Macroeconomic Stabilization When the Natural Real Interest Rate Is Falling

Abstract

The authors modify the Dynamic Aggregate Demand-Dynamic Aggregate Supply model in Mankiw's widely used intermediate macroeconomics textbook to discuss monetary policy when the natural real interest rate is falling over time. Their results highlight a new role for the central bank's inflation target as a tool of macroeconomic stabilization. They show that even when the zero lower bound is not binding, a prudent central bank must match every decrease in the natural real interest rate with an equal increase in the target rate of inflation in order to stabilize the risk of the economy falling into a deflationary spiral, which is an acute case of simultaneously falling output and inflation in which the economy's self-correcting forces are inactive.

Keywords:

• intermediate macroeconomics
• natural interest rate
• secular stagnation
• zero lower bound

• JEL codes E12
• E52
• E58

Notes

¹See Summers (2014a) and the collection of papers in Teulings and Baldwin (2014).

²Current editions of prominent intermediate macroeconomics textbooks (e.g., Mankiw 2013; Blanchard and Johnson 2013; Jones 2011; and Mishkin 2011) all discuss the ZLB, and all make the point that expansionary fiscal policy works at the ZLB, whereas expansionary monetary policy (at least of the conventional kind) does not. However, these textbooks do not explain the implications for macroeconomic stabilization of changes in the natural real interest rate. Carlin and Soskice (2015, Section 3.3.3) provide a detailed account of the deflationary spiral.

³The positively sloped segment of the DAD curve captures the idea that falling inflation is a special nightmare at the ZLB. As nominal interest rates cannot be reduced any further, any decline in inflation means an increase in the real interest rate, which in turn reduces aggregate demand and output.

⁴Several central banks, including the Swiss National Bank, the European Central Bank, and the Danish National Bank, have recently adopted a negative nominal interest rate policy and as a result, the zero lower bound is not a firm lower bound. Negative nominal interest rates are not an issue for our analysis, however, because the only assumption needed for our theoretical results to carry through is that nominal interest rates are bounded from below. The floor value, whether positive or negative, is inconsequential. The negative nominal interest rates charged by banks reflect the cost of storage, and because of competitive pressure, this cost is unlikely to become much greater than 1 percent of deposit, thereby creating a floor on nominal interest rates (Cecchetti and Schoenholtz 2014).

⁵In the extreme scenario where the natural real interest rate has fallen into negative territory, the economy could experience a deflationary spiral even though current inflation is positive (and presumably low).

⁶Fiscal stimulus also can reverse a deflationary spiral, as shown in Buttet and Roy (2014), but tax cuts and/or increases in government purchases necessarily require increases in government borrowing, which may not always be an available option, especially in a weak economy and especially if the government has already piled up so large a debt that private lenders would be leery of lending it more. Therefore, there is a need to avoid getting into a deflationary spiral in the first place, and to avoid a deflationary spiral tomorrow, it is necessary to ensure that today's inflation stays above the negative of the natural real interest rate, which is the danger level.

⁷Chadha and Perlman (2014), who analyzed the Gibson Paradox, note that in the presence of an uncertain natural rate, the need to stabilize the banking sector's reserve ratio can lead to persistent deviations of the market rate of interest from its natural level and consequently long-run swings in the price level.

⁸Note that real interest rates have been declining in the United States since the 1980s with steady decreases in the estimated natural real interest rate, but central banks have not raised their inflation targets during that period. (Even the Bank of Japan's recent move in this direction was to increase its inflation target from 2 percent to a mere 3 percent.) This unwillingness must be reexamined in the light of our article.

⁹In his address to the National Association for Business Economics and elsewhere, Summers (2014b, 67, 69) cautioned that even though the ZLB is not technically binding, low nominal and real interest rates undermine financial stability in various ways. The financial stability channel is not present in our article.

¹⁰Eichengreen (2014) emphasized four different causes of secular stagnation in his review essay: slower growth of technological progress (Gordon 2014); stagnant aggregate demand (Summers 2014b; Krugman 2014); the failure of countries like the United States to invest in infrastructure, education, and training; and finally atrophy of skills caused by long-term unemployment and forgone on-the-job training (Crafts 1989; Gordon and Krenn 2010). It would be very hard (let alone undesirable) to write an article which encompasses all aspects of secular stagnation, so we focus on analyzing only one aspect of secular stagnation.

¹¹A recent International Monetary Fund (IMF) report (IMF 2014) cited three main reasons for the decline in real rates since the mid-1980s: (a) higher saving rates in emerging market economies, (b) greater demand for safe assets reflecting the rapid reserve accumulation of emerging market economies as well as increased riskiness of equity relative to bonds, and (c) a sharp and persistent decline in investment rates in advanced economies since the global financial crisis. All three factors lead to greater saving propensities and lower investment propensities.

¹²Knut Wicksell (1898/1936, 102) offered the following definition for the natural real interest rate: “There is a certain rate of interest on loans which is neutral in respect to commodity prices, and tends neither to raise nor to lower them. This is necessarily the same as the rate of interest which would be determined by supply and demand if no use were made of money and all lending were effected in the form of real capital goods.” More recently, Kocherlakota (2014) referred to the natural real interest rate as the mandate-consistent real interest rate.

¹³Laubach and Williams (2003) used maximum likelihood to estimate changes in the natural real interest rate over time, while the equilibrium results in Barsky, Justiniano, and Melosi (2014) are derived from solving a dynamic utility-maximization problem. We believe that the technical and critical thinking skills needed to fully understand these two modeling techniques are beyond the skill set that students possess when they take their intermediate macroeconomics courses at most colleges.

¹⁴There are potential econometric issues with estimating changes in the natural rate using equation (1), such as co-integration of the variables, which could affect our estimates for the natural rate of interest. For the sake of space, however, and because our article proposes an innovation for intermediate macroeconomics courses, we do not discuss econometric issues related to estimating changes in the natural real interest rate here. Rather, we leave this discussion for an upper elective course on econometrics or time series analysis.

¹⁵Note that an increase in the real interest rate leads to a decrease in aggregate demand, as in the standard IS curve. For the graphical analysis in the rest of the article, we will make the simplifying assumption: for all t.

¹⁶The negative feedback loop between output and inflation is the mechanism that leads to a deflation-induced depression, as previously explained by Fisher (1933) and Krugman (1998). In normal times, when nominal interest rates are positive, the central bank can afford to cut interest rates following a negative demand shock to provide short-run stimulus to the economy. When the ZLB is binding, however, cutting rates is not feasible, and real interest rates spike up as a result of lower inflation. Higher real interest rates in turn depress the economy further, which put further pressure on real rates, which depress the economy further, and so on and so forth.

¹⁷The DAS curve through R″ has not been drawn for simplicity.

¹⁸To see the logic behind the unstable nature of the deflationary long-run equilibrium, D, and the deflationary spiral, see pages 46 and 47 of Buttet and Roy (2014). We saw above in figure 2 how an economy starting at R″ moves to R in the next period and further towards O in subsequent periods. It is straightforward to see the workings of the deflationary spiral by repeating that analysis, but starting at D′ instead of R″. Buttet and Roy (2014) emphasize the need to keep inflation above − ρ, and discuss how fiscal and monetary policy can be used (a) to stop inflation from falling below − ρ and thereby precipitating a deflationary spiral, and (b) to raise inflation above − ρ after it has already fallen below that level, thereby ending the deflationary spiral. They show that as the only way out of a deflationary spiral once it has begun is fiscal stimulus. Now, fiscal stimulus usually involves a tax cut or an increase in government purchases or both, and this usually requires an increase in government borrowing. And such borrowing, especially in conditions of economic weakness, may not be possible, especially for a government that has already borrowed a lot and is, therefore, treated warily by private lenders. That is why it is crucial that π_{t − 1} < −ρ be avoided at all costs.

¹⁹See figure 2 of Buttet and Roy (2014) for a more detailed explanation.

²⁰Recall our discussion of the stability result in Buttet and Roy (2014): if inflation falls below the negative of the natural real interest rate, the economy will thereafter be in a deflationary spiral (if there are no further shocks or parameter changes), with output and inflation falling repeatedly.

²¹A detailed discussion of this dynamic adjustment is provided in Mankiw (2013, 449–53).