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71-467: The IS–LM model , or Hicks–Hansen model , is a two-dimensional macroeconomic model which is used as a pedagogical tool in macroeconomic teaching. The IS–LM model shows the relationship between interest rates and output in the short run in a closed economy . The intersection of the " investment – saving " (IS) and " liquidity preference – money supply " (LM) curves illustrates a " general equilibrium " where supposed simultaneous equilibria occur in both

142-582: A draft of Harrod's paper, invented the IS–LM model (originally using the abbreviation "LL", not "LM"). He later presented it in "Mr. Keynes and the Classics: A Suggested Interpretation". Hicks and Alvin Hansen developed the model further in the 1930s and early 1940s, Hansen extending the earlier contribution. The model became a central tool of macroeconomic teaching for many decades. Between the 1940s and mid-1970s, it

213-750: A fellow of the American Academy of Arts and Sciences , and a three-time recipient of Berkeley's Graduate Economic Association's distinguished teaching and advising awards. Professor Romer is co-director of the Program in Monetary Economics at the National Bureau of Economic Research , and is a member of the NBER Business Cycle Dating Committee. Romer is the author of "Advanced Macroeconomics,"

284-482: A function of disposable income (income, Y , minus taxes, T ( Y ), which themselves depend positively on income), I ( r ) {\displaystyle I(r)} represents business investment decreasing as a function of the real interest rate, G represents government spending, and NX ( Y ) represents net exports (exports minus imports) decreasing as a function of income (decreasing because imports are an increasing function of income). The LM curve shows

355-506: A higher potential price level, in the IS–LM model the real money supply M/P will be lower and hence the LM curve will be shifted higher, leading to lower aggregate demand as measured by the horizontal location of the IS–LM intersection; hence at the higher price level the level of aggregate demand is lower, so the aggregate demand curve is negatively sloped. In the 2018 textbook "Macroeconomics" by Daron Acemoglu , David Laibson and John A. List ,

426-523: A learning rule whereby the strategy is adjusted according to its past success. Given these strategies, the interaction of large numbers of individual agents (who may be very heterogeneous) can be simulated on a computer, and then the aggregate, macroeconomic relationships that arise from those individual actions can be studied. DSGE and ACE models have different advantages and disadvantages due to their different underlying structures. DSGE models may exaggerate individual rationality and foresight, and understate

497-485: A lower interest rate raises real GDP. This explains the downward slope of the IS curve. In summary, the IS curve shows the causation from interest rates to planned fixed investment to rising national income and output. The IS curve is defined by the equation where Y represents income, C ( Y − T ( Y ) ) {\displaystyle C(Y-T(Y))} represents consumer spending increasing as

568-407: A particular instance of what Keynes called animal spirits . The model was part of a broader research agenda studying how beliefs may independently influence macroeconomic outcomes. Macroeconomic model Heterodox A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine

639-503: A relatively flat LM curve can increase output substantially with little change in the interest rate. On the other hand, a rightward shift in the IS curve along a vertical LM curve will lead to higher interest rates, but no change in output (this case represents the " Treasury view "). Rightward shifts of the IS curve also result from exogenous increases in investment spending (i.e., for reasons other than interest rates or income), in consumer spending, and in export spending by people outside

710-675: A standard graduate macroeconomics text, now in its 5th edition. He was an editor of the Brookings Papers on Economic Activity from 2009 to Fall 2015 and, according to a January 2022 AEA announcement, will become the lead editor of the Journal of Economic Literature beginning July 2022. Romer is married to Christina Romer , who was his classmate at MIT and is his colleague in the Economics Department at University of California, Berkeley . They have adjoining offices in

781-429: A vertical line – money supply is a constant, independent of the interest rate, GDP, and other factors. Mathematically, the LM curve is defined by the equation M / P = L ( i , Y ) {\displaystyle M/P=L(i,Y)} , where the supply of money is represented as the real amount M / P (as opposed to the nominal amount M ), with P representing the price level , and L being

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852-627: Is "A Contribution to the Empirics of Economic Growth," coauthored with Gregory Mankiw and David N. Weil and published in the Quarterly Journal of Economics in 1992. The paper argues that the Solow growth model , once augmented to include a role for human capital, does a reasonably good job of explaining international differences in standards of living. According to Google Scholar , it has been cited more than 20,000 times, making it one of

923-622: Is a variety of Agent-based modeling. Like the DSGE methodology, ACE seeks to break down aggregate macroeconomic relationships into microeconomic decisions of individual agents . ACE models also begin by defining the set of agents that make up the economy, and specify the types of interactions individual agents can have with each other or with the market as a whole. Instead of defining the preferences of those agents, ACE models often jump directly to specifying their strategies . Or sometimes, preferences are specified, together with an initial strategy and

994-472: Is also used as a building block for the demand side of the economy in more comprehensive models like the AD–AS model . The model was developed by John Hicks in 1937 and was later extended by Alvin Hansen as a mathematical representation of Keynesian macroeconomic theory . Between the 1940s and mid-1970s, it was the leading framework of macroeconomic analysis. Today, it is generally accepted as being imperfect and

1065-409: Is downward sloping (i.e. the willingness to hold cash increases as the interest rate decreases). Two basic elements determine the quantity of cash balances demanded: Money supply is determined by central bank decisions and willingness of commercial banks to loan money. Money supply in effect is perfectly inelastic with respect to nominal interest rates. Thus the money supply function is represented as

1136-505: Is in place. In the context of the Phillips curve, this means that the relation between inflation and unemployment observed in an economy where inflation has usually been low in the past would differ from the relation observed in an economy where inflation has been high. Furthermore, this means one cannot predict the effects of a new policy regime using an empirical forecasting model based on data from previous periods when that policy regime

1207-408: Is largely absent from teaching at advanced economic levels and from macroeconomic research, but it is still an important pedagogical introductory tool in most undergraduate macroeconomics textbooks. As monetary policy since the 1980s and 1990s generally does not try to target money supply as assumed in the original IS–LM model, but instead targets interest rate levels directly, some modern versions of

1278-456: Is possible to find the prices that equate supply with demand in every market. Thus these models embody a type of equilibrium self-consistency: agents choose optimally given the prices, while prices must be consistent with agents’ supplies and demands. DSGE models often assume that all agents of a given type are identical (i.e. there is a ‘ representative household’ and a ‘ representative firm’) and can perform perfect calculations that forecast

1349-498: Is still largely based on more traditional empirical models, which are still widely believed to achieve greater accuracy in predicting the impact of economic disturbances over time. A methodology that pre-dates DSGE modeling is computable general equilibrium (CGE) modeling. Like DSGE models, CGE models are often microfounded on assumptions about preferences, technology, and budget constraints. However, CGE models focus mostly on long-run relationships, making them most suited to studying

1420-521: Is the Aggregate Demand-Aggregate Supply model – the AD–AS model . In the aggregate demand-aggregate supply model, each point on the aggregate demand curve is an outcome of the IS–LM model for aggregate demand Y based on a particular price level. Starting from one point on the aggregate demand curve, at a particular price level and a quantity of aggregate demand implied by the IS–LM model for that price level, if one considers

1491-419: Is usually impossible without substantially augmenting the structure of the model. In the 1940s and 1950s, as governments began accumulating national income and product accounting data, economists set out to construct quantitative models to describe the dynamics observed in the data. These models estimated the relations between different macroeconomic variables using (mostly linear) time series analysis . Like

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1562-417: The accelerator effect , which helps long-term growth. Further, if government deficits are spent on productive public investment (e.g., infrastructure or public health) that spending directly and eventually raises potential output, although not necessarily more (or less) than the lost private investment might have. The extent of any crowding out depends on the shape of the LM curve. A shift in the IS curve along

1633-656: The comparative statics and dynamics of aggregate quantities such as the total amount of goods and services produced, total income earned, the level of employment of productive resources, and the level of prices . Macroeconomic models may be logical, mathematical, and/or computational; the different types of macroeconomic models serve different purposes and have different advantages and disadvantages. Macroeconomic models may be used to clarify and illustrate basic theoretical principles; they may be used to test, compare, and quantify different macroeconomic theories; they may be used to produce "what if" scenarios (usually to predict

1704-604: The valedictorian of his class. Romer completed a 138-page long senior thesis "A Study of the Effects of Population on Development, with Applications to Japan." Romer worked as a Junior Staff Economist at the Council of Economic Advisers from 1980 to 1981 before beginning his Ph.D. at the Massachusetts Institute of Technology , which he completed in 1985. A reduced version of his undergraduate thesis research

1775-692: The 1950s should lie with good policy made by the Federal Reserve, and that the members of the FOMC could at times have made better decisions by relying more closely on forecasts made by the Fed professional staff. Most recently, the Romers have focused on the impact of tax policy on government and general economic growth. This work looks at the historical record of US tax changes from 1945–2007, excluding "endogenous" tax changes made to fight recessions or offset

1846-453: The 1970s appeared to bear out their prediction. In 1976, Robert Lucas Jr. , published an influential paper arguing that the failure of the Phillips curve in the 1970s was just one example of a general problem with empirical forecasting models. He pointed out that such models are derived from observed relationships between various macroeconomic quantities over time, and that these relations differ depending on what macroeconomic policy regime

1917-449: The AS curve is normally derived from a Phillips curve relationship between inflation and the unemployment gap. As policymakers and economists are generally concerned about inflation levels and not actual price levels, this formulation is considered more appropriate. This variation is often referred to as a dynamic AD–AS model, but may also have other names. Olivier Blanchard in his textbook uses

1988-757: The Herman Royer Professor of Political Economy at the University of California, Berkeley , and the author of a standard textbook in graduate macroeconomics as well as many influential economic papers, particularly in the area of New Keynesian economics . He is also the husband and close collaborator of Council of Economic Advisers former Chairwoman Christina Romer . After graduating from Amherst Regional High School in Amherst, Massachusetts in 1976, he obtained his bachelor's degree in economics from Princeton University in 1980 and graduated as

2059-430: The IS and LM schedules intersect represents a short-run equilibrium in the real and monetary sectors (though not necessarily in other sectors, such as labor markets): both the product market and the money market are in equilibrium. This equilibrium yields a unique combination of the interest rate and real GDP . The IS curve shows the causation from interest rates to planned investment to national income and output. For

2130-481: The amount of demand for goods at each individual interest rate. An increased deficit by the national government shifts the IS curve to the right. This raises the equilibrium interest rate (from i 1 to i 2 ) and national income (from Y 1 to Y 2 ), as shown in the graph above. The equilibrium level of national income in the IS–LM diagram is referred to as aggregate demand . Keynesians argue spending may actually "crowd in" (encourage) private fixed investment via

2201-618: The basic assumptions of the IS-LM model is that the central bank targets the money supply. However, a fundamental rethinking in central bank policy took place from the early 1990s when central banks generally changed strategies towards targeting inflation rather than money growth and using an interest rate rule to achieve their goal. As central banks started paying little attention to the money supply when deciding on their policy, this model feature became increasingly unrealistic and sometimes confusing to students. David Romer in 2000 suggested replacing

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2272-500: The choice of which variables to include in each equation was partly guided by economic theory (for example, including past income as a determinant of consumption, as suggested by the theory of adaptive expectations ), variable inclusion was mostly determined on purely empirical grounds. Dutch economist Jan Tinbergen developed the first comprehensive national model, which he built for the Netherlands in 1936. He later applied

2343-403: The combinations of interest rates and levels of real income for which the money market is in equilibrium. It shows where money demand equals money supply. For the LM curve, the independent variable is income and the dependent variable is the interest rate. In the money market equilibrium diagram, the liquidity preference function is the willingness to hold cash. The liquidity preference function

2414-427: The corresponding model combining a traditional IS-LM setup with a relation for a changing price level is named an IS-LM-FE model (FE standing for "full equilibrium"). In many modern textbooks, the traditional AD–AS diagram is replaced by a variation in which the variables are not output and the price level, but instead output and inflation (i.e., the change in the price level). In this case, the relation corresponding to

2485-420: The cost of new government spending. It finds that such "exogenous" tax increases, made for example to reduce inherited budget deficits, reduce economic growth (though by smaller amounts after 1980 than before). Romer and Romer also find "no support for the hypothesis that tax cuts restrain government spending; indeed ... tax cuts may increase spending. The results also indicate that the main effect of tax cuts on

2556-416: The economy being modelled, as well as by exogenous decreases in spending on imports. Thus these too raise both equilibrium income and the equilibrium interest rate. Of course, changes in these variables in the opposite direction shift the IS curve in the opposite direction. The IS–LM model also allows for the role of monetary policy . If the money supply is increased, that shifts the LM curve downward or to

2627-585: The economy over many time periods. The variables that appear in these models often represent macroeconomic aggregates (such as GDP or total employment ) rather than individual choice variables, and while the equations relating these variables are intended to describe economic decisions, they are not usually derived directly by aggregating models of individual choices. They are simple enough to be used as illustrations of theoretical points in introductory explanations of macroeconomic ideas; but therefore quantitative application to forecasting, testing, or policy evaluation

2698-410: The effects of changes in monetary , fiscal , or other macroeconomic policies); and they may be used to generate economic forecasts . Thus, macroeconomic models are widely used in academia in teaching and research, and are also widely used by international organizations, national governments and larger corporations, as well as by economic consultants and think tanks . Simple textbook descriptions of

2769-512: The equilibria where total private investment equals total saving, with saving equal to consumer saving plus government saving (the budget surplus) plus foreign saving (the trade surplus). The level of real GDP (Y) is determined along this line for each interest rate . Every level of the real interest rate will generate a certain level of investment and spending: lower interest rates encourage higher investment and more spending. The multiplier effect of an increase in fixed investment resulting from

2840-494: The financial sector being transmitted to the goods market and consequently affecting aggregate demand. Similar models, though called slightly different names, appear in the textbooks by Charles Jones and by Wendy Carlin and David Soskice and the CORE Econ project. Parallelly, texts by Akira Weerapana and Stephen Williamson have outlined approaches where the LM curve is replaced with a real interest rate rule. By itself,

2911-485: The first part of the 20th century showed a negative correlation between inflation and unemployment called the Phillips curve . Empirical macroeconomic forecasting models, being based on roughly the same data, had similar implications: they suggested that unemployment could be permanently lowered by permanently increasing inflation. However, in 1968, Milton Friedman and Edmund Phelps argued that this apparent tradeoff

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2982-458: The future correctly on average (which is called rational expectations ). However, these are only simplifying assumptions, and are not essential for the DSGE methodology; many DSGE studies aim for greater realism by considering heterogeneous agents or various types of adaptive expectations . Compared with empirical forecasting models, DSGE models typically have fewer variables and equations, mainly because DSGE models are harder to solve, even with

3053-407: The goods and the money markets. The IS–LM model shows the importance of various demand shocks (including the effects of monetary policy and fiscal policy ) on output and consequently offers an explanation of changes in national income in the short run when prices are fixed or sticky . Hence, the model can be used as a tool to suggest potential levels for appropriate stabilisation policies. It

3124-525: The government budget is to induce subsequent legislated tax increases." Romer has also written papers on some unusual subjects for a macroeconomist, such as “Do Students Go to Class? Should They?”, and “Do Firms Maximize? Evidence from Professional Football.” Romer is a member of the American Economic Association Executive Committee, the recipient of an Alfred P. Sloan Foundation Research Fellowship,

3195-542: The help of computers . Simple theoretical DSGE models, involving only a few variables, have been used to analyze the forces that drive business cycles ; this empirical work has given rise to two main competing frameworks called the real business cycle model and the New Keynesian DSGE model . More elaborate DSGE models are used to predict the effects of changes in economic policy and evaluate their impact on social welfare . However, economic forecasting

3266-457: The importance of heterogeneity, since the rational expectations , representative agent case remains the simplest and thus the most common type of DSGE model to solve. Also, unlike ACE models, it may be difficult to study local interactions between individual agents in DSGE models, which instead focus mostly on the way agents interact through aggregate prices. On the other hand, ACE models may exaggerate errors in individual decision-making, since

3337-494: The interest rate level determined by the central bank. Notably this is the case in Olivier Blanchard 's widely-used intermediate-level textbook " Macroeconomics " since its 7th edition in 2017. In this case, the LM curve becomes horizontal at the interest rate level chosen by the central bank, allowing a simpler kind of dynamics. Also, the interest rate level measured along the vertical axis may be interpreted as either

3408-507: The investment–saving curve, the independent variable is the interest rate and the dependent variable is the level of income. The IS curve is drawn as downward- sloping with the interest rate r on the vertical axis and GDP (gross domestic product: Y ) on the horizontal axis. The IS curve represents the locus where total spending ( consumer spending + planned private investment + government purchases + net exports) equals total output (real income, Y , or GDP). The IS curve also represents

3479-456: The long-run effect of monetary policy depends on the way in which people form beliefs. The model was an attempt to integrate the phenomenon of secular stagnation in the IS-LM model. Whereas in the IS-LM model, high unemployment would be a temporary phenomenon caused by sticky wages and prices, in the IS-LM-NAC model high unemployment may be a permanent situation caused by pessimistic beliefs -

3550-409: The long-run impact of permanent policies like the tax system or the openness of the economy to international trade. DSGE models instead emphasize the dynamics of the economy over time (often at a quarterly frequency), making them suited for studying business cycles and the cyclical effects of monetary and fiscal policy. Another modeling methodology is Agent-based computational economics (ACE) , which

3621-516: The macroeconomy involving a small number of equations or diagrams are often called ‘models’. Examples include the IS-LM model and Mundell–Fleming model of Keynesian macroeconomics, and the Solow model of neoclassical growth theory . These models share several features. They are based on a few equations involving a few variables, which can often be explained with simple diagrams. Many of these models are static , but some are dynamic , describing

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3692-792: The model have changed the interpretation (and in some cases even the name) of the LM curve, presenting it instead simply as a horizontal line showing the central bank's choice of interest rate. This allows for a simpler dynamic adjustment and supposedly reflects the behaviour of actual contemporary central banks more closely. The IS–LM model was introduced at a conference of the Econometric Society held in Oxford during September 1936. Roy Harrod , John R. Hicks , and James Meade all presented papers describing mathematical models attempting to summarize John Maynard Keynes ' General Theory of Employment, Interest, and Money . Hicks, who had seen

3763-420: The money supply, as assumed by the original IS–LM model, but instead conduct their monetary policy by steering the interest rate directly, has led to increasing criticism of the traditional IS–LM setup since 2000 for being outdated and confusing to students. In some textbooks, the traditional LM curve derived from an explicit money market equilibrium story consequently has been replaced by an LM curve simply showing

3834-581: The most cited articles in the field of economics. In more recent work, Romer has worked with Christina Romer on fiscal and monetary policy from the 1950s to the present, using notes from the meetings of the Federal Open Market Committee (FOMC) and the materials prepared by Fed staff to study how the Federal Reserve makes its decisions. His work suggests that some of the credit for the relatively stable economic growth in

3905-532: The nominal or the real interest rate, in the latter case allowing inflation to enter the IS–LM model in a simple way. The output level is still determined by the intersection of the IS and LM curves. The LM curve may shift because of a change in monetary policy or possibly a change in inflation expectations, whereas the IS curve as in the traditional model may shift either because of a change in fiscal policy affecting government consumption or taxation, or because of shocks affecting private consumption or investment (or, in

3976-467: The open-economy version, net exports). Additionally, the model distinguishes between the policy interest rate determined by the central bank and the market interest rate which is decisive for firms' investment decisions, and which is equal to the policy interest rate plus a premium which may be interpreted as a risk premium or a measure of the market power or other factors influencing the business strategies of commercial banks. This premium allows for shocks in

4047-485: The real demand for money, which is some function of the interest rate and the level of real income. An increase in GDP shifts the liquidity preference function rightward and hence increases the interest rate. Thus the LM function is positively sloped. One hypothesis is that a government's deficit spending (" fiscal policy ") has an effect similar to that of a lower saving rate or increased private fixed investment, increasing

4118-448: The right, lowering interest rates and raising equilibrium national income. Further, exogenous decreases in liquidity preference, perhaps due to improved transactions technologies, lead to downward shifts of the LM curve and thus increases in income and decreases in interest rates. Changes in these variables in the opposite direction shift the LM curve in the opposite direction. The fact that contemporary central banks normally do not target

4189-719: The same modeling structure to the economies of the United States and the United Kingdom . The first global macroeconomic model, Wharton Econometric Forecasting Associates ' LINK project, was initiated by Lawrence Klein . The model was cited in 1980 when Klein, like Tinbergen before him, won the Nobel Prize . Large-scale empirical models of this type, including the Wharton model, are still in use today, especially for forecasting purposes. Econometric studies in

4260-416: The set of agents active in the economy, such as households, firms, and governments in one or more countries, as well as the preferences , technology , and budget constraint of each one. Each agent is assumed to make an optimal choice , taking into account prices and the strategies of other agents, both in the current period and in the future. Summing up the decisions of the different types of agents, it

4331-491: The simpler theoretical models, these empirical models described relations between aggregate quantities, but many addressed a much finer level of detail (for example, studying the relations between output, employment, investment, and other variables in many different industries). Thus, these models grew to include hundreds or thousands of equations describing the evolution of hundreds or thousands of prices and quantities over time, making computers essential for their solution. While

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4402-517: The strategies assumed in ACE models may be very far from optimal choices unless the modeler is very careful. A related issue is that ACE models which start from strategies instead of preferences may remain vulnerable to the Lucas critique : a changed policy regime should generally give rise to changed strategies. David Romer David Hibbard Romer (born March 13, 1958) is an American economist,

4473-591: The term IS–LM–PC model (PC standing for Phillips curve). Others, among them Carlin and Soskice, refer to it as the "three-equation New Keynesian model", the three equations being an IS relation, often augmented with a term that allows for expectations influencing demand, a monetary policy (interest) rule and a short-run Phillips curve. In 2016, Roger Farmer and Konstantin Platonov presented a so-called IS-LM-NAC model (NAC standing for "no arbitrage condition", in casu between physical capital and financial assets), in which

4544-419: The traditional IS-LM framework with an IS-MP model, replacing the positively sloped LM curve with a horizontal MP curve (where MP stands for "monetary policy"). He advocated that it had several advantages compared to the traditional IS-LM model. John B. Taylor independently made a similar recommendation in the same year. After 2000, this has led to various modifications to the model in many textbooks, replacing

4615-465: The traditional IS–LM model is used to study the short run when prices are fixed or sticky, and no inflation is taken into consideration. In addition, the model is often used as a sub-model of larger models which allow for a flexible price level . The addition of a supply relation enables the model to be used for both short- and medium-run analyses of the economy, or to use a different terminology: classical and Keynesian analyses. A main example of this

4686-454: The traditional LM curve and story of the central bank influencing the interest rate level indirectly via controlling the supply of money in the money market to a more realistic one of the central bank determining the policy interest rate as an exogenous variable directly. Today, the IS-LM model is largely absent from macroeconomic research, but it is still a backbone conceptual introductory tool in many macroeconomics textbooks. The point where

4757-456: Was illusory. They claimed that the historical relation between inflation and unemployment was due to the fact that past inflationary episodes had been largely unexpected. They argued that if monetary authorities permanently raised the inflation rate, workers and firms would eventually come to understand this, at which point the economy would return to its previous, higher level of unemployment, but now with higher inflation too. The stagflation of

4828-554: Was not in place. Lucas argued that economists would remain unable to predict the effects of new policies unless they built models based on economic fundamentals (like preferences , technology , and budget constraints ) that should be unaffected by policy changes. Partly as a response to the Lucas critique , economists of the 1980s and 1990s began to construct microfounded macroeconomic models based on rational choice, which have come to be called dynamic stochastic general equilibrium (DSGE) models. These models begin by specifying

4899-422: Was of little importance in the 1950s and early 1960s when inflation was not an important issue, but became problematic with the rising inflation levels in the late 1960s and 1970s, which led to extensions of the model to also incorporate aggregate supply in some form, e.g. in the form of the AD–AS model , which can be regarded as an IS-LM model with an added supply side explaining rises in the price level. One of

4970-732: Was published in the Review of Economics and Statistics . Upon completion of his doctorate, he started working as an assistant professor at Princeton University. In 1988 he moved to University of California, Berkeley and was promoted to full professor in 1993. Romer's early research made him one of the leaders of the New Keynesian economics . Specifically, an influential paper with Laurence M. Ball , published in 1989, established that real rigidities (that is, stickiness in relative prices) can exacerbate nominal rigidities (that is, stickiness in nominal prices). Romer's most widely cited paper

5041-479: Was the leading framework of macroeconomic analysis. It was particularly suited to illustrate the debate of the 1960s and 1970s between Keynesians and monetarists as to whether fiscal or monetary policy was most effective to stabilize the economy . Later, this issue faded from focus and came to play only a modest role in discussions of short-run fluctuations. The IS-LM model assumes a fixed price level and consequently cannot in itself be used to analyze inflation. This

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