  - The lags of German interest rates are too persistent to provide separate instruments for lags of followers’ interest rates, preventing further identification.

### Leverage and influence diagnostics
- Leverage plots (Figures A1 and A2) were computed by re-running OLS and IV regressions dropping one observation each period and recording the change in the estimated interest rate coefficient relative to the full-sample estimate (Table 1).
- For most countries the leverage coefficients are generally close to zero.
- Exceptions with higher leverage: Austria, the Netherlands, and Sweden. For these countries the OLS–IV difference is not significantly different from zero.

### Cross-country patterns and correlates of bias
- The OLS–IV difference (bias) is:
  - Decreasing with economic closeness to Germany, as measured by physical distance and trade with Germany.
  - Increasing with exchange rate volatility vis-à-vis the deutsche mark.
  - Smaller during the EMS pegged-exchange-rate period than during the post-1973 period as a whole.
- Comovements and first-stage estimates indicate substantial correlation between German and other countries’ nominal interest rates (see Tables 4 and 5 and pooled summaries in Tables 2–3).

### Analytical characterization of biases with imperfect instruments (Appendix)
- When the instrument zt is not purely exogenous and C[zt, ut | Wt−1] = a (a possibly small number), the OLS and IV estimands for θ̂ are:
  - θ̂OLSp = θ + (β3 a + C[ηt, ut | Wt−1]) / V[it | Wt−1]  (equation (A.1))
  - θ̂IVp = θ + a / C[zt, it | Wt−1]  (equation (A.2))
- From these, a relationship between OLS bias BOLS and IV bias BIV is derived:
  - BOLS = ρ2 BIV + b, where ρ denotes the correlation between zt and it conditional on Wt−1, and b ≡ C[ηt, ut | Wt−1] / V[it | Wt−1]  (equation (A.3)).
  - Under inequality (A.4): BOLS > BIV ⇐⇒ BIV < b / (1 − ρ2).
- Using an auxiliary population regression ut = η u*t + ωt (equation (A.5)) and approximations, the bias of the IV estimator is approximated as:
  - BIV ≈ η β3 b (equation (A.6)).
- Using pooled empirical magnitudes:
  - β3 is empirically close to 0.8 and ρ is close to 0.4, leading the right-hand side of inequality (A.7) to be over 0.95. Because output shocks are unlikely to be correlated more than moderately, this produces a fairly firm expectation that IV estimates will be less biased than OLS for the settings considered.
- The appendix also discusses plausible inequality chains when German OLS bias B*OLS differs from other countries and the effect of control-variable inclusion, yielding condition (A.8) as a slightly attenuated version of (A.7).

### Key numerical results (selected)
- Causal effect (IV): 5 percentage point increase in nominal interest rates → contraction in annual real growth of 2 to 3 percentage points.
- Naïve OLS implication: same 5 percentage point increase → contraction of 0.5 to 1 percentage points.
- Empirical pooled estimates referenced: β3 ≈ 0.8; ρ ≈ 0.4 → threshold over 0.95 in inequality (A.7).
- Leverage diagnostics identify Austria, the Netherlands, and Sweden as exceptions with higher leverage.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0586.pdf*

### REFERENCES

### _wp0586 - REFERENCES

### References
- Angrist, Joshua, and Alan Krueger, 1991, “Does Compulsory School Attendance Affect Earnings?” Quarterly Journal of Economics, Vol. 106 (November), pp. 979–1014.
- Benigno, Gianluca, 2004, “Real Exchange Rate Persistence and Monetary Policy Rules,” Journal of Monetary Economics, Vol. 51 (April), pp. 473–502.
- Bernanke, Ben, 1986, “Alternative Explanations of the Money-Income Correlation,” Carnegie Rochester Conference Series on Public Policy, (Autumn), pp. 49–99.
- ———, and Alan S. Blinder, 1992, “The Federal Funds Rate and the Channels of Monetary Transmission,” American Economic Review, Vol. 82 (September), pp. 902–921.
- Bernanke, Ben, and Ilian Mihov, 1998, “The Liquidity Effect and Long-Run Neutrality,” Carnegie Rochester Conference Series on Public Policy, Vol. 49 (December), pp. 149–194.
- Bernanke, Ben, and Jean Boivin, 2004, “Monetary Policy in a Data-Rich Environment,” Journal of Monetary Economics, Vol. 50, pp. 525–546.
- Bernanke, Ben, Jean Boivin, and Poitr Eliasz, 2003, “Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach,” (December) (unpublished; Washington: Federal Reserve Board; New York: Columbia University; and Princeton: Princeton University).
- Blanchard, Olivier J., and Mark Watson, 1986, “Are All Business Cycles Alike?” in Robert J. Gordon, ed., The American Business Cycle: Continuity and Change, (Chicago, IL: University of Chicago Press).
- Bofinger, Peter, 2000, “The European Monetary System (1979–1988): Achievements, Flaws and Applicability to Other Regions of the World,” (December) (unpublished; Würzburg: Universität Würzburg).
- Clarida, Richard, and Mark Gertler, 1997, “How the Bundesbank Conducts Monetary Policy,” in Reducing Inflation: Motivation and Strategy, ed. by Christina D. Romer and David H. Romer, (Chicago: University of Chicago Press).
- Clarida, Richard, Jordi Galí, and Mark Gertler, 1998, “Monetary Policy Rules in Practice: Some International Evidence,” European Economic Review, Vol. 42 (June), pp. 1033–1068.
- ———, 2000, “Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory,” Quarterly Journal of Economics, Vol. 115 (February), pp. 147–180.
- - 38 -
- Cushman, David O., and Tao Zha, 1997, “Identifying Monetary Policy in a Small Open Economy Under Flexible Exchange Rates,” Journal of Monetary Economics, Vol. 39 (August), pp. 433–448.
- Engel, Charles, and Kenneth D. West, 2004, “Taylor Rules and the Deutschmark-Dollar Real Exchange Rate,” NBER Working Paper No. 10995 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Frankel, Jeffrey A., and Andrew K. Rose, 1998, “The Endogenity of the Optimum Currency Area Criteria,” Economic Journal, Vol. 108 (July), pp. 1009–1025.
- Friedman, Milton, and Anna J. Schwartz, 1963, A Monetary History of the United States, 18670–1960 (Princeton: Princeton University Press).
- Galí, Jordi, and Tommaso Monacelli, 2002, “Monetary Policy and Exchange Rate Volatitliy in a Small Open Economy,” NBER Working Paper No. 8905 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Giavazzi, Francesco, and Alberto Giovannini, 1987, “Models of the EMS: Is Europe a Greater Deutschmark Area?” in Global Macroeconomics, ed. by Ralph C. Bryant and Richard Portes (New York: St. Martin’s Press).
- ———, 1989, Limiting Exchange Rate Flexibility: The European Monetary System (Cambridge, Massachusetts: The MIT Press).
- Giavazzi, Francesco, and Marco Pagano, 1988, “The Advantage of Tying One’s Hands: EMS Discpline and Central Bank Credibility,” European Economic Review, Vol. 32 (June), pp. 1027–1189.
- Hamilton, James D., 1994, Time Series Analysis (Princeton, NJ: Princeton University Press).
- Obstfeld, Maurice, Jay C. Shambaugh, and Alan M. Taylor, 2004a, “Monetary Sovereignty, Exchange Rates, and Capital Controls: The Trilemma in the Interwar Period,” (March), NBER Working Paper No. 10393 (Cambridge, Massachusetts: National Bureau of Economic Research).
- ———, 2004b, “The Trilemma in History: Tradeoffs Among Exchange Rates, Monetary Policies, and Capital Mobility,” (March), NBER Working Paper No. 10396 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Romer, Christina D., and David H. Romer, 1989, “Does Monetary Policy Matter? A New Test in the Spirit of Friedman and Schwartz,” in NBER Macroeconomics Annual 4, ed. by Oliver J. Blanchard and Stanley Fischer (Cambridge, Massachusetts: The MIT Press), pp. 121–170.
- - 39 -
- ———, 2004, “A New Measure of Monetary Shocks: Derivations and Implications,” American Economic Review, Vol. 94 (September), pp. 1055–1084.
- Shambaugh, Jay C., 2004, “The Effects of Fixed Exchange Rates on Monetary Policy,” Quarterly Journal of Economics, Vol. 119, pp. 301–352.
- Taylor, John B., 1993, “Discretion Versus Policy Rules in Practice,” Carnegie Rochester Conference Series on Public Policy, Vol. 93 (December), pp. 195–214.
- von Hagen, Juergen, and Michele Fratianni, 1990, “German Dominance in the EMS: Evidence from Interest Rates,” Journal of International Money and Finance, Vol. 9, pp. 358–375.

*Source: _wp0586 - REFERENCES*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2005/_wp0586.pdf_