Is Housing the Business Cycle?

Transcription

1 Is Housing the Business Cycle? Eyo I. Herstad 9th May 2016 University of Oslo, Department of Economics Thesis submitted for the degree of Master of Economic Theory and Econometrics

2 Abstract In this thesis I expand the results of Leamer (2007) to the rest of the OECD, to see if there is any generality to housing leading the business cycle. I find that some, but not all, recessions fit the pattern. I then move over to an econometric framework, where I test the ability of residential investment to predict recessions in the OECD. To get a benchmark of predictability, I compare the results to equivalent models where I use the term spread. I also combine the two into the same model to see if the two variables compliment each other. To get an idea of the generality of our results, I also estimate a panel version of the model. Using this framework, I find that residential investment outperforms the spread in predicting recession quarters, but is less effective at predicting the start of a recession. When I separate the effects before and during recessions, I find that residential investment predicts whether a recession continues well, but still struggles to predict the start of the recession. I also find that the panel model of residential investment outperforms the one for the spread, which may indicate that there is a more homogeneous link between housing and recessions than the link between the spread and recessions. Finally, I attempt to forecast the great recession using the different models. I find that the panel model performs best, which indicates that the panel model catches a general mechanism across countries, and as such has better out of sample performance than the country specific models.

3 Preface Working on this thesis has been both interesting and challenging, and I would not have been able to finish it if it was not for the support and input from a number of people. First and foremost, I would like to thank André Anundsen and Knut Are Aastveit who introduced me to the topic and the data for the thesis, in addition to giving invaluable support throughout the process. I would also like to thank my supervisor Ragnar Nymoen for his crucial help and guidance.in addition, I would like to thank Norges Bank, both for financial support and for letting me present an earlier version of the thesis at a seminar. I would like to thank all participants for the input and comments they gave before, during and after the presentation. I would also like to thank everyone who has helped me throughout the process of writing this thesis. Either directly by commenting or discussing the thesis, or indirectly by giving much needed moral support. This thesis is the accumulation of five years of study at the Department of Economics, and I would like to thank all my fellow students who have made those years both fun and stimulating. I am solely responsible for any inaccuracies or errors in the thesis. All the models in this thesis are estimated using MATLAB, and the data set is described in the data appendix. The data and codes used in the thesis are available on request from the author. i

4 Contents 1 Introduction 1 2 Replicating Leamer Responses to Leamer Replicating Leamer s Results Expanding the results to the rest of the OECD Predicting recessions using a generalized linear model Properties of the estimators Interpreting the results How to measure predictive power? Results Panel estimation results Predicting Recessions as individual events Separating effects before and during recessions Extensions and Robustness checks Using American data Alternative recession indicators More about the properties of the estimators An attempt to forecast the Great Recession Conclusion 57 Appendices 62 ii

5 A Data 62 B Additional graphical documentation to Chapter iii

6 Chapter 1 Introduction The connection between housing variables and the business cycle has been of great interest to researchers and policy makers following the housing collapse in the US in In a paper from the same year, Leamer (2007) declares that "Housing is the Business Cycle", and argues that almost all recessions in the United states can be explained by looking at housing variables. According to Leamer, the durability of housing and its clear connection to financial health of households make the housing market a major driving force in the business cycle. In his follow up paper from 2015, he discusses how the results were vindicated by what is now called the Great Recession in (Leamer 2015). In his two articles, Leamer argues that due to its durability, housing follows a volume cycle. Furthermore, he argues that this volume cycle leads the business cycle of the rest of the economy. As an example of this effect, Leamer argues that the Great Recession could have been avoided if policy makers in the US took this special link into account. There is a rich literature related to housing and how it effects other variables, and there is an increasing focus on using data from several countries. A recent paper by Jordà et al. (2015) uses a panel of 17 countries with data on credit, mortgages and house prices from 1870 to They find that an exogenous depression in interest rates leads to considerable increases in both mortgage lending and house prices. They also find that such increases increase financial risks. The usage of panels to find cross-country connections between housing variables and the business cycle is not new, for example, Anundsen et al. (2016) uses 1

7 a panel of 16 OECD countries to investigate the effect of house price booms on the likelihood financial crises. The paper finds the effect to be significant, and underline the importance of keeping track of house prices to ensure financial stability. While the focus in the article is primarily on credit and house prices, it would be interesting to compare these results to the ones I find when looking at residential investment, as I have data for most of the countries covered in this article. The theoretical work has generally been focused on housings effect on credit, though it has not always been focused on house prices. In a paper by Liu, Wang, and Zha (2013), macroeconomic fluctuations are found to be driven by co-movements in land prices and business investment. The paper goes on to create a framework where land prices affect the credit constraints of firms, which means land prices then become an amplifying mechanism to macroeconomic fluctuations. In this thesis I will try to find empirical evidence of housing variables, more specifically residential investment, leading the business cycle. I will do this both by graphical analysis in chapter 2, and by econometric analysis. I will focus on the behaviour around recessions, as most of the literature focuses on this aspect. However, in order to fully understand the connection between housing and business cycle movements it is necessary to not only look at recessions, but also look at the interaction during booms. An interesting theoretical connection between overbuilding in booms and protracted recessions is shown in Shleifer et al. (2015). This kind of connection is reminiscent of the Austrian theory of the business cycle (Hayek 1931), though, as has been pointed out in later works, in order to reconcile a fall in the rest of the economy, a Keynesian mechanism is needed (Krugman 1998). In this thesis I will try to achieve this by separating the effects of the variables before and during the recession. In order to get a general feeling of how residential investment and recessions interact, we will be looking at a panel of several countries, including most of the OECD. Should Leamer s theory be correct, we should find that it is possible to predict recessions in all these countries using residential investment. To get an idea of how well residential investment predicts recessions, we will compare our results with the term spread, which is well established as one of the best predictors of recessions (Estrella and Mishkin 1998). The rest of the thesis is structured as follows. Chapter 2 performs a graphical 2

8 analysis of the data similar to the one in Leamer (2007). Chapter 3 shows how you can use a discrete choice model to predict recessionary quarters, while chapter 4 uses a similar model while attempting to predict recession starts, and a model where we simultaneously model effects before and during the recession. Chapter 5 covers some robustness checks and extensions. Chapter 6 concludes. 3

9 Chapter 2 Replicating Leamer Leamer (2007) aims to show the importance of housing for the business cycle. It also describes the housing market cycle, and sketches how monetary policy should take these factors into account. To show this, Leamer s method was to calculate the cumulative de-trended contribution of each component to GDP before and during US recessions. He calls this the "cumulative abnormal contribution" of the component. These graphs, shown in figure 2.1, are the core of Leamer s analysis. They show how residential investment contributes abnormally much to weakness in GDP growth before each recession (downward sloping lines), but generally contributes abnormally to a strengthening in GDP growth during the recession itself (upward sloping lines). Despite residential investments total contribution to growth being fairly small (4.2 %), it is still the best ex-post predictor of US recessions. Leamer argues that this is due to housing following a persistent volume cycle, which is due to the persistence of house prices. The sluggishness of prices therefore cause the extreme volume cycles, which then spread to the rest of the economy, causing a recession. However, as the cycle turns around, residential investment starts contributing to growth again relatively quickly. Similar results can be found for consumer durables. This is the core of Leamer s theory of the business cycle. Leamer s theory is that the housing market follows a volume cycle due to the households reluctance to sell into a weak market. A drop in demand will therefore not cause a large price reduction, but instead lead to fewer sales, and lower construction of new homes, while the nominal price remains relatively high. 4

10 Figure 2.1: The original graph from Leamer (2007) 5

11 Leamer makes similar arguments based on households being backward-looking and loss averse, or by reference to transaction costs. It therefore appears that U.S recessions start in housing, and then spreads out to the rest of the economy. Leamer summarizes this idea by declaring that there is no business cycle, there is only a consumer cycle. He finds further proof for this by showing that by regressing growth on all its components lagged, only residential investment and consumer services have multipliers larger than one (2 and 1.7 respectively). Leamer s causality argument is derived from the temporal ordering of the events. He concludes that it must be residential investment that causes the recessions, as residential investment consistently falls before each recession. To further argue his points on a volume cycle in housing, Leamer uses micro data from Los Angeles to show that house sales fall before and during recession, while nominal house price almost never fall. This supports his behavioural theory for the housing market, where the reluctance to sell for a lower price than the one you bought the house for limits price falls in housing, as agents instead hold on to their houses. From the Los Angeles data, Leamer also concludes that when looking for issues in the housing market, it is most useful to look at changes in the price of the cheap properties. This feeds into increased debt, which can only be financed by continuously increasing house prices, thus creating a bubble with too high construction of housing. As housing is a durable good, high production this year steals demand from next year, which gives a slump in construction when the bubble bursts as there is an oversupply of housing. Based on his results, Leamer concludes that the cause of US recession lies in the housing market. Therefore, he suggests that the FED should follow a Housing target. Furthermore, he argues that there is a conflict between Housing targeting and Inflation targeting. This has resulted in the FED following policy which is directly destructive, most notably in the 2000s, where Leamer argues that the interest rate should have been higher to offset the massive bubble in housing. Interestingly, Leamer remarks that while he has not done a full analysis, he has looked at some international data, which he feels supports his argument, though the results are not as clear cut as they are for the US. 6

12 2.1 Responses to Leamer The paper by Leamer has caused a large reaction in the business cycle literature. In a comment to the paper, Smets (2007) argue that Leamer s result of housing causing the business cycle might come from housing being a proxy for monetary policy. If this is the case, it is futile to use housing, either measured in volume or prices, as a target for monetary policy. Smets also pointed out that both results from the paper and results from the literature suggest that residential investments and consumer durables strongly react to changes in the interest rates. He cites some papers that suggest that the leading effect of residential investment disappears in models that include the term spread. He continues by pointing out that Leamer has not convincingly shown a mechanism that makes a slump in construction spread to the rest of the economy, which is needed due to the small contribution of residential investment on growth. Furthermore, he argued that if the main effects are financial, then what the FED should be worried about is the financial position of households and banks, or more generally the stability of the financial system as a whole. In Leamer (2015), Leamer re-evaluates the results in light of the financial crisis in He shows that the recession behaved somewhat differently than previous recessions. Most noticeable, housing peaked earlier, and has recovered more slowly. However, as the pattern is generally the same, Leamer concludes that the episode confirms his original view. One large deviation from Leamer s theory is that in the recession prices fell heavily, which he deemed impossible in his 2007 article. According to Leamer this is due to large number of houses taken over by the banks instead of remaining the property of heavily indebted households. As the banks are less willing to hold on to houses during a downturn, the market was flooded with abandoned housing which lead to the fall in prices. As this can be considered a one-off event due to issues in the financial sector, the author feels his point about housing generally following a volume cycle still stands. Ghent and Owyang (2010) does an empirical check of Leamer s results using micro data from US cities. They do this by setting up a VAR-model with both national and local variables. Through various specifications of the model, they find that in general there appears to be little connection between an increase in 7

13 residential investment and local employment. On the other hand, there is some connection between local employment and national residential investment, which leads the authors to suggest that the leading effect of residential investment might be due to residential investment proxying for other variables not included in the model. One issue in their specification is that they use house permits as a proxy of residential investment. While the two correlate quite a lot, which they show in the paper itself, there is a fundamental timing difference between the two. House permits are often given several years before the house is finished, which is when the investment is registered in the data. However, as the VAR approach assumes that there is a proportional change in employment when there is a change in housing permits, the authors also use a Markov-switching model to investigate if housing permits instead affect the probability of being thrown into a recession. Such a change is much more in line with the discussions in the original paper by Leamer, where he claims that a fall in residential investment leads to a recession more or less directly. The authors find that housing does not significantly affect the probability of a recession on a local or a national level. They also find that the probability of a recession is unaffected by financial variables, but they nevertheless conclude that while they have been unable to find a link, there might still be one. It is notable that these checks all use US data, and that there has yet to be done a proper econometric test of Leamer s hypothesis using international data. There are some papers that touch on the same subjects, such as Kydland, Rupert, and Sustek (2012) which look at housing dynamics in the OECD from However this paper only uses data to parametrize a theoretical model of mortgages. Notably, they find that the effect from Leamer (2007) is found in Canada and the US, but not in the other countries in his sample, namely Australia, Belgium, France and the UK. 2.2 Replicating Leamer s Results Using data 1 from OECD EO, I have replicated Leamer s results with only some minor differences. The US data is from 1960 to the first quarter of By look- 1 The data from the OECD is generally taken from national sources, but has been revised in order to make it comparable across countries. For more details see the data appendix. 8

14 ing at the cumulative abnormal contribution of gross capital formation in housing to growth, I have created similar graphs to the ones in Leamer (2007). All of the data is available at OECDs webpage, except the nominal series of capital formation in housing, which was obtained directly from the OECD staff. The downside of using data from the OECD is that we lose the early part of the sample, which makes it difficult to classify the recession in the early 1960s. Figure 2.2 and 2.3 show my recreations of the two graphs from Leamer which show the Cumulative abnormal contribution of residential investment to growth before and during all the recessions in the sample. The graphs are made by detrending the contribution of residential investment on growth, and then summing up the deviations from trend in the relevant quarters. The start of the recession is normalized to zero. As we can see, the graphs are qualitatively the same, with residential investment falling markedly before the recession, and rebounding relatively quickly during the recession. The biggest deviation is in the recession in 2001, where investment fell in Leamer s graph, but was more or less constant in mine. However, as Leamer noted in his paper, the 2001 recession is unique in it being primarily a business downturn, and is as such already a special case. The difference in results might also stem from data revision, as the event is quite close in time to the end of Leamer s sample. 2.3 Expanding the results to the rest of the OECD To replicate similar graphs for the OECD countries, it is necessary to find a suitable recession indicator. In the original paper by Leamer, he uses the official recession indicator produced by the National Bureau of Economic Research (NBER). However this indicator is only available for the US, so this method would not work for our sample. The goal is then to find an indicator that is more or less similar to the recession dating by the NBER, which is consistent across the sample. As most countries either do not define official recessions in the same way as in the USA, or do not define official recessions at all, the indicator must either be based on a common rule, or come from the same source, in order to be consistent. The OECD publishes a panel of indicators for business cycle peaks and troughs 9

15 Figure 2.2: Cumulative "abnormal contribution" of residential investment to growth eight quarters after recession. American Data. 10

16 Figure 2.3: Cumulative "abnormal contribution" of residential investment to growth four quarters before recession. American Data. 11

17 called the Composite Leading Indicators, 2 which makes for a good start. These series are constructed based on the idea of a growth cycle, which means that a recession is determined as a period of below average growth. This is not really consistent with the NBER classification, which defines a recession as a period of diminishing economic activity, implying a negative growth rate. Since no other organization publish business cycle indicators for our sample, it is necessary to use a rule to identify the beginning of recessions. A rule that has been used occasionally in the literature is the Bry-Boschan (1971) indicator (Aastveit et al. 2016), which identifies potential peaks and troughs in the business cycle through identifying local minima and maxima in the level of GDP. These potential peaks and troughs are then sorted into actual peaks and troughs through a set of censoring rules. While this method has some success in replicating NBER recessions for the United States, it is also highly dependent on the censoring rules, which would require us to specify specific rules for each country in the sample. As we want to have an identification scheme which is as uniform across countries as possible, this method is somewhat undesirable. One of the most common ways of classifying recessions is by defining it as two consecutive quarters of negative growth. This simple method does a good job of approximating NBER recessions in the United States. A clear drawback of the method is that it may identify multiple recessions in countries that experience a period of sluggish growth, where a more nuanced approach might identify it as a single major event. This drawback will become clear for some of the countries in our sample, but the graphs will still work well as descriptive tools. We identify a recession as starting in the first quarter of at least two consecutive quarters of negative growth. By replicating Leamer s method on the sample of OECD countries, we can then investigate whether his results hold for the rest of the world. The results from this exercise are mixed, with most countries showing examples of recessions that both fit and do not fit the pattern described by Leamer. Unsurprisingly, the United States is the country that fits best with the pattern found in Leamer s original article. Other countries with good fit are Canada, Austria, Estonia, Finland, Spain, the Netherlands and Sweden, though all of these countries 2 The indicator can be found at 12

18 Figure 2.4: Cumulative "abnormal contribution" of residential investment to growth eight quarters after recession in Spain. Unlike the US there are no signs of a quick rebound. have some recessions that do not fit in the pattern. 3 The results show that none of the countries have the same degree of fit as the US. This does not mean we should dismiss Leamer s theories just because not all countries are a perfect fit. All of the countries in our sample are smaller countries than the US, they are therefore more vulnerable to be sent into recession by outside forces. For example, a country like New Zealand, which is heavily dependent on exports of dairy products, could easily be sent into recession whenever there is a sufficiently strong shock to world food prices. The US, as a significantly larger economy, is more robust to these kinds of shocks, which means more of its recessions will be due to domestic issues, such as residential investment. 3 To see graphs for all the countries, see appendix B. 13

19 Figure 2.5: Cumulative "abnormal contribution" of residential investment to growth four quarters before recession in Spain. The behaviour before a recession is quite similar to the behaviour in the US. 14

20 Figure 2.6: Cumulative "abnormal contribution" of residential investment to growth eight quarters after recession in Sweden. The pattern is more mixed than in the USA, but there is a bigger rebound effect than we see in Spain. 15

21 Figure 2.7: Cumulative "abnormal contribution" of residential investment to growth four quarters before recession in Sweden. The pattern from Leamer (2007) fits nicely for some, but not all, recessions. 16

22 Interestingly, even though there are several countries that fit the pattern of a sharp fall in residential investment before a recessionary period, very few countries show signs of residential investment rebounding quickly after the recession. This is a more serious blow for Leamer s general theory of the business cycle being driven by a volume cycle in housing, as this would imply that while housing may be a leading cause of recessions, it is not a big part of the rebound in the sample. This may be explained as the housing cycle being longer in other countries than the US, which means the graphs do not catch the rebound in housing. This may be explained by a recent finding by the OECD (Caldera and Johansson 2013) that the price responsiveness of housing is massively higher in the USA than in any other OECD country. The price elasticity of the US housing supply is approximately 2, massively higher than the second highest country, Sweden, which has an elasticity lower than 1.4. This means that the US housing market is somewhat unique amongst the OECD countries. If the US housing market truly is more reactive to price changes, we would expect the other OECD countries, which are less reactive, to have a different relationship between the price cycle and the volume cycle of housing than the one found in Leamer s 2007 paper. At the very least, the connection should be weaker. This means that when we are next moving towards the econometric specifications, we expect estimated effects of residential investment on the probability of a recession in the US to be larger than for other countries. Even so, we should still find some signs of the pattern mentioned before recessions in countries like Spain, which our graphs show to have a lot of similarities with the US pattern. 17

23 Chapter 3 Predicting recessions using a generalized linear model. To investigate the relationship between residential investment and recessions, we want to create a model where the probability of a recession is a function of residential investment in the preceding quarters, and potentially also on other controls. A common way of achieving this is by using a generalized linear model 1, as introduced in Nelder and Wedderburn (1972). If residential investment is truly causing recessions, or at least leading them, then we should be able to predict a recessionary quarter with a model using only information about residential investment in the period just before the recession. The model is defined by the following equations y i,t = { 1 if there is a recession in the quarter 0 if there is not a recession in the quarter (3.1) E(y y ) = P (y y ) = f(y ) (3.2) y i,t = α i + X i,t β i + ɛ i,t (3.3) 1 Some readers will recognize that this method is equivalent to a Discrete Choice model, or a logistical regression. While the term is rarely used in econometrics, it is well established in statistics. We use the term to avoid the potentially confusing common interpretations of a discrete choice model, which would not make sense given the topic. 18

24 where X is a 1xk matrix of independent variables, β is a kx1 vector of parameters, and ɛ is an error term. Countries and time are indexed with the indices i and t respectively. α is a country dependent constant term. The model is estimated using maximum likelihood. In order to estimate the model we need to make an assumption on the functional form of the probability of recession, f(y ). This can be thought of as the link function between the independent variables and the recessions. The results will generally not depend a lot on this specification. A commonly used specification is the logit specification, as this gives the parameters a clear interpretation corresponding to a change in the log - odds of recession. We will use this specification throughout the thesis. The logit specification implies the following form for f(y ) f(y ) = exp(y ) 1 + exp(y ) (3.4) Other possible choices are the probit specification, where f(y ) is the normal distribution. The difference in results between the logit specification and the probit specification is minimal in our models. We could also go for less complex models, for example a log specification, where f(y ) is the log of y, or making f(y ) a linear function. 3.1 Properties of the estimators. The primary requirement for consistency of estimation in the logit models we use in this and the following chapters is an assumption of independence between observations. However, this requirement is unlikely to hold in our case, as there is highly persistent auto-correlation in the residuals. This is not too surprising, as recessionary quarters come in clusters, followed by long strings of non-recessionary quarters. We cannot remove this auto-correlation without significantly changing the interpretation of the models. An example of such a model is the recession starts model in chapter 4. Fortunately, the estimates will still be consistent as long as the dependency between observations is not too large and not increasing in the sample size. However, there is good reason to believe that the models will be far away from complete dependency between observations. For example, in the model for the US 19

25 with residential investment, the residuals seem to follow an AR(1) process with a lag coefficient of about 0.5. As such, the dependency between observations is not too large, nor is there any reason to suspect that it should be increasing in the sample size. If anything, it might decrease, as the dependency might be caused by the low amount of recessions in each individual country. Hence, the parameters will be consistent and asymptotically normal, but the low number of observations in some countries should make us wary of making too strong conclusions based on the models. The residuals in a logit model are generally not normally distributed, but should have constant variance in both recessionary and non-recessionary quarters. This is difficult to test in our models, as the lack of observations of recessions makes any inference about residual behaviour during recessions difficult. Finally, as our models are somewhat simple, with only two variables, there is a high risk of omitted variable bias. In sum, it is possible that the parameter estimates we obtain are biased, however this is not too much of a problem as we are not trying to achieve estimates of the true effect of the variables on the recessionary probabilities, but rather to get an idea of the predictive power of residential investment as a lead-variable of recessions. The models will also generally overstate the statistical significance of the results, as they do not take the dependency between observations into account, and therefore overstate the amount of information in each observation. We should therefore be skeptical of barely significant results, but highly significant ones should be trustworthy. 3.2 Interpreting the results A consequence of this framework is that the fitted value of y from the model is equal to the probability of a recession in the given quarter. Figure 3.1 shows the estimated probability of a recession using a logit model with four lags of residential investment as the explanatory variable. The graph tells much of the same story as the graphs shown in chapter 2. Residential investment does a great job predicting the recessions, and has few cases where it predicts recessions that did not happen. 20

26 Implied Probability of Recession in the US, Residential investment. Figure 3.1: Estimated implied probability of recession for the US using four lags of residential investment. Shaded areas indicate the technical recessions that have been defined in the text. Implied Probability of Recession in the US, Spread. Figure 3.2: Estimated implied probability of recession for the US using four lags of the spread. Shaded areas indicate the technical recessions that have been defined in the text. 21

27 As the model is binary, it gives us predictions of positives (recession quarters) and negatives (non-recession quarters). We can therefore separate the results of the model in a recession quarter as being either true or false positives, where it correctly or incorrectly predicts a recession quarter. In a non-recession quarter, the result will either be a true or false negative, corresponding to the model either correctly or incorrectly predicting a non-recession quarter. An example of a false positive is the peak in the probability of recession in 2010 we see in figure 3.1. The greatest example of a false negative is the the recession in This recession is not in the sample, as GDP growth did not fall for two consecutive quarters during the recession. This implies that while the model does a great job of predicting some kinds of recessions, it does not pick up everything. This point is also made in Leamer (2007), who noted that the 2000 recession was something of a special case, as it was mainly connected to the dot-com stock bubble, and never really appeared in GDP data. In order to put our results into context, we compare the predictive power of residential investment with a similar model using the yield spread, which is commonly used in the literature as an indicator or lead-variable of recessions (Estrella and Mishkin (1998), Rudebusch and Williams (2009), Liu and Moench (2014)). Other potential candidates are stock prices, credit spreads and oil prices (Liu and Moench (2014), Hamilton (2003)). Figure 3.2 shows the results when we replace residential investment with the yield spread in the model. 2 This model is still quite good at predicting the recessions, though it shows some probability of a recession throughout the 1990 s through This in turn shows that the model makes a better prediction of the recession in When we look at data from the other countries, it becomes clear that the US is something of a special case, with both models being fairly good at predicting recessions. Figure 3.3 shows the estimated probabilities for Sweden using the same model. This model does a much worse job in predicting recessions, and it does not pick up the very severe recession that started in 1990 until it was almost over, and has several false alarms throughout the 1990s. This is not however, due to swedish recessions being particularly difficult to predict, as we see in figure 3.4. This figure shows the implied probabilities from a model where we use the yield spread instead of residential investment as the conditioning variable. This model 2 For details about the variables, see the data appendix. 22

28 Implied Probability of Recession in Sweden, Residential investment model. Figure 3.3: Estimated implied probability of recession in Sweden using four lags of residential investment. Shaded areas indicate the technical recessions that have been defined in the text. Implied Probability of Recession in Sweden, spread model. Figure 3.4: Estimated implied probability of recession in Sweden using four lags of the spread. Shaded areas indicate the technical recessions that have been defined in the text. 23

29 ROC cruve for the US, residential investment model. Figure 3.5: Recieving Operating Characteristics Curve for a model for the US using residential investment. clearly picks up the recession in 1990, and has much smaller reactions during the 1990s. Although the fit is not quite as good as the fit of residential investment in the US, it is difficult to quantify the difference in quality based on the graphs. We therefore need to find a way to summarize the information in the graphs, and ideally be able to represent how well the models predict recessions in a single number. In the next section we will introduce a measure of predictive power that can help us quantify the behaviour of these graphs, before we look at the results themselves. 3.3 How to measure predictive power? In order to compare model specifications, we need a way to compare the predictive power of different models. A method to measure the predictive power of a binary model is to graph the Receiver Operating Characteristic (ROC) curve. This curve shows the trade-off between the true positive rate, i.e. how well the model predicts a recession, against the false positive rate, which is how often the model correctly predicts that there is not a recession. In order to go from probabilities 24

30 to predictions we need to choose a cutoff value, which is the minimum level of the probability of recession which leads us to predict a recession. The trade-off between true positives and false positives will vary with this cutoff value, giving us the ROC curve. To get an intuitive understanding of how this works, look at Figure 3.5, which shows the ROC curve corresponding to the model in figure 3.1. Let us imagine that we start with a cutoff value of 1, meaning that we only predict that there will be a recession if the implied probability of a recession is equal to 1. In this case we will never mistakenly predict a recession in the US case, as we will never predict one, so the false positive rate is 0. As we lower the cutoff value, the false positive rate will continue to be zero, until we eventually start predicting recessions. Figure 3.5 shows us that the highest amount of correct recession calls we can make will still maintaining no false alarms, is about 40 %. As we accept more false positives, and thus reduce the cutoff value, we get more and more correct recession calls until we eventually correctly predict all of them. This however come at the cost that we now predict a recession in 10 % of the non-recession quarters. The diagonal line going through the graph illustrates how well a model which has no information on recession would have done, for example if we made our prediction of whether or not there is recession in a given quarter based on a cointoss. Figure 3.6 and 3.7 show graphs corresponding to similar models for Swedish residential investment and spread. While neither of these models are as good at characterizing recessions as residential investment is in the US, they are both doing better than the coin-toss. To summarize the information in the ROC curve in a number, we calculate the area underneath the curve (AUROC). This can be thought of as the average of the true positive rate over the false positive rates. Alternatively it can be interpreted as the probability that a given model assigns a randomly drawn recession quarter a higher implied recession probability than a randomly drawn non-recession quarter. The AUROC value of the coin-toss model is 0.5,so any model with an AUROC value of 0.5 or lower has no predictive power. If a model perfectly predicts both recession and non-recession quarters, then the AUROC value should be 1. Anything between 0.5 and 1 indicate a model with some predictive power. 25

31 Implied Probability of Recession in Sweden, spread model. Figure 3.6: Recieving Operating Characteristics Curve for a model for Sweden using residential investment. Implied Probability of Recession in Sweden, spread model. Figure 3.7: Recieving Operating Characteristics Curve for a model for Sweden using the spread. 26

32 Country Spread RI Both Sample AUS :Q1-2015:Q1 AUT :Q1-2015:Q1 BEL :Q1-2015:Q1 CAN :Q1-2015:Q1 CZE :Q2-2015:Q1 DEN :Q1-2015:Q1 FIN :Q1-2015:Q1 FRA :Q1-2015:Q1 GER :Q2-2015:Q1 HUN :Q2-2015:Q1 IRE :Q2-2015:Q1 ITA :Q2-2015:Q1 JPN :Q1-2013:Q2 LUX :Q1-2015:Q1 NLD :Q1-2015:Q1 NZL :Q1-2013:Q2 NOR :Q1-2015:Q1 POR :Q3-2015:Q1 ESP :Q1-2015:Q1 SWE :Q1-2015:Q1 GBR :Q1-2015:Q1 USA :Q1-2015:Q1 Total Table 3.1: Area Under ROC Curve (AUROC) values for different models using the spread, Residential investment (RI) and a combined model with both for all countries in the sample, in addition to the total predictive power of the models. 27

33 Country Sum of RI F - test Sum of Spread F - test Correlation AUS AUT BEL CAN CZE DEN FIN FRA GER HUN IRE ITA JPN LUX NLD NZL NOR POR ESP SWE GBR USA Table 3.2: Sum of all lagged parameters for each variable, and an F-test of the hypothesis that all lagged parameters are equal to zero for all countries in the sample. 28

34 3.4 Results Table 3.1 shows the AUROC values for all the countries in the sample where we have data for both the spread and residential investment. It also shows the total AUROC for each type of model, which is calculated by stacking the implied probabilities for each country, and then calculating a corresponding ROC curve. We see that residential investment beats the spread as a predictor during the sample in more than half of the countries we have data for. Notably, both the UK and France, where Kydland et al. (2012) found housing did not lead the business cycle, is amongst the countries where residential investment is the best predictor of a recession. This difference in results is probably due to methodological differences. The results from Kydland et al. are based on correlations across the entire sample, while my method primarily focuses on the effects around recessionary events. Even so, when we stack the data into one series and calculate the total AUROC value for the entire sample, residential investment barely outperforms the spread. The combined model strongly outperforms both of the separate models, implying that the spread may work well as a control for external shocks to the economy, while residential investment catches domestic shocks. Even so, in several countries the combined model barely outperforms the best of the separate models. In these cases, the two variables have little unique information about future recessions. Some notable exceptions are France, Canada, Austria, Finland, Luxembourg and Portugal, who all get more than a 0.03 increase in their AUC value when we include both variables in the model. Table 3.2 shows the sum of the lags on all the parameters and the result of a F-test of the hypothesis that all the lagged parameters are zero. As we see, the countries where both of the variables are significant heavily overlap the countries where the combined model does a better prediction than the best separate model. This is not surprising, as both these results mean that the two variables contribute separate information about future recessions. 3.5 Panel estimation results An interesting extension from the country by country analysis in the previous section is to combine all the countries into a panel, and to see if we can find any 29

35 Country Spread RI Both Sample AUS :Q1-2015:Q1 AUT :Q1-2015:Q1 BEL :Q1-2015:Q1 CAN :Q1-2015:Q1 CZE :Q2-2015:Q1 DEN :Q1-2015:Q1 FIN :Q1-2015:Q1 FRA :Q1-2015:Q1 GER :Q2-2015:Q1 HUN :Q2-2015:Q1 IRE :Q2-2015:Q1 ITA :Q2-2015:Q1 JPN :Q1-2013:Q2 LUX :Q1-2015:Q1 NLD :Q1-2015:Q1 NZL :Q1-2013:Q2 NOR :Q1-2015:Q1 POR :Q3-2015:Q1 ESP :Q1-2015:Q1 SWE :Q1-2015:Q1 GBR :Q1-2015:Q1 USA :Q1-2015:Q1 Total Table 3.3: Area Under ROC Curve (AUROC) values for different panel models using the spread, Residential investment (RI) and a combined model with both for all countries in the sample. 30

36 Combined models Separate models Variable Beta F/p-value Beta F/p-value Res. Invest lag Res. Invest lag Res. Invest lag Res. Invest lag Sum Res. Invest e e-34 Spread lag Spread lag Spread lag Spread lag Sum Spread e e-15 Table 3.4: Estimated parameters and p - value in the combined and separate panel models, in addition to the sum of the parameters and a F-test of the hypothesis that all are zero. generality in the results. We do this by stacking the variables from the previous model and adding country specific dummy variables. 3 Once we have estimated the parameters for the panel model, we can then see how well these parameters predict recessions in the separate countries, as well as in total. Table 3.3 shows the AUROC values for the different countries when using the parameters from the panel model. While the spread now has a AUROC value of less than 0.5 for some countries, residential investment still predicts well in all countries it predicted well for in the country-by-country estimation. We can also see that residential investment outperforms the spread as a predictor when we calculate the AUROC value across the entire sample. This finding is the opposite of what we found when we looked at the total AUROC value for the country-bycountry models, implying that residential investment has a more homogeneous effect on recessions than the spread has. This is supported by the parameter values found in table 3.2, which shows that almost all countries have clearly negative parameter values in the cases where they are statistically significant. The panel data results also allow us to look more closely at the specific para- 3 This setup requires us to either remove the constant or one of the dummies to avoid perfect multicolinearity. In the calculations done I removed the constant term, but the two formulations are completely equivalent. 31

37 meters of the model. Table 3.4 shows the estimated parameters for the panel model. As we see, residential investment has the highest explanatory power in the combined model, with all the lags being highly significant. For the spread, none of the lags are individually statistically significant with a significance level of 0.05, though the lags are jointly highly significant. The separate models show similar results. To summarize our findings, we see that the results from the panel model are consistent with residential investment being the best predictor of recessions. As the spread primarily reflects the expectations of households and firms about the future, this indicates that residential investment have predictive power beyond the expectations of the households in the economy. Furthermore, the effect of residential investment is more homogeneous than the effect of the spread. Together, this gives support to the claim of housing leading the business cycle in most countries. As such, we can not reject that the theory shown in Leamer (2007) is correct based on the results in this chapter. 32

38 Chapter 4 Predicting Recessions as individual events. In chapter 3 we used residential investment to predict whether or not the economy was in a recession. However, a method that would be closer in spirit to the framework of Leamer (2007) would be to investigate whether residential investment predicts the shift into a recession regime. We therefore consider each recession period as an individual event, instead of considering each recession quarter to be an event, as we did in chapter 3. To achieve this, we replace the y - variable from chapter 3 with an indicator variable which is equal to one in the first quarter of each recession, and zero otherwise. We enforce that a recession cannot start unless there has been at least two non-recession quarters before it. The amount of observations of recessions starts are naturally much lower than the amount of observations of recession quarters. This creates a problem for some of the countries in our sample due to a lack of sufficient number of recessions in the data. This will make our country-by-country analysis much more limited, but thankfully our panel analysis avoids all these problems, as we have more than enough observations once we have pooled observations across the entire sample. Nevertheless, it is worth noting that predicting recession starts is a massively different exercise to predicting recession quarters. The most important thing when predicting recession starts is the timing, which may be off to begin with as we are using a quite simple recession index. The results are still interesting and informative, especially when viewed together with the results from chapter 3. 33