Shtukas and the Taylor expansion of LL-functions (II)

For arithmetic applications, we extend and refine our results in \cite{YZ} to allow ramifications in a minimal way. Starting with a possibly ramified quadratic extension $F'/F$ of function fields over a finite field in odd characteristic, and a finite set of places $\Sigma$ of $F$ that are unramified in $F'$, we define a collection of Heegner--Drinfeld cycles on the moduli stack of $\mathrm{PGL}_{2}$-Shtukas with $r$-modifications and Iwahori level structures at places of $\Sigma$. For a cuspidal automorphic representation $\pi$ of $\mathrm{PGL}_{2}(\mathbb{A}_{F})$ with square-free level $\Sigma$, and $r\in\mathbb{Z}_{\ge0}$ whose parity matches the root number of $\pi_{F'}$, we prove a series of identities between: (1) The product of the central derivatives of the normalized $L$-functions $\mathcal{L}^{(a)}(\pi, 1/2)\mathcal{L}^{(r-a)}(\pi\otimes\eta, 1/2)$, where $\eta$ is the quadratic id\`ele class character attached to $F'/F$, and $0\le a\le r$; (2) The self intersection number of a linear combination of Heegner--Drinfeld cycles. In particular, we can now obtain global $L$-functions with odd vanishing orders. These identities are function-field analogues of the formulas of Waldspurger and Gross--Zagier for higher derivatives of $L$-functions.Comment: 90 page

Do External Interventions Work? The Case of Trade Reform Conditions in IMF Supported Programs

Trade reform conditions are common in IMF supported programs. Of the 99 countries that had IMF programs during 1993-2003, 77 had conditions on trade reforms in their programs. Since the WTO has not been found especially effective in promoting trade openness for most developing countries, it is of great interest to see if the IMF has been more effective as it combines carrots and sticks not available to the WTO. Yet, the effectiveness of trade conditions in IMF programs has not been systematically studied. Using a unique dataset, this paper provides such an assessment. It finds that trade conditions are associated with an increase in trade openness on average, but the effect comes mostly from countries that, by some measure, have a high degree of "willingness to reform."

Collateral Damage: Exchange Controls and International Trade

While new conventional wisdom warns that developing countries should be aware of the risks of premature capital account liberalization, the costs of not removing exchange controls have received much less attention. This paper investigates the negative effects of exchange controls on trade. To minimize evasion of controls, countries often intensify inspections at the border and increase documentation requirements. Thus, the cost of conducting trade rises. The paper finds that a one standard-deviation increase in the controls on trade payment has the same negative effect on trade as an increase in tariff by about 14 percentage points. A one standard-deviation increase in the controls on FX transactions reduces trade by the same amount as a rise in tariff by 11 percentage points. Therefore, the collateral damage in terms of foregone trade is sizable.