RDP 2010-05: Direct Effects of Money on Aggregate Demand: Another Look at the Evidence 2. Empirical Analysis

We follow Nelson (2002) and estimate empirical aggregate demand specifications in which a measure of de-trended real output, ỹ_t, is a function of its own lags, lags of a measure of the real interest rate, , and lags of a measure of real money growth, . Appendix A contains a full description of the data and its sources.

We update the empirical analysis of Nelson (2002) for the United States and the United Kingdom and then extend it to Australia and Japan. We do this for two reasons. First, we have 42 additional quarters of data. Second, and more importantly, the more recent data include some observations for which short-term nominal interest rates approach their zero lower bound. More observations always sharpen parameter estimates and extreme observations more so.

The regressions we report here, like those of Meltzer (2001) and Nelson (2002), are based on the growth rate of the real monetary base, although we have also considered a range of other measures of money, from narrow measures like currency to broader measures like M2.^[4] As a measure of the output gap, we use the estimate of the Congressional Budget Office for the United States, and we quadratically de-trend the log of real output for the other countries.

The first column of Table 1 estimates Nelson's specification over his sample period and the second column over the full sample 1961:Q1−2009:Q4 for the United States. Our results for the comparable sample are very close to his. For example, Nelson's estimate of the sum of real money growth coefficients is 0.33 while our estimate over that same sample period is 0.37. We estimate an associated long-run effect of 4.42 while Nelson's estimate is 3.05.^[5] Over the full sample, however, the sum of real money growth coefficients becomes insignificant. Although a formal test rejects the exclusion of the money terms over the sample period 1961:Q1–1999:Q2 (p-value = 0.001), it fails to do so over the full sample (p-value = 0.354).

Table 2 contains results using Nelson's preferred specification for the United Kingdom.^[6] These results are also in line with his over the sample period 1977:Q1–1999:Q2; we find that the sum of real money growth coefficients is positive and statistically significant at the 5 per cent level. As for the United States, a formal test rejects the exclusion of the money terms over the sample period 1977:Q1–1999:Q2, but fails to do so over the full sample.

Table 3 shows estimates of a similar specification for Australia. For both sample periods, individual real money growth terms and the sum of real money growth terms are insignificant, as are the long-run effects of real money growth. Formal tests fail to reject the exclusion of money terms.

Table 4 contains estimates with a similar specification for Japan.^[7] We find that over the period 1972:Q1 to 1999:Q2, the sum of real money growth coefficients is positive (0.184) and statistically significant with an associated long-run effect of 9.82. Over the full sample, the sum of real money growth terms becomes insignificant and F-tests (equivalent to the ones conducted above) suggest that real money growth should not be included in the regression.

For the United States and the United Kingdom, the most recent data is potentially relevant to identify any direct effects of money because it contains observations for which the nominal interest rate stays more or less constant (close to the zero lower bound) but the real money base increases sharply. If we thought that these regressions were able to capture the structural relationship between money and aggregate demand, then the results from this section would weaken the evidence for direct effects of money on aggregate demand. However, as we show below, these regressions are not reliable. The estimates, whatever they may be, should not be interpreted as evidence for, nor evidence against, the existence of direct effects; the coefficients in these regressions cannot be given a structural interpretation. This means, in particular, that the insignificant coefficients on the more recent data on real money growth for the United States and the United Kingdom do not imply that quantitative easing policies failed.

Because changes in policy often lead to changes in the correlations between variables, the instability of the estimated real money growth coefficients for Japan, the United Kingdom and the United States, is consistent with the idea that these regressions are misspecified.

Footnotes

The results are broadly similar. [4]

The long-run effect of money growth on output corresponds to the cumulative impact that a one percentage point increase in real money growth has on output over time. [5]

Following the UK Money Market Reform on 18 May 2006, the Bank of England discontinued the series for M0, the Bank's main narrow money measure, and instead continued publishing series for ‘reserve balances’ at the Bank of England to accompany ‘notes and coin’ in circulation. To account for this, we compute the growth rate of real money using M0 prior to 2006:Q2, and then use the growth rate of the sum of ‘reserve balances’ and ‘notes and coin’. [6]

We followed Nelson (2002) in using quadratically de-trended real output. For Japan, however, this method results in a positive estimate of the output gap towards the end of the sample. Consequently, we considered different measures of potential output, such as HP-filtered output and a measure published by the OECD. The results are qualitatively the same. [7]