## Quantitative Easing and Stock Market Bubbles in the

## Eurozone

**Lucas Carvalho Ribeiro **

**11829877 **

*University of Amsterdam, Amsterdam Business School *

MSc Finance - Asset Management Track Master Thesis

2

**Statement of Originality **

This thesis is written by Lucas Carvalho Ribeiro, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business of the University of Amsterdam is responsible solely for the supervision of completion of the work, not for the contents.

3

**Abstract **

This thesis addresses important side effects from the recent quantitative easing agenda carried
out by the ECB. More specifically, it investigates if the large Public Sector Purchase
Programme (PSPP) that targeted long-term sovereign bonds also impacted equity markets in
major Eurozone economies, causing price exuberance analogous to an asset bubble during its
implementation. By merging a two-part methodology, including the new developments of a
bubble-monitoring econometric tool from Phillips et al. (2015) – the GSADF procedure – it
was possible to show that the programme did cause temporary exuberance in some European
markets, making valuation levels deviate from fundamental drivers. The bubble scenario,
however, did not last the same duration of the overall PSPP, but only throughout its initial
months. Nevertheless, the evidence reinforces careful monitoring of central bank activities
**within such unusual agenda and its important spillovers. **

4

**Table of Contents **

1. Introduction ………5

2. Literature review………,…8

2.1. Fundamental equity indices levels………...8

2.2. The GSADF and test for exuberance in other markets………..11

2.3. Hypotheses……….13

3. Data and descriptive statistics………...14

4. Model and Methodology………...18

4.1. P/E Fundamentals………...18

4.2. Bubble detection with the GSADF test………..20

5. Results………...23

5.1. Fundamental drivers of P/E ratio………...………....23

5.2. GSADF test on P/E ratios………..26

5.3. GSADF test on corrected P/E series………..………28

5.4. Robustness check and limitations………..32

6. Conclusions………...35

5
**1. Introduction **

There is constant debate regarding the unconventional monetary measures adopted by central banks of the USA, EU, UK, and Japan over the past decade as efforts to rescue developed markets from the setbacks of recent financial crises. The aftermath of the European sovereign debt crisis and rising concerns about the general disinflationary state of EU economies from 2012 onwards have led the European Central Bank to implement its Quantitative Easing (QE) agenda, being the ambitious Expanded Asset Purchase Programme (EAPP), with start in 20141, the latest stage to be carried out and with immediate upward effects across asset classes worldwide, as confidence signals by the monetary authority were embraced by the market. Just as the ECB start a new fifty-percent reduction in monthly asset purchases beginning in Jan 2018, doubts remain about the sustainability of current valuation levels. Among the more sensitive classes, equities may be facing a particular dependency on QE policies and if stock prices are shown to be held high mostly based on this type of measures, a bubble-like scenario might be taking place, posing risk to a large variety of stakeholders.

The effects of the EAPP were recently addressed by van Lamoen, Mattheussens & Dröes (2017). The authors focused on the behavior of public bonds yields for a group of the most representative Eurozone economies and adopted a recently developed methodology to measure the programme impacts2. Namely, they extend the bubble-detection methodology of Phillips, Shi & Yu (2015) to identify that bond prices were no longer in accordance with underlying fundamentals around the time of the ECB announcements. Their two-part study consisted of identifying the fundamental drivers of government bond yields/prices – including fiscal, macroeconomic and financial variables, in order to estimate what would be rationally justifiable levels. The observed values were then compared to those estimated from fundamentals, on a monthly basis, and the resulting ratios incorporated into a panel-data series to be tested for explosiveness using the latest Phillips et al. (2015) framework – the Generalized Sup Augmented Dickey-Fuller (GSADF) test, an enhanced version of the standard ADF test which was found to outperform others of the kind by more accurately detecting periodically collapsing bubbles in longer time intervals. The challenge in addressing longer series typically

1_{ The EAPP is composed by several phases with different start dates but simultaneous implementation. The first }

stage under this macro programme was the (third) Covered Bond Purchase Program (CBPP3, starting in October 2014). It was followed by the Asset Backed Securities Purchase Program (ABSPP, Nov-2014) and then by the Public Sector Purchase Program (PSPP, Mar-2015). The last parallel phase is the Corporate Sector Purchase Program (CSPP, Jun-2016).

2_{ The authors focus on the Public Sector Purchase Program (PSPP), which represent most of the EAPP’s volume }

6 laid on one bubble period masking the buildup of previous/subsequent ones, however, this new development minimizes such disturbances and allows for a close monitoring of exuberant price behavior that can be extended to different asset classes.

Focusing in equity markets, there have been several studies addressing some of these impacts following the 2008 subprime crisis, both regarding announcement and implementation effects, with most of them making use of event study methodology. Fratzscher, Lo Duca & Straub (2013; 2014) find that the announcements of the ECB’s Securities Markets Programme (SMP) and the Outright Monetary Transactions (OMT) – previous stages of the QE agenda from 2010-2012 and 2012-2014, respectively, had positive impacts on stock markets worldwide and diminished sovereign and bank credit risk in developed countries. The same authors, however, as well as Roger, Scotti & Wright (2014) find that, unlike American, English and Japanese recent central banks actions, previous QE coordinated by the ECB have not caused substantial portfolio capital outflows towards emerging markets nor widespread rebalancing across regions in general. Therefore, one would expect a more pronounced effect in European equity markets from the latest stages of the EAPP taking place.

More recently, Georgiadis and Gräb (2015) further analyze the EAPP – especially the
Public Sector Purchase Programme (PSPP), officially announced on January 22nd,_{ 2015, its }

effects and transmission channels for different asset classes and markets, again using event study. The authors find influence of the announcements in boosting Eurozone equities. In particular, they directly link the consequent fall in real interest rates with the rise in stock prices, which motivates this thesis. Furthermore, differently than in other stages of the QE program, this time there has been an inflow of capital towards EU equities and no evidence of a rebalancing in bonds. This reinforces the possibility of a bubble in stock markets, which will be analyzed in the following sections.

This thesis develops and applies a method analogous to van Lamoen’s et al. (2017) to investigate the behavior of the main European stock markets prices during this unusual time in terms of monetary policy, with the EAPP in action. The unprecedently large intervention of central banks pushing interest rates down is an evident example of how driving forces are very different than in normal times. If the programme is found to be conditioning current valuation levels and causing explosive movements, it poses a great challenge to policymakers – How to reduce the stimulus without causing a burst and downward effect across the equity markets in the continent? The methodology therefore addresses the hypothesis that the ECB actions within the asset purchase programme have indeed driven price levels up beyond fundamentals, causing a bubble across stock markets in the region.

7 To do so, a metric to address market valuation level is adopted, namely, the Price-Earnings Ratio (P/E) – a widely employed measurement in the financial industry and academia. The high levels of the P/E ratio observed in recent times for most Eurozone markets, especially during the implementation of the EAPP, could signal a dangerous overvaluation, however, it is necessary to evaluate if the underlying forces driving the P/E have simultaneously changed, since without this relative comparison, the mere observation of absolute values can result in misleading conclusions. Therefore, this thesis employs a twofold methodology: an initial analysis breaks down the fundamentals of the P/E ratio, allowing for a more detailed observation of possible forces driving valuations up, followed by the GSADF testing routine to determine to which of these can the eventual exuberance be attributed to.

The first part of the methodology consists of a panel data regression considering eight of the largest Eurozone countries in terms of market value, with indices at a country level, to obtain the drivers of the ratio and estimate what would be justifiable valuation levels for these markets. The first stage is concluded by comparing the observed P/E levels with the estimated ones, which yields a monthly data series, per country, to be used in the second part of the method – the testing for bubbles with the GSADF framework, more detailed is subsequent sections.

This thesis contributes to the literature and stakeholders in several ways: it expands the range of studies attempting to explain the drivers of the P/E ratio in a more elaborate manner, which has been extensively investigated for American and Asia-Pacific markets, but only very limited to European ones; it also deploys the GSADF procedure for equities in Eurozone members and combines the two individual methods in a novel way to examine these markets in depth, with extended valuation fundamentals. Hopefully, the results obtained can help central banks and the Eurosystem understand the side effects of their broad monetary policy, as well as to help investors and asset managers to manage their equity portfolios and to get valuable insights from this unprecedent measures taken by the monetary authorities, setting a reference point for when similar economic scenario arise in the future. The study follows with a Literature Review (2) of the fundamental determinants of aggregate market Price/Earnings levels and of previous studies about bubble-detection methodologies, in special the GSADF test. The employed Data is exhibited in sequence (3), followed by the Methodology section (4). The empirical Results and Robustness Checks are discussed in section (5) and the thesis ends with a Conclusion section (6).

8
**2. Literature review **

**2.1. Fundamental equity indices levels **

The Price-Earnings ratio (P/E) – investors willingness to pay for a dollar earned by a company (or aggregate of companies) – is considered to be a very straightforward measure of relative valuation for equity markets and therefore is widely employed for analysts and researchers. It is frequently displayed with an emphasis in financial portals and specialized equity reports, as it can signal valuable opportunities for mispriced stocks and indices across markets as well as to raise red flags for potential overvaluation. It is, therefore, no surprise that several models attempting to explain levels of the ratio have been developed since its dissemination by Graham and Dodd in 1934. The work of Basu (1977) triggered a new strand of studies after showing evidence that portfolios made of low P/E stocks outperformed those consisting of high P/E, in the U.S. Some of these publications attempt to find the drivers for the ratio in order to evaluate the sustainability of observed prices, while others look for models with predictive power to develop enhanced trading strategies.

Most of the literature about the determinants of P/E is well grounded in the constant growth dividend discount model, introduced by Gordon and Shapiro (1956) and developed by Gordon (1959; 1962). From a basic pricing formula of discounted cash flow, the stock price is determined by its expected dividends and the discounting factor is composed by a required rate of return minus a growth rate for those dividends, assumed to be constant. When the model is adjusted for earnings, the relative price of a stock becomes a function of the dividend payout ratio, which in turn represents the proportion of net income distributed to stockholders in form of dividends. More detailed assumptions of this model are provided in later sections of this thesis. Naturally, other factors are believed to influence prices, such as macroeconomic variables and investors sentiment. Several authors have researched about these additional elements, which are outlined in the next paragraphs.

Among the recent literature about P/E determinants on an aggregate country level, White (2000) provides a good overview of past studies and incorporate some of the findings to his own. He focusses on the U.S market, using the S&P500 index between 1926 and 1997 and set the P/E as dependent variable. The main question of the research was whether the present valuation levels could be justifiable, given the substantial rise of the index on that year, with the build-up of the Dotcom bubble. The conclusion was that observed P/Es ranging from 30 to 35 could not be explained by current or expected fundamental conditions. From a previous similar study, with data from 1956-1995, the author finds significative and large negative effect

9 of inflation, attributed to the higher borrowing expense and rise in bond yields, which reduces equities attractivity (White, 1997). In addition to the variables from the Gordon model and inflation, he tests and finds significative explanatory power for the following variables: real GDP growth (direct relationship), long-term T-bond rates and market volatility (both inversely related to P/E). White also introduces S&P500 trailing results, claiming investors are willing to pay more for stocks when they have been performing well, and the so-called “FED P/E index”, which is supposedly a measure used by the American central bank to assess the current valuation levels. Both new variables are positively significant. This comprehensive study provides valuable information but has its limitations. Due to the long time-frame considered, it might be that variables related in the past or throughout certain phases within the interval are no longer so closely related or have alternating relationship signals.

The case for variables with changing correlation across time can be observed more clearly in expected inflation. Jain and Rosset (2006), based on the S&P500 for the period of 1952-2003, investigate conflicting outcomes of previous studies employing several macroeconomic variables as drivers for the E/P ratio. The authors are particularly motivated by the challenging finding of Modigliani and Cohen (1979), with data from 1952-1977, that expected inflation was positively correlated with the ratio (conversely, negatively related to P/E) when that should not be the case. Others find similar results, such as Reilly, Griggs and Wong (1983), Fama and Schwert (1997) and Hess and Lee (1999). They argue that based on the Gordon model considered, expected inflation should not play a role in determining P/E levels since the general pricing formula is insensitive to its inclusion.

Modigliani and Cohen (1979) write that investors are not aware of the hedging against inflation provided by gains with equity – via the counterbalancing effect in earnings – and therefore irrationally drive market prices low when expectations of inflation rise. However, Nissim and Penman (2003) find that this hedging is not perfect and so the inverse relationship between inflation and P/E cannot be attributed solely to market inefficiency. Similar conclusions that inflation has real negative effects on P/E levels are found in Feldstein (1980), via a corporate tax effect; Fama (1981), Bernard (1986), and Sharpe (2001) via lower future economic activity and more uncertainty in times of rising expected inflation3.

Jain and Rosset (2006) conduct their research to see if this anomaly was specific to certain time intervals and divide a greater time sample into two smaller subperiods to investigate the consistency of such finding. The period of 1952-1972 is characterized by an

10 inverse sign for inflation over the E/P, while in 1983-2003 it is shown to be significantly positive, both with considerable magnitudes. This instability across studies poses questions about the real effect of expected inflation over the P/E on the long-run.

Among other variables tested by the same authors, consumer confidence is introduced via the University of Michigan consumer sentiment index (MCSI). They hypothesize that this measure is likely to be a proxy for the aggregate effect of many macroeconomic variables over consumers, which affect future consumption decisions and earnings growth. Dudney, Jirasakuldech and Zorn (2008) further investigate effects of consumer/investor sentiment with the MSCI and the ratio of S&P500 volume to population (from 1953 to 2003). They posit that expectations from expert investors and average investors are different, and therefore it is justifiable to test both forces on the E/P ratio. On a perfectly rational market dominated by experts, all the other theoretical variables should capture the effects over the ratio. However, that is unlikely, and average investors tend to incur in over(under)reaction. Based on the work of Doms and Morin (2004) about news coverage effects on consumer sentiment, the authors find that the consumer index is more volatile than expert opinion about future market conditions and should bring additional explanatory power to the variation in E/P. The findings corroborate the hypothesis of direct effect of sentiment measurements over valuation levels. More recently, Jitmaneeroj (2013; 2017) explores sentiment variables specifically for P/E ratios in the U.S market, controlling for other fundamentals, considering market-based measures such as advance-decline ratio, trading and IPO volumes, and survey-based measures, both at firm, industry and aggregate market levels, and shows that downplaying variables of the kind may lead to erratic investment decisions, since valuable signals of forthcoming market trends are implicit in such metrics and have been increasingly adopted in scientific studies and by market practitioners.

Kane, Marcus and Noh (1996) report another driver when analyzing the North American market – returns volatility. Based on historical returns (1953-1994 interval), the authors apply an ARCH-M model to forecast the next-period market volatility4 and find an inverse relationship with P/E. The economic intuition supporting this result is found in the association between a measure of market risk, proxied by volatility, and the required rate of return, since in the presence of greater risk, investors demand higher premiums, raising the discounting rate and lowering prices.

4_{ Implied volatility series, thought to have superior explanatory power, were too recent to cover most of the interval }

11
**2.2. The GSADF and test for exuberance in other markets **

The occurrence of exuberant price behavior in financial markets is a generally accepted phenomena, however, there is greater discussion on what may cause such movements. Supporters of the efficient market hypothesis disregard the possibility of bubble components in asset pricing (Pastor and Veronesi, 2006; Cochrane, 2009). Instead, abrupt price changes should be attributed to equally unusual changes in underlying fundamentals, which might have increased sensitivity at a given point in time. On the other hand, behavioral theorists attribute these occurrences to investor biases and to seemingly irrational investment decisions, such as herding behavior or trend extrapolation. Such debate, however, has not stopped researchers from looking for objective econometric techniques aiming the identification of periods at which a commonly accepted random walk process in prices turns to an explosive one, indicating the existence of a bubble factor.

Among the recent literature about bubble-detection mechanisms, the strand considering bubbles of the rational type has experienced important improvements. Diba and Grossman (1988) study the U.S. equity market and introduce testing tools based on cointegration analysis. Departing from a basic pricing model driven by dividends, if the time series of stock prices and the series of dividends exhibit non-stationarity and a long-run trend in common – therefore being cointegrated – the presence of instability in this relationship might indicate a bubble. The inclusion of a bubble component in the basic model, with temporary activity on the pricing equation will cause price trend to deviate into an explosive process. The innovation in this kind of methodology is to perform a unit-root test considering the null hypothesis of a non-stationary random walk and the alternative hypothesis of an explosive root, instead of the commonly employed stationarity. However, most of the criticism over these primary methods involving unit root tests, as summarized by Arshanapalli and Nelson (2016), lay in the fact that they fail to accurately indicate the time when the inflationary phase occurs. Instead, they only indicate that a bubble is likely to have existed but fall short in providing support to monitor the build-up of one. These tests are also unable to identify the occurrence of periodic bubbles that happen in sequence over the course of a long time interval and to mark ending points (Evans, 1991).

Phillips, Wu and Yu (2011) introduce a method with the use of forward recursive right-tailed Augmented Dick-Fuller (ADF) test for stationarity where the sequential tests scan the data aiming to identify a mildly explosive or explosive process, which hints for the start of a bubble. Contrary to usual left-sided alternatives, their methodology has greater sensitivity to identify processes switching between unit-root and (mild) explosiveness and is able to signal

12 for alarming pricing movements, serving as a better monitoring tool. However, Homm and Breitung (2012) argue that the procedure still faced difficulties to pinpoint multiple cases of bubble surges and bursts in longer intervals. This limiting condition is surpassed with the enhanced methodology developed by Phillips, Shi and Yu (PSY) (2013; 2015) of a now rolling recursive ADF testing sequence that scans the pricing series multiple times with a flexible window. This technique employs a generalized supremum ADF (GSADF) statistic and is able to time-stamp the emergence of an explosive process as well as its ending. The properties of the test are explained in more detail at the methodology section of the thesis.

The emergence of a more robust bubble-detection mechanism such as the GSADF has allowed researchers to investigate times of potential exuberance in different asset classes and markets, such as in housing markets (Pavlidis et al., 2015), Oil prices (Caspi, Gupta and Katzke, 2015; Figuerola-Ferretti et al., 2016), food commodities (Etienne, Irwin and Garcia, 2014), exchange rates (Bettendorf and Chen, 2013; Jiang et al., 2015) and fixed income markets (Contessi and De Pace, 2017). In the equity markets context, Phillips et al. (2015) themselves apply the GSADF on the S&P500 price-dividends ratio and are able to identify periods commonly associated with bubbles, including the 1929 crash, 1987 Black Monday and the early 2000s Dotcom bubble. Liu, Han and Wang (2016) apply the test to Chinese stocks and report evidence of exuberance as recent as 2014-2015 on that market. Escobari, Garcia and Mellado (2017) apply the GSADF for several Latin American countries between 2000 and 2014 and point out that bubbles in the observed markets tend to be identified earlier and to last longer than in the U.S. (S&P500), a market highly correlated to those in that region. Brazil, Chile, Colombia and Mexico experienced bubbles at least from early-2005 to mid-2008. Additionally, by observing dynamic conditional correlations, the authors identify that links between markets are strengthened in the presence of bubbles.

Only a few studies have used the GSADF test to analyze the occurrence of bubbles in the context of quantitative easing. Van Lamoen et al. (2017) find that recent ECB monetary expansion with the EAPP, introduced in September 2014, served as a price driver and inflated government bond prices in the main Eurozone economies, causing deviation from fundamental determinants and signaling exuberant behavior. Most of the countries experienced continuous bubbles from October 2014 to April 20155. Huston and Spencer (2018) explore the effects of QE in the U.S. over different asset types. The authors find that the housing market experienced

5_{ Austria, Belgium, Spain and France experienced bubbles as early as July 2014, while Germany and the }

13 a bubble stretching from 1998 to 2008, just before the subprime crisis. Subsequent expansionary policies carried out by the FED did drive prices back up, but only to fluctuate around the GSADF statistic threshold that qualifies the movement as a bubble. For the case of corporate bonds, the largest and longest period of exuberance occurred exactly when American QE phases 2 and 3 were being implemented, for 18 straight months between September 2011 and February 2013. Additional bubbles are observed from November 2014 to April 2015. The GSADF, however, failed to qualify the stock market rise6 during the overall QE period (2009-2014) as an explosive process, ruling out the presence of a bubble.

**2.3. Hypotheses **

The literature referenced above leads to the formulation of the hypotheses to be tested in the
next sessions. The first hypothesis refers to the fundamentals of the P/E ratio, which will be
*essential to appropriately level market valuation and identify abrupt price movements: (1) For *

*European equity markets, do dividend payout ratio (DPR), expected real GDP growth and *
*consumer confidence index (CCI) drive the price-dividend ratio of the aggregate market *
*positively, while the long-term sovereign bonds yields, expected inflation and volatility *
*(VSTOXX) drive it negatively, pairing with North American and most of the Asia-Pacific *
*countries?. Session 2.1 provides evidence of strong relationships between those variables and *

P/E, with the exception of expected inflation, which has a more controversial role over the ratio. While DPR and GDP growth find grounding on the dividend discount model of Gordon (1962), volatility (Kane et al., 1996) and sovereign bonds represent risk, and CCI, sentiment (Dudney et al., 2008; Jitmaneeroj, 2017), expected inflation is debatable, from the diffuse conclusions from studies in the eighties and nineties (Jain and Rosset, 2006). Table (1) summarizes the variables selected for this thesis and their expected relationship with the P/E ratio.

With the use of GSADF testing, the second hypothesis addresses the direct role of the
*ECB’s QE on equity indices levels: (2) The quantitative easing agenda implemented through *

*the unprecedent amount of purchases in the Extended Asset Purchase Programme (EAPP), *
*more specifically via the Public Sector Purchase Programme (PSPP) phase, has led to *
*exuberant behavior in the pricing of equity markets across the Eurozone. The inclusion of the *

sovereign bonds as a P/E driver allows the study to investigate these effects, since yields were

6_{ The valuation metric used by Huston and Spencer (2018) is the cyclically adjusted price-earnings ratio, in }

14 directly affected by the central banks’ measures (van Lamoen et al., 2017). Also, given that the bulk of the EAPP was carried out in the PSPP, corresponding to approximately eighty-five percent of the purchased assets, focus will be given to this implementation phase (announced in Jan-2015 with implementation from Mar-2015). Evidence of the sharp increase in P/E ratios in most of the considered markets during this time is demonstrated in the following session.

**Table (1). Expected relationship between independent and dependent (P/E) variables **

Independent Variable Expected Relationship with P/E ratio

*Dividend Payout Ratio (DPR) * Direct

*Expected Real GDP Growth (GDPg) * Direct

*Long-Term Sovereign Bond (Bond10) * Inverse

*Expected Inflation (I) * Inverse

*VSTOXX * Inverse

*Consumer Confidence Index (CCI) * Direct

**3. Data and descriptive statistics **

This section details the selection and construction of variables that are used in this thesis. The QE policies developed by the ECB are to be carried out by central banks of all members of the monetary union and should impact equity markets in every Eurozone country. However, the necessary information for the complete performance of the proposed testing was not homogeneously available for all, causing some to be left out of the study. The sample consists of the following eight countries: Belgium, Finland, France, Germany, Italy, the Netherlands, Portugal and Spain. The stock markets of these countries are proxied by the Datastream Global Equity Indices series (TOTMK mnemonic), each covering at least 75% of total market capitalization per country. Subsequent financial market data and ratios are retrieved or calculated based on these indices, available at the Datastream database. To allow for pricing monitoring with more accuracy, this research adopts monthly frequency data for the period December 2002 to December 2017.

It can be seen from figure (1) that P/E ratios fluctuated substantially over the period, reaching its lowest levels on the months following the subprime crisis sell-off (September 2008) and very high levels in the subsequent year, given the depressed realized earnings. Most countries’ P/Es also rose immediately after the announcement of the PSPP phase of the EAPP,

15 in January 2015, with some countries experiencing uptrend scenarios since a few months before or peaking around PSPP implementation in March 2015.

**Figure (1): P/E ratios for selected European markets Dec 2003- Dec 2017 **
The arrows indicate Jan-2015, when the PSPP phase of the EAPP was announced.
Source: Datastream Global Equity Indices.

16 Excluding the severe distortions from the 2008-2009 crisis, four countries have their respective highest ratio level with the start of the PSPP, namely: France, Germany, Italy and the Netherlands, which remained at elevated levels until the end of the observed series, when multiple phases of the EAPP were still simultaneously taking place; only Spain did not experience any rise in P/E around the PSPP initiation. However, for the subsequent GSADF testing mechanism, the rates of change in the corrected P/E levels matter more than the actual observed levels, therefore, to observe if stock valuations experienced exuberant behavior, it is necessary to compare observed P/E ratios with the values predicted by its fundamental drivers and from that generate the series which will be tested for exuberant behavior. Based on the literature exposed in the previous section, these drivers can be either financial metrics or macroeconomic variables, which are better described in sequence.

The main variable, P/E, is the ratio of the index price (P) over 12-months trailing earnings per share (EPS) – it is available on Datastream under the code ‘DSPE’. Departing from Gordon’s (1962) constant growth model, the basic pricing formula of discounted cash flow, in which the stock price is the present value of future expected dividends (D), is expressed below:

### 𝑃

_{0}

### =

𝐷0(1+𝑔)𝑘−𝑔

### =

𝐷 𝑘−𝑔### (1)

where: 𝑃0 is the initial price; 𝐷0*, the current dividends per share (DPS); k, the required rate of *

return; and g, the constant growth rate of dividends, with k>g. Naturally, 𝑃0 and 𝐷0 are

calculated for the aggregate index level. When earnings is introduced as leveler for valuation purposes, one can obtain the P/E formula:

𝑃_{𝑡}
𝐸_{𝑡}

### =

(𝐷_{𝑡}/𝐸

_{𝑡})(1+𝑔) 𝑘−𝑔

### =

𝐷𝑃𝑅 𝑘−𝑔### (2)

Where: 𝐸_{𝑡} stands for earnings per share and DPR is the dividends per share over EPS, or
dividend payout ratio. The P/E ratio should be, consequently, positively related to the DPR and
growth rate, and negatively correlated to the required rate of return.

*The yields of national governments long-term bonds with 10 years maturity (Bond10) *
are considered as the initial required rate of return. However, this rate is not sufficient to cover
the entirety of required returns, since investing in stocks entails a much higher risk and
investors demand a premium for it. To account for the variation in this equity risk premium, a

17
measure of volatility is included as a driver for P/E – the VSTOXX index7_{, which is not based }

on historical volatility but on the implied volatility for the short-term period ahead, by using options prices for the EURO STOXX 50 index. Both variables are available at Datastream and the monthly values for the latter are the same for every country.

Following most of the literature about P/E determinants on economy-wide level, the
*variable chosen to measure growth is the real GDP expected growth rate (GDPg) (for example, *
White, 2000; Jain and Rosset, 2006; Dudney et al.,2009), since it is reasonable to assume that
the aggregate growth in national companies moves together with the overall economy of that
country. These values are obtained from the Consensus Forecasts database, which in turn are
based on expert opinion. On a monthly basis, financial and research institutions are asked their
estimates for the GDP growth rate on that year, and so a final ‘consensus’ number is calculated.

The model for P/E determinants is extended with other variables beyond the
Gordon-type. Firstly, a measure of inflation is added to investigate if it has explanatory power – Jain
and Rosset (2006) argue that even not playing a direct role in equations (1) and (2), since the
inclusion of an inflation term (I) on both components of the denominator would have a null
effect ((k + i) - (g + i)), it might be that when inflation expectations increase, the discount rate
is affected unevenly, with some negative effect in the expected growth which does not allow
for a full offset of I. In this thesis, the values used to represent expected inflation rate also
come from Consensus Data, calculated in the same manner as the GDP growth series described
*previously. Lastly, the Consumer Confidence Index (CCI), which represents the aggregate *
effect of macroeconomic variables over consumers decisions for expenditure and investing
(Dudney et al., 2008) and serves as a sentiment measure, is compiled by the OCDE.

After the regressions specified in the next section, the series (eight – one per country) with the ratios of observed P/E over predicted P/E are the input data for the second part in the methodology. Table (2) shows the descriptive statistics of variables of interest. P/E averages between 15 and 16 for most markets, with Germany being lower at 14 and Italy and Portugal almost reaching 17; Germany also has the lowest standard deviation. The DPR is roughly between 40% and 60% for all countries. Non-surprisingly, the expected GDP growth for the period is smaller for southern European countries, which went through a lot of turmoil recently, and the most stable rate is the German one, with a lower deviation. Related evidence can be seen in the expected inflation, where southern countries have higher and more volatile rates,

7_{It is analogous to the VIX index calculated by the Chicago Board Options Exchange }

18 with similarly higher long-term bond rates – notably, Portugal has a much higher yield than the others, which fluctuate around 3%, with 4,87%. Likewise, measures of sentiment are lower for the countries that suffered greatly with sovereign debt crises – Portugal, Spain and Italy.

**Table (2). Descriptive Statistics **

This table presents the descriptive statistics for the selected variables over the different countries for a balanced panel of 181 observations each. Dec-2002 to Dec-2017

Country BE DE ES FI FR IT NL PT
*P/E *
Mean 15.98 14.32 15.11 15.51 15.49 16.25 15.78 16.96
SD 5.65 3 4.15 3.35 3.17 4.14 4.86 4.76
*DPR (%) *
Mean 44.8 38.38 55.55 59.86 50.71 58.87 46.27 62.47
SD 17.6 11.59 14.61 12.81 8.69 8.15 13.24 14.54
*GDPg (%) *
Mean 1.55 1.54 1.7 1.93 1.46 1 1.52 0.96
SD 0.61 0.48 1.29 0.79 0.57 0.65 0.7 1.27
*I (%) *
Mean 1.77 1.43 1.94 1.55 1.4 1.69 1.58 1.67
SD 0.85 0.66 1.39 0.87 0.74 0.94 0.66 1.09
*Bond10 (%) *
Mean 3.02 2.52 3.71 2.71 3.1 3.22 2.7 4.87
SD 1.41 1.46 1.32 1.42 1.34 1.29 1.42 2.53
*CCI *
Mean 100.17 100.11 99.67 100.65 99.67 99.71 100.06 99.22
SD 0.71 1.41 1.36 1.49 0.71 1.27 1.11 1.42
*VSTOXX *
Mean 23.25 23.25 23.25 23.25 23.25 23.25 23.25 23.25
SD 8.6 8.6 8.6 8.6 8.6 8.6 8.6 8.6

**4. Model and Methodology **

**4.1. P/E Fundamentals **

Based on the selected data, a regression model is constructed to investigate the drivers of P/E ratio. Since the sample consists of eight countries observed for a common time interval, a balanced fixed effects panel data model is adopted. The basic specification is represented by:

19
Where 𝑃𝐸_{𝑖𝑡}* is the P/E ratio for country i at period t (month), 𝐷𝑃𝑅*_{𝑖𝑡}* is the dividend payout ratio, *

𝐺𝐷𝑃𝑔𝑖𝑡 is the expected growth in GDP for the current year, 𝑉𝑆𝑇𝑂𝑋𝑋𝑡 is the value of the

VSTOXX index, 𝐼_{𝑖𝑡} is the expected inflation for the current year, 𝐶𝐶𝐼_{𝑖𝑡} is consumer confidence
index value, 𝛼_{𝑖} is a fixed-effect specification at country level to address unobserved factors
particular to each market, τ𝑡 is a coefficient for time fixed-effects and µ𝑖𝑡 represents a white

noise residual term.

Fitting the P/E ratio in a model is a notoriously challenging task, especially in the time range considered, which included two financial crises of large direct impact in equity markets – the global subprime crisis and the sovereign debt crisis in Europe. Even though the objective of this thesis is to observe potential explosive price movements around the announcement and implementation of the PSPP, the series of observed P/E adjusted by its fundamental drivers, which will be tested with the GSADF procedure on the next step, is very sensitive to measurement errors and might flag explosive behavior when sharp downward movements occur giving a false-positive identification problem, since it distorts the ratio of [PE / Predicted PE]. To try and correct for potential shifts caused by financial crises, two dummies are included on an extended regression. For the subprime episode, the dummy considers the range from September 2008 to September 2009, because of the reflection in EPS; for the European crisis, the date ranges from January 2010 to December 2012 to cover the most impacting period. The new specification is:

𝑃𝐸_{𝑖𝑡} = 𝛽_{1}𝐷𝑃𝑅_{𝑖𝑡}+ 𝛽_{2}𝐺𝐷𝑃𝑔_{𝑖𝑡}+ 𝛽_{3}𝑉𝑆𝑇𝑂𝑋𝑋_{𝑡}+ 𝛽_{4}𝐼_{𝑖𝑡}+ 𝛽_{5}𝐶𝐶𝐼_{𝑖𝑡}+ 𝛽_{6}𝑆𝑢𝑏𝑝𝑟𝑖𝑚𝑒 +
𝛽_{7}𝐷𝑒𝑏𝑡𝐶𝑟𝑖𝑠𝑖𝑠 + 𝛼_{𝑖} + τ_{𝑡}+ µ_{𝑖𝑡} (4)

To investigate if the announcement and implementation of the PSPP have explanatory
power over P/E levels, one extended regression is developed, with the inclusion of the
long-term sovereign bond yield, since this variable was directly impacted by the purchase
programme and shown by van Lamoen et al. (2017) to be affected by exuberance. The extended
regression has the following specification, with 𝐵𝑜𝑛𝑑_{𝑖𝑡}* representing the bond yield for county *

*i at period t: *

𝑃𝐸_{𝑖𝑡} = 𝛽_{1}𝐷𝑃𝑅_{𝑖𝑡}+ 𝛽_{2}𝐺𝐷𝑃𝑔_{𝑖𝑡}+ 𝛽_{3}𝑉𝑆𝑇𝑂𝑋𝑋_{𝑡}+ 𝛽_{4}𝐼_{𝑖𝑡}+ 𝛽_{5}𝐶𝐶𝐼_{𝑖𝑡}+ 𝛽_{6}𝐵𝑜𝑛𝑑_{𝑖𝑡}+
𝛽_{7}𝑆𝑢𝑏𝑝𝑟𝑖𝑚𝑒 + 𝛽_{8}𝐷𝑒𝑏𝑡𝐶𝑟𝑖𝑠𝑖𝑠_{𝑖𝑡}+ τ_{𝑡}+ µ_{𝑖𝑡} (5)

After the inclusion of this new variable, which is expected to be significantly negatively correlated to P/E and the predicted ratio better adjusted to the actual number, a more critical analysis of an eventual bubble scenario is possible, together with a better discussion of causal

20 effects. However, this method has limitations, since the very dynamic equity markets are influenced by a conundrum of multiple factors and respond to several other announcements and economic reports. Nevertheless, it is reasonable to assume that a programme with such magnitude would dominate investors reactions when occurring together with other, probably less enduring, events.

After performing each regression, it is possible to estimate what the fundamental level
*of the P/E ratio would be for each country i at period t (P/E*), and this will be used to address *
if observed P/Es are disconnected from underlying drivers, which might signal to exuberance.
This is done by dividing the actual P/E ratio by its predicted value [(P/E) ÷ (P/E*)]. In the end
of this process, these corrected ratios are incorporated into a time series, per country, which
will be the focus object for the next step of the methodology. If the valuation metric rises at a
faster pace than what drivers predict, the gap widens and the GSADF testing will point out if a
bubble is present. Additionally, the regressions will also yield different series per country, and
this will put in evidence how substantially do they differ according to the selected set of
variables, allowing meaningful comparisons.

**4.2. Bubble detection with the GSADF test **

The framework of the GSADF test is built under the consideration of rational bubbles, just as Diba and Grossman’s (1988) cointegration test and Phillips’ et al. (2011) SADF test. As Homm and Breitung (2012) pose, to better understand the possibility of such a bubble, it is useful to consider the basic asset pricing model:

### 𝑃

_{𝑡}

### =

𝐸𝑡[𝑃𝑡+1+𝐷𝑡+1)1+𝑅

### (6)

Where the price 𝑃 at period t is equal to the expected value of the asset price in the next period plus the income flow – dividends in the case of equities, D – conditional to information available at that time, and discounted with the constant risk-free rate 𝑅. By using forward recursive iterations, one can obtain the so-called fundamental price, which is the present value of every expected dividend flow:

### 𝑃

_{𝑡}𝑓

### = ∑

𝐸𝑡[𝐷𝑡+𝑖](1+𝑅)𝑖

∞

𝑖=1

### (7)

However, if the possibility of a bubble is considered and investors anticipate its manifestation in future periods by incorporating a bubble component 𝐵𝑡 in the numerator of equation (7), the

21
premium and buy overpriced securities because they believe this pricing dynamic will persist
and a non-fundamental component will also appreciate at the same rate 𝑅 ∴ 𝐸_{𝑡}[𝐵_{𝑡+1}] = (1 +
𝑅)𝐵𝑡. Because this is consistent with the assumption of rational expectations, the term “rational

bubble” is widely adopted. It yields the modified equation:

### 𝑃

_{𝑡}

### = ∑

### (

11+𝑅

### )

𝑖 ∞𝑖=1

### 𝐸

𝑡### [𝐷

𝑡+𝑖### ] + 𝐸

𝑡### [𝐵

𝑡+𝑖### ]

(8)The term 𝐸𝑡[𝐷𝑡+𝑖] can be seen as the fundamental price component and 𝐸𝑡[𝐵𝑡+𝑖] as the bubble

component. A simplified version of the current price equation can be rewritten as:

### 𝑃

_{𝑡}

### = 𝑃

_{𝑡}𝑓

### + 𝐵

_{𝑡}

### (9)

In the absence of bubbles, the price will reflect the stationarity degree of the fundamentals.
Considering this basic pricing equation for equities, it is plausible and useful to assume that
dividends are characterized by a random walk with drift, and therefore so is the price8_{ (Evans, }

1991; Homm and Breitung, 2012). The presence of a bubble component, on the other hand, allows for testing if this non-stationarity condition turns into an explosive process, which signals price exuberance.

For the GSADF test itself, the starting point as proposed by Phillips et al. (2015) is to
*test for a random walk in the series of interest Y, the ratio [(P/E) ÷ (P/E*)] in this thesis, obtained *
in the first step of the methodology:

### 𝑌

_{𝑡}

### = 𝑑𝑇

−𝜂### + 𝜃𝑌

_{𝑡−1}

### + 𝑒

_{𝑡}

### (10)

In which 𝑑 is a constant, 𝜂 is a controlling coefficient for the drift as the sample size 𝑇 grows to infinity and assumed to be bigger the 0.5, and 𝜃 is an autoregressive parameter equal to 1. 𝑒𝑡 is a white noise error term. Because the next steps involve recursive testing with expanding

time windows, some notation is required to specify the necessary routine. Considering the
markers 𝑟_{1} and 𝑟_{2} as starting and ending time fractions of the sample, respectively, with 𝑟_{2} =
𝑟_{1}+ 𝑟_{𝑤}, and 𝑟_{𝑤} a positive value characterizing the width of the window, the initial test round
departs from the first observation (𝑟1= 0) with a pre-set minimum width 𝑟0. The initial window

expands at each round until it covers the whole sample (𝑟_{1} = 0; 𝑟_{2} = 1). It can be applied to
the standard ADF regression:

### ∆𝑌

_{𝑡}

### = 𝑎

_{𝑟1,𝑟2}

### + 𝛽

_{𝑟1,𝑟2}

### 𝑌

_{𝑡−1}

### + ∑

𝑘_{𝑖=1}

### 𝜓

_{𝑟1,𝑟2}𝑖

### ∆𝑌

_{𝑡−𝑖}

### +

### 𝑒

_{𝑡}

### (11)

8_{ Phillips et al. (2015) note that for sufficiently long periods of time the drift becomes asymptotically negligible, }

22
Where ∆𝑌_{𝑡}* is in first differences, [(P/E) ÷ (P/E*)] for the time t, ∆𝑌*_{𝑡−𝑖} is a lagged dependent
*variable and k is the lag order. 𝑒*𝑡 is again a white noise error term. Under the null hypothesis

𝐻_{0}: 𝛽_{𝑟1,𝑟2}= 0, the series contains a unit-root, while the alternative 𝐻_{1}: 𝛽_{𝑟1,𝑟2}> 1 characterizes
an explosive process. However, the method is different than previous alternatives because it
allows for both the starting and ending point, 𝑟1 and 𝑟2, respectively, to vary in an expanding

window. Consequentially, the window width ranges from its minimum 𝑟_{0}, in the beginning of
the series, to the maximum of covering the whole sample, and then returns to its minimum in
the end. Each round of this routine yields an ADF test statistic 𝐴𝐷𝐹_{𝑟1}𝑟2, nevertheless, to enhance
the time-stamp accuracy in the multiple-bubble case, this recursive approach that scans the
series thoroughly is performed backwards by Phillips et al., (2015). Initially, the ending point
is fixed at 𝑟_{2} and the rounds with different subsamples yield the Backward Supremum ADF
(BSADF) statistic. When the end point is also let to fluctuate, it turns into the GSADF – the
supremum value considering all flexible BSADF rounds, as defined below and depicted in the
figure (2).

### 𝐵𝑆𝐴𝐷𝐹

_{𝑟2}

### (𝑟

_{0}

### ) = 𝑠𝑢𝑝

_{𝑟1∈[0,𝑟}

_{2}

_{−𝑟}

_{0}

_{]}

### {𝐴𝐷𝐹

_{𝑟1}𝑟2

### }

(12)### 𝐺𝑆𝐴𝐷𝐹 (𝑟

_{0}

### ) = 𝑠𝑢𝑝

_{𝑟2∈[𝑟}

_{0}

_{,1]}

### {𝐵𝑆𝐴𝐷𝐹

_{𝑟}

_{2}

### (𝑟

_{0}

### )}

(13)**Figure (2) – BSADF and GSADF Tests. Source: Phillips et al. (2015) **

The recursive GSADF statistic will signal the presence of price exuberance if that is the case, while the BSADF statistic allows for the identification of starting and ending points of such bubbles, when compared to the right-tail critical values. For each window, the start date is determined when the BSADF statistic first surpasses the critical value, while the end

23
corresponds to the date when the statistic is again below the critical value. Because the limit
distributions of both BSADF and GSADF are not standard, the critical values must be
calculated by either a Monte Carlo simulation or by bootstrap methods and depend on 𝑟_{0}, the
minimum window width. On this thesis, these values are obtained by 2000 Monte Carlo
replications. Formally, the time-stamping is obtained by:

### 𝑟̂

_{𝑒}

### = 𝑖𝑛𝑓

_{𝑟2∈[𝑟}

_{0}

_{,1]}

### {𝑟

_{2}

### : 𝐵𝑆𝐴𝐷𝐹

_{𝑟}

_{2}

### (𝑟

0### ) > 𝑠𝑐𝑣

𝑟2 𝛽𝑇_{} }

_{(14)}

### 𝑟̂

_{𝑓}

### = 𝑖𝑛𝑓

_{𝑟2∈[𝑟̂}

_{𝑒}

_{,1]}

### {𝑟

_{2}

### : 𝐵𝑆𝐴𝐷𝐹

_{𝑟}

_{2}

### (𝑟

_{0}

### ) > 𝑠𝑐𝑣

_{𝑟}2 𝛽𝑇

_{} }

(15)
Where 𝑟̂𝑒 and 𝑟̂𝑓 are the origination and termination points and 𝑠𝑐𝑣𝑟2
𝛽𝑇_{ is the 100(1- 𝛽}

𝑇)% critical

value of the supremum ADF statistic based on [T𝑟_{2}] observations. Additionally, the minimal
window width for this study is calculated following the suggestion in Phillips et al., (2015),
based on many simulations performed by the authors in order to minimize potential distortions
in the bubble identification process: 𝑟_{0} = 0.01 +1.8

√𝑇 = 28 months. The investigation of number

of lags to be included in the regression of equation (11) points out to a lag order equal to (1), as determined by the Schwarz criterion (SBIC), for most of the countries’ series. A smaller number or country-series, when considering the Akaike information criterion (AIC), pointed out to a lag order of (3), and because of that a subsequent robustness check is performed with different lags to see if results hold.

**5. Results **

This section provides the results of the combined methodology used in this thesis to address drivers of P/E ratios in Europe; if these equity markets experienced exuberant price behavior, and if that was enough to characterize a bubble caused by the quantitative easing agenda of the ECB, specifically with the PSPP implementation. The first step of fundamental levels of P/E is presented next, and in following subsections, the results of the GSADF testing and robustness check.

**5.1. Fundamental drivers of P/E ratio **

The table (3) reports the regression results to investigate the main drivers of the P/E ratio. The first model (column 1) considers hypothesized drivers of the ratio including financial ratios and macroeconomic variables based on equation (3). The second model (column 2) extends the

24 initial version with dummy variables for the two most impacting financial crises at European markets in the time range of the observations, namely, the subprime crisis (Sep 2008 – Sep 2009) and the sovereign debt crisis (2010-2012), from equation (4). Both have coefficients for country-specific effects and monthly time-fixed effects.

The results show that most of the variables have the expected signs and do not change across models, however, not all of them are statistically significative. The Dividend Payout Ratio and the Expected Growth in GDP exhibit a meaningful direct relationship with P/E whereas the equity risk premium variation measured by the VSTOXX index has a negative relationship, all significative at the 1% confidence level for the first two models. The expectations over inflation rate, a more controversial variable, also has the hypothesized relationship found for these specifications, with a lower inflation implicating in higher P/E, however, it is consistently very statistically insignificant and do not contribute much for the explanatory factors. The same goes for the sentiment factor proxied by the Consumer Confidence Index, which despite exhibiting the expected direct relationship, also cannot be considered to statistically explain the dependent variable levels. Despite grounded in previous studies, these two weak results implicate that their potential explanatory power is absorbed by the other drivers investigated. The specification in model (2) shows the large significative (1% level) impact of the two financial crises over the P/E ratio, as thoroughly acknowledged. These two coefficients account for large shifts in valuation levels and are important to reduce the distortion in the fitted values used to construct the sensible series that will be tested for explosiveness. The adjusted R-squared values increase from 0.5458, in model (1), to approximately 0.5897 in model (2).

The last specification, in column (3), is based on equation (5) and takes into consideration the long-term sovereign bond yields. Most of the other explanatory variables remained unchanged in terms of economic and statistical meaning, and so do the control variables reflecting the crises. The exceptions were the expected inflation, which now exhibits a direct effect but again not significant, and the expected GDP growth, which becomes significant only at the 5% confidence level.

Matching most of the literature applied to other geographical areas, the dividend payout ratio (White, 2000; Jitmaneeroj, 2017), expected GDP growth (White, 2000; Jain and Rosset, 2006; Dudney et al. 2009), and volatility (Kane et al., 1996) are the key drivers of the PE ratio in European markets. The inconsistency over expected inflation investigated by Jain and Rosset (2006) in the U.S market also holds, and the variable seems to be innocuous within the Gordon

25 model-based factors capturing most of the explanatory power. Surprisingly, the sentiment variable does not add meaningful explanation either, when together with the other drivers.

**Table (3). Fundamental Drivers of P/E Ratio**

The results displayed on this table are the coefficients from the fixed effects regression of P/E ratios on its hypothesized drivers. Column (1) uses the basic equation (3), column (2) includes two dummy variables to account for financial crises with large impact in European markets, from equation (4), and column (3) is based on equation (5), which adds long-term sovereign bonds yields, used to capture the effects of PSPP announcements and implementation. All regressions account for monthly time fixed effects and country fixed effects. Standard errors are clustered by country for robustness against autocorrelation and heteroskedasticity and shown in parenthesis. Coefficients have the 1%, 5% and 10% significance levels denoted by ***, **, *, respectively.

*P/E Driver * Basic Model

(1)
Crises Included
(2)
L.T. Bonds Included
(3)
*DPR * 0.1773***
(0.0250)
0.1683***
(0.0221)
0.1668***
(0.0231)
*GDPg * 1.3430***
(0.3069)
1.0903***
(0.2703)
0.9892**
(0.3473)
*VSTOXX * -0.1690***
(0.0166)
-0.1115***
(0.0136)
-0.1095***
(0.0133)
*I * -0.5143
(0.3952)
-0.2353
(0.4155)
0.2291
(0.3673)
*CCI * 0.2084
(0.2530)
0.29352
(0.3575)
0.2169
(0.2542)
*Bond10 * -0.7780**
(0.3118)
*Subprime Crisis * -3.4627***
(0.8744)
-3.1921***
(0.9056)

*Sovereign Debt Crisis * -1.9328***

(0.5422)

-1.8737*** (0.5222)

Observations 1448 1448 1448

26
**5.2. GSADF test on P/E ratios **

Aiming to observe to what extent did markets across the region experience exuberance around the implementation of the PSPP, the table (4), below, depicts the results of an initial GSADF test procedure on the P/E ratios of individual countries. This is done with the basic Price-Earnings, as a simplified version in which the only fundamental is earnings itself and does not take into consideration the other drivers identified in the previous subsection. If one or more countries indeed experienced exuberance, the next step of using the GSADF test allows for the additional drivers to be analyzed in more detail, representing a potential causal effect.

**Table (4). GSADF test for P/E ratios in selected European markets Dec 2003- Dec 2017**
The graphics depicted below represent the GSADF test performed in the simple P/E ratio series, per
country, where the only fundamental is earnings itself. At each country figure, the first panel is the
P/E ratio across time, while in the second panel shows the results of the GSADF performed with a
lag order of (1), according to SBIC indications, and minimum window of 28 months, following
Phillips et al. (2015) recommendations, which depend on the sample size. Below each figure is the
GSADF stat of that respective country and coefficients have the 1% (CV:2.79), 5% (CV:2.04) and
10% (CV:1.78) confidence levels denoted by ***, **, *, respectively. The dotted lines are the
95% critical values obtained through 2000 Monte Carlo simulations.

GSADF BE: 1.4682 GSADF FI: -0.0091

27

GSADF IT: 2.2411** GSADF NL: 2.7564**

GSADF PT: 1.9469* GSADF ES: 1.4355

These results show that despite valuation ratios spiking in the months around the announcement of the PSPP, not every country experienced exuberant pricing behavior. In fact, only three of them did – France, Italy and the Netherlands. The procedure additionally pinpoints other periods of exuberance and arguably a bubble scenario around the 2008 crisis in Belgium, Germany and Spain, but these are likely due to the severe distortions suffered by the PE ratio with the intense sell-of of the period. Portugal exhibits another period of market bubble in 2007, but both these time intervals are not on the scope of this thesis.

With these indications, the next step is to observe if upon the inclusion of other fundamental drivers of P/E in the corrected series, from equation (4), these scenarios hold, and more specifically, if the inclusion of long-term bond yields – directly affected by the PSPP, from equation (5), alter these results.

28
**5.3. GSADF test on corrected P/E series **

The computation of the drivers’ coefficients in subsection 5.1 allows for the predicted P/E levels to be estimated and the sequence of [(P/E) ÷ (P/E*)] ratios undergoes the next GSADF test. The results obtained are based on the comparison between the GSADF stats and the GSADF critical values, which are estimated with a 95% confidence level after 2000 Monte Carlo simulations. Following Phillips et al. (2015) criterium for minimum window size, which yields 28 for this sample size of 181 months, for the recursive testing, the period at which it is possible to observe if exuberance happened ranges from May-2005 to Dez-2017. Based on SBIC calculations, the specification considered (1) lag on the tested series. Table (5) depicts simultaneously, per country, the results from the GSADF tests considering the original five main drivers plus crises dummies from equation (4) – specification (2) of table (3), and with the addition of long-term bond yields from equation (5) – specification (3) of table (3).

The results in column A, based on equation (4) are in line with the indications from the previous testing of the GSADF on the basic P/E levels. During the implementation of the EAPP (October 2014 onwards), the same countries exhibit periods of pricing exuberance – France, Italy and the Netherlands, where the GSADF stat surpasses the respective critical value, which happened during the PSPP announcement or during its implementation start. Germany also had a brief period of high GSADF stat at that time, and two countries, Finland and Spain, also show weaker signs of exuberance in later months, but it does not seem to suggest a connection with the QE policies. Instead, it is probably linked to temporary market conditions specific to those countries, since the spark occur in moments of sharp decrease at the P/E. Again, most of the countries also show signals of exuberance at earlier years (2008-2009), but as previously mentioned, this is probably due to the distortions from the subprime crisis.

Nevertheless, further discussion is needed in order to qualify periods of exuberance as bubbles. Aiming to prevent short-lived spikes from incurring in overidentification as such, Phillips et al. (2015) propose that a minimum exuberance duration of 𝐿𝑜𝑔(𝑇), where T is the sample length, is necessary in between the initial and final date stamping marks – this yields an interval of (3) months in the 181-months series length. France has its starting date stamped at January 2015 (GSADF stat: 2.0681), coinciding with the PSPP announcement, and remains above the critical values until June 2015, resulting in 6 months of exuberance and comfortably qualifying it as a bubble; Italy also experiences it for 6 months, from March 2015, exactly when the purchases under the PSPP started to take place, until August of the same year (GSADF stat: 2.1134); the last identified market, the Netherlands, exhibits exuberance for a smaller period

29 of 5 months, but also long enough to qualify as a bubble, from January to May 2015 (GSADF stat: 2.1209). All of these qualifications are made with a 95% confidence level, as the GSADF critical value obtained from the simulations is 2.0432. Germany’s series only has a spike in March 2015 (GSADF stat: 0.8910), Finland’s has it in May-June 2016, while Spain’s has it in September 2015, making these cases not enduring enough to sustain a bubble-like scenario.

**Table (5). GSADF tests for corrected P/E ratios Dec 2003- Dec 2017**

The graphics depicted below represent the GSADF tests performed in the corrected P/E ratio series [(P/E) ÷ (P/E*)], per country. Markets are represented in pairs, where column A is based on the equation (4) including primary drivers and crisis dummies, while column B is based on equation (5), which adds long-term bonds to the drivers. Figures depict the corrected series in black (right side axis), the GSADF sequence in gray and critical values in the dotted line (both from left hand-side axis). Regressions were performed with a lag order of (1), according to SBIC indications, and minimum window of 28 months, following Phillips et al. (2015) recommendations, which depend on the sample size – 181 months. Below each figure is the GSADF stat of that respective country and coefficients have the 1% (CV:2.79), 5% (CV:2.04) and 10% (CV:1.78) confidence levels denoted by ***, **, *, respectively. The dotted lines are the 95% critical values obtained through 2000 Monte Carlo simulations.

Column A Column B

GSADF BE: 0.5831 GSADF BE: 0.5291

GSADF FI: 0.7397 GSADF FI: 1.0492

30

Column A Column B

GSADF DE: 0.8910 GSADF DE: 0.4355

GSADF IT: 2.1134** GSADF IT: 0.6665

GSADF NL: 2.1209** GSADF NL: 1.2112

GSADF PT: 1.9599* GSADF PT: 1.6307

31 It can be observed that despite being closely integrated, the impacts of the PSPP did not equally affect all the countries, and contrary to what one could expect, just three out of the eight markets in question experienced bubbles around that time. Because of the sovereign debt crisis that motivated the EAPP in the first place, markets had been experiencing very particular realities in the years before, which altered the corrected P/E series in diffuse ways. Particularly Portugal and Spain, which suffered the most from the increased indebtment, had had brusque price movements in 2013 and 2014 with the negotiations to alleviate the crisis, and this increased volatility affected relative valuation levels and the GSADF identification of potential bubbles. Perhaps the most surprising result is the absence of long-standing exuberance in Germany. Despite generalized substantial increase in P/E levels across the continent sparkled by measures under the EAPP, the year of 2015 also experienced another financial event of great magnitude – a Chinese market panic, from late August onwards. Global markets were hit by fears of a sudden Chinese slowdown that could trigger sequential defaults and large sell-offs, which had implications until the start of the following year. The last days of August and the month of September were marked by indices dropping as much 15% in function of these developments in China and that helped to end the price momentum European countries had been experiencing from the PSPP implementation. Nevertheless, P/E levels did remain generally high for the subsequent months, as seen in table (4), until the end of the available time frame considered in this thesis; just not enough to hold the qualification of a continuous bubble.

The figures from column B, when long-term bond yields are included as fundamental
drivers of P/E, show a different situation. The modifications in the main corrected series of the
different markets make the exuberance disappear in France and Italy, and to substantially lower
in the Netherlands. The new configuration subsumes the GSADF sequence to underneath the
critical values in the first two countries (GSADF stats of 0.6349 and 0.6665, respectively) and
lowers the Dutch duration of exuberance to two months, falling short from the 3-month
threshold to qualify as a bubble (GSADF: 1.212). These results reinforce that the Eurozone
central banks actions under the PSPP conditioned the high valuation levels in the three markets
that experienced a bubble in equities, in line with the hypothesis from section 2.3. The variation
in bond yields – which suffered direct effect from the monetary policies – managed to capture
the explosiveness and therefore can explain price behavior in those markets when included in
the main regression. The shape of the GSADF stat sequences of other countries that did not
previously exhibited exuberance were also significantly altered around the time of
**announcement and implementation. **

32
**5.4. Robustness check and limitations **

The methodology used in this thesis has its limitations and in order to evaluate if previous results hold when parameters change, an additional test is performed. The GSADF procedure is dependent on several specifications that might not always have clear indications of appropriate values - especially the equations (10) and (11), which require that a trend parameter, presence or not of a constant, and lag order are set. From the natural price component of the P/E ratio of equity markets, it is plausible to remain with the assumption of a random walk with a (negligible) drift, for the size of the current sample, meaning that the previous choice of constant but no trend is adequate (Phillips et al., 2015; Caspi, 2016). More sensible, however, is the correct lag structure, since the earnings component is reported quarterly and can turn P/E values sticky within each quarter. When performing statistical tests to explore the appropriate number of lags, which in turn can vary per country, the Schwarz criterion (SBIC) pointed to (1) lag, as previously adopted, however, the Akaike criterion (AIC) often indicated (4) as the best number of lags to explain the series. To investigate potential inconsistencies, another set of GASDF was performed, similarly to the session 5.1 but with the new lag order (4); the results are depicted in table (6).

The new results show that little has changed in practical terms for the period of interest – around the PSPP phase. Column A still indicates that the same three countries, France, Italy and the Netherlands, experienced exuberance. France, however, exhibits a lasting period of five months this time, from January to May 2015 (GSADF: 2.0701), instead of the previous six, which is still long enough to be considered a bubble. Numbers for Italy also only marginally changed, with a bubble period lasting from February to August 2015 (GSADF: 2.1034), while the Netherlands kept the same interval, from January to May 2015 (GSADF: 2.2164). The level of confidence for these conclusions remained at the 95% level, with a critical value of 2.0532. Sporadic short-lived spikes are still present in Finland but no longer in Germany, while Spain experienced two moments of exuberance where it almost qualifies as a bubble, in Oct/Nov 2015 and Jan/Feb 2016 (GSADF: 1.7364). However, the Spanish case is triggered by a sharp decrease in the corrected P/E series, and likely related to specific events on that country.

Likewise, results in column B support the explanations in session 5.1. When including the long-term sovereign bond yields as a driver for P/E, the new corrected series no longer show evidence of exuberance for these three countries, meaning that the new variable indeed captures the component causing the bubble. New GSADF values for France, Italy and the Netherlands are, respectively, 0.9998, 1.0672 and 1.1420, Therefore, the phenomena can still