The Role of Economic Policy Uncertainty in Predicting U.S. Recessions: A Mixed-frequency Markov-switching Vector Autoregressive Approach

This paper analyzes the performance of the monthly economic policy uncertainty (EPU) index in predicting recessionary regimes of the (quarterly) U.S. GDP. In this regard, the authors apply a mixed-frequency Markov-switching vector autoregressive (MF-MS-VAR) model, and compare its in-sample and out-of-sample forecasting performances to those of a Markov-switching vector autoregressive model (MS-VAR, where the EPU is averaged over the months to produce quarterly values) and a Markov-switching autoregressive (MS-AR) model. Their results show that the MF-MS-VAR fits the different recession regimes, and provides out-of-sample forecasts of recession probabilities which are more accurate than those derived from the MS-VAR and MS-AR models. The results highlight the importance of using high-frequency values of the EPU, and not averaging them to obtain quarterly values, when forecasting recessionary regimes for the U.S. economy. JEL E32 E37 C32


Introduction
Theoretical explanations as to why uncertainty negatively affects economic activity can be traced back to the early works of Bernanke (1983) and Dixit and Pindyck (1994), and more recently in that of Bloom (2009). They assert that the interaction between high uncertainty and non-smooth adjustment frictions may lead firms to change their behavior in terms of hiring and investing. Facing high uncertainty firms wait and see how the future develops, and this in turn, leads to a drop in economic activity. In the aftermath of the "Great Recession", the emphasis seems to have shifted to developing quantifiable measures of uncertainty, either based on structural vector autoregressive (SVAR) models (Mumtaz and Zanetti, 2013;Alessandri and Mumtaz, 2014;Mumtaz and Theodoridis, 2016;Jurado et al., 2015), or based on newspaper articles (Baker et al., 2016). Irrespective of what is the source of the measure of uncertainty used, it is then, in general, incorporated into SVAR models, to analyze its impact on the economy (Aastveit et al., 2013;Colombo, 2013;Mumtaz and Zanetti, 2013;Alessandri and Mumtaz, 2014;Mumtaz and Theodoridis, 2016;Jurado et al., 2015). However, the newsbased measures of uncertainty seem to have gained tremendous popularity in various applications in macroeconomics and finance (see Redl, 2015, for a detailed review), most likely due to the fact that data on this measure (not only for the US, but also other European and emerging economies) is easily and freely available for use, and does not require any complicated estimation of a model to generate it in the first place. To construct the index, Baker et al. (2016) perform month-by-month searches of newspapers for terms related to economic and policy uncertainty.
While, it is true that the impact of economic policy uncertainty on macroeconomic and financial variables has been primarily based on SVARs (as discussed above), more recently, Jones and Olson (2013) studied time-varying correlation between industrial production (and inflation) and EPU using a multivariate DCC-GARCH model. Estimation results revealed that the sign of the correlation between EPU and output has been consistently negative. 1 Karnizova and Li (2014) took a different route, and used probit forecasting models to assess the ability of EPU to predict future US recessions. Based on both in-sample and out-of-sample anal-yses, their results suggested that policy uncertainty indexes are statistically and economically significant in forecasting recessions at the horizons beyond five quarters.
Over the last 50 years several financial and macroeconomic indicators have been developed and well-documented in the literature to predict U.S. recessions. Examples include the term structure of Treasury yield and stock prices by Estrella and Mishkin (1998), the index of Leading Economic Indicators by Berge and Jordà (2011), and employment and interest rate measures by Ng (2014). These indicators play an important role in predicting business cycle turning points. For households, firms, investors and policy makers it is crucial to correctly assess the current and, especially, the future states of the economic activity in order to make good economic policies and decisions. In this paper we want to analyze the usefulness of the EPU in predicting U.S. recessions probabilities using a mixed-frequency Markov-switching VAR (MF-MS-VAR) model, with our two variables being real GDP (at quarterly frequency) and EPU (at monthly frequency). The recently developed MF-MS-VAR model by Camacho (2013) is an extension of the Markovswitching vector autoregressive (MS-VAR) model to a mixed frequency one. The innovation in the MF-MS-VAR model is its capacity to model macroeconomic variables sampled at different frequencies. This means that for our analysis, we do not need to aggregate all the high-frequency variables to the frequency of the lowest frequency variable, and thus, will not loose a part of information in our data set, or to interpolate the low-frequency variable to the frequency of the highfrequency variable, which is usually performed via the Kalman filter, and thus avoid the awkwardness associated with the Kalman filter estimation. In addition, the presence of the Markov-switching components makes the MF-MS-VAR more robust against structural changes that may occur in our data set.
The use of a MS framework in predicting turning points in GDP is quite well-established, ever since the initial work of Hamilton (1989), and hence, is an easily justifiable model to use (see Chauvet and Hamilton, 2006;Hamilton, 2008, for detailed reviews in this regard). 2 In fact, the MS model includes different discrete regimes that are governed by a hidden Markov chain. So, the nonlinear dynamics generated in the MF-MS-VAR model stem from occasional and discrete shifts in regimes that allow the model to properly capture the structural changes that characterize many time series, and especially our data sets. In contrast to other nonlinear or time-varying parameter model the MS model allows us to endogenously estimate and forecast the probabilities of being in a given regime. All these ingredients make the MF-MS-VAR model more exceptional and appropriate for our analysis.
Our data covers the monthly period of 1947:01-2014:02, with the start date being determined by data availability of real GDP (first quarter of 1947), and the end date due to the same reasoning for EPU. 3 Note that, our mixed-frequency approach also allows us to develop a monthly indicator for the quarterly GDP growth rate based on the EPU, which in turn, controls for the (unrealistic) assumption that the real-time data flow of the variables involved in the empirical analyses occurs at the same time. In this regard, we compare the performance of the MF-MS-VAR with a linear mixed-frequency VAR (MF-VAR) model as well, in terms of the movements of the monthly indicator of the quarterly GDP growth rates. We also compare our results with MS-AR and MS-VAR models, where in the latter model, EPU is converted to quarterly frequency. It must be emphasized that, we not only predict recession probabilities in-sample, but also out-of-sample.
To the best of our knowledge, this is the first attempt to apply a MF-MS-VAR model to the quarterly U.S. GDP based on monthly EPU, and in turn, use it to predict, both in-and out-of-sample (1980:01-2014:02) recession probabilities. Our paper, can thus be considered to be an extension of the work of Karnizova and Li (2014), whereby, unlike these authors, when predicting recession probabilities, we do not average out the information over three months of the EPU to obtain its and EPU growth, respectively. These two tests, thus, provide even more motivation to model the growth process of real GDP in a nonlinear fashion. Complete details of these results are available upon request from the authors. 3 Though more recent data on EPU, starting in 1985:M1 (http://www.policyuncertainty.com/us_ monthly.html), is available, we decided to use the historical version of EPU (which in fact starts in 1900:01), to allow us to cover all the post World War II recessions. This specifically why we also did not use daily data on EPU (http://www.policyuncertainty.com/us_daily.html) and equity market uncertainty (http://www.policyuncertainty.com/equity_uncert.html), both of which starts on January 1, 1985.
www.economics-ejournal.org quarterly values, which in turn, could lead to possible loss of important information. In addition, unlike Karnizova and Li (2014), since we work with real GDP figures to predict the recession probabilities, our MF-MS-VAR approach also allows us to obtain a monthly indicator for the U.S. GDP contingent on the monthly information of the EPU. The remainder of the paper is organized as follows: Section 2 presents the data used in our analysis. In Section 3 we provide the basics of the econometric framework, while in Section 4 results of the empirical application is presented. Finally, Section 5 concludes.

Data
Our data set comprises of two variables: real GDP at quarterly frequency and the monthly EPU, and covers the period of 1947:01 to 2014:02, which matches the quarterly frequency of the former over 1947:Q1-2014:Q1. While the data on real GDP (in Billions of 2009 chained dollars and seasonally adjusted at an annual rate) is obtained from the FRED database of the Federal Reserve Bank of ST. Louis, the EPU is obtained from http://www.policyuncertainty.com/index.html. Two overlapping sets of newspapers are used for the creation of this index. The first spans 1900-1985 and is comprised of the Wall Street Journal, the New York Times, the Washington Post, the Chicago Tribune, the LA Times, and the Boston Globe. From 1985 onwards USA Today, the Miami Herald, the Dallas Morning Tribune, and the San Francisco Chronicle are added to the previously mentioned papers. To construct the index, month-by-month searches of each paper, starting in January 1900, is performed for articles containing the term "uncertainty" or "uncertain", the terms "economic", "economy", "business", "commerce", "industry", and "industrial" as well as one or more of the following terms: "congress", "legislation", "white house", "regulation", "federal reserve", "deficit", "tariff", or "war". In other words, for inclusion in the EPU, articles must include terms in all three categories pertaining to uncertainty, the economy and policy. 4 To gain insights about the time series properties of our data sets, we first plot the logarithmic changes in real US GDP and EPU, cf. Figure 1. We observe a higher variability in EPU than in real GDP growth. As is standard practice in time series econometrics, we then tested for the unit root properties of the log-levels of real GDP and the EPU index. In this regard, we used the Ng and Perron (2001) unit root test, which has been shown to have very good size and power properties, relative to other standard unit root tests. Under the assumptions of a constant, and constant and trend in the test equation, the null of unit root cannot be rejected for the levels of the series. However, first-differencing ensures that the two variables of concern (growth rate of real GDP and growth rate of EPU), are stationary. These results along with the summary statistics of the growth rates of the two variables have been reported in Table 1.
So we work with percentage changes, C, of real GDP or EPU, computed as: where data t denotes the real US GDP or EPU at period t.
Since we work with growth rates of the two variables to ensure stationarity, we loose one observation from the beginning of the sample period.

Methodology
The recently developed MF-MS-VAR model by Camacho (2013) in state space representation can be formalized as: is a vector that contains quarter-on-quarter and month-onmonth growth rates of the economic indicators, www.economics-ejournal.org is a vector of lagged month-on-month growth rates, Block matrix whose elements are given by: and ε t ∼ N(0, R). Note that N 1 is the number of quarterly indicators and N 2 denotes the same at monthly frequency. As stressed in Mariano and Murasawa (2003) the quarter-on-quarter growth rate of quarterly indicators calculated at each month of the sample can be obtained as the average sum of previous month-on-month growth rates as follows: Camacho (2013) assumed that the monthly growth rates of the economic indicators follow a Markov switching VAR(p) process, which is governed by a state variable δ t , that is assumed to evolve according to a first-order Markov chain with transition probability: where i, j = 0, 1 and ℑ t is the information set available at the time t. Using the Kalman filter, the MF-MS-VAR model can be easily estimated via maximum likelihood method, with easily computable filtered probabilities: Pr (δ t = j|ℑ t ), and smoothed probabilities: Pr (δ t = j|ℑ T ). We refer the reader to Camacho (2013) for more details on the estimation procedure.

Empirical Results
We use a lag-length (p) of one, as justified by the Bayesian Information Criterion (BIC), and following Camacho (2013), we allow only the drifts of the models to  (Davies, 1987) of the LR tests are given in brackets. * * * , * * , and * denote significance at 1%, 5% and 10%, respectively.
switch, since shifts do not depend on the dynamics of the autoregressive process or the covariance matrices (Hamilton, 1989). We first establish nonlinearity and perform several likelihood ratio (LR) tests in order to decide on the type of the Markov switching model. We consider both homoscedastic Markov switching, MS(k), and heteroscedastic, MSH(k), models with k = 2, 3 regimes. In the homoscedastic model, the covariance matrix of the residuals is constant across the regime, i.e., ε t ∼ N(0, R), and it varies with regimes in the heteroscedastic case, i.e., ε t ∼ N(0, R δ t ). Tests results are given in Table 2. First, the results in Table 2 show that linearity is strongly rejected against all MS models. Second, MS(2)-MF-VAR model is only rejected at 10% significance level agains the MSH(2)-MF-VAR. Third, both AIC and LR test select the three regime MS(3)-MF-VAR over the others. The smoothed regime probabilities of the MS(3)-MF-VAR model are plotted in Figure 4 in the Appendix indicate that second and third regimes both corresponds to the recession periods. Given that the second regime might indeed be a spurious regime corresponding to a few spikes in the recession periods and numerous empirical studies that only consider a two regime MS model for the business cycle analysis (see studies discussed in e.g., Hamilton and Raj, 2002) we use the two regime MS(2)-MF-VAR for the analysis in the rest of the paper. Panel (a) of Figure 2 compares the monthly estimates of the U.S. quarterly GDP growth rates that are obtained from the linear MF-VAR and the MF-MS-VAR  models. We also analyse and extend MF-MS-VAR model that includes inflation and 3-month treasury bill rate in addition to the economic policy uncertainty. Both indicators are in accordance with the NBER-referenced business cycles (indicated by the shaded areas in Figure 2). The positive growth rates are interrupted by large changes in the direction, which in turn, align quite well with the U.S. recessions.
Even though the MF-VAR and MF-MS-VAR performs similarly in terms of the construction of monthly indicators of the U.S. economic activity, the latter model can, in addition, be used to convert the business cycle signals provided by the economic indicators into recession probabilities. In order to determine the accuracy of the MF-MS-VAR model to account for the business cycles, Panel (b) of Figure 2 plots the values of the smoothed recession probabilities of state δ t = 1. The fact that the probability of state 1 corresponds to recessions is due to the reasonable match between the quarters of high probabilities of this state and the NBER recessions. The MF-MS-VAR model is observed to capture the recessions quite well. 5 Even though we observe a high correlation between the probabilities of recession and the NBER referenced recessions, the question is whether or not the MF-MS-VAR model outperforms other possible competitors used for business cycles dating. In this regard, we look at a MS-VAR model -where the monthly EPU are averaged over three-months to produce quarterly values of the same, and a MS-AR model, as two possible competitors. We start off with in-sample accuracy, and compute the quadratic probability score (QPS) in this regard, as proposed by Brier (1950). Formally, where p t is the forecast probability made at the time t, r t is the realization of the event at the time t, and T denotes the total number of the observations. We note that QPS ranges between 0 and 1, with a score of 0 indicating a perfect accuracy.
The computed values of QPS for our models are near zero and reported in Table 3. The Extended MF-MS-VAR model provides the smallest score, followed by the MF-MS-VAR, the MS-VAR, and MS-AR models for the in-sample. In addition to the QPS, we also apply the equal forecast accuracy (DM) test of Diebold and Mariano (1995). When we compare the MF-MS-VAR models with the MS-VAR (MS-AR), the null of equal predictive accuracy is rejected at 5% (10%) levels of significance. So results from the QPS and the Diebold and Mariano (1995) tests highlights the superiority of the MF-MS-VAR models relative to the MS-VAR and MS-AR models, based on an in-sample analysis.  Diebold and Mariano (1995) equal test for mixed-frequency Markovswitching vector autoregression (MF-MS-VAR), Markov-switching vector autoregression (MS-VAR), and Markov-switching autoregression (MS-AR) models. Extended MS-MF-VAR model includes inflation and 3month treasury bill rate in addition to the economic policy uncertainty. * * * , * * , and * denote significance at 1%, 5% and 10%, respectively.
However, the in-sample analysis does not account for the effect of the nonsynchronous releases that characterizes the real-time flow of macroeconomic information. To provide a more realistic assessment of the reliability of MF-MS-VAR results, we also look at a pseudo real-time analysis as proposed by Camacho (2013). Towards this end, we evaluate the ability of the MF-MS-VAR models, relative to the MS-VAR and MS-AR models, in predicting recession probabilities (based on recursive estimation of the models) over the out-of-sample period of 1980:01-2014:02, using an in-sample period of 1947:1-1979:12. The decision to start our out-of-sample forecasting exercise in 1980:01, which also gives us more or less a 50 percent split of the in-and out-of-samples, is in line with a major breakpoint due to changes in US monetary and fiscal policies (see Bekiros and Paccagnini, 2013, for a detailed discussion in this regard). As can be seen from Table 3, the Extended MF-MS-VAR is still the best model followed by the MF-MS-VAR model, 6 but the MS-AR model performs slightly better than the MS-VAR its smoothed recession probabilities are quite analogous to those of the MF-MS-VAR model and, therefore, not discussed here since our focus is the EPU. 6 Superiority of the Extended MF-MS-VAR over the MF-MS-VAR indicates that the inflation and the treasury bill rate help to better predict the GDP growth rate. model, based on the QPS statistic. In addition, the Diebold and Mariano (1995) rejects the null of equal forecast accuracy of the MF-MS-VAR model relative to both the MS-VAR and MS-AR models at 1% level of significance. So, as with the in-sample, the MF-MS-VAR model outperforms its two competitors in a pseudo real-time forecasting exercise as well. Our results, hence, provides convincing evidence in favor of the MF-MS-VAR model in predicting U.S. recession probabilities for both within and out-of-sample exercises.
In order to gain more insight on the relative performance of the MF-VAR and MS-MF-VAR models we carry out an out-of-sample forecasting exercise over the monthly sample period 1980:1-2014:2. The out-of-sample forecast exercise uses a recursive design where the starting point of the estimation is fixed at 1947:01 for the MF-VAR, MS-MF-VAR, and the Extended MS-MF-VAR models. We also include a rolling MF-VAR model, with a fixed window size of 60, in the exercise since it better adopts to structural breaks and, therefore, more comparable to MF-MS-VAR models. The forecasts are obtained for the monthly indicators of the quarterly GDP growth rate for h = 1, 4, 8 steps and the forecast errors are computed on a quarterly basis using the actual quarterly GDP growth rates. The out-of-sample forecasting performance of the models are compared in terms of root mean square error (RMSE). We also report the equal forecast accuracy DM tests for statistical comparison of the forecasting performances. Table 4 reports results for the out-of-sample forecasting exercise. In terms of RMSE, the results in Table 4 show that the Extended MS-MF-VAR has the best forecasting ability at all forecast horizons followed by the MS-MF-VAR model. The MS-MF-VAR models are followed by the Rolling MF-VAR and MF-VAR models, respectively. The DM tests show that the MS-MF-VAR models outperform the Rolling MF-VAR and MF-VAR models for all steps h = 1, 4, 8, but there is no statistically significant difference between the Extended MS-MF-VAR and MS-MF-VAR models.

Conclusion
This paper applies a mixed-frequency Markov-switching VAR (MF-MS-VAR) model for quarterly U.S. GDP to predict in-sample and out-of-sample US recession probabilities using the monthly index of news-based economic policy uncertainty  Diebold and Mariano (1995) equal forecast accuracy (DM) test for mixed-frequency vector autoregression (MF-VAR), Rolling MF-VAR, mixed-frequency Markov-switching vector autoregression (MF-MS-VAR), and Extended MF-MS-VAR. Extended MS-MF-VAR model includes inflation and 3-month treasury bill rate in addition to the economic policy uncertainty. The RMSE and DM reported in the table are for forecasting the quarterly real GDP growth. The out-of-sample period covers 1980:1-2014:1. The rolling window size for the Rolling MF-VAR is 60. The DM test is calculated for the difference of the squared forecast error of Model 1 minus the squared forecast error of Model 2. * * * , * * , and * denote significance at 1%, 5% and 10%, respectively.
(EPU) as a predictor. The MF-MS-VAR model yields a monthly indicator for the quarterly growth rates of real GDP based on the monthly EPU. But more importantly, our empirical results show that the MF-MS-VAR fits the different recession regimes and provides out-of-sample forecasts which are more accurate than those from a MS-VAR (where the EPU is averaged over the months to produce quarterly values) and MS-AR models. Our results not only highlight the importance of the monthly EPU in predicting the movements of the quarterly GDP growth rates and the associated recessionary regimes, but also shows that important information emanating from the EPU will be compromised if one averages its monthly values into quarterly ones.