# RDP 2022-02: The Yield and Market Function Effects of the Reserve Bank of Australia's Bond Purchases 4. Implementation Effects

In addition to the announcement effects described above, the Reserve Bank's bond purchases may also have lowered yields as and when they occurred. We assess the extent of these possible implementation effects in three main ways:

• First, we examine time-series evidence by using regressions to test whether larger purchases of an individual bond resulted in larger yield changes on the day of the purchases (or over subsequent days).[19] For purchases to support market function and purchases under the bond purchase program, we use the same functional form for our regression, as the way in which these purchases were conducted was similar, even if the aims were different. For purchases under the yield target we adapt the regression slightly to better suit the context for those purchases.
• Second, we perform a similar time-series analysis, but use inclusion or exclusion in a purchase operation as the key explanatory variable, rather than the purchase amount. We only consider purchases to support market function and purchases under the bond purchase program, as the concept of inclusion or exclusion is less relevant for yield target purchases.
• Third, we look at the cross-sectional evidence over the course of a program to see whether bond lines that were more heavily purchased by the Reserve Bank saw larger changes in yields that persisted for some time after the purchases were made. Again, we only consider purchases to support market function and purchases under the bond purchase program.

We do not examine directly the related question of whether the flow of new bond issuance leads to higher yields as and when it occurs, though new issuance indirectly enters our analysis by adding to the outstanding stock of bonds.

## 4.1 Time-series evidence using purchase amounts

### 4.1.1 Market function purchases and the bond purchase program

Following the approach of De Santis and Holm-Hadulla (2020), we use the time series of bond yields to measure the effect of bond purchases on those yields. In particular, we estimate the equation:

(1) $Δ y it =α+ β 1 purchase s it + β 2 purchases_adjacen t it + b i + v t + ∈ it$

where $\text{Δ}$ yit denotes, for bond i, the day t change in yield (for AGS) or spread to AGS (for semis); purchasesit denotes the amount of bond i purchased on day t relative to the remaining free float of bond i (that is, purchases of bond i divided by the outstanding stock of bond i not already held by the Reserve Bank); purchases _ adjacentit denotes the amount of bonds within one year's residual maturity of bond i purchased on day t relative to the remaining free float of bond i (that is, purchases of bonds within one year's residual maturity of bond i divided by the outstanding stock of bond i not already held by the Reserve Bank); and bi and vt are bond and time fixed effects.

We estimate this equation via ordinary least squares (OLS), and also via instrumental variables (IV) where we use a dummy variable indicating those bonds excluded from a given auction either because they had recently been issued or tapped by the issuing authority, or because they were not within the target purchase range, to instrument for purchasesit. For purchases _ adjacentit we instrument using the share of bonds with residual maturity within one year of bond i that are excluded because they have recently been issued or tapped by the issuing authority.[20] These instruments are both relevant – a bond cannot be purchased if it is not included in a given auction – and exogenous.

IV would be the more appropriate estimation method to employ if, within an auction, the amount of each bond purchased by the Reserve Bank depended on the level of, or changes in, the yield on that bond over the day in question. However, the Reserve Bank did not adjust its purchases in this way: within a given auction, the purchase amount of each bond was determined based on the relative attractiveness of offers to sell that bond, where attractiveness was assessed using the offered yield relative to prevailing mid-market rates. It is possible that counterparties adjusted the attractiveness of their offers to sell different bonds based on yield levels or changes, although any desire on the part of dealers to sell more or less of any individual bond should already have been reflected in the market price of that bond, so it is not clear that this would be the case. For these reasons, we prefer the OLS estimates, but for completeness also provide IV estimates.

Results are shown in Table 2. For AGS purchases in aid of market functioning, purchasing 1 percentage point of the free float of a bond reduces its yield and the yield on adjacent bonds by around ¼ basis points on average, although there is considerable noise in the data and these results are not statistically significant. For AGS purchases under the bond purchase program, the yield effects are smaller but statistically significant, at around 0.1 to 0.2 basis points. For semis, we find that purchases in aid of market function reduce spreads to AGS by between 0.1 and 0.5 basis points, depending on the estimation method, while purchases of adjacent bonds have no effect. For semis purchases under the bond purchase program, the effects are smaller, at around 0.1 basis points for direct purchases and again no effect for purchases of adjacent bonds. Overall, we tend to find larger effects when one would expect liquidity premia to be relatively high.

Table 2: One-day Impact of the Flow of Bond Purchases
Effect of purchasing 1 percentage point of the free float of eligible/adjacent bonds
Market functioning purchases   Bond purchase program
OLS IV OLS IV OLS IV OLS IV
Purchases of the eligible bond −0.34
(0.25)
−0.27
(0.37)
−0.14***
(0.04)
−0.48***
(0.14)
−0.11**
(0.04)
−0.22***
(0.08)
−0.08**
(0.03)
−0.14**
(0.06)
Purchases of its adjacent bonds −0.20
(0.15)
−0.25
(0.16)
−0.01
(0.01)
0.08
(0.06)
−0.10***
(0.02)
−0.17***
(0.03)
0.00
(0.00)
−0.02
(0.02)
Fixed effects Bond and time fixed effects for all regressions
No of obs 448 448   1,696 1,696   5,234 5,234   13,372 13,372
Adjusted R2 0.56 0.56   0.54 0.50   0.89 0.89   0.29 0.28
Notes: Heteroskedasticity and autocorrelation corrected (HAC) standard errors in parentheses; *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively. Yields and spreads in basis points. For market functioning purchases, the sample is from 20 March 2020 to 6 May 2020; for the bond purchase program, it is from 5 November 2020 to 10 February 2022. Bonds issued by Tasmania and the two territories are excluded. Adjacent bonds are those that mature within one year of the eligible bond. An F-test on the instrument equation rejects the null of weak instruments at the 1 per cent level for all models, while the Wu-Hausman test fails to reject the null that OLS is consistent for the AGS market function model and the semis bond purchase program model, but rejects the null for the other models.

Sources: Austraclear; Australian Office of Financial Management; Authors' calculations; RBA; Yieldbroker

### 4.1.2 The yield target

The yield on the 3-year AGS rose above target on occasion. One method that the Reserve Bank used to achieve the yield target was to purchase the target bond, and also AGS with residual maturity close to that of the target bond. From March to May 2020 such purchases were aimed at both supporting government bond market function and the yield target, while from August 2020 until October 2021 they were conducted in support of the yield target alone. Accordingly, we will look at only these later purchases.

The Reserve Bank conducted purchases in support of the yield target a total of 18 times between August 2020 and October 2021, buying a total of $29 billion across the November 2022, April 2023 and April 2024 AGS (Figure 8). On average, the yields on the target bonds fell by around 1 basis point on days when they were purchased by the Reserve Bank and were little changed on other days (Figure 9). The Reserve Bank's ownership shares of these bond lines increased to 8, 39 and 63 per cent of the outstanding amounts for the 2022, 2023 and 2024 bonds respectively, from 7, 10 and 5 per cent at the start of August 2020. However, the average change does not account for differences in the size of the Reserve Bank's purchases, or other potentially relevant factors such as changes in expectations for the cash rate. To assess more accurately the impact of the Reserve Bank's purchases, we estimate a regression that includes the size of the purchases, as well as the 3-month OIS rate and the 10-year AGS yield (Table 3).[21] Overall, we find that purchasing$1 billion of the target bond reduced the yield on that bond by 1 basis point. Using the share of free float purchased rather than the dollar value as the explanatory variable, we find that purchasing 1 percentage point of the free float reduced the yield by 0.2 basis points. Purchases were therefore effective in achieving the yield target, although the measured effect of purchases on the yield is estimated to have dissipated over time.

Table 3: On-the-day Impact of Yield Target Purchases
Linear regressions of daily open-to-close changes from 5 August 2020 to 2 November 2020
Purchases in \$b   Purchases as a share of free float of target bond
Target bond yields 3-year OIS rate Target bond yields 3-year OIS rate
Purchases of target bond −1.02***
(0.24)
0.60
(0.48)
−0.22***
(0.03)
0.14
(0.09)
(0.27)
0.44
(0.56)
−0.12*
(0.06)
0.16
(0.16)
Change in 3-month OIS rate 0.76**
(0.36)
1.12***
(0.19)
0.77**
(0.36)
1.11***
(0.18)
Change in 10-year AGS yield 0.31**
(0.15)
0.36***
(0.08)
0.31**
(0.15)
0.36***
(0.09)
No of obs 630 315   630 315
Adjusted R2 0.22 0.23   0.22 0.24
Notes: HAC standard errors in parentheses; *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively. Yields and rates in basis points.

Sources: Australian Office of Financial Management; Authors' calculations; Fenics; RBA; Yieldbroker

By contrast, a regression of daily changes in the 3-year OIS rate on similar factors indicates that purchases of the target bond were associated with increases in the 3-year OIS rate on average, although the moves were not statistically significant.[22] This suggests that, although the Reserve Bank tended to purchase bonds in response to sustained increases in market participants' expectations for the cash rate (when the increases were reflected in the yield on the 3-year AGS), the Reserve Bank's purchases did not – on their own, on the days of the purchases – dampen participants' cash rate expectations. This is consistent with the flow of Reserve Bank purchases being interpreted narrowly by the market as an operational tool for achieving the yield target on the relevant AGS, rather than as a new signal about the Board's future monetary policy decisions. See also Lucca and Wright (2022) for a discussion of the yield target and the effect of yield target bond purchases.

The announcements by the Reserve Bank of bond purchases to support the yield target typically contained an element of news for market participants, perhaps in part because participants were still learning about the Reserve Bank's reaction function for the use of this new tool. On days when such purchases were announced, the yield on the 3-year AGS tended to fall immediately after the announcement; by contrast, announcements of the Reserve Bank's regular and predictable purchases under the bond purchase program elicited negligible immediate market reaction (Figure 10). For the 3-year AGS, the element of news was consistent with the aim of the policy being to keep the yield on the target bond ‘around’ a certain level, rather than exactly at a certain level. Hence, participants could not predict whether the Reserve Bank would intervene on any particular day. It was also consistent with the Reserve Bank retaining operational flexibility in its purchases, rather than committing to a strict rule or pattern for these purchases.

## 4.2 Time-series evidence using inclusion and exclusion dummies

We estimate a dummy variable regression similar to that in Section 4.1.1, where we model the change in yield (for AGS) or spread to AGS (for semis) on a variable indicating whether a bond was included in an auction (i.e. eligible for purchase), and additionally control for the effect of each bond line and day (this is similar to performing an analysis of variance to test whether, on auction days, bonds that were in the auction saw statistically different yield changes from bonds that were not in the auction; see Fisher (1925)). Similar to the IV regressions discussed previously, taking the eligibility of a bond to be purchased in an auction as a ‘treatment’ (and ignoring how much of each bond is actually purchased) has the advantage of using only variables that we know to be exogenous as regressors.

As background, AGS purchases under the bond purchase program were conducted on Mondays and Thursdays, with Mondays for bonds with residual maturity of around 5 to 7 years, and Thursdays for bonds with residual maturity of around 7 to 10 years. Semis auctions under the bond purchase program were conducted on Wednesdays, and initially alternated between shorter-dated and longer-dated bonds on a fortnightly basis, before these auctions were combined in March 2021 into a single auction spanning all eligible bonds. Considering shorter-dated and longer-dated auctions separately, we find that eligibility within auctions has no statistically significant impact on the change in yield or spread (Table 4).

Table 4: One-day Impact of Eligibility within Auctions in the Bond Purchase Program
Ineligible bonds are those that were excluded due to being recently tapped or issued
Short-dated Long-dated Short-dated Long-dated Combined
Bond eligible for purchase −0.11
(0.14)
−0.02
(0.07)
0.41
(0.27)
0.37
(0.24)
0.02
(0.08)
Fixed effects Bond and time Bond and time   Bond and time Bond and time Bind and time
No of obs 495 486   148 179 1,877
Adjusted R2 0.94 0.99   0.54 0.37 0.40

Notes: Heteroskedasticity corrected (HC) standard errors in parentheses; *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively. Yields and spreads in basis points. The sample is purchase days from 5 November 2020 to 10 February 2022. Combined semis auctions replaced the short- and long-dated auctions from 24 March 2021. Bonds issued by Tasmania and the two territories are excluded.

Sources: Authors' calculations; RBA; Yieldbroker

Alternatively, we can consider the shorter-dated and longer-dated groupings of bonds together, such that for each auction the non-eligible bonds consist of not only those bonds within the relevant maturity grouping that were excluded due to being recently tapped or issued, but also all bonds from the other maturity grouping (which were also not eligible to be purchased). Using this approach, we find that purchases under the bond purchase program lowered AGS yields by 0.6 basis points on the day, and lowered semis spreads by 0.2 basis points on the day (Table 5).[23] These results, combined with those above, suggest that purchases in one segment of the yield curve affect yields and spreads in that part of the yield curve relative to other parts of the yield curve, even if they do not affect relative yields and spreads within that segment of the yield curve. The effect is short-lived, however, and dissipates after a few days (Figure 11). For bond purchases in support of market function, we find that an AGS being eligible to be purchased reduced its yield by 1.1 basis points, relative to other AGS not eligible to be purchased, while for semis, eligibility resulted in a 0.6 basis point reduction in spread to AGS (Table 5). Similar to purchases under the bond purchase program, the effect is short-lived and dissipates after a few days.

Table 5: One-day Impact of Eligibility across each Purchase Program
Ineligible bonds are those that were in the program but were not eligible for purchase on the day
Market functioning purchases   Bond purchase program
Bond eligible for purchase −1.12**
(0.52)
−0.64***
(0.17)
−0.57***
(0.07)
−0.17***
(0.05)
Fixed effects Bond and time Bond and time   Bond and time Bond and time
No of obs 448 1,696   5,234 13,372
Adjusted R2 0.56 0.54   0.89 0.29
Notes: HAC standard errors in parentheses; *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively. Yields and spreads in basis points. For market functioning purchases, the sample is from 20 March 2020 to 6 May 2020; for the bond purchase program, it is from 5 November 2020 to 10 February 2022. Bonds issued by Tasmania and the two territories are excluded.

Sources: Authors' calculations; RBA; Yieldbroker

## 4.3 Cross-sectional evidence

Finally, following the approach of D′Amico and King (2013), we use variation in the share of individual bond lines that were purchased over the course of a program to examine whether the purchase of a larger share of bonds resulted in larger yield changes that were persistent. In particular, for AGS we estimate the equation:

(2) $Δ y i =α+ β 1 purchase s i + β 2 purchases_adjacen t i + β 3 m i + β 4 m i 2 + β 5 c i + ∈ i$

where $\text{Δ}$yi denotes the change in yield on bond i from the day before purchases began until 6 May 2020 for purchases to restore market function, or 10 February 2022 for purchases under the bond purchase program; purchasesi denotes the share of free float of bond i that the Reserve Bank purchased; purchases _ adjacenti denotes the share of free float of bonds with residual maturity within one year of bond i that the Reserve Bank purchased; mi denotes the residual maturity of bond i; ${m}_{i}^{2}$ denotes the squared residual maturity of bond i; and ci denotes the coupon of bond i.[24] For semis, we estimate a similar equation, where $\text{Δ}$yi instead denotes the change in spread to AGS of bond i, and an additional term denoting issuer fixed effects is included.

We estimate this equation via OLS, also via IV where we use inclusion in a bond futures basket (of both bond i and also the share of bonds within one year's residual maturity of bond i ); the share of bonds held by the Reserve Bank just prior to the program commencement (of both bond i and also bonds within one year's residual maturity of bond i ); and yield curve fitting errors just prior to the program commencement, to instrument for purchasesi and purchases _ adjacenti.[25] These instruments are clearly exogenous, being determined before any purchases took place, and are relevant to the extent that Reserve Bank purchases are correlated with pricing anomalies (captured by yield curve fitting errors), previous ownership levels, and/or the liquidity of each bond line (captured by inclusion in a futures basket).[26]

We consider IV in case of any possible endogeneity between the yield change that we observe and the share of bonds purchased (this could occur, for example, if the Reserve Bank purchased bonds in part due to their higher yield, although as noted earlier this was not the case). As earlier, we prefer the OLS estimates (and cannot reject that they are consistent), but provide IV estimates for completeness.

For purchases in support of market function, we find that purchasing 1 percentage point of the free float of an AGS reduced the yield on that bond by 0.7 to 0.8 basis points, while purchases of adjacent bonds resulted in a fall in yield of 1.2 to 1.5 basis points; for semis, there was little to no additional impact on the spread to AGS for purchases of the bond itself or adjacent bonds (Table 6). For the bond purchase program, we find no statistically significant effect of purchases on AGS yields or semis spreads.

Table 6: Cross-sectional Impact of the Flow of Bond Purchases
Effect of purchasing 1 percentage point of the free float of eligible/adjacent bonds
Market functioning purchases   Bond purchase program
OLS IV OLS IV OLS IV OLS IV
Purchases of the eligible bond −0.82***
(0.16)
−0.69***
(0.16)
−0.12
(0.11)
0.38
(0.41)
0.17
(0.12)
0.20
(0.14)
0.02
(0.04)
0.00
(0.09)
Purchase of its adjacent bonds −1.54***
(0.36)
−1.21***
(0.27)
0.18
(0.12)
1.00
(0.66)
0.26
(0.21)
0.22
(0.27)
−0.01
(0.03)
−0.06
(0.08)
Residual maturity (years) 9.35***
(1.57)
6.63**
(2.23)
−7.08***
(1.14)
−2.89
(3.22)
11.08***
(3.19)
11.35***
(3.23)
5.51***
(0.96)
6.03***
(2.00)
Residual years2 (years2) −1.55***
(0.15)
−1.31***
(0.20)
0.61***
(0.10)
0.21
(0.26)
−0.96***
(0.25)
−0.98***
(0.25)
−0.46***
(0.07)
−0.49***
(0.17)
Coupon rate (per cent) −0.40
(0.37)
−0.13
(0.67)
0.33
(0.54)
0.84
(0.88)
0.84
(0.94)
0.88
(0.99)
1.02***
(0.33)
0.85*
(0.44)
Fixed effects None None   Issuer Issuer   None None   Issuer Issuer
No of obs 14 12   53 37   16 16   36 31
Adjusted R2 0.98 0.98   0.56 0.22   0.72 0.72   0.67 0.51
Notes: HC standard errors in parentheses; *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively. Yields and spreads in basis points. For market functioning purchases, the start and end dates are 19 March 2020 and 6 May 2020; for the bond purchase program, they are 4 November 2020 and 10 February 2022. Bonds issued by Tasmania and the two territories are excluded, and the bond purchase program regressions only include bonds that were included in the program from the start. An F-test on the instrument equation rejects the null of weak instruments for the market function AGS model but not the other IV models, while the Wu Hausman test fails to reject the null that OLS is consistent for all IV models.

Sources: Austraclear; Australian Office of Financial Management; Authors' calculations; Bloomberg; RBA; Yieldbroker

## 4.4 Summary

To summarise, our results suggest that the implementation effect for purchases under the bond purchase program was, at most, small and temporary. This conclusion can be supported by examining how the yields on AGS and semis just outside the purchase range evolved relative to the yields of AGS and semis just inside the purchase range. The difference in yields between these sets of non-purchased and purchased bonds did not steadily increase for either AGS or semis, as one might have expected if the implementation effect was strong and persistent, but rather tended to follow changes in the equivalent difference in OIS rates (which should have been largely unaffected by any implementation effect associated with bond purchases; Figure 12).

For purchases in support of market function and purchases in support of the yield target, the estimated implementation effects are on balance larger. The first finding is broadly consistent with the international literature on bond purchases, with the impact of purchases as and when they are made being more important during periods of market stress. The second finding is consistent with yield target purchases containing an element of news as market participants learned about the Reserve Bank's reaction function – that is, its commitment to this objective.

## Footnotes

Note that under the bond purchase program, the amount of purchases of any individual bond was determined by the relative attractiveness of offers to sell that bond, compared with other bonds also eligible to be purchased. That is, the Reserve Bank did not set purchase amounts for individual bonds. See below for further discussion. [19]

The Reserve Bank offered to purchase different sets of bonds on alternating days, and excluded recently tapped or issued bonds from its bond auctions – see ‘Reserve Bank Purchases of Government Securities’, 3 November 2020, available at <https://www.rba.gov.au/mkt-operations/announcements/rba-purchases-of-government-securities-2020-11.html>. [20]

Note that while only one bond was the target bond for the purpose of the yield target at any particular time, we consider the yields on both the April 2023 AGS and the April 2024 AGS throughout our analysis. This is for three reasons: both of these bonds were at some point the target bond; even prior to the April 2024 AGS becoming the target bond, the Reserve Bank made some purchases of the April 2024 AGS to smooth the transition between target bonds; and even after the April 2024 AGS became the target bond, the Reserve Bank made some purchases of the April 2023 AGS in order to reinforce the forward guidance associated with the yield target. See RBA (2020c) for further details. [21]

It is likely that any causation is going in the other direction, with higher 3-year OIS rates associated with higher 3-year AGS yields and therefore with the Reserve Bank deciding to conduct yield target purchases. [22]

Note that the regression results presented in Table 2 of Section 4.1.1 also included both auction buckets. [23]

Some authors such as D′Amico and King (2013) estimate a regression similar to the above, but use the change in price as the variable of interest, rather than the change in yield. We do not do this as the Reserve Bank's explicit aim under the bond purchase program was to lower bond yields, rather than raise bond prices (even if the two concepts are closely related). Changes in bond prices are also more likely to be mechanically affected by the coupon and term to maturity of each bond than are changes in yield. [24]

For semis, the futures basket instruments are not used (because bond futures contracts refer to AGS only). For AGS purchased to support market function, the pre-commencement holdings instruments are not used (because the Reserve Bank held none of the AGS purchased prior to the commencement of the program). [25]

Bonds included in a bond futures basket tend to be more liquid and actively traded than otherwise similar bonds, while yield curve fitting errors can be used as an indication of bond mispricing. [26]