Small-Country Mundell–Fleming (IS/LM/BP) Model Predictions Under Both Fixed and Flexible Exchange Rates: Evidence from Australia and S. Korea

Abstract

The small-country IS/LM/BP (Mundell–Fleming) model predicts that monetary policy is totally ineffective in countries with fixed exchange rates and super-effective in countries with flexible exchange rates. Furthermore, this model predicts that, under fixed exchange rates, fiscal policy is stronger the more mobile capital is in terms of moving in and out of the country, but it predicts the opposite for countries with flexible exchange rates; fiscal policy is stronger the less mobile capital is. This paper tests these predictions by applying reiterative truncated projected least squares (RTPLS) to quarterly data from Australia and the Republic of Korea when they employed fixed and then flexible exchange rates. RTPLS produces a separate total derivative estimate for each observation, where the differences in these estimates are due to omitted variables. By doing so, RTPLS makes it possible to see how the estimated relationship changes over time. I found that the effectiveness of monetary policy was not zero under fixed exchange rates but that its effectiveness did increase when Australia and S. Korea switched to flexible exchange rates. Under flexible exchange rates, I found that the effectiveness of fiscal policy was statistically higher than zero for both countries, which conflicts with the assumption of perfect capital mobility.

1. Introduction

The small-country Mundell–Fleming model (IS/LM/BP) explains how the exchange rate regime affects the effectiveness of fiscal and monetary policies. In this model, a change in the money supply (monetary policy) has no effect under a fixed exchange rate. In contrast, under a flexible exchange rate, the impact of a change in the money supply is magnified by the international adjustment that it causes. Specifically, economists expect an increase in the money supply to cause an increase in the Gross Domestic Product (GDP), and the small-country IS/LM/BP model predicts that what happens in the international money market makes the resulting increase in the GDP larger if the exchange rate is flexible.

The case for a change in fiscal policy (changes in government spending or taxing) is more complex than that for changes in monetary policy. The small-country IS/LM/BP predicts that fiscal policy is stronger the more mobile foreign capital is in terms of entering and exiting the country under a fixed exchange. The opposite is true for a flexible exchange rate regime; fiscal policy is stronger the less mobile foreign capital is in terms of entering and exiting the country under a flexible exchange rate. The reasons for these predictions are explained in Section 2 and tested in Section 4 of this paper. The reliability of Mundell–Fleming predictions is extremely important to any policy makers who want to decrease unemployment, decrease inflation, increase growth, or stabilize the economy that they are responsible for (if that economy is connected to the rest of the world).

Most of the empirical studies testing the predictions of a small-country IS/LM/BP model assume perfect capital mobility (for examples, see Nenkova and Kovachevich 2022; Ortiz and Rodriguez 2002; Wang et al. 2019; and Asogwa et al. 2014). However, Leightner (2024a, 2024b) examined how US fiscal and monetary policy affected Australia’s and the Republic of Korea’s (South Korea’s) GDP when these countries had fixed and then flexible exchange rates. When Australia and Korea had flexible exchange rates, his results fit the predictions of a large-country IS/LM/BP model, which assumes perfect capital mobility. However, when Australia had a fixed exchange rate, the large-country IS/LM/BP predictions did not hold (but they did hold for Korea when Korea had a fixed exchange rate); instead, Australia under a fixed exchange rate acted like a country with relatively immobile foreign capital. Furthermore, Leightner (2024a) showed that the assumption of relatively immobile capital fits the historical record of Australia under a fixed exchange rate, as Australia struggled with controlling foreign capital flows at that time. Leightner (2024a, 2024b) focused solely upon how US fiscal and monetary policy affected Australia’s and South Korea’s GDP; he did not discuss how Australia’s and South Korea’s own fiscal and monetary policies affected their GDPs, which is the subject of this paper. Australia and South Korea were picked for this analysis because they were the only countries in the world for which the OECD data site had sufficient data for both fixed and flexible exchange rate regimes.

Leightner (2024a, 2024b) used reiterative truncated projected least squares (RTPLS), a solution to the omitted-variable problem of regression analyses. He points out that, to correctly use traditional regression techniques to test the predictions of the Mundell–Fleming model, a researcher would need to create, justify, and estimate a model that explains the interest rates, exchange rates, exports, imports, capital flows, and GDP of all important countries in the world. Such a task is impossible. However, such herculean tasks are not required to use RTPLS. RTPLS uses the relative vertical position of observations as a measure of the combined influence of all omitted variables. RTPLS produces a separate slope estimate for every observation, where differences in these slope estimates are due to omitted variables. RTPLS is further explained in Section 3 of this paper.

The conclusions of this paper include the following: (1) the effectiveness of monetary policy increased for both countries when they switched to flexible exchange rates; (2) even under flexible exchange rate regimes, the effectiveness of monetary policy diminished over time for both countries; (3) the effectiveness of fiscal policy was not zero under flexible exchange rate regimes, which conflicts with the assumption of perfect capital mobility; and (4) the effectiveness of fiscal policy diminished over time for both countries under flexible exchange rates. This last result is consistent with the capital mobility of both countries increasing over time but never achieving perfect capital mobility.

The remainder of this paper is organized as follows: Section 2 explains the small-country Mundell–Fleming predictions under both fixed and flexible exchange rates, assuming different degrees of capital mobility. Section 3 briefly explains the intuition underlying the statistical technique used (RTPLS). Section 4 presents the empirical results, and Section 5 concludes the paper.

2. Small-Country IS/LM/BP Predictions

The most complex predictions for the small-country Mundell–Fleming model concern the effectiveness of fiscal policy. Consider Figure 1, a three-diagram representation of the domestic economy of South Korea, whose currency is called the won (w). In this diagram, “r” is the interest rate; “PL” is the price level (a measure of inflation); “I” is investment in tools, machinery, and buildings; “QAS” is the aggregate quantity supplied, which equals the GDP; and “QAD” is aggregate quantity demanded. In Figure 1, an increase in Korean government spending causes an increase in aggregate demand (Step 1). The increase in aggregate demand drives up the GDP (Step 2), which causes the transactions’ demand for money to rise (Step 3), which drives up Korea’s interest rate (Step 4). The increase in Korea’s GDP (Step 2) causes Korea’s imports to rise because part of the income is spent on imports. Meanwhile, the increase in interest rates (Step 4) causes more foreign capital to flow into Korea and fewer Koreans to move their assets abroad.

The effects on the international money market of a rise in Korea’s GDP causing Korea’s imports to increase is shown in Figure 2. The price of a Korean won is how many dollars it takes to purchase a won, which is measured on the y-axis. “S(M)” is the supply of won to the international money market from Korean imports. “D(X)” is the demand for won from other nations purchasing Korean exports. “Dnt” is the demand for won for “non-trade” purposes (in other words, for any reason other than to purchase Korean exports). “Snt” is the supply of won for “non-trade” purposes (for any reason other than for Korea to import). Thus, “Dnt-Snt” is the net non-trade demand for the Korean won. Dnt would include any demand for the won so that (1) foreigners can invest in Korea, (2) foreigners can travel to Korea, (3) Koreans living abroad can repatriate income back to Korea, etc. Likewise, Snt would include any supply of Korean won to the international market so that (1) Koreans can invest abroad, (2) Koreans can travel abroad, (3) foreigners living in Korea can repatriate income abroad, etc. By using three lines to explain the international money market, the effects on imports and exports can be separated from the effects of international capital flows, which makes explaining the small-country IS/LM/BP model easier. Also, using three lines makes it clear that what is financing Korea’s current trade deficit (imports exceeding exports) is Dnt being greater than Snt. Leightner (2015) was the first to present this three-line approach to the international money market.

Figure 2 shows the effects of an increase in GDP (Figure 1, Step 2) on the international money market (El-Shagi et al. 2022, conducts a meta-analysis of this), and Figure 3 shows the effects of an increase in Korea’s interest rate (Figure 1, Step 4) on the international money market. An increase in Korea’s interest rate (r) would cause foreigners to want to move their assets into Korea to obtain Korea’s higher interest rate, causing Dnt to rise. Meanwhile, Koreans would want to keep more of their assets in Korea instead of investing abroad, causing Snt to fall. Both a rise in Dnt and a fall in Snt would cause the D(X) + Dnt − Snt line to increase. If capital is completely mobile in and out of a country, then the effect shown in Figure 3 overwhelms the effect shown in Figure 2. However, the IS/LM/BP model can handle four different degrees of capital mobility.

Figure 4 depicts what an increase in government spending would do in the small-country IS/LM/BP model under two of the four possible degrees of capital mobility. The IS curve shows all the interest rate (r) and GDP (Y) combinations that would produce equilibrium in the real market (the right-hand side graph in Figure 1). An increase in government spending increases AD, causing an increase in GDP, which appears as a rightward shift in the IS curve in Figure 4. The LM curve shows all the interest rate and GDP combinations that produce equilibrium in the domestic money market. The BP line shows all the interest rate and GDP combinations that would produce equilibrium in the international money market.

If capital is prevented from entering or exiting a country, then the BP line would be vertical. If capital can freely enter and exit a country without any impediment, then the BP line would be horizontal at the world’s interest rate. If the movement of capital in and out of a country is less sensitive to the interest rate than the domestic money market is, then capital is “relatively immobile”, as depicted in Figure 4A, with the BP line being steeper than the LM line. If the movement of capital in and out of a country is more sensitive to the interest rate than the domestic money market is, then capital is “relatively mobile”, as depicted in Figure 4B, with the BP line being flatter than the LM line.

To use the small-country IS/LM/BP model, a researcher must (1) determine the mobility of capital because that degree of mobility determines how the BP line is drawn, (2) draw the IS/LM/BP diagram so that all three lines intersect at the same point (this assumes that the economy is in equilibrium in all three areas (the real market, the domestic money market, and the international money market), (3) show the initial shift, and (4) show the international adjustment.

The initial shift always destroys the three-way equilibrium, and something must adjust to re-establish a new three-way equilibrium. If the exchange rate is fixed, then the LM curve adjusts to create a new three-way equilibrium. If the exchange rate is flexible, then the BP line adjusts horizontally and the BP line pulls the IS line with it in the same horizontal direction (it is very important that the BP line is looked at to determine the direction of the adjustment, not the IS curve).

Notice that if the country depicted in Figure 4 had a fixed exchange rate, then LM would need to shift LEFT for Figure 4A and RIGHT for Figure 4B. Likewise, if the country depicted in Figure 4 had a flexible exchange rate, then the BP line would have to shift RIGHT in Figure 4A and LEFT in Figure 4B. The IS/LM/BP adjustment is as simple as looking to see which way LM must shift if the exchange rate is fixed or which way the BP line must shift if the exchange rate is flexible. However, the reason LM and BP lines must shift in opposite directions for the relatively immobile and relatively mobile cases is based on Figure 2 and Figure 3.

If capital is completely immobile (making the BP line vertical), then an increase in government spending causing the interest rate to rise would not cause the D(X) + Dnt − Snt line to shift; thus, the shift shown in Figure 3 would not occur. However, the increase in government spending causing GDP to rise would still cause an increase in imports, as shown in Figure 2. If the exchange rate is fixed at E1 in Figure 2, then a surplus of won on the international market results. If the Korean government does nothing about this international surplus of won, then the value of the won (USD/KRW) would fall. To prevent the USD/KRW from falling, the Korean government must buy up the surplus won on the international market, paying for it with Korea’s foreign reserves. The purchased won is pulled out of circulation, causing the Korean money supply to fall. A fall in Korea’s money supply shifts the LM curve to the left.

If capital is relatively immobile, relatively mobile, or perfectly mobile, then both the effects shown in Figure 2 and Figure 3 result from an increase in Korean government spending. However, if capital is relatively immobile, then the effect shown in Figure 2 is bigger than the effect shown in Figure 3. In such a case, which is depicted in Figure 4A, LM will shift to the left, creating a new equilibrium for the reasons given in the previous paragraph. If, however, capital is relatively mobile (as shown in Figure 4B) or perfectly mobile, then the effect from an increase in government spending shown in Figure 3 is bigger than the effect shown in Figure 2. In these cases, the increase in government spending causes the Korean interest rate to rise, which causes more foreign capital to move into Korea (Dnt rises) and less Korean capital to leave Korea (Snt falls), causing the D(X) + Dnt − Snt line to shift up. As Figure 3 shows, this causes an international shortage of Korean won. If the Korean government does nothing about this shortage, then the value of the won (USD/KRW) will rise. To prevent the USD/KRW exchange rate from rising, the Korean government can print more won and use it to purchase more foreign reserves. Because the newly printed won is put into circulation, the Korean money supply increases, which shifts the LM curve down and to the right. The LM curve shifting down and to the right is exactly what is needed in Figure 4B to achieve a new three-way equilibrium.

If the exchange rate is fixed, then the more mobile capital is into and out of Korea, the greater the effectiveness of fiscal policy. If capital is perfectly immobile (making BP vertical), then the leftward shift in LM to a new three-way equilibrium would cause an increase in government spending to have no final effect on GDP. If capital is perfectly mobile in and out of Korean, then the resulting rightward shift in LM would make an increase in government spending super strong. This is why the literature that assumes perfect capital mobility views fiscal policy as especially powerful under a fixed exchange rate (for example, see Nenkova and Kovachevich 2022).

The opposite of the above conclusion is found for countries with flexible exchange rates; the less mobile capital is moving in and out of Korea, the stronger fiscal policy is. If capital is perfectly immobile, then an increase in government spending driving up interest rates would not cause the D(X) + Dnt − Snt line to shift up; thus, the effect shown in Figure 3 would not occur. However, the effect shown in Figure 2 would occur. Under a flexible exchange rate, USD/KRW would fall, which would shift the BP line to the right. A fall in USD/KRW would also cause a movement down both the D(X) and the new S(M) lines, causing an increase in exports and a fall in imports (from what imports would have been if the exchange rate had not fallen). A rise in exports and a fall in imports would shift the aggregate demand curve to the right, causing the IS curve to also shift right. If capital is relatively immobile, the effect shown in Figure 3 is more powerful than the effect shown in Figure 2, resulting in both the BP and IS lines shifting right, as needed for Figure 4A.

If capital is relatively or perfectly mobile, then the effect of an increase in government spending shown in Figure 3 is more powerful than the effect shown in Figure 2, which causes the exchange rate to rise. An increase in the exchange rate causes the BP line to shift left. The USD/KRW exchange rate rising causes a movement up along both the D(X) and S(M) lines, resulting in a fall in exports and a rise in imports. Falling exports and rising imports would cause aggregate demand to fall, causing the IS curve to shift left. Thus, when capital is relatively mobile (as shown in Figure 4B) or perfectly mobile, BP must shift left and the BP pulls IS with it to the left. If capital is perfectly mobile (making the BP line horizontal), then the leftward shift in BP is invisible (a horizontal line shifting horizontally cannot be seen), but the leftward shift in the IS curve would put GDP back to the initial level, making fiscal policy totally ineffective under a flexible exchange rate and perfect capital mobility. Under a flexible exchange rate, fiscal policy is stronger the less mobile capital is in and out of a country.

Small-country IS/LM/BP predictions for the effectiveness of monetary policy are simpler than the IS/LM/BP predictions for the effectiveness of fiscal policy. Figure 5 depicts the domestic effects of an increase in the money supply using the three-diagram domestic model. Notice that an increase in the money supply would cause the interest rate to fall and GDP to rise. The increase in GDP would cause S(M) to increase, as shown in Figure 2. However, the fall in the interest rate would cause the opposite of Figure 3. Under a fixed exchange rate, Figure 2 shows a surplus of Korean won, and the opposite of Figure 3 would also show a surplus of Korean won. To maintain the fixed exchange rate, the Korean government would need to purchase the resulting surplus of won, pulling it out of circulation, which would decrease the money supply. In Figure 6A,B, LM would need to shift back to its initial position to achieve a new three-way equilibrium. Thus, trying to increase Korea’s money supply under a fixed exchange rate would require an equal drop in the money supply, making monetary policy totally ineffective, no matter how mobile capital is going in and out of Korea.

When Korea has a flexible exchange rate, the BP line moves to create a new three-way equilibrium and the BP line pulls the IS line horizontally with it. Thus, in Figure 6, the BP line would need to shift right and it would pull IS with it right no matter the mobility of capital. However, the more mobile capital is in and out of Korea, the stronger monetary policy is under a flexible exchange rate.

The literature is dominated by studies that assume perfect capital mobility; however, as demonstrated above, the IS/LM/BP model can clearly handle cases where capital is less than perfectly mobile. For examples of studies that focus on capital mobility, see Nenkova and Kovachevich (2022) and Wang et al. (2019). A very popular intermediate macroeconomic textbook that builds its model around perfect capital mobility is by Mankiw (2010).

3. Materials and Methods

This paper reports estimates that test the IS/LM/BP predictions under different degrees of capital mobility. In order to capture the influence of omitted variables, reiterative truncated projected least squares (RTPLS) was used. If a researcher estimates Equation (1) while ignoring Equation (2), the resulting estimate of β₁ is a constant, when in truth, β₁ varies with q_i, which ruins all estimates and all statistics (the αs and βs are coefficients to be estimated, X is the independent variable, Y is the dependent variable, and u is random error). This constitutes an “omitted variable” problem where “q_t” represents the combined influence of all omitted variables plus any random variation in β₁ itself.

Y_t = α₀ + β₁X_t + u

(1)

β₁ = α₁ + α₂q_t

(2)

One convenient way to model the omitted variable problem is to combine Equations (1) and (2) to produce Equation (3).

Y_t = α₀ + α₁X_t + α₂ X_t q_t + u_t.

(3)

Equation (7) can be derived from Equation (3), as shown below (Leightner 2015).

(dY_t/dX_t)^True = α₁ + α₂q_t            Derivative of (3)

(4)

Y_t/X_t = α₀/X_t + α₁ + α₂q_t + u_t/X_t     (3) divided by X

(5)

α₁ + α₂q_t = Y_t/X_t − α₀/X_t − u_t/X_t    (5) rearranged

(6)

(dY_t/dX_t)^True = Y_t/X_t − α₀/X_t − u_t/X_t    From (4) and (6)

(7)

If an estimate for α₀ could be found, then it could be used to calculate a separate slope estimate for each observation using Equation (8).

(dY_t/dX_t)^{^} = Y_t/X_t − α₀^_/X_t

(8)

Variations in the slope estimates for different observations would be due to omitted variables. The error due to such a procedure is shown in Equation (9).

(dY_t/dX_t)^True − (dY_t/dX_t)^{^} = (α₀^ − α₀)/X_t − u_t/X_t    From (7) and (8)

(9)

The u_t/X_t term in Equation (9) should be extremely small because random error, u_t, is usually tiny relative to the size of X_t, making u_t/X_t even smaller if X_t is greater than zero. This implies that the accuracy of calculating a separate slope estimate for each observation using Equation (8) depends primarily upon the accuracy of the α₀ estimate.

Leightner et al. (2021) explore three ways to obtain an estimate for the α₀ of Equation (1) which is then plugged into Equation (8) in order to estimate total derivatives that capture the influence of omitted variables. These three ways are (I) using Ordinary Least Squares (OLS) to estimate Equation (1), (II) using Generalized Least Squares (GLS) to estimate Equation (1), and (III) using reiterative truncated projected least squares (RTPLS), which produces separate slope estimates for layers of the data by peeling the data down layer by layer and then peeling the data up, after which Equation (10) is used with the resulting layer slopes ((dY_t/dX_t)^) to estimate α₀. Leightner (2015) explains the math that underlies RTPLS.

(dY_t/dX_t)^ − Y_t/X_t = −α₀^_/X_t    (8) rearranged

(10)

Leightner et al. (2021) show that when the omitted variable problem is ignored by estimating Equation (1) using OLS, the resulting estimate for β₁ is approximately α₁ + α₂E[q_t], which leaves an “error” for the t = ith observation of approximately α₂X_i(q_i − E[q_i]) + u_i. The three methods of correcting for the omitted-variable problem explored by Leightner et al. (2021) would be better than ignoring the omitted-variable problem if |(α₀^ − α₀)/X_i − u_i/X_i| from Equation (9) is less than |α₂{q_i − E[q_i]}|. Aitken (1935) implies that the GLS estimate of α₀ will be the Best Linear Unbiased Estimate (BLUE) if the q_is are i.i.d. N(μ_q, σ_q²) because GLS is BLUE for heteroscedastic models, and Leightner et al. (2021) show that Equation (3) is a heteroscedastic model if q_i is unknown. However, the use of Leightner et al.’s (2021) methods do not require that q be normally distributed. Indeed, these methods impose no restrictions on the structure of q: q can represent forces that affect the slope by being logged, squared, quadrupled, or in any other form. Furthermore, q shows the combined influence of all omitted variables on the slope where some omitted variables could be negatively related, some positively related, some logged, some squared, etc. What is essential for these methods (as it is for normal regression analysis) is that the relationship between the dependent variable (Y) and the known independent variable (X) be correctly modelled. However, q itself does not need to be modelled, and it can be complex, non-linear, discontinuous, etc.

Leightner et al. (2021) test the three methods using simulations (Leightner 2015 also provides simulation tests but solely for RTPLS). Leightner et al. (2021) run sets of 5000 simulations each for the 27 combinations of 100 observations, 250 observations, and 500 observations, with the omitted variable making a 10-percent difference to the slope, a 100-percent difference to the slope, and a 1000-percent difference to the slope, and with random error being zero, one percent, and ten percent. Leightner et al. (2021) gives the name “Variable Slope Ordinary Least Squares” (VSOLS) to the process of using OLS to estimate α₀, which is then plugged into Equation (8) to generate a separate slope estimate for each observation and the name “Variable Slope Generalized Least Squares” (VSGLS) to the process using GLS to estimate α₀, which is then plugged into Equation (8).

VSGLS and RTPLS noticeably outperformed VSOLS in all simulations. VSGLS and RTPLS outperformed using OLS while ignoring the omitted-variable problem except for the case where the omitted variable makes only a ten-percent difference to the slope and random error is ten percent. When the importance of the omitted variable was 100 times as big as random error, using OLS while ignoring omitted variables produced approximately 35 times the error of both VSGLS and RTPLS. When the importance of the omitted variable was 10 times as big as random error, then using OLS while ignoring omitted variables produced approximately 3.8 times the error of both VSGLS and RTPLS.

When there was no random error, then RTPLS produced less than half the error of VSGLS. This last result implies that, since VSGLS is BLUE, RTPLS must be better than BLUE when there is no random error, which is reasonable if RTPLS is better at capturing non-linear aspects of the data or if the omitted variables are not normally distributed.

Confidence intervals for RTPLS estimates can be calculated using the central limit theorem.

Confidence interval = mean ± (s/√n)t_{n−1, α/2}

(11)

In Equation (11), ‘s’ is the standard deviation, ‘n’ is the number of observations, and t_{n−1, α/2} is taken off the standard t table for the desired level of confidence. Leightner et al. (2021) used an estimate along with the 4 estimates before it and a 95% confidence level to create a moving confidence interval (much like a moving average) for a given set of RTPLS estimates. This 95% confidence interval can be interpreted as meaning that there is only a five-percent chance that the next RTPLS estimate will lie outside of this range if omitted variables maintain the same amount of variability that they recently had.

It is very important to realize that RTPLS produces total derivative estimates, not partial derivative estimates. Traditional regression analysis produces partial derivatives that show how the dependent variable (Y) is affected by each independent variable (X) while holding all other included independent variables constant. RTPLS produces total derivative estimates that capture all the ways that the dependent and independent variables are related, holding nothing else constant. Thus, RTPLS estimates are not a substitute for traditional regression estimates; instead, RTPLS estimates are compliments of traditional estimates in that these methods produce different sets of useful information. The more useful information policy makers have, the better they can help achieve good economic goals. One of the major advantages of RTPLS applied to time series or panel data is that RTPLS estimates can be plotted over time to show how omitted variables have affected the estimated relationship over time.

4. Results

Monthly data were downloaded from the OECD data base on Australia’s and South Korea’s money supply (M1) indices, where June 2015 was equal to 100. Quarterly data for M1 were calculated by averaging the three monthly values for each quarter. Quarterly data on Australia’s and South Korea’s Gross Domestic Product (GDP) and government consumption (G) were also downloaded from the OECD data website. The GDP and government consumption data were in millions of Australian dollars for Australia and in millions of Korean won for South Korea. The Australian data start in quarter 3 of 1960, and the South Korean data start in quarter 3 of 1962. The data for both countries go through the fourth quarter of 2022.

The numeric values for d(GDP)/d(M1) are confusing to interpret because the money supply data used are an index with June 2015 = 100. In June 2015, a one-unit change in M1 is the same as a one-percent change in M1, but a one-unit change in Australia’s M1 index in the third quarter of 1962 (when the M1 index was 0.5039) is equivalent to a 198-percent change in M1 and a one-unit change in Korea’s M1 index in the third quarter of 1962 (when the M1 index was 0.006567) is equivalent to a 15,228-percent increase in M1. To report results that are less confusing, the money supply results [d(GDP)/d(M1)] were multiplied by (M1/GDP) to produce elasticities: %d(GDP)/%d(M1). However, the numeric values for d(GDP)/d(G) are straightforward to interpret and were not converted to elasticities. For both countries, separate estimates were carried out for their fixed versus flexible exchange rate regimes.

The empirical results are presented in

Table 1. The empirical results.

	%dGDP/%dM1		dGDP/dG			%dGDP/%dM1		dGDP/dG			%dGDP/%dM1		dGDP/dG
	Austr.	Korea	Austr.	Korea		Austr.	Korea	Austr	Korea		Austr.	Korea	Austr.	Korea
1960.3	0.06		13.52		1981.2	0.90	1.01	5.91	8.22	2002.1	1.35	1.59	5.70	12.10
1960.4	0.06		12.90		1981.3	0.90	1.01	5.86	8.42	2002.2	1.34	1.58	5.82	12.01
1961.1	0.06		12.83		1981.4	0.90	1.01	6.01	8.77	2002.3	1.34	1.57	5.73	12.07
1961.2	0.04		12.34		1982.1	0.91	1.01	6.04	8.64	2002.4	1.33	1.56	5.76	11.70
1961.3	0.04		11.87		1982.2	0.91	1.01	5.71	8.85	2003.1	1.33	1.55	5.66	11.54
1961.4	0.05		12.10		1982.3	0.91	1.01	5.85	8.58	2003.2	1.33	1.55	5.67	11.35
1962.1	0.08		12.25		1982.4	0.91	1.01	5.61	8.01	2003.3	1.32	1.54	5.69	11.27
1962.2	0.10		12.25		1983.1	0.91	1.01	5.39	8.92	2003.4	1.31	1.52	5.73	11.26
1962.3	0.11	2.40	12.35	7.81	1983.2	0.91	1.01	5.56	8.94	2004.1	1.30	1.51	5.78	11.19
1962.4	0.13	2.23	12.28	10.64	1983.3	0.92	1.01	5.56	9.07	2004.2	1.30	1.50	5.69	10.96
1963.1	0.16	2.06	12.25	11.39	1983.4	0.92	1.01	5.68	9.08	2004.3	1.30	1.49	5.68	10.80
1963.2	0.15	2.02	11.73	11.30	1984.1	2.22	1.01	6.39	9.60	2004.4	1.29	1.49	5.66	10.66
1963.3	0.19	1.94	12.52	10.18	1984.2	2.19	1.01	6.43	9.44	2005.1	1.28	1.48	5.69	10.48
1963.4	0.21	1.84	12.36	11.78	1984.3	2.18	1.01	5.93	9.57	2005.2	1.28	1.48	5.67	10.44
1964.1	0.22	1.78	11.80	12.29	1984.4	2.16	1.01	6.19	9.34	2005.3	1.27	1.47	5.74	10.19
1964.2	0.25	1.70	11.64	13.67	1985.1	2.11	1.01	6.03	9.00	2005.4	1.27	1.46	5.68	10.32
1964.3	0.26	1.65	11.54	14.06	1985.2	2.07	1.01	5.91	9.46	2006.1	1.26	1.46	5.71	9.96
1964.4	0.28	1.59	11.40	14.57	1985.3	2.05	1.01	6.01	9.68	2006.2	1.26	1.45	5.62	9.85
1965.1	0.29	1.62	11.08	13.33	1985.4	2.03	1.01	5.87	9.56	2006.3	1.25	1.44	5.66	9.80
1965.2	0.30	1.61	11.15	11.65	1986.1	2.01	1.01	5.89	9.62	2006.4	1.25	1.44	5.68	9.77
1965.3	0.31	1.60	10.30	11.05	1986.2	1.99	1.00	5.76	9.68	2007.1	1.24	1.43	5.73	9.65
1965.4	0.31	1.56	10.35	13.84	1986.3	1.97	1.00	5.65	9.82	2007.2	1.24	1.42	5.78	9.65
1966.1	0.32	1.52	10.44	11.02	1986.4	1.94	1.00	5.83	9.87	2007.3	1.23	1.41	5.72	9.62
1966.2	0.34	1.46	10.42	11.43	1987.1	1.92	1.00	5.93	10.12	2007.4	1.23	1.40	5.70	9.52
1966.3	0.37	1.45	10.04	11.20	1987.2	1.88	1.00	5.90	9.39	2008.1	1.22	1.40	5.70	9.40
1966.4	0.38	1.44	10.27	11.17	1987.3	1.86	1.00	6.03	10.32	2008.2	1.22	1.39	5.78	9.30
1967.1	0.40	1.42	10.20	10.92	1987.4	1.83	1.00	6.05	10.29	2008.3	1.21	1.38	5.78	9.07
1967.2	0.41	1.38	10.01	10.38	1988.1	1.80	1.00	6.00	10.42	2008.4	1.21	1.39	5.62	8.59
1967.3	0.41	1.37	9.64	10.49	1988.2	1.78	1.00	6.07	10.03	2009.1	1.21	1.39	5.60	8.58
1967.4	0.43	1.35	9.52	11.54	1988.3	1.76	1.00	6.16	9.91	2009.2	1.21	1.38	5.46	8.51
1968.1	0.43	1.31	8.91	10.81	1988.4	1.73	1.00	6.22	10.04	2009.3	1.21	1.37	5.43	8.70
1968.2	0.45	1.29	9.43	10.75	1989.1	1.71	1.00	6.35	9.55	2009.4	1.21	1.36	5.49	8.68
1968.3	0.46	1.29	9.68	10.20	1989.2	1.69	1.00	6.06	9.28	2010.1	1.20	1.35	5.49	8.74
1968.4	0.49	1.28	9.69	9.85	1989.3	1.67	1.00	6.34	9.11	2010.2	1.20	1.34	5.54	8.80
1969.1	0.50	1.26	9.56	10.14	1989.4	1.66	1.00	6.20	9.30	2010.3	1.19	1.34	5.60	8.78
1969.2	0.51	1.24	9.31	10.75	1990.1	1.65	1.00	6.11	9.11	2010.4	1.19	1.33	5.54	8.61
1969.3	0.53	1.21	9.38	10.60	1990.2	1.64	1.00	6.00	9.00	2011.1	1.19	1.33	5.46	8.66
1969.4	0.54	1.20	9.15	10.46	1990.3	1.64	1.00	5.97	9.34	2011.2	1.18	1.33	5.50	8.60
1970.1	0.55	1.19	9.31	11.16	1990.4	1.63	1.00	5.97	9.02	2011.3	1.18	1.32	5.49	8.49
1970.2	0.57	1.19	9.14	10.49	1991.1	1.64	1.00	5.71	9.37	2011.4	1.18	1.32	5.42	8.45
1970.3	0.57	1.17	8.80	10.67	1991.2	1.64	1.00	5.73	9.39	2012.1	1.18	1.32	5.44	8.33
1970.4	0.58	1.16	8.61	9.64	1991.3	1.64	1.00	5.48	9.27	2012.2	1.18	1.31	5.41	8.40
1971.1	0.60	1.15	8.57	10.30	1991.4	1.63	1.00	5.50	9.20	2012.3	1.17	1.31	5.45	8.25
1971.2	0.60	1.15	8.50	9.75	1992.1	1.62	1.00	5.65	9.27	2012.4	1.17	1.31	5.47	8.27
1971.3	0.62	1.14	8.36	10.21	1992.2	1.62	1.00	5.66	9.21	2013.1	1.17	1.31	5.43	8.14
1971.4	0.62	1.14	8.22	10.10	1992.3	1.61	1.00	5.53	8.85	2013.2	1.17	1.30	5.47	8.10
1972.1	0.63	1.13	7.99	9.93	1992.4	1.60	1.00	5.59	8.87	2013.3	1.17	1.30	5.44	8.09
1972.2	0.64	1.12	8.16	9.79	1993.1	1.59	1.00	5.63	9.11	2013.4	1.17	1.30	5.43	8.04
1972.3	0.65	1.11	7.99	9.39	1993.2	1.59	1.00	5.61	9.27	2014.1	1.16	1.29	5.53	8.00
1972.4	0.66	1.11	8.05	9.94	1993.3	1.59	1.00	5.67	9.36	2014.2	1.16	1.29	5.51	7.94
1973.1	0.67	1.10	8.06	11.55	1993.4	1.57	1.00	5.75	9.48	2014.3	1.16	1.29	5.42	7.87
1973.2	0.69	1.09	7.71	11.24	1994.1	1.56	1.00	5.73	9.73	2014.4	1.16	1.28	5.38	7.81
1973.3	0.70	1.09	7.85	11.52	1994.2	1.56	1.00	5.83	9.62	2015.1	1.16	1.28	5.32	7.94
1973.4	0.72	1.08	8.06	11.46	1994.3	1.54	1.00	5.78	9.76	2015.2	1.16	1.27	5.29	7.80
1974.1	0.73	1.07	7.85	12.52	1994.4	1.54	1.00	5.87	9.83	2015.3	1.16	1.27	5.22	8.02
1974.2	0.74	1.07	7.59	11.83	1995.1	1.53	1.00	5.84	9.95	2015.4	1.16	1.27	5.16	7.84
1974.3	0.75	1.06	6.98	11.17	1995.2	1.53	1.00	5.63	10.00	2016.1	1.16	1.26	5.11	7.81
1974.4	0.76	1.06	6.73	8.24	1995.3	1.52	1.00	5.92	9.98	2016.2	1.16	1.26	5.10	7.81
1975.1	0.77	1.05	6.44	9.81	1995.4	1.51	1.00	5.70	9.93	2016.3	1.16	1.26	5.06	7.71
1975.2	0.78	1.05	6.40	9.11	1996.1	1.50	1.00	5.67	9.60	2016.4	1.15	1.26	5.22	7.71
1975.3	0.79	1.05	6.19	10.01	1996.2	1.49	1.00	5.75	9.67	2017.1	1.15	1.25	5.21	7.69
1975.4	0.80	1.04	6.08	7.93	1996.3	1.49	1.00	5.70	9.64	2017.2	1.15	1.25	5.12	7.59
1976.1	0.81	1.04	6.12	9.18	1996.4	1.48	1.00	5.93	9.60	2017.3	1.15	1.24	5.18	7.64
1976.2	0.81	1.03	6.13	9.87	1997.1	1.48	1.00	5.79	9.62	2017.4	1.15	1.24	5.10	7.52
1976.3	0.82	1.03	6.18	9.70	1997.2	1.47	1.00	5.91	9.77	2018.1	1.14	1.24	5.10	7.39
1976.4	0.83	1.03	6.22	8.63	1997.3	1.46	1.00	5.72	9.91	2018.2	1.14	1.24	5.13	7.34
1977.1	0.83	1.03	6.22	9.00	1997.4	1.45	1.00	5.83	9.88	2018.3	1.14	1.24	5.10	7.28
1977.2	0.83	1.03	6.20	8.91	1998.1	1.45	1.82	5.91	14.41	2018.4	1.14	1.24	5.03	7.09
1977.3	0.84	1.03	6.11	9.49	1998.2	1.44	1.85	5.85	13.93	2019.1	1.14	1.24	5.05	6.99
1977.4	0.84	1.02	6.02	10.16	1998.3	1.44	1.84	5.66	13.77	2019.2	1.13	1.23	4.93	6.89
1978.1	0.84	1.02	5.97	9.88	1998.4	1.43	1.83	5.76	13.73	2019.3	1.13	1.23	4.94	6.78
1978.2	0.85	1.02	6.05	9.63	1999.1	1.42	1.80	5.63	14.01	2019.4	1.13	1.23	4.85	6.64
1978.3	0.85	1.02	5.97	10.13	1999.2	1.42	1.78	5.66	13.91	2020.1	1.13	1.23	4.73	6.46
1978.4	0.86	1.02	6.11	10.81	1999.3	1.41	1.74	5.82	13.84	2020.2	1.14	1.24	4.25	6.36
1979.1	0.86	1.02	6.26	9.93	1999.4	1.41	1.72	5.77	13.78	2020.3	1.14	1.23	4.36	6.48
1979.2	0.87	1.02	6.25	10.11	2000.1	1.39	1.71	5.60	13.72	2020.4	1.13	1.23	4.51	6.50
1979.3	0.87	1.01	6.22	10.44	2000.2	1.39	1.70	5.68	13.80	2021.1	1.12	1.22	4.66	6.48
1979.4	0.88	1.01	6.20	10.30	2000.3	1.38	1.68	5.72	13.77	2021.2	1.12	1.22	4.71	6.36
1980.1	0.88	1.01	6.16	8.37	2000.4	1.38	1.68	5.68	13.32	2021.3	1.12	1.22	4.51	6.33
1980.2	0.88	1.01	6.05	8.48	2001.1	1.37	1.65	5.70	12.60	2021.4	1.12	1.21	4.56	6.24
1980.3	0.89	1.01	6.04	8.32	2001.2	1.37	1.64	5.70	12.63	2022.1	1.11	1.21	4.60	6.21
1980.4	0.89	1.01	5.82	8.51	2001.3	1.36	1.63	5.62	12.22	2022.2	1.11	1.21	4.79	6.22
1981.1	0.89	1.01	5.92	7.76	2001.4	1.36	1.63	5.78	11.92	2022.3	1.11	1.21	4.77	6.17
										2022.4	1.11	1.21	4.82	5.94

and graphically depicted in Figure 7, Figure 8, Figure 9 and Figure 10. All of the elasticities and slopes reported in Table 1 were significantly different from zero, as calculated using Equation (11). The 0.06 for the %dGDP/%dM1 for Australia in the third quarter of 1960 means that a one-percent increase in Australia’s money supply in that quarter was correlated with a 0.06-percent increase in GDP. The 13.52 value for dGDP/dG for Australia in the third quarter of 1960 implies that an AUD one million increase (or decrease) in Australian government consumption in that quarter was correlated with an AUD 13.52 million increase (or decrease) in GDP.

It is important to realize that the elasticities and slopes reported in this paper are total derivatives, not partial derivatives. Thus, a dGDP/dG of 13.52 would capture any increase in consumption, investment, and exports due to an increase in government consumption. For example, if the Australian government spent AUD 1 million on building more roads, those constructing the roads or making the materials used in constructing the roads were paid AUD 1 million. Those receiving this pay would spend their marginal propensities to consume on other goods. Those selling this second round of goods would spend their marginal propensity to consume of their pay on a third round of goods. This process continues, resulting in the following typical Keynesian multiplier equation:

Change in GDP = [(Initial change in QAD)][1/(1 − slope of QAD)]

(12)

Since quantity aggregate demand (QAD) equals private consumption plus investment in tools, machinery, and buildings plus government spending plus exports minus imports, an increase in government consumption would be an “initial change in QAD” in Equation (12). In Equation (12), the “slope of QAD” would include the marginal propensities to consume, to invest, and to import, as well as effects of changes in wealth, effects through changes in interest rates and exchange rates, etc. Moreover, if the Australian government typically augmented the stimulative effects of increasing government spending by lowering tax rates, encouraging Australian banks to extend more credit, subsidizing private investment, increasing the money supply, imposing tariffs, lowering Australia’s exchange rate to increase exports and decrease imports, and/or redistributing income to the relatively poor, etc., then the effects of these correlated policies would increase the estimate for dGDP/dG. dGDP/dG is a total derivative that shows all the ways that GDP and G are correlated, holding nothing constant.

Figure 7 shows that Australia’s dGDP/dG steadily fell from the third quarter of 1960 through the fourth quarter of 1975. When Australia had a crawling pegged exchange rate from 1976 through 1983, Australia’s dGDP/dG stopped its steep decline and looked more like Australia’s dGDP/dG for her flexible exchange rate period than it looked like her fixed exchange rate period. The Bank for International Settlements (n.d.) explained that Australia struggled to control foreign capital inflows during its fixed exchange rate period. Recall from Section 2 that the IS/LM/BP model would predict that fiscal policy would be stronger the more mobile capital is under a fixed exchange rate. Thus, the fall in Australia’s dGDP/dG from 1960 through 1975 is consistent with the IS/LM/BP predictions for a country with a decline in the mobility of capital, which fits the historical record.

The Bank for International Settlements (n.d., but the references and data in this source end in 2007) also says that, under Australia’s flexible exchange rate (starting in 1984), capital flows freely in and out of Australia. Recall that in Section 2 of this paper, it was shown that the IS/LM/BP model would predict that dGDP/dG would be zero under a flexible exchange rate and perfect capital mobility. In contrast to this IS/LM/BP prediction, dGDP/dG stayed between 6.43 and 4.25 under Australia’s flexible exchange rate. One explanation of the dGDP/dG estimates for Australia under a flexible exchange rate is that capital was relatively (not perfectly) mobile during that period, with capital becoming slightly more mobile over time.

Figure 8 shows that dGDP/dG fluctuated between 14.57 and 7.76 in South Korea under a fixed exchange rate; however, the amplitude of these fluctuations diminished over time. These fluctuations could be due to the successes and failures of the Korean government’s policies of financial repression and state-led development at that time. Specifically, the Korean government set below-market-clearing interest rates (which were often less than the inflation rate) which created a shortage of loans (Kwack 1986). The Korean government then told banks to which companies they should lend. The companies approved for loans obtained an interest rate windfall from the government, and those companies then supported the current government regime. Noland (2007) reports that these “policy loans” had increased to sixty percent of all loans by the late 1970s. The government also told those companies into what sectors of the economy they should expand. One consequence of these policies was that the largest ten conglomerates (the biggest chaebols) accounted for more than twenty percent of national income by the 1980s (Noland 2007). Of course, Korean savers would want to move their assets abroad to earn much higher returns than they could under Korean fixed-at-low-levels interest rates. Thus, this type of system requires strong capital controls preventing the outflow of savings. Recall from Section 2 that dGDP/dG should be zero for a country that has a fixed exchange rate and completely immobile capital. Thus, Figure 8, showing that dGDP/dG was noticeably above zero under Korea’s fixed exchange rate, implies that capital was not perfectly immobile in and out of Korea at that time. Thus, Figure 4A (for a fiscal expansion) and Figure 6A (for a monetary expansion) show the relevant IS/LM/BP models with relatively immobile capital. Using traditional statistical methods to estimate the effects of fiscal and monetary policy on South Korea would require correctly modelling how financial repression effects the economy, capital flows, trade flows, etc.; since RTPLS finds total derivatives (in contrast to partial derivatives), no such modelling is required by RTPLS.

Recall also that the IS/LM/BP model would predict that dGDP/dG would be zero under a flexible exchange rate if capital is perfectly mobile. Figure 8 shows that dGDP/dG for Korea steadily fell under her flexible exchange rate (starting in 1998) but remained noticeably above zero. These results best fit an IS/LM/BP model for a flexible exchange rate with increasingly mobile capital over time, which never achieved the status of perfectly mobile capital.

Figure 9 shows %dGDP/%dM1 for Korea. Under a fixed exchange rate (assuming no sterilization), the money supply must adjust to keep the exchange rate fixed. As Section 2 shows, if a country with a fixed exchange rate tried to increase its money supply to stimulate its economy, it would have to subsequently withdraw the same amount of money to maintain its exchange rate. Thus, holding all other things constant, a change in the money supply to stimulate the economy is impossible for countries with fixed exchange rates. However, in the real world, everything else is not held constant. Changes in GDP (Figure 2), interest rates (Figure 3), exports, imports, non-trade demand, and non-trade supply would result in a fixed exchange rate regime having to change its money supply to maintain its fixed exchange rate, and that change in the money supply could (as a secondary effect) change GDP. Thus, the IS/LM/BP model would predict that monetary policy is completely ineffective under a fixed exchange rate; however, that does not imply that %dGDP/%dM1 (an elasticity derived from a total derivative) would equal zero. Table 1 and Figure 9 show that %dGDP/%dM1 fell for Korea between 1960 and 1976, held relatively constant for 1977 to 1997, jumped up when Korea floated the won at the beginning of 1998, and then steadily fell again. Recall from Section 2 that under a flexible exchange rate, monetary policy would be stronger the more mobile capital is. Thus, the fall in %dGDP/%dM1 for Korea implies that capital has become less mobile over time, which is the opposite conclusion obtained from the dGDP/dG results.

Figure 10 shows the %dGDP/%dM1 results for Australia. Under fixed exchange rates, %dGDP/%dM1 fell to one over time in South Korea, but, in Australia, %dGDP/%dM1 rose to 0.92 over time. Thus, under fixed exchange rates, Korea’s and Australia’s %dGDP/%dM1 were converging from opposite directions. Perhaps these differences were due to Korea employing a policy of state-directed development with financial repression versus Australia taking a more free-market approach; however, both used capital controls. Both Figure 9 (Korea) and Figure 10 (Australia) show that %dGDP/%dM1 rose noticeably when these countries switched to flexible exchange rates, which is consistent with IS/LM/BP predictions.

In both Australia and Korea, %dGDP/%dM1 fell over time under flexible exchange rates, which is consistent with a decrease in the mobility of capital. In contrast, the fall in dGDP/dG for both countries under flexible exchange rates is consistent with an increase in the mobility of capital. One possible explanation for this apparent inconsistency is based on other countries increasing their money supplies more than Australia and South Korea did. If just Australia or South Korea increased its money supply, then the LM curve would shift right, as shown in Figure 6A,B. However, if other countries increase their money supplies at the same time so that the interest rates in these other countries fall by more than Australia’s and South Korea’s interest rates fall, then LM would shift left—the opposite as is shown in Figure 6A,B—which is consistent with my empirical results. The US and Europe increased their money supplies by unprecedented large amounts in 2007–2011 and then again in 2019–2021.

It is important to always remember that RTPLS produces a separate total derivative estimate for every observation where differences in these estimates are due to omitted variables. The noticeable changes over time for the estimates shown in Figure 7, Figure 8, Figure 9 and Figure 10 imply that omitted variables have dramatically affected the effectiveness of both fiscal and monetary policy in Australia and South Korea under both fixed and flexible exchange rates. Unfortunately, RTPLS cannot identify what those omitted variables are, nor can it reveal the mechanisms through which those omitted variables affect the estimated relationships.

Policy makers need to be aware that under flexible exchange rates, the effectiveness of both fiscal policy and monetary policy has been declining in a relatively smooth fashion over time (see Figure 7, Figure 8, Figure 9 and Figure 10). In the fourth quarter of 2022, the 95% confidence interval for dGDP/dG for Australia was 4.573 to 4.840, and that for South Korea was 6.017 to 6.296. This means that policy makers in Australia (South Korea) can be 95% sure that an AUD one million (KRW one million) increase in government spending in the fourth quarter of 2022 was correlated with an AUD 4.573 to 4.840 million (KRW 4.573 to 4.840 million) increase in GDP. Since these confidence intervals do not include zero, these estimates are significantly different from zero, contrary to what economists who assume perfect capital mobility would predict. However, if policy makers want to use these estimates when setting fiscal policy in 2025 or after, then they need to extend the downward trends shown in Figure 7 and Figure 8.

In the fourth quarter of 2022, the 95% confidence interval for %dGDP/%dM1 for Australia was 1.105 to 1.116, and that for South Korea was 1.208 to 1.212. This means that the central bank of Australia (South Korea) can be 95% sure that a one-percent increase in the money supply in the fourth quarter of 2022 would have been correlated with a 1.105- to 1.116-percent (1.208 to 1.212 percent) increase in GDP. The opposite also holds true; a one-percent decrease in Australia’s (South Korea’s) money supply, perhaps to combat inflation, would be correlated with a 1.105- to 1.116-percent (1.208 to 1.212 percent) fall in GDP. Again, if central banks want to use these estimates in 2025 and after, then they should extend the downward trends shown in Figure 9 and Figure 10.

5. Discussion

Policy makers can use the numerical estimates presented in this paper in their efforts to fine tune their policy responses to economic problems. Economists can also benefit by realizing that models that assume perfect capital mobility do not fit reality. In 1980, Feldstein and Horioka set off an economic firestorm when they argued that the strong correlation between a country’s savings and investment rates implied that capital was not perfectly mobile internationally, which implies that international capital markets do not work perfectly.

Coakley et al. (1998) and Apergis and Tsoumas (2009) survey the massive literature responding to Feldstein and Horioka (1980). These surveys show (1) that the strong correlation between a country’s savings and investment found by Feldstein and Horioka (1980) is extremely robust; (2) to solve the Feldstein-Horioka puzzle, economists have proposed explanations in which capital is perfectly mobile and in which domestic savings and investment can be highly correlated; and (3) there is concern about the possibility that the underlying model used could affect the results.

The first point—that the Feldstein and Horioka (1980) result is very robust—is also true for this paper’s results. There is a vast body of literature that estimates government spending multipliers for countries with flexible exchange rates, and most of this research finds values for dGDP/dG greater than zero. However, to the best of my knowledge, my paper is the first to point out that this very prevalent and robust result is inconsistent with the Mundell–Fleming model for flexible exchange rates with perfectly mobile capital.

Furthermore, my results are consistent with a large body of literature that shows that foreign direct investment (which is one of several types of international capital flows) is affected by more than just the interest rate. Thian and Yeh (2023) find that institutional quality (control of corruption, government efficiency, political stability, regulation quality, and rule of law) significantly affect Taiwan’s outward investments in Southeast Asia in the long run. Importantly, Thian and Yeh (2023) include the interest rate in their analysis, which implies that institutional quality influences capital flows independent of the interest rate. Chiappini and Viaud (2021) find that industry characteristics, as well as institutional characteristics, affect Japan’s outward foreign direct investment. Li et al. (2021) find that the host country’s level of innovation affects foreign direct investment in OECD countries.

Concerning the second point (possible solutions to the Feldstein–Horioka puzzle), several scholars have argued that frictions in the international market for goods and services (tariffs, quotas, transport costs, costs of regulatory compliance, etc.) can explain the Feldstein–Horioka puzzle even if capital is perfectly mobile (Horioka 2024 and Ford and Horioka 2017). However, even if my paper’s results are due to frictions in the international market for goods and services (which is doubtful) instead of capital not being perfectly mobile, the predictions of the Mundell–Fleming model fail. My results imply that either economists should throw out the Mundell–Fleming model as a failure or use that model assuming less than perfectly mobile capital. The less harsh approach is to assume that capital is relatively mobile or relatively immobile, not perfectly mobile.

Concerning the third point, but in a different context, Cogan et al. (2010) shows that the same set of data can produce extremely different results when different underlying models are used. Feldstein and Horioka (1980) did not impose a specific model; they simply regressed the ratio of investment to output on the ratio of savings to output. However, Feldstein and Horioka’s (1980) simple approach has been criticized for simultaneous equation bias, omitted variable bias, and for not testing for unit roots and cointegration (Coakley et al. 1998). My paper is not subject to the same criticisms that Feldstein and Horioka’s (1980) paper has endured. In this paper, I use reiterative truncated projected least squares (RTPLS), which is a solution to the omitted-variable problem of regression analysis. RTPLS produces a different total derivative estimate for each observation where differences in these total derivative estimates are due to omitted variables. Moreover, RTPLS is not model-dependent. Furthermore, since RTPLS estimates are total derivatives, simultaneous equation bias is not a problem.

It is time for economists to admit that capital is not perfectly mobile internationally. It is time to revise our many models that assume perfect capital mobility or create replacement models where different degrees of capital mobility are possible. It is time to change how we are teaching international economics and macroeconomics. It is time to use intermediate macroeconomics textbooks like Froyen’s (2013) that present different degrees of capital mobility. An international economics textbook that teaches different mobilities for capital is by Appleyard and Field (2014).

Clearly, directions for future research would include (1) creating economic models in which capital is not perfectly mobile, (2) conducting this paper’s analysis using data from other countries, and (3) determining why domestic savings are strongly correlated with investment.