Predicting Cycles in Economic Activity

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 926 April 2008 Predicting Cycles in Economic Activity Jane Haltmaier Note: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comments. References to International Finance Discussion Papers (other than an acknowledgement that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the WEB at www.federalreserve.gov/pubs/ifdp/

Predicting Cycles in Economic Activity Jane Haltmaier** Abstract: Predicting cycles in economic activity is one of the more challenging but important aspects of economic forecasting. This paper reports the results from estimation of binary probit models that predict the probability of an economy being in a recession using a variety of financial and real activity indicators. The models are estimated for eight countries, both individually and using a panel regression. Although the success of the models varies, they are all able to identify a significant number of recessionary periods correctly. Keywords: forecasting, turning points, business cycles, economic indicators JEL classification: E37 * The author is an Adviser in the Division of International Finance, Board of Governors of the Federal Reserve System, Washington, D.C. 20551. E-mail: Jane.T.Haltmaier@frb.gov Phone: 202-452-2374 Fax: 202-736-5638 The views expressed here are the sole responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System.

I. Introduction Accurate prediction of cycles in economic activity is one of the more challenging aspects of economic forecasting. At the same time, it is of key importance for policymaking. Expansionary policy may be appropriate when an economy is contracting, but once a turning point has been reached, the authorities may want to begin to shift to a more neutral stance fairly quickly. Similarly, policymakers do not want to allow an economy to overheat, but if a peak has been reached, they may want to switch early to stimulus to prevent a downward spiral. However, because business cycles are often highly influenced by forces that are hard to model, such as consumer and business confidence, structural models often have difficulty capturing cyclical turning points. An alternative approach for predicting turning points is the estimation of binary probit models, which calculate the probability that an economy is in either an expansion or a contraction. When the estimated probability crosses a specified threshold, a turning point is predicted. This type of approach has been applied to prediction of recessions in U.S. GDP by Estrella and Mishkin (1998), using financial indicators as explanatory variables. Chin, Geweke, and Miller (2000) apply a similar methodology to the prediction of turning points in monthly unemployment rates. These techniques are also similar in some respects to models that assess the probability of financial crises within a specific time period in developing economies.1 This paper uses monthly data from eight countries (the United States, Canada, Japan, Germany, the United Kingdom, Mexico, Korea, and Taiwan) to estimate the 1 See Edison (2000), Kaminsky and Reinhart (1999), and Kaminsky, Lizondo, and Reinhart (1998).

probability that these economies will be in either an expansion or contraction in a specific month, with both real and financial indicators as explanatory variables. Specifically, binary probit models in which the dependent variable takes on the value 0 during an expansion and 1 during a recession are estimated using lags of the explanatory variables that range from one to three months, depending on their relative timeliness. The time horizon has been deliberately kept short because the relationships become much less reliable further out. However, the indicators are generally available on a much more timely basis than is GDP; partial monthly data for financial indicators are available nearly in real time. Using indicators that are all lagged by at least one month, it is, for example, possible in October to make an assessment of the probability that an economy is currently in a recession, while fourth-quarter GDP for many regions will not be available until February or March. As noted above, the model is applied to eight countries, which were chosen mainly because of availability of long time series for the explanatory variables. All of the countries except Mexico have data available back to the 1970s, and Mexico’s is available beginning in 1980. The models were estimated both for the individual countries and using a panel regression. The results vary widely, but overall suggest that this type of model can play a useful role in forecasting cyclical activity. The paper is organized as follows: section 2 describes the data in general terms, with more detail provided in Appendix 1. Section 3 describes and evaluates the individual country models, and section 4 does the same for the panel regression. Section 5 concludes. 2

II. Data The recessionary and expansionary periods used in the model are based on monthly business cycle peaks and troughs identified by the NBER for the United States, by Statistics Canada for Canada,2 and by Economic Cycle Research Institute (ECRI) for the other countries. The peaks and troughs for each country are shown in table 1. There are three recessionary periods each for the United Kingdom, South Korea, and Taiwan, four for Japan and Germany, five for the United States and Canada, and six for Mexico. As noted earlier, the dependent variable in the binary probit regressions takes on the value 1 during the recessionary periods and 0 during expansions. The country-specific explanatory variables fall into five categories: exchange rates (both real and nominal trade-weighted exchange rates were used in alterative versions, as they are too collinear to use in the same regression); the change in a stock price index; the spread between short-term and long-term interest rates, if available, and the change in a short-term interest rate if no long-term rate is available for most of the period; a confidence or other leading indicator; and the change in an activity indicator (industrial production for most countries, employment for Canada because it is available on a more timely basis than industrial production). The change in oil prices (the U.S. spot price of West Texas Intermediate oil, which is available back to 1946) was also used in each initial equation. Most of the data were drawn from the Haver Analytics database, which includes data from the source countries. More details are provided in Appendix 1. 2 These dates, which are unofficial, were published by Statistics Canada in the Canadian Economic Observer in December 2001 and were obtained from the Haver Analytics database. The recessionary period December 2000 to September 2001 was not included in this publication and was added based on the behavior of Canadian monthly GDP over that period. 3

As indicated in table 2, the expected signs for stock prices, leading indicators, and activity variables are unambiguously negative, as improvement in any of these variables should reduce the probability of a recession and vice versa. Interest rate spreads are available back to the 1970s for all of the industrialized countries (the United States, Canada, Japan, the United Kingdom, and Germany), as well as for Taiwan. A decline in this variable (a flattening of the yield curve) should be associated with an increased probability of a recession, so the expected sign is negative. Long-term interest rates were not available for Korea and Mexico for a long period, so the change in a short-term rate was used instead of a spread. The sign on this variable should be positive—a rise in short-term interest rates should be associated with an increased probability of a recession. The expected signs on both oil prices and exchange rates are ambiguous. Increases in oil prices should increase the probability of a recession for oil-importing countries (resulting in an expected positive sign), but might reduce the probability for an oil exporter (such as Mexico). Declines in nominal exchange rates, particularly for developing countries, often precede a period of negative growth, especially for developing countries, as they may reflect a loss of confidence and may have adverse balance-sheet effects if currency mismatches are widespread. On the other hand, if the real exchange rate also declines, exports would become more competitive, potentially having a stimulative effect on output. However, if prices react quickly to upward pressure from the falling currency, real exchange rates may be little changed in such an episode. Versions of the model were estimated using both real and nominal exchange rates separately and the better version was used. 4

III. Country Models A. Estimation Binary probit models were estimated for each of the eight countries, with the recession-expansion indicator as the dependent variable and each of the variables described in the previous section as explanatory variables. The particular lags used for each variable were chosen based on their relative timeliness, which varied by country. For instance, financial variables (exchange rates and interest rates) are generally available one or two months sooner than other variables. Thus, lags from one to six months were included for these variables in the equation. Variables such as industrial production were lagged from two or three months to six months, depending on their timeliness for each country. The final model for each country was obtained by progressively eliminating the lags of the variables that were insignificant or incorrectly signed. This was done twice, once using the nominal exchange rate and again using the real rate. The better-fitting final equation was used in the evaluation. The models were estimated from the earliest available date, which was usually sometime in the mid-1970s, through the end of 2005. Full estimation results for the final model for each country are shown in Appendix 2. Table 3 is a summary table that shows the level of significance of each coefficient, thus allowing for comparison across countries of which variables are important. Oil prices are important for the United States, the United Kingdom, Korea, and Taiwan. At least one lag of the leading indicator is significant for all of the countries except Canada and Mexico. The yield spread (the change in the short-term interest rate for Korea) is significant all of the countries except Mexico and Taiwan. Stock prices are significant for all of the countries except Korea. Real activity indicators are important for Canada, 5

the United Kingdom, Mexico, and Korea. Exchange rates played a variety of roles. For the United Kingdom and Taiwan, the real exchange rate is positive and significant, indicating that an appreciation increases the probability of a recession, consistent with an important effect of trade on output. The real exchange rate for Mexico, and the nominal rate for Korea are negative and significant, suggesting that for those countries a currency depreciation is associated with a weakening of output. The fit of the models varies considerably across countries, but is generally better for the advanced economies. McFadden R2s range from around .4 for Mexico and Taiwan to about .5 for Korea and Japan, .6 for the United States and Germany, to a high of nearly .8 for the United Kingdom. Charts 1 through 8 show the actual and fitted values from each of the eight equations. Two general observations may be made: (1) the value of the indicator does appear to increase notably during most of the recessionary periods for most of the countries, but the timing is not usually exact. However, even though the indicator sometimes does not spike in advance, it can still be useful in identifying a recessionary period before it is evident in the data. (2) there are numerous “false positives”. The next section provides a more rigorous evaluation of the models’ performance. B. Evaluation In order to evaluate the success of the binary probit models in predicting turning points, it is necessary to choose a “threshold” above which the predicted probability is said to be signaling a recession. The choice of the threshold depends largely on the preferences of the policymaker. The higher the threshold the greater is the probability of 6

making a Type I error (not predicting a recession that actually occurs), but the lower the probability of making a Type II error (predicting a recession that does not occur). The choice of a threshold will thus depend on the relative weights placed on avoiding the two types of errors. The methodology used here to choose a threshold follows that used in Bussiere and Fratscher (2006). If the policymaker’s loss function is written as: L = α x π (T) + (1-α) x π (T) 1 2 where π (T) and π (T) are the probabilities of making Type I and Type 2 errors, 1 2 respectively, for each threshold T, then the threshold T that is chosen should be the one that minimizes the loss function for a given α. However, the choice of α is judgemental. In order to derive some empirical guidance for the choice of a threshold, the value of the loss function was calculated using the estimated error probabilities from each of the country equations for thresholds for the values from .1 to .9 (increasing by .1) for three values of α: .25, .5, and .75. The results are shown in table 4. For each country and value of α, the minimum value of the loss function is shown in bold. The last column shows the average value for the 8 countries. These results suggest that the optimal threshold is relatively low, certainly less than .5. When the policymaker puts equal weights on avoiding the two types of errors (α= .5), the optimal threshold ranges from .1 for the United Kingdom, Canada, Korea, and Taiwan, to .3 for Japan. It is .2 for the other four countries. The average optimal threshold for the eight countries also is .2. When the weight on Type I errors (missing an actual recession) rises to .75, the optimal threshold is .1 for six of the countries, .2 for the other two, and .1 for the average. When the weight on Type I errors falls to .25, the 7

optimal threshold ranges from .2 to .5, with the average at .4. In the analysis that follows a threshold of .2 is used on the assumption that the weight placed on avoiding a missed recession should be at least as large as the weight on a false signal. In-sample Evaluation Table 5 provides an indication of how well the model does at correctly categorizing recessions and expansions. The percentage of total observations that are successfully categorized (column 1) is generally quite high, around 90 percent for the United States, Canada, the United Kingdom, Germany, Korea, and Taiwan, and close to 80 percent for Japan and Mexico. The percentage of recessions correctly called (column 2) is usually lower, although there are a couple of exceptions. However, this percentage is over 80 percent for the United States, Canada, the United Kingdom, Japan, Germany, and Mexico. It is lower for Korea and Taiwan, which have the fewest recessions. The percentage of expansionary periods that are correctly categorized is likely to be high, given that the vast majority of both the actual and predicted observations will be expansions. A more telling statistic is “false alarms” (the percentage of predicted recessionary periods that occur during expansions), shown in column 3 vs. the corresponding percentage of predicted recessionary periods which do occur in actual recessions, column 4 (these two sum to 1). The value in column 4 is the in-sample probability of being in a recession when the predicted value is above the critical value. The probability of a false alarm is lowest for Germany and the United Kingdom (around 20 percent), and is around 30-40 percent for most of the other countries. It is highest for Taiwan at 59 percent. The probability of a recession when the indicator is less than .2 (column 5) is quite small for most countries. 8

Out-of-sample Evaluation The models were first re-estimated through 1999, and these equations were then used to derive out-of-sample forecasts for the period 2000-2006. Strictly speaking, this is not really an out-of-sample forecast, since the same form of the equation was used as in the full sample period. Thus, it is possible that some variables (at some lags) that were included in the models evaluated in the previous section might not be significant for the shorter period and vice versa. However, the exercise was done using the same equations in order to be able to compare these results with those obtained in-sample. The reestimated equations, also shown in appendix 2, are generally fairly similar to the original equations. Table 6 shows the same set of results as shown in table 5 for the full period. The total percentage of observations that are correctly categorized is similar for most countries to the in-sample results. The percentage of recessionary periods correctly categorized is higher for some countries, notably for the U.S. and Japan, where it is 100 percent. The percentage of false alarms when the indicator is above the critical value is higher for some, but lower for others. (Taiwan shows no predictions above the critical value during the out-of-sample period.) The probability of missing a recessionary period is still low for most countries, but is quite high at 27.5 percent for Mexico. However, it might be noted that this actually refers to one long recessionary period, and the indicator does categorize a substantial part of it correctly. Charts 9-16 give a more qualitative impression of how the indicators perform. One interesting result is that only one recession (Taiwan, 2003) is missed entirely. Another is that many false alarms are a result of inexact timing (i.e., they occur either just 9

before a recession begins or just after it ends), rather than occurring in the middle of an expansionary period. However, Korea provides a dramatic exception, as the indicator suggests four recessions during the out-of-sample period, compared with just one official recession. IV. Panel Estimation A panel regression with fixed effects was also estimated. Although the panel regression may be assuming a degree of conformity across countries that is not in fact the case, it has the advantage of having many more observations relative to the number of parameters being estimated. The results are shown in table 7. The equation is similar to the separate country equations: each of the independent variables was lagged between one and six months, depending on timeliness, in the initial estimation, and insignificant and/or incorrectly signed variables were progressively eliminated.3 All of the explanatory variables except oil prices were significant for at least one lag. The R2 is .43. Charts 17 through 24 compare the fitted values from the panel equation with both the actual values and the fitted values from the separate equations. A visual inspection suggests that the fitted indicators from the panel equation do tend to rise during recessionary periods, but often not as much as the fitted values from the separate equations. (However, this may not affect the ability of the indicator to signal a recession depending on the critical value.) As shown in table 8, the loss function is minimized at a critical value of .2 when equal weights are placed on avoiding the two types of errors, similar to the result from the single-equation estimation. Thus, .2 is used as the critical value in the evaluation. 3 Mexico and Korea did not have enough long-term interest rate data to calculate yield curves for a long period of time. As a proxy, the negative of the short-term interest rate was used, and a dummy was included for those countries. 10

Table 9 evaluates the success of the panel equation in predicting recessions insample for both the total and for each country. The percentage of observations correctly categorized is lower than for the individual equations (table 5) in all cases, although the size of the difference is generally fairly small. For the full regression, the percent of total observations correctly categorized is 85 percent, compared with a total of 89 percent for the individual equations taken together. The out-of-sample results are shown in table 10. These forecasts are better than those from the individual country models for six of the eight countries, although the Korean model does not register the recession that occurred during that period. The overall percentage of periods correctly categorized is 86 percent for the panel regression, compared with a composite of 82 percent for the individual regressions. Conclusion This paper reports the results of an estimation of binary probit models for eight countries, both individually and as part of a panel, in an effort to forecast cycles in economic activity. The results vary widely, but several of the explanatory variables are significant in each of the country equations and all of them are significant in the panel regression. A loss function that places equal weights on errors in the two types of periods suggests that the optimal critical value signaling a recession is relatively low at .2 for both the individual country equations and the panel regressions. Using this critical value the individual models correctly identify nearly 90 percent of both the total and the recessionary periods on average in-sample, although these percentages differ substantially across countries. The percentage of total periods correctly identified is a little lower for the panel regression on average, although the percentage of recessionary 11

periods correctly identified is about the same. The low critical value results in a relatively high percentage of false alarms, with 37 percent of fitted values above .2 occurring during expansionary periods for the individual equations on average, and 45 percent for the panel regression. Nevertheless, the overall results suggest that models such as these can provide some general guidance to policymakers interested in gauging early signs of a weakening economy during an expansion or a strengthening economy during a contraction. 12

REFERENCES Bussiere, Matthieu and Marcel Fratzscher (2006), “Towards a New Early Warning System of Financial Crises,” Journal of International Money and Finance, vol 25(6), 935-973. Chin, Dan, John Geweke, and Preston Miller (2000), APredicting Turning Points,@ Federal Reserve Bank of Minneapolis Research Department Staff Report #267 Edison, Hali (2000), ADo Indicators of Financial Crises Work? An Evaluation of an Early Warning System,@ Board of Governors of the Federal Reserve System, International Finance Discussion Paper #675. Estrella, Arturo and Frederic Mishkin (1998), APredicting U.S. Recessions: Financial Variables as Leading Indicators,@ The Review of Economics and Statistics, 80, 45-61. Goodwin, Thomas (1993), ABusiness-Cycle Analysis With a Markov-Switching Model,@ Journal of Business and Economic Statistics, vol. 11, #3, 331-339. Kamin, Steven, John Schindler, and Shawna Samuel (2001), AThe Contribution of Domestic and External Factors to Emerging Market Devaluation Crises: An Early Warning Systems Approach,@ International Finance Discussion Paper #711. Kaminsky, Graciela, and Carmen Reinhart (1999), AThe Twin Crises: Causes of Banking and Currency Crises,@ American Economic Review, June, 473-500. Kaminsky, Graciela, Saul Lizondo, and Carmen Reinhart (1998), ALeading Indicators of Currency Crises,@ International Monetary Fund Staff Papers, 45, #1. 13

Table 1 Business Cycle Peaks and Troughs United Canada Japan United Germany South Taiwan Mexico States Kingdom Korea peak 1973:11 1974:12 1973:11 1974:9 1973:8 1979:3 1973:12 1982:3 trough 1975:3 1975:3 1975:2 1974:8 1975:7 1980:10 1975:1 1983:7 peak 1980:1 1980:1 1992:4 1979:6 1980:1 1997:8 2000:8 1985:10 trough 1980:7 1980:6 1994:2 1981:5 1982:10 1998:7 2001:9 1986:11 peak 1981:7 1981:6 1997:3 1990:5 1991:1 2002:12 2003:2 1992:10 trough 1982:11 1982:10 1999:7 1992:3 1994:4 2003:9 2003:5 1993:10 peak 1990:7 1990:3 2000:12 2001:1 1994:11 trough 1991:3 1992:4 2003:7 2003:8 1995:7 peak 2001:3 2000:12 2000:8 trough 2001:11 2001:9 2003:8 peak 2004:12 trough 2005:6 Table 2 Expected Signs for the Explanatory Variables Variable Expected sign explanation + for oil importers, Oil prices Ambiguous - for oil exporters Exchange rate* Real Ambiguous Increase might either reduce Nominal net exports or increase confidence Stock price - Improvement in any of these Leading Indicator - indicators reduces the probability of a recession Activity - Narrowing of the spread - for spread, between long-term and short- Interest Rates (spread or + for change in short-term term rates is associated with change in short-term rate) rates an increased probability of a recession * assumes an increase in the exchange rate signals an appreciation. 14

Table 3 Estimated Coefficients (lags in parentheses) Region U.S. Canada Japan U.K. Germany Mexico Korea Taiwan Coeff. Oil Price .033(2)b .051(2)c .042(2)b .035(3)a .025(4)c .028(2)b Leading -.127(6)a -.061(1) -.064(3)a -.088(2)a -.964(3)a -.305(3)b Indicator -.097(6)b -.559(4)b -.360(5)a -.943(6)a -.251(6)b Yield -.332(3)a -.616(6)a -.705(1)a -.626(1)a -1.08(6)a .339(2)a+ Spread -.313(6)a Stock -.040(1)c -.040(2)c -.044(1)a -.079(2)b -.034(2)b -.023(1)a -.035(1)a Price -.087(2)a -.060(3)b -.064(2)a -.038(5)b -.020(2)b -.110(4)a -.053(4)b -.063(3)a -.040(6)a -.023(3)b -.110(6) a -052(5)b -.043(6)a -.022(5)b -.038(6)c Real -1.95(2)a -.281(3)c -.475(3)a -.124(8)b Activity -1.30(3)a -.587(4)a -.186(9)a -.865(4)b -.419(5)b -.152(6)c Nominal -.120(4)b Exchange -.173(6)a Rate Real .297(1)a -.064(2)c .151(4)b Exchange .277(2)b -.103(3)b .139(5)b Rate .364(3)a -.123(4)a .296(4)b -.063(5)c .317(5)a -.083(6)b .385(6)b McFadden R2 .66 .58 .46 .78 .62 .43 .46 .37 a significant at the 1 % level b significant at the 5% level. c significant at the 10 percent level. + change in short-term interest rate. 15

Table 4 Value of Loss Function for given α and threshold 25 UK CA JA GE KO TA MX Avg. Threshold α = .75 .1 6.93 1.80 7.74 13.59 7.07 13.80 16.90 13.92 8.63 .2 7.47 7.10 13.78 14.64 7.03 19.48 32.71 13.60 11.72 .3 9.89 11.28 24.85 17.35 10.13 28.21 44.59 19.16 17.20 .4 15.02 14.21 26.72 21.42 12.67 35.42 54.66 27.29 22.00 .5 17.37 16.97 30.32 26.87 19.28 48.64 54.45 27.54 26.47 .6 25.42 16.89 34.20 33.25 21.99 48.48 54.31 35.90 30.86 .7 35.08 19.81 35.27 43.31 25.80 50.24 54.31 40.38 35.74 .8 39.03 30.00 40.23 47.31 33.18 57.77 62.07 47.92 42.36 .9 55.62 40.25 46.55 59.84 40.14 59.62 64.66 54.40 50.79 Threshold α = .50 .1 8.29 3.61 10.30 20.37 13.34 14.77 16.56 24.55 12.39 .2 7.52 6.20 12.05 15.65 9.30 15.88 24.04 18.42 11.47 .3 8.66 8.57 18.66 15.37 9.95 20.52 30.57 18.54 13.83 .4 11.52 10.41 18.96 16.71 11.05 24.69 36.90 22.71 16.33 .5 12.52 11.94 20.98 19.64 14.74 33.18 36.49 21.01 18.74 .6 17.51 11.79 23.56 23.32 16.20 32.86 36.21 25.65 21.36 .7 23.86 13.63 23.99 29.80 18.26 33.82 36.21 28.01 24.38 .8 26.21 20.00 27.01 32.12 22.71 38.62 41.38 32.11 28.45 .9 37.18 26.94 31.04 40.12 27.12 39.75 43.11 36.27 33.95 Threshold α = .75 .1 9.66 5.41 12.87 27.14 19.62 15.75 16.22 35.17 16.16 .2 7.58 5.29 10.31 16.65 11.56 12.28 15.36 23.23 11.22 .3 7.44 5.85 12.48 13.40 9.76 12.83 16.54 17.91 10.46 .4 8.02 6.62 11.19 11.99 9.42 13.95 19.15 18.13 10.67 .5 7.67 6.91 11.63 12.42 10.21 17.71 18.52 14.47 11.00 .6 9.60 6.68 12.93 13.39 10.40 17.23 18.10 15.39 11.85 .7 12.63 7.44 12.71 16.28 10.73 17.39 18.10 15.64 13.02 .8 13.38 10.00 13.79 16.92 12.24 19.47 20.69 16.29 14.55 .9 18.73 13.62 15.52 20.41 14.09 19.87 21.55 18.13 17.12 16

Table 5 Model Evaluation (in-sample) % of total % of % of false prob of prob of observations recessionary alarms when recession recession correctly periods p.v. > .2 when p.v. > .2 when p.v. < .2 categorized correctly categorized U.S. 92.4 92.6 35.1 64.9 1.2 Canada 90.4 84.5 38.0 62.0 2.7 U.K. 95.1 92.0 23.3 76.7 1.3 Japan 83.3 86.4 40.2 59.8 4.8 Germany 89.0 95.2 24.5 75.5 2.4 Korea 89.7 76.9 47.4 52.6 3.1 Taiwan 90.7 58.6 58.5 41.5 3.5 Mexico 75.4 83.5 44.1 55.9 8.9 Total 88.6 86.7 37.0 63.0 3.1 p.v. = predicted value Table 6 Model Evaluation (out-of-sample) % of total % of % of false prob of prob of observations recessionary alarms when recession recession correctly periods p.v. > .2 when p.v. > .2 when p.v. < .2 categorized correctly categorized U.S. 84.5 100.0 61.9 38.1 0.0 Canada 94.0 55.6 16.7 83.3 5.1 U.K. 94.0 NA* 100.0 0.0 0.0 Japan 75.0 100.0 40.4 59.6 0.0 Germany 83.3 54.8 0.0 100.0 20.9 Korea 69.0 88.9 75.8 24.2 2.0 Taiwan 81.0 0.0 NA** NA** 19.0 Mexico 73.8 66.7 22.2 77.8 29.2 Total 81.8 66.4 42.9 57.1 9.8 p.v. = predicted value *there were no recessions in the U.K. during the out-of-sample period. **the predicted value never exceeded the critical value during the out-of-sample period for Taiwan. 17

Table 7 Results of Panel Regression (Preferred Equation) Sample: 1973:08 to 2005:12 Variable Coefficient Std. Error Z-Statistic Prob. C 0.952710 0.254163 3.748415 0.0002 Exchange rate(-1) -4.118604 1.597582 -2.578024 0.0099 Exchange rate(-3) -3.471046 1.705465 -2.035249 0.0418 Exchange rate(-6) -5.806483 1.758986 -3.301039 0.0010 Stock price (-1) -2.122200 0.484139 -4.383453 0.0000 Stock price (-2) -2.404494 0.488647 -4.920722 0.0000 Stock price (-3) -2.199412 0.482461 -4.558735 0.0000 Stock price (-4) -1.227985 0.489297 -2.509691 0.0121 Stock price (-5) -1.512747 0.497441 -3.041060 0.0024 Stock price (-6) -1.439765 0.489552 -2.940987 0.0033 Leading Ind. (-4) -0.017743 0.010174 -1.744001 0.0812 Leading Ind. (-6) -0.021621 0.009745 -2.218574 0.0265 Yield (-3) -0.247681 0.046183 -5.362998 0.0000 Yield -6) -0.294310 0.047251 -6.228588 0.0000 Yield(-3)*DUMK 0.159851 0.071256 2.243311 0.0249 Yield(-6)*DUMK 0.339984 0.070709 4.808242 0.0000 Yield(-3)*DUMM 0.189228 0.051366 3.683948 0.0002 Yield(-6)*DUMM 0.372996 0.053624 6.955807 0.0000 Activity (-3) -17.47433 2.314219 -7.550852 0.0000 Activity (-4) -21.76745 2.640760 -8.242875 0.0000 Activity (-5) -16.67411 2.502781 -6.662233 0.0000 Activity (-6) -9.079876 2.252303 -4.031374 0.0001 McFadden R-squared 0.427685 Mean dependent var 0.178632 S.D. dependent var 0.383109 S.E. of regression 0.282809 Akaike info criterion 0.556924 Sum squared resid 232.7446 Schwarz criterion 0.615988 Log likelihood -789.3998 Hannan-Quinn criter. 0.578191 Restr. log likelihood -1379.311 LR statistic 1179.823 Avg. log likelihood -0.268595 Prob(LR statistic) 0.000000 Obs with Dep=0 2414 Total obs 2939 Obs with Dep=1 525 18

Table 8 Value of Loss Function for panel regression for given α and threshold Threshold α = .25 α = .5 α = .75 .1 24.09 18.73 13.36 .2 15.49 15.03 14.56 .3 12.72 16.29 19.86 .4 12.45 19.48 26.50 .5 13.98 24.56 35.13 .6 15.74 29.42 43.09 .7 17.52 33.72 49.91 .8 19.94 39.01 58.07 .9 20.99 41.80 62.62 Table 9 Panel Equation Evaluation (In-Sample) % of total % of % of false prob of prob of observations recessionary alarms when recession recession correctly periods p.v*. > .2 when p.v. > when p.v. < categorized correctly .2 .2 categorized United States 91.5 90.7 36.4 63.6 1.6 Canada 85.8 77.6 48.3 51.7 4.3 U.K. 89.6 82.6 44.1 55.9 2.7 Japan 81.2 86.7 45.0 55.0 4.6 Germany 83.2 97.6 33.7 66.3 1.5 Korea 86.0 64.1 57.6 42.4 4.9 Taiwan 82.7 55.2 70.4 29.6 3.9 Mexico 72.1 95.6 48.2 51.8 2.9 Full Regression 84.8 86.5 45.2 54.8 3.4 * p.v. = predicted value Table 10 Panel Equation Evaluation (Out-of-Sample) % of total % of % of false prob of prob of observations recessionary alarms when recession recession correctly periods p.v.* > .2 when p.v. > when p.v. < categorized correctly .2 .2 categorized United States 94.0 87.5 36.4 63.6 1.4 Canada 95.2 66.7 14.3 85.7 3.9 U.K. 98.8 NA# 100.0 0.0 0.0 Japan 64.3 100.0 49.2 50.8 0.0 Germany 89.3 87.1 15.6 84.4 7.7 Korea 89.3 0.0 NA+ NA+ 10.7 Taiwan 79.8 18.8 25.0 75.0 16.3 Mexico 76.2 71.4 21.1 78.9 26.1 Full Regression 86.3 71.2 32.5 67.5 8.1 * p.v. = predicted value. # there were no UK recessions in the out-of-sample period. +the Korean indicator did not rise above the critical value in the out-of-sample period. 19

In-sample fitted values Chart 1 United States 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Chart 2 Canada 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 20

Chart 3 Japan 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Chart 4 Germany 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 M06 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 21

Chart 5 United Kingdom 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 Chart 6 Mexico 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 22

Chart 7 Korea 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 Chart 8 Taiwan 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 23

Out-of-Sample Forecasts Chart 9 United States 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 Chart 10 Canada 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 24

Chart 11 Japan 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 Chart 12 Germany 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 25

Chart 13 United Kingdom 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 Chart 14 Mexico 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 26

Chart 15 Korea 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 Chart 16 Taiwan 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 M01 M04 M07 M10 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003 2003 2004 2004 2004 2004 2005 2005 2005 2005 2006 2006 2006 2006 27

In-sample fitted values Chart 17 United States 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 M08 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 actual single equation panel Chart 18 Canada 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 actual single equation panel 28

Chart 19 Japan 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 actual single equation panel Chart 20 Germany 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 actual single equation panel 29

Chart 21 United Kingdom 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 M10 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 actual single equation panel Chart 22 Mexico 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 M11 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 actual single equation panel 30

Chart 23 Korea 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 M12 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 actual single equation panel Chart 24 Taiwan 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 M01 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 actual single equation panel 31

Appendix 1: Data General Oil prices: U.S. spot price of West Texas Intermediate (prior to 1982, the posted price), $/barrel Exchange rates: trade-weighted average exchanges rates, nominal and priceadjusted United States Leading indicator: manufacturing PMI composite index Yield curve: market yield on U.S. Treasury securities at 10-year constant maturity less the fed funds effective rate Activity: industrial production Stock market: Nasdaq composite index Canada Leading Indicator: composite index of 10 leading indicators Yield curve: 5 to 10 year bond yield average less the 3-month Treasury bill yield Activity: employment Stock market: Toronto stock exchange composite index Japan Leading indicator: Tankan survey: all enterprises forecast of business conditions Yield curve: yield on newly-issued 10-year government bonds less the official discount rate Activity: industrial production Stock market: Nikkei index of common share prices Germany Leading Indicator: IFO business climate index Yield curve: Estimated 10-year government debt yield less the 3-month interbank offered rate Activity: industrial production Stock market: DAX index United Kingdom Leading indicator: survey of industrial trends, optimism regarding business situation compared to three months earlier Yield curve: government war loan yield less the daily 3-month interbank rate Activity: industrial production Stock market: FTSE share price index 32

Mexico Leading Indicator: composite index of leading indicators Yield curve: U.S. yield curve (defined above) Activity: industrial production Stock market: IPC stock price index Korea Leading indicator: leading composite index Yield curve: U.S. yield curve (defined above) Activity: industrial production Stock market: KOSPI composite index Taiwan Leading Indicator: Composite leading index Yield curve: Base lending rate less the official rediscount rate Activity: industrial production Stock market: Taiwan stock price index 33

Appendix 2: Estimation results for Final Model Equations Table A2.1 United States Sample: 1972M01 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C 4.952632 1.144010 4.329185 0.0000 DOIL(-2) 0.032756 0.016939 1.933771 0.0531 DOIL(-4) 0.024560 0.012980 1.892114 0.0585 DOIL(-6) 0.028298 0.014639 1.933027 0.0532 USLI(-6) -0.127421 0.024671 -5.164772 0.0000 USYC(-3) -0.332561 0.090599 -3.670708 0.0002 USYC(-6) -0.313051 0.081703 -3.831560 0.0001 DUSSTKN(-1) -0.039853 0.022357 -1.782551 0.0747 DUSSTKN(-2) -0.087180 0.024165 -3.607744 0.0003 DUSSTKN(-4) -0.110286 0.025762 -4.280940 0.0000 McFadden R-squared 0.657685 Mean dependent var 0.132353 S.D. dependent var 0.339290 S.E. of regression 0.206623 Akaike info criterion 0.321499 Sum squared resid 16.94912 Schwarz criterion 0.429646 Log likelihood -54.58579 Hannan-Quinn criter. 0.364293 Restr. log likelihood -159.4608 LR statistic 209.7499 Avg. log likelihood -0.133789 Prob(LR statistic) 0.000000 Obs with Dep=0 354 Total obs 408 Obs with Dep=1 54 34

Table A2.2 Japan Sample: 1974M08 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.40877 0.299149 -1.36644 0.1718 JALI(-1) -0.06096 0.007498 -8.12905 0.0000 JAYC(-1) -0.70548 0.154951 -4.55293 0.0000 DJASTK(-1) -0.04448 0.016923 -2.62807 0.0086 DJASTK(-2) -0.06371 0.017347 -3.67271 0.0002 DJASTK(-3) -0.06269 0.017431 -3.59631 0.0003 DJASTK(-6) -0.04329 0.016672 -2.59674 0.0094 McFadden R-squared 0.460589 Mean dependent var 0.233422 S.D. dependent var 0.42357 S.E. of regression 0.302223 Akaike info criterion 0.623343 Sum squared resid 33.79539 Schwarz criterion 0.696356 Log likelihood -110.5 Hannan-Quinn criter. 0.652324 Restr. log likelihood -204.854 LR statistic 188.7065 Avg. log likelihood -0.2931 Prob(LR statistic) 0.000000 Obs with Dep=0 289 Total obs 377 Obs with Dep=1 88 35

Table A2.3 Canada Sample: 1972M01 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.682859 0.135067 -5.055703 0.0000 CAYC(-6) -0.616426 0.085131 -7.240948 0.0000 DCAEMP(-2) -1.951527 0.500282 -3.900851 0.0001 DCAEMP(-3) -1.299095 0.450365 -2.884540 0.0039 DCAEMP(-4) -0.865168 0.436657 -1.981345 0.0476 DCASTK(-2) -0.040201 0.022255 -1.806411 0.0709 DCASTK(-3) -0.060068 0.021564 -2.785619 0.0053 DCASTK(-4) -0.052912 0.022142 -2.389657 0.0169 DCASTK(-5) -0.051988 0.022342 -2.326880 0.0200 DCASTK(-6) -0.038192 0.023625 -1.616636 0.1060 McFadden R-squared 0.580765 Mean dependent var 0.142157 S.D. dependent var 0.349640 S.E. of regression 0.238403 Akaike info criterion 0.391836 Sum squared resid 22.62066 Schwarz criterion 0.490151 Log likelihood -69.93455 Hannan-Quinn criter. 0.430740 Restr. log likelihood -166.8147 LR statistic 193.7603 Avg. log likelihood -0.171408 Prob(LR statistic) 0.000000 Obs with Dep=0 350 Total obs 408 Obs with Dep=1 58 36

Table A2.4 United Kingdom Sample: 1975M04 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C -2.796258 0.452664 -6.177337 0.0000 DOIL(-5) 0.050923 0.028678 1.775667 0.0758 UKLI(-3) -0.064419 0.022320 -2.886184 0.0039 UKLI(-6) -0.097229 0.022904 -4.244980 0.0000 UKYC(-1) -0.626173 0.131496 -4.761924 0.0000 DUKIP(-3) -0.281261 0.160027 -1.757584 0.0788 DUKSTK(-2) -0.078702 0.039652 -1.984836 0.0472 DUKEXW(-1) 0.296612 0.120174 2.468183 0.0136 DUKEXW(-2) 0.277223 0.128866 2.151256 0.0315 DUKEXW(-3) 0.363771 0.146954 2.475404 0.0133 DUKEXW(-4) 0.295629 0.117450 2.517055 0.0118 DUKEXW(-5) 0.317239 0.120917 2.623624 0.0087 DUKEXW(-6) 0.385345 0.140052 2.751447 0.0059 McFadden R-squared 0.781619 Mean dependent var 0.135501 S.D. dependent var 0.342723 S.E. of regression 0.174453 Akaike info criterion 0.243730 Sum squared resid 10.83447 Schwarz criterion 0.381508 Log likelihood -31.96813 Hannan-Quinn criter. 0.298462 Restr. log likelihood -146.3868 LR statistic 228.8374 Avg. log likelihood -0.086635 Prob(LR statistic) 0.781619 Obs with Dep=0 319 Total obs 369 Obs with Dep=1 50 37

Table A2.5 Germany Sample: 1972M01 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C 8.715571 1.352739 6.442904 0.0000 GELI(-2) -0.088014 0.014072 -6.254779 0.0000 GEYC(-6) -1.086703 0.111377 -9.756989 0.0000 DGESTK(-2) -0.034200 0.015707 -2.177429 0.0294 DGESTK(-5) -0.037927 0.016318 -2.324208 0.0201 DGESTK(-6) -0.039561 0.015742 -2.513115 0.0120 McFadden R-squared 0.617676 Mean dependent var 0.308824 S.D. dependent var 0.462575 S.E. of regression 0.272929 Akaike info criterion 0.502084 Sum squared resid 29.94500 Schwarz criterion 0.561073 Log likelihood -96.42517 Hannan-Quinn criter. 0.525426 Restr. log likelihood -252.2077 LR statistic 311.5650 Avg. log likelihood -0.236336 Prob(LR statistic) 0.617676 Obs with Dep=0 282 Total obs 408 Obs with Dep=1 126 38

Table A2.6 Mexico Sample: 1980M08 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.169952 0.110653 -1.535909 0.1246 DMXIP(-3) -0.475197 0.106440 -4.464458 0.0000 DMXIP(-4) -0.586875 0.112055 -5.237366 0.0000 DMXIP(-5) -0.419026 0.098153 -4.269100 0.0000 DMXIP(-6) -0.151991 0.086973 -1.747570 0.0805 DMXSTK(-1) -0.025591 0.010087 -2.537056 0.0112 DMXSTK(-2) -0.020007 0.009617 -2.080441 0.0375 DMXSTK(-3) -0.022618 0.009880 -2.289308 0.0221 DMXSTK(-5) -0.021711 0.009037 -2.402409 0.0163 DMXEXW(-2) -0.064050 0.035699 -1.794150 0.0728 DMXEXW(-3) -0.102847 0.042923 -2.396065 0.0166 DMXEXW(-4) -0.122755 0.042992 -2.855273 0.0043 DMXEXW(-5) -0.062575 0.036142 -1.731389 0.0834 DMXEXW(-6) -0.083132 0.035796 -2.322374 0.0202 McFadden R-squared 0.431561 Mean dependent var 0.298361 S.D. dependent var 0.458291 S.E. of regression 0.345125 Akaike info criterion 0.784695 Sum squared resid 34.66143 Schwarz criterion 0.955463 Log likelihood -105.6659 Hannan-Quinn criter. 0.852998 Restr. log likelihood -185.8880 LR statistic 160.4442 Avg. log likelihood -0.346446 Prob(LR statistic) 0.000000 Obs with Dep=0 214 Total obs 305 Obs with Dep=1 91 39

Table A2.7 Korea Sample: 1976M11 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.55222 0.153915 -3.58781 0.0003 DOIL(-2) 0.041523 0.017324 2.396846 0.0165 DOIL(-3) -0.96416 0.257436 -3.74522 0.0002 DKOLI(-3) -0.55904 0.26935 -2.07552 0.0379 DKOLI(-4) -0.94321 0.242563 -3.8885 0.0001 DKOLI(-6) 0.339092 0.136872 2.477444 0.0132 DKOSR(-2) -0.12034 0.061974 -1.94177 0.0522 DKOEXN(-4) -0.17304 0.067649 -2.5579 0.0105 DKOEXN(-6) -0.55222 0.153915 -3.58781 0.0003 McFadden R-squared Mean dependent var 0.459481 0.111429 S.D. dependent var S.E. of regression 0.315113 0.242286 Akaike info criterion Sum squared resid 0.423528 20.0763 Schwarz criterion Log likelihood 0.51171 -66.1174 Hannan-Quinn criter. Restr. log likelihood 0.458627 -122.322 LR statistic Avg. log likelihood 112.4093 -0.18891 Prob(LR statistic) 0.000000 Obs with Dep=0 311 Total obs 350 Obs with Dep=1 39 40

Table A2.8 Taiwan Sample: 1973M09 2005M12 Variable Coefficient Std. Error z-Statistic Prob. C -1.751060 0.151228 -11.57896 0.0000 DOIL(-3) 0.035328 0.014206 2.486879 0.0129 DTALI(-3) -0.305428 0.127583 -2.393966 0.0167 DTALI(-5) -0.360367 0.130109 -2.769728 0.0056 DTALI(-6) -0.250712 0.126296 -1.985118 0.0471 DTASTK(-1) -0.034905 0.012834 -2.719728 0.0065 DTAEXW(-4) 0.150859 0.064824 2.327193 0.0200 DTAEXW(-5) 0.139373 0.067476 2.065516 0.0389 McFadden R-squared 0.370233 Mean dependent var 0.074742 S.D. dependent var 0.263315 S.E. of regression 0.214692 Akaike info criterion 0.375941 Sum squared resid 17.51525 Schwarz criterion 0.457611 Log likelihood -64.93261 Hannan-Quinn criter. 0.408322 Restr. log likelihood -103.1058 LR statistic 76.34630 Avg. log likelihood -0.167352 Prob(LR statistic) 0.000000 Obs with Dep=0 359 Total obs 388 Obs with Dep=1 29 41

Table A2.9 United States Sample: 1972M01 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C 6.435547 1.509281 4.263982 0.0000 DOIL(-2) 0.025732 0.017446 1.474996 0.1402 DOIL(-4) 0.025575 0.014564 1.75612 0.0791 DOIL(-6) 0.048283 0.023151 2.085595 0.0370 USLI(-6) -0.15624 0.032292 -4.83823 0.0000 USYC(-3) -0.38152 0.107047 -3.56408 0.0004 USYC(-6) -0.30818 0.094461 -3.26251 0.0011 DUSSTKN(-1) -0.10188 0.035109 -2.9017 0.0037 DUSSTKN(-2) -0.11312 0.035914 -3.1497 0.0016 DUSSTKN(-4) -0.21103 0.049825 -4.2355 0.0000 DUSSTKN(-6) -0.19571 0.050501 -3.87542 0.0001 McFadden R-squared 0.711316 Mean dependent var 0.136905 S.D. dependent var 0.344259 S.E. of regression 0.192309 Akaike info criterion 0.296022 Sum squared resid 12.01939 Schwarz criterion 0.420987 Log likelihood -38.7317 Hannan-Quinn criter. 0.345837 Restr. log likelihood -134.166 LR statistic 190.8693 Avg. log likelihood -0.11527 Prob(LR statistic) 0.000000 Obs with Dep=0 290 Total obs 336 Obs with Dep=1 46 42

Table A2.10 Japan Sample: 1974M08 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.25256 0.32282 -0.78236 0.4340 JALI(-1) -0.05203 0.007676 -6.77859 0.0000 JAYC(-1) -0.68727 0.163523 -4.20287 0.0000 DJASTK(-1) -0.04278 0.018744 -2.28257 0.0225 DJASTK(-2) -0.06002 0.019355 -3.10105 0.0019 DJASTK(-3) -0.05661 0.019483 -2.90536 0.0037 DJASTK(-6) -0.03523 0.018117 -1.94476 0.0518 McFadden R-squared Mean dependent var 0.389278 0.186885 S.D. dependent var S.E. of regression 0.39046 0.306949 Akaike info criterion Sum squared resid 0.634241 28.07686 Schwarz criterion Log likelihood 0.719625 -89.7217 Hannan-Quinn criter. Restr. log likelihood 0.668393 -146.911 LR statistic Avg. log likelihood 114.3782 -0.29417 Prob(LR statistic) 0.000000 Obs with Dep=0 248 Total obs 305 Obs with Dep=1 57 43

Table A2.11 Canada Sample: 1972M01 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.77981 0.144067 -5.41285 0.0000 CAYC(-6) -0.57687 0.08698 -6.63222 0.0000 DCAEMP(-2) -2.06606 0.530446 -3.89494 0.0001 DCAEMP(-3) -1.30049 0.458622 -2.83563 0.0046 DCAEMP(-4) -0.85409 0.455406 -1.87545 0.0607 DCASTK(-2) -0.02893 0.025495 -1.13463 0.2565 DCASTK(-3) -0.04466 0.024362 -1.8332 0.0668 DCASTK(-4) -0.02528 0.026079 -0.96944 0.3323 DCASTK(-5) -0.0379 0.025713 -1.4741 0.1405 DCASTK(-6) -0.01829 0.026964 -0.67818 0.4977 McFadden R-squared 0.578636 Mean dependent var 0.145833 S.D. dependent var 0.353465 S.E. of regression 0.237754 Akaike info criterion 0.409604 Sum squared resid 18.42785 Schwarz criterion 0.523208 Log likelihood -58.8134 Hannan-Quinn criter. 0.454889 Restr. log likelihood -139.579 LR statistic 161.5307 Avg. log likelihood -0.17504 Prob(LR statistic) 0.000000 Obs with Dep=0 287 Total obs 336 Obs with Dep=1 49 44

Table A2.12 United Kingdom Sample: 1975M04 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C -2.47021 0.463374 -5.33091 0.0000 DOIL(-5) 0.050074 0.029881 1.675791 0.0938 UKLI(-3) -0.06309 0.024201 -2.6068 0.0091 UKLI(-6) -0.09063 0.024243 -3.73845 0.0002 UKYC(-1) -0.52791 0.135246 -3.90332 0.0001 DUKIP(-3) -0.2931 0.174844 -1.67633 0.0937 DUKSTK(-2) -0.0779 0.038985 -1.99813 0.0457 DUKEXW(-1) 0.299492 0.123517 2.424707 0.0153 DUKEXW(-2) 0.299713 0.139487 2.148681 0.0317 DUKEXW(-3) 0.331681 0.144771 2.291077 0.0220 DUKEXW(-4) 0.275745 0.118103 2.334779 0.0196 DUKEXW(-5) 0.286123 0.121838 2.348386 0.0189 DUKEXW(-6) 0.372607 0.14205 2.623064 0.0087 McFadden R-squared 0.778081 Mean dependent var 0.16835 S.D. dependent var 0.374808 S.E. of regression 0.190251 Akaike info criterion 0.288717 Sum squared resid 10.2795 Schwarz criterion 0.450395 Log likelihood -29.8744 Hannan-Quinn criter. 0.353442 Restr. log likelihood -134.618 LR statistic 209.4879 Avg. log likelihood -0.10059 Prob(LR statistic) 0.000000 Obs with Dep=0 247 Total obs 297 Obs with Dep=1 50 45

Table A2.13 Germany Sample: 1972M01 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C 6.670281 1.380097 4.833196 0.0000 GELI(-2) -0.0694 0.014387 -4.82346 0.0000 GEYC(-6) -1.18085 0.134898 -8.75362 0.0000 DGESTK(-2) -0.01255 0.02355 -0.53278 0.5942 DGESTK(-5) -0.01344 0.022761 -0.59031 0.5550 DGESTK(-6) -0.02336 0.021856 -1.06888 0.2851 McFadden R-squared 0.682478 Mean dependent var 0.282738 S.D. dependent var 0.451002 S.E. of regression 0.248086 Akaike info criterion 0.413896 Sum squared resid 20.31032 Schwarz criterion 0.482059 Log likelihood -63.5345 Hannan-Quinn criter. 0.441067 Restr. log likelihood -200.095 LR statistic 273.121 Avg. log likelihood -0.18909 Prob(LR statistic) 0.000000 Obs with Dep=0 241 Total obs 336 Obs with Dep=1 95 46

Table A2.14 Mexico Sample: 1980M11 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.75586 0.162415 -4.65388 0.0000 DMXIP(-3) -0.5478 0.148074 -3.69946 0.0002 DMXIP(-4) -0.60023 0.150115 -3.99849 0.0001 DMXIP(-5) -0.36793 0.126535 -2.90773 0.0036 DMXIP(-6) -0.08565 0.112899 -0.75867 0.4481 DMXSTK(-1) -0.01854 0.012991 -1.42738 0.1535 DMXSTK(-2) -0.00958 0.012675 -0.75608 0.4496 DMXSTK(-3) -0.01994 0.012878 -1.54809 0.1216 DMXSTK(-5) -0.01654 0.01128 -1.46625 0.1426 DMXEXW(-2) -0.1031 0.043535 -2.36817 0.0179 DMXEXW(-3) -0.11178 0.051955 -2.15154 0.0314 DMXEXW(-4) -0.14198 0.056069 -2.53231 0.0113 DMXEXW(-5) -0.0545 0.039841 -1.36793 0.1713 DMXEXW(-6) -0.09514 0.040938 -2.32408 0.0201 McFadden R-squared 0.589762 Mean dependent var 0.2103 S.D. dependent var 0.408399 S.E. of regression 0.252765 Akaike info criterion 0.542187 Sum squared resid 13.99194 Schwarz criterion 0.749546 Log likelihood -49.1648 Hannan-Quinn criter. 0.625803 Restr. log likelihood -119.845 LR statistic 141.3596 Avg. log likelihood -0.21101 Prob(LR statistic) 0.000000 Obs with Dep=0 184 Total obs 233 Obs with Dep=1 49 47

Table A2.15 Korea Sample: 1976M11 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C -0.10711 0.259366 -0.41299 0.6796 DOIL(-2) 0.051578 0.023845 2.16302 0.0305 DOIL(-3) -1.24182 0.334256 -3.71517 0.0002 DKOLI(-3) -0.93739 0.373217 -2.51165 0.012 DKOLI(-4) -1.19601 0.360173 -3.32066 0.0009 DKOLI(-6) 0.319373 0.143444 2.226467 0.026 DKOSR(-2) -0.17654 0.094234 -1.87346 0.061 DKOEXN(-4) -0.1896 0.092255 -2.05522 0.0399 DKOEXN(-6) -0.10711 0.259366 -0.41299 0.6796 C 0.051578 0.023845 2.16302 0.0305 McFadden R-squared 0.575992 Mean dependent var 0.107914 S.D. dependent var 0.310831 S.E. of regression 0.205762 Akaike info criterion 0.347686 Sum squared resid 11.43121 Schwarz criterion 0.452078 Log likelihood -40.3284 Hannan-Quinn criter. 0.389567 Restr. log likelihood -95.1124 LR statistic 109.5681 Avg. log likelihood -0.14507 Prob(LR statistic) 0.000000 Obs with Dep=0 248 Total obs 278 Obs with Dep=1 30 48

Table A2.16 Taiwan Sample: 1973M09 1999M12 Variable Coefficient Std. Error z-Statistic Prob. C -3.112393 0.474242 -6.562874 0.0000 DOIL(-3) 0.046968 0.018933 2.480779 0.0131 DTALI(-3) -0.370344 0.197194 -1.878068 0.0604 DTALI(-5) -0.642545 0.211431 -3.039027 0.0024 DTALI(-6) -0.280629 0.187902 -1.493484 0.1353 DTASTK(-1) -0.041857 0.023825 -1.756831 0.0789 DTAEXW(-4) 0.432796 0.124400 3.479062 0.0005 DTAEXW(-5) 0.292244 0.111369 2.624110 0.0087 McFadden R-squared 0.654620 Mean dependent var 0.041139 S.D. dependent var 0.198927 S.E. of regression 0.121407 Akaike info criterion 0.169132 Sum squared resid 4.539833 Schwarz criterion 0.264214 Log likelihood -18.72278 Hannan-Quinn criter. 0.207116 Restr. log likelihood -54.20916 LR statistic 70.97276 Avg. log likelihood -0.059249 Prob(LR statistic) 0.000000 Obs with Dep=0 303 Total obs 316 Obs with Dep=1 13 49