2.1 A Simple Keynesian Model: The Setup

We propose a simple Keynesian model showing that revisions in expected future income affect short-term equilibria. The model assigns a key role to money hoarding, as money hoarded subtracts from aggregate demand, thereby decreasing the marginal propensity to spend (MPS).⁷ This is not in any way original. For instance, at the beginning of the XVIII century John Law explained that economic slumps occur when “subjects [. . .] hoard up those signs of transmission as a real treasure, being induced to it by some motive of fear or distrust”; Law appears to have even referred to the self-fulling nature of a negative change in expectations about future output when he expressed that “I always call blind [. . .] because it stops a circulation that puts a State to a loss, and which is more likely than anything else to bring that poverty which they fear, both upon others and to themselves”. A similar view was held by Thomas Joplin (a merchant and economic pamphleteer), who in the early XIX century explained that “[A] demand for money in ordinary times, and a demand for it in periods of panic [. . .] are diametrically different. The one demand is for money to put into circulation; the other for money to be taken out of it”.⁸ In the same vein, Keynes (1936) questioned the validity of Say’s law—that supply creates its own demand—in a monetary economy, because people can hoard money instead of purchasing goods, and this is indeed what people would do when prospects about future income deteriorate, resulting in a decrease of effective demand and MPS.

Our model describes a monetary economy in which fiat money plays the role of unit of account, has fixed nominal value, and is accepted as a mean of payment for goods and factor services. Given that money is readily accepted, it can be hoarded as a hedge against uncertain future conditions. In the model, only money for hoarding is modeled, while money used in transactions is assumed to “circulate”.⁹ This means that money in circulation is assumed to be used for transactions (i.e., to pay for factors of production or goods), but when money is hoarded, it is excluded from circulation.

We assume that the economy is closed and that it is populated by a few economic forecasters, and many workers and entrepreneurs.¹⁰ Perfect competition is prevalent in goods and factor markets, and thus, neither individual workers nor entrepreneurs can affect market outcomes. There are three periods: period 0, in which the economic forecasters receive signals of different quality in sequence and make forecasts; period 1 (interchangeably referred to as short-term in throughout the paper); and period 2 (or long-term). All economic transactions occur in periods 1 and 2, taking as given the forecasts produced in period 0.¹¹

Both workers and entrepreneurs have identical utility functions over present and future consumption. Workers supply a constant amount of labor and receive a wage for their services. In the short term, they decide how to allocate their labor income between consumption and money hoarding, while in the future they use labor income plus any hoarded money balances (in real terms) to consume.¹² Entrepreneurs maximize profits in the short term, demanding labor and using a fixed (given) capital stock. They allocate short-term profits among consumption, investment, and money hoarding. Investment in the short term determines the economy’s capital stock in the long term. In the long term, entrepreneurs’ consumption is financed by the real rents on capital plus the real value of money hoarded in the short term.

We introduce nominal rigidities by assuming that nominal wages are fixed in the short term. Fixed short-term nominal wages will result in unemployment if effective demand is sufficiently low.¹³ Sticky short-term nominal wages are the only nominal rigidity in the model—other prices are fully flexible both in the short term and in the long term.

The long-term real return to capital depends on total factor productivity (TFP), which is assumed to be stochastic. There exist two states of the world, good and bad. In the bad state of the world (which occurs with probability 0 < π^S < 1), TFP growth rate is lower than in the good state of the world. Workers and entrepreneurs do not have private information about the probability of the bad state of the world. To account for that probability, they use a consensus forecast (assumed to be the same for all agents), which ensures the model’s internal consistency.

Given a consensus forecast, the representative consumer (either worker or entrepreneur) maximizes the following utility function:

where j = W, F denotes either workers (W) or entrepreneurs (F), $C_1^j$ represents short-term consumption and $C_2^j$ long-term consumption, 0 < β ≤ 1 is the consumer’s subjective time preference, and E is the expectation operator.

Workers maximize their utility function subject to the following constraints:

where i = L, H denotes either the bad state of the world (L) or the good state of the world (H), P_t represents the price level, W_t denotes nominal wages, L_t is labor demand, and $M_1^{j,h}$ is money hoarding. Labor income in the short term depends on the exogenous level of money wages and on labor demand (and thus the supra-index d). If the (endogenously determined) level of short-term prices is too low, labor demand may be lower than the (fixed) supply $(L_1^d\le \overline{L}>0)$, and thus result in short-term unemployment.¹⁴

Entrepreneurs maximize their utility function subject to the following constraints:

where Π₁ denotes (nominal) short-term profits, and R₂ and K₂ represent the (stochastic) nominal return of investment and real investment, respectively. The profit maximization problem in the short term takes the capital stock as given:

where 0 < σ ≤ 1 is the MPS.¹⁵ This problem is subject to the following constraints:

where y₁ denotes short-term output, K₁ > 0 is the short-term (given) capital stock, A₁ > 0 is the exogenous neutral TFP in the short term, and 0 < α < 0 is the production function parameter. Importantly, short-term profit maximization takes the aggregate MPS as given. The short-term MPS is defined as:

The rationale to include the MPS in the short-term profit maximization is that entrepreneurs know that in an interior equilibrium (i.e., given a sufficiently high probability of the bad state of the world), money is hoarded. The counterpart of money hoarding is unsold production, which materializes in the accumulation of inventories. Short-term monetary profits are determined by the volume of effective sales for consumption and investment (i.e., by effective demand). Given that unsold production is costly, entrepreneurs try to anticipate the level of the aggregate MPS, which is of course determined by aggregate expectations about the bad state of the world. Put differently, entrepreneurs’ monetary costs are linked to total output, but receive monetary income only for sales, which is always below output in an interior equilibrium.

In the long term, profit maximization features all factors of production as variable:

and is subject to the following constraint:

where $0<A_2^L<A_2^H$. The level of prices in the short term results from a quantitative theory of money-type equation. The monetary authority determines the supply of money in period $M_1=\overline{M}>0$ (which could be interpreted as, e.g., discount window loans from the central bank), but money circulating in the economy is endogenous. Accordingly, the level of prices in the short term results from the interaction between exogenous money supply, endogenous money hoarding, and the level of output:

In the long term, the monetary authority conducts any operations necessary to ensure that inflation is aligned to a given inflation target (φ), and monetary policy is assumed to be fully credible. Given these assumptions, the long-term price level is given by:

The short-term price level determines the short-term level of real wages. If the probability about the bad state of the world in the consensus forecast is high enough, positive aggregate money hoarding results in a lower short-term price level. Money hoarding reduces money in circulation (in a loose sense, it limits the volume of credit), and thus, it results in a lower short-term price level. A lower price level combined with sticky wages may result in unemployment.

In an equilibrium (i.e., for each consensus forecast about the bad state of the world), workers pick $c_1^W,c_2^{W,i},and{M}_1^{W,h}$; entrepreneurs (as consumers) pick $c_1^F,c_2^{F,i},M_1^{F,h},and{K}_2$; and entrepreneurs (as profit maximizers) pick $y_1,L_1^d,y_2^i,K_2^{i,d},and{L}_2^{i,d}$. Monetary policy and money hoarding determine P₁ and $P_2^i$; in the long term, clearing in the market for factors of production (i.e., $L_2^{i,d}=\overline{L}>0and{K}_2^{i,d}=K_2$) determine values for $R_2^{i}and{W}_2^i$, while in the short term $W_1=\overline{W}>0,K_1=\overline{K}>0,and{L}_1^d\le \overline{L}$. The budget constraints for workers and entrepreneurs and the first order conditions (FOCs) derived from the problems faced by consumers and entrepreneurs close the model.

In particular, the workers’ FOC refers to the equalization of short-term marginal utility of consumption and expected long-term (discounted) marginal utility of consumption:

The entrepreneurs’ FOCs (as consumers) are two. The first one—like that of workers—equals short-term marginal utility of consumption to expected long-term (discounted) marginal utility of consumption:

The second FOC equals the marginal rate of substitution of consumption among different states of the world in the long term to the odds ratio times the difference in expected returns of different assets (namely money and capital):

The entrepreneurs’ FOC (as profit maximizers) in period 1 determines short-term output:

Note that short-term output depends (through the MPS) on effective demand, giving the model its Keynesian flavor. Short-term output determines labor demand as follows:

The entrepreneurs’ FOC (as profit maximizers) in period 2 determine their long-term demand of labor and capital, given factor prices and TFP in different states of the world:

2.2 Expectations about Long-Term Output

The model assumes that the consensus forecast used by economic agents is produced by N economic forecasters before other economic transactions take place. This assumption is somewhat artificial, but instrumental to provide a more straightforward connection with the empirical analysis. Forecasts are produced according to the game of incomplete information in Banerjee (1992). In what follows, we employ the same game structure but we deviate from it with respect to the interpretation of the results.

In period 0, the (structural or fundamental) probability of the bad of the state of the world, π^s, is unknown, but falls within $0<\overline{\pi }\le {\pi }^S\le \overline{\pi }<1$. Economic forecasters are divided between those who receive a signal and those who do not receive any signal. Those who receive a signal learn the correct value of π^S with probability 0 < ψ < 1, and otherwise receive a wrong signal. The probability distribution among signals is uniform, and since the range above is continuous, the probability of any given signal within the range is zero. If a forecaster guesses the correct probability of the bad state of the world, she receives compensation ξ > 0; in all other cases, she receives an equal, strictly positive, but lower compensation than if she was right. The aggregate cost of compensating the forecasters, Γ, is in the range 0 ≤ Γ ≤ ξN. To simplify the model, it is assumed that ξN is negligible with respect to the size of the economy, and that the cost to compensate the forecasters is distributed proportionally among the population in a lump-sum fashion in period 2. These assumptions ensure that the impact of forecasters’ activity is only limited to establishing the expectations about the bad state of the world that are used by the population. Forecasters make forecasts in sequence, and the turn of each forecaster to make her forecast is randomly assigned. A forecaster learns her type at the moment in which her turn comes, which is when she is able to observe the forecasts that were made before her turn. The structure of the game and Bayesian rationality are common knowledge.¹⁶

This setup allows for multiple equilibria depending on the ordering and signals that economic forecasters receive, many of them being the result of herding around wrong values of the bad state of the world. The consensus forecast (i.e., the average across forecasters) may thus potentially reflect herding, which results from the specific way in which individual information is aggregated. Although there are many other ways in which the model could have accounted for uncertainty about the actual probability of the bad state of the world and the formation of expectations, the mechanisms featured here account for problems with aggregation of information and herding that appear common in the way agents form aggregate expectations about the future. Thus, if herding results in a lower (higher) probability of the bad state of the world than the fundamental one, then there is an optimistic (pessimistic) equilibrium, with “animal spirits” working to increase current consumption, investment, and income.

2.3 Simulation

We now proceed to assign arbitrary values to the parameters, and exogenous and predetermined variables in order to simulate the results of the model for alternative values of expected long-term output. Table 1 reports the values assigned to variables and parameters and presents a summary of the results. A consensus forecast consistent with a probability of the bad state of the world above the true probability could be interpreted as a “pessimistic” forecast, while a consensus forecast that is below the actual probability of the bad state of the world could be interpreted as “optimistic”. Thus, the expectation of an increased probability of the bad state of the world, and the expectation of lower long-term output growth are broadly equivalent statements. Needless to say, in a pessimistic equilibrium, short-term output, consumption, and investment are lower than the levels that would be justified by fundamentals (and the converse for an optimistic equilibrium).

Table 1:

Numerical Example

Source: Authors’ calculations. Notes: E(y₂) refers to the expected growth rate of long-term real output, μ refers to the unemployment rate, and I₁ refers to aggregate investment (i.e., capital stock in period 2).

Table 1:

Numerical Example

Expectation about long-term output
E(y2)	0.06	0.04	0.01	−0.01	−0.04	−0.06
Selected endogenous variables
y1	3.15	3.13	3.10	3.08	3.05	3.03
μ	0.21	0.22	0.23	0.24	0.25	0.26
M1	1.67	1.82	1.96	2.10	2.24	2.38
σ	0.91	0.90	0.89	0.88	0.88	0.87
C1	2.31	2.27	2.23	2.19	2.16	2.13
I1	0.56	0.55	0.54	0.53	0.51	0.50
Parameters
β	0.99	0.99	0.99	0.99	0.99	0.99
α	0.30	0.30	0.30	0.30	0.30	0.30
Exogenous/predetermined variables
M1	20.00	20.00	20.00	20.00	20.00	20.00
φ	0.02	0.02	0.02	0.02	0.02	0.02
W1	3.30	3.30	3.30	3.30	3.30	3.30
A1	1.30	1.30	1.30	1.30	1.30	1.30
$A_2^L$	0.40	0.40	0.40	0.40	0.40	0.40
$A_2^H$	2.10	2.10	2.10	2.10	2.10	2.10
K1	1.00	1.00	1.00	1.00	1.00	1.00
LS	4.50	4.50	4.50	4.50	4.50	4.50

Source: Authors’ calculations. Notes: E(y₂) refers to the expected growth rate of long-term real output, μ refers to the unemployment rate, and I₁ refers to aggregate investment (i.e., capital stock in period 2).

View Table

Table 1:

Numerical Example

Expectation about long-term output
E(y2)	0.06	0.04	0.01	−0.01	−0.04	−0.06
Selected endogenous variables
y1	3.15	3.13	3.10	3.08	3.05	3.03
μ	0.21	0.22	0.23	0.24	0.25	0.26
M1	1.67	1.82	1.96	2.10	2.24	2.38
σ	0.91	0.90	0.89	0.88	0.88	0.87
C1	2.31	2.27	2.23	2.19	2.16	2.13
I1	0.56	0.55	0.54	0.53	0.51	0.50
Parameters
β	0.99	0.99	0.99	0.99	0.99	0.99
α	0.30	0.30	0.30	0.30	0.30	0.30
Exogenous/predetermined variables
M1	20.00	20.00	20.00	20.00	20.00	20.00
φ	0.02	0.02	0.02	0.02	0.02	0.02
W1	3.30	3.30	3.30	3.30	3.30	3.30
A1	1.30	1.30	1.30	1.30	1.30	1.30
$A_2^L$	0.40	0.40	0.40	0.40	0.40	0.40
$A_2^H$	2.10	2.10	2.10	2.10	2.10	2.10
K1	1.00	1.00	1.00	1.00	1.00	1.00
LS	4.50	4.50	4.50	4.50	4.50	4.50

Source: Authors’ calculations. Notes: E(y₂) refers to the expected growth rate of long-term real output, μ refers to the unemployment rate, and I₁ refers to aggregate investment (i.e., capital stock in period 2).

As shown in Figure 1, if the expectation about long-term growth deteriorates (i.e., people expect an increased probability of the bad state of the world), then money hoarding increases, the MPS and effective demand (both aggregate consumption and investment) fall and short-term unemployment increases. Conversely, improved expected future economic prospects reduce money hoarding, increases the MPS, effective demand, and output, and reduces unemployment. In other words, a change in the consensus forecast has an effect on short-term economic variables in the direction of the forecast change, no matter whether the change in the forecast reflects an actual change in the underlying (structural) probability of the bad state of the world. Lower expected future productivity decreases investment (reinforcing the negative effect on long-term output), and results in a decline in current output, further decreasing permanent income. A change in expectations is enough to affect output, consumption, investment, and unemployment.

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Expected Long-Term Growth and Short-Term Economic Performance

Citation: IMF Working Papers 2018, 001; 10.5089/9781484336748.001.A001

Source: Authors’ calculations.

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3.1 Data

We rely on data from the International Monetary Fund’s (IMF) World Economic Outlook (WEO), released twice a year (in the spring and the fall). The WEO database consists of actual macroeconomic data and forecasts submitted by country teams and vetted by the IMF’s Research Department for both internal and multilateral consistency. The Spring WEO was released in May up through 2001 and in April thereafter; the fall version is typically released in October, and occasionally in September. Starting in 1990, every vintage contains forecast for the next five years. Given the production lags, forecasts for the spring publication are performed during February or March. Given this timeline, in the Spring WEO data for the previous year are an estimate or forecast for some countries. The Fall WEO is based on final information, therefore we use fall vintages from 1990 to 2016.

3.2 Empirical Model

Our empirical framework is similar to the one employed by Blanchard et al. (2017). Our dependent variable is defined as the deviation of, alternatively, the observed real consumption growth, c, or real investment growth, i, from its previous year growth forecast.¹⁷ Thus, for year t and country j, we calculate such deviations as:

and

where C and I are the levels of real consumption and real investment, respectively. Forecasts for consumption and investment must be as of a time in which the information to prepare the revised forecasts of potential real GDP growth is not available yet. In our case, we will use data of the Fall WEO of year t – 1.

To construct the expectation measure about the economy j, we take the forecast available in the Fall WEO of year t of potential real GDP growth, y^*, for year t + (N – 1) (with N = 5 being the WEO forecast horizon), and denote it by E_j,t(y_j,t+(N-1)). Then, we define the forecast revision as its difference with respect to the forecast published in the previous vintage of the Fall WEO (at time t – 1) for the same year t + (N – 1):¹⁸

Given that every Fall WEO contains forecasts for the next five years, we can generate up to four different variables depending on the forecasting horizon. However, with the objective of isolating structural changes far into the future from cyclical movements, we select the farthest computable revision as our favorite measure.

The specification employed here assumes that households and corporations adjust consumption and investment based on two sources of information. In proportion α, they learn about future potential output growth at the time of the Fall WEO publication of year t, hence adjusting consumption and investment over t. In proportion (1 — α), they learn about future potential output growth from the same information used by the IMF to produce the forecasts, therefore adjusting their consumption and investment already in t — 1.

Thus, similar to Blanchard et al. (2017), we specify the following reduced form equation for private consumption and private investment:

where γ is a constant term, β is an encompassing coefficient on the forecast revision term, μ_j and τ_t are the time- and country-fixed effects, and ∈_jt is a vector of residuals. To retrieve the value of α, equation (26) can be rearranged as:

where α = αβ/β.

The possibility of reverse causality when estimating equation (27) deserves further discussion. As in Blanchard et al. (ibid.), we argue that unexpected cyclical movements in private consumption growth and private investment growth are unlikely to affect forecasts of potential output growth far into the future. If this true, we can then identify a causal relationship. One could argue that the use of statistical methods to compute the potential output could introduce a spurious correlation between the forecast error in private consumption and investment growth and the forecast revision of potential output growth. However, the review of the estimation method used by the IMF in De Resende (2014) notes:

“Survey evidence shows that in the Fund’s medium-term forecasting the use of any particular individual forecasting method is much less universal than the use of judgment-understood as a set of information and knowledge, not necessarily quantitative in nature, that desk economists and mission chiefs accumulate about the countries on which they work.”

Furthermore, as a robustness test, we use estimates of potential output from the OECD’s Economic Outlook database, assuming that this breaks further the spurious link with private consumption and investment growth from the IMF’s WEO database.

In order to retrieve the dynamics of the effect of a change in expectations about the potential output growth on consumption and investment, we construct impulse response functions employing the local projection method of Jordà (2005). Thus, we estimate h sets of regressions of the form:

where α^h and β^h describe the response of $D_{j,t+h}^{c,i}$ to the shock at horizon h.

Different from Blanchard et al. (2017) that focus only on the United States, cross-country differences not captured by time- and country-fixed effects may play a role in determining the forecast error of private consumption and private investment growth. Thus, to check the robustness of the results to the inclusion of other covariates, we estimate:

where $D_{j,t}^x$ is a vector of control variables X_j,t expressed in terms of deviation with respect to their forecast, S_j,t is another vector of control variables, and δ and ψ are the relative coefficients.¹⁹

Some of the control variables may be co-determined with the dependent variables, with each affecting the other, which results in endogeneity. Thus, we estimate equation (27) using the System Generalized Method of Moments (S-GMM) estimator, which relies on a system of two simultaneous equations, one in levels (with lagged first differences as instruments) and the other in first differences (with lagged levels as instruments).²⁰,²¹

5.1 Baseline

Similar to Blanchard et al. (2017), we start with a baseline specification for both real private consumption growth and real private investment growth. This includes both the revision of potential output growth forecasts and the difference between its value in t + 1 and t, which allow to compute how much is learned at the time of the Fall WEO publication and how much at the time the same information is used by the IMF to produce its forecasts; country-fixed effects; and time-fixed effects. Table 3 reports the results of OLS estimations for the full sample (columns 1 and 2), AE (columns 3 and 4), and EMDE (columns 5 and 6).

Table 3:

Baseline Estimations

Source: Authors’ calculations. Notes: PC and PI denote private consumption and private investment, respectively. All estimations include country and time-fixed effects. ***, **, and * next to a number indicate statistical significance at 1, 5, and 10 percent, respectively.

Table 3:

Baseline Estimations

	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error
	Full sample	Full sample	AE	AE	EMDE	EMDE
$R_{t+1}^4-R_t^4$	0.874*** (0.239)	2.288*** (0.687)	0.875*** (0.253)	2.550*** (0.860)	0.930** (0.452)	2.178* (1.182)
$R_t^4$	1.872*** (0.365)	5.212*** (1.674)	2.493*** (0.440)	7.234*** (1.781)	1.391** (0.626)	3.871 (2.858)
Constant	−0.514* (0.281)	−4.969* (2.527)	−0.245 (0.283)	−5.249** (2.535)	−0.125 (1.063)	5.464* (3.186)
Observations	782	566	598	396	184	170
R2	0.199	0.187	0.332	0.274	0.082	0.124
Countries	89	83	36	33	53	50
α	0.467	0.439	0.351	0.353	0.669	0.563
β	1.872	5.212	2.493	7.234	1.391	3.871

Source: Authors’ calculations. Notes: PC and PI denote private consumption and private investment, respectively. All estimations include country and time-fixed effects. ***, **, and * next to a number indicate statistical significance at 1, 5, and 10 percent, respectively.

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Table 3:

Baseline Estimations

	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error
	Full sample	Full sample	AE	AE	EMDE	EMDE
$R_{t+1}^4-R_t^4$	0.874*** (0.239)	2.288*** (0.687)	0.875*** (0.253)	2.550*** (0.860)	0.930** (0.452)	2.178* (1.182)
$R_t^4$	1.872*** (0.365)	5.212*** (1.674)	2.493*** (0.440)	7.234*** (1.781)	1.391** (0.626)	3.871 (2.858)
Constant	−0.514* (0.281)	−4.969* (2.527)	−0.245 (0.283)	−5.249** (2.535)	−0.125 (1.063)	5.464* (3.186)
Observations	782	566	598	396	184	170
R2	0.199	0.187	0.332	0.274	0.082	0.124
Countries	89	83	36	33	53	50
α	0.467	0.439	0.351	0.353	0.669	0.563
β	1.872	5.212	2.493	7.234	1.391	3.871

Source: Authors’ calculations. Notes: PC and PI denote private consumption and private investment, respectively. All estimations include country and time-fixed effects. ***, **, and * next to a number indicate statistical significance at 1, 5, and 10 percent, respectively.

The results show that both the revision of potential output growth forecasts and its time difference are significant across country groups and for both real private consumption and investment growth. The only exception is the coefficient on the time difference in the real private investment growth equation for EMDE, but this is likely due to a reduced number of observations. For the full sample, these factors explain about one fifth of the variation in consumption and investment growth.

In the estimations for the full sample, the coefficient α—denoting how much agents learn about future potential output growth at the time of the Fall WEO publication of year t—is not too far from 0.5, suggesting that households and corporations learn about future potential output growth both at the time of the WEO publication and at the same time the IMF produces its forecasts. However, in the results for AE, α is substantially smaller than in the results for EMDE, suggesting that in the former (latter) economic agents learn mostly at the same time of the IMF (Fall WEO publication). This is consistent with the notion for which economic agents are more sophisticated in AE in that they have wider access to information about the potential output growth of the economy and a more refined ability to elaborate it than in EMDE. The coefficient for β ranges between 1.9 and 2.5 in the private consumption specifications, and between 3.9 and 7.2 in the private investment specifications. This implies that a 0.1 pp downward revision in the potential output growth forecast is associated with a 0.19 to 0.25 (0.39 to 0.72) percent reduction in private consumption (investment) growth. For the average country with a share of private consumption (investment) to GDP of 65 (16) percent, this would bring about a reduction in GDP growth by 0.09 to 0.16 (0.06 to 0.11) percent.

Figure 4 presents the scatter plots of the weighted average of the revisions to potential output growth forecasts in t and t + 1 against real private consumption and investment growth forecast error. Specifically, the measure of the horizontal axis is equal to $[(1-\alpha )R_{j,t}^{N-1}+\alpha R_{j,t+1}^{N-1}]$, where α takes the value in columns 1 and 2 of Table 3. The measures on the vertical axis are the ones described in equation (23) for the left panel and equation (24) for the right panel. Both panels depict a well-defined positive relationship, confirming that households and corporations increase demand to adjust to more optimistic expectations.

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Revisions in Potential Output Growth Forecasts and Consumption and Investment Forecast Error

(Percent)

Citation: IMF Working Papers 2018, 001; 10.5089/9781484336748.001.A001

Source: Authors’ calculations.

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Figure 5 shows the impulse response functions derived by applying the local projections method, which allow to appreciate the dynamic effect of better expectations. The black line one period after the shock displays the β coefficient of Table 3. Similarly, the red dot one period after the shock displays the α coefficient.²³ The red lines define the band of possible values of the α coefficient. In the case of real private consumption growth (first row of panels), the positive effect of an improvement in expectations phases out after two years for the full sample and AE, while it only lasts one year for EMDE. This also holds for the impact on private investment growth (second row of panels), with the exception of EMDE, for which the effect is not significant. The red dots provide information regarding the learning of economic agents over time. As expected, these red dots tend to approach one over time, consistent with the idea that as the time goes by, economic agents are increasingly informed by the WEO Fall publication.²⁴

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Responses to a One pp Upward Revision in the Potential Output Growth Forecast

(Percent)

Citation: IMF Working Papers 2018, 001; 10.5089/9781484336748.001.A001

Source: Authors’ calculations.Notes: The responses for EMDE are calculated on a shorter time span due to data limitations. The value for α is shown only when significant.

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5.2 Extensions

One can think of a series of factors that could shape non-linearities in the relationship between expectations and consumption and investment. As we discussed in Section 4, the GFC came with a great deal of uncertainty that may have changed the sensibility of economic agents to an improvement or a worsening of expectations. Similarly, households and corporations may adjust asymmetrically to worse and better expectations. Lastly, large revisions in expectations may produce non-proportional effects on consumption and investment.

Table 4 tests for these possible non-linearities by adding interaction terms to the specification to be estimated. In columns 1 and 2, we interact our variables of interest with a dummy that takes value one after the GFC to test for differential effects since then. In columns 3 and 4, we add an interacting dummy that takes value one when revisions to potential output growth forecasts are negative, hence testing if economic agents react differently to pessimistic expectations with respect to positive ones. Finally, in columns 5 and 6, we add the expectations terms squared to proxy large revisions. For every column, we calculate α and β with and without interaction terms.

Table 4:

Interactions

Source: Authors’ calculations. Notes: PC and PI denote private consumption and private investment, respectively. All estimations include country and time-fixed effects. ***, **, and * next to a number indicate statistical significance at 1, 5, and 10 percent, respectively.

Table 4:

Interactions

	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error
$R_{t+1}^4-R_t^4$	1.102*** (0.393)	3.116*** (1.072)	0.710** (0.342)	2.484* (1.341)	0.868*** (0.229)	2.358*** (0.705)
$R_t^4$	2.498*** (0.724)	8.546*** (2.329)	1.167** (0.526)	3.375 (3.382)	1.817*** (0.356)	5.252*** (1.855)
$D^{afterGFC}*(R_{t+1}^4-R_t^4)$	−0.324 (0.485)	−1.139 (1.324)
$D^{afterGFC}*\left(R_t^4\right)$	−0.873 (0.843)	−4.569 (3.055)
DafterGFC	−0.130 (0.526)	4.251 (2.697)
$D^{pessimism}*(R_{t+1}^4-R_t^4)$			0.234 (0.433)	−0.221 (1.616)
$D^{pessimism}*\left(R_t^4\right)$			1.134 (0.775)	3.053 (3.564)
Dpessimism			0.042 (0.249)	−0.205 (0.861)
${(R_{t+1}^4-R_t^4)}^2$					0.186* (0.101)	−0.577 (0.478)
${\left(R_t^4\right)}^2$					−0. 238 (0.	0. (0.410)
Constant	−0.542* (0.290)	−4.860* (2.448)	−0.399 (0.305)	−4.176 (2.587)	−0.668** (0.317)	−4.639* (2.560)
Observations	782	566	782	566	782	566
R 2	0.202	0.197	0.203	0.193	0.205	0.195
Countries	89	83	89	83	89	83
α w/o interaction	0.441	0.365	0.608		0.478	0.449
β w/o interaction	2.498	8.546	1.167		1.817	5.252
α w/ interaction	0.441	0.365	0.608		0.580	0.449
β w/ interaction	2.498	8.546	1.167		1.817	5.252

Source: Authors’ calculations. Notes: PC and PI denote private consumption and private investment, respectively. All estimations include country and time-fixed effects. ***, **, and * next to a number indicate statistical significance at 1, 5, and 10 percent, respectively.

View Table

Table 4:

Interactions

	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error	Dep: real PC growth forecast error	Dep: real PI growth forecast error
$R_{t+1}^4-R_t^4$	1.102*** (0.393)	3.116*** (1.072)	0.710** (0.342)	2.484* (1.341)	0.868*** (0.229)	2.358*** (0.705)
$R_t^4$	2.498*** (0.724)	8.546*** (2.329)	1.167** (0.526)	3.375 (3.382)	1.817*** (0.356)	5.252*** (1.855)
$D^{afterGFC}*(R_{t+1}^4-R_t^4)$	−0.324 (0.485)	−1.139 (1.324)
$D^{afterGFC}*\left(R_t^4\right)$	−0.873 (0.843)	−4.569 (3.055)
DafterGFC	−0.130 (0.526)	4.251 (2.697)
$D^{pessimism}*(R_{t+1}^4-R_t^4)$			0.234 (0.433)	−0.221 (1.616)
$D^{pessimism}*\left(R_t^4\right)$			1.134 (0.775)	3.053 (3.564)
Dpessimism			0.042 (0.249)	−0.205 (0.861)
${(R_{t+1}^4-R_t^4)}^2$					0.186* (0.101)	−0.577 (0.478)
${\left(R_t^4\right)}^2$					−0. 238 (0.	0. (0.410)
Constant	−0.542* (0.290)	−4.860* (2.448)	−0.399 (0.305)	−4.176 (2.587)	−0.668** (0.317)	−4.639* (2.560)
Observations	782	566	782	566	782	566
R 2	0.202	0.197	0.203	0.193	0.205	0.195
Countries	89	83	89	83	89	83
α w/o interaction	0.441	0.365	0.608		0.478	0.449
β w/o interaction	2.498	8.546	1.167		1.817	5.252
α w/ interaction	0.441	0.365	0.608		0.580	0.449
β w/ interaction	2.498	8.546	1.167		1.817	5.252

Source: Authors’ calculations. Notes: PC and PI denote private consumption and private investment, respectively. All estimations include country and time-fixed effects. ***, **, and * next to a number indicate statistical significance at 1, 5, and 10 percent, respectively.