Search

Climate economics has been criticized for ignoring uncertainty, catastrophic changes, and tipping points (Stern 2016). The present paper addresses these issues. We consider multiple climate shocks which are recurring, random, uninsurable, and potentially large. The associated damages and the hazard rate are endogenously driven by the stock of greenhouse gases. We provide closed-form solutions for the optimal climate policy and the growth rate of the economy. The optimal path is characterized by a constant growth rate of consumption and of the capital stock until a shock arrives, triggering a downward jump in both variables. The mitigation policy consists of a simple and intuitive rule which requires spending a constant fraction of output on emissions abatement. In a quantitative assessment we show that under favorable conditions the abatement expenditure represents 0.5% of output, equivalent to $37 per ton carbon. Under less favorable conditions with respect to abatement technology and damages, coupled with a relative risk aversion which exceeds unity, the abatement propensity increases to 2.9%, equivalent to $212 per ton carbon, and it jumps to a striking 10% in the pessimistic scenario involving severe shocks and a possible crossing of a tipping point.

Soils are often subject to environmental shocks which are caused by negative externalities linked to overexploitation. We present a stochastic model of a dynamic agricultural economy where natural disasters are sizeable, multiple, and random. Expansion of agricultural activities raises effective soil units (an index of quality and quantity) but contributes to an aggregate loss of soil-protective ecosystem services, which increases the extent of soil degradation at the time of a shock. We provide closed-form analytical solutions and show that optimal development is characterized by a constant growth rateof effective soil units and crop consumption until an environmental shock arrives causing both variables to jump downwards. Optimal policy consists of spending a constant fraction of output on soil preservation. This fraction is an increasing function of the shocks arrival rate, degradation intensity of agricultural practices, and the damage intensity of environmental impact. Implications for the optimal propensity to save are also discussed. An extension of the model provides a solution for the optimal preservation policy when both the hazard rate and damages are endogenous., Economics Working Paper Series, 16/232

Countries with strict immigration policies often resort to deportation measures to reduce their stocks of illegal immigrants. Many of their undocumented foreign workers, however, are not deported but rather choose to return home voluntarily. This paper studies the optimizing behavior of undocumented immigrants who continuously face the risk of deportation, modeled by a stochastic process, and must decide how long to remain in the host country. It is found that the presence of uncertainty with respect to the length of stay abroad unambiguously reduces the desired migration duration and may trigger a voluntary return when a permanent stay would otherwise be optimal. Voluntary return is motivated by both economic and psychological factors. Calibration of the model to match the evidence on undocumented Thai migrants in Japan suggests that the psychological impact of being abroad as an illegal alien may be equivalent to as large as a 68% cut in the consumption rate at the point of return., Economics Working Paper Series, 15/218

Climate physics predicts that the intensity of natural disasters will increase in the future due to climate change. One of the biggest challenges for economic modeling is the inherent uncertainty of climate events, which crucially affects consumption, investment, and abatement decisions. We present a stochastic model of a growing economy where natural disasters are multiple and random, with damages driven by the economy's polluting activity. We provide a closed-form solution and show that the optimal path is characterized by a constant growth rate of consumption and the capital stock until a shock arrives, triggering a downward jump in both variables. Optimum mitigation policy consists of spending a constant fraction of output on emissions abatement. This fraction is an increasing function of the arrival rate, polluting intensity of output, and the damage intensity of emissions. A sharp response of the optimum growth rate and the abatement share to changes in the arrival rate and the damage intensity justifies more stringent climate policies as compared to the expectation-based scenario. We subsequently extend the baseline model by adding climate-induced fluctuations around the growth trend and stock-pollution effects, demonstrating robustness of our results. In a quantitative assessment of our model we show that the optimal abatement expenditure at the global level may represent 0.9% of output, which is equivalent to a tax of $71 per ton carbon.