In public finance, a lender of last resort (LOLR) is a financial entity, generally a central bank, that acts as the provider of liquidity to a financial institution which finds itself unable to obtain sufficient liquidity in the interbank lending market when other facilities or such sources have been exhausted. It is, in effect, a government guarantee to provide liquidity to financial institutions. Since the beginning of the 20th century, most central banks have been providers of lender of last resort facilities, and their functions usually also include ensuring liquidity in the international markets in general.

The objective is to prevent economic disruption as a result of financial panics and bank runs spreading from one bank to the others due to a lack of liquidity in the first one.

There are varying definitions of a lender of last resort, but a comprehensive one is that it is "the discretionary provision of liquidity to a financial institution (or the market as a whole) by the central bank in reaction to an adverse shock which causes an abnormal increase in demand for liquidity which cannot be met from an alternative source".

While the concept itself had been used previously, the term "lender of last resort" was supposedly first used in its current context by Sir Francis Baring, in his Observations on the Establishment of the Bank of England, which was published in 1797.

Classical theory Although Alexander Hamilton, in 1792, was the first policymaker to explain and implement a lender of last resort policy, the classical theory of the lender of last resort was mostly developed by two Englishmen in the 19th century: Henry Thornton and Walter Bagehot. Although some of the details remain controversial, their general theory is still widely acknowledged in modern research and provides a suitable benchmark. Thornton and Bagehot were mostly concerned with the reduction of the money supply. That was because they feared that the deflationary tendency caused by a reduction of the money supply could reduce the level of economic activity. If prices did not adjust quickly, it would lead to unemployment and a reduction in output. By keeping the money supply constant, the purchasing power remains stable during shocks. When there is a shock-induced panic, two things happen:

The depositors fear that they will not be able to convert their deposits into suitably safe liquid assets: in 19th-century Britain, that meant gold or Bank of England notes, the latter being a component of high-powered money. They increase the amount of cash they hold relative to deposits. Banks, on the other hand, afraid of becoming illiquid, increase their reserves. Taken together, it reduces the money multiplier which, multiplied by the amount of base money, gives the money supply. This equation shows the relation: where M is the money supply, B is the money base, C/D is the ratio of cash to deposits held by the public, and R/D is the ratio of reserves to deposits held by the banks. If the multiplier is reduced from a shock and the amount of base money is constant, the money supply will decrease as a consequence. Thornton and Bagehot, therefore, suggested that the lender of last resort should increase the money base to offset the reduction of the multiplier. That was meant to keep the money supply constant and prevent an economic contraction.

Thornton's foundations Thornton first published An Enquiry into the Nature and Effects of the Paper Credit of Great Britain in 1802. His starting point was that only a central bank could perform the task of lender of last resort because it holds a monopoly in issuing bank notes. Unlike any other bank, the central bank has a responsibility towards the public to keep the money supply constant, thereby preventing negative externalities of monetary instability, such as unemployment, price instability, bank runs, and financial panic.

Bagehot's contribution Bagehot was the second important contributor to the classical theory. In his book Lombard Street (1873), he mostly agreed with Thornton without ever mentioning him but also develops some new points and emphases. Bagehot advocates: "Very large loans at very high rates are the best remedy for the worst malady of the money market when a foreign drain is added to a domestic drain." His main points can be summarized by his famous rule: lend "it most freely... to merchants, to minor bankers, to 'this and that man', whenever the security is good".

Summary of the classical theory Thomas M. Humphrey, who has done extensive research on Thornton's and Bagehot's works, summarizes their main proposals as follows: (1) protect the money supply instead of saving individual institutions; (2) rescue solvent institutions only; (3) let insolvent institutions default; (4) charge penalty rates; (5) require good collateral; and (6) announce the conditions before a crisis so that the market knows exactly what to expect.

Many of the points remain controversial today but it seems to be accepted that the Bank of England strictly followed these rules during the last third of the 19th century.

Bank runs and contagion Most industrialized countries have had a lender of last resort for many years. Models explaining why propose that a bank run or bank panic can arise in any fractional reserve banking system and that the lender of last resort function is a way of preventing panics from happening. The Diamond and Dybvig model of bank runs has two Nash equilibria: one in which welfare is optimal and one where there is a bank run. The bank run equilibrium is an infamously self-fulfilling prophecy: if individuals expect a run to happen, it is rational for them to withdraw their deposits early: before they actually need it. That makes them lose some interest, but that is better than losing everything from a bank run.

In the Diamond–Dybvig model, introducing a lender of last resort can prevent bank runs from happening so that only the optimal equilibrium remains. That is because individuals are no longer afraid of a liquidity shortage and so have no incentive to withdraw early. The lender of last resort will never come into action because the mere promise is enough to provide the confidence necessary to prevent a panic.

Subsequently, the model has been extended to allow for financial contagion: the spreading of a panic from one bank to another, by Allen and Gale, and Freixas et al. respectively.

Allen and Gale introduced an interbank market into the Diamond–Dybvig model to study contagion of bank panics from one region to another. An interbank market is created by banks because it insures them against a lack of liquidity at certain banks as long as the overall amount of liquidity is sufficient. Liquidity is allocated by the interbank market so that banks that have excess liquidity can provide this to banks that lack liquidity. As long as the total demand for liquidity does not exceed the supply, the interbank market will allocate liquidity efficiently and banks will be better off. However, if demand exceeds supply, it can have disastrous consequences. The interregional cross-holdings of deposits cannot increase the total amount of liquidity. Thus, long-term assets have to be liquidated, which causes loss.

The degree of contagion depends on the interconnectedness of the banks in different regions. In an incomplete market (banks do not exchange deposits with all other banks), a high degree of interconnectedness causes contagion. Contagion is not caused if the market is either complete (banks have exchanged deposits with all other banks) or if the banks are little-connected. In Allen and Gale's model, the role of the central bank is to complete the markets to prevent contagion.

Freixas et al.'s model is similar to the one by Allen and Gale, except that in Freixas et al.'s model, individuals face uncertainty about where they will need their money. There is a fraction of individuals (travelers) who need their money in a region other than home. Without a payment system, an individual has to withdraw his deposit early (when he finds out that he will need the money in a different place in the next period) and simply take the money along. That is inefficient because of the foregone interest payment. Banks therefore establish credit lines to allow individuals to withdraw their deposits in different regions. In the good equilibrium, welfare is increased just as in the Diamond–Dybvig model, but again there is a bank run equilibrium, too. It can arise if some individuals expect too many others to want to withdraw money in the same region in the next period. It is then rational to withdraw money early instead of not receiving any in the next period. It can happen even if all banks are solvent.

Disputed matters There is no universal agreement on whether a nation's central bank or any agent of private banking interests should be its lender of last resort. Nor is there on the pros and cons of actions such a lender takes and their consequences.

Moral hazard Moral hazard has been an explicit concern in the context of the lender of last resort since the days of Thornton. It is argued, for example, that the existence of a LOLR facility leads to excessive risk-taking by both bankers and investors, which would be dampened if illiquid banks were allowed to fail. Therefore, the LOLR can alleviate current panics in exchange for increasing the likelihood of future panics by risk-taking induced by moral hazard.

That is exactly what the Report of the International Financial Institution Advisory Commission in 2000 accused the IMF of doing when it lends to emerging economies: "By preventing or reducing losses by international lenders, the IMF had implicitly signalled that, if local banks and other institutions incurred large foreign liabilities and government guaranteed private debts, the IMF would provide the foreign exchange needed to honour the guarantees." Investors are protected against the downside of their investment and, at the same time, receive higher interest rates to compensate them for their risk. That encourages risk-taking and reduces the necessary diversification and led the Commission to conclude, "The importance of the moral hazard problem cannot be overstated."

However, not having a lender of last resort for fear of moral hazard may have worse consequences than moral hazard itself. Consequently, many countries have a central bank that acts as lender of last resort. These countries then try to prevent moral hazard by other means such as suggested by Stern: "official regulation; encouragement for private sector monitoring and self-regulation; and the imposition of costs on those who make mistakes, including enforcement of bankruptcy procedures when appropriate." Some authors also suggest that moral hazard should not be a concern of the lender of last resort. The task of preventing it should be given to a supervisor or regulator that limits the amount of risk that can be taken.

Macro or micro responsibility Whether or not the lender of last resort has a responsibility for saving individual banks has been a very controversial topic. Does the lender of last resort provide liquidity to the market as a whole (through open market operations) or should it (also) make loans to individual banks (through discount window lending)?