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The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.

We discuss the Markov-switching vector autoregressive (MS-VAR) class of nonlinear time series models that can be used to analyze recurring discrete structural changes in time series. Hamilton's (1989) seminal Markovswitching (MS) model of the U.S. business cycle triggered considerable interest in the MS approach in economics. Most empirical applications to date have focused on the business cycle and financial markets, but we see potential for MS-VAR models in agricultural economics, for example, in price transmission analysis. In the following, we first provide an overview of the MS-VAR framework. We then present an illustrative application to maize price transmission between Tanzania and Kenya. The article closes with a discussion of strengths, weaknesses, and potential uses of the MS-VAR approach in price transmission analysis. A Brief Overview of MS-VAR ModelsFollowing Krolzig (1997), the basic idea behind the MS-VAR class of models is that the parameters of a VAR process are allowed to depend on an unobserved regime variable s t ∈ {1, . . . , M}, representing M possible states of the world. In its most general form, the MS-VAR is given bywhere y t = (y 1t , . . . , y Kt ) , t = 1, . . . , T is a Kdimensional time series vector, (s t ) and A j (s t ) are matrices of intercepts and autoregressive (AR) parameters of appropriate dimension, and (s t ) is the variance-covariance matrix of a Gaussian zero-mean error process u t . In (1) the terms (s t ), A j (s t ), and (s t ) describe the dependence of the respective parameters on the unobserved regime s t . The intercept in (1), for example, will be regime-dependent as follows:Hence, the nonlinear data generating process in (1) can be described as piecewise linear (i.e., as linear conditional on the regimes).Depending on which parameters in (1) are allowed to be regime-dependent, different subclasses of the MS-VAR result. Krolzig (1997) proposes the terminology MSx(M)-VAR(p) to distinguish between them, where M is the number of regimes, p the order of the VAR, and x indicates which parameters are regime-dependent. Thus, a MSI(M)-VAR(p) refers to a model in which the intercept is regime-dependent, while MSA(M)-VAR(p) and MSH(M)-VAR(p) refer to regime-dependence in the AR terms A j (s t ) and the error covariance (s t ), respectively. These elements can be combined, so that the "full-blown" model in (1) can be considered a MSIAH(M)-VAR(p).A further sub-class of MS-VAR models that is not immediately apparent from (1) is the MSM(M)-VAR(p) in equation (3) y t − (s t ) = p j=1 A j (y t− j − (s t− j )) + u t ,

S ub-Saharan Africa has just experienced one of the best decades of growth since the 1960s. Between 2000 and 2012, gross domestic product (GDP) grew more than 4.5 percent a year on average, compared to around 2 percent in the prior 20 years (World Bank various years). In 2012, the region's GDP growth was estimated at 4.7 percent-5.8 percent if South Africa is excluded (World Bank 2013). About one-quarter of countries in the region grew at 7 percent or better, and several African countries are among the fastest growing in the world. Medium-term growth prospects remain strong and should be supported by a rebounding global economy. At the same time, many Africans are dissatisfied with this economic progress. According to the latest Afrobarometer data, 65 percent of the surveyed population consider economic conditions in their country to be the same or worse than the year prior, 53 percent rate their national economic condition as "very bad" or "fairly bad," and 48 percent say the same about their personal economic condition (Afrobarometer 2011-12. www.afrobarometer.org).

is prepared by Sergiy Zorya (ARD), Varun Kshirsagar (AFTAR), Madhur Gautam (SAARD), Willy Odwongo (AFTAR), Jos Verbeek (AFTP2), and Rachel Sebudde (AFTP2). It draws on various background studies recently undertaken for the Uganda Inclusive Growth Project. 2 Inclusive growth is defined as economic growth .