Keynesian and Monetary Approach to the Liquidity Trap – looking for cointegration evidence from 2008 – Crisis in the United States

Th e paper refl ects on the phenomenon of the liquidity trap in the U.S. during 2008fi nancial crisis. Th e modern history of economics indentyfi ed strictly only one such a case: Japan since mid – 1990’s. Th e main focus is to collect evidence on the liquidity trap using both: monetary approach and Neo-keynesian. Standard Johansen cointegration anlaysis is used to catch the structural macroeconomic change since the Lehman Bros. collapse. Findings provide the evidence for: a) money demand function change due to zero-bond policy; b) the role of expectations in the liquidity trap condition; c) excessive raise of ‘lemon’ cost on the fi nancial intermediation market.


INTRODUCTION
Liquidity trap is the condition, when central bank increases the money supply with eff ect on neither prices nor output.Th e idea was discovered originally by J.M. Keynes and Hicks (1937), as it was said to occur during the great recession of the 1930's for the fi rst time.
Since the 1970's central banks in the developed world was interested in fi ghting infl ation rather to stimulate the economy by increasing money supply, as they follow Milton Friedman (1969, pp. 1-50) rule.In the 1990's and 2000's the main central bank's objective was to ensure the credible monetary policy with infl ation target (Svensson, 2010) clearly stated.As economic agents used the same forecasting models as the central banks that time, they were able to predict monetary policy more accurate.Th is in turn led to decrease in economic aggregates volatility such as: output, infl ation etc., which Bernanke (2004) called this period 'Th e Great Moderation'.Woodford (2003, p.268) shows the path of learning dynamics by economic agents, when the Taylor rule is satisfi ed much more in recent decade than in previous periods.
In the late 1990's B. Bernanke, L. Svensson, M. Woodford and P. Krugman (Krugman, 2010) researched the Japan's lost decade.Th eir outcome clearly shows that Japan's economy has been caught into the liquidity trap since mid-1990.Krugman (1998) argue that if liquidity trap has occurred in Japan, it can occur elsewhere anytime now.
Crisis 2008-and the quantitative easing policy in the United States, which was targeted not only to restore liquidity on the fi nancial markets but also to lower right-tail of yield-curve, might cause elements of the liquidity trap.Th e aim of this paper so, is to fi nd if some aspects of liquidity trap are visible in the United States.
Th e literature review shows two approaches to assessing liquidity trap.Th e standard Keynesian view augmented by rational expectation and the monetary, which focus on monetary aggregates cointegration.If evolutions of monetary aggregates become irrelevant to prices and output, economy may be caught into liquidity trap.
Th e paper is organized as follows: the two sections provide literature survey on Keynesian and monetary approach to liquidity trap.Th e third one asses some cointegration evidence and the fourth conclude.

LIQUIDITY TRAP  KEYNESIAN APPROACH
Liquidity trap was originally discovered by J.M. Keynes (1936) and Hicks (1937).Th is phenomena is due to nominal interest rate positive only.When it is no possible to make lower nominal interest rate than zero, further monetary stimulation of aggregate demand is ineff ective.Additionally LL curve is sloped upward since an increase of income and further it goes into perfect inelastic (Hicks, 1937).Th e model has got into standard macroeconomic textbook and was not developed much until famous Krugman's paper (1998).According to Krugman (1998), the lack of economists' interest in this fi led was due to the lack of faith that liquidity trap will ever happen.Krugman (1998) sheds new light on liquidity trap, which was proposed by standard IS-LM model.Krugman's model combines interest rate, consumption, money supply and expectations: Where: i -interest rate, D -discount factor, P* -future price level, P -current price level, y*/y -the relation between future output (expected) and current output, ρ -relative risk aversion.Th e relation (1) can be viewed as a model, which assumes sticky or fl exible futures prices.Th e risk aversion coeffi cient comes from agent's utility function, as they are to decide whether they won't to buy bonds at interest rate i or spend money on consumption (which drives output).Th erefore if future prices remains fi xed (P*), any raise in current prices (P) will produce future defl ation, as higher P means lower i and i cannot be negative.If nominal interest rate was negative, agents would hold money instead of bonds.When interest rate is close to zero bonds and money become perfect substitutes and further increase in money supply will not change neither output nor price level.
Th e Krugman's (1998) model incorporated fi nancial intermediation in the above.Th e evidence for fi nancial intermediation to liquidity trap is also visible in the evolution of monetary aggregates.In Japan for example monetary base in years 1994-97 rose by 25.6 per cent, while bank credit rose only by .9 per cent (Krugman 1998, table 7).Similar data provided Friedman and Schwartz (1963, table A-1).Between 1930 and1933 in the United States currency held by public rose by ca.46 per cent, while commercial bank total deposits fall by ca.41 per cent1 .As it was associated with banking crisis that had begun in the early 1930.Krugman's (1998) provides a way to escape the liquidity trap.Th is is a credible overshoot of infl ation target by central bank.In other words central bank should set agent's expectations of the future price level to rise.Sevensson (2001) sketched an open economy model that analysis the evolution of output gap, domestic infl ation, CPI-infl ation and real interest rate in a condition of liquidity trap: Sevensson (2001) sketched an open economy model that analysis the evolution of output gap, domestic infl ation, CPI-infl ation and real interest rate in a condition of liquidity trap: Where: , , , α β γ ρ are parameters to estimate, above relation are in logarithms; asterisk (*) denotes the foreign economic aggregates (eg.y* -rest of the world output).
Th e relation (2a) is a hybrid-forward-looking Phillips curve in which expected infl ation rate ρ + , the expected deviation of the real interest rate from the steady-state real interest rate (natural interest rate in Kunt Wicksell's sense).When agents expect the real interest rate not to fall, they will expect no raise in current output in the future; assuming everything equal domestic demand will not raise, until monetary authority lower the real interest rate in the future.Th e latter one is sensitive to the monetary policy credibility.(2f ) explain real interest rate as the (log) diff erence between nominal interest rate and in-fl ation.(2g and 2h) are the yield curve -relation between interest rate and instrument's maturity.Eggertson and Woodford (2003) concludes that in a condition of zero-interest bond, diff erent maturity assets turn to be perfect substitutes In the Keynesian approach liquidity trap condition can be seen through market friction in the fi nancial intermediation sector.Bernanke and Gertler (1995) introduce the term 'external fi nance premium'.Th e premium comes from the 'lemons problem' directly.Financial intermediation assesses the borrowers' creditworthiness, which cost is incorporated to the 'external fi nance premium'.Th e level of an average 'premium' is varying over the business cycle.Usually during the economic downturn 'premium' raises, which in turn makes the interest rate that entrepreneurs and consumers faces higher; even though central bank's short-term interest rate is very low.Th e raise in cost of 'lemons' in some circumstances can sharply decrease the transaction volume, as suggested by Akerlof (1970).Kacperczyk and Schnabl (2010) shows that fi nancial market in the United States was blocked by the problem of 'lemons'.Liquidity trap in that sense should occur, when fi nancial sector is reluctant to lend money to private sector in spite of high banks reserves.Th is condition is somehow similar to the mentioned above problem of natural interest rate, as the 'premium' raises the nominal interest rate.Martens and Raven (2011) evidence shows, that credit channel in the United States depressed the expectations and hence caused the liquidity trap recession recently.

LIQUIDITY TRAP  MONETARY APPROACH
Friedman's 'helicopter drop' in some way excluded the existence of liquidity trap.If there is an additional and unanticipated increase in money stocks that inhabitance holding, there will be an increase in spending due to change in relation between marginal utility of holding money and marginal utility of possession of goods and services which was in equilibrium before.In other words people will spend additional money, which is provided by eg.central bank, because the new money changes the marginal-utility relation and fi nally economy reaches its equilibrium with higher prices (Stein, 1970).
Among small number of publications, which were published in pre-Kurgman (1998) times, we can fi nd an interesting example of Grandmont and Laroque (1976).Th ey consider the statement: "the demand for money may tend to infi nity when the rate of interest goes to zero" (Grandmont and Laroque, 1976, p. 132).Th ey conclude that liquidity trap arises in the condition of trade-off between the short run demand for long-terms bonds and short run money stock.Th e model can be sketched briefl y as follows: In the closed economy are: central bank, which issues fi at money by open market bond purchase; there is the spot market for: goods, money and bonds; there are assets prices and good prices; on the spot market agents expect future prices of assets and goods When central bank open market purchases tend to infi nity, assets prices tend to infi nity too; eventually the money value is rising as long as agents expect goods prices not to rise.
When agents expect rise in goods prices, the value of money tends to zero.Eventually there is a short run trade-off between long-term bonds and money stock, which is depended on expectation of future goods prices or assets prices.
Bank accounting identity: ( ( 1 ) )/ ( 1 ) Where M denotes money demand, b j -amount of bonds outstanding held by central bank, b i are bonds hold by investors, r -the interest rate set by central bank and t is time.Th e model assumes that M tends to infi nity when r tends to zero under liquidity trap condition.
Japan is now the most vital example of liquidity trap since the middle of 1990's, as there is a vast of papers exploring this case from monetary approach.Fujiki and Watanabe (2004) assumed the existence of liquidity trap "as a nonlinear M1 demand function with respect to the short-term nominal interest rate".Cointegration between real M1, real cash, demand deposits and Indices of Industrial Production, call rate failed to reject the null hypothesis of no cointegration.Bae, Kakkar, Ogaki (2006) have also test the liquidity trap conditions in case when money demand is infi nitely elastic as the consequence of zero-interests bond.Th ey estimated the following money-demand equations: Where: i -is the short-term interest rate, P is a price level, Y is the output and M is the money supply measure; all in logarithms.Th e test for liquidity trap was to check whether functional better fi ts the data.Th ey conclude that non-linear money demand function fi ts better to the Japanese data and it is an evidence for liquidity trap

LIQUIDITY TRAP  LOOKING FOR THE U.S. EVIDENCE IN THE 2008 CRISIS
Th e aim of the study is to fi nd evidence on liquidity trap in the United States during the unconventional monetary policy introduced by Ben Bernanke in period after Lehman Bros. collapse in september 2008.Th is example is somewhat diff erent from Japanese case.

Figure 1. Real output growth and CPI (yoy) in the USA and Japan
Source: data FRED.
Figure 1 shows the evolution of the main economics aggregate in the USA and Japan.Th e Japan case, as stressed in the literature is the classical liquidity trap.In the USA overall infl ation rate is positive and output rose in the 2010 and 2011.On the other hand the share of the monetary base in GDP rose sharply in the US since quantitative easing policy was introduced (2008-2009), similar to the Japan's case.In the beginning of the 2000's National Bank of Japan introduced large-scale asset purchase, which caused the raise of the share of monetary base in real GDP (fi gure 2) Th e monetary approach in the assessing the liquidity trap will be based on money demand equation.Th e theory of money assumes that real cash balance should be relevant to the real economic activities.As stated above liquidity trap can be assessed by transactional money demand function.Estimating long-run relation is limited by data availability -quarterly sample is too short.Kruszka (2004) estimated money demand using monthly data.Th is model measures income elasticity of money with respect to income a 1 , which should be positive and a 2 is money demand elasticity with respect to interest rate, which should be negative.Th e accounting procedure for U.S. monetary aggregates indicates that Monetary Base is the currency in circulation plus deposits held by all depository institutions.M1 on the other hand is currency in circulation without bank vaults.Th e raise in the Monetary Base was associated with the raise in bank reserves, which means that banks are reluctant to lend money to other banks and public and set aside excessive reserves.For this reason bank reserves (WRESBAL) will be in the analysis included.Th e critical value at the 5% level of signifi cance is 0,463.All the variables in the table 1 are integrated processes.A questionable is the interest rate as the process is integrated in the period 1992m1 -2012m11 and is not integrated in the subsamples.Findings in table 2 provide that there is at least one cointegrating vector among analyzed variables.Outcomes in the table 3 show the structural change between periods 1992-2008 and 2008-2012.Th e period 1992-2008 indicate a stable relation as suggested by (5).Th e elasticity of demand for money with respect to interest rate seems to be stable and is ca.0,03 -0,04, which means that raise in the interest rate by one pp.decrease the demand for legal tender by 0,03 -0,04 percent.Kruszka (2004) for example found similar elasticity in the Eastern Europe.In the period 2008 -2012 the mentioned elasticity turns to be negative or insignifi cant.On the other hand income elasticity of demand for money increases, which indicate that money demand, tends to infi nity, when the interest rate approaches to zero, as monetary approach to the liquidity trap suggests.Findings in the table 4 and 5 assess the cointegration between real money balance and bank reserves.According to the credit channel theory, cost of 'lemons' catch the economy into liquidity trap.Raise in money supply will be not transmitted to the price level or output gap, as excessive money supply is set aside as a reserves in the central bank.
Th e cointegration between real money, when using Monetary Base as monetary aggregate is insignificant in the period 1992-2008. 2In the period 2008 -2012 the signifi cance of cointegration is very high, which indicate that raising Monetary Base was strictly associated with the raise in bank reserves.
Neo-Keynesian approach to the liquidity trap comes from economic expectations strictly.Since expectations to the future economic growth are absent, aggregate demand will not raise, as stated in the relation (1) and ( 2).Th e data used to asses this approach are: the diff erence between the expected retail sales (University of Michigan Sentiment Indexy*) and actual real retail sales (RRSFS)y; the interest rate: 3-Month Treasury Constant Maturity Rate (DGS3MO)i.Th e data are prepared as follows: .   Outcomes from cointegration shows that there is no cointegration in the period 1992 -2008 between interest rate and the y*/y.In the period 2008 -2012 cointegration is signifi cant at 5% level.Th e sign of normalized vector is consistent with the theory suggested in (1).In case of fi xed future expectations (y*), any raise in retail sales creates expected decrease in current sales, as real interest rate raises (higher y means higher i).Hence economy delivers equilibrium interest rate no matter the nominal production, as suggested by Krugman (1998).

CONCLUSIONS
Liquidity trap occurs, when violent monetary stimulation is not transformed by economy to rise in prices and output.Usually central bank enlarges monetary aggregates by bonds purchase.Th e aim of such a monetary policy is to: a) lower interest rates, as excessive demand raise bond's price, hence lower the interest rate, b) provide economy with more cash holding instead of holding longer-maturity assets.As monetary theory predicts larger cash holding and low interest rate should deter economy from defl ation and depression as Friedman suggests that great depression of the 1930's was caused by decrease of money supply in the economy.
On the other hand Keynesian approach suggests that when demand is reluctant to grow, excessive money supply will not raise prices and output, as bonds and money turns to be perfect substitutes, when interest rate tends to zero.An expectations seems to be crucial in monetary transmission channel.Unsuccessful monetary policy can caused by monetary intermediation frictions and associated cost of 'lemons'.Additional money supply will therefore be stored in banks' vaults instead of providing economy with the credit.
Th e aim of conintegration analysis is to confi rm long-term relation between economic aggregate.Th e 2008-crisis has last only for four years, but using monthly data is possible to fi nd some persistent economic relation.Th e analysis is based on comparison between 2008-crisis relation and those which was observed during the 1990's and 2000's.Th e outcome provides at least a structural change in the U.S. economy since Lehman Bros. collapse.Th e analysis provide an evidence of structural economy change suggesting the liquidity trap condition in following aspects: a) money demand elasticity with respect to the interest rate; b) money demand elasticity with respect to the income; c) raise a cost of 'lemons' in the fi nancial intermediation sector; d) increased sensitivity of output expectations with respect to the interest rate.
Further research can assess the relation between diff erent maturity interest rate, economic expectation and monetary aggregates.
determined by infl ation inertia t π , expected infl ation rate in the future 2 t π + and π α parameter denotes rule-of-thumb of the hybrid-forward-looking expectation.In other words agent's expectations of the future price level are based on both past infl ation evolution (infl ation inertia) and expected future economic trends that will infl uence on the price level.Th e current output t y (2b) is the outcome of the output gap and long term potential output (the model assumes exogenous shock as well -(2d) shows how liquidity trap condition enters the expected output.Th e expectation is the central issue in assessing liquidity trap in the Keynesian model.Th e future output (

Figure 2 .
Figure 2. Monetary base as the share of real GDP in the U.S. and Japan Source: data FRED and Bank of Japan.
calculations; data: FRED.Standard errors are in parentheses.
Food Service Sales (RRSFS) are used; fi nally i is the interest rate 3-Month Treasury Constant Maturity Rate (DGS3MO).
integrated time trends, so the fi rst step is to run unit root test.Th e data used are: (m -p) -monetary aggregate divided by price level.Monetary Base, M1, M2 and CPI; y -is the measure of economic activity, which provide transactional money demand -Industrial Production Index (INDPRO) and Real Retail and

Table 1
Th e KPSS Unit root test for data used in (5) in levels

Table 2
Johansen test of cointegration rank in (5)

Table 4
Johansen test of cointegration rank between real money balance and bank reserves

Table 5
Normalized cointegrating vectors for real money balance and bank reserves

Table 6
Th e KPSS and PP Unit root test for in levels for y*/yIn the table 6 all the subsample are integrated according to PP unit root test at 5% signifi cance level, but KPSS indicate that in the period 2008m9 -2012m6 y*/y is not integrated.

Table 7
Johansen test of cointegration rank between i and y*/y Source: own calculations.Data: FRED (*) denotes rejection of the null hypothesis at 5% signifi cance.

Table 8
Normalized cointegrating vectors for i and y*/y