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Inflation and economic growth in the long run
Economics Letters 80 (2003) 167–173 www.elsevier.com / locate / econbase
Inflation and economic growth in the long run ´ Carlos G. Fernandez Valdovinos* ˜ ´ , Paraguay del Carmen 254, c / Sacramento, Asuncion Banco Central del Paraguay, Nuestra Senora Received 22 August 2002; accepted 8 January 2003
Abstract This paper tests the proposition that the growth rate of the economy and the level of inflation are negatively correlated in the long run. Even though the original data illustrate the absence of a clear relationship between inflation and growth over time, after using the Baxter and King filter to extract the long run components of the data, a clear negative relation emerges between the two time series. 2003 Elsevier B.V. All rights reserved. Keywords: Inflation; Growth JEL classification: E31; N16
1. Introduction It is well known that a wide variety of external environment and policy variables could affect the growth rate of the economy by changing its long run potential income and its rate of productivity growth. For example, based on the results from previous empirical research, the following variables could be mentioned as important determinants of long-run per capita income: the stock of physical capital, the stock of human capital in the forms of educational attainment and health, the ratio of government consumption to GDP, the ratio of domestic investment to GDP, movements in the terms of trade, measures of political instability and the rule of law, etc. Additionally, in recent years, the contours of an inverse connection between inflation and growth across countries have begun to emerge from econometric studies. For example, Barro (1991) reports a negative, but weak, relationship between inflation and the growth rate of real GDP during 1970–1985 in a cross-section of 117 countries. Even so, he finds a significant negative relationship between the intensification of inflation (from 1960–1970 to 1970–1985) and growth, as do Kormendi and Meguire * Tel.: 1595-21-608-158; fax: 1595-21-608-150. ´ Valdovinos). E-mail address: [email protected] (C.G. Fernandez 0165-1765 / 03 / $ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0165-1765(03)00085-5
168
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
(1985) in a cross-section of 47 countries during 1950–1977. Fischer’s (1993) cross-section regression estimates, from 1960 to 1989, indicate that an increase in inflation from, say, 5 to 50% a year from one country to another reduces the growth of GDP by 1.8% per year, other things being equal. And, using panel data from 12 Latin America countries from 1950 to 1985, De Gregorio (1992) finds a semi elasticity of per capita growth with respect to average inflation equal to 2 0.008. This means that an increase in annual inflation from 5 to 50% from one country to another reduces per capita growth by 0.7% a year, ceteris paribus 1 . Although empirical studies based on cross-country data seem to support the hypothesis that high inflation is correlated with a lower level of economic growth in the long run, it is important to test if these findings hold for a single country over time. However, a test on a time series data for a single country could be difficult to carry out. One element of the problem could be to obtain a suitable approach to defining the long run and detecting long run relationships. As a result, in this article, the basic proposition that the growth rate of the economy and the level of inflation are correlated is examined from a non-structural, low frequency point of view. The methodology employed in this work is based on Lucas (1980). In this paper, Lucas presents empirical illustrations of two central implications of the quantity theory of money: that a given change in the rate of change in the quantity of money induces: (i) an equal change in the rate of price inflation; and, (ii) an equal change in nominal rates of interest. Since the two quantity-theoretic propositions hold only in the ‘long run’, Lucas constructs a filter to smooth the original data (i.e. to extract its long run components) before testing the implications of the theory.
2. The filter Alternatively to the Lucas filter, this study uses the approximate band-pass filter developed by Baxter and King (1995) to obtain the low frequency components of the time series. For the empirical applications, I adopt the definition of the business cycle suggested by the procedures and findings of NBER researchers, like Burns and Wesley (1946), that specified business cycles as the cyclical components between 18 months and 8 years. I adopt these limits as the definition of the business cycles so, to isolate the trend or low frequency of the data, I consider those frequencies with a periodicity of 8 years or higher. Specifying the business cycle as fluctuations with a specified range of periodicity results in a particular two-sided moving average (a linear filter). In the particular case of the NBER definition of the business cycle, the desired filter is a band-pass filter, i.e. a filter which passes through components of the time series with fluctuations of 8 years or higher while removing components at higher frequencies. However, the resulting moving average is of infinite order and an approximation to this filter is necessary for it to be applicable to finite time series. Therefore, in order to analyze the hypothetical relationship in the log run between economic growth and each of the factors considered, I first apply the following filter to the original time series data:
1
Complementarily, several theoretical models founded a negative relationship between inflation and economic growth. See ´ for example, Jones and Manuelli (1995), Wu and Zhang (1998) and Fernandez Valdovinos (1999).
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
Oay
169
k
y t* 5
j
(1)
t 1j
j 52k
where y *t is the value of the filtered series. The optimal approximate filter weights, a j , are functions of the weights of the ideal low-pass filter, b j , and an adjustment term, u. Thus, a j 5 b j 1 u.2 A parameter to be chosen is the value of k, the number of leads and lags in the filtered series. I have set this value equal to six 3 . Thus the approximate band-pass used in this analysis is the BP6 (8) filter described in Baxter and King (1995). The notation reflects the fact that the filter passes through components of the data with cycles higher than 8 years and the subscript ‘6’ means that six leads and lags of the data were used in constructing the filter (i.e. six annual observations are lost at the beginning and end of the sample period for the filtered data).
3. Data and results The data used in this section are from the International Monetary Fund, ‘International Financial Statistics’. Eight different Latin American countries were selected. Additionally, for every variable, the original annual data runs from 1970 to 2000, so given the value chosen for k, we have 19 observations for the filtered data. Figs. 1B–8B plot the long run relationship between the growth rate of GDP and inflation for the
Fig. 1. Inflation and growth. (A) Unfiltered data; (B) filtered data.
2
For a more detailed discussion of the issues involved in constructing the approximate band-pass filters for economic time series (i.e. how to calculate the ideal weights and the adjustment term), see Baxter and King (1995). 3 There is a trade-off when choosing the value of k: increasing k leads to a better approximation to the ideal filter, but results in more lost observations. Baxter and King (1995) proposed a value of three or six to filter annual data.
170
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
Fig. 2. Inflation and growth. (A) Unfiltered data; (B) filtered data.
different countries. I have used the filtered data and, for comparison, for each country I have also plotted, in Figs. 1A–8A, the raw (original) data for the period 1976–94 giving also a total of 19 observations for every country 4 . For all the countries considered, the plots of the original data illustrate the absence of a clear relationship (or at most a negative, but weak, relationship) between inflation and growth over time. However, after filtering the data and extracting only its long run components, a clear negative relation between these two time series emerges. Table 1 gives the correlation coefficients, for the different countries, of the growth rate of GDP per capita and inflation. This table confirms the impression from Figs. 1A–8B. The negative correlation between the original series is small, but it is clearly negative at the low frequencies: the absolute value of the (negative) correlation coefficients is much higher for the filtered data.
Fig. 3. Inflation and growth. (A) Unfiltered data; (B) filtered data. 4
For presentation purposes, I have eliminated some observations in the original data with (relatively to the country history) very high inflation rate. Thus, two observations were excluded for Bolivia (1984, 1985), Chile (1976, 1978) and Peru (1989, 1990).
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
Fig. 4. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Fig. 5. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Fig. 6. Inflation and growth. (A) Unfiltered data; (B) filtered data.
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´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
172
Fig. 7. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Fig. 8. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Table 1 Correlation coefficients
Brazil Bolivia Chile Colombia Costa Rica ´ Mexico Paraguay Peru´
Original data
Filtered data
20.1454 20.3092 20.0085 20.3218 20.8303 20.6420 20.1000 20.4112
20.8224 20.8874 20.8648 20.4855 20.9242 20.7220 20.8383 20.6175
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
173
4. Conclusions Empirical researchers have found that the average long-run rate of inflation in a country is negatively associated with the country’s long run rate of growth. In this paper, the basic proposition that the growth rate of the economy and the level of inflation are correlated were examined from a non-structural, low frequency point of view and using the tools of spectral analysis. For all the countries considered, the negative correlation between the original series is small and weak. However, after filtering the data and extracting only its long run components, a clear and stronger negative relationship emerges between these two time series.
References Barro, R., 1991. Economic growth in a cross section of countries. Quarterly Journal of Economics 104, 407–433. Baxter, M., King, R., 1995. Measuring business cycles approximate band-pass filters for economic time series. National Bureau of Economic Research Working Paper No. 5022. National Bureau of Economic Research, New York. Burns, A., Wesley, M., 1946. Measuring Business Cycles. National Bureau of Economic Research, New York. De Gregorio, J., 1992. Economic growth in Latin America. Journal of Development Economics 39, 59–84. ´ Fernandez Valdovinos, C., 1999. Inflation and welfare in an endogenously growing economy. Unpublished dissertation, University of Chicago, Chicago, IL. Fischer, S., 1993. The role of macroeconomic factors in growth, Working Paper No. 4565, National Bureau of Economic Research, New York. Kormendi, R.L., Meguire, P.G., 1985. Macroeconomic determinants of growth: Cross-country evidence. Journal of Monetary Economics 16, 141–163. Lucas, R., 1980. Two illustrations of the quantity theory of money. American Economic Review 70, 1005–1014. Jones, L., Manuelli, R., 1995. Growth and the effects of inflation. Journal of Economic Dynamics and Control 19, 1405–1428. Wu, Y., Zhang, J., 1998. Endogenous growth and the welfare costs of inflation: a reconsideration. Journal of Economic Dynamics and Control 22, 465–482.
Inflation and economic growth in the long run ´ Carlos G. Fernandez Valdovinos* ˜ ´ , Paraguay del Carmen 254, c / Sacramento, Asuncion Banco Central del Paraguay, Nuestra Senora Received 22 August 2002; accepted 8 January 2003
Abstract This paper tests the proposition that the growth rate of the economy and the level of inflation are negatively correlated in the long run. Even though the original data illustrate the absence of a clear relationship between inflation and growth over time, after using the Baxter and King filter to extract the long run components of the data, a clear negative relation emerges between the two time series. 2003 Elsevier B.V. All rights reserved. Keywords: Inflation; Growth JEL classification: E31; N16
1. Introduction It is well known that a wide variety of external environment and policy variables could affect the growth rate of the economy by changing its long run potential income and its rate of productivity growth. For example, based on the results from previous empirical research, the following variables could be mentioned as important determinants of long-run per capita income: the stock of physical capital, the stock of human capital in the forms of educational attainment and health, the ratio of government consumption to GDP, the ratio of domestic investment to GDP, movements in the terms of trade, measures of political instability and the rule of law, etc. Additionally, in recent years, the contours of an inverse connection between inflation and growth across countries have begun to emerge from econometric studies. For example, Barro (1991) reports a negative, but weak, relationship between inflation and the growth rate of real GDP during 1970–1985 in a cross-section of 117 countries. Even so, he finds a significant negative relationship between the intensification of inflation (from 1960–1970 to 1970–1985) and growth, as do Kormendi and Meguire * Tel.: 1595-21-608-158; fax: 1595-21-608-150. ´ Valdovinos). E-mail address: [email protected] (C.G. Fernandez 0165-1765 / 03 / $ – see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016 / S0165-1765(03)00085-5
168
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
(1985) in a cross-section of 47 countries during 1950–1977. Fischer’s (1993) cross-section regression estimates, from 1960 to 1989, indicate that an increase in inflation from, say, 5 to 50% a year from one country to another reduces the growth of GDP by 1.8% per year, other things being equal. And, using panel data from 12 Latin America countries from 1950 to 1985, De Gregorio (1992) finds a semi elasticity of per capita growth with respect to average inflation equal to 2 0.008. This means that an increase in annual inflation from 5 to 50% from one country to another reduces per capita growth by 0.7% a year, ceteris paribus 1 . Although empirical studies based on cross-country data seem to support the hypothesis that high inflation is correlated with a lower level of economic growth in the long run, it is important to test if these findings hold for a single country over time. However, a test on a time series data for a single country could be difficult to carry out. One element of the problem could be to obtain a suitable approach to defining the long run and detecting long run relationships. As a result, in this article, the basic proposition that the growth rate of the economy and the level of inflation are correlated is examined from a non-structural, low frequency point of view. The methodology employed in this work is based on Lucas (1980). In this paper, Lucas presents empirical illustrations of two central implications of the quantity theory of money: that a given change in the rate of change in the quantity of money induces: (i) an equal change in the rate of price inflation; and, (ii) an equal change in nominal rates of interest. Since the two quantity-theoretic propositions hold only in the ‘long run’, Lucas constructs a filter to smooth the original data (i.e. to extract its long run components) before testing the implications of the theory.
2. The filter Alternatively to the Lucas filter, this study uses the approximate band-pass filter developed by Baxter and King (1995) to obtain the low frequency components of the time series. For the empirical applications, I adopt the definition of the business cycle suggested by the procedures and findings of NBER researchers, like Burns and Wesley (1946), that specified business cycles as the cyclical components between 18 months and 8 years. I adopt these limits as the definition of the business cycles so, to isolate the trend or low frequency of the data, I consider those frequencies with a periodicity of 8 years or higher. Specifying the business cycle as fluctuations with a specified range of periodicity results in a particular two-sided moving average (a linear filter). In the particular case of the NBER definition of the business cycle, the desired filter is a band-pass filter, i.e. a filter which passes through components of the time series with fluctuations of 8 years or higher while removing components at higher frequencies. However, the resulting moving average is of infinite order and an approximation to this filter is necessary for it to be applicable to finite time series. Therefore, in order to analyze the hypothetical relationship in the log run between economic growth and each of the factors considered, I first apply the following filter to the original time series data:
1
Complementarily, several theoretical models founded a negative relationship between inflation and economic growth. See ´ for example, Jones and Manuelli (1995), Wu and Zhang (1998) and Fernandez Valdovinos (1999).
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
Oay
169
k
y t* 5
j
(1)
t 1j
j 52k
where y *t is the value of the filtered series. The optimal approximate filter weights, a j , are functions of the weights of the ideal low-pass filter, b j , and an adjustment term, u. Thus, a j 5 b j 1 u.2 A parameter to be chosen is the value of k, the number of leads and lags in the filtered series. I have set this value equal to six 3 . Thus the approximate band-pass used in this analysis is the BP6 (8) filter described in Baxter and King (1995). The notation reflects the fact that the filter passes through components of the data with cycles higher than 8 years and the subscript ‘6’ means that six leads and lags of the data were used in constructing the filter (i.e. six annual observations are lost at the beginning and end of the sample period for the filtered data).
3. Data and results The data used in this section are from the International Monetary Fund, ‘International Financial Statistics’. Eight different Latin American countries were selected. Additionally, for every variable, the original annual data runs from 1970 to 2000, so given the value chosen for k, we have 19 observations for the filtered data. Figs. 1B–8B plot the long run relationship between the growth rate of GDP and inflation for the
Fig. 1. Inflation and growth. (A) Unfiltered data; (B) filtered data.
2
For a more detailed discussion of the issues involved in constructing the approximate band-pass filters for economic time series (i.e. how to calculate the ideal weights and the adjustment term), see Baxter and King (1995). 3 There is a trade-off when choosing the value of k: increasing k leads to a better approximation to the ideal filter, but results in more lost observations. Baxter and King (1995) proposed a value of three or six to filter annual data.
170
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
Fig. 2. Inflation and growth. (A) Unfiltered data; (B) filtered data.
different countries. I have used the filtered data and, for comparison, for each country I have also plotted, in Figs. 1A–8A, the raw (original) data for the period 1976–94 giving also a total of 19 observations for every country 4 . For all the countries considered, the plots of the original data illustrate the absence of a clear relationship (or at most a negative, but weak, relationship) between inflation and growth over time. However, after filtering the data and extracting only its long run components, a clear negative relation between these two time series emerges. Table 1 gives the correlation coefficients, for the different countries, of the growth rate of GDP per capita and inflation. This table confirms the impression from Figs. 1A–8B. The negative correlation between the original series is small, but it is clearly negative at the low frequencies: the absolute value of the (negative) correlation coefficients is much higher for the filtered data.
Fig. 3. Inflation and growth. (A) Unfiltered data; (B) filtered data. 4
For presentation purposes, I have eliminated some observations in the original data with (relatively to the country history) very high inflation rate. Thus, two observations were excluded for Bolivia (1984, 1985), Chile (1976, 1978) and Peru (1989, 1990).
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
Fig. 4. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Fig. 5. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Fig. 6. Inflation and growth. (A) Unfiltered data; (B) filtered data.
171
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
172
Fig. 7. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Fig. 8. Inflation and growth. (A) Unfiltered data; (B) filtered data.
Table 1 Correlation coefficients
Brazil Bolivia Chile Colombia Costa Rica ´ Mexico Paraguay Peru´
Original data
Filtered data
20.1454 20.3092 20.0085 20.3218 20.8303 20.6420 20.1000 20.4112
20.8224 20.8874 20.8648 20.4855 20.9242 20.7220 20.8383 20.6175
´ Valdovinos / Economics Letters 80 (2003) 167–173 C.G. Fernandez
173
4. Conclusions Empirical researchers have found that the average long-run rate of inflation in a country is negatively associated with the country’s long run rate of growth. In this paper, the basic proposition that the growth rate of the economy and the level of inflation are correlated were examined from a non-structural, low frequency point of view and using the tools of spectral analysis. For all the countries considered, the negative correlation between the original series is small and weak. However, after filtering the data and extracting only its long run components, a clear and stronger negative relationship emerges between these two time series.
References Barro, R., 1991. Economic growth in a cross section of countries. Quarterly Journal of Economics 104, 407–433. Baxter, M., King, R., 1995. Measuring business cycles approximate band-pass filters for economic time series. National Bureau of Economic Research Working Paper No. 5022. National Bureau of Economic Research, New York. Burns, A., Wesley, M., 1946. Measuring Business Cycles. National Bureau of Economic Research, New York. De Gregorio, J., 1992. Economic growth in Latin America. Journal of Development Economics 39, 59–84. ´ Fernandez Valdovinos, C., 1999. Inflation and welfare in an endogenously growing economy. Unpublished dissertation, University of Chicago, Chicago, IL. Fischer, S., 1993. The role of macroeconomic factors in growth, Working Paper No. 4565, National Bureau of Economic Research, New York. Kormendi, R.L., Meguire, P.G., 1985. Macroeconomic determinants of growth: Cross-country evidence. Journal of Monetary Economics 16, 141–163. Lucas, R., 1980. Two illustrations of the quantity theory of money. American Economic Review 70, 1005–1014. Jones, L., Manuelli, R., 1995. Growth and the effects of inflation. Journal of Economic Dynamics and Control 19, 1405–1428. Wu, Y., Zhang, J., 1998. Endogenous growth and the welfare costs of inflation: a reconsideration. Journal of Economic Dynamics and Control 22, 465–482.