Buletin USAMV-CN, 64/2007 (-) ISSN 1454-2382
THE IMPACT OF MACROECONOMIC VARIABLES ON AGRICULTURAL PRICES. ANALYSIS BASED ON VAR
METHODOLOGY
Criveanu R.C., E. RăduŃ
University of Craiova, Faculty of Economy and Business Administration, No. 13, A. I. Cuza Street, Craiova, Dolj
raducrv@gmail.com
Key words: VAR methodology, macroeconomic variables, agricultural prices, shocks analyze
Abstract. The present paper wants to estimate the impact of macroeconomic variables on agricultural prices, using the methodology of auto regressive vector. The VAR methodology is used for evaluating the impact of selected macroeconomic variables (PIB per inhabitant, the index of consumption prices, exchange rate and interest rate) on agricultural prices between 1997-2006. Choosing the period of analysis and the strategy of shaping takes into account the use of econometry in transition. The beginning of the analysis with year 1997 is justified because of the major changes of the system (prices and exchange rate) before this date. In the present paper we will take into account a certain number of economical and agricultural variables which interact to each other inside the system. Choosing this methodology is justified by the nature of investigation on which the work is based, analyses of system type (simultaneous equations) being able to astound the interconnections between the macroeconomic variables and the agricultural ones (the price index at agricultural inputs and the producers index price).
The auto regressive vector VAR shapes each endogenous variable from the system according to the past values of all the variables from the system. In the same time it is used to forecast the time series whom evolution is mutual influenced and to analyse the dynamic of the impact on random perturbations (shocks) on the system of variables (the impulse response function and the analysis of spreading).
INTRODUCTION
The auto regressive vector analysis VAR has imposed itself on the macroeconometrical studies from the ’70s, its most important promoter being Christopher Sims1. VAR represent an analysis of system type, in which all the variables are included, a priori, endogenous, that because of that, shaped together.
The VAR models are focused on the analysis of shocks on the studied variables. The shocks or the “innovations” represent that part of a variable which can not be explained by the history (past values) of that variable or other variables from the system. Thus. an innovation appears like error term (residual) in the aleatory equation of the system. For example, in the system:
t t t
t a a X a Y
X = 0 + 1 −1+ 2 −1 +ε1 (1)
t t t
t b b X b Y
Y = 0 + 1 −1+ 2 −1+ε2 (2)
1 Sims, C (1986), “Are forecasting models usable for policy analysis?“, Quarterly Review, Federal Reserve Bank of Minneapolis.
t
ε1 and ε2t represents the shocks, in a t period, on X and Y variables. In every equation, the rest of the terms represent the part explained by the history of the system.
The main purpose of VAR analysis is to evaluate the effects of various shocks on the system’s variables. Each variable is affected by its own innovations and by innovations in other variables.
The macroeconomic variables took into account in this work are: PIB per inhabitant, the index of consumption prices, exchange rate and interest rate. The selected macroeconomic index are the ones who reveal best the essential characteristic of a economy, this reason being the bases of the selection. All these variables are influenced by the macroeconomic policy, and if they have a significant influence on the agricultural sector, then the macroeconomic policy has important implications on the agriculture.
The main agricultural variables are the price of the inputs (IPI) and the price of the outputs (IPP). The index of the inputs’ price is expressed like the price of goods and services spent in agriculture and index of outputs’ price is expressed like the producers’ price.
The VAR analysis ends in determining the response function at shock (impulse response function) and forecast error variance decomposition.
MATERIAL AND METHOD
Sims (1980) suggest the VAR methodology as a response to simultaneous equations :
1 1
) 0
(demand =a +a P+ε
X (3)
2 1
) 0
(offer =b +bP+ε
Y (4)
) ( )
(demand Y offer
X = (5)
2 2 1
) 0
(offer =b +bP+bVr +ε
Y (6)
In this way, we can answer very important questions for the authorities, like “How do agricultural prices react to changes in the economic policy?” The difficult part appears at establishing the exogenous variables which must be introduced in the system. Thus, as a response to the difficult part of choosing which variables are endogenous and which are exogenous, Sims suggest a model which doesn’t make distinctions between endogenous and exogenous variables.
A model of auto regressive vectors VAR is a model in which we have a K variable effect vector, expressed in report with previous performances of its components, meaning it is expressed reported to a number of L lags of each variable and L lags of other K-1 variables (Johansen, S., 1991). So a VAR model can be written like this:
t t l t l t
t v AY AY Bx
y = + 1 −1+...+ − + +ε (7) where
Al
A ....1 are matrix of KxK order of the coefficients x is a Mx1 vector t
εt is a vector of innovations
B is a matrix of KxM order of the coefficients v is a Kx1 vector of the parameters
Impulse response function (IRF) is a function which identifies the effect that a major shock a standard deviation from ε t innovation on present and past values of the variables
affected by the shock (the ones we want to determine the reaction at shock). The impulse response function is defined as:
s t
s
yt
ε =ϖ
∂
∂ +
(8)
The formula is explained like this: the element from I row, j colon of the matrix ω s identifies the effect that the raise with one unit of the variable ε j,t has, at a t time on y t + s variable, considering we maintain constant the other variables.
For understanding the model, we can imagine that the impulse function is a function that measures the response of a system when removing it from the equilibrium position. A shock (impulse) on the system is generated by modifying one of the ε j,t variables for a period of time. The response of y t + s variable is a reaction at this shock, reaction which can be manifested as a removal from the equilibrium position or as a returning at that equilibrium position or finding another equilibrium position. In other words, the impulse response function measures the response of y i , t + s variable at a t+s moment, considering the other variables maintain constant. Intuitive, the impulse response function (IRF) describes the reaction of y i , t + s variable at a shock manifested on it.
Laying out of the VAR model requires covering of two stages: verifying the stationary series analysed using ADF test (Augmented Dicky Fuller) and identifying the number of lags used in the model.
In this paragraph, the VAR methodology is used for evaluating the impact of selected macroeconomic variables (PIB per inhabitant, consumption index prices, exchange and interest rate) on the agricultural prices during 1997-2006. Choosing the period of analysis and the strategy of shaping takes into account the use of econometry in transition. The beginning of the analysis with year 1997 is justified because of the major changes of the system (prices and exchange rate) before this date.
For more relevant results of this analysis, it is absolutely necessary that the econometric lay out model should be submissive in every stage of the shaping to the diagnosis type analysis for testing statistical properties (Kmenta, J., 1986). The main stages of shaping are2:
- testing the integration order of interested variables - selection of lags number of VAR
- testing for the co-integration existence - testing VAR stability
- testing the qualities of white noise and of residual terms of VAR equations
Testing the integration order. The test of co-integration existence is necessary for choosing the specification of the model. In this case, we have different situations:
- if all the selected variables are stationary – incorporated of zero order – then the estimation using the variables with the initial specification does not have any problems
- if the series are un-stationary, but co-integrated, then the estimation with specification on stages or in the correction model are allowed
- if the series are un-stationary and are not co-integrated, it is necessary the specification of variables as differences (modifications from one period to another) For the six variables included in this study the testing was made using ADF test. The results of the test shows that all six variables are not stationary.
2 Because of the many results generated by the model, only a few of them will be presented as conclusions
Selection of lags number of VAR was based on the synthesis of the results for the minimizing errors criteria given by Akaike and Schwartz. Taking into account the limited number of observation in the sample, we considered only models with maximum 2 lags.
The test for co-integration existence was realized using the methodology elaborated by Johansen (1991, 1995) and the results were positive. For the identified model, both criteria used λtrace and λmax identifies at a static level of 5% a number of co-integration vectors r, so that 0<r<n=3110. These results corroborated with the results of stationary test show that the models can be estimated like VARs with variables expressed in stages.
Testing VAR stability. A VAR model is stable (stationary) if the effects of the shocks on system variables diminish to exhausting after a time period. If VAR is not stable (e.g. is explosive), then the trust intervals for the impulse response function (FRS) can not be lay out, because the standard errors can not be calculated with the usual methods. This condition has been tested and it is satisfied.
Testing the white noise qualities. The concept of white noise means that the errors are completely random. More precisely, they must be normally distributed, must have constant variation and not to be auto-correlated. For validating VAR analysis results it is necessary that the white noise hypothesis be tested. The tested hypothesis (auto-correlation lack, normality and homoschedasticity) are not reject at significant levels from 1% to 5%, which means that the results are the expected ones.
RESULTS AND DISCUSIONS
The main results of VAR analysis are materialized in impulse response functions, variance decomposition and Granger casualty. With the help of impulse response function we can determine the sign of the effects (positive or negative) and their persistence. The shocks’
effects are pursued on different time horizons. In the present analysis we will present these shocks on horizons till 10 years.
The variance decomposition calculates in what measure (proportion) the variation of a variable is due to own innovations (shocks) and how much it is due to variation of other variables. These can also be calculated on different time horizons. We choose a 10 years horizon in this case, too.
Figure 1 present as an impulse response function, the responses of producers’ prices index (IPP) to the shocks from all the other 5 selected variables. So, we can notice that the prices of the producers respond positive to their own shocks, at the shock of consumption price index (IPC) and the exchange rate. Obviously, the IPP and IPC effects are the dominating ones. The prices of the inputs transmit negative effects on IPP evolution.
Figure 2 presents the responses of agricultural inputs prices’ index at the shocks from selected variables. Analysing the results of IPI impulse response function, we can observe that the input prices’ index responds positive at its own innovations, IPC shocks and exchange rate. The same conclusion is available for IPP starting with the third year from the producing of the shock. IPI responds negative at the shocks from interest rate evolution especially from the second year.
Fig.1. The response of producer prices’ index at structural shocks
Fig.2. The response of input prices’ index at structural shocks
CONCLUSIONS
In this work, we have used VAR methodology for evaluating the impact of selected macroeconomic variables on agricultural prices between 1997-2006. The choose of analysed period and the shaping strategy took into account the use of econometric in transition. Starting
the analysis with year 1997 was justified due to the major system changes (prices and exchange rate) before this date.
The main purpose of the VAR analysis was to evaluate the effects of different shocks on system’s variables. The macroeconomic variables took into account were: PIB per inhabitant, consumption prices’ index, exchange rate and interest rate.
The main agricultural variables considered werw input price (IPI) and output price (IPP). Input prices’ index is expressed as the price of goods and services spent in agriculture, while the output price is expressed as producer price’s index.
The conclusion resulted from the analysis is that macroeconomic variables have a significant static effect on agricultural output and input prices, but not as much as we would espected. Between the macroecnomic variables we can observe that consumption prices’
index has a significant impact after the first year from transmitting the shock; it follows the input prices’ index in the second year, PIB per inhabitant and exchange rate from the third year.
If we decompose the IPP and IPI variation, we will notice that the input price has a bigger impact on output price then vice-versa. So, in a case like that, we have a mechanism of price transmitting through costs.
However, we must not forget the fact that, the response of the two analysed agricultural variables at the macroeconomic shocks are still redused. This is an expected result, considering the existence of other agricultural and comercial policies which interfere between the agriculture and economy, generally speaking.
BIBLIOGRAPHY
1. Breth S., (2002), Integration of Sustainable Agriculture and Rural Development Issues in Agricultural Policy, FAO and Winrok International
2. Johansen, S. (1991) Estimation and hypothesis testing of cointegrating vectors in Gaussian vector autoregressive models, Econometrica 59 (November)
3. Johansen, S. (1995) Likelihood based inference in cointegrated vector autoregressive models, Oxford University Press, Oxford;
4. Kmenta, J. (1986), Elements of econometrics, 2nd edition, Macmillan, New York;
5. Lutkepol, H. (1991), Introduction to multiple time series analysis, Springer-Verlag, Berlin;
6. Phillips, P. and Perron, P. (1988), Testing for a unit root in time series regression“, Biometrica 75, (June);
7. Sims, C. (1986), Are forecasting models usable for policy analysis?, Quarterly Review, Federal Reserve Bank of Minneapolis, Winter;
8. Sims, C, Stock, J.H., and Watson, M.W. (1990), Inference in linear time series models with some unit roots, Econometrica, January;
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