Modelling real GDP per capita in the USA: cointegration test

A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per capita itself, with the nominator being constant through time. The second component is responsible for fluctuations around the economic trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the USA is tested for cointegration. For linearization of the problem, a predicted population time series is calculated using the original relationship. Both single year of age population time series, the measured and predicted one, are shown to be integrated of order 1 – the original series have unit roots and their first differences have no unit root. The Engel-Granger approach is applied to the difference of the measured and predicted time series and to the residuals or corresponding linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since a cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in the VAR representation. The VECM provides consistent, statistically reliable, and significant estimates of the coefficient in the cointegrating relation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the USA from the economic trend, as defined by the constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.GDP per capita; population estimates; cointegration; VAR; VECM; USA

Inflation as a Function of Labor Force Change Rate: Cointegration Test for the USA

Previously, a linear and lagged relationship between inflation and labor force change rate, π(t)= A1dLF(t-t1)/LF(t-t1)+A2 (where A1 and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for the USA is characterized by A1=4.0, A2=-0.03075, and t1=2 years. It provides a root mean square forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best among other inflation forecasting models) and has a perfect parsimony - only one predictor. The relationship is tested for cointegration. Both variables are integrated of order one according to the presence of a unit root in the series and its absence in their first differences. Two methods of cointegration testing are applied - the Engle-Granger one based on the unit root test of the residuals including a variety of specification tests and the Johansen cointegration rank test based on the VAR representation. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds. According to the Granger causality test, the labor force change is proved to be a weakly exogenous variable - a natural result considering the time lead and the existence of a cointegrating relation. VAR and VECM representations do not provide any significant improvement in RMSFE. There are numerous applications of the equation: from purely theoretical - a robust fundamental relation between macroeconomic and population variables, to a practical one - an accurate out-of-sample inflation forecasting at a two-year horizon and a long-term prediction based on labor force projections. The predictive power of the relationship is inversely proportional to the uncertainty of labor force estimates. Therefore, future inflation research programs should start from a significant improvement in the accuracy of labor force estimations

Linear Lagged Relationship Between Inflation, Unemployment and Labor Force Change Rate in France: Cointegration Test

A linear and lagged relationship between inflation, unemployment and labor force change rate, p(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+A2 (where A0, A1, and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a root mean square forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between 1971 and 2004. The relationship is tested for cointegration. All three variables involved in the relationship are proved to be integrated of order one. Two methods of cointegration testing are used. First is the Engle-Granger approach based on the unit root test in the residuals of linear regression, which also includes a number of specification tests. Second method is the Johansen cointegration rank test based on a VAR representation, which is also proved to be an adequate one via a set of appropriate tests. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds together with statistical estimates of goodness-of-fit and RMSFE. Relationships between inflation and labor force and between unemployment and labor force are tested separately in appropriate time intervals, where the Banque de France monetary policy introduced in 1995 does not disturb the long-term links. All the individual relationships are cointegrated in corresponding intervals. The VAR and vector error correction (VEC) models are estimated and provide just a marginal improvement in RMSFE at the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on the results obtained in the regression study. The VECM approach also allows re-estimation of the coefficients in the individual and generalized relationship between the variables both for cointegration rank 1 and 2. Comparison of the standard cointegration approach to the integral approach to the estimation of the coefficients in the individual and generalized relationships between the studied variables demonstrates the superiority of the latter. The cumulative inflation curve or inflation index, which is the actually measured evolution of price level, is much better predicted in the framework of the integral approach, which is a powerful tool for revealing true relationships between non-stationary variables and can be potentially used for rejection of spurious regression. The cumulative curves allow avoiding obvious drawbacks of the VECM representation and cointegration tests – increasing signal to noise ratio after differentiation and severe dependence on statistical properties of error terms. The confirmed validity of the linear lagged relationship between inflation, unemployment and labor force change indicates that since 1995 the Banque de France has been wrongly applying the policy fixing the monetary growth to the reference value around 4.5%. As a result of the policy, during the last ten years unemployment in France was twice as large as the one dictated by its long-term equilibrium link to labor force change. This increased unemployment compensates the forced price stability.

Modeling Real GDP Per Capita in the USA: Cointegration Test

A two-component model for the evolution of real GDP per capita in the USA is presented and tested. The first component of the GDP growth rate represents an economic trend and is inversely proportional to the attained level of real GDP per capita itself, with the nominator being constant through time. The second component is responsible for fluctuations around the economic trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the USA is tested for cointegration. For linearization of the problem, a predicted population time series is calculated using the original relationship. Both single year of age population time series, the measured and predicted one, are shown to be integrated of order 1 – the original series have unit roots and their first differences have no unit root. The Engel-Granger approach is applied to the difference of the measured and predicted time series and to the residuals or corresponding linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since a cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, RMSE. The highest R2=0.95 and the best RMSE is obtained in the VAR representation. The VECM provides consistent, statistically reliable, and significant estimates of the coefficient in the cointegrating relation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the USA from the economic trend, as defined by the constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.

Comprehensive macro-model for the U.S. economy

We present a comprehensive macroeconomic model for the U.S. There exist strict long-term relations between real GDP, price inflation, labor force participation, productivity, and unemployment. The evolution of real GDP depends only on exogenous demographic forces. Other macro-variables follow up the real GDP. The links between the variables have been valid during the last several decades. All relations were (successfully) tested for cointegration. Statistical estimates are also presented. The relationships allow a reliable prediction of the macroeconomic state at very large (more than 9 years) time horizons.US economy, macroeconomic model, real GDP, inflation, unemployment, labor force, productivity, demography

Relationship between inflation, unemployment and labor force change rate in France: cointegration test

A linear and lagged relationship between inflation, unemployment and labor force change rate, π(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+A2 (where A0, A1, and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a root mean square forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between 1971 and 2004. The relationship is tested for cointegration. All three variables involved in the relationship are proved to be integrated of order one. Two methods of cointegration testing are used. First is the Engle-Granger approach based on the unit root test in the residuals of linear regression, which also includes a number of specification tests. Second method is the Johansen cointegration rank test based on a VAR representation, which is also proved to be an adequate one via a set of appropriate tests. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds together with statistical estimates of goodness-of-fit and RMSFE. Relationships between inflation and labor force and between unemployment and labor force are tested separately in appropriate time intervals, where the Banque de France monetary policy introduced in 1995 does not disturb the long-term links. All the individual relationships are cointegrated in corresponding intervals. The VAR and vector error correction (VEC) models are estimated and provide just a marginal improvement in RMSFE at the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on the results obtained in the regression study. The VECM approach also allows re-estimation of the coefficients in the individual and generalized relationship between the variables both for cointegration rank 1 and 2. Comparison of the standard cointegration approach to the integral approach to the estimation of the coefficients in the individual and generalized relationships between the studied variables demonstrates the superiority of the latter. The cumulative inflation curve or inflation index, which is the actually measured evolution of price level, is much better predicted in the framework of the integral approach, which is a powerful tool for revealing true relationships between non-stationary variables and can be potentially used for rejection of spurious regression. The cumulative curves allow avoiding obvious drawbacks of the VECM representation and cointegration tests – increasing signal to noise ratio after differentiation and severe dependence on statistical properties of error terms. The confirmed validity of the linear lagged relationship between inflation, unemployment and labor force change indicates that since 1995 the Banque de France has been wrongly applying the policy fixing the monetary growth to the reference value around 4.5%. As a result of the policy, during the last ten years unemployment in France was twice as large as the one dictated by its long-term equilibrium link to labor force change. This increased unemployment compensates the forced price stability.cointegration; inflation; unemployment; labor force; forecasting; France; VAR; VECM

MODELLING REAL GDP PER CAPITA IN THE USA:COINTEGRATION TESTS

A two-component model for the evolution of real GDP per capita in the United States is presented and tested. First component of the growth rate of GDP represents the growth trend and is inversely proportional to the attained level of real GDP per capita, with the nominator being constant through time. Second component is responsible for the fluctuations around the growth trend and is defined as a half of the growth rate of the number of 9-year-olds. This nonlinear relationship between the growth rate of real GDP per capita and the number of 9-year-olds in the US is tested for cointegration. For linearization of the problem, the population time series is predicted using the relationship. Both single year of age population time series, the measured and predicted one, are shown to be nonstationary and integrated of order 1 � the original series have unit roots and their first differences have no unit root. The Engel-Granger procedure is applied to the difference of the measured and predicted time series and to the residuals of a linear regression. Both tests show the existence of a cointegrating relation. The Johansen test results in the cointegrating rank 1. Since the cointegrating relation between the measured and predicted number of 9-year-olds does exist, the VAR, VECM, and linear regression are used in estimation of the goodness of fit and root mean-square errors, (RMSE). The highest R2=0.95 and the lowermost RMSE is obtained in the VAR representation. The VECM provides consistent, statistically reliable, and significant estimates of the slope in the cointegrating relation. Econometrically, the tests for cointegration show that the deviations of real economic growth in the US from the growth trend, as defined by constant annual increment of real per capita GDP, are driven by the change in the number of 9-year-olds.real GDP per capita, population estimates, cointegration, VAR, VECM, USA

COMPREHENSIVE MACRO � MODEL FOR THE US ECONOMY

We present a comprehensive macroeconomic model for the US There exist strict long�term relations between real GDP, price inflation, labor force participation, productivity, and unemployment. The evolution of real GDP depends only on exogenous demographic forces. Other macro�variables follow up the real GDP. The links between the variables have been valid during the last several decades. All relations were (successfully) tested for cointegration. Statistical estimates are also presented. The relationships allow a reliable prediction of the macroeconomic state at very large (more than 9 years) time horizons.US economy, GDP, inflation, unemployment, labor force, productivity, demography

Relationship between inflation, unemployment and labor force change rate in France: cointegration test

A linear and lagged relationship between inflation, unemployment and labor force change rate, π(t)=A0UE(t-t0)+A1dLF(t-t1)/LF(t-t1)+A2 (where A0, A1, and A2 are empirical country-specific coefficients), was found for developed economies. The relationship obtained for France is characterized by A0=-1, A1=4, A2=0.095, t0=4 years, and t1=4 years. For GDP deflator, it provides a root mean square forecasting error (RMFSE) of 1.0% at a four-year horizon for the period between 1971 and 2004. The relationship is tested for cointegration. All three variables involved in the relationship are proved to be integrated of order one. Two methods of cointegration testing are used. First is the Engle-Granger approach based on the unit root test in the residuals of linear regression, which also includes a number of specification tests. Second method is the Johansen cointegration rank test based on a VAR representation, which is also proved to be an adequate one via a set of appropriate tests. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds together with statistical estimates of goodness-of-fit and RMSFE. Relationships between inflation and labor force and between unemployment and labor force are tested separately in appropriate time intervals, where the Banque de France monetary policy introduced in 1995 does not disturb the long-term links. All the individual relationships are cointegrated in corresponding intervals. The VAR and vector error correction (VEC) models are estimated and provide just a marginal improvement in RMSFE at the four-year horizon both for GDP deflator (down to 0.9%) and CPI (~1.1%) on the results obtained in the regression study. The VECM approach also allows re-estimation of the coefficients in the individual and generalized relationship between the variables both for cointegration rank 1 and 2. Comparison of the standard cointegration approach to the integral approach to the estimation of the coefficients in the individual and generalized relationships between the studied variables demonstrates the superiority of the latter. The cumulative inflation curve or inflation index, which is the actually measured evolution of price level, is much better predicted in the framework of the integral approach, which is a powerful tool for revealing true relationships between non-stationary variables and can be potentially used for rejection of spurious regression. The cumulative curves allow avoiding obvious drawbacks of the VECM representation and cointegration tests – increasing signal to noise ratio after differentiation and severe dependence on statistical properties of error terms. The confirmed validity of the linear lagged relationship between inflation, unemployment and labor force change indicates that since 1995 the Banque de France has been wrongly applying the policy fixing the monetary growth to the reference value around 4.5%. As a result of the policy, during the last ten years unemployment in France was twice as large as the one dictated by its long-term equilibrium link to labor force change. This increased unemployment compensates the forced price stability