Exercise: inflation and GDP deflator

You have the following table containing information about country Y's GDP deflator, nominal, and real GDP. If the base year is 2015, fill in the blanks and then find the annual inflation rate for each year.

Year	Nominal GDP	GDP Deflator	Real GDP
2015	$23,457	100	$23,457
2016	$25,752	...	$23,943
2017	$25,982	108.1	...
2018	$26,016	...	$25,431.1
2019	$26,323	105.5	...

Solution:

Year	Nominal GDP	GDP Deflator	Real GDP	Inflation rate
2015	$23,457	100	$23,457	n.a
2016	$25,752	107.6	$23,943	7.6%
2017	$25,982	108.1	$24,035.2	0.45%
2018	$26,016	102.3	$25,431.1	-5.37%
2019	$26,323	105.5	$24,950.6	3.13%

GDP deflator for the year 2018:

$\textit{GDP deflator }_{2018}= \frac{ \$26,016}{ \$25,431.1} \cdot 100\approx 102.3$

Real GDP for the year 2017:

$\textit{Real GDP }_{2017}= \frac{ \100}{ \108.1} \cdot \$25,982\approx \$ 24,035.2$

General formula to find real GDP by re-arranging the GDP deflator formula:

$\textit{Real GDP }_{i}= \frac{ \100}{ \textit{GDP deflator}_i} \cdot \textit{Nominal GDP }_i$

Notice that the sub-index i is for the year.

The (annual) inflation rate is simply the growth rate of prices from a year to its previous year:

$\textit{Inflation rate }_{i}= \frac{ \textit{GDP deflator}_i - \textit{GDP deflator}_{i-1}}{\textit{GDP deflator}_{i-1}} \cdot 100$

Inflation rate of the year 2018:

$\textit{Inflation rate }_{2018}= \frac{ 102.3 - 108.1}{108.1} \cdot 100\approx -5.37%$

Notice that in 2018 country Y experienced a negative inflation rate (i.e deflation). This means that from 2017 to 2018 prices dropped by about 5.3%.

Comments

Econometrics: Bivariate population model

Hello I'm finally back from my extended break. I thought that we should start studying Econometrics. Let's begin by analyzing a simple bivariate regression. Assume that this equation describes the relationship between two variables X and Y. We say that Y is the dependent variable, whereas X is the independent variable. In other words, we assume that Y (the output) depends on X (the input). Epsilon is the error term, it represents other factors that affect Y. The error term must be uncorrelated with the variable X so that we do not need to include them in our regression, and thus the coefficient of X (beta) should not change, even though Epsilon also determines Y. beta-0 is the constant term. It tells us what would be Y if X=0. beta-1 is the effect on Y if X changes by one unit. To see this, assume X=education is a continuous function, let's take the derivative of Y=wage with respect to X: Thus, if education goes up by one unit, we should expect, on average, wage to go up

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP). Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest rate,

Econometrics: OLS estimates

Let X and Y be column vectors and the sample has the size n: The vector beta contains both the coefficient of X as well as the coefficient for the intercept. This is equivalent to writing this equation: We will assume that the expected value of the error term is 0 (this can be done by construction), and that X is uncorrelated to epsilon. Assume the following is for population data. Let's prove that statement: Since we know that the covariance between X and epsilon is 0, it follows that the expected value of X times the error term must also be 0. Since we do not have access to the actual expected value of the distribution, let's use the sample data instead: The hat on the covariance signifies that this is a MM estimator. Let's use the fact that the sample mean of epsilon is also equal to 0, then: Using the estimation for the covariance and that the expected value of the error term equals 0: Then we have: To get this result, you must use the properties of the summation op

Economics and Statistics

Search This Blog