Chapter 11 Inflation and Short-Run Dynamics

1. Chapter 11Inflation and Short-Run Dynamics © Pierre-Richard Agénor and Peter J. Montiel

2. Models of Inflationary Process. • Dynamics of Monetary and Exchange-Rate Rules.

3. Models of Inflationary Process

4. “Orthodox” view: • Inflation results from money creation by governments faced with limited borrowing options New structuralists: • Inflation results from the worker-capitalist conflict over distribution of income between real wages and profits.

5. Inflation, Money and Fiscal Deficits. • Adaptive Expectations. • Perfect Foresight. • Food Supply, Distribution, and the Wage-Price Cycle. • A Structuralist-Monetarist Model.

6. Inflation, Money and Fiscal Deficits • Closed economy with exogenous output. • Demand for money function takes the Cagan semilogarithmic form: m = exp(-a),  > 0, m M/P: M is base money stock and P is price level; a: expected inflation rate. (1) .

7. Government cannot issue bonds to the public and finances its primary budget deficit d entirely through seigniorage: d = M/P = m,   M/M. • Combining (1) and (2) d =  exp(-a). • (3): how primary fiscal deficit affects equilibrium rate of growth of the money stock, and inflation rate. . (2) . (3)

8. “Seigniorage Laffer curve”: two steady-state rates of inflation that generate any given amount of seigniorage. • Figure 11.1: (3) is plotted. • D: combinations of  and a for which d is constant. • Since (3) indicates that d =  when a is zero, d is measured by the distance between the origin and the intercept of the D curve on the -axis. • Since government budget constraint always binds, economy is always located on the D curve. • Differentiating (1) with respect to time yields  -  = -a. . (4)

10. In steady state:  = a = . • (4): 45o line in Figure 11.1. • D and the 45o line intersect twice. • Thus there are two potential steady-state positions: • low-inflation equilibrium (point A); • high-inflation equilibrium (point B). • At A the elasticity of the demand for real money balances is less than unity, whereas at point B it is greater than unity. • Suppose that d is constrained by the amount of revenue that can be generated through money creation. (5)

11. Inflation rate that maximizes steady-state seigniorage revenue is s = 1/. • Corresponding level of revenue: ds = exp(-1)/. • Assume that d that the government wishes to finance is fixed at d. • Depending on size of deficit target, there may be zero, one, or two equilibria. • Since the government cannot obtain more than ds in the long-run equilibrium, there is no steady state if d > ds. • For d = ds or d < 0, there is a unique steady state. ~ ~ ~

12. ~ • 0 < d < ds: two steady states, and the economy may be “stuck” at high-inflation equilibrium (point B). • Two alternative assumptions about the formation of inflation expectations.

13. Adaptive Expectations • When inflation expectations are adaptive: a = ( - a),  > 0. • Combining (3), (4) and (6) determines the time path of actual and expected inflation, for a given d. • From (4) and (6), changes in expected inflation are determined by a = ( - a)/(1 - ). . (6) .

14. Actual rate is  = ( - a)/(1 - ), which implies that in the steady state  = a = . • With an adaptive expectational scheme, A is a stable equilibrium whereas B is unstable, if  < 1/. • Points located to the right of B lead to hyperinflation. • Government prints money at an ever-increasing rate. • This prevents a from ever coinciding with the actual rate of increase in prices. • Although real money balances are reduced at an increasing rate, rapid printing money helps financing the deficit.

15. Suppose that the economy is initially at A, and consider effect of an increase in d. • Small increase: D shifts to the right to D’ but continues to intersect the 45o line twice. • Increase in d leads to jump in  from A to C. • Then gradual increase in both actual and expected inflation rate from point C to A’. • Once expectations begin to adjust, demand for real money balances starts falling. • Government must print money at an accelerated pace to compensate for the reduction in the inflation tax base. • If increase in d is large, D may not intersect the 45o line at all (D’’).

16. There is no steady state, and inflation increases continually. • Economy jumps from A to F and follows a hyperinflationary path, moving to northeast along D’’. • If bonds can be used as an additional source of financing, unique steady-state inflation rate is attained when the government sets a nominal anchor.

17. Perfect Foresight • Rational expectations can be implemented by • setting    in (6); • allowing expected and actual prices to jump. • In this case, B is a stable equilibrium and A is unstable. • Since a can jump on impact, all points located on D are short-run equilibria. • Increase in d leads to an instantaneous jump to a new equilibrium. • But there is no guarantee that the economy will be on D’D’. • Thus, inflation may be unnecessarily high under perfect foresight.

18. So large d leads to hyperinflation only when private agents have adaptive expectations. • Bruno and Fischer (1990) and Kiguel (1989): • Large d may lead to hyperinflation even under perfect foresight, if there is sluggish adjustment toward equilibrium in the money market. • Assume that money market adjusts according to m/m = (lnmd – lnm),  > 0, md: desired real balances; : speed of adjustment. . (7)

19. (7) can be written as  =  - (lnmd – lnm). • (8): inflation rate adjusts one-for-one with , but adjusts partially in response to differences between desired and actual levels of real money balances. • Thus inflation rate is sticky, but real balances are predetermined. • Solving for the logarithm of money demand from (1) and using the identity m M/P - m in (8) yields m = [/( - 1)](d + m lnm). (8) . . . (9)

20. Figure 11.2: plot (9) for a value of the deficit equal to d0 and  < 1/. • Two equilibria: A is unstable; B is stable. • When  , (9) becomes m d + -1m lnm. If policymaker increases d from d1 to d0: • m = 0 schedule moves down. • It may no longer intersect the horizontal axis. • In such conditions system will be unstable: • decreasing real money balances; • rising rates of inflation. . .

22. Thus too large d leads to a hyperinflationary path. • Under perfect foresight, instability in inflation process depends on the assumption of sluggish adjustment in money market. • Increase in money growth creates a temporary excess supply in the money market. • This leads to an increase in inflation. • Higher inflation rate exerts two conflicting effects on the equilibrium of the money market: • it reduces supply of real money balances (reequilibrate the market); • it leads to fall in demand for real money balances (amplify initial disequilibrium).

23. When the system does not possess a stable long-run equilibrium, the latter effect dominates the former. • This results in accelerating inflation. • Possibility of following unstable inflationary path becomes more likely if erosion in tax revenue results in positive relation between d and .

24. Key results: • Money financing of fiscal deficits may lead to multiple steady-state equilibria. • Hyperinflation is an unstable process that emerges as due to large, unsustainable d financed by money creation. • Essential feature of stabilization programs must be a significant fiscal adjustment. • In small, open countries, additional factor that may affect inflation in the short run is exchange rate. • Nominal depreciation affects domestic-currency price of import-competing goods and exportables. • Indirect effect: if cost of imported inputs affects pricing decisions.

25. Fluctuations in unofficial exchange rate may affect inflation if domestic price setters take into account marginal cost of foreign exchange when setting prices. • Depreciation of exchange rate may affect inflation by raising nominal wages, through implicit or explicit indexation mechanisms. • Despite these effects of exchange rate on inflation, fiscal deficits play a key role in the long run. Rodríguez (1978): • His model explains this result. • If d is financed through credit creation by the central bank, monetary expansion leads to an increase in prices and a progressive erosion of foreign reserves.

26. This triggers a devaluation if the central bank has limited access to borrowing in international capital markets. • Devaluation-inflation spiral may develop.

27. Food Supply, Distribution, and the Wage-Price Cycle • Link between inflation, food supply, and competing claims for the distribution of income is important in new structuralist approach to inflation. • Here modified version of a model developed by Cardoso (1981) s presented. • Closed economy producing two goods: • agricultural good, yA; • manufactured good, yI. • Food supply is given in the short-run at yA. • Output is demand determined in the industrial sector. ~

28. Equilibrium conditions in both markets: yA = cA(y, ),   PA/PI, yI = cI (y, ) + g, cA: food demand; y: real factor income; : relative price of agricultural goods; cI : private expenditure on manufactured goods; g: autonomous government expenditure on industrial goods. - + ~ d + + d d d

29. Real factor income: y = yA + yI. • Assume that direct effect of changes in  on demand is zero. • 0 <  <1 denote marginal propensity to consume. • 0 <  < 1: proportion of consumption spent on agricultural goods. • Equilibrium condition of food market: yA = y = (yA + yI). ~ ~ ~ (10)

30. Market-clearing condition for industrial goods: yI = (1 - )(yA + yI) + g. • Assuming that prices of industrial goods remain constant and that output in industrial sector responds gradually to excess demand for manufactured goods: yI = I[(1 - )(yA + yI) + g – yI], I > 0. • Agricultural prices respond gradually to the excess demand for food: PA/PA = A[(yA + yI) - yA], A > 0. ~ (11) . ~ (12) . ~ ~ (13)

31. . -A(1 - ) A PA PA = . yI I(1 - ) -I (1 - (1 - )) yI • (12) and (13): dynamic behavior over time of production in industrial sector and agricultural prices: • For stability, trace of coefficient matrix must be negative and its determinant positive. • Figure 11.3: equilibrium of the economy. • Curve [PA = 0]: combinations of industrial output and relative price that maintain equilibrium in the food market. • It has a positive slope. .

33. Left of it: excess supply of food and falling prices. • Right of it: excess demand and rising food prices. • Curve [yI = 0] : equilibrium condition for industrial good market. • It has a positive slope. • Left of it: excess demand for industrial goods and rising output. • Right of it: excess supply of manufactured goods and falling output. • E: steady-state equilibrium. • Economy is at A initially: excess supply of food and excess demand for manufactured goods. • Increase in output in the industrial sector dampens excess demand for manufactured goods. .

34. Increase in output in the industrial sector dampens excess demand for manufactured goods. • This increases income and demand for agricultural products. • Thus, this reduces excess supply in agricultural sector. • Food prices fall at first and then rise. • Industrial output rises continuously until long-run equilibrium is reached. • Thus, there is no tendency toward instability since it is assumed that industrial prices remain constant. • Suppose that industrial sector set prices as a fixed mark-up  over labor costs.

35. Industrial prices: PI = (1 + )w,  > 0. • Suppose: workers have a constant real wage target *. • Thus, nominal wages are determined by w = P, P is consumer price index, defined as P - PAPI1-, 0 <  < 1. (14) ~ (15) (16)

36. Using (14), (15), and (16) yields “required” relative price, consistent with workers' real wage target: * = [(1 + )*]-1/, *: required price ratio. • Rate of change of nominal wages is determined by difference between * and . • Using (14), rate of change of industrial prices: I = w/w = ( - *),  > 0, : speed of wage adjustment. (17) . (18)

37. Thus, * is relative price at which wage inflation is zero and industrial prices remain constant. • Using (13) and (18), / = A[(yA + yI) - yA] - ( - *). • Figure 11.4: solution of the system consisting of (12), (13), and (19). • Curve AA: identical to curve [PA = 0]. • Curves [yI = 0] and [ = 0]: both upward sloping, with the former having a steeper slope to ensure stability. • Slope of AA is also steeper than slope of [ = 0]. • AA and [ = 0] intersect at B:  = * and food market is in equilibrium. . ~ ~ (19) . . . . .

39. . . • [yI = 0] and [ = 0] intersect at E:  > *. • [yI = 0] and AA intersect at G. • None of the points represents a long-run equilibrium. Point G: • Food and industrial goods markets are both in equilibrium but real wages are lower than desired level. • Thus, nominal wages increase, raising industrial prices and lowering the relative price of agricultural goods. • Negative income effect reduces output in industrial sector. Point B: • Real wages are at the desired level and food market is in equilibrium. • But there is an excess demand for manufactured goods. .

40. Industrial production begins rising. • But, increase in income exerts upward pressure on the relative price of food products. Point F: • There is an excess demand in the food market. • Upward pressure on agricultural prices causes a rise in nominal wages. • This leads to an increase in industrial prices and higher output in that sector. • If excess demand for food remains large relative to the difference between actual and desired real wage, nominal wages and industrial prices increase less rapidly than agricultural prices. • Thus,  rises over time.

41. This leads to excess demand for manufactured goods, and industrial output rises. • Economy moves toward E, where [yI = 0] and [ = 0] intersect, and both industrial output and the relative price remain constant. • But at that point, excess demand for agricultural products maintains upward pressure on their price. • Since real wage is lower than desired, both nominal wages and industrial prices continue to rise. • Thus, there is no stable long-run equilibrium. • Outcome may be a self-perpetuating inflationary process. • Stable, long-run equilibrium can be achieved by government policies. . .

42. . • Reduction in g that is large enough to shift [yI = 0] to the left until it intersects AA and [ = 0] at B can halt inflationary spiral, at the cost of lower industrial output. • Income policy that reduces  can increase * toward  and eliminate inflationary cycle. Price controls: • It prevents capitalists in the industrial sector from raising their prices and maintain the relative share of profits in national income, without necessarily leading to a reduction in output. General implication of the analysis: • When workers' desired real wage is high relative to the level compatible with long-run equilibrium, inflation stabilization is impossible to achieve without a shift in income distribution. . ~

43. A Structuralist-Monetarist Model • Assumption in new structuralist models of inflation: monetary policy fully accommodates changes in the price level. • Integrated framework that accounts explicitly for money supply dynamics in the new structuralist model, is introduced. • Link between prices, money, and fiscal deficits is captured by • introducing food subsidies; • accounting for the government budget constraint.

44. In the presence of a subsidy at the rate 0 < s < 1, the consumer price index: P = [(1-s)PA]dP1-. • Government levies a uniform tax on factor income at the rate 0 <  < 1. • Its expenditures consist of demand for industrial goods (g) and food subsidies. • The government budget constraint can be written as M = PIg + sPAyA - (PAyA+PIyI). I . ~ ~

45. In real terms: m = g + (s-)yA - yI - Im, m: real money balances measured in terms of industrial prices. • Assume: demand for food products is a positive function of real money balances. . ~ (21)

46. Equilibrium condition of the food market in the presence of food subsidies: (1-s)yA = (1-)(yA+yI) + m, : propensity to consume out of disposable income. • Left-hand side: post-subsidy value of the supply of food, measured in terms of industrial goods. • Last term on the right-hand side: real balance effect. • Dynamics of output adjustment in the market for manufactures: yI = I[(1-)(1-)(yA+yI) + (1-)m + g - yI]. ~ ~ . ~ (23)

47. Assuming that workers pursue a real wage target, the required relative price: * = (1-)-1[(1+)*]-1/. • Behavior of relative price is determined by: / = A[(/(1-s))(yA+yI) + (/(1-s))m - yA] - (-*). • Using (18), (21) can be approximated at t = 0 by m g + [(s-)yA - m0] - yI + (0-*)m. . ~ ~ (25) . ~ (26)

48. Equations (23), (25), and (26): dynamic system in yI, , and m. • Assume: output adjustment in the market for industrial goods is instantaneous (I  ). • Solving (23) for yI with yI = 0 and substituting the result in (25) and (26) yields a system of two differential Equations in  and m. • Figure 11.5: graphical presentation of the equilibrium. • [ = 0]: positively sloped. • Reason: increase in money holdings raises demand for agricultural and manufactured goods, requiring an increase in the relative price of food to maintain equilibrium. • [m = 0]: negatively sloped under the assumption that (s-)yA > m0. . . . ~

50. Long-run effect of an increase in the subsidy rate on inflation is ambiguous. • Two opposite effects: • Increase in subsidy payments increases government spending and reduces the wedge between the actual price ratio and its required level which tends to raise real money balances. • Higher activity in the industrial sector raises income tax revenue and reduces the fiscal deficit, exerting a downward pressure on money growth. • If subsidy rate is high enough initially, raising it further leads to higher money growth and inflation. • If wages are fully flexible, increasing subsidies on food is always inflationary.