The recently published Intergovernmental Panel on Climate Change (IPCC) projections to 2100 give likely ranges of global temperature increase in four scenarios for population, economic growth and carbon use1. However these projections are not based on a fully statistical approach. Here we use a country-specific version of Kaya’s identity to develop a statistically-based probabilistic forecast of CO2 emissions and temperature change to 2100. Using data for 1960-2010, including the UN’s probabilistic population projections for all countries2–4, we develop a joint Bayesian hierarchical model for GDP per capita and carbon intensity. We find that the 90% interval for cumulative CO2 emissions includes the IPCC’s two middle scenarios but not the extreme ones. The likely range of global temperature increase is 2.0–4.9°C, with median 3.2°C and a 5% (1%) chance that it will be less than 2°C (1.5°C). Population growth is not a major contributing factor. Our model is not a “business as usual” scenario, but rather is based on data which already show the effect of emission mitigation policies. Achieving the goal of less than 1.5°C warming will require carbon intensity to decline much faster than in the recent past.

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Recent research based on variance ratios and multiperiod-return autocorrelations concludes that the stock market exhibits mean reversion in the sense that a return in excess of the average tends to be followed by partially offsetting returns in the opposite direction. Dividing history into pre-1926, 1926-46, and post-1946 subperiods, we find that the mean-reversion phenomenon is a feature of the 1926-46 period, but not of the post-1946 period which instead exhibits persistence of returns. Evidence for pre-1926 data is mixed. The statisticai significance of test statistics is assessed by estimating their distribution using stratified randomization. Autocorrelations of multiperiod returns imply a forecast of future returns, which is presented for postwar three-year returns using 1926-46, full sample, and sequentially updated coefficient estimates. The correlation between actual and forecasted returns is negative in each case. We conclude that evidence of mean reversion in U.S. stock returns is substantially weaker than reported in the recent literature. If mean-reversion continues to be a feature of the stock market, then the experience of the past forty years has been an aberration.

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Following Hamilton (1989), estimation of Markov regime-switching regressions typically relies on the assumption that the latent state variable controlling regime change is exogenous. We relax this assumption and develop a parsimonious model of endogenous Markov regime-switching. Inference via maximum likelihood estimation is possible with relatively minor modifications to existing recursive filters. The model nests the exogenous switching model, yielding straightforward tests for endogeneity. In Monte Carlo experiments, maximum likelihood estimates of the endogenous switching model parameters were quite accurate, even in the presence of certain model misspecifications. As an application, we extend the volatility feedback model of equity returns given in Turner, Startz and Nelson (1989) to allow for endogenous switching.Keywords: Endogeneity, Regime-Switching JEL Classification: C13, C22, G12 * Kim: Dept. of Economics, Korea University, Seoul, Korea, (cjkim@korea.ac.kr 1Recent decades have seen extensive interest in time-varying parameter models of macroeconomic and financial time series. One notable set of models are regime-switching regressions, which date to at least Quandt (1958). Goldfeld and Quandt (1973) introduced a particularly useful version of these models, referred to in the following as a Markov-switching model, in which the latent state variable controlling regime shifts follows a Markov-chain, and is thus serially dependent. In an influential article, Hamilton (1989) extended Markov-switching models to the case of dependent data, specifically an autoregression.The vast literature generated by Hamilton (1989) typically assumes that the regime shifts are exogenous with respect to all realizations of the regression disturbance. In this paper we work with Markov-switching regressions of the type considered by Hamilton (1989) and various extensions, but relax the exogenous switching assumption. We develop a model of endogenous Markov regime-switching that is based on a probit specification for the realization of the latent state. The model is quite parsimonious, and admits a test for endogenous switching as a simple parameter restriction. The model parameters can be estimated via maximum likelihood with relatively minor modifications to the recursive filter in Hamilton (1989).Why are we motivated to investigate Markov-switching regressions with endogenous switching? Many of the model's applications are in macroeconomics or finance in situations where it is natural to assume the state is endogenous. As an example, it is often the case that the estimated state variable has a strong business cycle correlation. This can be seen in recent applications of the regime-switching model to identified monetary VARs, such as Sims andZha (2002) andOwyang (2002). It is not hard to imagine that the shocks to the regression, such as the macroeconomic shocks to the VAR, would be correlated with the business cycle. As another example, some applications of the model contain parameters that represent the reaction...