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I find that real US GDP is better characterized as a trend stationary Markov-switching process than as having a (regime-dependent) unit root. I examine the effects of both assumptions on the analysis of business cycle features and their implications for the persistence of the dynamic response of output to a random disturbance.
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... two features are also appreciated in US output growth. Figure 2 shows that while output growth fluctuates around its positive sample mean, there are episodes of lower and even negative growth that coincide with NBER recessions. Since the work by Hamilton (1989), it has been generally accepted that the business cycle dynamics of output can be appropriately modeled by using an unobserved Markov-switching process. ...
Similar publications
This article examines the unit root hypothesis for real GDP per capita in 25 of China's provinces. When we test for unit roots assuming either no structural breaks or one structural break, the evidence supports the unit root hypothesis. With multiple structural breaks, the evidence against a unit root is mixed. When both breaks in the trend functio...
Citations
... The critical values thereby obtained will ensure correct size and power properties. Following Hamilton (1990), Hall et al. (1999), Kanas and Genius (2005), Kanas (2006, 2009), and Camacho (2011 have used the EM algorithm for constructing the test statistic of the unit root null in their regime switching extensions of the ADF test. However, we show that the Simplex method has a remarkable advantage over the hill-climbing methods and EM with regards to obtaining accurate parameter estimates and critical values for the ADF unit root test with MS breaks. ...
In this study, we investigate the performance of different optimization algorithms in estimating the Markov switching (MS) deterministic components of the traditional ADF test. For this purpose, we consider Broyden, Fletcher, Goldfarb, and Shanno (BFGS), Berndt, Hall, Hall, Hausman (BHHH), Simplex, Genetic, and Expectation-Maximization (EM) algorithms. The simulation studies show that the Simplex method has significant advantages over the other commonly used hill-climbing methods and EM. It gives unbiased estimates of the MS deterministic components of the ADF unit root test and delivers good size and power properties. When Hamilton’s (Econometrica 57:357–384, 1989) MS model is re-evaluated in conjunction with the alternative algorithms, we furthermore show that Simplex converges to the global optima in stationary MS models with remarkably high precision and even when convergence criterion is raised, or initial values are altered. These advantages of the Simplex routine in MS models allow us to contribute to the current literature. First, we produce the exact critical values of the generalized ADF unit root test with MS breaks in trends. Second, we derive the asymptotic distribution of this test and provide its invariance feature.
... These methods consider that turning points are intrinsic behavioral factors of the series; to be precise, the internal dynamics of the series generate special points (moments) enclosing intervals (phases). A broadly used example of these analyses is the MS-AR models proposed by Hamilton (1989) (Camacho, 2005(Camacho, , 2011Chen, 2006;Harding & Pagan, 2002;Layton, 1996). The downside of these models is that the results obtained are heavily dependent on the size of the sample and require a correct specification of the model for a particular series. ...
... To determine the detection of turning point effectiveness in our method (WM), we compare its results with the most popular methods for this type of analysis: the Markov switching model (MSM) proposed by Hamilton (1989) using the results by Camacho (2011) and the algorithm by Bry and Boschan (1971) in the version proposed by Harding and Pagan (2002) (BBQ). We then compare our results to those of the NBER-dated reference. ...
This paper presents a new method for detecting turning points in business cycles using the discrete wavelet transform. A methodology is proposed to select the ideal wavelet function and optimize the identification method. We illustrate the method by analyzing the 1957–2021 United States business cycle. We compare the effectiveness of wavelet functions with the classical detection technique usually employed for this type of analysis.
... For the steps needed to perform the Monte Carlo simulations, seeCamacho (2011).9 For a discussion on this procedure, seeCheng et al. (2014).10 ...
The inflation rate is a key variable in many macroeconomic models that are used to guide policy analysts and lead to effective decisions. However, achieving this outcome depends, to a large extent, upon the validity of these macroeconomic models whose successes, in turn, critically depend on whether inflation is stationary or not. In this paper, we investigate the dynamics of inflation in the Gulf Cooperation Council countries using both linear and non-linear tests. To add an extra layer of robustness to our results, we avoid the pitfalls of the econometrics of stationarity by applying the MS-ADF and Fourier ADF tests. After using a battery of tests, the analysis provides more reliable inferences on the question of whether the inflation rates of these countries are I(0) or I(1). The findings convincingly support the view that not only are the inflation rates of these countries non-linear, but they are also characterized by mean-reversion behaviour. The policy implication of our findings is that random shocks will not have permanent effects and that active monetary policies are not needed, as these effects will eventually disappear in the long run.
... Switching models are also widely used to model the processes in the real sector of economy as well as socio-economic processes. Camacho (2011) investigated the persistence of the dynamic output response to the random disturbances and showed that US GDP was described by the trend -stationary Markov switching process better than by having a regime-dependent unit root. Alizadeh, Huang and Dellen (2015) investigated the input of petroleum transportation and production in the energy supply chain during 2005 -2013 and developed the regime switching GARCH specification and the bivariate Markov Regime Switching GARCH model. ...
This paper investigates the unemployment rate dynamics in Poland, and Ukraine during 2000-2017. To analyze the dynamics of unemployment rate we constructed economet-ric regression models with nonlinearities that arose due to discrete changes in modes. We developed Markov switching model that allowed capturing the regularities by modeling the asymmetry in the unemployment rate during contractionary and expansionary states of the labor market. We evaluated two regimes of unemployment behavior that were associated with high and low unemployment levels and estimated the transition probabilities of regime change and average expected durations in each regime. The comparison of mean and volatility of different regimes and the one-step ahead predictions of the regime probabilities for different countries revealed the labor market specifics for each country and showed differences in the flexibility of their reactions to changing economic environment.
... In addition, Kocaaslan (2016) finds that Turkish output is stationary in one regime and non-stationary in another regime, and output shocks are highly persistent and transitory in recession and expansion regimes, respectively. Camacho (2011), employing Markov-switching trend stationary specification for the USA, finds that recessions have less transitory effects on the level of output. In summary, the above studies have employed a two-regime Markovswitching model for inflation and output growth, but the effects of IT are largely unexplored. ...
... Inflation is calculated as the annual change in the log of the monthly CPI. Following Camacho (2011) and Kocaaslan (2016), real output growth rates are calculated as the annual log difference of the quarterly real GDP data. The data set is sourced from IMF's International Financial Statistics. Figure 1 shows the inflation target ranges in four Asian IT countries represented by blue lines and the actual inflation pattern. ...
Purpose
This paper considers whether or not the introduction of inflation targeting impacts on the mean-reversion properties of inflation and output growth.
Design/methodology/approach
Focusing on eight Asian countries of which four are inflation-targeters, we employ a two-state Markov switching model which characterizes the behavior of inflation and output growth as regime-dependent based on periods of stationarity or non-stationarity.
Findings
In contrast to a literature that offers mixed findings, we find the presence of stationary inflation and output growth in one regime for all inflation targeting countries, except for South Korea which is characterized by stationary output growth in both regimes. In the cases of South Korea and Thailand, inflation targeting reduces the probability of inflation remaining in a non-stationary regime. Inflation targeting increases the probability of South Korea remaining in a regime of low persistence output growth. While inflation targeting is important in understanding behavior, so are other considerations such as exchange rate volatility, as well as the Asian and global financial crises.
Originality/value
In contrast to other unit root tests of inflation and output growth, a novelty of our approach is that we obtain new insights in terms of two concepts of stationarity that allow for inflation and output growth to switch between stationary and non-stationary regimes (partial stationarity), or between stationary regimes of differing degrees of persistence (varied stationarity).
... While industrial production index fluctuates around the positive sample mean, there are smaller and even negative output growth episodes that overlap with OECD recessions. Following Hall et al. (1999) and Camacho (2011), a regime-switching extension of the Augmented Dickey-Fuller (ADF) test is employed to provide further evidence on the uncertain unit root in monthly IPI. Usually, comparative analyses are undertaken for Turkey and the studies conducted exhibit qualitative rather than quantitative approaches. ...
... In this article, a single economic variable is preferred as reference series and, although GDP is the "reference" series that determines the situation of economic activity, monthly industrial production index (IPI) series is used instead of quarterly basis GDP. Following Hall et al. (1999) and Camacho (2011), a regime-switching extension of the Augmented Dickey-Fuller (ADF) test is employed to provide further evidence on the uncertain unit root in monthly IPI. Usually, comparative analyses are undertaken for Turkey and the studies conducted exhibit qualitative rather than quantitative approaches. ...
... In other words, the Markov switching model offers a rather general and convenient framework for the purpose of unit-root testing in the presence of a priori unknown multiple structural breaks due to either abrupt or gradual changes in time series behavior. Camacho (2005Camacho ( , 2011 and Camacho and Perez (2007) have used this model to analyze the stochastic trends of U.S. output series. As shown below, structural changes in both the mean and variance also play a vital role in the dynamic properties of rice price series. ...
... Second, when rice prices do not follow a random walk, shocks in rice markets are less easily transmitted through the rest of the economy. In this case, the role for active macroeconomic policy actions would diminish because aggregate output or the overall price level will be more likely to be mean-reverting as well (Camacho, 2005(Camacho, , 2011. ...
This study revisits the issue of mean reversion in the import rice prices of six Asian countries over the period between 1995 and 2015. Augmented Dickey Fuller tests with a conventional linear regression model support the presence of a unit root in the levels of the price data. However, when regressions allow for Markov switching in coefficients and variances to capture periodic shifts in levels and volatilities, there is strong evidence against the unit-root null hypothesis in favor of stationarity over much of the observation period.
... Standard likelihood ratio test cannot be used to test the null of linearity against the alternative of Markov regime switching model. The reason is that under 1 Several researchers have used MSADF methodology for different variables as real exchange rates Genius, 2005, Kanas, 2006;2009, Holmes, 20082010, Lee andYoon, 2013), stock prices (Chen, 2008, Shen andHolmes, 2014), short-term interest rates (Chua and Suardi, 2007), external debt (Takeuchi, 2010), inflation rate (Chen, 2010), current account deficits (Chen, 2011), real GDP (Camacho, 2011), unemployment rate (Cevik and Dibooglu, 2013), international art market prices . ...
In this paper, we investigate the nonlinearity and nonstationarity of Turkish output series applying a Markov regime switching augmented Dickey Fuller unit root test. We document that the output series are characterized by a two-regime Markov switching unit root process. We show that output series is stationary in one regime and nonstationary in the other one. Moreover, we observe that the nonstationary regime corresponds to the recessionary periods in the Turkish economy. That is, the shocks to output are highly persistent in the recession regime, but they are transitory in the expansion regime. In addition, the time period in which the output series is found as stationary is longer than the one in which the output series has a unit root.
... To indirectly verify the hypothesis that after 2000 the Bank of the Republic of Colombia began to satisfy the Taylor principle with a change to an IT policy, we must verify that the inflation rate should have a unit root in the regime that prevailed before October 2000 and then becomes a weakly stationary time series in the regime that prevailed after October 2000. To do this, a unit root test is implemented for a Markov-switching model following Camacho (2010), using a bootstrapping procedure, based on a regime-switching augmented Dickey-Fuller regression. 23 Table 4 shows the results of the estimation under maximum likelihood, while Table 5 resports the test of the hypothesis in question using standard errors under a bootstrapping procedure with 2,000 replicas, which is a more conservative procedure. ...
... The null hypothesis is the existence of the unit root, that is, H 0 : ρ S t = 0 versus the alternative H 1 : ρ S t < 0, that is, a stationary process. It should be pointed out that this statistic is calculated as the ratio of the estimated coef ficient and its standard deviation, derived from the negative inverse of the Hessian matrix of the likelihood function evaluated at the maximum (see Camacho, 2010 andHall et al., 1999). The construction of the unit root test for the existence of a unit root in the inflation rate, where there are two economic regimes during the period of study, requires taking the following steps: ...
An optimal monetary policy Taylor rule is developed for an open economy, which we then estimate following a Markov regime-switching model for quarterly data from Colombia during 1990-2011. We nd two opposite monetary regimes characterized by di erent policy rules: until October 2000 the Central Bank of Colombia reacted only statistically to output gap changes while after October 2000, when in ation targeting was of cially adopted, monetary policy reacted only statistically to changes in the in ation rate. The latter regime is consistent with the Taylor principle as shown analytically and veri ed empirically by a unit root test for a Markov regime-switching model.
... Since we use a Markov-switching model, it is of interest to see whether the unit root findings stay valid when nonlinearity is allowed in the Markov-switching unit root tests, leading to nonlinear root tests. 8 We use the Markovswitching ADF (MS-ADF) test of Hall et al. (1999) and Camacho (2011) to check the robustness of the unit roots. The MS-ADF is appropriate since we also use the Markov-switching model to capture the nonlinear dynamics among the series. ...
... PP, Phillips-Perron unit root test (Phillips and Perron, 1988). MS-ADF, nonlinear Markov-switching ADF unit root test of Hall et al. (1999) and Camacho (2011). For the ADF and MS-ADF unit root tests, the lag orders are selected by the AIC. ...
This objective of this study is to examine the linkages between real (economic) and financial variables in the United States in a regime-switching environment that accounts explicitly for high volatility in the stock market and high stress in financial markets. Since the linearity test shows that the linear model should be rejected, we employ the Markov-switching VECM to examine the same objective using the Bayesian Markov-chain Monte Carlo method. The regime-dependent impulse response function (RDIRF) highlights the increasing importance of the financial sector of the economy during stress periods. The responses and their fluctuations are significantly greater in the high-volatility regime than in the low-volatility regime.
