Part I. Considering how the data may be generated using economic theory.
- The quantity theory of money suggests a relationship (in the long run) between money growth and inflation. Explain the economic intuition behind this relationship.
In the long run,
The quantity theory of money (M) means an increase in the quantity of money brings an equal percentage rise in the price level. Velocity of circulation (V) is the average number of times money is used annually to buy goods and services that makeup GDP. GDP is the price level (P) multiplied by real GDP (Y): GDP = PY. V is determined by: V = PY/M.
The equation of exchange becomes M if the quantity of money does not influence V or Y. This tells us that the price level in the long run is determined by M: P = M(V/Y), where (V/Y) is independent of M, meaning a change in M equals a proportional change in P.
The equation of exchange can also be expressed in growth rates: Money growth rate + Rate of velocity change = Inflation rate + Real GDP growth rate. The rate of velocity change, in the long run, is not affected by the money growth rate. The rate of velocity change is approximately zero. Therefore, in the long run: Inflation rate = Money growth rate – Real GDP growth rate.
In the long run, with full employment, real GDP equals potential GDP, so the real GDP growth rate equals the potential GDP growth rate. The growth rate might be influenced by inflation but is likely small and therefore assume it is zero. Inflation is correlated with money growth as the real GDP growth rate is given and does not change when the rate changes.
Part II. Describing the data
- Describe the two variables (i.e. Inflation and money growth). For each variable, use an appropriate chart (i.e. histogram) and the following descriptive statistics to support your answer: mean, standard deviation, maximum, minimum.
Money growth is defined as Money growth = Inflation + Real GDP growth. Money growth is a direct cause of inflation.
The diagram above shows a histogram of Money Growth from the Coursework Data for 2019-20. One measure of central location is the mean. The mean for money growth is 14.95(424) to 2 decimal places. The standard deviation, a measure of dispersion, for the money growth data is 6.80 (2. d.p), which indicates a low amount of variation, meaning the values tend to be close to the mean for money growth. The maximum number in the data recorded for money growth is 33.34 (2. d.p). While the minimum number for money growth is 4.34 (2. d.p).
Inflation is defined as a constant increase in the general price level in an economy, resulting in a rise in living costs as the prices of goods and services increase. This means the price level is constantly rising as money loses value.
The diagram above shows a histogram of Inflation from the Coursework Data for 2019-20. One measure of central location is the mean. The mean for inflation is 5.98 to 2 decimal places. The mean for inflation is significantly lower than the mean calculated for money growth above. The standard deviation for inflation is 3.81 (2. d.p), which indicates a low amount of variation, so the values tend to be close to the mean. The standard deviation is also lower than the standard deviation for money growth. The maximum and minimum for inflation are also substantially lower than for money growth.
Produce an XY scatter chart with inflation on the y-axis and money growth on the x-axis. Describe the key features of this chart. Calculate (and interpret) the correlation between the two variables.
The correlation between inflation and money growth is 0.73, therefore, the XY scatter chart above shows the relationship between inflation and money growth has a positive correlation. The correlation is positive when the values increase together, and the correlation is negative when one value decreases as the other increases. The XY scatter chart is suitable for examining the relationship between pairs of variables and in this instance the relationship between inflation and money growth from the data set ‘Coursework data 2019-20’.
Part III. Exploring relationships within your data
4. Consider the linear equation below.
- Where is inflation, is money growth, and are fixed parameters, and is a standard error term. Using the economic theory outlined in (1), explain the statistical hypotheses that would be sensible for the values of the parameters where the dependent variable, is the independent variable, and the growth rate of inflation expected if money growth () was zero. Would expect a positive relationship for the parameter.
Estimate the parameters and using observed values of Y and X and obtain a generalized relationship between Y and X. We identify estimates for, and as, respectively, and. To analyze whether X determines Y, need to test the hypothesis that. is essentially the value of Y when X=0 and is the unit change in Y for a unit increase in X.
A two-sided test, where, if I can reject the hypothesis that, then X explains Y. Testing at a 95% confidence interval. If the confidence interval does not include 0 – we can reject the hypothesis at a 5% significance level.
5. Run a regression for the equation displayed in (4).
- Interpret the results of this regression. Your answer should consider relevant economic theory, the estimated parameters, the t-statistics/p-values for the estimated parameters, the hypotheses you stated in (4), and the statistics.
The hypothesis stated above is a two-sided test, testing at the 95% confidence interval.
The confidence intervals are as stated:
As 0.334 (lower 95%) > 0.0000, we can reject at the 5% significance level as the 95% confidence interval does not include 0. This means that Y, inflation, explains X, money growth.
Coefficients’ estimate
Standard error
t-statistic
p-value (Sig.)
Lower 95%
Upper 95%
Constant
- -0.162
- 0.629
- -0.257
- 0.798
- -1.410
- 1.087
Money growth
- 0.410
- 0.038
- 10.708
- 0.000
- 0.334
- 0.487
Both and rejecting at the 5% significance level suggest a positive and significant relationship. Therefore, is consistent with the expectation from the quantity theory of money that there is a relationship, in the long run, between money growth and inflation. The coefficients’ estimate, is 0.410, which means that one unit of change in inflation represents a 0.41 % change in money growth.
This means the linear equation becomes. For example, if: And if: Therefore, the difference, 0.41, represents the change in Y when you change one unit of X. This is the change in inflation when there is one unit of money growth.
To examine if a single explanatory variable has explanatory power, the t-statistic test is used. However, to test if all the explanatory variables have any explanatory power for the dependent variable, the test is used. This is done through the p-value.
The p-value can also be used to work out the confidence level: The p-value can be used to determine if the relationship observed in the sample can exist in the larger population. The F-statistic is 114.658 and the P-value is 0.000, and therefore below the 5% significant level, so evidence to reject the null hypothesis and conclude. Thus, no correlation is made, so there is no association between the changes in inflation and the shifts in money growth, meaning there is insufficient evidence to conclude there is an effect at the population level.
Provides an assessment of the model’s explanatory power. Adding (potentially) relevant variables into a model would tend to increase as more of the variation in Y would be explained. The statistic is 0.537, which measures the fit of the regression model, The fit of the regression model is good as it is closer to 1 than to 0. The variation in X, money growth, explains 53.7% of the variation in Y, inflation. If so, then X does not have any explanatory power for Y. However, as the model above shows, there is some explanatory power at 53.7%. Although a high obtained from a few observations might not be of significance, a low from many observations might indicate a small but genuine explanatory power.
Part IV. Reflect upon your analysis
- 6. Identify and briefly discuss potential limitations of your econometric model (e.g. aspects related to sample size, possible omitted variables, etc.)
The sample should be representative of the population, so be as large as possible. The sample size is 101 countries, however, there are more than 101 countries in the world. The sample size will affect how close is to as having more data points will improve the accuracy of the estimation. The problem with the statistical properties, which should be representative of the population, is unknown so we can only estimate and make assumptions. However, by calculating the confidence interval and hypothesis tests we can gauge how accurate our estimates are. The spread of prediction errors will affect how close is to as smaller errors will improve the accuracy of the estimates. The spread of values of the explanatory variable (X) will also affect how close is to as having a larger spread improves the accuracy of estimation.
References
- Koop, G., 2013. Analysis of Economic Data. 4th edition.
- Parkin, M., Powell, M., and Matthew, K., 2014. Economics. 9th edition. Harlow: Pearson Education UK.
- Sloman, J., Garratt, D., and Guest, J., 2018. Economics. 10th edition. Harlow: Pearson Education Limited.
- Inflation and Money Growth relationship
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Money Growth and Inflation Essay.
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