Economic Volatility and Financial Markets: The Case of Mortgage-Backed Securities

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Economic Volatility and Financial Markets: The Case of Mortgage-Backed Securities Gaetano Antinolfi and Celso Brunetti 2013-42 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Economic Volatility and Financial Markets: The Case of Mortgage-Backed Securities∗ Gaetano Antinolfi† Celso Brunetti‡ April 29, 2013 Abstract ThevolatilityofaggregateeconomicactivityintheUnitedStatesdecreasedmarkedly in the mid eighties. The decrease involved several components of GDP and has been linked to a more stable economic environment, identified by smaller shocks and more effective policy, and a diverse set of innovations related to inventory management as well as financial markets. We document a negative relation between the volatility of GDP and some of its components and one such financial development: the emergence of mortgage-backed securities. We also document that this relationship changed sign, from negative to positive, in the early 2000’s. ∗We wish to thank without implicating Sean Campbell, Steve Fazzari, Michael Gordy, James Kennedy, James Morley, Bruce Petersen, Jeremy Piger, Todd Prono, Frank Schorfheide, Tara Sinclair, and seminar participants at the Board of Governors and Midwest Macroeconomics Meetings for constructive comments. We also would like to thank Leah Brooks and Jane Dokko for their help with data. Katherine Hamilton, Matt Hayward, Bobak Moallemi, Waldo Ojeda, and Ran Tao provided excellent research assistance. All errors are our own. Any views are of the authors alone and do not represent the views of the Board of Governors of the Federal Reserve System. †Board of Governors of the Federal Reserve System and Washington University in Saint Louis, gaetano@wustl.edu ‡Board of Governors of the Federal Reserve System, celso.brunetti@frb.gov 1

1 Introduction The volatility of aggregate economic activity in the United States decreased in the mid eighties. The consensus date for a significant decrease, termed The Great Moderation by Stock and Watson (2003), is the last quarter of 1984. Three broad reasons have been suggested to explain this phenomenon: a structural change in the economy, an improvement in the implementation of economic policy, especially monetary policy, and a lucky draw in the sequence of random shocks that affect the economy. These explanations are not mutually exclusive, and can well interact with one another. A challenge has been to identify more precisely which channels of transmission from shocks to economic activity have been affected and how. Among the channels that have received much attention are monetary policy, technological change and especially inventory management, financial markets development, and international integration. Again, focusing on one aspect is dictated by convenience at some level; the idea that the decrease in volatility is diffuse across several components and therefore is not likely to be completely explained by one event is clearly expressed by Kim, Nelson and Piger (2004) and Stock and Watson (2003), among others. We establish a link between a particular form of financial market development, the process of securitization of mortgage debt, and real economic activity. There are several reasons to focus on such an aspect of the evolution of financial markets over the last thirty to forty years. First, mortgage backed securities (MBS) markets were small as a fraction of GDP in the late seventies, but have become enormous in present days, and the timing of the market development is consistent with the timing of the Great Moderation. By the early 2000’s, about sixty percent of household mortgages had been securitized. Because household mortgage debt is almost the size of GDP, the mortgage-backed securities market grew from a relatively small fraction to over half of GDP in about twenty years. It is therefore an interesting question to document whether real effects are detectable in aggregate real variables. Second, mortgage backed securities have a direct link to an important household decision, the purchase of a house, and lenders’ decisions to finance the purchase. Thus, the evidence that we document points (indirectly) to the possibility that the availability of risk diversification through mortgage pools generated a smoother allocation of credit and thereby acted as a coordination mechanism for the supply side as well. This channel of transmission does not rely on or require that financial innovation be related to the quantity of credit available or to the relaxation of credit constraints. Third, mortgage backed securities allow for the diversification of different kinds of risks, in particular interest rate risk and credit risk. The credit risk or counterparty risk inherent in mortgage loans has been historically relatively 2

low, in part because of the collateral and the fractional support of the house purchase, in part because the amount of counterparty risk is to a large extent under the control of the lender. Interest rate risk, on the other hand, is largely aggregate in nature, and not easily diversifiable by the lender. Diversification of prepayment risk is, initially, the main purpose of the creation of pools. The idea that both credit risk and interest rate risk are pooled in mortgage backed securities is important, because when one considers the potential effects of introducing a market for financial derivatives that create risk-diversification possibilities that were previously unavailable, there are at least two effects to consider. The diversification of prepayment risk could increase the resilience of intermediaries to shocks, but also increase the amount of counterparty risk that they are willing to undertake. Indeed, one of the hypothesis that we consider is that in the aggregate mortgage backed securities were associated with a decrease in aggregate volatility until about 2000, but that in the last part of the sample the relation changed sign and higher volatility is related to the growth of mortgage securities markets. A corollary of this hypothesis is that even if financial market developments contributed to the Great Moderation, their contribution could have been temporary, to the point of not only fading away over time but change direction. In light of the recent history, focusing on a transmission mechanism that highlights the potential temporary nature of changes in volatility seems particularly relevant. Finally, the structure of the mortgage pools market, which was completely dominated by agency and government sponsored enterprises until the early to mid nineties, allows us to test whether pools issued by government sponsored enterprises and private intermediaries were linked in different ways to aggregate economic activity. We study the empirical relation between the volatility of economic activity and MBS markets between 1976 and 2011 using quarterly observations on GDP and some of its components and quarterly observations on MBS issued by government sponsored enterprises (GSE’s) and private intermediaries. In particular, we construct various measures of volatility for the growth rates of real GDP, consumption, housing consumption, residential investment, and investment in single housing, and then examine the empirical relation between real and financial variables with two statistical models: a linear autoregressive model first and non-linear, Markov switching model next. Empirical evidence is supportive of a negative relationship between issuance of mortgage-backed securities and the volatility of real activity in the first part of the sample, between the mid seventies and roughly 2000; in the second part of the sample the relationship is to some extent reversed, and volatility in real economy growth is positively related to volumes in MBS markets. 3

2 Related Literature TheGreatModerationwasidentifiedbyasetofpapersbyKimandNelson(1999),McConnell and Perez-Quiros (2000), and Blanchard and Simon (2001); Stock and Watson (2003) provide a comprehensive review of this large literature and analysis of the phenomenon.1 These papers document a break in volatility in the mid eighties, and attribute it to smaller shocks, better implementation of monetary policy, and structural changes in the economy, especially related to technology and financial-market innovation. A particular aspect, for example stressed by Blanchard and Simon (2001), and Bernanke (2004), is the role played by a decrease in the variability of inflation during the Great Moderation, thus establishing a strong link between aggregate volatility monetary policy implementation. Financial-market development is discussed by Dynan, Elmendorf, and Sichel (2005); although they do not consider a specific form of financial innovation, they conclude that financial market developments played an important role in the Great Moderation. A type of analysis closer in spirit to ours, in the sense that it attempts to link the Moderation mainly to a single economic factor, is Kahn, McConnell and Perez-Quiros (2002). They analyze the role of inventories, and point to the technological innovations that allowed for a structural change in inventory management. Blanchard and Simon (2001) already note a reversion in the correlation between inventories and sales in the nineties; Kahn et al. (2002) go on to notice that much of the Great Moderation can be explained by a reduction in the variability in the production of durable goods, and that this reduction is not accompanied by a reduction in the volatility of sales of durable goods. A follow-up paper, Ramey and Vine (2003), however, points out that for the case of the auto industry, the explanation of the decrease in industry-output volatility is due to a structural change of the sale process rather than technical changes in inventory or production management. These ideas are in a way similar to and consistent with our approach: there is a structural change in the way a market works that leads to decreased volatility, and this change can be traced to more than one factor; we just use financial markets instead of durable goods markets. Therearetworecentpapersthataredirectlylinkedtoouranalysis. ThefirstisDenHaan and Sterk (2010) which looks at a specific consequence of financial innovation, the reduction in credit constraints. Although they conclude that the alleviation of credit constraints does not seem to be correlated with reduction in volatility of real economic activity, Den Haan and Sterk (2010) find that the shift in who holds the economy’s mortgage debt, from banks 1There is an earlier literature documenting the lower volatility of economic activity after second world war that is not the focus of our analysis - see for example Diebold and Rudebusch (1992). 4

to other institutions, does seem to play an important role. Of course, the shift was a consequence of the securitization process of mortgages. The second paper is Bezemer and Grydaki (2012) who show with a multivariate GARCH approach that mortgage lending played an important role in the Great Moderation. Finally, two papers analyze the role of investment. Justiniano and Primiceri (2008) point to investment as the main variable whose change can explain the moderation in the volatility of aggregate output. Peek and Wilcox (2006), with a different methodology, consider residential investment and mortgage pools and find that securitization played an important role in the reduction of the volatility of residential investment. The important message that emerges from these papers is that to see reduction in the volatility of output it is also essential to see reduction in the volatility of investment, not surprisingly, and that this reduction can be brought about indirectly, and not necessarily through direct shocks. The change in volatility, in other words, is diffuse and systemic. 3 Descriptive Statistics We use five series from the National Income and Product Accounts (NIPA) to measure the change in volatility of economic activity. These are quarterly observations on the seasonal adjusted annual growth rates of real gross domestic product, real personal consumption, real consumptionofhousingservices, realresidentialinvestment, andrealsinglefamilyresidential investment. The full sample under consideration goes from the first quarter of 1974 to the second quarter of 2011.2 We employ personal housing consumption and investment in single-family homes in addition to aggregate variables because these variables correspond more closely to the financial derivatives that we consider. Specifically, we consider mortgagebackedsecuritiesissuedbygovernment-sponsoredenterprisesandoverthefullsampleperiod, and mortgage-backed securities issued by private conduits from the fourth quarter of 1984 to the end of our sample. Observations about mortgage pools come from the Flow of Funds of the United States. We consider only mortgage pools composed of single-family mortgages. This is by far the biggest component in the mortgage pools, much larger than multifamily and commercial pools(whichareofcoursenotheldbygovernment-sponsoredenterprises)andistheaggregate for which most consistent observations are available throughout the sample. 2Note that because volatility measures have been constructed with lags between 10 and 20 quarters, the actual sample starts in 1969, first quarter. 5

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of the rolling standard deviation of a series using a twenty-quarter window (SD ). This y,t is the measure used, for example, by Blanchard and Simon (2001) and Stock and Watson (2003). We then compute two realized volatility measures. Denote g the growth rate of y,t variable y, we first run the following regression g = α +α g +η (1) y,t 0,y 1,y y,t−1 y,t and then consider the absolute value of the residuals to compute realized volatilities (cid:32) (cid:33) J (cid:88) RVJ = log | η | . (2) y,t y,t−j j=1 Here J indicates the number of lags of absolute residuals that are used in the computation of realized volatility;3 we compute two measures of realized volatility for J = 10,and J = 20. The final measure of volatility that we use is an AR(1)-GARCH(1,1) specification4: g = γ +γ g +η y,t 0,y 1,y y,t−1 y,t (3) h2 | Ω = ω +ω η2 +ω h2 y,t t−1 0,y 1,y y,t−1 2,y y,t−1 where Ω represents the information available at time t−1 and η = h (cid:15) where (cid:15) ∼ t−1 y,t y,t y,t y,t N (0,1). The first three volatility measures (SD , RV10 and RV20) are non-parametric y,t y,t y,t while the fourth measure (h2 ) is parametric. y,t Figures 3 to 7 give a visual representation of the different volatility measures for each of the variables in the NIPA accounts used in the paper: the deseasonalized real growth rates GDP, consumption, consumption of housing services, residential investment, and investment in single housing. The graphs are similar to others in this literature (see for example Blanchard and Simon, 2001), and it is clearly visible a drop in volatility of GDP growth starting in 1984. It is also noticeable that volatility picks up, though at a reduced rate from a historic point of view, after 2000. Note that the pattern of GDP is repeated by the two residential investment measures employed, whereas consumption measure are historically much more stable, and show correspondingly a lower change in volatility both in 1984 and 2000 relative to GDP. It is also interesting to note the different magnitudes and variabilities of the volatility estimates. GDP volatility ranges between 1.4 and 7.2 percent across the different 3See Bansal, Khatchatrian and Yaron (2002) for details. 4See Bansal, Khatchatrian and Yaron (2002) for details. 8

(cid:10) (cid:11)(cid:12)(cid:13)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20) (cid:9) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:17)(cid:27)(cid:28)(cid:12)(cid:15)(cid:16)(cid:29) (cid:8) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:17)(cid:27)(cid:18)(cid:30)(cid:12)(cid:31)(cid:19)(cid:29) !(cid:11)"#(cid:17)(cid:27)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:29) (cid:7) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1) (cid:2)(cid:10)(cid:8)(cid:5) (cid:2)(cid:10)(cid:8)(cid:7) (cid:2)(cid:10)(cid:8)(cid:9) (cid:2)(cid:10)(cid:9)(cid:1) (cid:2)(cid:10)(cid:9)(cid:3) (cid:2)(cid:10)(cid:9)(cid:5) (cid:2)(cid:10)(cid:9)(cid:7) (cid:2)(cid:10)(cid:9)(cid:9) (cid:2)(cid:10)(cid:10)(cid:1) (cid:2)(cid:10)(cid:10)(cid:3) (cid:2)(cid:10)(cid:10)(cid:5) (cid:2)(cid:10)(cid:10)(cid:7) (cid:2)(cid:10)(cid:10)(cid:9) (cid:3)(cid:1)(cid:1)(cid:1) (cid:3)(cid:1)(cid:1)(cid:3) (cid:3)(cid:1)(cid:1)(cid:5) (cid:3)(cid:1)(cid:1)(cid:7) (cid:3)(cid:1)(cid:1)(cid:9) (cid:3)(cid:1)(cid:2)(cid:1) Figure 3: GDP Growth Volatility (%) measures5; consumption volatility, for both consumption and consumption of housing services, is lower and ranges between 1.1 and 5.4 percent. Real residential investment and real investment in single housing exhibit a much higher variability (between 3 and 114 percent) indicating that the volatility of these variables is itself very volatile. The next step that we perform is to formally investigate the empirical relationships between the volatility of real variables and mortgage-backed securities. 4 Empirical Analysis and Results We analyze the relationship between the volatility of real variables and mortgage-backed securities with two empirical approaches. First, we estimate a linear model where we regress the different volatility measures of real variables described above, on mortgage-backed security variables (MBS and ABS). Here we assume that the sample period is divided in two sub-periods. For GSE securities, the first sub-sample runs from 1974-Q1 to 2003-Q4 and the second from 1999-Q1 to 2011-Q2. For ABS, the first sub-sample starts in 1984-Q4, and before that the size of the market is negligible. The two sub-samples correspond to a decline 5Detailed summary statistics are reported in Table 7 in the Appendix. 9

(cid:8) (cid:11)(cid:12)(cid:13)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:17)(cid:27)(cid:28)(cid:12)(cid:15)(cid:16)(cid:29) (cid:7) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:17)(cid:27)(cid:18)(cid:30)(cid:12)(cid:31)(cid:19)(cid:29) (cid:6) !(cid:11)"#(cid:17)(cid:27)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:29) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1) (cid:2)(cid:9)(cid:8)(cid:5) (cid:2)(cid:9)(cid:8)(cid:7) (cid:2)(cid:9)(cid:8)(cid:10) (cid:2)(cid:9)(cid:10)(cid:1) (cid:2)(cid:9)(cid:10)(cid:3) (cid:2)(cid:9)(cid:10)(cid:5) (cid:2)(cid:9)(cid:10)(cid:7) (cid:2)(cid:9)(cid:10)(cid:10) (cid:2)(cid:9)(cid:9)(cid:1) (cid:2)(cid:9)(cid:9)(cid:3) (cid:2)(cid:9)(cid:9)(cid:5) (cid:2)(cid:9)(cid:9)(cid:7) (cid:2)(cid:9)(cid:9)(cid:10) (cid:3)(cid:1)(cid:1)(cid:1) (cid:3)(cid:1)(cid:1)(cid:3) (cid:3)(cid:1)(cid:1)(cid:5) (cid:3)(cid:1)(cid:1)(cid:7) (cid:3)(cid:1)(cid:1)(cid:10) (cid:3)(cid:1)(cid:2)(cid:1) Figure 4: Real Consumption Growth Volatility (%) (cid:8) (cid:11)(cid:12)(cid:13)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20) (cid:27)(cid:28)(cid:12)(cid:15)(cid:16)(cid:29) (cid:7) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20) (cid:27)(cid:18)(cid:30)(cid:12)(cid:31)(cid:19)(cid:29) !(cid:11)"#(cid:17)(cid:27)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:29) (cid:6) (cid:5) (cid:4) (cid:3) (cid:2) (cid:1) (cid:2)(cid:9)(cid:8)(cid:5) (cid:2)(cid:9)(cid:8)(cid:7) (cid:2)(cid:9)(cid:8)(cid:10) (cid:2)(cid:9)(cid:10)(cid:1) (cid:2)(cid:9)(cid:10)(cid:3) (cid:2)(cid:9)(cid:10)(cid:5) (cid:2)(cid:9)(cid:10)(cid:7) (cid:2)(cid:9)(cid:10)(cid:10) (cid:2)(cid:9)(cid:9)(cid:1) (cid:2)(cid:9)(cid:9)(cid:3) (cid:2)(cid:9)(cid:9)(cid:5) (cid:2)(cid:9)(cid:9)(cid:7) (cid:2)(cid:9)(cid:9)(cid:10) (cid:3)(cid:1)(cid:1)(cid:1) (cid:3)(cid:1)(cid:1)(cid:3) (cid:3)(cid:1)(cid:1)(cid:5) (cid:3)(cid:1)(cid:1)(cid:7) (cid:3)(cid:1)(cid:1)(cid:10) (cid:3)(cid:1)(cid:2)(cid:1) Figure 5: Real Consumption of Housing Services Growth Volatility (%) 10

(cid:2)(cid:1) (cid:6)(cid:2) (cid:11)(cid:12)(cid:13)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20) (cid:6)(cid:1) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:17)(cid:27)(cid:28)(cid:12)(cid:15)(cid:16)(cid:29) (cid:5)(cid:2) (cid:11)(cid:22)(cid:24)(cid:13)(cid:14)(cid:25)(cid:22)(cid:26)(cid:17)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:17)(cid:27)(cid:18)(cid:30)(cid:12)(cid:31)(cid:19)(cid:29) (cid:5)(cid:1) !(cid:11)"#(cid:17)(cid:27)(cid:18)(cid:19)(cid:20)(cid:17)(cid:21)(cid:22)(cid:23)(cid:20)(cid:29) (cid:4)(cid:2) (cid:4)(cid:1) (cid:3)(cid:2) (cid:3)(cid:1) (cid:2) (cid:1) (cid:3)(cid:7)(cid:8)(cid:6) (cid:3)(cid:7)(cid:8)(cid:9) (cid:3)(cid:7)(cid:8)(cid:10) (cid:3)(cid:7)(cid:10)(cid:1) (cid:3)(cid:7)(cid:10)(cid:4) (cid:3)(cid:7)(cid:10)(cid:6) (cid:3)(cid:7)(cid:10)(cid:9) (cid:3)(cid:7)(cid:10)(cid:10) (cid:3)(cid:7)(cid:7)(cid:1) (cid:3)(cid:7)(cid:7)(cid:4) (cid:3)(cid:7)(cid:7)(cid:6) (cid:3)(cid:7)(cid:7)(cid:9) (cid:3)(cid:7)(cid:7)(cid:10) (cid:4)(cid:1)(cid:1)(cid:1) (cid:4)(cid:1)(cid:1)(cid:4) (cid:4)(cid:1)(cid:1)(cid:6) (cid:4)(cid:1)(cid:1)(cid:9) (cid:4)(cid:1)(cid:1)(cid:10) (cid:4)(cid:1)(cid:3)(cid:1) Figure 6: Real Residential Investment Growth Volatility (%) (cid:3)(cid:4)(cid:1) (cid:4)(cid:2) (cid:3)(cid:1)(cid:1) (cid:4)(cid:1) (cid:7)(cid:1) (cid:3)(cid:2) (cid:6)(cid:1) (cid:3)(cid:1) (cid:5)(cid:1) (cid:2) (cid:4)(cid:1) (cid:1) (cid:1) (cid:3)(cid:8)(cid:9)(cid:5) (cid:3)(cid:8)(cid:9)(cid:6) (cid:3)(cid:8)(cid:9)(cid:7) (cid:3)(cid:8)(cid:7)(cid:1) (cid:3)(cid:8)(cid:7)(cid:4) (cid:3)(cid:8)(cid:7)(cid:5) (cid:3)(cid:8)(cid:7)(cid:6) (cid:3)(cid:8)(cid:7)(cid:7) (cid:3)(cid:8)(cid:8)(cid:1) (cid:3)(cid:8)(cid:8)(cid:4) (cid:3)(cid:8)(cid:8)(cid:5) (cid:3)(cid:8)(cid:8)(cid:6) (cid:3)(cid:8)(cid:8)(cid:7) (cid:4)(cid:1)(cid:1)(cid:1) (cid:4)(cid:1)(cid:1)(cid:4) (cid:4)(cid:1)(cid:1)(cid:5) (cid:4)(cid:1)(cid:1)(cid:6) (cid:4)(cid:1)(cid:1)(cid:7) (cid:4)(cid:1)(cid:3)(cid:1) (cid:22)(cid:21)(cid:1)(cid:20)(cid:19)(cid:8)(cid:7)(cid:13)(cid:3)(cid:8)(cid:16)(cid:18)(cid:2)(cid:17)(cid:8)(cid:16)(cid:11)(cid:15)(cid:8)(cid:14)(cid:13)(cid:5)(cid:4)(cid:4)(cid:10)(cid:1) (cid:12)(cid:11)(cid:5)(cid:4)(cid:5)(cid:11)(cid:3)(cid:4)(cid:10)(cid:9)(cid:8)(cid:7)(cid:2)(cid:6)(cid:5)(cid:4)(cid:3)(cid:2)(cid:1) (cid:10)(cid:11)(cid:12)(cid:12)(cid:13)(cid:14)(cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:16)(cid:20)(cid:21)(cid:22)(cid:19) (cid:23)(cid:24)(cid:10)(cid:25)(cid:26)(cid:16)(cid:27)(cid:17)(cid:18)(cid:19)(cid:16)(cid:20)(cid:21)(cid:22)(cid:19)(cid:28) (cid:10)(cid:21)(cid:29)(cid:12)(cid:13)(cid:30)(cid:21)(cid:31)(cid:16)(cid:17)(cid:18)(cid:19)(cid:16)(cid:20)(cid:21)(cid:22)(cid:19)(cid:16)(cid:27) (cid:11)(cid:14)(cid:15)(cid:28) (cid:10)(cid:21)(cid:29)(cid:12)(cid:13)(cid:30)(cid:21)(cid:31)(cid:16)(cid:17)(cid:18)(cid:19)(cid:16)(cid:20)(cid:21)(cid:22)(cid:19)(cid:16)(cid:27)(cid:17)!(cid:11)"(cid:18)(cid:28) Figure 7: Real Investment in Single Housing Growth Volatility (%) 11

and to an increase in the volatility of the macro variables considered.6 In the first sub-period we expect to find a negative relationship between real variables and mortgage-backed securities - i.e. MBS should reduce the volatility of real variables; in the second sub-period we expect mortgage-backed securities to increase volatility levels of real variables. For the linear approach, we need to make sure that our variables are stationary. 7We, therefore, perform four stationarity tests, the generalized least squares Dickey–Fuller (DF) testproposedbyElliott, Rothenberg, andStock(1996), theAugmentedDickey-Fuller(ADF) test, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) test, and the Phillips-Perron (PP) test, for each variable and each sub-sample. The results are displayed in Table 11 in the Appendix. Stationarity is often a philosophical issue more than a substantive one and it strongly depends on the selected sample. We consider a variable to be stationary - i.e. I(0) if at least two out of the four tests indicate that the variable is stationary (either by rejecting the null of non-stationarity, as for the DF, ADF and PP tests, or by failing to reject the null of stationarity, as in the KPSS test). Our data run over a relatively short time period (GSE emerged in the second half of the ’80s). Therefore, we are generous with our critical values which we set at twenty percent level. In a second approach, we postulate a non-linear relationship and estimate a Markovswitching model in which we assume that there are two possible regimes: one in which real variablesarecharacterizedbyhighvolatilityandoneinwhichrealvariablesarecharacterized by low volatility. We first estimate transition probabilities assuming that they are constant. Then, we estimate the model allowing the transition probabilities to be time varying as function of mortgage-backed securities. Stabilizing effects consist of increasing the probability of transitioning in the low-volatility state and/or decreasing the probability of leaving it. A change in transition probabilities with different sign would denote a destabilizing effect. In what follows we describe the linear and non-linear model and discuss the estimation results. 4.1 Linear Model We estimate the following equation for each variable that survives the stationarity tests: Vol = β +β Vol +β x +(cid:15) , (4) y,t 0 1 y,t−1 2 r,t−n t 6We also consider different sub-sample definitions. Our main results are not affected by the definition of the sub-samples. 7Standardtestsforcointegrationindicatethatthereisnoevidenceofcointegratingrelationshipsbetween the volatility of real variables and mortgage-backed security variables. 12

where Vol represents one of the volatilities: SD (rolling standard deviation), RV10 (rey,t y,t y,t alized volatility with ten lags), RV20 (realized volatility with 20 lags), and h2 (GARCH y,t y,t volatility);8 y refers to the real variables: GDP, consumption, consumption of housing services, residential investment and investment in single housing; and x represents the r,t−n nth-lag of the first difference of a measure of mortgage-backed securities outstanding, either issued by GSE’s or private conduits (ABS). We normalize GSE and ABS alternatively by the totalsingle-familymortgagedebtoutstanding(GSEM andABSM)andbytheaveragehouse price (GSEH and ABSH).9 We let the lag of the explanatory variable, measured in quarters, to be determined by best fit, so potentially this is different across different combinations of variables.10 Tables 1 - 5 display the results (missing estimated parameters indicate that at least one of the variable is not stationary).11 Table 1 shows that, in the first sub-period (1974- 2003), GSE is reducing the volatility of GDP. ABS, in the second sub-period (1984 - 2003) also reduces GDP volatility levels. In the third sub-period, both GSE and ABS increase GDP volatility.These results are confirmed by Table 2, which refers to the volatility of real consumption. In Tables 1 and 2, the estimated parameters are strongly significant and have negative signs in the first two sub-periods and positive signs in the last sub-period. We interpret the difference in lag-length as a statistical artifact. In fact, we report results for the optimal lag. Our main findings, however, hold for a range of lag-lengths. Table 3 reports the results for the volatility of Real Consumption of Housing Services. In sub-periods one and two, GSE and ABS reduce volatility levels. In the third sub-period, however, ABS is increasingvolatility,asexpected,whileGSEisdecreasingvolatility. Althoughthisresultmay seem counter intuitive, it can be explained by the behavior of housing consumption. In fact, how we shall see in the next sub-section, low activity in the housing market is concentrated during recessions and, consequently, the volatility of housing consumption behaves inversely withrespecttothevolatilityoftheotherrealvariablesweconsider. Table4showsestimation results for the volatility of Real Residential Investment. GSE always reduces volatility, while ABS isonly marginally significant. Finally, Table 5shows estimationresults for thevolatility 8Alternatively, when we add x directly in the conditional variance equation of the GARCH model, r,t−n the results are qualitatively similar to those reported below. 9We also control for the effect of interest rate but it is never significant. 10An alternative approach to deal with stationarity issues is to use filtering procedures (e.g., Hodrick- Prescott). All dependent variables in equation (4) are estimates of second moments and the use of filtering techniques for higher moments might be challenging. 11Given the persistency of the observations, we bootstrap standard errors. As a robustness check, we also computed robust standard errors, and the results hold. 13

of Single-Housing Investment. GSE and ABS reduce volatility in the first two sub-periods and increase volatility in the last sub-period. Overall, our linear estimates confirm that MBS reduce volatility of real variables in the first two sub-periods and increased the same volatility in the latest period when the recent sub-prime crisis hit the economy.12 4.2 Non-Linear Model We now take a different approach, and instead of postulating the presence of different subperiodsweestimatearegime-switchingmodelovertheentiresample. Theassumptioninthis case is that the process described by the dependent variable can shift between two regimes, one of high and one of low volatility, and that the process followed by the two regimes evolves according to a two-state first-order Markov process. The advantage of this approach is that, unlike the previous case, we need not be concerned with stationarity issues and do not have to partition exogenously the whole sample period in sub-samples. The disadvantage is that we have to estimate a much larger number of parameters. The specific equation that we estimate is given by g = µ +(cid:15) . y,t i,y y,t Here (cid:15) ∼ N (0,σ ) where i represent the state s(i) . We assume that transition probabiliyt i,y t ties evolve according to a probit model p(s = i | s = j) = Φ(z ) t t−1 t where Φ is the standard normal distribution. Here z = a + bx + δ where the error t r,t−n t term δ is normally distributed and orthogonal to (cid:15) . The meaning of the explanatory t y,t variable x is the same discussed in the previous section: it represents the nth-lag of r,t−n a measure of mortgage-backed securities outstanding, either issued by GSE’s or private conduits (GSEM, GSEH, ABSM and ABSH), and the lag is determined optimally by best fit. Estimation is by maximum likelihood using the EM algorithm by Hamilton (1994). Tables 6-10 show the results. The first column of each table reports estimation results for the model with constant transition probabilities. Table 6 refers to GDP estimates. The highvolatility state (σ = 5.022) is characterized by a low growth rate, whereas the low-volatility 0 state (σ = 1.683) is characterized by a higher growth rate. The low-volatility regime is 1 12We also performed the same estimates using the real mortgage interest rate as a control variable, and found that it was never statistically significant. 14

Volatility Indep. Var. Coeff. St.Err. Lag R2 Sub-Period 1: 1974 - 2003 h2 GSEH −0.242∗∗ 0.130 -2 0.825 h2 GSEM −2.816∗ 2.137 -2 0.822 Sub-Period 2: 1984 - 2003 SD ABSH 0.305∗∗∗ 0.153 -1 0.970 RV20 ABSH −0.140∗ 0.092 -6 0.841 RV10 ABSH −0.340∗∗∗ 0.149 -2 0.735 h2 ABSH −0.450∗∗ 0.243 -1 0.718 SD ABSM 5.671 4.631 -1 0.970 RV20 ABSM −4.704∗∗∗ 1.993 -5 0.847 RV10 ABSM −5.543∗ 3.453 -1 0.724 h2 ABSM −10.46∗∗∗ 5.165 -3 0.718 Sub-Period 3: 1999 - 2011 RV10 GSEH 0.056∗ 0.036 -3 0.817 h2 GSEH 0.162∗∗ 0.085 -1 0.809 RV10 GSEM 0.858 1.554 -1 0.806 h2 GSEM 4.016∗ 2.917 -1 0.784 RV10 ABSH 0.103∗∗∗ 0.044 -6 0.827 h2 ABSH 0.245∗∗ 0.140 -10 0.802 RV10 ABSM 5.219∗∗∗ 1.787 -10 0.846 h2 ABSM 7.653 4.104 -10 0.799 Table 1: Linear regression results. Dependent variable: Volatility of Real GDP. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. SD, RV20, RV10 and h2 indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgage-backed securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits. 15

Volatility Indep. Var. Coeff. St.Err. Lag R2 Sub-Period 1: 1974 - 2003 h2 GSEH −0.221∗∗∗ 0.094 -10 0.653 h2 GSEM 0.727 1.386 -5 0.676 Sub-Period 2: 1984 - 2003 SD ABSH −0.124 0.101 -8 0.925 RV10 ABSH −0.417∗∗∗ 0.135 -8 0.838 h2 ABSH −0.454∗∗∗ 0.206 -8 0.596 SD ABSM −2.392 2.590 -8 0.925 RV10 ABSM −7.307∗∗∗ 2.937 -8 0.831 h2 ABSM −9.095∗∗ 5.072 -6 0.595 Sub-Period 3: 1999 - 2011 SD GSEH 0.077∗∗∗ 0.018 -2 0.953 RV10 GSEH 0.096∗∗∗ 0.015 -2 0.870 h2 GSEH 0.128∗∗∗ 0.044 -1 0.826 SD GSEM 3.029∗∗∗ 0.799 -1 0.946 RV10 GSEM 2.260∗∗∗ 0.915 -1 0.812 h2 GSEM 3.454∗∗ 1.849 -1 0.785 SD ABSH 0.095∗∗∗ 0.039 -9 0.934 RV10 ABSH 0.120∗∗∗ 0.034 -10 0.840 h2 ABSH 0.173∗∗∗ 0.079 -10 0.804 SD ABSM 3.127∗∗∗ 1.399 -10 0.932 RV10 ABSM 4.122∗∗∗ 1.050 -10 0.844 h2 ABSM 5.158∗∗∗ 2.376 -10 0.797 Table 2: Linear regression results. Dependent variable: Volatility of Real Consumption. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. SD, RV20, RV10 and h2 indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgage-backed securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits. 16

Volatility Indep. Var. Coeff. St.Err. Lag R2 Sub-Period 1: 1974 - 2003 RV20 GSEH −0.072∗∗∗ 0.027 -9 0.838 RV10 GSEH −0.092∗∗∗ 0.035 -7 0.772 h2 GSEH −0.048∗∗∗ 0.022 -4 0.387 RV20 GSEM −1.527∗∗∗ 0.616 -5 0.835 RV10 GSEM −1.830∗∗ 0.936 -4 0.765 h2 GSEM −0.461 0.450 -3 0.375 Sub-Period 2: 1984 - 2003 RV20 ABSH −0.167∗∗ 0.100 -10 0.831 RV10 ABSH −0.189∗∗ 0.112 -6 0.783 h2 ABSH −0.127∗ 0.083 -7 0.431 RV20 ABSM −3.855∗∗∗ 1.819 -10 0.833 RV10 ABSM −3.946∗∗ 2.201 -6 0.782 h2 ABSM −2.682∗ 1.633 -7 0.430 Sub-Period 3: 1999 - 2011 SD GSEH −0.034∗∗∗ 0.011 -9 0.821 RV20 GSEH −0.014∗ 0.009 -5 0.811 RV10 GSEH −0.024∗∗ 0.014 -5 0.701 h2 GSEH −0.013∗∗ 0.007 -6 0.154 SD GSEM −1.670∗∗∗ 0.487 -9 0.830 RV20 GSEM −0.711∗ 0.458 -9 0.815 RV10 GSEM −0.951∗ 0.596 -7 0.699 h2 GSEM −0.538 0.554 -9 0.138 SD ABSH 0.084∗∗∗ 0.021 -9 0.835 RV20 ABSH 0.024∗ 0.016 -6 0.813 RV10 ABSH 0.037∗∗ 0.019 -2 0.703 h2 ABSH 0.016 0.014 -3 0.134 SD ABSM 3.169∗∗∗ 0.673 -10 0.846 RV20 ABSM 0.849∗ 0.536 -4 0.814 RV10 ABSM 1.074∗ 0.651 -4 0.696 h2 ABSM 0.622 0.571 -6 0.134 Table 3: Linear regression results. Dependent variable: Volatility of Real Consumption of Housing Services. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. SD, RV20, RV10 and h2 indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgage-backed securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits. 17

Volatility Indep. Var. Coeff. St.Err. Lag R2 Sub-Period 1: 1974 - 2003 h2 GSEH −1.779∗∗∗ 0.797 -7 0.859 h2 GSEM −28.64∗∗∗ 12.61 -6 0.857 Sub-Period 2: 1984 - 2003 SD ABSH 2.714∗ 1.373 -5 0.979 RV10 ABSH 0.011 0.126 -1 0.847 h2 ABSH −0.658 1.206 -1 0.781 SD ABSM 78.50∗∗∗ 36.03 -5 0.980 RV10 ABSM 5.658∗ 3.506 -4 0.852 h2 ABSM −13.79 29.23 -2 1.388 Table 4: Linear regression results. Dependent variable: Volatility of Real Residential Investment. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. SD, RV20, RV10 and h2 indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgage-backed securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits. 18

Volatility Indep. Var. Coeff. St.Err. Lag R2 Sub-Period 1: 1974 - 2003 RV20 GSEH −0.060∗∗∗ 0.030 -9 0.956 RV10 GSEH −0.087∗∗∗ 0.042 -7 0.930 h2 GSEH −5.436∗∗∗ 2.604 -8 0.472 RV20 GSEM −1.700∗∗ 0.989 -10 0.956 RV10 GSEM −2.887∗∗∗ 1.365 -7 0.933 h2 GSEM −72.79∗∗∗ 37.29 -8 0.462 Sub-Period 2: 1984 - 2003 SD ABSH 4.503∗∗ 2.727 -5 0.975 RV20 ABSH −0.187∗∗ 0.095 -4 0.918 RV10 ABSH 0.119 0.119 -10 0.855 h2 ABSH −4.697∗ 3.587 -4 0.444 SD ABSM 133.6∗ 70.58 -5 0.976 RV20 ABSM −7.324∗∗∗ 2.787 -4 0.923 RV10 ABSM −4.277∗ 3.152 -1 0.856 h2 ABSM −114.1∗ 87.71 -4 0.445 Sub-Period 3: 1999 - 2011 h2 GSEH 5.796∗∗ 3.355 -3 0.435 h2 GSEM 160.3∗∗∗ 74.00 -1 0.361 h2 ABSH 3.803∗ 2.276 -7 0.308 h2 ABSM −177.3∗ 105.8 -1 0.337 Table 5: Linear regression results. Dependent variable: Volatility of Real Single-Housing Investment. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. SD, RV20, RV10 and h2 indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgage-backed securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits. 19

more persistent than the high-volatility regime.13 The graphs of the transition probabilities are reported in the Appendix. When we introduce explanatory variables in the transition probabilities we allow those probabilities to change over time. GSE’s securities, both as a fraction of total mortgage lending and normalized by house prices, has a significant negative coefficient in the p(s = 0 | s = 0), i.e. the probability of remaining in the high-volatility t t−1 state decreases with the introduction of securitized mortgages. The opposite result holds for ABS normalized by mortgage debt outstanding. As expected, Log-likelihood values improve when we introduce an additional explanatory variable in the transition probabilities. Table 7 reports results for real consumption. In this case the low-volatility state is much more persistent (see Figure 9). The probability of remaining in the low-volatility state increases with GSE’s securities, and decreases with ABS. Similarly to the GDP results, GSE’s are stabilizing whereas ABS are destabilizing. Table 8 refers to consumption of housing services. Contrary to the other models, the high-volatility regime (σ = 2.445) is characterized by 0 high growth (µ = 2.926), whereas the low-volatility regime (σ = 1.278) is accompanied 0 1 by a low growth rate (µ = 0.754). A possible reason is that low activity in the housing 1 market is concentrated during recessions (see Figure 10 in the Appendix). GSE’s increase the probability of staying in the state with high growth while ABS reduce that probability. Interestingly, GSE’s also increase the probability of remaining in the low-volatility state. Tables 9 and 10 concern respectively residential investment and investment in single housing, which are among of the most volatile aggregate in the National Income Accounts. For both aggregates results are consistent: the introduction of mortgage backed securities issued by GSE’s tends to decrease the probability of remaining in the high-volatility state and increase the probability of leaving the high volatility state, whereas the opposite is true for securities issued by private conduits. An important remark refers to the combined evidence from the linear and non-linear models. As the sign change the coefficient relating mortgage backed securities and real variables tends to be positive in the second sub-sample for all issuing institutions, it is likely that the different sign in the non-linear model between GSE’s and private conduits is due to different samples: all signs tend to be positive over the period 1999-2011 in the linear model and private conduits become a relevant fraction of the market only in the 90’s. The same phenomenon could be behind the different levels of statistical significance between GSE securities and private issuers. As in the case of the linear model, estimates are broadly consistent across models. (Time lags are also in line between the linear and non-linear specifications.) Moreover, again like 13These results are in line with the literature, see for example Yang (2012). 20

GSEH (2) GSEM (4) ABSH (4) ABSM (5) µ 1.910∗∗∗ 2.066∗∗∗ 2.142∗∗∗ 2.240∗∗∗ 2.361∗∗∗ 0 (0.689) (0.679) (0.759) (0.734) (0.696) µ 3.217∗∗∗ 3.209∗∗∗ 3.197∗∗∗ 3.179∗∗∗ 3.217∗∗∗ 1 (0.209) (0.213) (0.228) (0.212) (0.204) σ 5.022∗∗∗ 5.000∗∗∗ 5.134∗∗∗ 5.117∗∗∗ 4.962∗∗∗ 0 (0.556) (0.544) (0.566) (0.624) (0.555) σ 1.683∗∗∗ 1.693∗∗∗ 1.889∗∗∗ 1.721∗∗∗ 1.666∗∗∗ 1 (0.185) (0.233) (0.197) (0.219) (0.168) TVP0 constant 1.269∗∗∗ 1.490∗∗∗ 2.143∗∗∗ 1.550∗∗∗ 1.633∗∗∗ (0.305) (0.324) (0.769) (0.507) (0.440) TVP0 expl. var. −0.307∗ −1.042∗∗ 0.823 0.803∗ (0.210) (0.611) (0.787) (0.576) TVP1 constant 1.669∗∗∗ 1.876∗∗∗ 2.137∗∗∗ 1.787∗∗∗ 1.766∗∗∗ (0.292) (0.402) (0.439) (0.388) (0.352) TVP1 expl. var. −0.378 0.175 −0.143 −0.15 (0.339) (0.322) (0.245) (0.247) Log-likelihood −2.469 −2.453 −2.444 −2.447 −2.434 Table 6: Estimation results: regime-switching model, Real GDP. in the linear model, estimates pertaining to ABS markets tend to be statistically weaker due to the smaller sample. 5 Conclusions We have shown evidence of a strong and persistent statistical link between the volatility of certain real economic aggregates and financial products that ought to be directly linked to the decision process that leads to the determination of those same variables. The intent of the approach was to “let the data speak” as much as possible. The next step is to attempt to establish a closer link between mortgage backed securities and real variables. This can be done in several ways, but two seem particularly important. One is to look at empirical evidence in a different way, and use loan-level observations in mortgage pools to understand more precisely what risks mortgage pools insured and the extent to which different risks had different emphasis over time. The other is theoretical and would attempt to measure the phenomena discussed in this paper in a general equilibrium model. With regards to the housing market, our results indicate pretty explicitly that it is important to model 21

GSEH (8) GSEM (8) ABSH (8) ABSM (8) µ −0.522 0.472 0.405 0.261 0.167 0 (1.079) (0.698) (0.763) (0.742) (0.790) µ 3.727∗∗∗ 3.781∗∗∗ 3.735∗∗∗ 3.754∗∗∗ 3.737∗∗∗ 1 (0.210) (0.199) (0.203) (0.205) (0.206) σ 3.085∗∗∗ 3.039∗∗∗ 3.172∗∗∗ 3.032∗∗∗ 3.069∗∗∗ 0 (0.475) (0.435) (0.514) (0.459) (0.490) σ 1.955∗∗∗ 1.929∗∗∗ 1.924∗∗∗ 1.940∗∗∗ 1.937∗∗∗ 1 (0.134) (0.136) (0.136) (0.136) (0.135) TVP0 constant 0.804∗∗ 1.333∗∗∗ 1.197∗∗∗ 1.781∗ 1.457∗∗ (0.418) (0.439) (0.647) (1.176) (0.829) TVP0 expl. var. −0.539 −1.945 1.541 1.023 (0.477) (2.097) (2.192) (1.324) TVP1 constant 1.799∗∗∗ 2.159∗∗∗ 1.914∗∗∗ 1.822∗∗∗ 1.843∗∗∗ (0.252) (0.443) (0.352) (0.284) (0.291) TVP1 expl. var. 0.937∗ 0.445∗ −0.411∗ −0.358 (0.600) (0.322) (0.292) (0.293) Log-likelihood −2.273 −2.241 −2.238 −2.244 −2.244 Table 7: Estimation results: regime-switching model, Real Consumption. GSEH (4) GSEM (4) ABSH (1) ABSM (1) µ 2.926∗∗∗ 2.950∗∗∗ 2.887∗∗∗ 2.947∗∗∗ 2.948∗∗∗ 0 (0.240) (0.252) (0.231) (0.235) (0.235) µ 0.754∗∗∗ 0.756∗∗∗ 0.727∗∗∗ 0.786∗∗∗ 0.829∗∗∗ 1 (0.255) (0.252) (0.238) (0.255) (0.245) σ 2.445∗∗∗ 2.425∗∗∗ 2.425∗∗∗ 2.460∗∗∗ 2.470∗∗∗ 0 (0.161) (0.169) (0.162) (0.163) (0.164) σ 1.278∗∗∗ 1.301∗∗∗ 1.270∗∗∗ 1.294∗∗∗ 1.294∗∗∗ 1 (0.178) (0.174) (0.165) (0.170) (0.166) TVP0 constant 1.970∗∗∗ 2.407∗∗∗ 2.697∗∗∗ 2.300∗∗∗ 2.262∗∗∗ (0.290) (0.593) (0.611) (0.413) (0.389) TVP0 expl. var. 1.142∗∗ 1.053∗∗∗ −0.694∗∗∗ −0.624∗∗∗ (0.612) (0.402) (0.287) (0.286) TVP1 constant 1.878∗∗∗ 1.370∗∗∗ 2.264∗∗∗ 2.124∗∗∗ 2.523∗∗ (0.584) (0.565) (0.838) (0.749) (1.407) TVP1 expl. var. 0.910∗ 0.689∗ −0.539∗ −0.898 (0.690) (0.455) (0.397) (0.755) Log-likelihood −2.246 −2.218 −2.208 −2.232 −2.234 Table8: Estimationresults: regime-switchingmodel, RealConsumptionofHousingServices. 22

GSEH (6) GSEM (5) ABSH (3) ABSM (4) µ −2.819 −1.107 −0.554 −2.057 −1.301 0 (3.634) (4.081) (3.015) (3.759) (3.703) µ 4.744∗∗∗ 4.647∗∗∗ 4.754∗∗∗ 4.769∗∗∗ 4.816∗∗∗ 1 (0.961) (0.924) (0.909) (0.963) (0.983) σ 27.97∗∗∗ 28.85∗∗∗ 27.45∗∗∗ 28.44∗∗∗ 27.92∗∗∗ 0 (2.810) (3.066) (2.619) (3.008) (2.995) σ 7.81∗∗∗ 7.819∗∗∗ 7.637∗∗∗ 7.774∗∗∗ 7.752∗∗∗ 1 (0.641) (0.628) (0.626) (0.644) (0.649) TVP0 constant 1.505∗∗∗ 1.458∗∗∗ 2.103∗∗∗ 1.650∗∗∗ 1.567∗∗∗ (0.292) (0.301) (0.607) (0.383) (0.344) TVP0 expl. var. −0.139 −0.935∗∗ 0.358 0.169 (0.185) (0.524) (0.290) (0.251) TVP1 constant 1.872∗∗∗ 2.363∗∗∗ 2.424∗∗∗ 2.038∗∗∗ 2.067∗∗∗ (0.290) (0.485) (0.548) (0.376) (0.406) TVP1 expl. var. 1.164∗∗∗ 0.691∗∗ −0.434∗ −0.444∗ (0.573) (0.381) (0.313) (0.336) Log-likelihood −4.098 −4.043 −4.047 −4.076 −4.072 Table 9: Estimation results: regime-switching model, Real Residential Investment. GSEH (7) GSEM (7) ABSH (4) ABSM (5) µ 0.043 0.702 0.706 1.387 2.008 0 (0.774) (4.209) (4.241) (6.062) (6.716) µ 4.987∗∗∗ 4.746∗∗∗ 4.584∗∗∗ 4.846∗∗∗ 4.788∗∗∗ 1 (1.289) (1.254) (1.280) (1.274) (1.295) σ 43.24∗∗∗ 47.03∗∗∗ 46.86∗∗∗ 44.86∗∗∗ 45.44∗∗∗ 0 (4.193) (5.006) (5.149) (4.559) (4.865) σ 10.75∗∗∗ 11.40∗∗∗ 11.45∗∗∗ 10.86∗∗∗ 11.03∗∗∗ 1 (0.954) (0.879) (0.884) (0.967) (1.035) TVP0 constant 1.479∗∗∗ 1.317∗∗∗ 1.748∗∗∗ 1.515∗∗∗ 1.461∗∗∗ (0.275) (0.298) (0.539) (0.315) (0.293) TVP0 expl. var. −0.538∗ −2.144∗∗ 0.328 0.223 (0.346) (1.197) (0.298) (0.288) TVP1 constant 1.821∗∗∗ 2.494∗∗∗ 2.180∗∗∗ 1.918∗∗∗ 1.926∗∗∗ (0.276) (0.589) (0.484) (0.302) (0.313) TVP1 expl. var. 1.605∗∗∗ 0.853∗∗ −0.423∗ −0.406 (0.817) (0.503) (0.322) (0.325) Log-likelihood −4.475 −4.416 −4.410 −4.451 −4.450 Table 10: Estimation results: regime-switching model, Real Single-Housing Investment. 23

the housing market and housing finance together to understand the aggregate behavior of the economy. In particular, it is important to model explicitly the behavior of financial institutions with some precision in terms of the risks that financial derivatives are meant to capture and the incentives that financial institutions face. With respect to the more general questionof thejointbehaviorofreal andfinancialvariables, ouranalysis pointstoa direction of analysis that explores financial products and the risk transfer that they operate jointly with the real variables on which they are written. References 1. Bezemer, D., and M. Grydaki, “Mortgage Lending and the Great Moderation: A Multivariate Garch Approach, Working Paper, January 2012. 2. Blanchard, O., and J. Simon, “The Long and Large Decline in U.S. Output Volatility,” Brookings Papers on Economic Activity, Vol. 2001, No. 1, 135-164. 3. Davis, S. J., and J. A. Kahn, “Interpreting the Great Moderation: Changes in the Volatility of Economic Activity at the Macro and Micro Levels,” Journal of Economic Perspectives, Vol. 22, No. 4, Fall 2008, 155-180. 4. Den Haan, W. J., and V. Sterk, “The Myth of Financial Innovation and the Great Moderation,” The Economic Journal, 2010, Vol. 121, 107-139. 5. Dynan, K., D. Elmendorf, and D. Sichel, “Can Financial Innovation Help to Explain the Reduced Volatility of Economic Activity,” Journal of Monetary Economics, 2006, 53, 123-150. 6. Kahn, J., M. McConnell, and G. Perez-Quiros, “On the Causes of the Increased Stability of the U.S. Economy,” Federal Reserve Bank of New York Economic Policy Review, 2002, 8, 183-202. 7. Kim, C., and C. Nelson, “Has The U.S. Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle,” Review of Economics and Statistics, 1999, 81, 8-16. 8. M. McConnell, and G. Perez-Quiros, “Output Fluctuations in the United States: What Has Changed since the Early 1980s?” American Economic Review, 2000, Vol. 90 No. 5, 1464-76. 24

9. Peek,J.,andJ.A.Wilcox,“Housing,CreditConstraints,andMacroStability: TheSecondary Mortgage Market and Reduced Cyclicality of Residential Investment,” American Economic Review, Vol. 96 No. 2, May 2006, 135-140. 10. Ramey, V. A., and D. J. Vine, “Tracking the Source of the Decline in GDP Volatility: An Analysis of the Automotive Industry,” Working Paper, 2004. 11. Stock, J., and M. Watson, “Has the Business Cycle Changed and Why?” National Bureau of Economic Research, Working Paper 9127, August 2002. 12. Yang, W., “ Business Cycles and Regime-Shift Risk,” mimeo 2012. 25

Appendix This appendix presents tables with summary statistics, the results of the stationarity tests, and the graphs of the (exogenous) transition probabilities estimates from the Markov switching model. Mean Median Max Min Std. Dev. Skew Kurt. GDP 3.063 3.150 16.700 −7.900 3.451 −0.081 5.143 SD (GDP) 3.330 2.578 5.697 1.424 1.408 0.229 1.374 RV20(GDP) 3.301 3.210 4.064 2.574 0.427 0.195 1.656 RV10(GDP) 2.862 2.781 3.860 2.130 0.466 0.288 1.761 h2 (GDP) 3.257 2.650 7.250 1.896 1.254 1.085 3.317 CONSUMPTION 3.322 3.550 8.800 −8.800 2.735 −1.067 6.113 SD (CONS) 2.706 2.464 4.092 1.142 0.871 0.156 1.667 RV20(CONS) 3.172 3.252 3.745 2.395 0.345 −0.391 2.378 RV10 (CONS) 2.745 2.817 3.446 1.908 0.382 −0.259 2.226 h2(CONS) 2.673 2.575 5.373 1.849 0.653 1.530 6.220 HOUS CONS 2.708 2.750 8.000 −4.500 2.435 −0.255 2.930 SD (HOUS CONS) 2.400 2.424 3.411 1.631 0.409 0.071 2.166 RV20(HOUS CONS) 3.168 3.167 3.600 2.432 0.213 −0.607 3.703 RV10(HOUS CONS) 2.744 2.741 3.242 2.021 0.267 −0.353 2.869 h2(HOUS CONS) 2.433 2.392 3.095 2.276 0.143 1.840 6.915 RESID INV 4.142 3.200 87.700 −55.900 19.316 0.869 6.768 SD (RESID INV) 17.863 14.089 34.211 4.888 9.380 0.157 1.531 RV20 (RESID INV) 4.681 4.699 5.750 3.464 0.621 −0.074 1.957 RV10 (RESID INV) 4.233 4.193 5.465 3.009 0.665 0.095 2.016 h2(RESID INV) 15.095 11.880 43.761 4.668 9.623 1.281 3.804 SING HOUS INV 6.546 4.950 153.600 −65.200 28.218 1.495 9.119 SD (SING HOUS INV) 25.822 22.082 55.336 8.301 13.723 0.570 2.392 RV20 (SING HOUS INV) 5.022 5.079 6.177 4.165 0.542 0.147 1.893 RV10 (SING HOUS INV) 4.581 4.467 5.749 3.745 0.582 0.357 1.863 h2 (SING HOUS INV) 20.626 15.109 114.006 8.930 15.391 3.032 15.287 ∆GSEH 0.456 0.371 1.487 −0.212 0.376 0.735 2.866 ∆GSEM 0.014 0.012 0.057 −0.018 0.016 0.800 3.702 ∆ABSH 0.083 0.034 0.351 −0.088 0.115 0.945 2.631 ∆ABSM 0.003 0.001 0.015 −0.006 0.005 0.964 3.278 Table 11: Summary Statistics: 1974-2003 Sub-sample (120 observations). 26

Mean Median Max Min Std. Dev. Skew Kurt. GDP 3.177 3.300 8.000 −3.500 2.157 −0.290 3.629 SD (GDP) 2.452 2.336 5.255 1.424 0.918 1.714 5.363 RV20(GDP) 3.023 2.981 3.602 2.574 0.237 0.408 2.454 RV10(GDP) 2.574 2.503 3.278 2.130 0.278 0.782 2.832 h2 (GDP) 2.489 2.346 4.012 1.896 0.466 1.394 4.458 CONSUMPTION 3.490 3.600 7.800 −3.100 2.113 −0.237 3.229 SD (CONS) 2.167 2.262 3.996 1.142 0.557 0.978 4.968 RV20(CONS) 3.004 3.005 3.487 2.395 0.297 −0.309 2.128 RV10(CONS) 2.575 2.589 3.161 1.908 0.334 −0.143 1.950 h2(CONS) 2.384 2.378 3.277 1.849 0.372 0.516 2.379 HOUS CONS 2.545 2.500 7.000 −4.500 2.228 −0.322 3.145 SD (HOUS CONS) 2.344 2.380 3.411 1.738 0.416 0.520 2.518 RV20(HOUS CONS) 3.106 3.094 3.600 2.432 0.225 −0.242 3.593 RV10(HOUS CONS) 2.677 2.666 3.242 2.021 0.276 −0.079 2.910 h2(HOUS CONS) 2.409 2.366 3.095 2.276 0.138 2.655 11.433 RESID INV 3.691 3.400 24.100 −21.800 9.601 −0.345 3.418 SD (RESID INV) 12.879 10.154 34.005 4.888 7.809 1.357 3.760 RV20 (RESID INV) 4.310 4.276 5.018 3.464 0.421 −0.173 2.045 RV10 (RESID INV) 3.843 3.840 4.691 3.009 0.435 −0.070 2.078 h2(RESID INV) 9.346 9.078 17.216 4.668 2.965 0.480 2.552 SING HOUS INV 4.857 5.400 55.700 −34.900 14.496 −0.010 4.491 SD (SING HOUS INV) 20.407 16.500 54.622 8.301 13.072 1.331 3.559 RV20 (SING HOUS INV) 4.733 4.636 5.628 4.165 0.416 0.652 2.278 RV10 (SING HOUS INV) 4.257 4.131 5.284 3.745 0.400 1.051 3.313 h2 (SING HOUS INV) 14.803 13.345 47.642 8.930 6.396 2.489 11.488 ∆GSEH 0.576 0.573 1.487 −0.212 0.399 0.258 2.461 ∆GSEM 0.013 0.012 0.057 −0.018 0.016 0.597 3.139 ∆ABSH 0.129 0.103 0.351 −0.088 0.121 0.242 1.959 ∆ABSM 0.005 0.003 0.015 −0.006 0.005 0.239 2.446 Table 12: Summary Statistics: 1984-2003 Sub-sample (77 observations). 27

Mean Median Max Min Std. Dev. Skew Kurt. GDP 1.924 2.350 8.000 −8.900 2.963 −1.278 6.444 SD (GDP) 2.412 2.404 3.577 1.521 0.684 0.507 2.040 RV20(GDP) 3.047 3.048 3.569 2.378 0.371 −0.288 1.654 RV10(GDP) 2.600 2.538 3.339 1.625 0.474 −0.036 1.995 h2 (GDP) 2.782 2.512 5.418 1.815 0.866 1.324 4.332 CONSUMPTION 2.384 2.400 6.400 −5.100 2.324 −0.907 4.596 SD (CONS) 1.827 1.738 2.647 1.164 0.434 0.544 2.226 RV20(CONS) 2.877 2.819 3.383 2.502 0.269 0.421 2.038 RV10(CONS) 2.450 2.367 3.217 2.031 0.324 1.050 3.078 h2(CONS) 2.296 2.109 4.029 1.820 0.488 1.932 6.231 HOUS CONS 1.802 1.250 6.700 −1.500 2.139 0.532 2.346 SD (HOUS CONS) 2.108 2.121 2.443 1.729 0.177 0.030 2.634 RV20(HOUS CONS) 3.107 3.133 3.363 2.714 0.171 −0.700 2.961 RV10(HOUS CONS) 2.697 2.747 3.016 1.925 0.225 −1.274 4.713 h2(HOUS CONS) 2.399 2.400 2.563 2.267 0.070 0.467 2.898 RESID INV −3.164 2.300 22.800 −35.400 14.450 −0.543 2.490 SD (RESID INV) 9.512 7.456 16.075 4.888 4.218 0.487 1.482 RV20 (RESID INV) 4.300 4.174 5.376 3.464 0.564 0.483 2.149 RV10 (RESID INV) 3.940 3.871 5.152 3.009 0.624 0.389 2.041 h2(RESID INV) 10.987 8.649 32.299 4.668 6.553 1.513 4.730 SING HOUS INV −4.700 1.600 72.800 −64.700 24.218 −0.050 4.160 SD (SING HOUS INV) 15.620 11.279 32.384 8.177 8.431 0.954 2.405 RV20 (SING HOUS INV) 4.736 4.576 5.768 4.165 0.497 0.934 2.565 RV10 (SING HOUS INV) 4.382 4.235 5.527 3.745 0.559 0.878 2.451 h2 (SING HOUS INV) 19.394 14.209 93.045 9.055 14.372 3.056 15.118 ∆GSEH 0.796 0.571 3.992 −1.435 1.231 0.814 3.435 ∆GSEM 0.004 0.005 0.050 −0.061 0.031 −0.283 2.331 ∆ABSH 0.241 0.213 1.865 −1.664 0.851 0.101 2.482 ∆ABSM 0.004 0.003 0.046 −0.031 0.023 0.263 2.077 Table 13: Summary Statistics: 1999-2011 Sub-sample (50 observations). 28

1102-9991 3002-4891 3002-4791 elpmaSlluF SSPK PP FDA FD SSPK PP FDA FD SSPK PP FDA FD SSPK PP FDA FD †92.0 †71.4− †52.4− †24.2− †80.0 †21.7− †78.3− †61.2− †60.0 †99.7− †99.7− †26.2− †71.0 †90.8− †90.8− †78.2− PDG †13.0 12.1− 54.1− 01.1− †74.0 †41.3− †61.3− 45.0− 89.0 01.1− 98.0− 14.0− 09.0 74.1− 53.1− 29.0− )PDG(DS †61.0 83.1− 79.0− 49.0− †51.0 †63.3− †15.3− 59.0− 87.0 85.1− 63.1− 86.0− †37.0 00.2− 56.1− 20.1− )PDG(02VR †21.0 77.1− 90.2− †60.2− †11.0 †70.3− †48.2− †34.1− 57.0 01.2− 58.1− 69.0− 57.0 †54.2− 00.2− 49.0− )PDG(01VR †41.0 †42.2− †06.2− †72.2− †91.0 †42.3− †40.3− †35.1− 67.0 †63.2− †34.2− †20.2− †17.0 †67.2− †37.2− †51.2− )PDG(2h †84.0 †73.3− †73.2− †77.1− †31.0 †98.7− †88.2− †09.2− †01.0 †31.9− †09.8− 72.1− †71.0 †82.9− †60.4− †54.1− NOITPMUSNOC †03.0 43.1− 07.1− †16.1− 29.0 †21.3− †50.3− 13.0− 51.1 81.1− 81.1− 27.0− 41.1 05.1− 94.1− 49.0− )SNOC(DS †82.0 03.1− 79.0− 40.1− 47.0 46.1− 65.1− 70.1− 99.0 47.1− 94.1− 69.0− 29.0 90.2− 70.2− †05.1− )SNOC(02VR †91.0 40.2− 75.1− †93.1− †95.0 10.2− 00.2− †55.1− 19.0 †72.2− 91.2− 61.1− 39.0 †56.2− †62.2− 60.1− )SNOC(01VR †42.0 91.2− †52.2− †57.1− †75.0 †40.3− †21.3− †89.2− 49.0 †25.3− †75.3− †79.2− 48.0 †77.3− †67.3− †49.2− )SNOC(2h †04.0 †99.4− †19.4− †63.4− †42.0 †97.01− †97.01− †76.01− †82.0 †31.21− †31.21− †51.21− †96.0 †81.21− †44.5− †92.5− SNOCUOH †71.0 09.1− †01.3− †64.2− 98.0 83.1− 83.1− 97.0− †74.0 21.2− 50.2− 89.0− †26.0 31.2− 69.1− 70.1− )SNOCUOH(DS †72.0 25.1− 84.1− †84.1− †32.0 †53.2− 19.1− †15.1− †15.0 †16.2− †58.2− †17.2− †93.0 †80.3− †41.3− †59.2− )SNOCUOH(02VR †91.0 50.2− 80.2− †40.2− †11.0 †24.2− 21.2- †08.1− †53.0 †11.3− †06.2− †43.2− †62.0 †26.3− †90.3− †37.2− )SNOCUOH(01VR †81.0 †03.4− †82.4− †51.4− †42.0 †20.4− †89.3− †64.3− †24.0 †24.5− †93.5− †52.5− †24.0 †80.6− †50.6− †49.5− )SNOCUOH(2h †04.0 †78.3− †05.2− †94.1− †51.0 †46.4− †95.4− †41.4− †40.0 †17.5− †40.6− †47.3− †12.0 †55.6− †75.6− †51.4− VNIDISER †37.0 40.0− 71.0− 03.0− 18.0 †07.2− †26.2− 32.0− 20.1 94.0− 49.0− 17.0− 89.0 62.1− 24.1− 51.1− )VNIDISER(DS 68.0 16.0 12.0 31.0 †84.0 30.2− 70.2− 87.0− 98.0 61.1− 50.1− 58.0− †16.0 04.1− 91.1− 22.1− )VNIDISER(02VR 68.0 51.0 90.0 65.0 †63.0 †49.2− †20.3− 92.1− 38.0 38.1− 79.1− †48.1− †45.0 19.1− 50.2− †00.2− )VNIDISER(01VR 77.0 20.0 13.2 70.2 †84.0 †34.3− †14.3− 00.1− 98.0 †63.2− †83.2− †93.2− †96.0 †85.2− †16.2− †26.2− )VNIDISER(2h †13.0 †27.3− †17.3− †64.3− †70.0 †87.4− †86.4− 68.0− †40.0 †04.4− †67.5− †85.3− †52.0 †24.5− †37.5− †81.4− VNIUOHNIS †17.0 87.0 54.0 62.0 67.0 †84.2− †25.2− 33.0− 67.0 11.1− 83.1− 03.1− †86.0 35.1− 17.1− †36.1− )VNIUOHNIS(DS 18.0 86.0 14.0 76.0 †04.0 †43.2− †95.2− 20.1− †37.0 44.1− 06.1− †45.1− †84.0 16.1− 66.1− †86.1− )VNIUOHNIS(02VR 08.0 70.0− 13.0− 72.0 †03.0 †33.3− †44.3− 41.1− †96.0 39.1− 30.2− †99.1− †14.0 40.2− 41.2− †51.2− )VNIUOHNIS(01VR †06.0 †16.3− †37.3− †76.3− †52.0 †37.3− †18.3− †05.3− †86.0 †96.4− †18.4− †94.4− †23.0 †28.5− †28.5− †84.5− )VNIUOHNIS(2h †42.0 31.2− †96.2− †17.2− †01.0 †26.3− †25.2− †45.2− †04.0 †78.3− †32.2− 72.1− †62.0 †62.3− †31.4− †70.3− HESG∆ †03.0 63.1− †92.2− †02.2− †96.0 †63.2− 20.2− 07.0− †54.0 11.2− †53.2− †22.2− †42.0 †57.2− †84.2− †64.2− MESG∆ †52.0 31.1− 79.1− †08.1− †32.0 †10.3− †10.3− †71.2− 08.0 †06.2− †86.2− †91.2− †21.0 90.2− †02.3- †88.2− HSBA∆ †72.0† 53.1− †93.2− †04.2− †70.0 †61.3− †26.3− †01.3− †14.0 †72.3− †28.3− †34.3− †90.0 †55.2− †42.3− †02.3− MSBA∆ detargetni si elbairav eht taht llun eht rof tset eht fo eulav eht troper ew PP dna FDA ,FD roF .stluseR ytiranoitatS :41 elbaT eht ot srefer FDA .)6991( kcotS dna ,grebnehtoR ,ttoillE yb desoporp tset relluF–yekciD eht ot srefer FD .)1(I eno redro fo .tset nihS–tdimhcS–spillihP–ikswoktaiwK eht ot srefer SSPK .tset norreP-spillihP eht ot srefer PP .tset relluF–yekciD detnemguA tsael ta PP dna FDA ,FD rof llun )1(I eht fo noitcejer snaem † .)0(I yranoitats si elbairav eht taht si llun eht SSPK eht roF .level %1 eht ta tsael ta SSPK rof )0(I fo llun eht tcejer ot eruliaf dna ,level %02 eht ta 29

(cid:3) (cid:1)(cid:2)(cid:11) (cid:1)(cid:2)(cid:10) (cid:1)(cid:2)(cid:9) (cid:1)(cid:2)(cid:8) (cid:1)(cid:2)(cid:7) (cid:1)(cid:2)(cid:6) (cid:1)(cid:2)(cid:5) (cid:1)(cid:2)(cid:4) (cid:1)(cid:2)(cid:3) (cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:3)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:3)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:3)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:1)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:9)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:4)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:8)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:10)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:11)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:2)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:12)(cid:1)(cid:12)(cid:7) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:1) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:3) Figure 8: Transition Probabilities: GDP (cid:3) (cid:1)(cid:2)(cid:11) (cid:1)(cid:2)(cid:10) (cid:1)(cid:2)(cid:9) (cid:1)(cid:2)(cid:8) (cid:1)(cid:2)(cid:7) (cid:1)(cid:2)(cid:6) (cid:1)(cid:2)(cid:5) (cid:1)(cid:2)(cid:4) (cid:1)(cid:2)(cid:3) (cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:3)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:3)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:3)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:1)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:9)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:4)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:8)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:10)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:11)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:2)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:12)(cid:1)(cid:12)(cid:7) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:1) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:3) Figure 9: Transition Probabilities: Personal Consumption 30

(cid:3) (cid:1)(cid:2)(cid:11) (cid:1)(cid:2)(cid:10) (cid:1)(cid:2)(cid:9) (cid:1)(cid:2)(cid:8) (cid:1)(cid:2)(cid:7) (cid:1)(cid:2)(cid:6) (cid:1)(cid:2)(cid:5) (cid:1)(cid:2)(cid:4) (cid:1)(cid:2)(cid:3) (cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:3)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:3)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:3)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:1)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:9)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:4)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:8)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:10)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:11)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:2)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:12)(cid:1)(cid:12)(cid:7) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:1) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:3) Figure 10: Transition Probabilities: Housing Consumption (cid:3) (cid:1)(cid:2)(cid:11) (cid:1)(cid:2)(cid:10) (cid:1)(cid:2)(cid:9) (cid:1)(cid:2)(cid:8) (cid:1)(cid:2)(cid:7) (cid:1)(cid:2)(cid:6) (cid:1)(cid:2)(cid:5) (cid:1)(cid:2)(cid:4) (cid:1)(cid:2)(cid:3) (cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:3)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:3)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:3)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:1)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:9)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:4)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:8)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:10)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:11)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:2)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:12)(cid:1)(cid:12)(cid:7) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:1) (cid:12)(cid:13)(cid:14)(cid:15)(cid:2)(cid:16)(cid:17)(cid:18)(cid:19)(cid:18)(cid:20)(cid:16)(cid:3) Figure 11: Transition Probabilities: Residential Investment 31

(cid:7) (cid:1)(cid:2)(cid:6) (cid:1)(cid:2)(cid:5) (cid:1)(cid:2)(cid:4) (cid:1)(cid:2)(cid:3) (cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:3)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:3)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:3)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:3)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:11)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:11)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:11)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:11)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:1)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:9)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:4)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:8)(cid:2)(cid:2)(cid:1) (cid:4)(cid:6)(cid:5)(cid:10)(cid:2)(cid:2)(cid:1) (cid:1)(cid:6)(cid:5)(cid:11)(cid:2)(cid:2)(cid:1) (cid:7)(cid:6)(cid:5)(cid:2)(cid:2)(cid:2)(cid:1) (cid:9)(cid:6)(cid:5)(cid:12)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:1)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:9)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:4)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:8)(cid:12)(cid:12)(cid:7) (cid:4)(cid:6)(cid:5)(cid:10)(cid:12)(cid:12)(cid:7) (cid:1)(cid:6)(cid:5)(cid:11)(cid:12)(cid:12)(cid:7) (cid:7)(cid:6)(cid:5)(cid:2)(cid:12)(cid:12)(cid:7) (cid:9)(cid:6)(cid:5)(cid:12)(cid:1)(cid:12)(cid:7) (cid:8)(cid:9)(cid:10)(cid:11)(cid:2)(cid:12)(cid:13)(cid:14)(cid:15)(cid:14)(cid:16)(cid:12)(cid:1) (cid:8)(cid:9)(cid:10)(cid:11)(cid:2)(cid:12)(cid:13)(cid:14)(cid:15)(cid:14)(cid:16)(cid:12)(cid:7) Figure 12: Transition Probabilities: Investment in Single Housing 32