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Prévisions des crises

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In the last two decades, international financial markets have integrated to an extent remarkable
in history. This process has profound implications for the transmission of shocks,
both across financial asset prices and to the real economy. Therefore, the role of asset prices
including interest rates, stock returns, dividend yields and exchange rates are considered
as predictors of inflation as well as growth.

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Prévisions des crises

  1. 1. The Yield Curve as a Predictor of U.S. Recessions Based on (Estrella & Mishkin 1996) Work Lin Jibin and Verny Tania Universit´e Paris 1 Panth´eon Sorbonne Dissertation submitted to MOSEF, Faculty of Economics, Universit´e Paris 1 Panth´eon Sorbonne, as a partial fulfilment of the requirement for the Master 1 of Economie Quantitative. May 2015
  2. 2. Contents List of Figures ii 1 Introduction 1 2 Probit Model 4 3 Economic Indicators 6 3.1 Treasury Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 S&P500 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Consumer Price Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.4 Crude Oil Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Unemployment Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4 Comparisons of the forecasted probability of recession of different indicators 29 4.1 Comparison of Spread & Consumer Price Index . . . . . . . . . . . . . . . . 30 4.2 Comparison of Spread & Crude Oil Price . . . . . . . . . . . . . . . . . . . . 31 4.3 Comparison of Spread & S&P500 . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.4 Comparison of Spread & Unemployment Rate . . . . . . . . . . . . . . . . . 33 5 Conclusion 34 Bibliography 35 i
  3. 3. List of Figures 3.1 Means of the Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Statistical Description of the Indicators . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Statistical Distribution of spread . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Treasury Spread: Ten-Year Bond Rate minus Three-Month Bill Rate Monthly Average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.5 Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the Trea- sury Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.6 Statistical Distribution of S&P500 index . . . . . . . . . . . . . . . . . . . . . 14 3.7 S&P500 monthly index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.8 Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the S&P500 index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.9 Statistical Distribution of CPI . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.10 CPI monthly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.11 Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the Con- sumer price index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.12 Statistical Distribution of crude oil price . . . . . . . . . . . . . . . . . . . . . 22 3.13 Crude oil monthly price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.14 Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the Crude oil price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.15 Statistical Distribution of unemployment rate . . . . . . . . . . . . . . . . . . 26 3.16 Unemployment rate monthly . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 ii
  4. 4. LIST OF FIGURES 3.17 Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the unem- ployment rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.1 Graph of Forecasted probability of recessions of Spread and CPI . . . . . . . 30 4.2 Graph of Forecasted probability of recessions of Spread and Crude oil price 31 4.3 Graph of Forecasted probability of recessions of Spread and S&P500 . . . . 32 4.4 Graph of Forecasted probability of recessions of Spread and Unemployment rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 iii
  5. 5. Chapter 1 Introduction In the last two decades, international financial markets have integrated to an extent re- markable in history. This process has profound implications for the transmission of shocks, both across financial asset prices and to the real economy. Therefore, the role of asset prices including interest rates, stock returns, dividend yields and exchange rates are considered as predictors of inflation as well as growth. Recently, numerous empirical studies have been carried out in order to evaluate the usefulness of spreads between long and short-term interest rates as leading indicators of real economic activity. In most these studies linear regression-based techniques are applied to forecast output growth rate and also even though, some well-known authors have done probit estimations in order to calculate the likelihood of future economic recessions. In such probit models the dependent variable is a recession dummy that equals one if the economy is in recession and zero otherwise, whereas the explanatory variable is a lagged potential recession predictor. This particular model translates the steepness of the yield curve at the present time into a likelihood of a recession sometime in the future. Thus, we need to identify three components: a measure of steepness, a definition of recession, and a model that connects the two. The approach which is in fact the most appropriate is the probit equation as mentioned previously make use of the normal distribution to convert the value of a measure of yield curve steepness into a probability of recession one year ahead. The input to this calculation is the value of the term spread, that is, the difference between long and short-term interest rates in month t. The output is the probability of a recession occurring in month t + 12 from the viewpoint of information available in month 1
  6. 6. t. Both of these variables, however, need to be defined more precisely that is, we need to specify what we mean by a recession and which long and short term interest rates we will use to produce the spread that constitutes our measure of steepness. Moreover, recent survey (Stock & Watson 2003) have determined that the slope of the yield curve is referred as one of the main asset prices studied and the one which has proved most useful for forecasting. The latter has come into particular focus in the recent pe- riod, as its inversion in the US triggered a lively debate as to whether it would signal a recession. In this framework, the usefulness of the slope of the yield curve as a predic- tor of future growth has been challenged vigorously ((Greenspan 2005); (Estrella 2005); (Bernanke 2006)). The yield curve is confirmed to be a quite reliable recession predictor across the evaluated countries, because on average it signals recessions a considerable time before they actually begin, and produces only a few signals that falsely indicate business cycle turning points. (Estrella & Hardouvelis 1991) and (Estrella & Mishkin 1997) pro- vide various evidence for the United States that the yield spread significantly outperforms other popular financial and macroeconomic indicators in forecasting recessions, particu- larly with horizons beyond one quarter. In his recent study, (Dueker 1997) confirms the US results presented by (Estrella & Mishkin 1998) using a modified probit model which includes a lagged dependent variable and additionally allows for Markov-switching coef- ficient variation. Building upon the expectations hypothesis, two straightforward arguments explaining why the yield curve contains information about future recessions. The first argument re- lates to the role of monetary policy. When a central bank raises short-term interest rates, agents may view this contraction as temporary and, consequently, raise their expectations of future short-term rates by less than the observed current change in the short rate. From the expectations theory it follows that long-term rates rise by less than the short-term rate, resulting in a flat or inverted yield curve. Since the real sector of the economy is affected by monetary policy measures with a considerable time lag, agents expect future real eco- nomic growth to decline. Hence, the monetary tightening flattens the yield curve and simultaneously increases the likelihood of a recession onset. The second one focusses on inflationary expectations that are contained in long-term interest rates. Since recessions are generally associated with low inflation rates, an anticipation of a recession probably results in a falling long-term rate. Consequently, when the short rate does not change, the 2
  7. 7. yield curve flattens or inverts. Using information across the whole yield curve, rather than just the long maturity segment, may lead to more efficient and more accurate forecasts of GDP. But in an OLS framework, since yields of different maturities are highly cross-correlated, it is difficult to use multiple yields as regressors because of the occurrence of collinearity problems. This collinearity suggests that we may be able to condense the information contained in many yields down to a parsimonious number of variables. We would also like a consistent way to characterize the forecasts of GDP across different horizons to different parts of the yield curve. With OLS, this can only be done with many sets of different regressions. These regressions are clearly related to each other, but there is no obvious way in an OLS frame- work to impose cross-equation restrictions to gain power and efficiency. However, the reliability of the yield curve’s predictive ability has been challenged lately. (Greenspan 2005) argues that many factors can affect its slope, including the gap between near-term and long-term inflation expectations or near-term and long-term risk premia. Yet, all these factors do not have similar implications for future growth. For in- stance, as he recalls, the yield curve flattened sharply from 1992 to 1994, shortly before the US economy entered its longest expansion of the post-war period. Consequently, a flattening of the yield curve might also well signal a deceleration in inflation accompa- nied by a favorable growth outlook, e.g. once the impact of an adverse oil price shock has dampened. In our study, we have decided to base our work on those of (Estrella & Mishkin 1996) as well as adding additional variables such as five indicators over 10 years as monthly that is the spread, the price of crude oil, the rate of unemployment, the S&P500 index and the consumer price index. An outline of the report is given as follows: In chapter 2, we give the explanation of the probit model. Chapter 3 describes briefly the five indicators, their graphical representations of forecasted probability during different quarters. In chapter 4, we identify the comparisons between the indicators through graphical representation. Finally, we conclude our study in chapter 5. 3
  8. 8. Chapter 2 Probit Model In order to quantify the predictive power of the variables examined with respect to future recessions, the probit model is being used. The name come from PRObability probIT. This model is a particular type of regression where the dependent variable can only take two possible values that is whether the economy is or is not in a recession. It is defined in reference to a theoretical linear relationship of the form In statistics, a probit model is a type of regression where the dependent variable can only take two values, for example married or not married. The name is from probability + unit. The purpose of the model is to estimate the probability that an observation with par- ticular characteristics will fall into a specific one of the categories; moreover, if estimated probabilities greater than 1/2 are treated as classifying an observation into a predicted category, the probit model is a type of binary classification model. y∗ t+h = αi + βixt + t where y∗ t refers to an unobservable variable that determines the occurrence of a recession at time t, h refers to the length of forecast horizon, β is the vector of coefficients, t is the normally distributed error term and xt is a vector of independent variables. So , the observable recession indicator Recessiont form part of this model by: Recessiont = 1 if y∗ t > 0 and, Recessiont = 0 otherwise. 4
  9. 9. The form of the estimated equation is given as follows: P(Recessiont+h = 1) = F(βixt), where F refers to the cumulative normal distribution function corresponding to − . The probit model is being estimated by the maximum likelihood which is defined by the following: L = (ΠRecessiont+h=1)F(βixt)(ΠRecessiont+h=0)(1 − F(βixt)) In practice, the recession indicator is given from the standard National Bureau of Economic Research recession dates, that is, Recessiont = 1 if the economy is in recession in quarter t, = 0 otherwise. In the following chapters, we has decided to apply the probit model on different eco- nomic indicators and hence give a significant interpretation on each results obtained through statistical descriptions tables as well as graphical representations. 5
  10. 10. Chapter 3 Economic Indicators In our study for the forecasting of crisis, we have decided to choose monthly data from 01/04/1953 to 01/03/2015 as well as additional variables with those of (Estrella & Mishkin 1996) and they are the Treasury Spread: Ten-Year Bond Rate minus Three-Month Bill Rate Monthly Average, the S&P500 index, the Consumer price index, the crude oil price and additionally the unemployment rate. To be able to assess how well each indicator variable predicts recessions, we use the so-called probit model described previously, which, in our application, directly relates the probability of being in a recession to a particular explana- tory variable such as the yield curve. In order to understand more clearly, let see a brief explanation on each on them as well as their graphical representations of forecasted prob- ability at h = 1, 2, 4 that is at different horizons so as to see more clearly the difference of forecasting at different quarters. Firstly, we start the application on the whole data that is from 01/04/1953 to 01/03/2015 by using the probit model and we obtained the following: Figure 3.1: Means of the Indicators 6
  11. 11. Figure 3.2: Statistical Description of the Indicators Conclusion: We notice that only the consumer price index and the unemployment rate are rejected at a critical value of 0, 05 whereas the other indicators are under the null hypothesis that is presence of correlation is there with the recession. Now, we will study furthermore, with forecasting under different horizons h as mentioned before. 7
  12. 12. 3.1 Treasury Spread 3.1 Treasury Spread The interest rates generally used to compute the spread between long-term and short-term rates on the yield curves predictive power. For example, market analysts usually choose to focus on the difference between the ten-year and two-year Treasury rates, while some academic researchers have favored the spread between the ten-year Treasury rate and the federal funds rate. In our research, we have decided to choose Ten-Year Bond Rate and Three-Month Bill Rate Monthly. We then applied the probit model at different horizons and obtained the following results: 8
  13. 13. 3.1 Treasury Spread (a) Treasury Spread: Ten-Year Bond Rate minus Three- Month Bill Rate Monthly Average; one quarter ahead (b) Treasury Spread: Ten-Year Bond Rate minus Three- Month Bill Rate Monthly Average; two quarters ahead (c) Treasury Spread: Ten-Year Bond Rate minus Three- Month Bill Rate Monthly Average; four quarters ahead Figure 3.3: Statistical Distribution of spread Conclusion: We can see that whatever the horizon used that is the h, the impact of the spread on the recession remains highly correlated. The p-value is extremely high that is p-value= 0, 1269 with h = 1, p-value = 0, 6436 with h = 2 and p-value = 0, 3164 with h = 4, then we do not reject the null hypothesis, thus it means that there is the presence of correlation during periods of recession. 9
  14. 14. 3.1 Treasury Spread Conclusion: It is similar there between the short-term and long-term. We can deduce through the graphs 3.4 and 3.5 the high presence of correlation during recession times. We can see the steepness when we do the forecast at h = 4 and clearly see that a high signal occur when approaching near the recession period. 10
  15. 15. 3.1 Treasury Spread (a) Treasury Spread: Ten-Year Bond Rate minus Three- Month Bill Rate Monthly Average; one quarter ahead (b) Treasury Spread: Ten-Year Bond Rate minus Three- Month Bill Rate Monthly Average; two quarters ahead (c) Treasury Spread: Ten-Year Bond Rate minus Three- Month Bill Rate Monthly Average; four quarters ahead Figure 3.4: Treasury Spread: Ten-Year Bond Rate minus Three-Month Bill Rate Monthly Average 11
  16. 16. 3.1 Treasury Spread (a) One quarter ahead (b) Two quarters ahead (c) Four quarters ahead Figure 3.5: Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the Treasury Spread 12
  17. 17. 3.2 S&P500 Index 3.2 S&P500 Index So we applied again the probit model on the S&P500 index at different horizons and ob- tained the following results: 13
  18. 18. 3.2 S&P500 Index (a) S&P500 index; one quarter ahead (b) S&P500 index; two quarters ahead (c) S&P500 index; four quarters ahead Figure 3.6: Statistical Distribution of S&P500 index Conclusion: We can notice that it is similar to the consumer price index, the forecasting is not efficient when the horizon is small that is when h = 1, the p-value is 0, 2573, when h = 2, the p-value is 0, 6315. When h = 4, the forecast is very efficient and its p-value is 0, 0009. 14
  19. 19. 3.2 S&P500 Index (a) S&P500 index; one quarter ahead (b) S&P500 index; two quarters ahead (c) S&P500 index; four quarters ahead Figure 3.7: S&P500 monthly index Conclusion: According to the graphs 3.7 and 3.8, we can clearly notice that the signal is high when the economic condition change. In fact, the reversal of the curve of the S&P500 before crisis period allow a better forecasting of recession, therefore it indicates that it is a good indicator for forecasting recession. 15
  20. 20. 3.2 S&P500 Index (a) One quarter ahead (b) Two quarters ahead (c) Four quarters ahead Figure 3.8: Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the S&P500 index 16
  21. 21. 3.3 Consumer Price Index 3.3 Consumer Price Index We applied again the probit model on the consumer price index at different horizons and obtained the following results: 17
  22. 22. 3.3 Consumer Price Index (a) Consumer price index; one quarter ahead (b) Consumer price index; two quarters ahead (c) Consumer price index; four quarters ahead Figure 3.9: Statistical Distribution of CPI Conclusion: For the consumer index price, we can notice that the forecasting done with the horizon h = 1 and h = 2 with p-value 0, 5559 and 0, 7259 respectively allow to prevent at short-term the risk of recession. However, it is not efficient when the horizon is large for example at h = 4. 18
  23. 23. 3.3 Consumer Price Index (a) Consumer price index; one quarter ahead (b) Consumer price index; two quarters ahead (c) Consumer price index; four quarters ahead Figure 3.10: CPI monthly Conclusion: The graphical representations 3.14 and 3.13 shows clearly that the the data of the CPI with h = 4 are correlated with period of recession, we can notice that the reversal of the curves of the CPI forecasting the arrival of crisis. 19
  24. 24. 3.3 Consumer Price Index (a) One quarter ahead (b) Two quarters ahead (c) Four quarters ahead Figure 3.11: Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the Con- sumer price index 20
  25. 25. 3.4 Crude Oil Price 3.4 Crude Oil Price We applied again the probit model on the crude oil price at different horizons and obtained the following results: 21
  26. 26. 3.4 Crude Oil Price (a) Crude oil price; one quarter ahead (b) Crude oil price; two quarters ahead (c) Crude oil price; four quarters ahead Figure 3.12: Statistical Distribution of crude oil price Conclusion: We reject the null hypothesis at horizon 1 which has a p-value of 0, 0879 with a critical value at 0, 05 and at h = 2, 4, we do not reject the null hypothesis with p-value of 0, 2233 and 0, 6176 respectively. 22
  27. 27. 3.4 Crude Oil Price (a) Crude oil price; one quarter ahead (b) Crude oil price; two quarters ahead (c) Crude oil price; four quarters ahead Figure 3.13: Crude oil monthly price Conclusion: The graphs 3.14 and 3.13 show clearly that there is a signal effect before the recession with the oil price and this increase as h increases. Consequently, we deduce that the price of oil is a good indicator because it refers to one which is easily affected by the change of financial markets. 23
  28. 28. 3.4 Crude Oil Price (a) One quarter ahead (b) Two quarters ahead (c) Four quarters ahead Figure 3.14: Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the Crude oil price 24
  29. 29. 3.5 Unemployment Rate 3.5 Unemployment Rate So we applied again the probit model on the unemployment rate at different horizons and obtained the following results: 25
  30. 30. 3.5 Unemployment Rate (a) Unemployment rate; one quarter ahead (b) Unemployment rate; two quarters ahead (c) Unemployment rate; four quarters ahead Figure 3.15: Statistical Distribution of unemployment rate Conclusion: We can see that whatever the horizon h, there will be correlation that is the p-value will be large, thus it refers to a suitable indicator. 26
  31. 31. 3.5 Unemployment Rate (a) Unemployment rate; one quarter ahead (b) Unemployment rate; two quarters ahead (c) Unemployment rate; four quarters ahead Figure 3.16: Unemployment rate monthly Conclusion: However, through the graphical representations 3.17 and 3.16, the corre- lation is extremely high at h = 1. But the fact that the rate of unemployment is a good indicator of long-term and that it can be the results of crisis, this can call into question its predictive power of crisis. 27
  32. 32. 3.5 Unemployment Rate (a) One quarter ahead (b) Two quarters ahead (c) Two quarters ahead Figure 3.17: Probability of U.S. Recession at h = 1, 2, 4 ahead, as Predicted by the unem- ployment rate 28
  33. 33. Chapter 4 Comparisons of the forecasted probability of recession of different indicators Now we will combine some indicators together in order to see the difference between those indicators chosen during recession periods. 29
  34. 34. 4.1 Comparison of Spread & Consumer Price Index 4.1 Comparison of Spread & Consumer Price Index Figure 4.1: Graph of Forecasted probability of recessions of Spread and CPI Conclusion: The figure 4.1 shows that the forecasting of the two indicators do vary in a similar case but the only thing that is different is their degree of amplitude. Indeed, the spread’s variation is less important in relation of the consumer price index. Moreover, the spread has become more reactive than the CPI, that is, it is always in advance according to the crisis than the CPI. 30
  35. 35. 4.2 Comparison of Spread & Crude Oil Price 4.2 Comparison of Spread & Crude Oil Price Figure 4.2: Graph of Forecasted probability of recessions of Spread and Crude oil price Conclusion: This graphical representation 4.2 demonstrates that the two curves are rela- tively different. This means that it does not vary when the economic conditions is good but when a recession approaches, there is convergence of the variations which we can defined them as good indicators. 31
  36. 36. 4.3 Comparison of Spread & S&P500 4.3 Comparison of Spread & S&P500 Figure 4.3: Graph of Forecasted probability of recessions of Spread and S&P500 Conclusion: This graph 4.3 is clearly similar to that of the spread and CPI where the sen- sibility of the S&P500 index seems to be larger than the spread. Indeed, there are higher peaks which can be observed through the S&P500 curve than the spread. This means that it is more volatile and thus conclude that both indicators give better forecasting at the same times. 32
  37. 37. 4.4 Comparison of Spread & Unemployment Rate 4.4 Comparison of Spread & Unemployment Rate Figure 4.4: Graph of Forecasted probability of recessions of Spread and Unemployment rate Conclusion: Here the forecasting seems to be non significant compared to the spread which is more significant. But we can suppose that it refers to a long-term indicators and hat it does not forecast crisis efficiently. 33
  38. 38. Chapter 5 Conclusion After our research study on the yield curve as a leading indicator based on the work of (Estrella & Mishkin 1996) with additional variables, we can notice that better indicators do exist for the forecasting of the arrival of periods of recessions either in a partial way or an efficient one. In fact, the spread is considered to be the variable that represents the very high capacity to forecast growth at a horizon of 12 months. On the other hand, other indicators as the S&P500, the price of crude oil have a fundamental impact on short-term and indicators such as consumer price index and the unemployment rate are more long-term. According to the important economic condition and their different features, we have obtained results which satisfied the forecasting at different horizons chosen that is at h = 1, 2, 4. However, it seems that the forecasting cannot be done immediately, it would need four quarters for the overall indicators to be able to measure appropriately the crisis. Nevertheless, it also seems that their predictive power is not the same for all of them. In relation to their different sensibility, we can conclude that the choice of indicator is fundamental in order to anticipate future crisis and even though to avoid repeating the same history, thus to reduce the effect when anticipating the arrival of it. So, the question to ask is whether the financial variables are useful to anticipate the economic growth? (L. 2010). 34
  39. 39. Bibliography Bernanke (2006), ‘Reflections on the yield curve and monetary policy’, Remarks Before the Economic Club of New York, Federal Reserve Board . Dueker (1997), ‘Strengthening the case for the yield curve as a predictor of u.s. recessions’, Federal Reserve Bank of St. Louis Review 79 113, 41–51. Estrella (2005), ‘Why does the yield curve predict output and inflation’, Federal Reserve Bank of New York, mimeo . Estrella & Hardouvelis (1991), ‘The term structure as a predictor of real economic activity’, Journal of Finance pp. 555–576. Estrella & Mishkin (1996), ‘The yield curve as a predictor of u.s. recessions’, Federal Reserve Bank of New York Current Issues in Economics and Finance 2 7. Estrella & Mishkin (1997), ‘The predictive power of the term structure of interest rates in europe and the united states: Implications for the european central bank’, European Economic Review pp. 1375–1401. Estrella & Mishkin (1998), ‘Predicting u.s. recessions: financial variables as leading indica- tors’, Review of Economics and Statistics pp. 45–61. Greenspan (2005), ‘Letter to the honourable jim saxton, chairman of the joint economic committee’. L., F. (2010), Revue Economique 61. Stock & Watson (2003), ‘Forecasting output and inflation: the role of asset prices’, Journal of Economic Literature (41), 778–829. 35

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