2. Shock-restricted SVAR model

We consider the following structural relation between the variables of interest:

(1) \begin{equation}A_{0}X_{t}=a+A_{1}X_{t-1}+A_{2}X_{t-2}+\cdots +A_{p}X_{t-p}+\varepsilon _{t}\end{equation}

where $X_{t}=(U_{{R_{t}}}, Y_{t}, U_{{F_{t}}},p_{t}, i_{t}, q_{t}, ebp_{t},i_{t}^{*})'$ , $U_{{R_{t}}}$ is the real uncertainty index, $Y_{t}$ is the log US industrial production, $U_{{F_{t}}}$ is the financial uncertainty index, $p_{t}$ is the log US CPI, $i_{t}$ is the one-year US government bond rate following Gertler and Karadi (Reference Gertler and Karadi2015), $q_{t}$ is the log US real effective exchange rate, $ebp_{t}$ is the excess bond premium, and $i_{t}^{*}$ is the trade-weighted foreign interest rate. The source of the data for each variable is explained in Section 3. $\varepsilon _{t}=(\varepsilon _{{R_{t}}}, \varepsilon _{{Y_{t}}}, \varepsilon _{{F_{t}}}, \varepsilon _{{p_{t}}}, \varepsilon _{{i_{t}}}, \varepsilon _{{q_{t}}},\varepsilon _{{b_{t}}},\varepsilon _{i_{t}^{*}})'$ contains structural shocks that are serially uncorrelated and $\varepsilon _{t}\sim (0, I_{k})$ where $k=8$ . $\varepsilon _{{i_{t}}}$ denotes monetary policy shocks.Footnote ² The structural relation expressed in (1) is usually suggested by theoretical models and/or historical events but is not readily observable. However, the reduced form of (1) is readily observable and can be expressed as follows:Footnote ³

(2) \begin{equation}X_{t}=b+B_{1}X_{t-1}+B_{2}X_{t-2}+\cdots +B_{p}X_{t-p}+u_{t}\end{equation}

From equations (1) and (2), $A_{0}^{-1}\varepsilon _{t}=u_{t},$ which implies $A_{0}^{-1}A_{0}^{-1^\prime}=\sum _{u},$ where $\sum _{u}$ is the covariance matrix of $u_{t}$ . To understand the structural relation in (1), we need to determine $k^{2}$ elements in $A_{0}^{-1}$ , but the symmetrical nature of $\sum _{u}$ provides only $\frac{k(k+1)}{2}$ independent elements, which indicates that we need $\frac{k(k-1)}{2}$ restrictions to identify unique $A_{0}^{-1}$ . Previous studies have solved this identification issue by putting $\frac{k(k-1)}{2}$ zeros at certain points in $A_{0}^{-1}$ based on suggestions from theoretical models and historical experience.

Unlike previous studies, we take a shock-restricted SVAR approach and do not put zeros in $A_{0}^{-1}$ a priori to identify $A_{0}^{-1}$ . Instead, we select $A_{0}^{-1}$ from infinitely many candidates when the corresponding $\varepsilon _{t}$ is consistent with historical events and satisfies the correlation conditions with external variables. Hence, the intuition of the shock-restricted SVAR method is that the data itself often offers valuable insights into the quantitatively important shocks observed in the sample. The methodology is based on the premise that a reliable identification system should generate $\varepsilon _{t}$ estimates that align well with ex-post interpretation of historical events (event constraints) or conform to accepted economic concepts regarding the defining features of a shock (external variable constraints). The restrictions based on shocks prove beneficial for identification because even if two feasible structural models $A_{0}^{-1}$ and $\tilde{A}_{0}^{-1}$ produce shocks $\varepsilon _{t}$ and $\tilde{\varepsilon }_{t}$ with similar first and second moment, they may differ in specific time periods or in how they relate to external variables. Therefore, introducing two different types of inequality constraints (event and external variable constraints) directly onto the shocks suggest narrowing down the range of possible solutions.Footnote ⁴

Specifically, the strategy employed in our shock-restricted identification is as follows. Let $\hat{P}$ be the unique lower-triangular Cholesky factor of . Hence, . Each rotation begins by obtaining an orthonormal matrix $Q$ through the $QR$ decomposition of a $k \times k$ matrix $M$ drawn from NID (0,1). For a random orthonormal matrix $Q$ , we also have , which means that $\hat{P}Q$ satisfies the restrictions required for $A_{0}^{-1}$ . In our bootstrap replications, we rotate $\hat{P}$ ten million times and compute the corresponding $\hat{\varepsilon }_{t}=(\hat{P}Q)^{-1}\hat{u}_{t}$ for each generated $Q$ . Of these generated $\hat{\varepsilon }_{t}$ , we consider those $\hat{\varepsilon }_{t}$ that satisfy the conditions for a plausible structural shock and conduct our analysis using those $\hat{\varepsilon }_{t}$ . Similar to LMN, the conditions for our shock-restricted SVAR approach consist of event and external variable constraints, which are summarized below.

Event constraints:

1. 1. $\varepsilon _{{F_{{t_{1}}}}}({\hat{A}}_{0}^{-1})\geq {\overline{k}}_{F,\ BM}$ and $\varepsilon _{{b_{{t_{1}}}}}({\hat{A}}_{0}^{-1})\leq {\overline{k}}_{b,\ BM}$ at $t_{1}=$ 1987:10 (Black Monday).

2. 2. $\varepsilon _{{R_{{t_{2}}}}}({\hat{A}}_{0}^{-1})\geq {\overline{k}}_{R, LB}$ and $\varepsilon _{{F_{{t_{2}}}}}({\hat{A}}_{0}^{-1})\geq {\overline{k}}_{F,\ LB}$ at $t_{2}=$ 2008:09 (Collapse of Lehman Brothers).

3. 3. $\varepsilon _{{b_{{t_{3}}}}}({\hat{A}}_{0}^{-1})\geq {\overline{k}}_{b,LB}$ at $t_{3}=$ 2008:09 or 2008:10 (Collapse of Lehman Brothers).

4. 4. $\sum _{t=2007\colon 12}^{2009\colon 06}\varepsilon _{{Y_{t}}}({\hat{A}}_{0}^{-1})\leq {\overline{k}}_{GR}\leq 0$ (Great Recession).

5. 5. $\sum _{t=1985\colon 09}^{1987\colon 01}\varepsilon _{{q_{t}}}({\hat{A}}_{0}^{-1})\leq {\overline{k}}_{PA}\leq 0$ (Plaza Accord).

The first constraint states that a plausible $\varepsilon _{{F_{t}}}$ should be high when the stock market crashed in October 1987. However, $\varepsilon _{{b_{t}}}$ should be low in October 1987 which was emphasized in Caggiano et al. (Reference Caggiano, Castelnuovo, Delrio and Kima2021) in the identification of structural shocks.Footnote ⁵ The second constraint dictates that $\varepsilon _{{F_{t}}}$ and $\varepsilon _{{R_{t}}}$ must be high in September 2008 when Lehman Brothers filed for bankruptcy. The third constraint requires that the excess bond premium in September or October 2008 is extremely high. As noted in Ludvigson, et al. (Reference Ludvigson, Ma and Ng2020), the Lehman Brothers collapse triggered a sharp deterioration in financial conditions, with credit spreads surging abruptly. We therefore impose that the structural credit-supply shock is large in September or October 2008. The fourth constraint requires that the sum of the real output shocks during the Great Recession must be below average.Footnote ⁶ We set ${\overline{k}}_{F,BM}$ equal to the 60th percentile for $\varepsilon _{{F_{t}}}$ in the set of generated structural shocks for the event date $t_{1}$ , while setting ${\overline{k}}_{b,\ BM}$ equal to the 50th percentile for $\varepsilon _{{b_{t}}}$ at the same date. We also set ${\overline{k}}_{R,LB}$ , and ${\overline{k}}_{F,LB}$ equal to the 50th percentile for $\varepsilon _{{R_{t}}}$ and $\varepsilon _{{F_{t}}}$ and ${\overline{k}}_{b,LB}$ equal to the 60^th percentile for $\varepsilon _{{b_{t}}}$ in the set of generated structural shocks for the event date $t_{2}$ and $t_{3}$ , respectively.Footnote ⁷ Also, we set ${\overline{k}}_{GR}$ the 50th percentile (median) of $\varepsilon _{{Y_{t}}}$ for the great recession. These four constraints are similar to those considered by LMN.Footnote ⁸

The last event constraint requires that the sum of $\varepsilon _{{q_{t}}}$ be non-positive, which reflects the depreciation of the US dollar, from the time of the agreement of the Plaza Accord until it was replaced by the Louvre Accord in 1987. The Plaza Accord was a joint agreement signed by five countries to depreciate the US dollar against the Japanese Yen and the Deutsche mark via intervention in currency markets.Footnote ⁹ As shown in Figure C2, the US real effective exchange rate depreciated by almost 21% during the Plaza Accord period due to the interventions of participating central banks. This final constraint requires that the sum of $\varepsilon _{{q_{t}}}$ during the Plaza Accord period be below zero, which corresponds to the 25th percentile for $\varepsilon _{{q_{t}}}$ in the set of generated structural shock, to reflect this trend in the US exchange rate.

External Variable Constraints:

1. 1. $corr(\varepsilon _{{F_{t}}}, S_{1t})\leq {\overline{k}}_{corr(F,{S_{1}})}\leq 0$ .

2. 2. $corr(\varepsilon _{{R_{t}}}, S_{2t})\geq {\overline{k}}_{corr(R,{S_{2}})}\geq 0$ .

3. 3. $corr(\varepsilon _{{i_{t}}}, S_{3t})\geq {\overline{k}}_{corr(i,S_{3})}\geq 0$ .

$S_{1t}$ denotes the real return of the S&P 500 index, $S_{2t}$ is the intra-daily changes in the price of gold measured in Piffer and Podstawski (Reference Piffer and Podstawski2018), and $S_{3t}$ represents the federal funds rate shock identified in Nakamura and Steinsson (Reference Nakamura and Steinsson2018). All of these variables are external to the SVAR system described above. The first external variable constraint states that $\varepsilon _{{F_{t}}}$ should be negatively correlated with the aggregate stock returns. That is, when $\varepsilon _{{F_{t}}}$ raises the financial uncertainty, the S&P 500 index returns tend to fall. The second constraint requires that, when real uncertainty in the US rises due to $\varepsilon _{{R_{t}}}$ , the gold price also tends to rise.Footnote ¹⁰ The third constraint means that the monetary policy shock $\varepsilon _{{i_{t}}}$ identified in this study is (at least mildly) correlated with the federal funds rate shock identified using the different approach by Nakamura and Steinsson (Reference Nakamura and Steinsson2018). The first two external variable constraints are similar to those in LMN while the third constraint is consistent with those considered by Kang and Park (Reference Kang and Park2024). Table 1 shows the parameter values for all shock-based restrictions to obtain the results for the benchmark case.

Table 1.

Parameter values and percentiles for shock-based restrictions in the benchmark case

Notes: Table shows parameter values for event constraints and external variable constraints in the benchmark case for the shock-restricted SVAR. $\Phi ^{-1}(\cdot )$ denotes the inverse of cumulative density functions for structural shocks on the event time point. $\Theta ^{-1}(\cdot )$ denotes the inverse of cumulative density functions for the correlation in interests.

To account for parameter and sampling uncertainty, we also conduct inference using the wild bootstrap method developed by Gonçalves and Kilian (Reference Gonçalves and Kilian2004). We extend the wild bootstrap procedure to our setting following Berthold (Reference Berthold2023). A detailed description of the bootstrap implementation is provided in Appendix.

The approach employed in this study is distinct from other studies examining the exchange rate response to monetary policy shocks with SVAR approach. First, the inclusion of uncertainties in the VAR system not only reflects recent findings about the effect of uncertainties on economic activity but also delineates more precise dynamics of monetary policy shocks. Second, the shock-restricted SVAR approach in this study can allow contemporaneous relation between variables, especially between interest rate and exchange rate, in the VAR system.

3. Data

The real and financial uncertainty measures used in this study are those proposed by Jurado et al. (Reference Jurado, Ludvigson and Ng2015) and used in previous studies such as Aastveit et al. (Reference Aastveit, Natvik and Sola2013) and LMN. These uncertainty measures demonstrate the degree of the difficulty in forecasting real activity variables or financial variables, which can be formulated as follows:

(3) \begin{equation}U_{jt}^{C}(h)\equiv \sqrt{E[(y_{jt+h}^{C}-E(y_{jt+h}^{C}\left| I_{t})^{2}\right| I_{t}]}\end{equation}

where $y_{j}^{C}$ is a variable related to the real and financial variables, category indicator $C\in \{R,F\}$ , and $I_{t}$ represents all information available at time $t$ . The real and financial uncertainty measures are the weighted average of these squared forecast errors, and we use a one-month forecast horizon as in LMN.Footnote ¹¹ The real and financial uncertainty measures are presented in Figure C3 in the Appendix. As shown in Figure C3, both uncertainty measures are countercyclical and are notably high during the Great Recession, while the financial uncertainty is also notable in October 1987.

We use the monthly industrial production index for the output data. The monthly CPI is used for the price. Industrial production, CPI, and the one-year US government bond data are taken from the website for the Federal Reserve Bank of St. Louis.Footnote ¹²

Data for the US real and nominal effective exchange rates are obtained from the Bank for International Settlements (BIS).Footnote ¹³ Other countries’ central bank policy rates are also extracted from the BIS website. We calculate US trade weights for the top 20 countries that the US trades with each year.Footnote ¹⁴ We then multiply the central bank policy rates with the relative trade weights for these countries to produce the trade-weighted foreign policy rate for the US.Footnote ¹⁵ The sum of the trade weights for the countries included in the construction of the trade-weighted foreign policy rate for the US covers most of the total trade for the US during the sample period. For example, the sum of trade weights for countries included in the construction of the trade-weighted foreign policy rate for the US is above 82% of the US total trades in 2019. The sample period of this study is January 1985–December 2019. We exclude the COVID-19 period when unconventional monetary policy was conducted not only in the US but also in most countries. Figure C4 plots the US industrial production, CPI, the excess bond premium, the US interest rate, and the trade-weighted foreign policy rate.

4. Dynamic responses to monetary policy shocks under shock-restricted SVAR

This section provides empirical results from shock-restricted SVAR for eight variables, $X_{t}=(U_{{R_{t}}}, Y_{t}, U_{{F_{t}}},p_{t}, i_{t}, q_{t}, ebp_{t},i_{t}^{*})'$ . With randomly generated orthonormal matrices $Q$ , we rotate $\hat{P}$ (where ) and generate the same number of structural shocks $\hat{\varepsilon }_{t}$ . Figures 1 and 2 present the time series of the structural shocks $\varepsilon _{t}=(\varepsilon _{{R_{t}}}, \varepsilon _{{Y_{t}}}, \varepsilon _{{F_{t}}}, \varepsilon _{{p_{t}}}, \varepsilon _{{i_{t}}}, \varepsilon _{{q_{t}}},\varepsilon _{{b_{t}}},\varepsilon _{i_{t}^{*}})'$ for one solution satisfying all constraints. All identified shocks are negatively skewed and show excess kurtosis, which is similar to the results in LMN. $\varepsilon _{{F_{t}}}$ record large shocks in magnitude around October 1987. Large shocks are also noted for $\varepsilon _{{Y_{t}}}$ , $\varepsilon _{{R_{t}}}$ , $\varepsilon _{{F_{t}}}$ , and $\varepsilon _{{b_{t}}}$ in September 2009 when Lehman Brothers filed for bankruptcy. Moreover, there is a large variation in $\varepsilon _{{q_{t}}}$ during Plaza Accord from September 1985 to January 1987.

Figure 1.

One solution of structural shocks to real uncertainty, output, financial uncertainty, excess bond premium. Notes: Figure reports the time series of $\varepsilon _{{R_{t}}}$ , $\varepsilon _{{Y_{t}}}$ , $\varepsilon _{{F_{t}}}$ , and $\varepsilon _{{b_{t}}}$ for one solution satisfying all constraints.

Figure 2.

One solution of structural shocks to CPI, monetary policy, real exchange rate, and foreign interest rate. Notes: Figure reports the time series of $\varepsilon _{{p_{t}}}$ , $\varepsilon _{{i_{t}}}$ , $\varepsilon _{{q_{t}}}$ , and $\varepsilon _{i_{t}^{*}}$ for one solution satisfying all constraints.

Figure 3 presents the median impulse responses of each variable in the SVAR to contractionary monetary policy shocks, along with 68% confidence intervals constructed using the wild bootstrap method.Footnote ^{16 ,} Footnote ¹⁷ In general, contractionary monetary policy shocks are expected to raise the interest rate but lower output and the price level. The impulse responses in the first row of Figure 3 are consistent with these predictions. Output declines immediately in response to a contractionary monetary policy shock, with the maximum reduction occurring within 12 to 18 months. The CPI drops instantly in response to a contractionary monetary policy shock, which is consistent with the common theoretical prediction. The US interest rate rises immediately in response to a tighter US monetary policy stance but the initial impact disappears within 10 months, which indicates a temporary increase in the interest rate. The trade-weighted foreign interest rate also rises temporarily, which is consistent with the results in Rüth (Reference Rüth2020). The propagation of the effect of tightening monetary policy shown in the first row of Figure 3 is consistent with the predictions in the literature, which supports the validity of the identification strategy employed in this study.

Figure 3.

Impulse response to contractionary monetary policy shocks. Notes: Figure presents impulse responses to contractionary monetary policy shocks identified through the shock-restricted SVAR. The confidence intervals and median response are derived using the extension of the wild bootstrap procedure described in Section 2 and Appendix A.

The first two panels of the second row in Figure 3 present the dynamic effect of contractionary monetary policy shocks on real and financial uncertainty measures. Both uncertainty measures rise in response to tightening monetary policy shocks. In the median response, real uncertainty rises gradually, peaks at four months, and then declines gradually. This response may be related to the delay in investment and consumption decisions caused by the temporarily higher interest rate accompanied by a contractionary monetary policy shock. Financial uncertainty rises significantly in response to tightening monetary policy, with its median response peaking after three months, which is similar to Bekaert et al. (Reference Bekaert, Hoerova and Duca2013). As shown in the third panel of the second row, the excess bond premium also increases following positive monetary policy shocks, broadly consistent with the literature.

The last panel of the second row in Figure 3 shows the response of the real effective exchange rate to contractionary monetary policy shocks. The US real effective exchange rate appreciates immediately in response to tighter monetary policies, and the appreciation is statistically significant from one to fourteen-month horizons. In contrast to previous studies that have reported that real appreciation peaks two to three years after a shock, the maximum appreciation in Figure 3 occurs almost immediately. The last panel of the second row in Figure 3 also shows the point-wise median response (the black-thick line) of the US real effective exchange rate to contractionary monetary policy shocks. In the median response, the US real effective exchange rate appreciates immediately, with appreciation peaking at one month. After peaking, the real exchange rate gradually depreciates back toward its initial level, which is consistent with the Dornbusch (Reference Dornbusch1976) model.

We have tested the robustness of our results in various aspects in the following sub-sections.

4.1. Robustness checks: nominal effective exchange rate

We further examine whether the main results hold when substituting the US real effective exchange rate with the US nominal effective exchange rate, denoted by $e_{t}$ , in the SVAR system. Specifically, we consider $X_{t}=(U_{{R_{t}}}, Y_{t}, U_{{F_{t}}},p_{t}, i_{t}, e_{t}, ebp_{t},i_{t}^{*})'$ in the shock-restricted SVAR. The first panel in Figure 4 shows the impulse response of the US nominal effective exchange rate to contractionary monetary policy shocks.Footnote ¹⁸ The US nominal exchange rate appreciates instantly and peaks within one to two months after monetary policy shocks occur, which aligns with the benchmark result in Figure 3.

Figure 4.

Robustness checks (nominal exchange rate, $\Psi _{t}$ , FF future rates, one-year forecast horizon uncertainties, EPU, shadow rate). Notes: Figure presents the impulse response of the US effective exchange rate to contractionary monetary policy shocks across various robustness check cases. The confidence intervals and median response are derived using the extension of the wild bootstrap procedure described in Section 2 and Appendix A.

Using the nominal effective exchange rate in the SVAR system also allows us to examine its consistency with the UIP. We define $\Psi$ as the excess return of US dollar currency, which is given by $\Psi _{t+1}=12\times (e_{t+1}-e_{t})- (i_{t}-i_{t}^{*})$ . According to the UIP hypotheses, the conditional expectation of the excess return, $E_{t}\Psi _{t+s}$ , should be zero for all $s\gt 0$ when a monetary policy shock occurs at $s=0$ . The second panel in Figure 4 shows the dynamic response of the excess return, $\Psi _{t+s}$ , to contractionary monetary policy shocks. On impact, $\Psi _{t}$ shows a significantly positive response; thereafter, $\Psi _{t}$ oscillates around zero. This pattern in the response is qualitatively identical to the results in Rüth (Reference Rüth2020).

5. Potential sources of anomalous exchange rate response

The impulse responses of exchange rates presented in Figures 3 through 4 differ from the ambiguous instant response and delayed overshooting reported in many existing studies. The last panel in Figures 3 through 4 show immediate appreciation and no delayed overshooting of the exchange rate in response to contractionary monetary policy shocks. In this section, we investigate whether this difference arises from the use of novel uncertainty measures in the SVAR or from the identification strategy employed in the shock-restricted SVAR.

5.1. Role of uncertainty measures

We isolate both real and financial uncertainties from other variables in the SVAR to understand their roles in producing the immediate appreciation of the exchange rate following contractionary monetary policy shocks discussed in the previous sections. Specifically, we mute endogenous responses of real and financial uncertainties to other structural shocks by constraining the elements that govern their contemporaneous responses in the $\hat{P}Q=A_{0}^{-1}$ matrix. We then compare the results of this experiment with those from the benchmark case. The first panel of Figure 5 presents an insignificant response of the real effective exchange rate to tightening monetary policy shocks when the endogenous responses of both uncertainties are shut off. Similar insignificant responses appear when we mute the endogenous response of either real uncertainty or financial uncertainty, as shown in the second and third panels of the first row in Figure 5. We also shut off the contemporaneous effect caused by $\varepsilon _{{R_{t}}}$ or $\varepsilon _{{F_{t}}}$ on other variables in the SVAR by restricting relevant elements in $\hat{P}Q=A_{0}^{-1}$ , and then examine the response of the exchange rate to monetary policy shocks. The panels of the second row in Figure 5 show an insignificant response of the exchange rate to contractionary monetary policy shocks.

Figure 5.

Response of the real effective exchange rate to contractionary monetary policy shocks when uncertainty measures are isolated from other variables in the SVAR. Notes: Figure presents the impulse response of the US real effective exchange rate to contractionary monetary policy shocks acrossr various cases designed to isolate real or financial uncertainty from other variables in the SVAR. The confidence intervals and median response are derived using the extension of the wild bootstrap procedure described in Section 2 and Appendix A.

All panels in Figure 5 show that accounting for both real and financial uncertainties is essential to obtain the significant immediate appreciation of the exchange rate following tightening monetary policy shocks, which is consistent with theoretical models such as Dornbusch (Reference Dornbusch1976). In addition to the results shown in Figure 5, isolating real or financial uncertainty from other variables in the SVAR yields an insignificant response of the CPI to contractionary monetary policy shocks.Footnote ²³ These findings imply that including uncertainty measures in the VAR system clarifies the impact and propagation mechanism of monetary policy shocks. These results also align with Kang and Park (Reference Kang and Park2024), who emphasize that including uncertainty measures is crucial for successfully identifying the effect of US monetary policy.

5.2. Identification restrictions without contemporaneous interaction between the interest rate and the exchange rate

The previous sub-section highlights the importance of uncertainty measures for understanding the responses of the exchange rate to tighter monetary policy. In this sub-section, we examine the response of the real effective exchange rate to contractionary monetary policy shocks when the uncertainty measures are incorporated under recursive identification restrictions rather than the shock-restricted SVAR constraints.

To impose the recursive identification restrictions, we order of the eight variables in the SVAR as $X_{t}=(i_{t}^{*}, U_{{R_{t}}}, U_{{F_{t}}},Y_{t}, p_{t}, i_{t}, ebp_{t},q_{t})'$ . In this ordering, the foreign interest rate is treated as exogenous, consistent with previous studies such as Bjørnland (Reference Bjørnland2009). Following the recursive identification assumptions in Bloom (Reference Bloom2009) and subsequent studies, we place the uncertainty measures ahead of the other macro variables. The impulse response of the real exchange rate to contractionary monetary policy shocks under this recursive restriction is plotted with the 68% confidence interval in the first panel of Figure 6. Although the response shows an instant appreciation, it subsequently exhibits delayed overshooting, with the peak occurring after 24 months, a pattern reported as a puzzle in earlier studies.

Figure 6.

Impulse responses under recursive identification or no contemporaneous interaction between the interest rate and the exchange rate. Notes: Figure presents the dynamic effects of contractionary monetary policy shocks on the real effective exchange rate under recursive restrictions (left panel) and in the case where the contemporaneous interaction between the interest rate and the exchange rate is shut off (right panel). The confidence intervals and median response are derived using the extension of the wild bootstrap procedure described in Section 2 and Appendix A.

Studies such as Kim and Roubini (Reference Kim and Roubini2000), Bjørnland (Reference Bjørnland2009), and Rüth (Reference Rüth2020) emphasize the contemporaneous interaction between interest rate and the exchange rate in the identification strategy, an interaction that recursive identification restrictions cannot accommodate, and they argue that the delayed overshooting puzzle can be resolved with non-recursive restrictions on $A_{0}^{-1}$ . Because the shock-restricted SVAR permits contemporaneous interaction between the interest rate and the exchange rate is possible, we shut off this contemporaneous interaction by restricting the relevant elements in $\hat{P}Q=A_{0}^{-1}$ to assess its role in our benchmark results. The second panel of Figure 6 shows the response of the real exchange rate to tightening monetary policy shocks after we shut off the contemporaneous interaction between the interest rate and the exchange rate. The response of the real exchange rate is not significant, and the overshooting is delayed relative to the benchmark case.

In summary, the impulse responses in Figure 6 indicate that delayed overshooting persists under recursive identification restrictions, even when uncertainty measures are included in the SVAR or when identification restrictions prevent contemporaneous interaction between the interest rate and the exchange rate. These results imply that delayed overshooting is a consequence of strong identification restrictions that disallow contemporaneous interactions between certain variables, especially between the interest rate and the exchange rate.