MEASURING DYNAMIC INFLATION IN BRAZIL

Transcription

1 MEASURING DYNAMIC INFLATION IN BRAZIL Angelo Polydoro Vagner Ardeo - Getulio Vargas Foundation 13 th OTTAWA GROUP MEETING DENMARK May 3th, 2013

2 MOTIVATION The static COLI framework considers a representative consumer who lives for just one period, faces no uncertainty about prices, preferences or income, and decides on which goods and services to allocate his budget (Konus, 1924). This framework fails to account to the fact that when the price of good rises, consumer substitute away not only to other goods at the same moment (static substitution), but also to future consumption. Hence, using static measure of inflation we may not be able to access the full impact of changes in the price of houses or other durables. 2

3 MOTIVATION (cont.) To mitigate these dynamic problems, Reis (2005) proposed a Dynamic Cost of Living Price Index (DPI), based on the modern theory of consumption by Deaton (1992). It assumes a representative consumer that lives for many periods and is subject to shocks in the price of goods/services and financial assets. The DPI is then the compensating variation in the income that keeps the lifetime utility unchanged. Hence, It provides a unifying economic framework to incorporate the price of financial instruments in the cost of living. By financial instruments we mean all the ways in which the consumer can transfer income to the future (real property, other durable goods, and the traditional financial assets). 3

4 MOTIVATION (cont.) Reis (2009) developed a dynamic measure of inflation for the USA from 1970 to 2008, with results that differs markedly that from the CPI. In the last decade, Brazil suffered important changes in terms of its real interest rates and in the prices of durable goods. So, we decided to make an exploratory attempt to calculate a monthly DPI for Brazil, trying to incorporate the impact of these shocks is a more broadly concept of consumer inflation. 4

5 MODEL This representative consumer lives forever and at each period t chooses a consumption and saving plan that optimizes its future expected discounted utility, based in an initial fixed wealth and in its expectations about the future prices of goods/services and the returns of the financial assets. The consumer transfer wealth in time by means of: buying and selling financial assets. buying and re-selling durable goods that suffers depreciation. The only source of uncertainty is future prices of goods/services and returns of the financial assets. 5.

6 CONSUMER OPTIMIZATION PROBLEM 6

7 DYNAMIC PRICE INDEX Defined as the scalar adjustment in the nominal wealth that keep constant the expected discounted utility in the face of a change in prices/returns of assets. The dynamic price index is such that: 7

8 SOME PROPERTIES OF THE DPI Well defined. If prices and wealth are positive and finite, the DPI exists and it is unique. Since the stage utility function is homothetic and time separable, the discount utility function V is also homothetic. Hence, the DPI is independent of wealth. If prices follow random walks and financial assets returns are independent and identically distributed, then the DPI equals the static cost of living price index. 8

9 DATA AND MODEL CALIBRATION We calculate the DPI at sub-group level using the data from the CPI for Brazil calculated by IBRE - 19 series total, out of which 14 are nondurables. Relative taste weight equals the relative shares in the Brazilian household expenditure survey. Time period: Jan/ Dec/2012 at monthly frequency. The depreciation rate for each durable category comes from the Fixed Asset Table from the BEA. 9

10 DATA AND MODEL CALIBRATION (CONT.) Financial Assets: Savings deposit and equity (BOVESPA) We set the discount rate to match an annual rate of return of 8%. Consumer forecasting model: first differences of log-prices and returns follows a first order Markov process to estimate several VAR models. We implemented a unrestricted VAR(1) model to all series. We solved the consumer decision problem using a first order approximation around the non-stochastic steady state. 10

11 RESULTS 11

12 RESULTS (CONT.) 12

13 RESULTS (CONT.) CPI and DPI follow the same trend, but the correlation between their monthly variation is only DPI monthly variation presents a high volatility, with a standard deviation of 0,86. Over the 11 years of this study, the accumulated difference between the DPI and the CPI was -21%. Relative average dynamic weights of durable goods seems very high compared to the 2008 household expenditure survey. 13

14 CONCLUSIONS The econometric nature of the DPI makes it hard to calculate and to explain it. The DPI results presents high volatility and some problems related with the assumption of using durable goods to generate capital gains to the consumer. Lack of surveys on financial holdings in Brazil. Lack of empirical evidence of how consumers forecast prices/returns on assets. Future work depends crucially on new data from which we could possibly infer the dynamic consumer behavior. 14

15 Rio de Janeiro Rua Barão de Itambi, Rio de Janeiro - RJ São Paulo Av. Paulista, 548-6º andar São Paulo - SP