This dissertation consists of three essays examining the impacts of Sanitary and Phytosanitary (SPS) Measures on agricultural trade. The first essay estimates the impact of the 2003 Bovine Spongiform Encephalopathy (BSE) outbreak in the US on Japanese beef imports. I develop a source-differentiated demand system of fresh/chilled and frozen beef imports augmented with endogenous smooth transition functions. Results suggest that over one-half of the estimated income, own-price, and cross-price elasticities reached a new regime in the post-BSE period of Japanese beef imports where the competitive relationship and substitutability between US and Australian beef exports changed significantly. The second essay develops a product-line structural gravity model to estimate the trade flow effects of SPS measures that have been flagged as specific trade concerns in the World Trade Organization's (WTO's) SPS Committee meetings for the top 30 agricultural trading countries covering four major product sectors. Our findings are striking and call attention to the need for a deeper understanding of the impacts of SPS measures on WTO members' agricultural trade. Results show that the trade effects of SPS trade concern measures reduce exporters' agricultural trade by 67%, on average, during periods in which concerns were active. Significant heterogeneity in the trade effect of SPS measures exists with average estimated ad valorem equivalent tariffs ranging from 33% to 106%. The AVE effect of SPS concern measures maintained by the US is estimated at 42%, less than a half (a third) of the AVE effects of SPS concern measures imposed by the European Union (China). China's restrictions on Avian Influenza and ractopamine restrictions in pork exports are estimated to be the most prohibitive, causing an AVE effect of 120.3% and 88.9%, respectively. The third essay develops a discrete-time duration model to examine the extent to which these SPS concern measures affect the hazard rate of US agri-food exports during the 1995-2016 period. Results show that SPS concern measures raise the hazard rate of US agri-food exports by a range of 2.1%~15.3%, causing the predicted hazard rate to increase from 21.8% to a range of 23.6%~27.9%. This effect is heterogeneous across different agricultural sectors, with the most substantial effects occurring in US exports of meat, fruits, and vegetables. / Doctor of Philosophy / This dissertation consists of three essays on the examination of Sanitary and Phytosanitary (SPS) Measures and their impacts on agricultural trade. The first essay estimates the impact of the US 2003 Bovine Spongiform Encephalopathy (BSE) outbreaks on Japanese beef imports. Using a source-differentiated demand system of fresh/chilled and frozen beef imports embedded with endogenous smooth transition functions, we find that over one-half of the estimated income, own-price, and cross-price elasticities have changed remarkably, causing the Japanese beef import market to reach a new regime in the post-BSE period where the substitution and/or competition relationships between the US and Australia have changed. The second essay develops a product-line structural gravity model to estimate the trade effects of SPS measures flagged as concerns in the WTO's SPS Committee meetings for the top 30 agricultural trading countries covering four major product sectors. Results show that the trade effects of SPS concern measures are negative and significant, with the average estimated AVE tariffs ranging 33%~106%. The AVE effect of SPS concern measures maintained by the US is estimated to be 42%, less than a half (a third) of the AVE effects of SPS concern measures imposed by the European Union (China). China's restrictions on Avian Influenza and various ractopamine restrictions in the production and export of pork products are estimated to be the most prohibitive, causing an AVE effect of 120.3% and 88.9%, respectively. The third essay applies a discrete-time duration model to examine the extent to which SPS concern measures affect the hazard rate of US agri-food exports in 1995-2016. Results show that SPS concern measures raise the hazard rate of US agri-food exports by a range of 2.1%~15.3%, causing the predicted hazard rate to increase from 21.8% to a range of 23.6%~27.9%. This effect is heterogeneous across different agricultural sectors, with the most substantial effects occurring in US exports of meat, fruits, and vegetables.