The volatility of aggregate economic activity in the United States decreased markedly 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 mortgagebacked securities. We also document that this relationship changed sign, from negative to positive, in the early 2000's.
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 mortgagebacked 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 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 riskdiversification 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 nonlinear, Markov switching model next. Empirical evidence is supportive of a negative relationship between issuance of mortgagebacked 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.
The Great Moderation was identified by a set of papers by Kim and Nelson (1999), McConnell and PerezQuiros (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 financialmarket 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. Financialmarket 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 PerezQuiros (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 followup paper, Ramey and Vine (2003), however, points out that for the case of the auto industry, the explanation of the decrease in industryoutput 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.
There are two recent papers that are directly linked to our analysis. The first is Den Haan 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 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.
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 consumption of housing services, real residential investment, and real single family residential 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 singlefamily homes in addition to aggregate variables because these variables correspond more closely to the financial derivatives that we consider. Specifically, we consider mortgagebacked securities issued by governmentsponsored enterprises and over the full sample period, and mortgagebacked 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 singlefamily mortgages. This is by far the biggest component in the mortgage pools, much larger than multifamily and commercial pools (which are of course not held by governmentsponsored enterprises) and is the aggregate for which most consistent observations are available throughout the sample.
Mortgage debt, as a fraction of GDP, was about 28 percent in 1974, and it has increased to about 68 percent in 2011 after a peak of about 78 percent in 2009. The total increase in the weight of mortgage debt over GDP is mirrored by the emergence of mortgage pools. The fraction of mortgages pooled in mortgagebacked derivatives by governmentsponsored enterprises (GSE's) out the total amount of (singlefamily) mortgage debt outstanding was slightly below 10 percent in 1974, to reach 56 percent in 2011. Mortgage pools issued by other financial institutions (i.e. not GSE's) constituted about 1 percent of all singlefamily mortgages in 1988, and the size of the market was negligible before then. By the end of the sample period this share had increased to 11 percent. Thus, the size of all mortgagebacked securities market went from practically negligible in the early seventies to well over two thirds of singlefamily mortgages in about thirty years. Figures 1 and 2 give a graphic overview of the evolution of these markets.
The main differences between mortgages in GSE's pools versus other pools concern size of the underlying loans and quality of the borrowers. GSE's are limited by regulation to create pools only with smaller mortgages (the current upper limit is $417,000 per mortgage loan) and to borrowers with high credit scores. Other institutions do not face these limits. Their pools, which we will refer to as asset backed securities (ABS) pool, are composed by mortgage loans that are characterized as jumbo, subprime, or altA. The first label refer to the size of the loan,
the second to the quality of the borrower and the third to loans that could in principle qualify for purchase by a GSE but because of some limitations not directly imputable to size and credit score, were not held by GSE's. Thus, at the level of the aggregate economy, the main difference between GSE's and nonGSE's mortgage pools is that the latter are designed to pool a potentially larger amount of credit risk. Both financial instruments pool interest rate risk.Because of the explosive growth of MBS markets, we normalize its size and perform several stationarity tests on the resulting series. In particular, we normalize mortgagebacked securities pools, which are denominated in nominal terms in the Flow of Funds observations, in two ways: first, we express each series as a fraction of the total singlefamily mortgage debt outstanding (Figure 1); second, we use the average house price as a normalizing variables. We obtain average singlefamily house prices from the Census Bureau. Essentially, the normalization of outstanding mortgagebacked securities with average house prices supplies a (rough) measure of the average number of houses for which the "insurance coverage" is provided by mortgage pooling.
For both GSE and ABS pools we use both normalizations, by mortgage pools and house prices, throughout the analysis.
For each of the five NIPA variables (real growth of GDP, personal consumption, consumption of housing services, residential investment, singlefamily residential investment) we construct four measures of volatility. One is commonly used in the literature and consists of the rolling standard
deviation of a series using a twentyquarter window (). This is the measure used, for example, by Blanchard and Simon (2001) and Stock and Watson (2003). We then compute two realized
volatility measures. Denote the growth rate of variable , we first run the
following regression
(1) 
(2) 
(3) 
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
measures^{5}; 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 mortgagebacked securities.
We analyze the relationship between the volatility of real variables and mortgagebacked securities with two empirical approaches. First, we estimate a linear model where we regress the different volatility measures of real variables described above, on mortgagebacked security variables (MBS and ABS). Here we assume that the sample period is divided in two subperiods. For GSE securities, the first subsample runs from 1974Q1 to 2003Q4 and the second from 1999Q1 to 2011Q2. For ABS, the first subsample starts in 1984Q4, and before that the size of the market is negligible. The two subsamples correspond to a decline
and to an increase in the volatility of the macro variables considered.^{6} In the first subperiod we expect to find a negative relationship between real variables and mortgagebacked securities  i.e. MBS should reduce the volatility of real variables; in the second subperiod we expect mortgagebacked securities to increase volatility levels of real variables.For the linear approach, we need to make sure that our variables are stationary.^{7} We, therefore, perform four stationarity tests, the generalized least squares DickeyFuller (DF) test proposed by Elliott, Rothenberg, and Stock (1996), the Augmented DickeyFuller (ADF) test, the KwiatkowskiPhillipsSchmidtShin (KPSS) test, and the PhillipsPerron (PP) test, for each variable and each subsample. 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 nonstationarity, 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 nonlinear relationship and estimate a Markovswitching model in which we assume that there are two possible regimes: one in which real variables are characterized by high volatility and one in which real variables are characterized 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 mortgagebacked securities. Stabilizing effects consist of increasing the probability of transitioning in the lowvolatility 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 nonlinear model and discuss the estimation results.
We estimate the following equation for each variable that survives the stationarity tests:
(4) 
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 subperiod (19742003), GSE is reducing the volatility of GDP. ABS, in the second subperiod (1984  2003) also reduces GDP volatility levels. In the third subperiod, 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 subperiods and positive signs in the last subperiod. We interpret the difference in laglength as a statistical artifact. In fact, we report results for the optimal lag. Our main findings, however, hold for a range of laglengths. Table 3 reports the results for the volatility of Real Consumption of Housing Services. In subperiods one and two, GSE and ABS reduce volatility levels. In the third subperiod, however, ABS is increasing volatility, as expected, while GSE is decreasing volatility. Although this result may seem counter intuitive, it can be explained by the behavior of housing consumption. In fact, how we shall see in the next subsection, low activity in the housing market is concentrated during recessions and, consequently, the volatility of housing consumption behaves inversely with respect to the volatility of the other real variables we consider. Table 4 shows estimation results for the volatility of Real Residential Investment. GSE always reduces volatility, while ABS is only marginally significant. Finally, Table 5 shows estimation results for the volatility of SingleHousing Investment. GSE and ABS reduce volatility in the first two subperiods and increase volatility in the last subperiod. Overall, our linear estimates confirm that MBS reduce volatility of real variables in the first two subperiods and increased the same volatility in the latest period when the recent subprime crisis hit the economy.^{12}
Dependent variable: Volatility of Real GDP. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. and indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgagebacked securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits.
Volatility  Indep. Var.  Coeff.  St.Err.  Lag  
: SubPeriod 1: 1974  2003  GSEH  0.242^{**}  0.130  2  0.825 
: SubPeriod 1: 1974  2003  GSEM  2.816^{*}  2.137  2  0.822 
SD:SubPeriod 2: 1984  2003  ABSH  0.305^{***}  0.153  1  0.970 
: SubPeriod 2: 1984  2003  ABSH  0.140^{*}  0.092  6  0.841 
: SubPeriod 2: 1984  2003  ABSH  0.340^{***}  0.149  2  0.735 
:SubPeriod 2: 1984  2003  ABSH  0.450^{**}  0.243  1  0.718 
SD:SubPeriod 2: 1984  2003  ABSM  5.671  4.631  1  0.970 
: SubPeriod 2: 1984  2003  ABSM  4.704^{***}  1.993  5  0.847 
: SubPeriod 2: 1984  2003  ABSM  5.543^{*}  3.453  1  0.724 
: SubPeriod 2: 1984  2003  ABSM  10.46^{***}  5.165  3  0.718 
:SubPeriod 3: 1999  2011  GSEH  0.056^{*}  0.036  3  0.817 
: SubPeriod 3: 1999  2011  GSEH  0.162^{**}  0.085  1  0.809 
: SubPeriod 3: 1999  2011  GSEM  0.858  1.554  1  0.806 
: SubPeriod 3: 1999  2011  GSEM  4.016^{*}  2.917  1  0.784 
:SubPeriod 3: 1999  2011  ABSH  0.103^{***}  0.044  6  0.827 
: SubPeriod 3: 1999  2011  ABSH  0.245^{**}  0.140  10  0.802 
: SubPeriod 3: 1999  2011  ABSM  5.219^{***}  1.787  10  0.846 
: SubPeriod 3: 1999  2011  ABSM  7.653  4.104  10  0.799 
Dependent variable: Volatility of Real Consumption. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. and indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgagebacked securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits.
Volatility  Indep. Var.  Coeff.  St.Err.  Lag  
: SubPeriod 1: 1974  2003  GSEH  0.221^{***}  0.094  10  0.653 
: SubPeriod 1: 1974  2003  GSEM  0.727  1.386  5  0.676 
SD: SubPeriod 2: 1984  2003  ABSH  0.124  0.101  8  0.925 
: SubPeriod 2: 1984  2003  ABSH  0.417^{***}  0.135  8  0.838 
: SubPeriod 2: 1984  2003  ABSH  0.454^{***}  0.206  8  0.596 
SD: SubPeriod 2: 1984  2003  ABSM  2.392  2.590  8  0.925 
:SubPeriod 2: 1984  2003  ABSM  7.307^{***}  2.937  8  0.831 
:SubPeriod 2: 1984  2003  ABSM  9.095^{**}  5.072  6  0.595 
SD:SubPeriod 3: 1999  2011  GSEH  0.077^{***}  0.018  2  0.953 
: SubPeriod 3: 1999  2011  GSEH  0.096^{***}  0.015  2  0.870 
: SubPeriod 3: 1999  2011  GSEH  0.128^{***}  0.044  1  0.826 
SD: SubPeriod 3: 1999  2011  GSEM  3.029^{***}  0.799  1  0.946 
: SubPeriod 3: 1999  2011  GSEM  2.260^{***}  0.915  1  0.812 
: SubPeriod 3: 1999  2011  GSEM  3.454^{**}  1.849  1  0.785 
SD: SubPeriod 3: 1999  2011  ABSH  0.095^{***}  0.039  9  0.934 
:SubPeriod 3: 1999  2011  ABSH  0.120^{***}  0.034  10  0.840 
:SubPeriod 3: 1999  2011  ABSH  0.173^{***}  0.079  10  0.804 
SD: SubPeriod 3: 1999  2011  ABSM  3.127^{***}  1.399  10  0.932 
: SubPeriod 3: 1999  2011  ABSM  4.122^{***}  1.050  10  0.844 
: SubPeriod 3: 1999  2011  ABSM  5.158^{***}  2.376  10  0.797 
Dependent variable: Volatility of Real Consumption of Housing Services. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. , and indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgagebacked securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits.
Volatility  Indep. Var.  Coeff.  St.Err.  Lag  
: SubPeriod 1: 1974  2003  GSEH  0.027  9  0.838  
GSEH  0.092^{***}  0.035  7  0.772  
GSEH  0.048^{***}  0.022  4  0.387  
GSEM  1.527^{***}  0.616  5  0.835  
GSEM  1.830^{**}  0.936  4  0.765  
GSEM  0.461  0.450  3  0.375  
: SubPeriod 2: 1984  2003  ABSH  0.167^{**}  0.100  10  0.831 
: SubPeriod 2: 1984  2003  ABSH  0.189^{**}  0.112  6  0.783 
: SubPeriod 2: 1984  2003  ABSH  0.127^{*}  0.083  7  0.431 
: SubPeriod 2: 1984  2003  ABSM  3.855^{***}  1.819  10  0.833 
: SubPeriod 2: 1984  2003  ABSM  3.946^{**}  2.201  6  0.782 
: SubPeriod 2: 1984  2003  ABSM  2.682^{*}  1.633  7  0.430 
:SubPeriod 3: 1999  2011  GSEH  0.034^{***}  0.011  9  0.821 
:SubPeriod 3: 1999  2011  GSEH  0.014^{*}  0.009  5  0.811 
:SubPeriod 3: 1999  2011  GSEH  0.024^{**}  0.014  5  0.701 
:SubPeriod 3: 1999  2011  GSEH  0.013^{**}  0.007  6  0.154 
SD: :SubPeriod 3: 1999  2011  GSEM  1.670^{***}  0.487  9  0.830 
:SubPeriod 3: 1999  2011  GSEM  0.711^{*}  0.458  9  0.815 
:SubPeriod 3: 1999  2011  GSEM  0.951^{*}  0.596  7  0.699 
:SubPeriod 3: 1999  2011  GSEM  0.538  0.554  9  0.138 
SD:SubPeriod 3: 1999  2011  ABSH  0.084^{***}  0.021  9  0.835 
:SubPeriod 3: 1999  2011  ABSH  0.024^{*}  0.016  6  0.813 
:SubPeriod 3: 1999  2011  ABSH  0.037^{**}  0.019  2  0.703 
:SubPeriod 3: 1999  2011  ABSH  0.016  0.014  3  0.134 
SD :SubPeriod 3: 1999  2011  ABSM  3.169^{***}  0.673  10  0.846 
:SubPeriod 3: 1999  2011  ABSM  0.849^{*}  0.536  4  0 .814 
:SubPeriod 3: 1999  2011  ABSM  1.074^{*}  0.651  4  0.696 
:SubPeriod 3: 1999  2011  ABSM  0.622  0.571  6  0.134 
Dependent variable: Volatility of Real Residential Investment. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. and indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgagebacked securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits.
Volatility  Indep. Var.  Coeff.  St.Err.  Lag  
: SubPeriod 1: 1974  2003  GSEH  1.779^{***}  0.797  7  0.859 
:SubPeriod 1: 1974  2003  GSEM  28.64^{***}  12.61  6  0.857 
SD: SubPeriod 2: 1984  2003  ABSH  2.714^{*}  1.373  5  0.979 
SubPeriod 2: 1984  2003  ABSH  0.011  0.126  1  0.847 
: SubPeriod 2: 1984  2003  ABSH  0.658  1.206  1  0.781 
: SubPeriod 2: 1984  2003

ABSM  78.50^{***}  36.03  5  0.980 
: SubPeriod 2: 1984  2003  ABSM  5.658^{*}  3.506  4  0.852 
: SubPeriod 2: 1984  2003  ABSM  13.79  29.23  2  1.388 
We now take a different approach, and instead of postulating the presence of different subperiods we estimate a regimeswitching model over the entire sample. The assumption in this 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 twostate firstorder 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 subsamples. The disadvantage is that we have to estimate a much larger number of parameters. The specific equation that we estimate is given by
As in the case of the linear model, estimates are broadly consistent across models. (Time lags are also in line between the linear and nonlinear specifications.) Moreover, again like in the linear model, estimates pertaining to ABS markets tend to be statistically weaker due to the smaller sample.
Dependent variable: Volatility of Real GDP. ***, **, * refer to 5%, 10%, and 20% significance level, respectively. and indicate rolling standard deviation, realized volatility with lags 20 and 10 and GARCH volatility. GSEH and GSEM denote mortgagebacked securities issued by government sponsored enterprises normalized by house prices and mortgage lending. ABSH and ABSM denote the same variables issued by private conduits.
Volatility  Indep. Var.  Coeff.  St.Err.  Lag  
: SubPeriod 1: 1974 2003  GSEH  0.060^{***}  0.030  9  0.956 
: SubPeriod 1: 1974 2003  GSEH  0.087^{***}  0.042  7  0.930 
: SubPeriod 1: 1974 2003  GSEH  5.436^{***}  2.604  8  0.472 
: SubPeriod 1: 1974 2003  GSEM  1.700^{***}  0.989  10  0.956 
:SubPeriod 1: 1974 2003  GSEM  1.700^{**}  0.989  10  0.956 
:SubPeriod 1: 1974 2003  GSEM  0.461  0.450  3  
: SubPeriod 2: 1984  2003  ABSH  4.503^{**}  2.727  5  0.975 
:SubPeriod 2: 1984  2003  ABSH  0.187^{**}  0.095  4  0.918 
:SubPeriod 2: 1984  2003  ABSH  0.119^{*}  0.119  10  0.855 
:SubPeriod 2: 1984  2003  ABSM  4.697^{*}  3.587  4  0.444 
:SubPeriod 2: 1984  2003  ABSM  133.6^{*}  70.58  5  0.976 
:SubPeriod 2: 1984  2003  ABSM  7.324^{***}  2.787  4  0.923 
:SubPeriod 2: 1984  2003  GSEH  4.277^{*}  3.152  1  0.856 
:SubPeriod 2: 1984  2003  GSEH  114.1^{*}  87.71  4  0.445 
:SubPeriod 3: 1999  2011  GSEH  5.796^{**}  3.355  3  0.435 
:SubPeriod 3: 1999  2011  GSEH  160.3^{***}  74.00  1  0.361 
:SubPeriod 3: 1999  2011  GSEH  3.803^{*}  2.276  7  0.308 
:SubPeriod 3: 1999  2011  GSEH  177.3^{*}  105.8  1  0.337 
GSEH (2)  GSEM (4)  ABSH (4)  ABSM (5)  
1.910^{***}  2.066^{***}  2.142^{***}  2.240^{***}  2.361^{***}  
: Standard Deviation  (0.689)  (0.679)  (0.759)  (0.734)  (0.696) 
3.217^{***}  3.209^{***}  3.197^{***}  3.179^{***}  3.217^{***}  
: Standard Deviation  (0.209)  (0.213)  (0.228)  (0.212)  (0.204) 
5.022^{***}  5.000^{***}  5.134^{***}  5.117^{***}  4.962^{***}  
: Standard Deviation  (0.556)  (0.544)  (0.566)  (0.624)  (0.555) 
1.683^{***}  1.693^{***}  1.889^{***}  1.721^{***}  1.666^{***}  
: Standard Deviation  (0.185)  (0.233)  (0.197)  (0.219)  (0.168) 
TVP0 constant  1.269^{***}  1.490^{***}  2.143^{***}  1.550^{***}  1.633^{***} 
TVP0 constant: Standard Deviation  (0.305)  (0.324)  (0.769)  (0.507)  (0.440) 
TVP0 expl. var.  0.307^{*}  1.042^{**}  0.823  0.803^{*}  
TVP0 expl. var.: Standard Deviations  (0.210)  (0.611)  (0.787)  (0.576)  
TVP1 constant  1.669^{***}  1.876^{***}  2.137^{***}  1.787^{***}  1.766^{***} 
TVP1 constant: Standard Deviation  (0.292)  (0.402)  (0.439)  (0.388)  (0.352) 
TVP1 expl. var.  0.378  0.175  0.143  0.15  
TVP1 expl. var.: Standard Deviation  (0.339)  (0.322)  (0.245)  (0.247)  
Loglikelihood  2.469  2.453  2.444  2.447  2.434 
GSEH (8)  GSEM (8)  ABSH (8)  ABSM (8)  
0.522  0.472  0.405  0.261  0.167  
: Standard Deviation  (1.079)  (0.698)  (0.763)  (0.742)  (0.790) 
3.727^{***}  3.781^{***}  3.735^{***}  3.754^{***}  3.737^{***}  
: standard deviation  (0.210)  (0.199)  (0.203)  (0.205)  (0.206) 
3.085^{***}  3.039^{***}  3.172^{***}  3.032^{***}  3.069^{***}  
: standard deviation  (0.475)  (0.435)  (0.514)  (0.459)  (0.490) 
1.955^{***}  1.929^{***}  1.924^{***}  1.940^{***}  1.937^{***}  
:standard deviation  (0.134)  (0.136)  (0.136)  (0.136)  (0.135) 
TVP0 constant  0.804^{**}  1.333^{***}  1.197^{***}  1.781^{*}  1.457^{**} 
TVP0 constant: standard deviation  (0.418)  (0.439)  (0.647)  (1.176)  (0.829) 
TVP0 expl. var.  0.539  1.945  1.541  1.023  
TVP0 expl. var.: standard deviation  (0.477)  (2.097)  (2.192)  (1.324)  
TVP1 constant  1.799^{***}  2.159^{***}  1.914^{***}  1.822^{***}  1.843^{***} 
TVP1 constant: standard deviation  (0.252)  (0.443)  (0.352)  (0.284)  (0.291) 
TVP1 expl. var.  0.937^{*}  0.445^{*}  0.411^{*}  0.358  
TVP1 expl. var.: standard deviation  (0.600)  (0.322)  (0.292)  (0.293)  
Loglikelihood  2.273  2.241  2.238  2.244  2.244 
GSEH (4)  GSEM (4)  ABSH (1)  ABSM (1)  
2.926^{***}  2.950^{***}  2.887^{***}  2.947^{***}  2.948^{***}  
: standard deviation  (0.240)  (0.252)  (0.231)  (0.235)  (0.235) 
0.754^{***}  0.756^{***}  0.727^{***}  0.786^{***}  0.829^{***}  
: standard deviation  (0.255)  (0.252)  (0.238)  (0.255)  (0.245) 
2.445^{***}  2.425^{***}  2.425^{***}  2.460^{***}  2.470^{***}  
: standard deviation  (0.161)  (0.169)  (0.162)  (0.163)  (0.164) 
1.278^{***}  1.301^{***}  1.270^{***}  1.294^{***}  1.294^{***}  
: standard deviation  (0.178)  (0.174)  (0.165)  (0.170)  (0.166) 
TVP0 constant  1.970^{***}  2.407^{***}  2.697^{***}  2.300^{***}  2.262^{***} 
TVP0 constant: standard deviation  (0.290)  (0.593)  (0.611)  (0.413)  (0.389) 
TVP0 expl. var.  1.142^{**}  1.053^{***}  0.694^{***}  0.624^{***}  
TVP0 expl. var.: standard deviation  (0.612)  (0.402)  (0.287)  (0.286)  
TVP1 constant  1.878^{***}  1.370^{***}  2.264^{***}  2.124^{***}  2.523^{**} 
TVP1 constant: standard deviation  (0.584)  (0.565)  (0.838)  (0.749)  (1.407) 
TVP1 expl. var.  0.910^{*}  0.689^{*}  0.539^{*}  0.898  
TVP1 expl. var.: standard deviation  (0.690)  (0.455)  (0.397)  (0.755)  
Loglikelihood  2.246  2.218  2.208  2.232  2.234 
GSEH (6)  GSEM (5)  ABSH (3)  ABSM (4)  
2.819  1.107  0.554  2.057  1.301  
: standard deviation  (3.634)  (4.081)  (3.015)  (3.759)  (3.703) 
4.744^{***}  4.647^{***}  4.754^{***}  4.769^{***}  4.816^{***}  
: standard deviation  (0.961)  (0.924)  (0.909)  (0.963)  (0.983) 
27.97^{***}  28.85^{***}  27.45^{***}  28.44^{***}  27.92^{***}  
: standard deviation  (2.810)  (3.066)  (2.619)  (3.008)  (2.995) 
7.81^{***}  7.819^{***}  7.637^{***}  7.774^{***}  7.752^{***}  
: standard deviation  (0.641)  (0.628)  (0.626)  (0.644)  (0.649) 
TVP0 constant  1.505^{***}  1.458^{***}  2.103^{***}  1.650^{***}  1.567^{***} 
TVP0 constant: standard deviation  (0.292)  (0.301)  (0.607)  (0.383)  (0.344) 
TVP0 expl. var.  0.139  0.935^{**}  0.358  0.169  
TVP0 expl. var.: standard deviation  (0.185)  (0.524)  (0.290)  (0.251)  
TVP1 constant  1.872^{***}  2.363^{***}  2.424^{***}  2.038^{***}  2.067^{***} 
TVP1 constant: standard deviation  (0.290)  (0.485)  (0.548)  (0.376)  (0.406) 
TVP1 expl. var.  1.164^{***}  0.691^{**}  0.434^{*}  0.444^{*}  
TVP1 expl. var.: standard deviation  (0.573)  (0.381)  (0.313)  (0.336)  
Loglikelihood  4.098  4.043  4.047  4.076  4.072 
GSEH (7)  GSEM (7)  ABSH (4)  ABSM (5)  
0.043  0.702  0.706  1.387  2.008  
: standard deviation  (0.774)  (4.209)  (4.241)  (6.062)  (6.716) 
4.987^{***}  4.746^{***}  4.584^{***}  4.846^{***}  4.788^{***}  
: standard deviation  (1.289)  (1.254)  (1.280)  (1.274)  (1.295) 
43.24^{***}  47.03^{***}  46.86^{***}  44.86^{***}  45.44^{***}  
: standard deviation  (4.193)  (5.006)  (5.149)  (4.559)  (4.865) 
10.75^{***}  11.40^{***}  11.45^{***}  10.86^{***}  11.03^{***}  
: standard deviation  (0.954)  (0.879)  (0.884)  (0.967)  (1.035) 
TVP0 constant  1.479^{***}  1.317^{***}  1.748^{***}  1.515^{***}  1.461^{***} 
TVP0 constant: standard deviation  (0.275)  (0.298)  (0.539)  (0.315)  (0.293) 
TVP0 expl. var.  0.538^{*}  2.144^{**}  0.328  0.223  
TVP0 expl. var.: standard deviation  (0.346)  (1.197)  (0.298)  (0.288)  
TVP1 constant  1.821^{***}  2.494^{***}  2.180^{***}  1.918^{***}  1.926^{***} 
TVP1 constant: standard deviation  (0.276)  (0.589)  (0.484)  (0.302)  (0.313) 
TVP1 expl. var.  1.605^{***}  0.853^{**}  0.423^{*}  0.406  
TVP1 expl. var.: standard deviation  (0.817)  (0.503)  (0.322)  (0.325)  
Loglikelihood  4.475  4.416  4.410  4.451  4.450 
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 loanlevel 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 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 question of the joint behavior of real and financial variables, our analysis points to a direction of analysis that explores financial products and the risk transfer that they operate jointly with the real variables on which they are written.
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 
(GDP)  3.301  3.210  4.064  2.574  0.427  0.195  1.656 
(GDP)  2.862  2.781  3.860  2.130  0.466  0.288  1.761 
(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 
(CONS)  3.172  3.252  3.745  2.395  0.345  0.391  2.378 
(CONS)  2.745  2.817  3.446  1.908  0.382  0.259  2.226 
(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 
(HOUS CONS)  3.168  3.167  3.600  2.432  0.213  0.607  3.703 
(HOUS CONS)  2.744  2.741  3.242  2.021  0.267  0.353  2.869 
(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 
(RESID INV)  4.681  4.699  5.750  3.464  0.621  0.074  1.957 
(RESID INV)  4.233  4.193  5.465  3.009  0.665  0.095  2.016 
(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 
(SING HOUS INV)  5.022  5.079  6.177  4.165  0.542  0.147  1.893 
(SING HOUS INV)  4.581  4.467  5.749  3.745  0.582  0.357  1.863 
(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 
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 
(GDP)  3.023  2.981  3.602  2.574  0.237  0.408  2.454 
(GDP)  2.574  2.503  3.278  2.130  0.278  0.782  2.832 
(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 
(CONS)  3.004  3.005  3.487  2.395  0.297  0.309  2.128 
(CONS)  2.575  2.589  3.161  1.908  0.334  0.143  1.950 
(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(CONS)  2.344  2.380  3.411  1.738  0.416  0.520  2.518 
(HOUS CONS)  3.106  3.094  3.600  2.432  0.225  0.242  3.593 
(HOUS CONS)  2.677  2.666  3.242  2.021  0.276  0.079  2.910 
(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 
(RESID INV)  4.310  4.276  5.018  3.464  0.421  0.173  2.045 
(RESID INV)  3.843  3.840  4.691  3.009  0.435  0.070  2.078 
(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 
(SING HOUS INV)  4.733  4.636  5.628  4.165  0.416  0.652  2.278 
(SING HOUS INV)  4.257  4.131  5.284  3.745  0.400  1.051  3.313 
(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 
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 
(GDP)  3.047  3.048  3.569  2.378  0.371  0.288  1.654 
(GDP)  2.600  2.538  3.339  1.625  0.474  0.036  1.995 
(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 
(CONS)  2.877  2.819  3.383  2.502  0.269  0.421  2.038 
(CONS)  2.450  2.367  3.217  2.031  0.324  1.050  3.078 
(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 
(HOUS CONS)  2.108  2.121  2.443  1.729  0.177  0.030  2.634 
(HOUS CONS)  3.107  3.133  3.363  2.714  0.171  0.700  2.961 
(HOUS CONS)  2.697  2.747  3.016  1.925  0.225  1.274  4.713 
(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 
(RESID INV)  9.512  7.456  16.075  4.888  4.218  0.487  1.482 
(RESID INV)  4.300  4.174  5.376  3.464  0.564  0.483  2.149 
(RESID INV)  3.940  3.871  5.152  3.009  0.624  0.389  2.041 
(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 
(SING HOUS INV)  15.620  11.279  32.384  8.177  8.431  0.954  2.405 
(SING HOUS INV)  4.736  4.576  5.768  4.165  0.497  0.934  2.565 
(SING HOUS INV)  4.382  4.235  5.527  3.745  0.559  0.878  2.451 
(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 
For DF, ADF and PP we report the value of the test for the null that the variable is integrated of order one  I(1). DF refers to the DickeyFuller test proposed by Elliott, Rothenberg, and Stock (1996). ADF refers to the Augmented DickeyFuller test. PP refers to the PhillipsPerron test. KPSS refers to the KwiatkowskiPhillipsSchmidtShin test. For the KPSS the null is that the variable is stationary  I(0). means rejection of the I(1) null for DF, ADF and PP at least at the 20% level, and failure to reject the null of I(0) for KPSS at least at the 1% level.
Full Sample: DF  Full Sample:ADF  Full Sample:PP  Full Sample:KPSS  19742003: DF  19742003:ADF  19742003:PP  19742003:KPSS  19842003:DF  19842003:ADF  19842003:PP  19842003:KPSS  19992011:DF  19992011:ADF  19992011:PP  19992011:KPSS  
GDP  2.87†  8.09†  8.09†  0.17 †  2.62†  7.99†  7.99†  0.06†  2.16†  3.87†  7.12†  0.08†  2.42†  4.25†  4.17†  0.29† 
SD(GDP)  0.92  1.35  1.47  0.90  0.41  0.89  1.10  0.98  0.54  3.16†  3.14†  0.47†  1.10  1.45  1.21  0.31† 
(GDP)  1.02  1.65  2.00  0.73†  0.68  1.36  1.58  0.78  0.95  3.51†  3.36†  0.15†  0.94  0.97  1.38  0.16 † 
(GDP)  0.94  2.00  2.45†  0.75  0.96  1.85  2.10  0.75  1.43†  2.84†  3.07†  0.11†  2.06†  2.09  1.77  0.12 † 
(GDP)  2.15 †  2.73 †  2.76 †  0.71†  2.02 †  2.43 †  2.36 †  0.76 †  1.53 †  3.04 †  3.24 †  0.19 †  2.27 †  2.60 †  2.24 †  0.14 † 
CONSUMPTION  1.45†  4.06†  9.28†  0.17†  1.27  8.90 †  9.13 †  0.10 †  2.90 †  2.88 †  7.89 †  0.13 †  1.77 †  2.37 †  3.37†  0.48 † 
SD (CONS)  0.94  1.49  1.50  1.14  0.72  1.18  1.18  1.15  0.31  3.05 †  3.12 †  0.92  1.61 †  1.70  1.34  0.30 † 
(CONS)  1.50 †  2.07  2.09  0.92  0.96  1.49  1.74  0.99  1.07  1.56  1.64  0.74  1.04  0.97  1.30  0.28 † 
(CONS)  1.06  2.26 †  2.65 †  0.93 †  1.16  2.19  2.27 †  0.91  1.55 †  2.00  2.01  0.59†  1.39†  1.57  2.04  0.19† 
(CONS)  2.94†  3.76†  3.77†  0.84  2.97†  3.57†  3.52†  0.94  2.98†  3.12†  3.04†  0.57†  1.75†  2.25†  2.19  0.24† 
HOUS CONS  5.29†  5.44†  12.18†  0.69†  12.15†  12.13†  12.13†  0.28†  10.67†  10.79†  10.79†  0.24†  4.36†  4.91†  4.99†  0.40† 
(HOUS CONS)  1.07  1.96  2.13  0.62†  0.98  2.05  2.12  0.47†  0.79  1.38  1.38  0.89  2.46†  3.10†  1.90  0.17† 
(HOUS CONS)  2.95†  3.14†  3.08†  0.39†  2.71†  2.85†  2.61†  0.51†  1.51†  1.91  2.35†  0.23†  1.48†  1.48  1.52  0.27† 
(HOUS CONS)  2.73†  3.09†  3.62†  0.26†  2.34†  2.60†  3.11†  0.35†  1.80†  2.12†  2.42†  0.11†  2.04†  2.08  2.05  0.19† 
(HOUS CONS)  5.94†  6.05†  6.08†  0.42†  5.25†  5.39†  5.42†  0.42†  3.46†  3.98†  4.02†  0.24†  4.15†  4.28†  4.30†  0.18† 
RESID INV  4.15†  6.57†  6.55†  0.21†  3.74†  6.04†  5.71†  0.04†  4.14†  4.59†  4.64†  0.15†  1.49†  2.50†  3.87†  0.40† 
SD(RESID INV)  1.15  1.42  1.26  0.98  0.71  0.94  0.49  1.02  0.23  2.62†  2.70†  0.81  0.30  0.17  0.04  0.73† 
(RESID INV)  1.22  1.19  1.40  0.61†  0.85  1.05  1.16  0.89  0.78  2.07  2.03  0.48†  0.13  0.21  0.61  0.86 
(RESID INV)  2.00†  2.05  1.91  0.54†  1.84†  1.97  1.83  0.83  1.29  3.02†  2.94†  0.36†  0.56  0.09  0.15  0.86 
(RESID INV)  2.62†  2.61†  2.58†  0.69†  2.39†  2.38†  2.36†  0.89  1.00  3.41†  3.43†  0.48†  2.07  2.31  0.02  0.77 
SING HOUS INV  4.18†  5.73†  5.42†  0.25†  3.58†  5.76†  4.40†  0.04†  0.86  4.68†  4.78†  0.07†  3.46†  3.71†  3.72†  0.31† 
(SING HOUS INV)  1.63†  1.71  1.53  0.68†  1.30  1.38  1.11  0.76  0.33  2.52†  2.48†  0.76  0.26  0.45  0.78  0.71† 
(SING HOUS INV)  1.68†  1.66  1.61  0.48†  1.54†  1.60  1.44  0.73†  1.02  2.59†  2.34†  0.40†  0.67  0.41  0.68  0.81 
(SING HOUS INV)  2.15†  2.14  2.04  0.41†  1.99†  2.03  1.93  0.69†  1.14  3.44†  3.33†  0.30†  0.27  0.31  0.07  0.80 
(SING HOUS INV)  5.48†  5.82†  5.82†  0.32†  4.49†  4.81†  4.69†  0.68†  3.50†  3.81†  3.73†  0.25†  3.67†  3.73†  3.61†  0.60† 
GSEH  3.07†  4.13†  3.26†  0.26†  1.27  2.23†  3.87†  0.40†  2.54†  2.52†  3.62†  0.10†  2.71†  2.69†  2.13  0.24† 
GSEM  2.46†  2.48†  2.75†  0.24†  2.22†  2.35†  2.11  0.45†  0.70  2.02  2.36†  0.69†  2.20†  2.29†  1.36  0.30† 
ABSH  2.88†   3.20†  2.09  0.12†  2.19†  2.68†  2.60†  0.80  2.17†  3.01†  3.01†  0.23†  1.80†  1.97  1.13  0.25† 
ABSM  3.20†  3.24†  2.55†  0.09†  3.43†  3.82†  3.27†  0.41†  3.10†  3.62†  3.16†  0.07†  2.40†  2.39†  1.35  0.27† 