This repository contains code for the paper
Food inflation is often considered as an important topic as it impacts greatly every single person in a society. Thus, being able to forecast it, up to certain degree of precision, is of interest of related individuals, public and private entities involved in food supply chains. In this work, we aimed to contribute to this problem, for the colombian scenario, proposing an index (SIPSA index) and assessing its relevance when it comes to forecast food inflation. Three models were used:
- Seasonal Autoregressive Integrated Moving Average with exogenous regressors (SARIMAX) model, which provides a manner to forecast food inflation using the proposed SIPSA index as an exogenous variable
- Structural Vectorial Autoregressive (SVAR) model, which provides a glimpse on the dynamics on the short-term relation between variables and the variance descomposition for the forecast of food inflation. We estimate that 40% of food inflation can be explained with the proposed index.
- Structural Vector Error Correction (SVEC) model, which provides a glimpse on the dynamics on the long-term relation between variables and the equilibrium equation stablishing the linear combination of variables being I(0). This is, the proposed index succeed to capture the dynamics of the food inflation in the long-run.
Proposed SIPSA index is merely based on how much does food items cost in various market places across regions. So, if data is available, similar approaches could be used in order to determine suitable forecasting for food inflation allowing decision-makers on government entities, food supplies chain managers and, in general, the public; to have better information available leading to better decisions.
SIPSA is actually a branch of DANE (Departamento Administrativo Nacional de Estadística - National Administrative Department of Statistics, public agency in Colombia dealing with national statistics) in charge of collecting food prices for every product sold in marketplaces located in every city ranging from medium to big sized, across the country. The main aim was to utilize such information as a proxy for understanding and thus, predicting, food inflation (wich, for colombian market, represents ~25% of overall inflation). Several conclusions:
- Construct an index based on information available directly from DANE's webpage.
- Using such index, an improvement of 40% is observed when attempting to forecast food inflation (based on train/test samples split) using a Box-Jenkins approach (SARIMAX model).
- The proposed index displays, in the short run, a similar behaviour as food inflation, leading to an improvement of ~20% in joint forecast (based on train/test samples split) using VAR models
- The proposed index displays, in the long run, a similar behaviour as food inflation, leading to a equilibrium in the sense of Johansen, leading to the conclusion that index is worthy tool to be considered when approaching food inflation's forecasting.
SIPSA weekly reports would display the price of each product at each marketplace clustered by food type: i) vegetables and greens, ii) fresh fruit, iii) tubers, roots and bananas, iv) grains and cereals, v) fish, vi) eggs and dairy products, vii) meats, and viii) processed products. Each dataset cotains ~4500 rows. Weekly data raging from late 2012 to mid 2018 was considered (310 datasets). Then, weekly, median price for each product and median price for clustered products were considered. Finally, a unique weekly value was obtained considering the participation of such clusters in food inflation (i), 9.4% ii) 5%, iii) 4.1%, iv) 18.6%, v) 21.4%, vi) 23.7, vii) 3% and viii) 15.87$, respectively). Data files were obtained directly from DANE's official webpage.
Once the proposed index was computed, it was compared with correspondant food inflation. A correlation of 0.6 was found. In the following figure, the red line displays food variation and blue line displays the proposed SIPSA index.
Three approaches were used in order to study the relation between food inflation and the proposed SIPSA index: i) SARIMAX model (for individual forecasting purposes), ii) VAR model (for joint forecasting purposes) and iii) VEC model (for equilibrium equation purposes).
After an exhaustive search process, a was established as the best model. Such model is indexed by the following parameters.
| Parameter | |||||||
|---|---|---|---|---|---|---|---|
| Estimation | -0.466 | -0.261 | -0.492 | 0.323 | -0.457 | 0.300 | 0.157 |
| Standard error | 0.1147 | 0.1115 | 0.1357 | 0.1246 | 0.1130 | 0.0425 | 0.0434 |
| t-value | -4.06 | -2.34 | -3.62 | 2.60 | -4.04 | 7.06 | 3.63 |
After an exhaustive search process, a SVAR(1) was established as the best model. Such model is indexed by the following parameters.
Where
| i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| -1.1881 | -1.055 | -0.941 | -1.384 | -1.417 | -0.991 | -1.567 | -1.131 | -1.428 | -1.147 | -0.877 | |
| -0.930 | -0.293 | -0.590 | -1.755 | -1.210 | -0.060 | -1.597 | -0.895 | -0.655 | -0.535 | -0.200 |
At the end, the proposed model aims to provide a reasonable pattern understanding in the short run relation between the proposed SIPSA index and food inflation. This is clearly determined by the variance descomposition. SIPSA proposed index explains ~40% of the variance in the forecast of food inflation.
After an exhaustive search process, a SVAR was established as the best model to determine the relation between variables in the long run. Such model implies the following equilibrium equation.
This stablishes that the proposed index captures the dynamics of food inflation in the long run.
- To propose a SIPSA index based on another methodology (different from the calculation of medians) to obtain a more robust index that helps to better capture the information present in the reports given by SIPSA.
- Based on the SIPSA index presented, investigate a complementary methodology that incorporates the dynamics of food consumption out of home (which is 30% of food inflation in Colombia).
- To understand how the SIPSA index may be leveraged if other variables could be included, such as: fuel prices, weather, some infrastructure index, etc.
- To formulate other indices, not necessarily based on SIPSA, to see their relationship over time with the variation and with the index proposed here.
- To assess the impact of the Covid-19 pandemics on food inflation despite the fact that various countries implemented regulation on food and good prices at the beggining of the pandemics. So, what can we learn about the relation of the pandemic with food pricing?