Review. Time Series Models

Transcription

1 Revew Topcs & Authors Fnal exam s not cumulatve, but stll need to know IS-LM (no multplers) Shfts n IS - IS (.e., curve shfts to the rght) f T (C ), or π e (I ), or G ; results n larger output () for gven nterest rate () Shfts n LM - LM (.e., curve shfts to the rght) f M, P, or L ; results n larger output () for gven nterest rate () Investment Modglan & Mller - "The Cost of Captal, Corporaton Fnance and the Theory of Investment"; f frms have same expected stream of ncome and same varance (rsk), then market value of equty plus debt s constant (e.g., frm 1 has no debt and frm 2 has debt D 2 : V 1 = V 2 + D 2 ) Tme Seres Models Money Demand Baumol - "The Transactons Demand for Cash: An Inventory Theoretc Approach"; based on transacton demand for money; looks at keepng money lke stockng nventory; short on ntuton, but emprcally testable Tobn - "The Interest Elastcty of the Transactons Demand for Cash"; smlar to Baumol's model, but more ntutve (ddn't come up wth specfc equaton) Meltzer - "The Demand for Money: Evdence From the Tme Seres"; emprcal work tryng to estmate parameters from Baumol & Tobn's money demand models Sweeney & Sweeney - "Monetary Theory and the Great Captol Hll Baby Sttng Co-op Crss"; admnstraton's budget surplus took "money" (scrp) out of crculaton; soluton was to have admnstrators redstrbute the "surplus" (monetary polcy) Goldfeld - "The Case of the Mssng Money"; Goldfeld argued that money demand may adjust slowly because there are two components to the cost of reachng equlbrum: holdng cost (for not holdng proper amount) and adjustment cost (to get to proper amount); end result: overestmatng real money balances s equvalent to underestmatng nflaton; problem wasn't mssng money, but too much nflaton Inflaton & Unemployment Phllps - "The Relatonshp Between Unemployment and the Rate of Change of Money Wages n the U.K "; plotted rate of change of money wage rates vs. unemployment (data from Brttan, 1861 to 1913) and concluded that there's a trade off between nflaton and unemployment; hgher nflaton means lower unemployment Fredman - "The Role of Monetary Polcy"; explaned why Phllps curve does ft U.S data; came up wth long-run Phllp's Curve; multple short-run curves each at dfferent π e ; equlbrum at natural rate of unemployment; only tme we trade off π for u s when t's unexpected (π π e ); also examned 3 possble roles for monetary polcy: "peggng" u, I, or π... concluded that π s the only thng we can control n long-run wth monetary polcy Llen - "Sectoral Shfts and Cyclcal Unemployment"; emprcal work tryng to measure mpact of shocks on unemployment; Tobn - "Inflaton and Unemployment"; argued that long-run Phllps curve s not vertcal because wages are stcky downward; as below a certan level, u 1 of 6

2 Monetary Polcy and Stablzaton Fredman - "The Optmum Quantty of Money"; looked at costs and benefts for hgher or lower nflaton rate to determne the best rate; also sad there's a postve externalty to money holdng; government should nduce negatve nflaton to subsdze money holdng Cagan - "The Monetary Dynamcs of Hypernflaton"; studed classc example of hypernflaton; post-world War I Germany; unpopular government couldn't ncrease taxes; t borrowed untl credtors wouldn't lend anymore; then t prnted money to cover spendng Lucas - "Some Internatonal Evdence on Output Inflaton Tradeoffs"; tred to explan why some countres experence swngs n prces (π) and other n output () n response to demand shocks ( x); sad more prce stable (.e., predctable ) countres confuse relatve demand shocks wth aggregate demand shocks so (and u) are more lkely to be adjusted the P Ball, Mankw & Romer - "The New Keynesan Economcs and the Output-Inflaton Tradeoff"; alternatve explanaton for swngs n prces vs. output usng menu costs (costly for frms to change prces so frms respond slowly to shocks; they rather change output than prces so nflaton looks more lke a step functon) Old Exam Questons 1. Recently, the possblty that developed economes may fnd themselves n a lqudty trap seems to have ncreased. How does a lqudty trap alter the degree to whch a recesson can be ended by: (a) monetary polcy? (b) fscal polcy? (c) a 'lassez fare' recovery? IS 0 (a) M LM (shft rght); goal s to get I, but doesn't work because can't be < 0 (graph on left) (b) G IS (shft rght); ths s not only effectve (IS 1 ), but f government wats to act or uses monetary polcy n conjuncton ( ), the economy moves to potental output wthout mpactng nterest rates (IS 2 ; no crowdng out) (graph on rght) (c) P M/P (.e., LM ) I ; doesn't work for same reason as monetary polcy (graph on left) Whch economy s n more danger of slppng nto a lqudty trap? An economy wth a (d) hgh savng rate or low savng rate? (e) hgh nflaton rate or low nflaton rate? IS 2 IS 1 (d) hgh savng rate means less consumpton so IS curve s lower (IS 1 vs. IS 2 for low savng rate) hgh savng rate s n more danger (e) hgh nflaton rate means hgher so IS curve s hgher (IS 2 vs. IS 1 for low nflaton rate) low nflaton rate s n more danger IS 0 IS 2 IS 1 2 of 6

3 2. We have examned the work of three sets of authors on the effects of a sustaned decrease n the nflaton rate: Ball, Mankw and Romer, Fredman, and Tobn. The models deal wth the effect of lower nflaton on: (1) the level of real money balances, (2) the poston on the long-run Phllps Curve, (3) the slope of the short-run Phllps curve. (a) whch author deals wth whch ssue? (b) n each case what s the effect of lower nflaton and s t benefcal or not? (c) Explan the reasonng n each case. Ball, Mankw & Romer - dd (3); argued that π P adjusted less frequently so demand shocks goes nto and u... bad Fredman - dd (1); argued that π M/P whch s good because of the benefts of hgher money balances (pecunary servces [shoe-leather costs] and non-pecunary servces [utlty]) Tobn - dd (2); argued that π u because short-run Phllps curve s curved from stcky wages; sad low π s bad (hgher π allows wages to respond qucker) 3. Suppose nterest rate rse permanently. (a) Accordng to the "accelerator" specfcaton of the nvestment functon, wll the ntal declne n nvestment be larger than, smaller than, or of the same magntude as the eventual declne n nvestment? Explan. K* I t = K t - K t-1 + δk t-1 (05 p.2) If optmal level of captal doesn't change, nvestment = δk (.e., just makng up for deprecaton); f the nterest rates rse, the optmal level of captal wll declne. In ths case, nvestment wll drop as frms let deprecaton reduce the captal stock to the new optmal level. Eventually nvestment wll pck up agan to cover the deprecaton of the new (lower) captal stock ntal declne wll be larger than eventual declne n I I Tme Partal adjustment One perod Tme (b) Accordng to the "partal adjustment" specfcaton commonly used n emprcal work, wll the ntal declne n the demand for real money balances be larger than, smaller than or of the same magntude as the eventual declne n the demand for real money balances? Explan. ln(m/p) t = b 0 + b 1 ln() t + b 2 ln() t cln(m/p) t-1 (06 p.7) If L changes, there are costs for not beng at L, but also for changng too quckly. People wll adjust M/P slowly assumng there's some adjustment cost ntal M/P wll be smaller than the total change n M/P 4. Currently the fracton of ncome Amercan's save s low. Suppose ths savng rate ncreases. Descrbe the short-run and long-run effects on: (a) output, (b) nvestment, (c) nterest rates, (d) exports L M/P Tme Tme S C IS (shft left); short-run: & I ; also lookng at exchange rate from pont of vew as U.S. as home country, the $ deprecates because nterest rates are lower so captal flows move away from U.S.; dollar worth less so t takes more $ to buy foregn currency: E (alternatvely, fewer unts of foregn currency to buy $) EX (Note: bascally E and EX always move opposte the nterest rate) Long-run: W LM (shft rght) (net change s 0) and 3 of 6 IS 0 IS 1 -- I E EX

4 5. Use the expectatons augmented Phllps Curve, developed by Mlton Fredman and others, to descrbe the short-run and long-run effect of a sustaned ncrease n the rate of money growth on (a) unemployment, (b) nterest rates, (c) the nflaton rate, (d) real nterest rates µ LM (shfts rght) short-run u,, π, r... long-run π e IS (shfts rght), u (back to orgnal); also P LM (shfts left), r (back to orgnal) Long Verson (wth #'s): assume we start at = 8%, u = 6% and π = π e = 5% ( r = - π e = 8-5 = 3%), µ by 3% π 3% (and π e unchanged so π > π e so we move along Phllps Curve and u ); also from µ, LM curve shfts rght lowerng nterest to say 7% (exact amount doesn't matter n short-run); note ths means r = - π e = 7-5 = 2%; r ); eventually π e 3% to match π; ths moves us to new short-run Phllps Curve and brngs u back to orgnal level; π e also shfts IS curve to rght whch combned wth LM shft left from P results n ; fnal = π = µ = 3%; r = - π e s unchanged IS 1 IS 0 2 = 11% 0 = 8% 1 = 7% LM 2 π π 1 = 8% π 0 = 5% u 1 u SRPC (π e 1) SRPC (π e 0) u u -- π r (a) In hs artcle on nflaton and unemployment, James Tobn presented a model whch mples that the central bank should am an nflaton rate whch s greater than zero. Explan hs reasonng. (b) In hs artcle "The Optmum Quantty of Money", Mlton Fredman presented a model n whch the optmal nflaton rate s less than zero. Explan hs reasonng. For a & b see #2 (c) Suppose that Tobn s rght that there s a beneft to havng a postve nflaton rate but Fredman s also rght that there s a separate beneft to the proper amount of deflaton. Explan whch beneft s lkely to be most mportant. Lower u better than lower π... estmated beneft of 0 vs 5% π to be $60B... but by Okn's law 1% n u results n 2% n... that's more sgnfcant 7. Accordng to estmates by Phllp Cagan, the spendng whch can be supported on a sustaned bass by prntng money reaches a maxmum when money and prce ncrease about 50% per year and the amount of spendng whch s thus fnanced s not very large as a porton of GDP. (a) Why does so lttle spendng lead to so much nflaton? (b) Why can't governments rase more revenue by ncreasng the money supply at an even faster rate? (c) If ths s the case, why do governments often produce nflaton rates much hgher than 50% per year? (a) Inflatonary fnance s effectvely a tax on real money balances; n real terms government prnts M/P... multply by M/M and we get ( M/M)(M/P). That s µ = M/M (money growth rate) s the "tax rate" and M/P (real money balances) s tax base. End up wth large nflaton because large µ s needed snce M/P (tax base) s small relatve to GDP. (b) As "tax rate" ( M/M), tax base (M/P)... people try to avod tax by holdng less money. (c) Tryng to collect more money and can only do t f people don't expect π 4 of 6

5 8. Recently, government purchases have rsen n the U.S. Descrbe the short-run and long-run effects of ths ncrease on: (a) output, (b) prces, (c) nvestment, (d) the exchange rate, (e) exports). G IS (shft rght); short-run: & ; from AS-AD (graph not shown) P ; because of I, E, and EX (see #4; Note: f askng about real exchange rate, e because e = E/P) Long-run: W LM (shft left) (net change s 0) and IS IS P I E EX How would your (short-run and long-run) answers change f the Federal Reserve were usng monetary polcy to keep prces from changng? To counter P, Fed would M LM (shft left)... bascally automatcally goes to long-run equlbrum (same as before except no change n P) Long-run: already at long-run equlbrum ARIMA 2. Suppose that the rate of output (y t ) s defned as the change n the log of output ( t ). That s, y t = t - t-1. Suppose further than growth s descrbed by the process: y t = 3 + e t where e t = u t + 0.5u t-1 and u s a "whte nose" error. (a) f t s descrbed as an ARIMA(P,D,Q), what are the values for P,D, and Q? (b) If 2001 = 1000 and u 2001 = -2, what s the optmal forecast for 2002? 2003? 2020? P I E EX 1 dfference term ( t and t-1 ) D = 1 1 movng average term (u t-1 ) Q = 1 0 autoregressve terms (no lagged e) P = 0 Combne equatons: t = t u t + 0.5u t-1 Remember that E(u t ) = 0 at tme t because t's "whte nose" 2002 = E(u 2002 ) + 0.5u 2001 = (-2) = 1002 Any perod after 2002 wll have E(u t ) and E(u t-1 ) = 0 (those perods haven't occurred) 2003 = E(u 2003 ) + 0.5u 2002 = = 1005 So every perod, wll ncrease by s 17 years from = (3) = of 6

6 3. Suppose that output grows, on average at 3% per year wth devatons above and below that trend: t = t e t ( s the log of output). Suppose further that devatons from trend ft the followng pattern: e t = u t + 0.4e t-1 where u s a "whte nose" error term. Fnally, suppose that recent values of are 2000 = 1, 2001 = 1.05, 2002 = 1.06 (a) In the ARIMA classfcaton ths s an ARIMA(P,D,Q). What are the values for P, D, and Q? What s optmal condtonal forecast for next year's : E( 2003 ) 2002? E( 2004 ) 2002? E( 2005 ) 2002? 1 dfference term ( t and t-1 ) D = 1 0 movng average term (No lagged u t ) Q = 0 1 autoregressve terms (e t-1 ) P = 1 Use data we have to fnd error terms 2001 = e 2001 e 2001 = = = e 2002 e 2002 = = Remember that E(u t ) = 0 at tme t because t's "whte nose" E(e 2003 ) 2002 = E(u 2003 ) e 2002 = (-0.02) = E( 2003 ) 2002 = E(e 2003 ) 2002 = = Fnd next error term, then fnd t E(e 2004 ) 2002 = E(u 2004 ) e 2003 = (-0.008) = E( 2004 ) 2002 = E(e 2004 ) 2002 = = E(e 2005 ) 2002 = E(u 2005 ) e 2004 = ( ) = E( 2005 ) 2002 = E(e 2005 ) 2002 = = (b) Suppose nstead t = t u t where u s a "whte nose" error term. How would your answers change? 1 dfference term ( t and t-1 ) D = 1 0 movng average term (No lagged u t ) Q = 0 0 autoregressve terms (No lagged e t ) P = 0 Remember that E(u t ) = 0 at tme t because t's "whte nose" E( 2003 ) 2002 = E(u 2003 ) 2002 = = 1.09 E( 2004 ) 2002 = E(u 2004 ) 2002 = = 1.12 E( 2005 ) 2002 = E(u 2005 ) 2002 = = of 6