## Tag Archives: Macroeconomics

Using a variety of identification methods and samples, I find that in most cases private spending falls significantly in response to an increase in government spending. These results imply that the average GDP multiplier lies below unity.

## Sargent on Calibration

Thomas Sargent and his wife Carolyn at Santorini, Greece.

“Calibration is less optimistic about what your theory can accomplish because you’d only use it if you didn’t fully trust your entire model, meaning that you think your model is partly misspecified or incompletely specified, or if you trusted someone else’s model and data set more than your own. My recollection is that Bob Lucas and Ed Prescott were initially very enthusiastic about rational expectations econometrics. After all, it simply involved imposing on ourselves the same high standards we had criticized the Keynesians for failing to live up to. But after about five years of doing likelihood ratio tests on rational expectations models, I recall Bob Lucas and Ed Prescott both telling me that those tests were rejecting too many good models. The idea of calibration is to ignore some of the probabilistic implications of your model but to retain others. Somehow, calibration was intended as a balanced response to professing that your model, though not correct, is still worthy as a vehicle for quantitative policy analysis.”

## External Debt and Country bankruptcy

Open economies can borrow resources from the rest of the world and lend them abroad. This way a temporary income shortfall can avoid a sharp contraction of consumption and investment. Similarly, a country with ample savings can lend and participate in productive investment project oversees. Because international borrowing and lending are possible, there is no reason for an economy’s consumption and investment to be closely tied to its current output.

The change in the net foreign assets of a country (the change in the value of its net claims on the rest of the world) is called the current account balance. The latter is said to be in surplus if the economy as a whole is lending, and in deficit if the economy is borrowing. The current account balance over period t is defined as

$CA_t = B_{t+1}-B_t$

where $B_{t+1}$ is the value of the economy’s net foreign assets at the end of a period t. Equivalently:

$CA_t = Y_t + r_t B_t - C_t - G_t - I_t$

where $Y_t$ is the country’s national product, $r_t B_t$ is the interest earned on foreign assets acquired by the economy, $C_t$ is the private consumption, $G_t$ is the government consumption and $I_t$ is the investment.

Note also that the national saving is defined as

$S_t = Y_t + r_t B_t - C_t - G_t$

Hence $CA_t = S_t - I_t$. The national saving in excess of domestic capital formation flows into net foreign asset accumulation. So do protective measures (such as trade tariffs) improve the current account? That depends on how those measures affect savings and investment.

Note that the current account balance is equivalently the net exports of good and services. A country with positive net exports must be acquiring foreign assets of equal value while a country with negative net exports must be borrowing an equal amount to finance its deficit.

Tagged , ,

## Why is the Hodrick-Prescott filter often inappropriate?

The Hodrick-Prescott (HP) filter is the optimal estimator of the trend component in a smooth trend model with signal-to-noise ratio parameter fixed at 1/1600. It gives the detrended observations, $X_{t}$,  for large samples and t not near the beginning or end of the series

$\displaystyle X_{t}= \left[ \frac{(1-L)^{2}(1-L^{-1})^{2}}{\bar{q}_{\zeta}+ (1-L)^{2}(1-L^{-1})^{2}}\right] Y_{t}$

where $\bar{q}_{\zeta}= \sigma_{\zeta}^{2} / \sigma_{\epsilon}^{2}$.

Bear in mind that if the  smooth trend model was believed to be the true model there would be no reason to apply the HP filter. The filtered data of a smooth trend model contain nothing more than white noise. The belief here is clearly different.

We can easily show that the gain from the detrending filter is given by:

$G(\lambda) = \frac{4(1-cos \lambda)^{2}}{\bar{q}_{\zeta}+4(1-cos \lambda)^{2}} = \frac{16sin^{4}( \lambda /2)}{\bar{q}_{\zeta}+16sin^{4}( \lambda /2)}$

Note that the smaller the ${\bar{q}_{\zeta}}$ the more the filter concentrates on removing low frequencies.

Gain for HP filter

## Phillips Curve with UC 1 – Australian Cycles

The Phillips curve is not dead!