Rethinking the Implications of Monetary Policy: How a Transactions Role for Money Transforms the Predictions of Our Leading Models* BY JULIA K. THOMAS

ver the past several decades, economists have everything from car and home sales to consumer spending over the Christmas O devoted ever-growing effort to developing holiday season. Whenever business economic models to help us understand conditions are widely perceived to be weak, most people welcome cuts in the how changes in interest rates brought federal funds rate. about by monetary policy actions affect the production Despite these observations, however, the means through which and provision of goods and services in the economy. changes in an interest rate affect Although New Keynesian models have broad appeal in business activity is, in fact, far from obvious. Over the past few decades, explaining how changes in the money stock can affect economists have devoted ever-growing business activity, these models generate results that are effort to developing formal economic models to help us understand precisely inconsistent with what we know about how interest rates how changes in interest rates brought move with policy-induced changes in the money stock. about by monetary policy actions affect the production and provision of goods In this article, Julia Thomas argues that by extending the and services throughout the economy. New Keynesian model to reintroduce money’s liquidity While there are several different types role, we can resolve some of the remaining divorce of models describing how monetary policy actions drive short-run changes between economic theory and the patterns observed in in total employment and GDP, a the workings of actual economies. growing consensus has emerged. Most often, when an economic model is used as an additional tool with which to analyze the consequences of alternative monetary policy actions, it is drawn from a class of models known Each meeting of the FOMC is met to the cashier at your local grocery as New Keynesian (or sticky price) with widespread interest by everyone store. People perceive changes in the models. from financial market participants FOMC’s target for the federal funds New Keynesian models have broad on Wall Street, to real estate agents, rate — the interest rate at which banks appeal because they provide a relatively borrow and lend to each other, usually simple explanation for how changes in overnight, through the federal funds the stock of money can affect business Julia Thomas is an market — as relevant and important activity and because they are, in some associate professor in their everyday lives. Business people respects, quite consistent with what of economics at Ohio State view changes in this interest rate as economists know about how actual University. When an important determinant influencing changes in the money stock affect she wrote this the economy. Unfortunately, though, article she was an economic advisor versions of these models capable of and economist in generating realistic effects of changes the Philadelphia *The views expressed here are those of the in the money stock for production and Fed’s Research author and do not necessarily represent Department. This article is available free of the views of the Federal Reserve Bank of employment are, at their most basic charge at www.philadelphiafed.org/research- Philadelphia or the Federal Reserve System. level, inconsistent with what we know and-data/publications/. www.philadelphiafed.org Business Review Q1 2009 19 about how interest rates move with spread throughout the economy can increases the difference between a policy-induced changes in the stock of depend importantly on how much bond’s payoff at maturity (its par value) money. money is typically held and how relative to its purchase price today, This article argues that, by rapidly it changes hands, on average. ultimately raising the rate of return on extending the New Keynesian model In short, our extended theoretical bonds — that is, the interest rate. to reintroduce an abandoned liquidity model offers new insights about how Macroeconomists generally role of money found in earlier models, associate an easing of monetary policy we can resolve some of the remaining with a cut in interest rates. As Nobel divorce between our economic theory Macroeconomists Laureate Milton Friedman put it in and the patterns we observe in the generally associate his 1968 presidential address to the workings of actual economies.1 What American Economic Association, is this role of money? It is the idea, an easing of monetary “The initial impact of increasing the from classical economics, that money policy with a cut in quantity of money at a faster rate serves a special purpose in allowing than it has been increasing is to make transactions to take place between interest rates. interest rates lower for a time than buyers and sellers, since it is the only they would otherwise have been.” financial asset universally accepted as the effects of monetary policy are Indeed, there is such consensus about a means of payment. Other assets, such transmitted throughout the economy. the inverse relationship between short- as stocks and bonds, are typically not term interest rates and the growth rate accepted as a means of payment and WHAT HAPPENS FOLLOWING of the aggregate money supply that the cannot be directly used to buy goods A CHANGE IN MONETARY relationship has been given a name: 3 and services. Thus, in contrast to POLICY? the liquidity effect. money, these nonmonetary assets are For many economists, at the There is even greater consensus relatively illiquid. most basic level, the changes in the that changes in nominal variables, When we introduce the classic economy associated with a change such as the interest rate, have notable liquidity role of money into the New in monetary policy may be traced to consequences for the paths of real Keynesian model, and we acknowledge changes in the rate at which the supply the fact that it is costly to convert of money grows over time, rather than nonmonetary assets into monetary to movements in the interest rate. 3 Most evidence of the liquidity effect is indirect, ones (and vice versa), we arrive at a Indeed, the means through which in that the relationship is inferred by examin- richer model that is consistent with ing economic data through the lens of complex central banks actually move their key empirical models beyond the scope of this article. our knowledge of how interest rates interest rates is through open market However, Seth Carpenter and Selva Demiralp are affected by changes in the stock operations, wherein government directly establish the existence of the liquidity of money. At the same time, the effect at a daily frequency by studying the forecast bonds — a nonmonetary asset — are errors made at the New York Fed’s Trading Desk mechanics of the New Keynesian exchanged for money. For example, in conducting open market operations on behalf model become more complicated with of the Federal Reserve System. Using these errors the monetary authority can reduce the to identify exogenous changes in the supply of re- this improvement, because the level of overall level of money in the economy serves to the banking system, the authors establish an individual’s monetary assets takes by undertaking an open market sale of a negative and statistically significant correlation between unanticipated changes in high-powered on an independent role in his or her 2 government bonds for money. In the money and the federal funds rate. Elsewhere, spending decisions. Exploring the process of such a contractionary open John Cochrane provides direct evidence that effects of changes in monetary policy the liquidity effect exists for broader measures of market operation, the overall supply money and interest rates. He examines changes in this richer environment, we find of bonds for sale is increased, which in the growth of M1 (total currency and check- that the overall magnitude of these puts downward pressure on the price at able deposits) and in the nominal yields on U.S. effects and the rate at which they Treasuries between October 1979 and November which each bond is sold. This, in turn, 1982 (a historical episode throughout which the Federal Reserve expressly targeted the quantity of money held by commercial banks). Cochrane uncovers statistically significant negative effects of M1 growth on both three-month Treasury bill 1 The expanded model we pursue throughout 2 See the article by Frederic Mishkin or Dean rates and 20-year Treasury bond rates and thereby this discussion is drawn from my article with Croushore’s book for a more thorough discus- establishes that increases in the rate of money Robert King, which builds upon my work with sion of the implementation of open market growth are associated with declines in nominal Aubhik Khan. operations. interest rates lasting up to one year.

20 Q1 2009 Business Review www.philadelphiafed.org variables like GDP and employment. local suppliers typically harvest and actively watching for the outcome Such real effects arising from a sell 50 mangos each week. The single of each meeting of the FOMC, change in monetary policy are termed currency used to purchase these goods economists generally accept that nonneutralities. Perhaps the most is the seashell; that is, islanders buy changes in the supply of money induce celebrated example of nonneutrality and sell mangos using only seashells. temporary movements in output, is the observation that reductions in There are 100 seashells on the island employment, and the real return to inflation caused by contractionary this week, as in many previous weeks, holding assets measured in units of monetary policy are associated with and all mangos are sold (and all consumption — the real (or inflation- temporary increases in unemployment, seashells are exchanged for mangos) adjusted) interest rate, to which we a relationship termed the Phillips curve tradeoff.4

NEW KEYNESIAN MODELS It is not easy to reproduce the patterns in It is not easy to reproduce the the movements of money, interest rates, patterns in the movements of money, interest rates, employment, and employment, and output observed in actual output observed in actual economies economies within our economic models. within our economic models; however, doing so is an important step toward understanding why these patterns 5 arise and how they may be influenced precisely once each week. Under these will return later in this article. Let by monetary policy. To generate circumstances, the price of a mango us reconsider our island economy of nonneutralities in our models, we will be two seashells. seashells and mangos in light of this must first find a way to overcome their Next, let us suppose that a nearby consensus view. tendency to exhibit a related, and hurricane causes 100 additional If the price of each mango does quite opposite, phenomenon known seashells to wash up on the island’s not immediately double in response to as the neutrality of money. This beaches next week, unexpectedly the unexpected doubling of seashells term applies whenever changes in an doubling the supply of currency (or on the island, the quantity of mangos economy's money stock are transmitted money). This would seem to imply supplied must rise to prevent unfilled immediately into the overall level of twice as many island dollars next week demand for mangos and undesired prices and have no effect at all on the chasing after the same weekly harvest idle seashells. But how might this real quantities of goods and services of 50 mangos. So what will happen to happen? New Keynesian models have produced and sold. the price of a mango? One possibility a simple answer to the question. They Neutrality of Money. To illustrate is that it will immediately rise to assume that the firms supplying goods the neutrality of money, consider four seashells, thereby doubling the and services — in our example, the the following simple example of a island price level, with no change in islanders gathering mangos — cannot remote island with a single good and the number of mangos harvested and a single currency. Let us assume that sold. If this happens, the rise in the money supply will have simply led to the mango is the only good valued 5 a proportionate rise in the price level, Economists use rich empirical methods to study by inhabitants of the island and that the joint movement of interest rates, prices, and with no consequence at all for the output. Their findings suggest that a persistent island’s real activity – its employment increase in the nominal interest rate is initially accompanied by a small decline in the growth rate and GDP – and we have a textbook of output, with little or no change in the growth 4 This relationship is named after Alban William case of the neutrality of money. rate of the price level. Over the course of several Phillips, who documented an inverse relationship Nonneutrality of Money. In subsequent quarters, it is followed by declines between changes in unemployment and nominal in both output growth and inflation. At some wages in the United Kingdom across roughly 100 contrast to the scenario suggested point thereafter, the changes in the quantities years of data. However, some argue that acknowl- above, most economists are convinced of goods and services produced in response to edgment should instead go to Irving Fisher, who the change in the interest rate eventually van- had suggested a similar relationship roughly 20 that actual economies exhibit short- ish. For further discussion, see the articles by years earlier. The relationship was theoretically term departures from the neutrality Lawrence Christiano, Martin Eichenbaum, and formalized to consider its policy implications by of money. Like the many individuals Charles Evans; Harald Uhlig; and Robert King Paul Samuelson and Robert Solow. and Mark Watson.

www.philadelphiafed.org Business Review Q1 2009 21 always change their prices at will. unexpected increase in the amount of rate! This is where the problems begin Rather, some must honor prices that currency on the island will have real for the basic New Keynesian model. they set in the past.6 effects, raising employment and/or the Interest Rate Movements. In For simplicity, suppose that average hours worked per employee, as contrast to the liquidity effect observed one-third of the mango sellers on our well as total production (real GDP). in actual economies, the formal island are able to change their prices The real effects of the rise in relationships between money, interest in any given week, with a single crayon the island’s money supply are not rates, inflation, and output at the core used to reset prices on cardboard permanent, however. Instead, the of the New Keynesian model lead it advertisements alternating between initial week’s high level of real activity to predict that the interest rate rises each of the three groups of sellers on will begin to subside as the economy’s when the money supply is expanded. the island each week. In this case, price level continues responding to Why do interest rates move the wrong when the new seashells arrive, the average price of a mango will not immediately jump to four seashells. In contrast to the liquidity effect observed in Instead, the island price level will rise only part way in the first week, actual economies, the formal relationships since only one-third of all sellers can between money, interest rates, inflation, and respond to the increase in the supply of seashells with an increase in their output at the core of the New Keynesian model prices. lead it to predict that the interest rate rises Assuming that all sellers are when the money supply is expanded. forced to supply the quantity of mangos that is demanded of them at their posted prices (or that they face sufficiently harsh penalties for not the doubled supply of seashells. In way in the model? To understand this, doing so that they choose to comply), the following week, as an additional we must consider a key relationship the staggered price adjustment one-third of sellers are able to raise between (nominal) interest rates and described above is all that is needed their prices, the average price of a real interest rates: the Fisher equation, to break the neutrality of money mango will rise further. Thus, while named after Irving Fisher.7 The in our island economy. With the total demand will remain higher than Fisher equation says that the interest average price in the economy not usual, it will be less so than initially, rate — the ratio of the dollar payoff on initially doubling, and assuming that and total mango production and sales an asset relative to its dollar purchase all consumers on the island spend will move nearer to their customary price — is approximately equal to the their extra seashells, the total demand level. Eventually, as all sellers have sum of the real interest rate and the for mangos will rise above the usual had the opportunity to respond to the expected rate of inflation. To see why weekly supply of 50, and more mangos new economic conditions, the island it is natural that this equation should will have to be harvested. As a result, price level will reach precisely double hold, at least approximately, we begin mango suppliers (and their employees) its original level, and the quantity with a broad definition of the real will work more relative to the normal of mangos harvested each week will interest rate. The real interest rate is level of labor effort on the island, and return to the same 50 as existed before the ratio of an asset’s payoff in units more fruit will be sold. Put another the hurricane. of future consumption of goods and way, given temporary price stickiness The example above illustrates how services relative to the consumption among a fraction of sellers, the unexpected increases in the money supply can temporarily stimulate economic activity. However, its 7 Fisher’s exposition of the relationship in The mechanics are very different from the Theory of Interest, published in 1930, is now out 6 See the articles by William Kerr and Robert way we usually think of a change in of print. However, it is available online at the Li- King; Bennett McCallum and Edward Nelson; monetary policy. Note, in particular, brary of Economics and Liberty (www.econlib.org/ and Michael Woodford for analytically tractable library/classics.html). The topic is also routinely examples of the basic New Keynesian environ- that our example never even covered in most macroeconomics texts; see, for ment. mentioned a change in the interest example, Robert Barro’s book.

22 Q1 2009 Business Review www.philadelphiafed.org that must be forgone today for its — the inverse relationship between acknowledge the fact that individuals purchase; in other words, it is the changes in interest rates and changes hold low-yield liquid assets, or money, return on savings measured not in in the money supply observed in actual because they must draw on them for money but in goods and services. economies. transactions. Quite simply, goods and Returning to the island analogy services can be purchased only with above, let us suppose that our islanders EXTENDING THE MODEL: money (which we might think of as are able to borrow and save. In partic- TRANSACTIONS ROLE FOR currency, checkable deposits, and time ular, if an inhabitant saves 10 seashells MONEY AND INFREQUENT and savings deposits). At the same this week, an island banker will lend PORTFOLIO ADJUSTMENTS time, individuals also choose to hold them to some other islander and re- Basic New Keynesian models higher-yield nonmonetary assets, such turn to the original lender 11 seashells fail to reproduce the liquidity effect as government bonds, as a means of next week. Thus, the weekly nominal essentially because they place no saving. While these assets cannot be interest rate is 10 percent. Suppose emphasis on the nature of the open used directly for transactions, they also that the price of a mango will market operations that implement pay significantly higher rates of return rise over the course of the week from monetary policy.8 We can correct this than money. one seashell to 1.01 seashells; in other problem if we extend our theoretical Various events — some expected, words, the weekly rate of inflation is 1 model to reflect the fact that some unexpected — occasionally lead percent. Under these circumstances, individuals hold both liquid assets, people to adjust their asset portfolios, a mango forgone this week implies broadly interpretable as money, as well moving wealth out of bonds (illiquid one seashell of savings deposited with the island banker that will return 1.1 seashells next week (each worth 1/1.01 mangos), allowing the lender to buy When there is a change in the quantity of 1.089 additional mangos at that time. Notice that the real interest rate, mea- bonds in the economy, it affects those people sured in units of island goods, is then who are active in the bond market at that time, approximately 9 percent. In this way, whether directly or through their brokers. we have arrived at the key relationship defined by Irving Fisher; the interest rate on our island is roughly equal to the sum of the real interest rate and as illiquid assets, such as stocks and assets) into money (liquid assets), or the inflation rate. government bonds, and we also take vice versa. When an individual puts Given the discussion above, it account of the fact that individuals a down payment on a mortgage, she is straightforward to summarize why infrequently adjust their portfolios may do so by converting CDs or other the basic New Keynesian model fares between these two types of assets. high-yield assets into money that is poorly with regard to the liquidity ef- In this extension of the model, deposited into her bank account and fect. In the basic model economy, an we allow money to serve a particular then write a check from that account increase in the money supply implies purpose not reflected in the basic New to make the down payment. However, very little change in the real inter- Keynesian environment. Here, we for the average person, such events est rate. However, at the same time, are relatively infrequent. Thus, in any it leads to comparatively substantial given month, most individuals are not increases in future inflation rates. actively adjusting their asset portfolios Referring back to the Fisher equa- 8 More elaborate versions of these models do suc- — or what we will loosely term “active ceed in generating a liquidity effect. However, in the bond market.” tion, it is then natural that the model Bill Dupor, Jing Han, and Yi-Chan Tsai raise an should predict that the interest rate inherent tension regarding this success. They find When there is a change in the initially rises when the supply of money that the additional assumptions needed to make quantity of bonds in the economy, it the basic New Keynesian model consistent with in the economy is expanded. This is the observed responses in interest rates, inflation, affects those people who are active a somewhat disconcerting feature of and output following changes in monetary policy in the bond market at that time, have the unfortunate consequence of making it whether directly or through their our standard model, given the broad inconsistent with observed responses following consensus regarding the liquidity effect nonmonetary disturbances. brokers. It is with these individuals

www.philadelphiafed.org Business Review Q1 2009 23 that the monetary authority conducts model reduces the upward pressure on real interest rate while simultaneously an open market operation.9 For inflation relative to that in the basic reducing the upward pressure on example, the monetary authority might New Keynesian model. How might inflation, and thus it has the ability to repurchase bonds from them and pay this alter the model’s performance with reproduce the liquidity effects we see for the bonds by making deposits into regard to the liquidity effect? Recalling following expansionary open market their bank accounts. When these the Fisher relationship from above, operations in actual economies. individuals are induced to sell bonds we know that the more gradual rise in and receive the associated payments inflation increases the likelihood that MONEY VELOCITY IN THE of money into their bank accounts, the interest rate will fall in response to EXTENDED MODEL the overall supply of money in the a money injection. All that is required To reconcile reductions in short- economy is increased. However, the for this to happen is that the real term nominal interest rates with full rise in the stock of money does interest rate exhibit a fall of sufficient expansionary monetary policy that not find its way into economic activity magnitude to outweigh the initial rise stimulates output and employment right away. Instead, much of it remains in inflation. over the short run, we have extended in the recipients’ bank accounts for some time. It is precisely the fact that most people are active in the bond market To reconcile reductions in short-term nominal only occasionally in our extended interest rates with expansionary monetary model that implies that a change in the overall money supply is not policy that stimulates output and employment immediately transmitted throughout over the short run, we have extended the the economy. Most of the individuals New Keynesian model to introduce an explicit involved in the expansionary open market operation from above do transactions role for money, alongside not expect to sell more bonds in infrequent trading of bonds by the typical the near future, so they save much of the current increase in their individual. bank accounts to finance their expenditures over future months and boost their spending only gradually. This brings us to the fall in the the New Keynesian model to introduce Thus, the injection of new money real interest rate. For the increase in an explicit transactions role for money, into the economy does not lead to the money supply to find its way into alongside infrequent trading of bonds an immediate equivalent increase in general economic activity, individuals by the typical individual. However, aggregate spending but instead induces participating in the open market the repercussions of this extension go a more protracted rise in spending operation must be induced to increase beyond merely resolving the problem as more and more of the additional their spending and thus their real of the absent liquidity effect. In fact, money is drawn from the recipients’ consumption of goods and services. the new elements we have introduced accounts. This can only happen, however, if into the model can have large and The slow increase in overall the opportunity cost of an increase important implications for the way nominal spending in our extended in their current consumption (the in which monetary policy affects the forgone return of a greater increase economy, because they, in turn, create in consumption next month) is not a prominent role for movements in the intolerably high. To ensure that this velocity of money. 9 For expositional convenience, we proceed through the remainder of this discussion as is the case, the real interest rate Velocity Defined. The velocity though the monetary authority directly interacts must fall relative to its average level, of money is another classic feature with individuals when conducting open market which is precisely what happens in of models of the monetary economy operations. In reality, of course, interactions between the Federal Reserve System and indi- our extended version of the New that has been largely ignored in New viduals are not direct, since the Desk actually Keynesian model. On balance, our Keynesian models. It is a very basic conducts open market operations through the primary dealers. extended model delivers a fall in the concept reflecting the average number

24 Q1 2009 Business Review www.philadelphiafed.org of times a unit of money is used within weekly level of 1 to 0.75. This is analo- the velocity of money have no further a specific time period, and it lies at gous to what happens in our extended role.10 Put another way, changes in the heart of traditional monetary version of the New Keynesian model interest rates always affect output, theory. To compute velocity, we need following an expansionary open mar- employment, and inflation in the same only take the ratio of total nominal ket operation. Because only a fraction way, irrespective of the money supply spending on goods and services relative of all individuals actually take part in and the resulting number of times each to the overall stock of money in the the open market operation, and those currency unit is used. economy. This observation comes individuals that do participate elect In our expanded model, by straight from the velocity equation to save much of the increased money contrast, individuals’ bank balances MV = PY, wherein M represents the stock in their bank accounts to finance help determine their spending over aggregate money stock, V is velocity, and above their total income or P is the aggregate price level, and Y wealth. An individual with a total is real aggregate output. Notice that wealth of $1000, but with only $100 by simply rearranging the velocity When an open market currently available as money in her equation, we have V = PY/M. operation increases bank account, will spend less on Let us consider our island nondurable goods this week than will economy once again. There, within the bank balances of another individual who has the same a typical week, all seashells changed individuals who are $1000 but who holds it entirely in hands exactly one time, with a total trading bonds, their her bank account. Because money of 100 available seashells being used is necessary for transactions in our to buy 100 seashells' worth of mangos. spending rises, but it expanded model economy, the role Thus, the weekly velocity of money rises by less than the of the aggregate money stock and its was one. Now, let us suppose that, velocity does not end with the interest when the extra 100 seashells wash increase in their bank rate. Rather, the quantity of money onto the island in the week of the accounts. that individuals hold and the rates hurricane, only one person is out on at which they spend it have a direct the beach to receive the unexpected influence on the aggregate demand “money injection,” so that he is for goods and services even after the the only inhabitant to receive any near-term expenditures, there too interest rate has been determined. additional money or even know of it. velocity falls with an increase in the Thus, we cannot anticipate the If we further suppose that this islander money supply. changes in production, employment, spends only 50 of the extra seashells How Changes in Velocity and inflation that will follow a given this week and tucks the remainder Influence the Transmission of change in monetary policy by simply away for future use (holding them Monetary Policy. Changes in knowing the implied path of interest idle in his hut for quick and costless velocity over time can have important access), total nominal spending on the consequences for the rate at which island will rise to only 150 seashells out nominal phenomena, such as of a total seashell supply of 200. Thus, unexpected movements in the supply 10 This is essentially because the system of equa- of money, transmit themselves into real tions governing the model has only a single equa- the average number of times any one tion involving the demand for real balances, and seashell changes hands in the week effects. In the basic New Keynesian that equation is effectively quarantined from the will be 150/200, implying a money model, where money has no distinct rest of the economy in that it links real balances only to the nominal interest rate and the money velocity of 0.75. role in facilitating transactions, growth rate. Apart from the money demand In our example above, when movements in velocity do not feed equation, there is a core block of equations that contain no monetary variables at all but that only one islander was on the beach to back into the operation of the real together determine output, inflation, and the receive the unexpected injection of economy. It is true that money helps real interest rate as a function of the interest rate. seashells, and he chose to hold half of to determine the interest rate through In the most basic formulation of the model, this block of equations is simply (1) an Euler equation the injection idle rather than imme- the interaction of money demand and describing households’ optimal savings behavior, diately spending it or investing it in the aggregate money supply. However, (2) the Fisher relation discussed above, and (3) a Phillips curve relating current inflation and the island bonds, we saw that the velocity once the interest rate is determined, aggregate supply of goods and services to expected of money dropped from its average the aggregate quantity of money and inflation.

www.philadelphiafed.org Business Review Q1 2009 25 rates; instead, we must also know how output. At the same time, the rises slowly, and the fall in aggregate individuals’ money holdings and their in aggregate nominal spending must velocity following an expansionary money spending rates (velocities) will also serve to prop up the inflation open market operation only reinforces respond to the change in policy. rate. Thus, we see that, while the this fact. In that setting, it will take When an open market operation initial decline in velocity dampens the far longer for the full effects of the increases the bank balances of initial changes in both real quantities same increase in the aggregate money individuals who are trading bonds, and inflation, these subsequent supply to be transmitted through the their spending rises, but it rises by upward movements in velocity serve economy, since it will take far more less than the increase in their bank to protract those changes. For this time for the new balances to fully enter accounts. Thus, we see a rise in the reason, our economy’s responses to into circulation. fraction of the money supply sitting an open market operation cannot be The movements in velocity arising idle awaiting future use, money completed until velocity has recovered in our expanded New Keynesian changes hands less frequently than to its normal level, when the full model are, in truth, an attempt to before, and velocity falls. Unlike increase in the money supply has found formalize Milton Friedman’s views the basic New Keynesian model, where changes in velocity have no independent influence on the When velocity falls, there are fewer dollars in economy, the decline in velocity in our expanded model has an important role circulation for undertaking transactions than in shaping the economy’s response to there would be otherwise. the expansion of the money supply. When velocity falls, there are fewer dollars in circulation for undertaking transactions than there would be its way into circulation and individuals on the transmission of monetary otherwise. This places a restraint on have resumed their usual spending policy. In his words, “The initial effect the economy’s overall demand for rates. of a change in monetary growth is goods and services and thus dampens As indicated above, the time it an offsetting movement in velocity, the initial rise in production and takes for an open market operation to followed by changes in the growth of employment. Moreover, recalling our flow throughout our model economy spending initially manifested in output money velocity equation from above, will depend on how long it takes and employment, and only later in we know that the fall in velocity for velocity to return to its ordinary inflation.”11 If the nominal interest (V) means that aggregate nominal level. In a setting where velocity is rate is cut when velocity is low, we will spending (PY) initially rises by less initially very high, money changes observe a slow and gradual response than the rise in the money supply (M). hands very frequently. There, despite in output, employment, and prices Thus, the fall in velocity helps to some resulting decline in velocity in our model economy. However, restrain the rise in the aggregate price as described above, the effects of the transmission of an expansionary level, and the inflation rate rises by less a change in monetary policy that change in policy will look quite than it would were velocity unchanged are unique to our expanded model different if velocity is high. In that or irrelevant (as in the basic model). are likely to vanish rapidly. This case, the increase in money supply Over time, as the individuals is because new money held by corresponding to a nominal interest who participated in the open market individuals participating in an open rate cut will quickly find its way into operation begin to spend more and market operation will not be left circulation, yielding a more abrupt rise more of the extra money they are idle for long but will instead rapidly in production and employment and holding, aggregate velocity begins enter circulation. After that has more quickly bringing about the full to rise back toward its normal level. happened, the aggregate responses Over the early part of this transition, in our expanded model economy will as more and more money balances closely resemble those of the basic enter circulation, aggregate demand New Keynesian model. By contrast, 11 This passage is drawn from Friedman’s testimony a setting with low initial velocity is to the House of Commons Select Committee in continues to rise, thereby propping 1979; for the full text, see the 1980 reference to up the responses in employment and one where people spend their money Friedman.

26 Q1 2009 Business Review www.philadelphiafed.org implied rise in inflation. this too will influence how velocity vary from one economy to another By extending the New Keynesian responds to a change in the growth depending on how much money model to correct its prediction rate of the money supply. individuals need to hold against their regarding the liquidity effect, we coming spending and depending on have arrived at a richer setting where CONCLUSION how willing they are to alter their movements in the velocity of money Economists use New Keynesian money savings patterns in response over time themselves feed back models to study how short-term to changes in aggregate conditions. through the economy to influence nonneutralities allow monetary policy Our theory predicts that the effects how much and for how long changes to affect real economic activity. The of changes in monetary policy will in monetary policy affect real activity. basic New Keynesian model explains depend on both the average velocity in As a result, our expanded theory how changes in money supply can an economy as well as its movements suggests that central bankers must be yield temporary changes in output and over time. Thus, to anticipate the attentive to more than just the change employment. However, it does not effects of a particular change in policy, in the nominal interest rate and a explain why nominal interest rates fall we need to be able to predict how simple Phillips curve relationship in when the central bank increases the velocity will evolve in response to the considering the effects of a change money supply through an open market change in the nominal interest rate. in policy. They must also take into operation. We have discussed an On balance, when we extend our account the ways in which velocity will extension of the model that corrects standard model to achieve greater affect the transmission of monetary this problem by introducing an explicit realism with regard to interest rate policy. Since velocity is, in part, transactions role for money and taking movements, we find that monetary determined by individuals’ bank into account the fact that individuals policy becomes a more complicated account balances, these balances adjust their portfolios of bonds and exercise than we may have thought become relevant as we anticipate the money infrequently. and that it cannot be well understood consequences of a policy change. This more complex model without explicit attention to the Moreover, our theory suggests that reconciling the New Keynesian determinants underlying the we need to know something about theory with a liquidity effect exhibits overall demand for money balances individuals’ willingness to alter their important changes in the velocity throughout the economy. BR money spending rates over time, since of money over time. These changes

www.philadelphiafed.org Business Review Q1 2009 27 REFERENCES

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