The Paper Is Organized As Follows

The Paper Is Organized As Follows

Commodity Price Fluctuations and Stock Adjustment: A Structuralist Macro Model of Sectoral Interlinkage under Rational Expectation

By

Jonaki Sen Gupta

Charuchandra college

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And

Ishita Mukhopadhyay

Calcutta University

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Abstract:

This paper discusses terms of trade issues in developing countries with macroeconomic structure of a ‘dual economy.’ Accordingly, the paper appreciates the necessity to modify the existing literature on commodity price volatility in different directions so as to accommodate structural features of a developing country within the broad framework of ‘development macroeconomics’ and the technique used in this paper is the ‘rational expectation saddle path behaviour.’ This paper focuses on the link between terms of trade and adjustment in stock of agricultural goods. In the context of this paper agricultural price is primarily an asset price and we try to explore mechanism through which asset price volatility impinges on inflation rate. Moreover, this paper makes an intervention in the existing literature on commodity price volatility by introducing unemployment through wage indexation and inventory dynamics of agricultural products with specific focus on flow conditions of production and consumption of agricultural goods. Since terms of trade movements provide information about shocks, the paper highlights importance of stabilization policies to mitigate adverse effects of shocks. It is found that both increase in production of agricultural goods as well as increase in government expenditure cause fall in industrial output along with rise in industrial price inflation. But, increase in money supply will raise industrial output although industrial price inflation will enhance.

Key words: Dual economy, terms of trade.

Jel Classification: E20 , E31.

Introduction:

The persistent decline in long – term prices of commodities is the trend that has dominated agricultural commodity markets for over five decades. There has been a nominal recovery in prices in recent years mainly due to a structural shift in demand. Although this increase in demand is mostly concentrated on oil and minerals, it has also some impacts on agricultural commodities. It is seen that world prices of wheat, coarse grains, rice and oilseed crops all nearly doubled between 2005 and 2007 and continued rising in early 2008. Figure 1 shows the evolution – in nominal and in real terms – of annual average world prices of wheat, coarse grains, rice, and oilseeds from 1971 to 2007 with projections from 2008 to 2017.

Figure 1: Food commodity price trends

Note: Real prices deflated by USA GDP deflator 2007=1

Source: OECD-FAO Agricultural Outlook, 2008-2017

Nevertheless this commodity price volatility leads to macroeconomic instability, which is detrimental to economic development. These stylized facts have generated increasing interest in macroeconomic models of sectoral interlinkage in which commodity price fluctuation is put at the centre of all concerns. These models have been seen as a way to formulate policy guidelines to reduce these fluctuations. A key element in many of these models is overshooting of agricultural price[1] caused by unanticipated monetary expansion. The point is obvious. If stock of primary good is an asset and its price adjusts instantaneously, while industrial price adjusts slowly, agricultural price overshoots in response to monetary expansion. It is in this context that a brief survey of relevant literature is imperative.

Frankel makes seminal contribution to emerging literature on commodity price volatility. He (1986) used a closed economy monetary macro model to explain overshooting of agricultural prices following an unanticipated expansion in money stock. He emphasized the distinction between fix price sectors (manufactures), where prices adjust slowly and flex price sector (agriculture), where prices adjust instantaneously in response to a change in the money supply.[2] Lai, Hu and wang (1996) extended Frankel’s model to investigate how both anticipated and unanticipated monetary shocks influence commodity prices. Moutos and Vines (1992) performed similar exercise in more detailed framework in which industrial output is demand determined and industrial inflation follows some kind of Phillip’s curve relation. Saghaian et.al (2002) explains monetary impacts and overshooting of agricultural prices in open economy framework under flexible exchange rate. There have also been matching empirical works on issue of commodity price volatility. C David Orden and Paul L. Fackler (1989), Fabio Ghironi (2000), build up econometric models to show that an increase in money supply raises agricultural prices relative to the general price level in the long run. Bakucs and Ferto (2005) tested the overshooting hypothesis with reference to Hungarian agriculture prices. Sayed H, Saghain, Mohamad F. Hasan, Michael R. Reed (2005) also studied the overshooting of agricultural prices in four Asian countries (Korea, Philippines, Thailand and Indonesia.).

Given this existing literature, however, there arise some immediate questions: Is the commodity price fluctuation solely attributable to monetary shock? How can we introduce role of government intervention in the food grain economy and analyze its macroeconomic implications? And finally what are the real economy implications particularly in terms of unemployment, output and inflation rate?

This paper will make a theoretical attempt to find answers to these questions. We make the following contributions. First, the paper explicitly introduces the adjustment of the food grain stock.[3] Change in food grain stock is simply the difference between food production and absorption. Food price is an asset price in this model. Once forward looking expectation is introduced in presence of speculative holdings of food, commodity price volatility becomes imminent. We also try to explore mechanism through which asset price volatility impinges on output and inflation rate.[4]

Second, Most of the models in the existing literature assume full employment of labour and accordingly these models obtain long run neutrality of money. However, we incorporate unemployment through wage indexation. Therefore money is not neutral in the long run. This non–neutrality of money is supported by empirical findings by Sayed H. Saghain, Mohamad F. Hasan, Michael R. Reed (2005). They showed that in the case of Korea and Thailand, the relationship between agricultural price and money supply is significantly different from zero, but in the long run, agricultural price does not increase proportionally to the rate of increase in the money supply. Thus long run money neutrality does not hold in these cases.

Thirdly, the paper pays explicit attention to both monetary and real shocks as sources of the volatility of terms of trade.

The paper is organized as follows. In section 1, we develop and study the basic structure of the model. In section 2, we examine dynamic adjustment in 2X2 system and also analyse saddle path stability of steady state. In section 3, we consider few comparative static exercises. Section 4 concludes the paper.

Section 2: The Model

In this section, we construct a monetary macromodel of sectoral interlinkage. There are two sectors in the model- one is industrial sector and other is agricultural sector. We assume wage indexation for industrial workers, which allows unemployment. Food price is a jump variable where as industrial price is sticky which leads to disequilibrium in the market for industrial goods. Moreover, we assume that the economy is closed. Thus, the model in this paper is disequilibrium, dual economy model with unemployment under perfect foresight.

A. Agricultural Sector: Agricultural output is determined by supply side factors. In our model, we take agricultural output to be fixed. Thus, we get the following supply function of the agricultural output:

(1)

Demand for agricultural output consists of consumption and government expenditure. Shares of expenditure on food and industrial sector are constant, viz (1-β) and β respectively and total consumption is function of aggregate output (Z) and total financial assets (A)[5]. Government purchases food grains at a constant price, known as procurement price,[6]. Therefore the total agricultural demand can be given by

DF = [(1-β) C (Z, A)]/θ+ Gw (2)

where Gw is the amount of government purchase at procurement price and θ= PF/ PY, is terms of trade where Py and PF are the price of industrial goods and agricultural goods respectively.

B. Industrial Sector: Production function for industrial production takes the following form:

(3)

Employment in the industrial sector is derived from the condition of profit-maximization, namely equality between marginal product of labour and real product wage. Thus we get the labour demand function as:

(4)

where W denotes the money wage.

Next we consider money wage determination. Instead of assuming flexible adjustment in money wage, we take money wage to be determined as an outcome of a bargaining process. Specifically, we assume that money wage is determined by a social pact, which protects the real consumption wage. Wage indexation is as follows-

(5)

Now, (6)

From equations (3), (5) and (6) we get the supply function of industrial goods:

with <0.

Next, we consider demand side of the industrial sector. Demand for manufactured goods consists of private consumption expenditure, and government expenditure.

Consumption demand for industrial goods is given by Cy = β C (Z, A) where A is total financial assets. Government expenditure (Gy) is parametrically given.

Thus the aggregate demand for the industrial goods is β C (Z, A) + Gy.

C. Aggregate Output: Let Z denote aggregate output (or real income) measured in units of industrial goods,

(7)

The response of Z in response to is calculated as follows:

where eL is the elasticity of demand for labour in the industrial sector[7].

D. Financial sector: In a developing country food grains stocks constitute a widely used financial asset. In this paper, financial sector is represented in terms of an asset structure, which includes money (M) and stock of food grains (H).

Thus total value of assets (A) is given by

A= M + Pf H

The value of assets in terms of industrial goods is represented by

a =A/Py=m + ( Pf / Py) H

=m + θ H (8)

The desired ratio of money to stock of primary goods is assumed to depend on expected return of the assets, that is, on the expected percentage change in the price of foodgrains. Under perfect foresight, expected change in food price is equal to actual change in food price i.e. = and therefore we can write

= h ; h/ <0 (9)

The term represents expected change (and actual change under the assumption of perfect foresight) in food price. The term k is the difference between the convenience yield and the storage cost of holding primary commodities. Hence, return on stocks of primary commodities is

It will be useful to express the equation (8) as

=L (m / θ H); L/ <0 (10)

E. Inflation Mechanism of industrial sector:

Next we consider inflation dynamics. Instead of allowing instantaneous market clearing of industrial goods, we assume the industrial price to be sticky. However, the inflation rate can change in response to excess demand for the industrial goods. Now, since the price of industrial goods cannot jump, the industrial sector can remain in disequilibrium. The form of disequilibrium determines the inflation rate. Thus, the current industrial price level is determined by the past rates of inflation and the current inflation rate determines the future price level. At any particular point in time the industrial price is predetermined.[8] Now inflation mechanism can be expressed as

= γ [βC (Z, A) + Gy – Ys]; γ >0 (11)

3. Dynamic Adjustment and Stability:

A. Stock of Primary Commodity Adjustment:

Any excess supply of agricultural output over domestic absorption generates adjustment in stock of primary commodities i.e.

= - DF

= - (1-β) C/θ - (Gw / θ) (12)

Equation (12) represents dynamic adjustment of stock of primary commodities. We begin with initial steady state value such that and examine effect on following any change in variables that appear in equation 12.

In an implicit form this stock of primary commodity adjustment can be written as

= (θ, H, F, M, GF) with < 0, <0, >0, <0,<0. (13)

= <0 (We assume that consumption elasticity greater than one).

<0 (Again also we assume that consumption elasticity greater than one).

>0 (We assume supply side effect dominates demand side effect).

<0 (We assume that asset effect dominates income effect.)

<0

Beginning at an initial steady state value of H such that, we examine effect on following any change in variables that appear in equation 13.

Increase in θ leads to increase in aggregate output as well as total asset, and hence consumption demand will increase. Assuming consumption elasticity is greater than one, increase in consumption demand makes <0. Next, we consider increase in H. Increase in H, will raise total asset. Therefore from the asset market equilibrium, food price will decrease. Again, increase in total asset will raise consumption demand where as decrease in food price and hence, terms of trade will reduce consumption demand. We assume that asset effect dominates the terms of trade effect and also assuming consumption elasticity greater than one, we get Increase in GF causes an increase in demand for food and this makes <0 (followed from equation 12). Now, we consider increase in agricultural output. This increase in agricultural output directly makes > 0. But increase in agricultural output will also cause an increase aggregate real income. As a result consumption demand will increase and this increase in consumption will make < 0. However, we assume that supply side effect will dominate the demand side effect such that > 0. Next, we consider increase in M. Increase in M leads to increase in total asset. Therefore, from the asset market equilibrium it follows that food price will increase leading to increase in terms of trade. Both increase in total asset as well as increase in terms of trade will raise consumption demand assuming consumption elasticity greater than one, we get <0. Lastly, we consider increase in government purchase. Increase in government purchase causes increase in demand for food and hence we get, .

B. Terms of trade Adjustment:

Equations 9 and 10 can be combined together to produce the dynamic adjustment in

the terms of trade. Noting that, we get

= L (m / θ H) – k - (14)

In an implicit form terms of trade adjustment can be expressed as

with g1 >o, g2>o, g3<o, g4<0, g5<0. (15)

We begin with initial steady state value such that and examine effect on following any change in variables that appear in equation 14.

>0 since we assume that food price inflation is greater than industrial price inflation. (A is a constant).

>0

<0

<0

The sign restrictions can be explained as follows:

First we consider increase in θ. The increase in θ leads to increase in real income leading to increase in consumption demand. This increase in consumption demand will generate industrial price inflation. On the other hand, increase in θ causes food price inflation follows from equation (9). However, we assume that food price inflation exceeds industrial price inflation in response to increase in θ such that >0. Next, we consider increase in H. From the asset market equilibrium it follows that rise in H will cause food price inflation. This makes >0. Now, we consider increase in M. Increase in M leads to increase in total assets and therefore from asset market equilibrium we will obtain decrease in change in food price and this makes <0. Again increase in total asset will increase consumption demand. This increase in consumption will generate industrial price inflation. Therefore decrease in change in food price as well as industrial price inflation will make <0. Next, we consider increase in agricultural output. Increase in agricultural output will increase real income and therefore consumption demand will increase. This increase in consumption demand will generate industrial price inflation which leads to <0. Finally, we consider increase in Gy. This increase in Gy leads to industrial price inflation which makes <0.

C. Steady State:

In the steady state and

locus denotes the combination of the θ and H such that food price inflation equals industrial price inflation.

The slope of is.

locus denotes the combination of the θ and H such that food market is cleared.

The slope of is.

Equations 12 and 13 constitute a system of differential equations in the stock of primary commodities and terms of trade. Stock of primary commodity is predetermined at any given moment, but, terms of trade is free to make discrete jumps in response to new information. Unanticipated current or future (announced) policy changes or other parameter changes cause to jump onto the unique convergent saddle path. This is the implication of complete (short run and long run perfect foresight) and an efficient asset market. Figure 1 describes the dynamics of the system. In presence of perfect foresight the existence of unique convergent saddle path requires that there must be one positive and one negative characteristic root such that the determinant, where

Thus <0 implies

Thus we get unique convergent saddle path if the locus is steeper than the locous as shown in figure 1.

Figure1: saddle path stability

The saddle path SS is downward sloping and flatter than the locus. The equation of the saddle path is

4. Comparative statics:

A. Increase in Agricultural Output:

Increase in agricultural output may generate contractionary effect on industrial output along with increase in rate of industrial price inflation. Explanation of effect of increase in agricultural output is straightforward. Increase in agricultural output will directly make > 0. But, with increased agricultural output, aggregate real income will increase leading to increase in consumption demand.This increase in consumption will make < 0. However, we assume that supply side effect will dominate the demand side effect such that > 0 and hence, stock of agricultural output has to increase. Diagrammatically, =0 curve shifts rightward. On the other hand, increase consumption demand generates industrial price inflation. As a result <0 and therefore terms of trade has to increase. Therefore curve also shifts rightward.[9] In the long run, terms of trade may increase or decrease. In case terms of trade rises in the final steady state, real wage in terms of industrial goods increases which leads to fall in employment and output. This result is paradox of plenty.[10] However, there is a possibility of expansion of industrial output due to fall in terms of trade.