Relación entre los niveles de precios de las siete principales ciudades de Colombia: Evidencia para el nuevo siglo

Resumen:El documento presenta evidencia estadística acerca de si se cumple la hipótesis de la Paridad del Poder Adquisitivo entre las siete principales ciudades de Colombia (Bogotá, Medellín, Cali, Bucaramanga, Manizales, Barranquilla y Pasto) para el periodo comprendido entre Enero de 2000 y Diciembre de 2014, desde un enfoque que establece la relación de largo plazo entre el nivel de precios de estas ciudades empleando un modelo VEC sugerido por johansen y juselius (1990). Los resultados muestran que las series de los precios no son estacionarios (o estacionarias alrededor de una tendencia), la prueba de cointegración permite determinar que existe relación de largo plazo entre los niveles de precios de las siete ciudades estudiadas.Abstract:Introduction Parity of Purchasing Power (PPA) is perhaps one of the concepts found at the center of classical macroeconomic theory. The empirical works to prove the existence of the PPA between countries is abundant. At the same time, another literature has been developed that tries to prove the existence of PPP within the countries. The PPP implies that the exchange rate in the long term will tend to balance the purchasing power of the different currencies; in order to comply with the Law Of One Price (LOOP) in the market. The Single Price Law implies that, under the existence of efficient markets, the goods will have the same value (discounting the transaction costs) in two different places. This law, in principle, must be fulfilled between any group of countries, regions or cities, especially between cities, since, since there are no clear barriers to trade between them, costs are zero, there are only transport costs. If the law of the single price is met between cities of the same country, this will imply that arbitrage possibilities between them cannot exist. But the non-existence of purchasing power parity between cities implies an opportunity to arbitrate, taking advantage of the imbalance between prices (differential): buy at a lower cost in one place to sell at a higher price in another. Methodology This paper presents statistical evidence about whether the hypothesis of purchasing power parity holds between the seven main cities of Colombia, Bogota, Medellin, Cali, Bucaramanga, Manizales, Barranquilla and Pasto, for the period between January 2000 and December 2014. From one approach that establishes the long-run relationship between the price level of these cities using a VEC model suggesting by Johansen and Juselius (1990). Specifically, untied root tests, ADF, and the Johansen cointegration test are used, the VEC model is estimated and the Granger causality test is applied. The data used correspond to the monthly series of the Consumer Price Index (CPI) at a general level in the seven main cities of Colombia, taken from the DANE, for the period between 2000: 1 and 2014: 12. For this we use the logarithm of the IPC (ln (IPC)) of each of the main cities. With these data, two analyzes are carried out, the first for the set of the 7 main cities, presented in subsection 3.1, and the second for the three main cities of Colombia, presented in subsection 3.2. Main Results First, according to the unit root tests applied to each of the series of the 7 cities, they are integrated in order one, I (1). Second, for both cases of analysis, there is cointegration between the set of price variables. In the seven main cities version the VEC model determined that, in the face of external shocks such as changes in technology, in productivity, in the costs of inputs, or in the level of income of consumers or their expectations, the CPI of Manizales, Cali, Bogotá, Medellín, Barranquilla and Bucaramanga, tends to decrease, while that of Pasto tends to increase. Therefore, one could think of buying in some of the previous cities and selling in Pasto to obtain an extra-economic benefit. As can be seen in Annex 1 - Table 6, with a confidence level of 99%, the price indexes of 4 of the 7 cities respond to the adjustment mechanism; The CPI of Bogotá, Bucaramanga and Pasto have a statistic of correction of errors approximately equal to zero statistically, reason why it does not have a relation in the short term with the indices of prices of the other cities, that is to say with the whole system. By presenting an imbalance in the long run, Cali and Medellin are the cities that will adjust faster with a rate of 16.64% adjustment and 13.29% respectively, followed by Barranquilla with an adjustment of 7.91% over a period, in this case a period is a month. It is important to note that, in the face of imbalances in the CPI in the long term, the price level in cities tends to rise, given the sign of the adjustment coefficient, this implies that the imbalance is corrected from a value below zero, while in Pasto the adjustment will be negative but not significant. If only Cali, Medellín and Bogotá are considered, it is observed that these have the same sense in the adjustment, that is to say, in the face of external shocks, the price levels decrease, but they do so at different speeds, the fastest being Medellín, followed by Cali and Bogotá, so there may be some possibility of arbitration, of course without taking into account transport costs and other factors that affect the exchange of goods. In the three main cities version the VEC model determined that, faced with unexpected imbalances in the long term, ie unexpected or asymmetric shocks, the CPI of the three cities will decrease in the short term by 6.37% for Bogotá, 22.80% for Medellín and 23.85% for Cali, the latter city being the one that will present a faster adjustment. Conclusions The evidence presented indicates that the PPA is fulfilled among the seven main cities of Colombia, and also for the 3 main cities. The existence of a long-term relationship between the series of non-stationary prices, that is, I(1), implies that prices converge at a stable level in the long term, and that they are not susceptible to move away from their tendency permanently before external shocks, in such a way that there is no possibility of arbitration. Using the Granger's causality tests results we can conclude that Medellín can be understood as a "center" city since the movements in its CPI precede the movements in the CPI of a good number of the 7 cities studied; possibly this is due to its importance as a producer, distributor and marketer of the goods that are in the basic basket of Colombians. In the three main cities version, there is bi-directional causality between Bogotá and Medellin. That is, there is a feedback effect between Bogotá and Medellín. In the case of Cali, according to the results, the prices of Cali do not cause in the Granger sense the prices of Medellín or Bogotá, Table 5 presents these results. The results of the Vector Error Correction analysis are important to develop economic policies, since they allow to correctly determine the shocks that will affect the price level both at the national level and in the particular case of the cities under study. The results obtained in this study are important for developing economic policies, since they allow to correctly determine the shocks that will affect the price level both at the national level and in the particular case of the principal and intermediate cities under study.