Event studies and the random walk hypothesis: Why the end of bond buying by the ECB is a non-event
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Event studies and the random walk hypothesis: Why the end of bond buying by the ECB is a non-event

The ending of the ECB's bond buying programme had no impact on interest rates. In this post, Ansgar Belke and Daniel Gros argue that this is because while the programme might have lowered rates when it was announced, the impact was only transitory.

The ECB has now stopped its bond buying programme. It will keep its stock unchanged, but will make no new net purchases.  But neither the announcement nor the phasing out of the purchases seems to have had any impact on interest rates. 

Most of the evidence on central bank bond buying, often called quantitative easing (QE), comes from ‘event studies’. These studies look at changes in interest rates around the dates when central banks announce their intention to buy large amounts of government bonds.

There are a large number of these studies (for surveys, see Borio and Zabai 2016, Urpschap and Watzka 2017, Dell’Ariccia et al. 2018). The first ones obviously dealt with the US case, since the Federal Reserve was the first to engage in lage-scale asset purchases. However, it did so when market volatility was close to a peak. The ECB’s big asset purchase programme, the Public Sector Purchase Program (PSPP), only started six years later in early 2015, when market volatility had already subsided. The the PSPP thus constitutes a much better measure of the pure ‘monetary policy’ impact of central bank bond buying. 

Event studies, random walks, and the efficient market hypothesis

Event studies can only measure the ‘impact’ of QE policies on the event day (sometimes they use a two-day horizon; e.g. Altavilla et al. 2015). But a key, often overlooked, question is whether the announcement effect is permanent (Neely 2015, Andrade et al. 2016).

Under the usual assumption of the efficient market hypothesis that bond returns follow a random walk process (Fama 1970, Lo and MacKinley 1999), all ‘surprises’ induced by the announcement of central bank bond buying should be permanent.

The idea of stock prices following a random walk is closely connected to that of the efficient market hypothesis. The prior is that investors react instantaneously to any informational advantages they have, thus eliminating any remaining profit opportunities. Hence, asset prices always fully reflect the available information. Moreover, no profit can be made from information-based trading (Lo and MacKinley 1999). This leads to a random walk where the more efficient the market is, the more random the sequence of price changes turns out to be (Shleifer 2000). 

Event studies use the random walk hypothesis in two ways: 

1) Announcements rather than actual implementation of the bond buying constitute the decisive moments when market prices move, since investors will anticipate the impact of the bond buying.

2) The announcement effect is permanent. The random walk hypotheis implies that the movement of yields on the day of the announcement constitutes a permanent innovation to the future time path of yields.

The random walk hypothesis is thus essential to establish a permanent effect of QE. 

Figure 1 illustrates this view of event studies for the Italian risk premium on ten-year bonds (or spreads) using the announcement dates and results from Altavilla et al. (2015). The solid line shows the actual data (which incorporate the announcement effects). The dashed line was created by setting for each announcement date the change in the spread to zero, instead of the fall caused by the announcement. After the last announcement (March 2015) the difference between the two lines remains constant at the value found by Altavilla et al. 2015) of around 50 basis points.

The implicit reasoning of event studies is thus that the macroeconomic benefits of the PSPP can be calculated by using a standard macrcoeconomic model and lowering the interest rate by the announcement effect for the entire period since the announcement (e.g. Altavilla et al. 2015). 

The focus of our contribution is on the question of whether the announcement effects found in many studies of the euro area should be considered permanent. 

(We just note an inherent contradiction in many event studies. The view that bond buying by central banks can affect returns on assets is based on a portfolio balance view of the world. But portfolio balance effects can operate only if markets are not efficient, i.e. if there are arbitrage opportunities which cannot be exploited. This contradicts the basic hypothesis of event studies that the entire effect is incorporated in market prices on the day of the announcement.) 

Figure 1 Illustration of implicit reasoning of event studies

Source: Own calculations based on ECB data and Altavilla et al. (2015)

In the following we therefore test the random walk hypothesis for the yields and yield spreads of sovereign bonds of the most important euro area member countries. 

We proceed as follows. As a first step, we conduct unit root tests for the levels and first differences of the yields and yield spread time series. As a second step, we check for the significance of autoregressive (AR) components in the first difference of the variables of interest. Any significant AR component indicates a violation of the efficient market hypothesis.

Data and results

We test the the efficient market hypothesis on the ten-year government bond yields and the corresponding spreads (i.e. the difference relative to German yields) for Spain, France, Greece, Ireland, Italy, and Portugal.

Our sample period ranges from from 2 September 2013 to 15 January 2018 (over 1,000 observations). We start from 2013 –  about one year after Mario Draghi’s “whatever it takes” speech and the subsequent creation of the Outright Monetary Transactions (OMT) programme – in order to avoid structural breaks in the series not linked to the asset purchase programme of the ECB.

1 Unit root tests

In Table 1 we present the results of Augmented Dickey Fuller (ADF) tests.

Table 1 Results of unit root tests (ADF test statistics and probabilities)

Source: Compiled by authors.

Note: Table displays empirical realisations of the Augmented Dickey-Fuller test with a constant (MacKinnon (1996) one-sided p-values). The sample period ranges from 8 February 2013 to 15 January 2018. The lag length of the ADF test equation (third column) was determined by the Schwarz information criterion.

We find that the random walk hypothesis is rejected for many variables, especially Spanish, Irish and Italian yields and, even more significantly, Spanish, Irish and Italian spreads over German bonds.

2 Test of autoregressive elements

A similar result is obtained when one estimates autoregressive equations for the first differences in the different yields (and the spreads). Table 2 shows the empirical realisations of autoregressive coefficients in AR estimations for the first differences in the yields and the spreads.

Table 2 Results from AR regressions (first differences) 

Note: The Table displays empirical realisations of autoregressive coefficients in AR-estimations for the first differences in the yields and the spreads. Only significant entries are displayed. In the case of Spain also lags 4 and 5 enters with a significant negative sign. In the case of Ireland also the significant lag four is included with a negative sign. In the case of Italy also lags 4 and 5 are significant with a negative sign and for Portugal lags 3 (significant, with a positive sign, 4 and 5 (both with a significant negative sign) enter as well. The complete estimated AR equations are available on request. For further details see Table 1.

Processes of first differences cannot be rejected to follow a white noise process in the case of France (yields and borderline also spreads) and Ireland (borderline yields). However, in the cases of Germany and the at that time financially distressed countries Spain, Ireland (for spreads), Italy and Portugal we find significant AR components. Except for Portugal, bond returns and spreads exhibit (very significant) negative autocorrelation, which implies that shocks tend to be reversed over time. More broadly, this implies that the hypothesis of a random walk is rejected by the data for the spreads of three out of the four peripheral countries considered here. The basic hypothesis necessary for event studies is thus rejected by the data.

The finding that the impact of bond purchases has been only temporary for yield spreads should not be surprising. These spreads are based on market estimates of the risk of default or denomination (Gros 2018b), but this risk was not reduced by the PSPP since that programme did not involve any risk sharing. Each national central bank bought the bonds of its own government at its own risk.  The national central banks are part of the national public sector, and it is difficult to see why the risk spread should fall when one arm of the government buys the debt of another.

Concluding remarks

The title of a recent Brookings conference, “Quantitative easing lowered interest rates. Why isn’t quantitative tightening lifting them more?”, encapsulates well the conundrum facing central bankers as they exit their balance sheet expansion policies. The conundrum is particularly acute for the ECB, which has terminated its programme of buying public sector bonds (PSPP) as of January 2019, although risk-free interest rates (and expected inflation rates) in the euro area are at about the same level as when the ECB started to buy bonds.

Our explanation is simple, at least for the euro area: the bond buying programme of the ECB might have lowered rates when it was announced, but the impact was transitory. The data reject decisively the random walk hypothesis necessary for event studies to measure a permanent effect.  


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