The distribution of sales revenues from pharmaceutical innovation.

OBJECTIVE: This report updates our earlier work on the returns to pharmaceutical research and development (R&D) in the US (1980 to 1984), which showed that the returns distributions are highly skewed. It evaluates a more recent cohort of new drug introductions in the US (1988 to 1992) and examines how the returns distribution is emerging for drugs with life cycles concentrated in the 1990s versus the 1980s. DESIGN AND SETTING: Methods were described in detail in our earlier reports. The current sample included 110 new drug entities (including 28 orphan drugs), and sales data were obtained for the period 1988 to 1998, which represented between 7 and 11 years of sales for the drugs included. 20 years was chosen as the expected market life for this cohort, and a 2-step procedure was used to project future sales for the drugs--during the period until patent expiry and then beyond patent expiry until the 20-year time-horizon was completed. Thus, the values in the first half of the life cycle are essentially based on realised sales, while those in the second half are projected using information on patent expiry and other inputs. MAIN OUTCOME MEASURES AND RESULTS: Peak annual sales for the top decile of drugs introduced between 1988 and 1992 in the US amounted to almost $US1.1 billion compared with peak sales of less than $US175 million (1992 values) for the mean compound. In particular, the top decile accounted for 56% of overall sales revenue. Although the sales distributions were skewed in both our earlier and current analysis, the top decile in the later time-period exhibited more rapid rates of growth after launch, a peak that was more than 50% greater in real terms than for the 1980 to 1984 cohort, and a faster rate of expected decline in sales after patent expiry. One factor contributing to the distribution of sales revenues becoming more skewed over time is the orphan drug phenomenon (i.e. most of the orphan drugs are concentrated at the bottom of the distribution). CONCLUSION: The distribution of sales revenues for new drug compounds is highly skewed in nature. In this regard, the top decile of new drugs accounts for more than half of the total sales generated by the 1988 to 1992 cohort analysed. Furthermore, the distribution of sales revenues for this cohort is more skewed than that of the 1980 to 1984 cohort we analysed in previous research.

Optimal Capital Requirements in Financial Networks with Fire Sales

I explore and analyze a problem of finding the socially optimal capital requirements for financial institutions considering two distinct channels of contagion: direct exposures among the institutions, as represented by a network and fire sales externalities, which reflect the negative price impact of massive liquidation of assets.These two channels amplify shocks from individual financial institutions to the financial system as a whole and thus increase the risk of joint defaults amongst the interconnected financial institutions; this is often referred to as systemic risk. In the model, there is a trade-off between reducing systemic risk and raising the capital requirements of the financial institutions. The policymaker considers this trade-off and determines the optimal capital requirements for individual financial institutions. I provide a method for finding and analyzing the optimal capital requirements that can be applied to arbitrary network structures and arbitrary distributions of investment returns.

In particular, I first consider a network model consisting only of direct exposures and show that the optimal capital requirements can be found by solving a stochastic linear programming problem. I then extend the analysis to financial networks with default costs and show the optimal capital requirements can be found by solving a stochastic mixed integer programming problem. The computational complexity of this problem poses a challenge, and I develop an iterative algorithm that can be efficiently executed. I show that the iterative algorithm leads to solutions that are nearly optimal by comparing it with lower bounds based on a dual approach. I also show that the iterative algorithm converges to the optimal solution.

Finally, I incorporate fire sales externalities into the model. In particular, I am able to extend the analysis of systemic risk and the optimal capital requirements with a single illiquid asset to a model with multiple illiquid assets. The model with multiple illiquid assets incorporates liquidation rules used by the banks. I provide an optimization formulation whose solution provides the equilibrium payments for a given liquidation rule.

I further show that the socially optimal capital problem using the ``socially optimal liquidation" and prioritized liquidation rules can be formulated as a convex and convex mixed integer problem, respectively. Finally, I illustrate the results of the methodology on numerical examples and

discuss some implications for capital regulation policy and stress testing.